Research ArticleShaking Table Model Test and Seismic PerformanceAnalysis of a High-Rise RC Shear Wall Structure
Shujin Li Cai Wu and Fan Kong
School of Civil Engineering and Architecture Wuhan University of Technology Luoshi Road No 122 Wuhan 430070 China
Correspondence should be addressed to Shujin Li sjliwhuteducn
Received 13 February 2019 Revised 1 April 2019 Accepted 21 April 2019 Published 9 May 2019
Academic Editor Evgeny Petrov
Copyright copy 2019 Shujin Li et al (is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A building developed by Wuhan Shimao Group in Wuhan China is a high-rise residence with 56 stories near the Yangtze River(e building is a reinforced concrete structure featuring with a nonregular T-type plane and a height 1796m which is out of therestrictions specified by the China Technical Specification for Concrete Structures of Tall Building (JGJ3-2010) To investigate itsseismic performance a shaking table test with a 130 scale model is carried out in Structural Laboratory in Wuhan University ofTechnology(e dynamic characteristics and the responses of the model subject to different seismic intensities are investigated viathe analyzing of shaking table test data and the observed cracking pattern of the scaled model Finite element analysis of theshaking table model is also established and the results are coincident well with the test An autoregressivemethod is also presentedto identify the damage of the structure after suffering from different waves and the results coincide well with the test andnumerical simulation (e shaking table model test numerical analysis and damage identification prove that this building is welldesigned and can be safely put into use Suggestions and measures to improve the seismic performance of structures arealso presented
1 Introduction
With the fast urbanization in China the population growthin cities has led to ever-increasing demand for high-risebuildings to accommodate commercial and residentialneeds High-rise buildings are very common in the denselypopulated cities all over the world such as New York andLondon [1 2] Accordingly pertinent regulations have beendeveloped to ensure the safety and reliability requirements ofhigh-rise buildings High-rise buildings that are designedand constructed according to codes and standards aredeemed as complied with all regulatory requirements for thebuildings With the innovation and advancement of tech-nology and materials some high-rise buildings are plannedand designed beyond the specifications of codes and stan-dards particularly for fast-developing countries such asChina To ensure the safe and reliable function of thesebuildings it is imperative to investigate the behaviors ofthese buildings in particular the behavior under horizontalloadings such as wind and earthquake It is also essential to
identify and quantify if possible the characteristics of thesebuildings with a view to provide guidance for the futuredesign of similar buildings
(e shaking table test is one of the most widely usedtechniques to assess the seismic performance of structuresmade of various materials Commonly it is widely used forassessing linearnonlinear and elasticinelastic dynamic re-sponse of structures Martinelli et al [3] presented thenonlinear dynamic response of a shaking table test for a full-scale seven-story reinforced concrete shear wall buildingwhere four simulated earthquake records with increasingintensity were used as excitation Saranik et al [4] conducteda shaking table test to investigate the inelastic behavior of atwo-story steel portal frame with bolted connections Fur-thermore it is not only used for structural dynamic tests butalso for geotechnical behavior Chen et al [5] conducted aseries of shaking table tests on a plaster model of a three-story and three-span subway station to investigate theseismic failure characteristics of the structure on the liq-uefiable ground Lin et al [6] undertook shaking table tests
HindawiShock and VibrationVolume 2019 Article ID 6189873 17 pageshttpsdoiorg10115520196189873
on three embankment slope models to study the seismicresponse of the embankment slope with different reinforcingschemes (e effectiveness of shaking table tests has alsobeen studied For example Srilatha et al [7] investigated theeffect of frequency of base shaking on the dynamic responseof unreinforced and reinforced soil slopes through a series ofshaking table tests
In shaking table tests most researchers used scaledmodels as specimens For example Liu et al [8] carriedout shaking table tests on a 130 scaled model with andwithout base isolation bearings to assess the seismicperformance of an isolated museum structure in highearthquake intensity regions Lu et al [9] tested a 150scale high-rise building model on a shaking table forShanghai World Financial Center Tower (e dynamiccharacteristics seismic responses and failure mechanismof the structure were investigated and weak positionsunder seldom-occurred earthquakes were identifiedSome researchers use prototype structures For exampleLignos et al [10] conducted a shaking table test on a full-scale high-rise building to demonstrate the effectiveness ofthe numerical models used Graziotti et al [11] performeda shaking table test on a two-story full-scale unreinforcedmasonry building to study its response characteristicsdamage mechanism and evolution during the experi-mental phases
(e above literature review suggests that the shakingtable test is an essential tool to assess and verify thedynamic behavior of structures It is particularly imper-ative for those structures that exceed the limits of thespecification of design codes and standards It is with thisregard that the present paper is in order (e ShimaoBuilding (numbered 1ndash3 in the A2 block) is an iconicbuilding in the central business district area of WuhanChina located on the bank of Yangtze River It is acombined commercial and residential building with 56stories (e lateral-force resisting system of the structureis the reinforced concrete (RC) shear wall with a height of1796m exceeding the limit for high-rise buildingsspecified by Chinese Regulation Technical Specificationfor Concrete Structures of Tall Building (JGJ3-2010) [12](erefore it is required to verify the structural seismicperformance after the regular structural designingaccording to the codes Besides the irregular buildingshape in both plane and elevation complicates the analysisand determination of seismic resistance of the structureTo ensure the safety of the building it is necessary toexamine the behavior of the building under seismicloading For this purpose a shaking table test and itsnumerical analysis as well as structural damage identifi-cation were also conducted
(is paper focuses on the investigation of the seismicbehavior of Shimao Building Firstly the results of ashaking table test on the 130 scale building model will bepresented (e structural dynamic characteristics and theresponses under different levels of earthquake loading willbe investigated and the failure mechanism and crackingpattern of the tested model will also be obtained (en thecorresponding finite element model will be established to
analyze its seismic performance At last a damage iden-tification method based on the autoregressive (AR) modelwill also be presented to identify the damage of the testbuilding According to the analysis of experiment finiteelement model and theoretical identification of the testbuilding seismic performance of the prototype buildingwill be obtained and this study can make sure that theprototype building is designed reasonably and can be putinto use safely Finally suggestions and measures to im-prove the prototype building seismic performance will alsobe presented
2 Design of Model Building
21 Prototype Building A 130 model of Shimao Buildingwas designed and built for the shaking table test to rep-resent the main characteristics of the prototype building(e experiment was undertaken in the laboratory of Schoolof Civil Engineering and Architecture at Wuhan Universityof Technology China Figure 1 shows the representing planand elevation of the prototype building It can be seen fromFigure 1(b) that the plan of the building is shaped as ldquoTrdquo(maximum 3285m in length and maximum 195m inwidth) and this shape of building may be susceptible toearthquake excitation (e vertical configuration of thebuilding consists of a core tube accommodating staircaselift well and pipe shaft and shear walls located at the outerwalls and some inner walls (e floors and roof of thebuilding are reinforced concrete beam-slab structures Inaddition the upper (vertical) structure is fixed on thereinforced concrete base
According to the ldquoTechnical Points (No 65 2015) ofSpecial Inspection for Seismic Fortification of Out-of-CodeHigh-rise Buildingsrdquo [13] issued by the Chinese Con-struction Ministry the total height of the building 1886m(including the roof truss) with 56 stories exceeds the limitheight of 170m specified by the Class B shear wall struc-tures according the Chinese code (JGJ3-2010) [12] Fur-thermore the building has a set back at the height of12835m (the 41st story) as shown in Figure 1 leading to adisagreement between the centroid and stiffness center Asa consequence the eccentricity violates the requirements ofseismic conceptual design that building structures shouldbe symmetric in both plan and elevation Overall a shakingtable test of this building can be quite necessary
Dynamic characteristics of the prototype building werecalculated through Chinese structural design softwarePKPM Although the maximum seismic responses of thestructure under Frequent 6 (defined at Section 3) shown inTable 1 satisfy the requirements of the code (specified by theChinese Seismic Design Code of Building Structures)considering larger earthquakes happen and making extracertain the shaking table test is still needed for furtherverification
22 Similitude Law In this paper the similitude law isdetermined by the dimensional analysis method [14] Firstlysimilar conditions Π are obtained and then other similarity
2 Shock and Vibration
constants are obtained based on Π Inertia force restoringforce and gravity are required to be simulated in the testand thus elastic modulus E and density ρ of the modelmaterial are strictly controlled e essential requirement is(Eρal)m (Eρal)p where the subscripts m and p repre-sent the scaled model and the prototype building re-spectively at is
SESρSaSl
1 (1)
where SE Sρ Sa and Sl denote the similitude ratio of elasticmodulus equivalent density acceleration and geometryrespectively In the present case three controllable simili-tude ratios should be determined in advance to obtainothers Specically SE Sρ and Sl are chosen in this paperand thus Sa can be calculated using Equation (1)
Considering the shaking table size and the height re-quirement of the laboratory the dimension scaling parameter
Sl is chosen as 130 Based on the tested characteristics ofmaterials in the test the similitude law of elastic modulus SE isdetermined as 1305e total weight of themodel (includingself-weight and articial mass) and prototype building are306 ton and 40400 ton (including live load) respectivelyus the mass ratio Sm is 1132026 and the similitude ratioof equivalent density Sρ can be obtained as 20245 all themainmodel similitude relationships and calculation formulas areshown in Table 2
23 Model Constructing Since the aim of the shaking tabletest is to investigate the seismic behavior of the originalstructure subjected to dierent intensity of earthquakesincluding failure mode and mechanisms it is necessary touse the same materials as the prototype building e ma-terials used for model construction (specimen) are micro-concrete (mix proportion is shown in Table 3) galvanized
188618260
18070
188618260
(a)
X
Y
8300
Li wellPipe sha
32850
1160
0
1950
0
7900
(b)
Figure 1 Sketch of prototype building (a) elevation view (b) oor plan below the 41st story (units mm)
Table 1 Dynamic characteristics and seismic response of the prototype building
Direction Maximum lateral stiness (kNm) Frequencies (Hz) Maximum displacement (mm) Story drift Torsion displacement ratioX 109times108 29303 3772 13500 115Y 109times108 35724 5416 12359 119Torsion 17173
Shock and Vibration 3
steel wires and meshes which are similar to the materials inthe prototype building Ordinary Portland Cement PO 325is chosen to construct concrete A batch of specimens in theform of cubic and prism type were cast to measure thestrength and elastic modulus of microconcrete (e testingmethod of the specimens strictly followed the requirementsof the Standard for Test Methods of Concrete Structures(GB50152-2012) [15] (e microconcrete mix proportionsare shown in Table 3 (e elastic modulus of materials isshown in Table 4 (e height of the model is 6437m with6287m for the model itself and 015m for the base (ephoto of the completed model is shown in Figure 2
3 Testing Methodology
31TestVariables andFacility (e test variables include twotypes different fortification intensity and different types ofearthquake waves According to related researches on thestatistics of the peak acceleration of ground motions inChina the seismic intensity of a specific site exhibits theextreme distribution of the III type (Weibull distribution)(e fortification intensity is defined as the intensity with10 exceedance probability which is also called as themoderate or basic intensity for simplicity Similarly the rareand frequent intensity is defined as the intensity with 2ndash3and 65 exceedance probability respectively Furthermorefor the moderate intensity of a specific site the frequent andrare intensity is about 155deg lower and 1deg higher than themoderate intensity respectively In this paper the scaledbuilding under investigation is located in Wuhan withDegree 6 as the fortificationbasic intensity [16] (is in-tensity is associated with medium occurrence (10)(erefore Moderate 6 means ground motion with Intensity6 (the peak ground acceleration (PGA) is 005 g) and Fre-quency 6 means ground motion with Intensity 445 (PGA
0018 g) whereas Rare 6 means ground motion with In-tensity 7 (PGA 01 g) Ultralarge earthquakes are not spec-ified in GB50011-2010 [17] and Rare 7 (actually Intensity 8)is introduced here for the purpose of studying the nonlinearor even collapse performance of the scaled building For achosen recorded seismic excitation the similitude law(shown in Table 1) was used to scale the acceleration andtime
According to the dynamic characteristics and site con-dition of the prototype structure three seismic runs arechosen for simulating the shaking table test input wave (1)El Centro wave with a peak acceleration of 341ms2 (2) Taftwave with a peak acceleration of 153ms2 and (3) artificialseismic wave (USER1) supplied by the construction de-signers with a peak acceleration of 018ms2 (e time-history curves are shown in Figure 3(emain specificationsof the shaking table used in the present experiment areshown in Table 5
32 Testing Procedure and Layout of Sensors (e testingprocedure is shown in Table 6 It can be seen that the EICentro wave is the first wave in each test condition followedby the Taft wave and artificial seismic wave Before and afterinputting different fortification intensity seismic waves lowpeak white noise excitation is conducted to measure thedynamic characteristics parameters such as natural fre-quency mode and damping ratio
(e main measurement of structural response is accel-eration displacement strain etc Several acceleration sen-sors displacement sensors and strain gauges are arranged atthe different heights of the model to measure the responsesof the model structure under different seismic fortificationintensities Accelerations and displacements were measuredby the large dynamic signal acquisition and analysis systemDASP2003 developed by Orient Institute of Noise andVibration 14 acceleration sensors were used for differentpurposes namely 2 for measuring vertical accelerations 10for horizontal accelerations and 2 for torsion of thebuilding Dynamic strain was obtained by the dynamic andstatic testing instrument DH3817 Five displacement sensorswere used to measure the deformation along the direction of
Table 2 Similitude law
Contents Physical quantity Similitude equation Similitude law
Geometric relationship
Length Sl 130Linear displacement SX Sl 130
Area SA S2l 1900Angular displacement 1 1
Material relationship
Elastic modulus SE 1305Concrete strength Sc Sσ 1692Equivalent mass Sm Sρ middot S3l 1132026Equivalent density Sρ 2045
Dynamic relationship
Period ST 1Sω 0083Frequency Sω [Sσ(SρS
2l )]12 12012
Acceleration Sa Sl middot S2ω 481Acceleration of gravity Sg 1
shaking e positions of acceleration sensors and dis-placement sensors are shown in Figure 4
4 Test Results and Analysis
41 Damage Patterns When subjected to Frequent 6 therewere no noticeable shaking and visible damages it can bepredicted that the test model can remain in a serviceablecondition after Frequent 6 and there was no damage In thecase of Moderate 6 the model responded with little vibra-tion but no cracks and structural damages which mayindicate that the model is still in serviceable conditions andthere was no need to strengthen No visible cracks andsignicant damages occurred after Rare 6 However themodel responded with more vibrations and little crackwhich indicated that the model was minor damaged eventhough the test building was still in the serviceable condition
Some part of it might need to be repairedWhen subjected toRare 7 it is observed that the model vibrates signicantlytogether with a large number of cracks in the upper part ofthe model and spalling of concrete It can be concluded thatthe test building is not collapsed even when subject to Rare 7but lost much of its lateral load resisting capacity Since theprototype building is represented as the model the damagepattern of the prototype building can be obtained edamage of dierent oors after the test is shown in Figure 5
42 Dynamic Characteristic Low peak white noise excita-tion was used before and after seismic excitation for cap-turing the dynamic characteristic of the model Results areshown in Table 7 It can be seen that the natural frequenciesof the test model maintain the same under Frequent 6indicating linear behaviors of the structure in this stage
(a)
015
m
628
7m
(b)
Figure 2 Pictures of the model (a) model under construction (b) completed model
Table 4 Elastic modulus of materials
Floor Prototype building (times104Nmm2) Test model (times104Nmm2) Ratio1stsim7th 355 121 12938thsim17th 345 121 128518thsim27th 335 109 130728thsim37th 325 109 129838thsim46th 315 095 133247thsimtop oor 300 095 1316
Shock and Vibration 5
0 10 20 30 40 50ndash300
ndash200
ndash100
0
100
200
300
400A
ccel
erat
ion
(cm
s2 )
Time (sec)
(a)
0 10 20 30 40 50 60ndash200
ndash100
100
200
0
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(b)
0 5 10 15 20ndash20
ndash10
0
10
20
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(c)
Figure 3 Input seismic loading sequence (a) El Centro wave (b) Taft wave (c) articial seismic wave
Table 5 Characteristics of the shaking table
Item ParameterTable size 3times 3mVibrating direction One dimensionalMaximum displacement plusmn100mmMaximum velocity 500mmsMaximum acceleration plusmn20 g (no load) plusmn13 g (full load)Maximum model mass 10 tFrequency range 04sim40Hz
Table 6 Sequence of the shaking table test
Test condition Sequence number Input seismic wave
Frequent 6
1 White noise2 El Centro wave3 Taft wave4 Articial seismic wave
Moderate 6
5 White noise6 El Centro wave7 Taft wave8 Articial seismic wave
Rare 6
9 White noise10 El Centro wave11 Taft wave12 Articial seismic wave
Rare 7
13 White noise14 El Centro wave15 Taft wave16 White noise
Furthermore the second- and the third-order frequenciesof the test model decreased slightly after Moderate 6reflecting slight decrease of the structurersquos stiffness Nextafter Rare 6 the natural fundamental frequency decreasedby 39 indicating that damages may occur at a certainlateral-force resisting component of the model structureFinally after Rare 7 the natural frequencies of the testmodel decreased significantly It can be inferred that the 1stmode of the prototype structure is the Y direction the 2ndmode is the X direction and the 3rd mode is torsion (eratio of the 1st mode periods between torsion to the Y and Xdirection is 033 and 049 respectively which is far smallerthan the limit value 085 given by the Chinese code (JGJ3-2010) [12] Furthermore after analyzing the structurestiffness degradation curves in accordance with the 1storder natural frequencies of the model it can be obtainedthat the stiffness of the structure declines with the in-creasing magnitude of earthquake excitation with aminimum stiffness to 819
43 Acceleration Response Acceleration amplification fac-tor is the ratio of the maximum absolute value of accel-eration response of each story to the maximum inputacceleration at the bottom of the model (is factor is ofgreat significance to analyze the seismic performance of
structures describing how many times the accelerations ateach story are amplified compared to the base seismicexcitation Hence the acceleration amplification factor canbe obtained through dividing the peak accelerations of thetesting stories by the peak accelerations of the shaking tablein this test (en the envelope diagram of the building indifferent test conditions can be drawn Figure 6 shows theenvelope of acceleration amplification factors in the mainvibration direction (Y direction) with different seismicintensities and the peak acceleration of some floors in aspecific condition and acceleration amplification factor arelisted in Table 8
As can be seen the acceleration amplification factorsalong the floors of the structure are nearly invariable exceptfor the top floor reflecting the lateral stiffness at differentfloors (except for the top floor) is uniformly distributedFurthermore the acceleration amplification factor was al-most unchanged after suffering from Frequent and Mod-erate 6 which indicated that the lateral-force resistingcomponents of the model are seldom damaged Howeverthe acceleration amplification factor increases sharply on thetop floor and roofing layer indicating that the whiplasheffect cannot be ignored in this case Usually when damagesare increasing the stiffness of structures is reducing leadingto the elastic-plastic phrase which can result in a smalleracceleration amplification It can be seen in Figure 6 that the
(a) (b) (c)
Figure 5 Damages of the test model after seismic input (a) floors 1 to 3 (b) 42nd floor (c) 52nd floor
Table 7 Dynamic characteristic of the model before and after the earthquake excitation
Earthquake intensity Test itemsY Torsion X
1st order 2nd order 3rd order 1st order 2nd order 3rd order
Before earthquakeFrequency (Hz) 254 1211 2941 762 2130 371
Period (s) 03937 00826 00340 01312 00469 02695Damping ratio () 325 261 212 236
Frequent 6Frequency (Hz) 254 1211 2921 762 2110
Period (s) 03937 00826 00342 01312 00474Damping ratio () 441 271 283
Moderate 6Frequency (Hz) 254 1192 2872 752 2091
Period (s) 03937 00839 00348 01330 00478Damping ratio () 420 304 337
Rare 6Frequency (Hz) 244 1133 2775 730 1993
Period (s) 04098 00883 00360 01370 00502Damping ratio () 401 311 335
Rare 7Frequency (Hz) 234 1075 684 1866
Period (s) 04274 00930 01462 00536Damping ratio () 387 380
Shock and Vibration 7
Frequent 6Moderate 6
Rare 6Rare 7
1 2 3 4 5 6 70K
10
20
30
40
50
60
Stor
y
(a)
Frequent 6Moderate 6
Rare 6Rare 7
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(b)
Frequent 6Moderate 6
Rare 6
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(c)
Figure 6 Envelope of acceleration amplication factor under dierent earthquake levels (a) El Centro seismic excitation (b) Taft seismicexcitation (c) articial seismic wave (USER1)
Table 8 Peak acceleration and acceleration amplication factors
Floor El Centro wave Taft wave Articial seismic waveamax (ms2) K amax (ms2) K amax (ms2) K
Top oor 2212 2402 2962 2692 3973 2693Roof 3022 3281 3358 3052 4066 2756
8 Shock and Vibration
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
on three embankment slope models to study the seismicresponse of the embankment slope with different reinforcingschemes (e effectiveness of shaking table tests has alsobeen studied For example Srilatha et al [7] investigated theeffect of frequency of base shaking on the dynamic responseof unreinforced and reinforced soil slopes through a series ofshaking table tests
In shaking table tests most researchers used scaledmodels as specimens For example Liu et al [8] carriedout shaking table tests on a 130 scaled model with andwithout base isolation bearings to assess the seismicperformance of an isolated museum structure in highearthquake intensity regions Lu et al [9] tested a 150scale high-rise building model on a shaking table forShanghai World Financial Center Tower (e dynamiccharacteristics seismic responses and failure mechanismof the structure were investigated and weak positionsunder seldom-occurred earthquakes were identifiedSome researchers use prototype structures For exampleLignos et al [10] conducted a shaking table test on a full-scale high-rise building to demonstrate the effectiveness ofthe numerical models used Graziotti et al [11] performeda shaking table test on a two-story full-scale unreinforcedmasonry building to study its response characteristicsdamage mechanism and evolution during the experi-mental phases
(e above literature review suggests that the shakingtable test is an essential tool to assess and verify thedynamic behavior of structures It is particularly imper-ative for those structures that exceed the limits of thespecification of design codes and standards It is with thisregard that the present paper is in order (e ShimaoBuilding (numbered 1ndash3 in the A2 block) is an iconicbuilding in the central business district area of WuhanChina located on the bank of Yangtze River It is acombined commercial and residential building with 56stories (e lateral-force resisting system of the structureis the reinforced concrete (RC) shear wall with a height of1796m exceeding the limit for high-rise buildingsspecified by Chinese Regulation Technical Specificationfor Concrete Structures of Tall Building (JGJ3-2010) [12](erefore it is required to verify the structural seismicperformance after the regular structural designingaccording to the codes Besides the irregular buildingshape in both plane and elevation complicates the analysisand determination of seismic resistance of the structureTo ensure the safety of the building it is necessary toexamine the behavior of the building under seismicloading For this purpose a shaking table test and itsnumerical analysis as well as structural damage identifi-cation were also conducted
(is paper focuses on the investigation of the seismicbehavior of Shimao Building Firstly the results of ashaking table test on the 130 scale building model will bepresented (e structural dynamic characteristics and theresponses under different levels of earthquake loading willbe investigated and the failure mechanism and crackingpattern of the tested model will also be obtained (en thecorresponding finite element model will be established to
analyze its seismic performance At last a damage iden-tification method based on the autoregressive (AR) modelwill also be presented to identify the damage of the testbuilding According to the analysis of experiment finiteelement model and theoretical identification of the testbuilding seismic performance of the prototype buildingwill be obtained and this study can make sure that theprototype building is designed reasonably and can be putinto use safely Finally suggestions and measures to im-prove the prototype building seismic performance will alsobe presented
2 Design of Model Building
21 Prototype Building A 130 model of Shimao Buildingwas designed and built for the shaking table test to rep-resent the main characteristics of the prototype building(e experiment was undertaken in the laboratory of Schoolof Civil Engineering and Architecture at Wuhan Universityof Technology China Figure 1 shows the representing planand elevation of the prototype building It can be seen fromFigure 1(b) that the plan of the building is shaped as ldquoTrdquo(maximum 3285m in length and maximum 195m inwidth) and this shape of building may be susceptible toearthquake excitation (e vertical configuration of thebuilding consists of a core tube accommodating staircaselift well and pipe shaft and shear walls located at the outerwalls and some inner walls (e floors and roof of thebuilding are reinforced concrete beam-slab structures Inaddition the upper (vertical) structure is fixed on thereinforced concrete base
According to the ldquoTechnical Points (No 65 2015) ofSpecial Inspection for Seismic Fortification of Out-of-CodeHigh-rise Buildingsrdquo [13] issued by the Chinese Con-struction Ministry the total height of the building 1886m(including the roof truss) with 56 stories exceeds the limitheight of 170m specified by the Class B shear wall struc-tures according the Chinese code (JGJ3-2010) [12] Fur-thermore the building has a set back at the height of12835m (the 41st story) as shown in Figure 1 leading to adisagreement between the centroid and stiffness center Asa consequence the eccentricity violates the requirements ofseismic conceptual design that building structures shouldbe symmetric in both plan and elevation Overall a shakingtable test of this building can be quite necessary
Dynamic characteristics of the prototype building werecalculated through Chinese structural design softwarePKPM Although the maximum seismic responses of thestructure under Frequent 6 (defined at Section 3) shown inTable 1 satisfy the requirements of the code (specified by theChinese Seismic Design Code of Building Structures)considering larger earthquakes happen and making extracertain the shaking table test is still needed for furtherverification
22 Similitude Law In this paper the similitude law isdetermined by the dimensional analysis method [14] Firstlysimilar conditions Π are obtained and then other similarity
2 Shock and Vibration
constants are obtained based on Π Inertia force restoringforce and gravity are required to be simulated in the testand thus elastic modulus E and density ρ of the modelmaterial are strictly controlled e essential requirement is(Eρal)m (Eρal)p where the subscripts m and p repre-sent the scaled model and the prototype building re-spectively at is
SESρSaSl
1 (1)
where SE Sρ Sa and Sl denote the similitude ratio of elasticmodulus equivalent density acceleration and geometryrespectively In the present case three controllable simili-tude ratios should be determined in advance to obtainothers Specically SE Sρ and Sl are chosen in this paperand thus Sa can be calculated using Equation (1)
Considering the shaking table size and the height re-quirement of the laboratory the dimension scaling parameter
Sl is chosen as 130 Based on the tested characteristics ofmaterials in the test the similitude law of elastic modulus SE isdetermined as 1305e total weight of themodel (includingself-weight and articial mass) and prototype building are306 ton and 40400 ton (including live load) respectivelyus the mass ratio Sm is 1132026 and the similitude ratioof equivalent density Sρ can be obtained as 20245 all themainmodel similitude relationships and calculation formulas areshown in Table 2
23 Model Constructing Since the aim of the shaking tabletest is to investigate the seismic behavior of the originalstructure subjected to dierent intensity of earthquakesincluding failure mode and mechanisms it is necessary touse the same materials as the prototype building e ma-terials used for model construction (specimen) are micro-concrete (mix proportion is shown in Table 3) galvanized
188618260
18070
188618260
(a)
X
Y
8300
Li wellPipe sha
32850
1160
0
1950
0
7900
(b)
Figure 1 Sketch of prototype building (a) elevation view (b) oor plan below the 41st story (units mm)
Table 1 Dynamic characteristics and seismic response of the prototype building
Direction Maximum lateral stiness (kNm) Frequencies (Hz) Maximum displacement (mm) Story drift Torsion displacement ratioX 109times108 29303 3772 13500 115Y 109times108 35724 5416 12359 119Torsion 17173
Shock and Vibration 3
steel wires and meshes which are similar to the materials inthe prototype building Ordinary Portland Cement PO 325is chosen to construct concrete A batch of specimens in theform of cubic and prism type were cast to measure thestrength and elastic modulus of microconcrete (e testingmethod of the specimens strictly followed the requirementsof the Standard for Test Methods of Concrete Structures(GB50152-2012) [15] (e microconcrete mix proportionsare shown in Table 3 (e elastic modulus of materials isshown in Table 4 (e height of the model is 6437m with6287m for the model itself and 015m for the base (ephoto of the completed model is shown in Figure 2
3 Testing Methodology
31TestVariables andFacility (e test variables include twotypes different fortification intensity and different types ofearthquake waves According to related researches on thestatistics of the peak acceleration of ground motions inChina the seismic intensity of a specific site exhibits theextreme distribution of the III type (Weibull distribution)(e fortification intensity is defined as the intensity with10 exceedance probability which is also called as themoderate or basic intensity for simplicity Similarly the rareand frequent intensity is defined as the intensity with 2ndash3and 65 exceedance probability respectively Furthermorefor the moderate intensity of a specific site the frequent andrare intensity is about 155deg lower and 1deg higher than themoderate intensity respectively In this paper the scaledbuilding under investigation is located in Wuhan withDegree 6 as the fortificationbasic intensity [16] (is in-tensity is associated with medium occurrence (10)(erefore Moderate 6 means ground motion with Intensity6 (the peak ground acceleration (PGA) is 005 g) and Fre-quency 6 means ground motion with Intensity 445 (PGA
0018 g) whereas Rare 6 means ground motion with In-tensity 7 (PGA 01 g) Ultralarge earthquakes are not spec-ified in GB50011-2010 [17] and Rare 7 (actually Intensity 8)is introduced here for the purpose of studying the nonlinearor even collapse performance of the scaled building For achosen recorded seismic excitation the similitude law(shown in Table 1) was used to scale the acceleration andtime
According to the dynamic characteristics and site con-dition of the prototype structure three seismic runs arechosen for simulating the shaking table test input wave (1)El Centro wave with a peak acceleration of 341ms2 (2) Taftwave with a peak acceleration of 153ms2 and (3) artificialseismic wave (USER1) supplied by the construction de-signers with a peak acceleration of 018ms2 (e time-history curves are shown in Figure 3(emain specificationsof the shaking table used in the present experiment areshown in Table 5
32 Testing Procedure and Layout of Sensors (e testingprocedure is shown in Table 6 It can be seen that the EICentro wave is the first wave in each test condition followedby the Taft wave and artificial seismic wave Before and afterinputting different fortification intensity seismic waves lowpeak white noise excitation is conducted to measure thedynamic characteristics parameters such as natural fre-quency mode and damping ratio
(e main measurement of structural response is accel-eration displacement strain etc Several acceleration sen-sors displacement sensors and strain gauges are arranged atthe different heights of the model to measure the responsesof the model structure under different seismic fortificationintensities Accelerations and displacements were measuredby the large dynamic signal acquisition and analysis systemDASP2003 developed by Orient Institute of Noise andVibration 14 acceleration sensors were used for differentpurposes namely 2 for measuring vertical accelerations 10for horizontal accelerations and 2 for torsion of thebuilding Dynamic strain was obtained by the dynamic andstatic testing instrument DH3817 Five displacement sensorswere used to measure the deformation along the direction of
Table 2 Similitude law
Contents Physical quantity Similitude equation Similitude law
Geometric relationship
Length Sl 130Linear displacement SX Sl 130
Area SA S2l 1900Angular displacement 1 1
Material relationship
Elastic modulus SE 1305Concrete strength Sc Sσ 1692Equivalent mass Sm Sρ middot S3l 1132026Equivalent density Sρ 2045
Dynamic relationship
Period ST 1Sω 0083Frequency Sω [Sσ(SρS
2l )]12 12012
Acceleration Sa Sl middot S2ω 481Acceleration of gravity Sg 1
shaking e positions of acceleration sensors and dis-placement sensors are shown in Figure 4
4 Test Results and Analysis
41 Damage Patterns When subjected to Frequent 6 therewere no noticeable shaking and visible damages it can bepredicted that the test model can remain in a serviceablecondition after Frequent 6 and there was no damage In thecase of Moderate 6 the model responded with little vibra-tion but no cracks and structural damages which mayindicate that the model is still in serviceable conditions andthere was no need to strengthen No visible cracks andsignicant damages occurred after Rare 6 However themodel responded with more vibrations and little crackwhich indicated that the model was minor damaged eventhough the test building was still in the serviceable condition
Some part of it might need to be repairedWhen subjected toRare 7 it is observed that the model vibrates signicantlytogether with a large number of cracks in the upper part ofthe model and spalling of concrete It can be concluded thatthe test building is not collapsed even when subject to Rare 7but lost much of its lateral load resisting capacity Since theprototype building is represented as the model the damagepattern of the prototype building can be obtained edamage of dierent oors after the test is shown in Figure 5
42 Dynamic Characteristic Low peak white noise excita-tion was used before and after seismic excitation for cap-turing the dynamic characteristic of the model Results areshown in Table 7 It can be seen that the natural frequenciesof the test model maintain the same under Frequent 6indicating linear behaviors of the structure in this stage
(a)
015
m
628
7m
(b)
Figure 2 Pictures of the model (a) model under construction (b) completed model
Table 4 Elastic modulus of materials
Floor Prototype building (times104Nmm2) Test model (times104Nmm2) Ratio1stsim7th 355 121 12938thsim17th 345 121 128518thsim27th 335 109 130728thsim37th 325 109 129838thsim46th 315 095 133247thsimtop oor 300 095 1316
Shock and Vibration 5
0 10 20 30 40 50ndash300
ndash200
ndash100
0
100
200
300
400A
ccel
erat
ion
(cm
s2 )
Time (sec)
(a)
0 10 20 30 40 50 60ndash200
ndash100
100
200
0
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(b)
0 5 10 15 20ndash20
ndash10
0
10
20
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(c)
Figure 3 Input seismic loading sequence (a) El Centro wave (b) Taft wave (c) articial seismic wave
Table 5 Characteristics of the shaking table
Item ParameterTable size 3times 3mVibrating direction One dimensionalMaximum displacement plusmn100mmMaximum velocity 500mmsMaximum acceleration plusmn20 g (no load) plusmn13 g (full load)Maximum model mass 10 tFrequency range 04sim40Hz
Table 6 Sequence of the shaking table test
Test condition Sequence number Input seismic wave
Frequent 6
1 White noise2 El Centro wave3 Taft wave4 Articial seismic wave
Moderate 6
5 White noise6 El Centro wave7 Taft wave8 Articial seismic wave
Rare 6
9 White noise10 El Centro wave11 Taft wave12 Articial seismic wave
Rare 7
13 White noise14 El Centro wave15 Taft wave16 White noise
Furthermore the second- and the third-order frequenciesof the test model decreased slightly after Moderate 6reflecting slight decrease of the structurersquos stiffness Nextafter Rare 6 the natural fundamental frequency decreasedby 39 indicating that damages may occur at a certainlateral-force resisting component of the model structureFinally after Rare 7 the natural frequencies of the testmodel decreased significantly It can be inferred that the 1stmode of the prototype structure is the Y direction the 2ndmode is the X direction and the 3rd mode is torsion (eratio of the 1st mode periods between torsion to the Y and Xdirection is 033 and 049 respectively which is far smallerthan the limit value 085 given by the Chinese code (JGJ3-2010) [12] Furthermore after analyzing the structurestiffness degradation curves in accordance with the 1storder natural frequencies of the model it can be obtainedthat the stiffness of the structure declines with the in-creasing magnitude of earthquake excitation with aminimum stiffness to 819
43 Acceleration Response Acceleration amplification fac-tor is the ratio of the maximum absolute value of accel-eration response of each story to the maximum inputacceleration at the bottom of the model (is factor is ofgreat significance to analyze the seismic performance of
structures describing how many times the accelerations ateach story are amplified compared to the base seismicexcitation Hence the acceleration amplification factor canbe obtained through dividing the peak accelerations of thetesting stories by the peak accelerations of the shaking tablein this test (en the envelope diagram of the building indifferent test conditions can be drawn Figure 6 shows theenvelope of acceleration amplification factors in the mainvibration direction (Y direction) with different seismicintensities and the peak acceleration of some floors in aspecific condition and acceleration amplification factor arelisted in Table 8
As can be seen the acceleration amplification factorsalong the floors of the structure are nearly invariable exceptfor the top floor reflecting the lateral stiffness at differentfloors (except for the top floor) is uniformly distributedFurthermore the acceleration amplification factor was al-most unchanged after suffering from Frequent and Mod-erate 6 which indicated that the lateral-force resistingcomponents of the model are seldom damaged Howeverthe acceleration amplification factor increases sharply on thetop floor and roofing layer indicating that the whiplasheffect cannot be ignored in this case Usually when damagesare increasing the stiffness of structures is reducing leadingto the elastic-plastic phrase which can result in a smalleracceleration amplification It can be seen in Figure 6 that the
(a) (b) (c)
Figure 5 Damages of the test model after seismic input (a) floors 1 to 3 (b) 42nd floor (c) 52nd floor
Table 7 Dynamic characteristic of the model before and after the earthquake excitation
Earthquake intensity Test itemsY Torsion X
1st order 2nd order 3rd order 1st order 2nd order 3rd order
Before earthquakeFrequency (Hz) 254 1211 2941 762 2130 371
Period (s) 03937 00826 00340 01312 00469 02695Damping ratio () 325 261 212 236
Frequent 6Frequency (Hz) 254 1211 2921 762 2110
Period (s) 03937 00826 00342 01312 00474Damping ratio () 441 271 283
Moderate 6Frequency (Hz) 254 1192 2872 752 2091
Period (s) 03937 00839 00348 01330 00478Damping ratio () 420 304 337
Rare 6Frequency (Hz) 244 1133 2775 730 1993
Period (s) 04098 00883 00360 01370 00502Damping ratio () 401 311 335
Rare 7Frequency (Hz) 234 1075 684 1866
Period (s) 04274 00930 01462 00536Damping ratio () 387 380
Shock and Vibration 7
Frequent 6Moderate 6
Rare 6Rare 7
1 2 3 4 5 6 70K
10
20
30
40
50
60
Stor
y
(a)
Frequent 6Moderate 6
Rare 6Rare 7
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(b)
Frequent 6Moderate 6
Rare 6
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(c)
Figure 6 Envelope of acceleration amplication factor under dierent earthquake levels (a) El Centro seismic excitation (b) Taft seismicexcitation (c) articial seismic wave (USER1)
Table 8 Peak acceleration and acceleration amplication factors
Floor El Centro wave Taft wave Articial seismic waveamax (ms2) K amax (ms2) K amax (ms2) K
Top oor 2212 2402 2962 2692 3973 2693Roof 3022 3281 3358 3052 4066 2756
8 Shock and Vibration
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
constants are obtained based on Π Inertia force restoringforce and gravity are required to be simulated in the testand thus elastic modulus E and density ρ of the modelmaterial are strictly controlled e essential requirement is(Eρal)m (Eρal)p where the subscripts m and p repre-sent the scaled model and the prototype building re-spectively at is
SESρSaSl
1 (1)
where SE Sρ Sa and Sl denote the similitude ratio of elasticmodulus equivalent density acceleration and geometryrespectively In the present case three controllable simili-tude ratios should be determined in advance to obtainothers Specically SE Sρ and Sl are chosen in this paperand thus Sa can be calculated using Equation (1)
Considering the shaking table size and the height re-quirement of the laboratory the dimension scaling parameter
Sl is chosen as 130 Based on the tested characteristics ofmaterials in the test the similitude law of elastic modulus SE isdetermined as 1305e total weight of themodel (includingself-weight and articial mass) and prototype building are306 ton and 40400 ton (including live load) respectivelyus the mass ratio Sm is 1132026 and the similitude ratioof equivalent density Sρ can be obtained as 20245 all themainmodel similitude relationships and calculation formulas areshown in Table 2
23 Model Constructing Since the aim of the shaking tabletest is to investigate the seismic behavior of the originalstructure subjected to dierent intensity of earthquakesincluding failure mode and mechanisms it is necessary touse the same materials as the prototype building e ma-terials used for model construction (specimen) are micro-concrete (mix proportion is shown in Table 3) galvanized
188618260
18070
188618260
(a)
X
Y
8300
Li wellPipe sha
32850
1160
0
1950
0
7900
(b)
Figure 1 Sketch of prototype building (a) elevation view (b) oor plan below the 41st story (units mm)
Table 1 Dynamic characteristics and seismic response of the prototype building
Direction Maximum lateral stiness (kNm) Frequencies (Hz) Maximum displacement (mm) Story drift Torsion displacement ratioX 109times108 29303 3772 13500 115Y 109times108 35724 5416 12359 119Torsion 17173
Shock and Vibration 3
steel wires and meshes which are similar to the materials inthe prototype building Ordinary Portland Cement PO 325is chosen to construct concrete A batch of specimens in theform of cubic and prism type were cast to measure thestrength and elastic modulus of microconcrete (e testingmethod of the specimens strictly followed the requirementsof the Standard for Test Methods of Concrete Structures(GB50152-2012) [15] (e microconcrete mix proportionsare shown in Table 3 (e elastic modulus of materials isshown in Table 4 (e height of the model is 6437m with6287m for the model itself and 015m for the base (ephoto of the completed model is shown in Figure 2
3 Testing Methodology
31TestVariables andFacility (e test variables include twotypes different fortification intensity and different types ofearthquake waves According to related researches on thestatistics of the peak acceleration of ground motions inChina the seismic intensity of a specific site exhibits theextreme distribution of the III type (Weibull distribution)(e fortification intensity is defined as the intensity with10 exceedance probability which is also called as themoderate or basic intensity for simplicity Similarly the rareand frequent intensity is defined as the intensity with 2ndash3and 65 exceedance probability respectively Furthermorefor the moderate intensity of a specific site the frequent andrare intensity is about 155deg lower and 1deg higher than themoderate intensity respectively In this paper the scaledbuilding under investigation is located in Wuhan withDegree 6 as the fortificationbasic intensity [16] (is in-tensity is associated with medium occurrence (10)(erefore Moderate 6 means ground motion with Intensity6 (the peak ground acceleration (PGA) is 005 g) and Fre-quency 6 means ground motion with Intensity 445 (PGA
0018 g) whereas Rare 6 means ground motion with In-tensity 7 (PGA 01 g) Ultralarge earthquakes are not spec-ified in GB50011-2010 [17] and Rare 7 (actually Intensity 8)is introduced here for the purpose of studying the nonlinearor even collapse performance of the scaled building For achosen recorded seismic excitation the similitude law(shown in Table 1) was used to scale the acceleration andtime
According to the dynamic characteristics and site con-dition of the prototype structure three seismic runs arechosen for simulating the shaking table test input wave (1)El Centro wave with a peak acceleration of 341ms2 (2) Taftwave with a peak acceleration of 153ms2 and (3) artificialseismic wave (USER1) supplied by the construction de-signers with a peak acceleration of 018ms2 (e time-history curves are shown in Figure 3(emain specificationsof the shaking table used in the present experiment areshown in Table 5
32 Testing Procedure and Layout of Sensors (e testingprocedure is shown in Table 6 It can be seen that the EICentro wave is the first wave in each test condition followedby the Taft wave and artificial seismic wave Before and afterinputting different fortification intensity seismic waves lowpeak white noise excitation is conducted to measure thedynamic characteristics parameters such as natural fre-quency mode and damping ratio
(e main measurement of structural response is accel-eration displacement strain etc Several acceleration sen-sors displacement sensors and strain gauges are arranged atthe different heights of the model to measure the responsesof the model structure under different seismic fortificationintensities Accelerations and displacements were measuredby the large dynamic signal acquisition and analysis systemDASP2003 developed by Orient Institute of Noise andVibration 14 acceleration sensors were used for differentpurposes namely 2 for measuring vertical accelerations 10for horizontal accelerations and 2 for torsion of thebuilding Dynamic strain was obtained by the dynamic andstatic testing instrument DH3817 Five displacement sensorswere used to measure the deformation along the direction of
Table 2 Similitude law
Contents Physical quantity Similitude equation Similitude law
Geometric relationship
Length Sl 130Linear displacement SX Sl 130
Area SA S2l 1900Angular displacement 1 1
Material relationship
Elastic modulus SE 1305Concrete strength Sc Sσ 1692Equivalent mass Sm Sρ middot S3l 1132026Equivalent density Sρ 2045
Dynamic relationship
Period ST 1Sω 0083Frequency Sω [Sσ(SρS
2l )]12 12012
Acceleration Sa Sl middot S2ω 481Acceleration of gravity Sg 1
shaking e positions of acceleration sensors and dis-placement sensors are shown in Figure 4
4 Test Results and Analysis
41 Damage Patterns When subjected to Frequent 6 therewere no noticeable shaking and visible damages it can bepredicted that the test model can remain in a serviceablecondition after Frequent 6 and there was no damage In thecase of Moderate 6 the model responded with little vibra-tion but no cracks and structural damages which mayindicate that the model is still in serviceable conditions andthere was no need to strengthen No visible cracks andsignicant damages occurred after Rare 6 However themodel responded with more vibrations and little crackwhich indicated that the model was minor damaged eventhough the test building was still in the serviceable condition
Some part of it might need to be repairedWhen subjected toRare 7 it is observed that the model vibrates signicantlytogether with a large number of cracks in the upper part ofthe model and spalling of concrete It can be concluded thatthe test building is not collapsed even when subject to Rare 7but lost much of its lateral load resisting capacity Since theprototype building is represented as the model the damagepattern of the prototype building can be obtained edamage of dierent oors after the test is shown in Figure 5
42 Dynamic Characteristic Low peak white noise excita-tion was used before and after seismic excitation for cap-turing the dynamic characteristic of the model Results areshown in Table 7 It can be seen that the natural frequenciesof the test model maintain the same under Frequent 6indicating linear behaviors of the structure in this stage
(a)
015
m
628
7m
(b)
Figure 2 Pictures of the model (a) model under construction (b) completed model
Table 4 Elastic modulus of materials
Floor Prototype building (times104Nmm2) Test model (times104Nmm2) Ratio1stsim7th 355 121 12938thsim17th 345 121 128518thsim27th 335 109 130728thsim37th 325 109 129838thsim46th 315 095 133247thsimtop oor 300 095 1316
Shock and Vibration 5
0 10 20 30 40 50ndash300
ndash200
ndash100
0
100
200
300
400A
ccel
erat
ion
(cm
s2 )
Time (sec)
(a)
0 10 20 30 40 50 60ndash200
ndash100
100
200
0
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(b)
0 5 10 15 20ndash20
ndash10
0
10
20
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(c)
Figure 3 Input seismic loading sequence (a) El Centro wave (b) Taft wave (c) articial seismic wave
Table 5 Characteristics of the shaking table
Item ParameterTable size 3times 3mVibrating direction One dimensionalMaximum displacement plusmn100mmMaximum velocity 500mmsMaximum acceleration plusmn20 g (no load) plusmn13 g (full load)Maximum model mass 10 tFrequency range 04sim40Hz
Table 6 Sequence of the shaking table test
Test condition Sequence number Input seismic wave
Frequent 6
1 White noise2 El Centro wave3 Taft wave4 Articial seismic wave
Moderate 6
5 White noise6 El Centro wave7 Taft wave8 Articial seismic wave
Rare 6
9 White noise10 El Centro wave11 Taft wave12 Articial seismic wave
Rare 7
13 White noise14 El Centro wave15 Taft wave16 White noise
Furthermore the second- and the third-order frequenciesof the test model decreased slightly after Moderate 6reflecting slight decrease of the structurersquos stiffness Nextafter Rare 6 the natural fundamental frequency decreasedby 39 indicating that damages may occur at a certainlateral-force resisting component of the model structureFinally after Rare 7 the natural frequencies of the testmodel decreased significantly It can be inferred that the 1stmode of the prototype structure is the Y direction the 2ndmode is the X direction and the 3rd mode is torsion (eratio of the 1st mode periods between torsion to the Y and Xdirection is 033 and 049 respectively which is far smallerthan the limit value 085 given by the Chinese code (JGJ3-2010) [12] Furthermore after analyzing the structurestiffness degradation curves in accordance with the 1storder natural frequencies of the model it can be obtainedthat the stiffness of the structure declines with the in-creasing magnitude of earthquake excitation with aminimum stiffness to 819
43 Acceleration Response Acceleration amplification fac-tor is the ratio of the maximum absolute value of accel-eration response of each story to the maximum inputacceleration at the bottom of the model (is factor is ofgreat significance to analyze the seismic performance of
structures describing how many times the accelerations ateach story are amplified compared to the base seismicexcitation Hence the acceleration amplification factor canbe obtained through dividing the peak accelerations of thetesting stories by the peak accelerations of the shaking tablein this test (en the envelope diagram of the building indifferent test conditions can be drawn Figure 6 shows theenvelope of acceleration amplification factors in the mainvibration direction (Y direction) with different seismicintensities and the peak acceleration of some floors in aspecific condition and acceleration amplification factor arelisted in Table 8
As can be seen the acceleration amplification factorsalong the floors of the structure are nearly invariable exceptfor the top floor reflecting the lateral stiffness at differentfloors (except for the top floor) is uniformly distributedFurthermore the acceleration amplification factor was al-most unchanged after suffering from Frequent and Mod-erate 6 which indicated that the lateral-force resistingcomponents of the model are seldom damaged Howeverthe acceleration amplification factor increases sharply on thetop floor and roofing layer indicating that the whiplasheffect cannot be ignored in this case Usually when damagesare increasing the stiffness of structures is reducing leadingto the elastic-plastic phrase which can result in a smalleracceleration amplification It can be seen in Figure 6 that the
(a) (b) (c)
Figure 5 Damages of the test model after seismic input (a) floors 1 to 3 (b) 42nd floor (c) 52nd floor
Table 7 Dynamic characteristic of the model before and after the earthquake excitation
Earthquake intensity Test itemsY Torsion X
1st order 2nd order 3rd order 1st order 2nd order 3rd order
Before earthquakeFrequency (Hz) 254 1211 2941 762 2130 371
Period (s) 03937 00826 00340 01312 00469 02695Damping ratio () 325 261 212 236
Frequent 6Frequency (Hz) 254 1211 2921 762 2110
Period (s) 03937 00826 00342 01312 00474Damping ratio () 441 271 283
Moderate 6Frequency (Hz) 254 1192 2872 752 2091
Period (s) 03937 00839 00348 01330 00478Damping ratio () 420 304 337
Rare 6Frequency (Hz) 244 1133 2775 730 1993
Period (s) 04098 00883 00360 01370 00502Damping ratio () 401 311 335
Rare 7Frequency (Hz) 234 1075 684 1866
Period (s) 04274 00930 01462 00536Damping ratio () 387 380
Shock and Vibration 7
Frequent 6Moderate 6
Rare 6Rare 7
1 2 3 4 5 6 70K
10
20
30
40
50
60
Stor
y
(a)
Frequent 6Moderate 6
Rare 6Rare 7
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(b)
Frequent 6Moderate 6
Rare 6
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(c)
Figure 6 Envelope of acceleration amplication factor under dierent earthquake levels (a) El Centro seismic excitation (b) Taft seismicexcitation (c) articial seismic wave (USER1)
Table 8 Peak acceleration and acceleration amplication factors
Floor El Centro wave Taft wave Articial seismic waveamax (ms2) K amax (ms2) K amax (ms2) K
Top oor 2212 2402 2962 2692 3973 2693Roof 3022 3281 3358 3052 4066 2756
8 Shock and Vibration
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
steel wires and meshes which are similar to the materials inthe prototype building Ordinary Portland Cement PO 325is chosen to construct concrete A batch of specimens in theform of cubic and prism type were cast to measure thestrength and elastic modulus of microconcrete (e testingmethod of the specimens strictly followed the requirementsof the Standard for Test Methods of Concrete Structures(GB50152-2012) [15] (e microconcrete mix proportionsare shown in Table 3 (e elastic modulus of materials isshown in Table 4 (e height of the model is 6437m with6287m for the model itself and 015m for the base (ephoto of the completed model is shown in Figure 2
3 Testing Methodology
31TestVariables andFacility (e test variables include twotypes different fortification intensity and different types ofearthquake waves According to related researches on thestatistics of the peak acceleration of ground motions inChina the seismic intensity of a specific site exhibits theextreme distribution of the III type (Weibull distribution)(e fortification intensity is defined as the intensity with10 exceedance probability which is also called as themoderate or basic intensity for simplicity Similarly the rareand frequent intensity is defined as the intensity with 2ndash3and 65 exceedance probability respectively Furthermorefor the moderate intensity of a specific site the frequent andrare intensity is about 155deg lower and 1deg higher than themoderate intensity respectively In this paper the scaledbuilding under investigation is located in Wuhan withDegree 6 as the fortificationbasic intensity [16] (is in-tensity is associated with medium occurrence (10)(erefore Moderate 6 means ground motion with Intensity6 (the peak ground acceleration (PGA) is 005 g) and Fre-quency 6 means ground motion with Intensity 445 (PGA
0018 g) whereas Rare 6 means ground motion with In-tensity 7 (PGA 01 g) Ultralarge earthquakes are not spec-ified in GB50011-2010 [17] and Rare 7 (actually Intensity 8)is introduced here for the purpose of studying the nonlinearor even collapse performance of the scaled building For achosen recorded seismic excitation the similitude law(shown in Table 1) was used to scale the acceleration andtime
According to the dynamic characteristics and site con-dition of the prototype structure three seismic runs arechosen for simulating the shaking table test input wave (1)El Centro wave with a peak acceleration of 341ms2 (2) Taftwave with a peak acceleration of 153ms2 and (3) artificialseismic wave (USER1) supplied by the construction de-signers with a peak acceleration of 018ms2 (e time-history curves are shown in Figure 3(emain specificationsof the shaking table used in the present experiment areshown in Table 5
32 Testing Procedure and Layout of Sensors (e testingprocedure is shown in Table 6 It can be seen that the EICentro wave is the first wave in each test condition followedby the Taft wave and artificial seismic wave Before and afterinputting different fortification intensity seismic waves lowpeak white noise excitation is conducted to measure thedynamic characteristics parameters such as natural fre-quency mode and damping ratio
(e main measurement of structural response is accel-eration displacement strain etc Several acceleration sen-sors displacement sensors and strain gauges are arranged atthe different heights of the model to measure the responsesof the model structure under different seismic fortificationintensities Accelerations and displacements were measuredby the large dynamic signal acquisition and analysis systemDASP2003 developed by Orient Institute of Noise andVibration 14 acceleration sensors were used for differentpurposes namely 2 for measuring vertical accelerations 10for horizontal accelerations and 2 for torsion of thebuilding Dynamic strain was obtained by the dynamic andstatic testing instrument DH3817 Five displacement sensorswere used to measure the deformation along the direction of
Table 2 Similitude law
Contents Physical quantity Similitude equation Similitude law
Geometric relationship
Length Sl 130Linear displacement SX Sl 130
Area SA S2l 1900Angular displacement 1 1
Material relationship
Elastic modulus SE 1305Concrete strength Sc Sσ 1692Equivalent mass Sm Sρ middot S3l 1132026Equivalent density Sρ 2045
Dynamic relationship
Period ST 1Sω 0083Frequency Sω [Sσ(SρS
2l )]12 12012
Acceleration Sa Sl middot S2ω 481Acceleration of gravity Sg 1
shaking e positions of acceleration sensors and dis-placement sensors are shown in Figure 4
4 Test Results and Analysis
41 Damage Patterns When subjected to Frequent 6 therewere no noticeable shaking and visible damages it can bepredicted that the test model can remain in a serviceablecondition after Frequent 6 and there was no damage In thecase of Moderate 6 the model responded with little vibra-tion but no cracks and structural damages which mayindicate that the model is still in serviceable conditions andthere was no need to strengthen No visible cracks andsignicant damages occurred after Rare 6 However themodel responded with more vibrations and little crackwhich indicated that the model was minor damaged eventhough the test building was still in the serviceable condition
Some part of it might need to be repairedWhen subjected toRare 7 it is observed that the model vibrates signicantlytogether with a large number of cracks in the upper part ofthe model and spalling of concrete It can be concluded thatthe test building is not collapsed even when subject to Rare 7but lost much of its lateral load resisting capacity Since theprototype building is represented as the model the damagepattern of the prototype building can be obtained edamage of dierent oors after the test is shown in Figure 5
42 Dynamic Characteristic Low peak white noise excita-tion was used before and after seismic excitation for cap-turing the dynamic characteristic of the model Results areshown in Table 7 It can be seen that the natural frequenciesof the test model maintain the same under Frequent 6indicating linear behaviors of the structure in this stage
(a)
015
m
628
7m
(b)
Figure 2 Pictures of the model (a) model under construction (b) completed model
Table 4 Elastic modulus of materials
Floor Prototype building (times104Nmm2) Test model (times104Nmm2) Ratio1stsim7th 355 121 12938thsim17th 345 121 128518thsim27th 335 109 130728thsim37th 325 109 129838thsim46th 315 095 133247thsimtop oor 300 095 1316
Shock and Vibration 5
0 10 20 30 40 50ndash300
ndash200
ndash100
0
100
200
300
400A
ccel
erat
ion
(cm
s2 )
Time (sec)
(a)
0 10 20 30 40 50 60ndash200
ndash100
100
200
0
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(b)
0 5 10 15 20ndash20
ndash10
0
10
20
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(c)
Figure 3 Input seismic loading sequence (a) El Centro wave (b) Taft wave (c) articial seismic wave
Table 5 Characteristics of the shaking table
Item ParameterTable size 3times 3mVibrating direction One dimensionalMaximum displacement plusmn100mmMaximum velocity 500mmsMaximum acceleration plusmn20 g (no load) plusmn13 g (full load)Maximum model mass 10 tFrequency range 04sim40Hz
Table 6 Sequence of the shaking table test
Test condition Sequence number Input seismic wave
Frequent 6
1 White noise2 El Centro wave3 Taft wave4 Articial seismic wave
Moderate 6
5 White noise6 El Centro wave7 Taft wave8 Articial seismic wave
Rare 6
9 White noise10 El Centro wave11 Taft wave12 Articial seismic wave
Rare 7
13 White noise14 El Centro wave15 Taft wave16 White noise
Furthermore the second- and the third-order frequenciesof the test model decreased slightly after Moderate 6reflecting slight decrease of the structurersquos stiffness Nextafter Rare 6 the natural fundamental frequency decreasedby 39 indicating that damages may occur at a certainlateral-force resisting component of the model structureFinally after Rare 7 the natural frequencies of the testmodel decreased significantly It can be inferred that the 1stmode of the prototype structure is the Y direction the 2ndmode is the X direction and the 3rd mode is torsion (eratio of the 1st mode periods between torsion to the Y and Xdirection is 033 and 049 respectively which is far smallerthan the limit value 085 given by the Chinese code (JGJ3-2010) [12] Furthermore after analyzing the structurestiffness degradation curves in accordance with the 1storder natural frequencies of the model it can be obtainedthat the stiffness of the structure declines with the in-creasing magnitude of earthquake excitation with aminimum stiffness to 819
43 Acceleration Response Acceleration amplification fac-tor is the ratio of the maximum absolute value of accel-eration response of each story to the maximum inputacceleration at the bottom of the model (is factor is ofgreat significance to analyze the seismic performance of
structures describing how many times the accelerations ateach story are amplified compared to the base seismicexcitation Hence the acceleration amplification factor canbe obtained through dividing the peak accelerations of thetesting stories by the peak accelerations of the shaking tablein this test (en the envelope diagram of the building indifferent test conditions can be drawn Figure 6 shows theenvelope of acceleration amplification factors in the mainvibration direction (Y direction) with different seismicintensities and the peak acceleration of some floors in aspecific condition and acceleration amplification factor arelisted in Table 8
As can be seen the acceleration amplification factorsalong the floors of the structure are nearly invariable exceptfor the top floor reflecting the lateral stiffness at differentfloors (except for the top floor) is uniformly distributedFurthermore the acceleration amplification factor was al-most unchanged after suffering from Frequent and Mod-erate 6 which indicated that the lateral-force resistingcomponents of the model are seldom damaged Howeverthe acceleration amplification factor increases sharply on thetop floor and roofing layer indicating that the whiplasheffect cannot be ignored in this case Usually when damagesare increasing the stiffness of structures is reducing leadingto the elastic-plastic phrase which can result in a smalleracceleration amplification It can be seen in Figure 6 that the
(a) (b) (c)
Figure 5 Damages of the test model after seismic input (a) floors 1 to 3 (b) 42nd floor (c) 52nd floor
Table 7 Dynamic characteristic of the model before and after the earthquake excitation
Earthquake intensity Test itemsY Torsion X
1st order 2nd order 3rd order 1st order 2nd order 3rd order
Before earthquakeFrequency (Hz) 254 1211 2941 762 2130 371
Period (s) 03937 00826 00340 01312 00469 02695Damping ratio () 325 261 212 236
Frequent 6Frequency (Hz) 254 1211 2921 762 2110
Period (s) 03937 00826 00342 01312 00474Damping ratio () 441 271 283
Moderate 6Frequency (Hz) 254 1192 2872 752 2091
Period (s) 03937 00839 00348 01330 00478Damping ratio () 420 304 337
Rare 6Frequency (Hz) 244 1133 2775 730 1993
Period (s) 04098 00883 00360 01370 00502Damping ratio () 401 311 335
Rare 7Frequency (Hz) 234 1075 684 1866
Period (s) 04274 00930 01462 00536Damping ratio () 387 380
Shock and Vibration 7
Frequent 6Moderate 6
Rare 6Rare 7
1 2 3 4 5 6 70K
10
20
30
40
50
60
Stor
y
(a)
Frequent 6Moderate 6
Rare 6Rare 7
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(b)
Frequent 6Moderate 6
Rare 6
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(c)
Figure 6 Envelope of acceleration amplication factor under dierent earthquake levels (a) El Centro seismic excitation (b) Taft seismicexcitation (c) articial seismic wave (USER1)
Table 8 Peak acceleration and acceleration amplication factors
Floor El Centro wave Taft wave Articial seismic waveamax (ms2) K amax (ms2) K amax (ms2) K
Top oor 2212 2402 2962 2692 3973 2693Roof 3022 3281 3358 3052 4066 2756
8 Shock and Vibration
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
shaking e positions of acceleration sensors and dis-placement sensors are shown in Figure 4
4 Test Results and Analysis
41 Damage Patterns When subjected to Frequent 6 therewere no noticeable shaking and visible damages it can bepredicted that the test model can remain in a serviceablecondition after Frequent 6 and there was no damage In thecase of Moderate 6 the model responded with little vibra-tion but no cracks and structural damages which mayindicate that the model is still in serviceable conditions andthere was no need to strengthen No visible cracks andsignicant damages occurred after Rare 6 However themodel responded with more vibrations and little crackwhich indicated that the model was minor damaged eventhough the test building was still in the serviceable condition
Some part of it might need to be repairedWhen subjected toRare 7 it is observed that the model vibrates signicantlytogether with a large number of cracks in the upper part ofthe model and spalling of concrete It can be concluded thatthe test building is not collapsed even when subject to Rare 7but lost much of its lateral load resisting capacity Since theprototype building is represented as the model the damagepattern of the prototype building can be obtained edamage of dierent oors after the test is shown in Figure 5
42 Dynamic Characteristic Low peak white noise excita-tion was used before and after seismic excitation for cap-turing the dynamic characteristic of the model Results areshown in Table 7 It can be seen that the natural frequenciesof the test model maintain the same under Frequent 6indicating linear behaviors of the structure in this stage
(a)
015
m
628
7m
(b)
Figure 2 Pictures of the model (a) model under construction (b) completed model
Table 4 Elastic modulus of materials
Floor Prototype building (times104Nmm2) Test model (times104Nmm2) Ratio1stsim7th 355 121 12938thsim17th 345 121 128518thsim27th 335 109 130728thsim37th 325 109 129838thsim46th 315 095 133247thsimtop oor 300 095 1316
Shock and Vibration 5
0 10 20 30 40 50ndash300
ndash200
ndash100
0
100
200
300
400A
ccel
erat
ion
(cm
s2 )
Time (sec)
(a)
0 10 20 30 40 50 60ndash200
ndash100
100
200
0
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(b)
0 5 10 15 20ndash20
ndash10
0
10
20
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(c)
Figure 3 Input seismic loading sequence (a) El Centro wave (b) Taft wave (c) articial seismic wave
Table 5 Characteristics of the shaking table
Item ParameterTable size 3times 3mVibrating direction One dimensionalMaximum displacement plusmn100mmMaximum velocity 500mmsMaximum acceleration plusmn20 g (no load) plusmn13 g (full load)Maximum model mass 10 tFrequency range 04sim40Hz
Table 6 Sequence of the shaking table test
Test condition Sequence number Input seismic wave
Frequent 6
1 White noise2 El Centro wave3 Taft wave4 Articial seismic wave
Moderate 6
5 White noise6 El Centro wave7 Taft wave8 Articial seismic wave
Rare 6
9 White noise10 El Centro wave11 Taft wave12 Articial seismic wave
Rare 7
13 White noise14 El Centro wave15 Taft wave16 White noise
Furthermore the second- and the third-order frequenciesof the test model decreased slightly after Moderate 6reflecting slight decrease of the structurersquos stiffness Nextafter Rare 6 the natural fundamental frequency decreasedby 39 indicating that damages may occur at a certainlateral-force resisting component of the model structureFinally after Rare 7 the natural frequencies of the testmodel decreased significantly It can be inferred that the 1stmode of the prototype structure is the Y direction the 2ndmode is the X direction and the 3rd mode is torsion (eratio of the 1st mode periods between torsion to the Y and Xdirection is 033 and 049 respectively which is far smallerthan the limit value 085 given by the Chinese code (JGJ3-2010) [12] Furthermore after analyzing the structurestiffness degradation curves in accordance with the 1storder natural frequencies of the model it can be obtainedthat the stiffness of the structure declines with the in-creasing magnitude of earthquake excitation with aminimum stiffness to 819
43 Acceleration Response Acceleration amplification fac-tor is the ratio of the maximum absolute value of accel-eration response of each story to the maximum inputacceleration at the bottom of the model (is factor is ofgreat significance to analyze the seismic performance of
structures describing how many times the accelerations ateach story are amplified compared to the base seismicexcitation Hence the acceleration amplification factor canbe obtained through dividing the peak accelerations of thetesting stories by the peak accelerations of the shaking tablein this test (en the envelope diagram of the building indifferent test conditions can be drawn Figure 6 shows theenvelope of acceleration amplification factors in the mainvibration direction (Y direction) with different seismicintensities and the peak acceleration of some floors in aspecific condition and acceleration amplification factor arelisted in Table 8
As can be seen the acceleration amplification factorsalong the floors of the structure are nearly invariable exceptfor the top floor reflecting the lateral stiffness at differentfloors (except for the top floor) is uniformly distributedFurthermore the acceleration amplification factor was al-most unchanged after suffering from Frequent and Mod-erate 6 which indicated that the lateral-force resistingcomponents of the model are seldom damaged Howeverthe acceleration amplification factor increases sharply on thetop floor and roofing layer indicating that the whiplasheffect cannot be ignored in this case Usually when damagesare increasing the stiffness of structures is reducing leadingto the elastic-plastic phrase which can result in a smalleracceleration amplification It can be seen in Figure 6 that the
(a) (b) (c)
Figure 5 Damages of the test model after seismic input (a) floors 1 to 3 (b) 42nd floor (c) 52nd floor
Table 7 Dynamic characteristic of the model before and after the earthquake excitation
Earthquake intensity Test itemsY Torsion X
1st order 2nd order 3rd order 1st order 2nd order 3rd order
Before earthquakeFrequency (Hz) 254 1211 2941 762 2130 371
Period (s) 03937 00826 00340 01312 00469 02695Damping ratio () 325 261 212 236
Frequent 6Frequency (Hz) 254 1211 2921 762 2110
Period (s) 03937 00826 00342 01312 00474Damping ratio () 441 271 283
Moderate 6Frequency (Hz) 254 1192 2872 752 2091
Period (s) 03937 00839 00348 01330 00478Damping ratio () 420 304 337
Rare 6Frequency (Hz) 244 1133 2775 730 1993
Period (s) 04098 00883 00360 01370 00502Damping ratio () 401 311 335
Rare 7Frequency (Hz) 234 1075 684 1866
Period (s) 04274 00930 01462 00536Damping ratio () 387 380
Shock and Vibration 7
Frequent 6Moderate 6
Rare 6Rare 7
1 2 3 4 5 6 70K
10
20
30
40
50
60
Stor
y
(a)
Frequent 6Moderate 6
Rare 6Rare 7
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(b)
Frequent 6Moderate 6
Rare 6
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(c)
Figure 6 Envelope of acceleration amplication factor under dierent earthquake levels (a) El Centro seismic excitation (b) Taft seismicexcitation (c) articial seismic wave (USER1)
Table 8 Peak acceleration and acceleration amplication factors
Floor El Centro wave Taft wave Articial seismic waveamax (ms2) K amax (ms2) K amax (ms2) K
Top oor 2212 2402 2962 2692 3973 2693Roof 3022 3281 3358 3052 4066 2756
8 Shock and Vibration
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
0 10 20 30 40 50ndash300
ndash200
ndash100
0
100
200
300
400A
ccel
erat
ion
(cm
s2 )
Time (sec)
(a)
0 10 20 30 40 50 60ndash200
ndash100
100
200
0
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(b)
0 5 10 15 20ndash20
ndash10
0
10
20
Acc
eler
atio
n (c
ms
2 )
Time (sec)
(c)
Figure 3 Input seismic loading sequence (a) El Centro wave (b) Taft wave (c) articial seismic wave
Table 5 Characteristics of the shaking table
Item ParameterTable size 3times 3mVibrating direction One dimensionalMaximum displacement plusmn100mmMaximum velocity 500mmsMaximum acceleration plusmn20 g (no load) plusmn13 g (full load)Maximum model mass 10 tFrequency range 04sim40Hz
Table 6 Sequence of the shaking table test
Test condition Sequence number Input seismic wave
Frequent 6
1 White noise2 El Centro wave3 Taft wave4 Articial seismic wave
Moderate 6
5 White noise6 El Centro wave7 Taft wave8 Articial seismic wave
Rare 6
9 White noise10 El Centro wave11 Taft wave12 Articial seismic wave
Rare 7
13 White noise14 El Centro wave15 Taft wave16 White noise
Furthermore the second- and the third-order frequenciesof the test model decreased slightly after Moderate 6reflecting slight decrease of the structurersquos stiffness Nextafter Rare 6 the natural fundamental frequency decreasedby 39 indicating that damages may occur at a certainlateral-force resisting component of the model structureFinally after Rare 7 the natural frequencies of the testmodel decreased significantly It can be inferred that the 1stmode of the prototype structure is the Y direction the 2ndmode is the X direction and the 3rd mode is torsion (eratio of the 1st mode periods between torsion to the Y and Xdirection is 033 and 049 respectively which is far smallerthan the limit value 085 given by the Chinese code (JGJ3-2010) [12] Furthermore after analyzing the structurestiffness degradation curves in accordance with the 1storder natural frequencies of the model it can be obtainedthat the stiffness of the structure declines with the in-creasing magnitude of earthquake excitation with aminimum stiffness to 819
43 Acceleration Response Acceleration amplification fac-tor is the ratio of the maximum absolute value of accel-eration response of each story to the maximum inputacceleration at the bottom of the model (is factor is ofgreat significance to analyze the seismic performance of
structures describing how many times the accelerations ateach story are amplified compared to the base seismicexcitation Hence the acceleration amplification factor canbe obtained through dividing the peak accelerations of thetesting stories by the peak accelerations of the shaking tablein this test (en the envelope diagram of the building indifferent test conditions can be drawn Figure 6 shows theenvelope of acceleration amplification factors in the mainvibration direction (Y direction) with different seismicintensities and the peak acceleration of some floors in aspecific condition and acceleration amplification factor arelisted in Table 8
As can be seen the acceleration amplification factorsalong the floors of the structure are nearly invariable exceptfor the top floor reflecting the lateral stiffness at differentfloors (except for the top floor) is uniformly distributedFurthermore the acceleration amplification factor was al-most unchanged after suffering from Frequent and Mod-erate 6 which indicated that the lateral-force resistingcomponents of the model are seldom damaged Howeverthe acceleration amplification factor increases sharply on thetop floor and roofing layer indicating that the whiplasheffect cannot be ignored in this case Usually when damagesare increasing the stiffness of structures is reducing leadingto the elastic-plastic phrase which can result in a smalleracceleration amplification It can be seen in Figure 6 that the
(a) (b) (c)
Figure 5 Damages of the test model after seismic input (a) floors 1 to 3 (b) 42nd floor (c) 52nd floor
Table 7 Dynamic characteristic of the model before and after the earthquake excitation
Earthquake intensity Test itemsY Torsion X
1st order 2nd order 3rd order 1st order 2nd order 3rd order
Before earthquakeFrequency (Hz) 254 1211 2941 762 2130 371
Period (s) 03937 00826 00340 01312 00469 02695Damping ratio () 325 261 212 236
Frequent 6Frequency (Hz) 254 1211 2921 762 2110
Period (s) 03937 00826 00342 01312 00474Damping ratio () 441 271 283
Moderate 6Frequency (Hz) 254 1192 2872 752 2091
Period (s) 03937 00839 00348 01330 00478Damping ratio () 420 304 337
Rare 6Frequency (Hz) 244 1133 2775 730 1993
Period (s) 04098 00883 00360 01370 00502Damping ratio () 401 311 335
Rare 7Frequency (Hz) 234 1075 684 1866
Period (s) 04274 00930 01462 00536Damping ratio () 387 380
Shock and Vibration 7
Frequent 6Moderate 6
Rare 6Rare 7
1 2 3 4 5 6 70K
10
20
30
40
50
60
Stor
y
(a)
Frequent 6Moderate 6
Rare 6Rare 7
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(b)
Frequent 6Moderate 6
Rare 6
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(c)
Figure 6 Envelope of acceleration amplication factor under dierent earthquake levels (a) El Centro seismic excitation (b) Taft seismicexcitation (c) articial seismic wave (USER1)
Table 8 Peak acceleration and acceleration amplication factors
Floor El Centro wave Taft wave Articial seismic waveamax (ms2) K amax (ms2) K amax (ms2) K
Top oor 2212 2402 2962 2692 3973 2693Roof 3022 3281 3358 3052 4066 2756
8 Shock and Vibration
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Furthermore the second- and the third-order frequenciesof the test model decreased slightly after Moderate 6reflecting slight decrease of the structurersquos stiffness Nextafter Rare 6 the natural fundamental frequency decreasedby 39 indicating that damages may occur at a certainlateral-force resisting component of the model structureFinally after Rare 7 the natural frequencies of the testmodel decreased significantly It can be inferred that the 1stmode of the prototype structure is the Y direction the 2ndmode is the X direction and the 3rd mode is torsion (eratio of the 1st mode periods between torsion to the Y and Xdirection is 033 and 049 respectively which is far smallerthan the limit value 085 given by the Chinese code (JGJ3-2010) [12] Furthermore after analyzing the structurestiffness degradation curves in accordance with the 1storder natural frequencies of the model it can be obtainedthat the stiffness of the structure declines with the in-creasing magnitude of earthquake excitation with aminimum stiffness to 819
43 Acceleration Response Acceleration amplification fac-tor is the ratio of the maximum absolute value of accel-eration response of each story to the maximum inputacceleration at the bottom of the model (is factor is ofgreat significance to analyze the seismic performance of
structures describing how many times the accelerations ateach story are amplified compared to the base seismicexcitation Hence the acceleration amplification factor canbe obtained through dividing the peak accelerations of thetesting stories by the peak accelerations of the shaking tablein this test (en the envelope diagram of the building indifferent test conditions can be drawn Figure 6 shows theenvelope of acceleration amplification factors in the mainvibration direction (Y direction) with different seismicintensities and the peak acceleration of some floors in aspecific condition and acceleration amplification factor arelisted in Table 8
As can be seen the acceleration amplification factorsalong the floors of the structure are nearly invariable exceptfor the top floor reflecting the lateral stiffness at differentfloors (except for the top floor) is uniformly distributedFurthermore the acceleration amplification factor was al-most unchanged after suffering from Frequent and Mod-erate 6 which indicated that the lateral-force resistingcomponents of the model are seldom damaged Howeverthe acceleration amplification factor increases sharply on thetop floor and roofing layer indicating that the whiplasheffect cannot be ignored in this case Usually when damagesare increasing the stiffness of structures is reducing leadingto the elastic-plastic phrase which can result in a smalleracceleration amplification It can be seen in Figure 6 that the
(a) (b) (c)
Figure 5 Damages of the test model after seismic input (a) floors 1 to 3 (b) 42nd floor (c) 52nd floor
Table 7 Dynamic characteristic of the model before and after the earthquake excitation
Earthquake intensity Test itemsY Torsion X
1st order 2nd order 3rd order 1st order 2nd order 3rd order
Before earthquakeFrequency (Hz) 254 1211 2941 762 2130 371
Period (s) 03937 00826 00340 01312 00469 02695Damping ratio () 325 261 212 236
Frequent 6Frequency (Hz) 254 1211 2921 762 2110
Period (s) 03937 00826 00342 01312 00474Damping ratio () 441 271 283
Moderate 6Frequency (Hz) 254 1192 2872 752 2091
Period (s) 03937 00839 00348 01330 00478Damping ratio () 420 304 337
Rare 6Frequency (Hz) 244 1133 2775 730 1993
Period (s) 04098 00883 00360 01370 00502Damping ratio () 401 311 335
Rare 7Frequency (Hz) 234 1075 684 1866
Period (s) 04274 00930 01462 00536Damping ratio () 387 380
Shock and Vibration 7
Frequent 6Moderate 6
Rare 6Rare 7
1 2 3 4 5 6 70K
10
20
30
40
50
60
Stor
y
(a)
Frequent 6Moderate 6
Rare 6Rare 7
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(b)
Frequent 6Moderate 6
Rare 6
10
20
30
40
50
60
Stor
y
1 2 3 4 5 6 70K
(c)
Figure 6 Envelope of acceleration amplication factor under dierent earthquake levels (a) El Centro seismic excitation (b) Taft seismicexcitation (c) articial seismic wave (USER1)
Table 8 Peak acceleration and acceleration amplication factors
Floor El Centro wave Taft wave Articial seismic waveamax (ms2) K amax (ms2) K amax (ms2) K
Top oor 2212 2402 2962 2692 3973 2693Roof 3022 3281 3358 3052 4066 2756
8 Shock and Vibration
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Top oor 2212 2402 2962 2692 3973 2693Roof 3022 3281 3358 3052 4066 2756
8 Shock and Vibration
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
acceleration amplification factor of the same floor continuedto decrease with an increasing excitation intensity reflectinga decreasing structural lateral stiffness and an increasingdegree of damage as the seismic intensity increases How-ever the decline of the acceleration amplification factor wasnot obvious after suffering from Rare 6 which indicated thatsome lateral-force resisting components of the model havealready be damaged (us the experimental phenomenoncoincided well with the theory
44 Displacement Response of Prototype Building (e dis-placement response of the model was converted to thedisplacement response of the prototype by a similar law(eformula to translate the maximum displacement responsefrom the test model to the prototype building should be asfollows
Di αmg times Dmi times Sd
αtg (2)
Di is the maximum displacement of the prototype on the ithfloor Dmi is the maximum displacement of the model at ithfloor αmg is the maximum acceleration of the shaking tabledetermined by the similitude law αig is the maximum ac-celeration of the shaking table measured during the test andSd is the displacement similarity coefficient
(e maximum displacement and corresponding dis-placement angle of the prototype structurersquos roof underdifferent seismic levels are listed in Table 9 It can be seenthat as the seismic wave intensity increases both themaximum displacement and displacement angle of the roofincrease Both the maximum displacement and displace-ment angle of the prototype structure can meet the re-quirements of the Chinese code (JGJ3-2010) [12] (eprototype building will not collapse and even have a rela-tively good integrity after severe earthquake action
Figure 7 shows the envelope diagrams of maximumdisplacement in the Y direction of the prototype structurealong the floors It can be seen that the displacements of theprototype structure increase as the stories increase Fur-thermore the effect of the El Centro wave was significantlylarger than that of the other two waves Owning to thewhiplash effect the displacement response of the top floorand roofing layer is much larger than that of other floors(elateral displacement curves under Frequent and Moderate 6were not flat which was small and had obvious bendingshear deformation characteristics So the structure had notbeen damaged yet (e lateral displacement curves underRare 6 and 7 were relatively flat and obvious which meansthat some components have already been damaged and thestiffness of the structure has declined
(e story drift of representative floors under differentseismic waves is listed in Table 10 It can be seen that all themaximum story drift of the structure occurred in the top ofthe structure especially on the 56th floor which means thatthe upper part of the structure is relatively weaker thanothers (e stiffness is reduced as the structure becomessmaller above 41st floors which leads to the increase of storydrift All story drifts of the structure under the testing
earthquakes are smaller than the value specified in theChinese code (JGJ3-2010) [12] which indicates that thestructure canmeet the seismic resistance requirements of thecode
45 Torsion Effect (ere are symmetrical accelerometersarranged at the 41st and the top floor (e displacementsunder different seismic intensities of these two stories can beobtained by integrating the accelerations Hence the torsioncan be obtained by the ratios of the displacements to thesensorsrsquo distances Torsion angle of the model under dif-ferent seismic levels is shown in Figure 8 It can be seen thatthe torsion deformation is small before the inputting of Rare6 reflecting a good torsional stiffness However the torsiondeformation became larger under Rare 7 which indicatesthat some part of the structure has been damaged
According to transformation formula the hysteresiscurve of the prototype structure under different earthquakelevels can be obtained by the displacement historical re-sponse and shear historical responses (e shear responsescan be calculated by quality distribution of floors andcorresponding acceleration responses Taking Rare 6 as anexample considering the limited pages of this paper thehysteresis curve under different waves is shown in Figure 9Actually the hysteresis curve of the structure under Fre-quent Moderate and Rare 6 change with the external ex-citation while the change of stiffness is however not obviouswhich indicates that the building is basically in the elasticworking stage However it can be seen that the hysteresiscurve becomes irregular under Rare 7 which indicates thatsome parts of the structure have already been damaged andthe structure has gone into the elastic-plastic phase
5 Finite Element Analysis
In order to verify the experimental results a finite elementmodel of the test model was established by ANSYS Elastic-plastic analysis of the test model was conducted (ree-dimensional BEAM4 element was used to simulate thebeams and embedded columns and SHELL63 was used tosimulate the floors and shear walls (e material propertieswere obtained from the measured tests and the nonlinearperformance of materials had been considered (e inputseismic waves used in the finite element model were thesame as the shaking table test Real properties of the ma-terials of the model had been taken into account (e finiteelement mode contained 78899 nodes beam elements 4599and shell elements 72414 totally (e height is 1794mwhich is the same as the prototype building
51 DynamicCharacteristic (e results of the finite elementanalysis indicate that first three order vibration modes of themodel include the translation mode in Y direction X di-rection and torsion mode (e first three order vibrationmodes are shown in Figure 10 All the three vibration modesreflect the coupling between translation and torsion
Table 11 shows the free vibration characteristics ofthe model in experimental results and finite element
Shock and Vibration 9
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
simulation results It can be seen that the nite elementsimulation result of the rst periods and second periods issimilar to those of experiment results and divergencesbetween the two are 007 and 241 respectively
However the divergences of the third periods becamemuch more signicant which is still within an acceptablelevel e ratio of the rst mode periods between torsionand translation in the Y direction is 038 in the nite
Table 9 Maximum displacement and displacement angle of the roof of the prototype building
Seismic intensity Test condition Seismic wave Displacement of vertex (m) Displacement angle of vertex
Frequent 6Condition 2 El Centro wave-Y direction 0016 14654Condition 3 Taft wave-Y direction 0010 17670Condition 4 Articial seismic wave-Y direction 0008 19848
Moderate 6Condition 6 El Centro wave-Y direction 0043 11573Condition 7 Taft wave-Y direction 0026 12642Condition 8 Articial seismic wave-Y direction 0023 12932
Rare 6Condition 10 El Centro wave-Y direction 0060 1953Condition 11 Taft wave-Y direction 0048 11196Condition 12 Articial seismic wave-Y direction 0052 11110
Rare 7 Condition 14 El Centro wave-Y direction 0139 1456Condition 15 Taft wave-Y direction 0144 1439
10 Shock and Vibration
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
element simulation while the test result is 033 Both thetwo results are far less than the limited value of the Chinesecode (JGJ3-2010) [12] Moreover the inuence of highervibration modes to the structure can be quite large becauseof the high aspect ratio for high-rise buildings It is usuallydisectcult to capture the higher vibration modes of thebuilding by an experiment and the computational analysisthus shows its advantage and is an important supplemente rst 30 vibration modes and periods were analyzed
through the nite element method It can be concludedthat the vibration modes became localized after the 15thorder and the vibration of the top model is much moreobvious than others which indicates that the whiplasheect is quite remarkable Based on mass participationratio and vibration maps it can be concluded that thevibration mode of the structure is coupled translation andtorsion and the torsion has great inuence on the seismicresponse of the structure
Table 10 Story drift of the structure under dierent seismic waves
Seismic intensity Seismic wave 20th oor 41st oor 56th oor (top)
Frequent 6El Centro 0045 0069 0159
Taft 0039 006 0096Articial 0039 0054 0075
Moderate 6El Centro 0141 0189 0432
Taft 0099 0165 0258Articial 0099 0177 0234
Rare 6El Centro 0255 0324 0603
Taft 0219 0351 048Articial 0276 0384 0519
El CentroTaftArtificial
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
Tors
ion
angl
e
Frequent 6 Rare 6Moderate 6 Severe 7Test condition
(a)
El CentroTaftArtificial
00000
00005
00010
00015
00020
00025
Tors
ion
angl
e
Moderate 6Frequent 6 Rare 7Rare 6Test condition
(b)
Figure 8 Torsion angle under dierent oors (a) 41st oor (b) 51st oor
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(a)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(b)
Rare 6
ndash3000
ndash2000
ndash1000
0
1000
2000
3000
Shea
r for
ce (k
N)
ndash005 000 005 010ndash010Displacement (m)
(c)
Figure 9 Hysteresis curve of the prototype structure under dierent waves (a) El Centro wave (b) Taft wave (c) articial seismic wave
Shock and Vibration 11
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
52 Acceleration Response Table 12 shows the maximumacceleration amplication factor in the main vibration di-rection (Y direction) under dierent seismic levels and boththe measured and calculated values are listed
It can be seen in Table 12 that both the accelerationamplication factor of the nite element model and ex-perimental model continued to decrease after suering fromFrequent 6 Moderate 6 and Rare 6 reecting that the lateralstiness of the structure has decreased and the damage of thestructure increased e acceleration response of nite el-ement simulation is similar to the shaking table test
53 Displacement Response In order to compare the ex-perimental results with the calculated results the maxi-mum displacement of the test oors under dierentearthquake levels is listed in Table 13 e envelope ofinterstory drift under dierent earthquake waves is shownin Figure 11
It can be calculated that both the story drift angle of thenite element model and test model under Frequent andModerate 6 can meet the seismic resistance requirementsin the code specication (1800) e maximum story driftangle of the nite element model under Rare 6 is 1350which is larger than the limited elastic value however itstill can meet the requirements of plastic story drift anglein the Chinese code (JGJ3-2010) [12] As can be seen inFigure 11 all the peak story drift occurs in the upper partof the structure especially near the 50th oor which isrelatively weaker than the other parts of the structureFurthermore story drift has increased above 41st oorsreecting a decline of the stiness which coincides wellwith the experimental analysis Hence we can reach the
conclusion that all the results of nite element simulationcoincides well with the results of the experiment whichindicates that both the nite element simulation and theshaking table model test are reasonable
6 Damage Identification
In this section an identication method based on the ARmodel is presented to identify the damage location anddegree of the test model after suering from simulatedearthquakes Firstly the AR model is briey introducedand established by the acceleration response of the testmodel Secondly the plain version of the least squares (LS)method is used to solve the unknown parameters of theestablished AR model en a judging factor based on theresidual variance of the AR model is proposed to estimatethe degree of structural damage Finally the proposeddamage factor of the model building after dierentearthquake intensities is calculated by MATLAB edamage location and degree identied by this method arecompared with the testing results as well as the numericalresults
61 AR Model and Parameter Identication e AR modelis widely used in the eld of structural damage identi-cation [18] and it is attempt to account for the correlationsof the current time parameter with its predecessors in timeseries in which the output variable depends linearly on itsown previous values and on a stochastic term It can beimplemented to represent the dynamic response ofstructures [19] e AR model does not need any specicstructural characteristics but the output response data
(a) (b)
HEAR-WALL
(c)
Figure 10 First three vibration modes (a) 1st (Y direction) (b) 2nd (X direction) (c) 3rd (torsion)
Table 11 Comparison of free vibration characteristics
Vibration mode Experimental result Finite element resultFrequency (Hz) Period (s) Frequency (Hz) Period (s)
Y Direction 1st order 254 03937 25348 03942nd order 1211 00826 97863 0102
X direction 1st order 371 02695 38012 02632nd order mdash mdash 12833 0077
Torsion 1st order 762 01312 66293 01512nd order 2130 00469 27641 0036
12 Shock and Vibration
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
hence it is widespread for complex structures [20 21] Inthis research the AR time-series model is used to describethe acceleration time histories of the shaking table A noisyAR model of order m is described by equation [22]
where xt is the output of the ARmodel it is the discrete-timesignal and in this paper the acceleration responses are usedext is the random noise m is the unknown order of this
model at prior and varies from 0 to tminus 1 β denotes the ARcoesectcients which need to be estimated is model can besimplied as follows [23]
y Aβ + ] (4)
where y [xt xtminus1 middot middot middot xtminusm+1]T β [β1 β2 middot middot middot βm]T and
] [ext ex(tminus1) middot middot middot ex(tminusm+1)]TIn this paper a famous approach the least square (LS)
method is used to estimate unknown vector β It is solved by
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
the Lagrange ExtremumMethod and the estimation result isshown as follows [24]
1113954β ATWA1113872 1113873minus1
ATWy (5)
Estimated residual is as follows
v A1113954βminusy (6)
However finding out the optimal order m of the ARmodel is not trivial(e order is not as larger as better Whenthe order of the AR model increases the residual sum ofsquares theoretically decreases while the calculating errorsrise (erefore these two aspects should be both consideredin the modeling In literature there are some criterionsachieved this goal [25] such as Akaikersquos Information Cri-terion (AIC) or Bayesian information criterion (BIC)proposed by Akaike and Schwarz respectively (e AICwill be used in this paper and it is presented as follows
AIC(n) ln 1113954σ2a(n) +2n
N (7)
where 1113954σ2a is the estimated variance of residual errors whenthe order of the AR model is n
62 Damage Factor After the unknown parameter β of theARmodel is obtained a factor needs to be proposed to judgethe damage of the structure (e step of the method can beclarified as follows
(1) Dividing the obtained response acceleration databefore damage into two parts part A0 and part B0A0serves as benchmark data from which β0 of theundamaged situation will be estimated While B0serves as the unknown inspection data to be esti-mated in the healthy state of structure
(2) Estimating β0 by equation (5) and the residential v0of B0 based on β0 by equation (6)
(3) Dividing all the observed data into part Ai and BiEstimating the residential vAi
of Ai and vBiof Bi based
on the obtained β0(4) Calculating the average of vAi
and vBito obtain vi vi
represents the final residential of ith observed data tobe estimated after damage
(5) (e damage identification factor is calculated as theratio between the residential variance of vi to v0shown as
IF σ2 ]i( 1113857
σ2 ]0( 1113857 (8)
It is clear that if the data to be estimated is coming fromthe undamaged structure IF will be close to one Otherwiseσ2(]i) will be larger than σ2(]0) that is the IF will increaseas the damages of the structure rise
63 Identification Results In this part the IF of differentstories and seismic intensities will be presented It can be
seen in Table 6 that before and after all the testing waves thewhite noise is used to test the model hence the identifi-cation of white noise will be conducted here Figure 12 liststhe IF after different earthquake intensities of some repre-senting floors based on the white noise excitation It can beconcluded that the IF becomes larger as the intensity ofearthquake increases indicating that the damage of the testbuilding rises while intensity increases Furthermore the IFof the top story is larger than that of other stories reflectingthe whiplash effect too
When comparing the damages of all stories after thesame seismic intensity the damage variation along storiescan be studied For the sake of simplicity Figure 13 showsthe IF along some stories taking the white noise responseafter suffering from Frequent 6 and Rare 7 as examples here
It can be concluded that after Frequent 6 all the IFranges from 10 to 125 indicating very little damages oc-curred in the model building Even though the IF of the 1st
floor and top floor is the smallest and largest respectivelythere is only a little difference However after suffering fromRare 7 the damage increases obviously the damage degreeof 50th 52nd and top floors is larger than that of other floorsand the damage of 14th 28th and 8th stories is quite sig-nificant as well while the damage of the first story is thesmallest (is variation can also be found in Table 8 of thepeak acceleration and acceleration amplification factors (eIF of 41st floor is not quite large but increased rapidly above41st floor indicating that the 41st floor is not in a seriousdamage condition as the floors above (is is not limited tothe earthquake intensities in Figure 13 and the same con-clusion can be drawn after analyzing all the white noiseresponse data of the model building
Moreover after studying the IF of the three types ofwaves used in the test the variation of IF is nearly the samewith that of white noise and the results will not be detailedhere However the comparison of the effectiveness betweendifferent types of waves cannot be obtained probably due tono relative data to be used to calculate the healthy residentialof benchmark data (]i)
To summarize we can reach the conclusion that theidentification results are reasonable and coincide well withthe results of the experiment and numerical simulationwhich indicates that the identification method presentedhere is effective and not only the location but also the degreeof the damage can be identified by the new identificationfactor
7 Conclusion
(e prototype building is represented as the testing modelin this paper Based on all the analysis it can be concludedthat after Frequent 6 almost no changes occur in thestructure which is still in the elastic stage After Moderate6 no visible damages occur and natural frequency de-creased slightly which indicates that the stiffness of theprototype building was changed slightly in this conditionHowever under Rare 6 the 1st natural frequency decreasedby 39 and other parameters had little of changes whichsuggests that some part of the prototype building will be
14 Shock and Vibration
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
damaged in this condition Under Rare 7 visible cracksand spalling of concrete occur and the natural frequencyof the model decreased signicantly which means that theprototype building has been damaged signicantly in thiscondition
Acceleration response of the top part of the structure isrelatively large which indicates that the whiplash eect ofthe building is signicant e torsional deformation isnot apparent when an earthquake is small but it becamemore substantial when the level of input earthquake
Figure 12 IF of some oors after dierent earthquake intensities (a) 1st oor (b) 8th oor (c) 41st oor (d) top oor
IF
08
09
10
11
12
13
IF
8 14 28 41 50 52 Top1Story
(a)
IF
8 14 28 41 50 52 Top1Story
02468
10121416
IF
(b)
Figure 13 IF along stories (a) Frequent 6 (b) Rare 7
Shock and Vibration 15
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
increased which indicates that the effect of torsion onseismic response of the structure is increased Further-more the effect of torsion is large above the 41st floorsespecially on the 52nd floor showing that these floors maybe weaker than other parts relatively However as for thesame level of earthquake intensity the maximum dis-placement displacement angle story drift and torsionalangle of the model caused by the El Centro wave are thelargest among the three types of input waves followed bythe Taft wave and artificial seismic wave (us the ElCentro wave may be the most dangerous wave to theprototype building
Finite element simulation results coincide well with theexperimental results Higher vibration modes of the buildingshow that vibration modes have become localized after 15thorder and the vibration mode of the structure is translation-torsion coupled the whiplash effect at the top of thestructure is quite remarkable
(e damage degree and location identified by the pro-posed factor in this paper also show that the upper part of thebuilding has more damage than the lower part but thedamage of 8thsim28th floor is also quite significant With theincrease of the earthquake acceleration the damage of thebuilding increases apparently (e identification resultsindicate that the identification method is effective and can beused in other similar cases
(e results of the test the numerical analysis and theidentification prove that the building in the A2 blockdeveloped by Wuhan Shimao Group was designed rea-sonably which can entirely meet the requirement in theChinese Code and can be safely put into use Even thoughthe design of this building can meet the seismic designrequirements some measures should be taken to improvethe seismic performances Firstly the connection betweenthe shear wall of the bottom floor and the base can bestrengthened to avoid horizontal joined-up cracks underbig earthquakes (en the effect of torsion is large abovethe 41st floor of the building but the damage of the 8thsim28thfloor cannot be neglected either More structural re-inforcements may be necessary for these floors (e top ofthe structure also needs to be strengthened since thewhiplash effect is obvious
Data Availability
(e data of this study are available from the correspondingauthor upon request
Conflicts of Interest
(e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
(is work was supported by the National Natural ScienceFoundation of China (NSFC) (grant no 51678464) andthe China Government Scholarship Council (CSC no201706950038)
References
[1] H Aoyama Design of Modern High-Rise Reinforced ConcreteStructures Imperial College Press London UK 2001
[2] X Zhou and G Li ldquoShaking table model test of a steel-concrete composite high-rise buildingrdquo Journal of EarthquakeEngineering vol 14 no 4 pp 601ndash625 2010
[3] P Martinelli and F C Filippou ldquoSimulation of the shakingtable test of a seven-story shear wall buildingrdquo EarthquakeEngineering amp Structural Dynamics vol 38 no 5 pp 587ndash607 2009
[4] M Saranik D Lenoir and L Jezequel ldquoShaking table test andnumerical damage behaviour analysis of a steel portal framewith bolted connectionsrdquo Computers amp Structures vol 112-113 no 4 pp 327ndash341 2012
[5] G Chen Z Wang X Zuo X Du and H Gao ldquoShaking tabletest on the seismic failure characteristics of a subway stationstructure on liquefiable groundrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 10 pp 1489ndash1507 2013
[6] Y-l Lin W-m Leng G-l Yang L Li and J-S YangldquoSeismic response of embankment slopes with differentreinforcing measures in shaking table testsrdquoNatural Hazardsvol 76 no 2 pp 791ndash810 2015
[7] N Srilatha G Madhavi Latha and C G Puttappa ldquoEffect offrequency on seismic response of reinforced soil slopes inshaking table testsrdquo Geotextiles and Geomembranes vol 36no 1 pp 27ndash32 2013
[8] W G Liu C Qin Y Liu et al ldquoShaking table tests onearthquake response characterization of a complex museumisolated structure in high intensity areardquo Shock and Vibrationvol 2016 Article ID 7974090 23 pages 2016
[9] X Lu Y Zou W Lu and B Zhao ldquoShaking table model teston Shanghai world financial center towerrdquo Earthquake En-gineering amp Structural Dynamics vol 36 no 4 pp 439ndash4572007
[10] D G Lignos Y Chung T Nagae and M NakashimaldquoNumerical and experimental evaluation of seismic capacityof high-rise steel buildings subjected to long durationearthquakesrdquo Computers amp Structures vol 89 no 11-12pp 959ndash967 2011
[11] F Graziotti U Tomassetti S Kallioras A Penna andG Magenes ldquoShaking table test on a full scale URM cavitywall buildingrdquo Bulletin of Earthquake Engineering vol 15no 12 pp 5329ndash5364 2017
[12] National Standard Technical Specification for ConcreteStructures of High-rise Building (JGJ3-2010) Beijing China2010
[13] National Standard Tall building Earthquake-Proof Engi-neering Special Review of Technical Points (No 65) BeijingChina 2015
[14] G Rastogi K Moin and S M Abbas ldquoDimensional analysisand development of similitude rules for dynamic structuralmodelsrdquo International Journal of Emerging Technology andAdvanced Engineering vol 5 no 3 pp 68ndash72 2015
[15] National Standard Standard for Test Methods of ConcreteStructures (GB50152-2012) Beijing China 2012
[16] National Standard Seismic Ground Motion Parameters Zo-nation of China Beijing China 2016
[17] National Standard Code of Seismic Design of Buildings(GB50011-2010) Beijing China 2010
[18] G Mustafa Investigation of Damage detection Methodologiesfor Structural Health Monitoring Bogaziccedili UniversityIstanbul Turkey 2009
16 Shock and Vibration
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
[19] M Krishnan B Bhowmik B Hazra and V Pakrashi ldquoRealtime damage detection using recursive principal componentsand time varying auto-regressive modelingrdquo MechanicalSystems and Signal Processing vol 101 pp 549ndash574 2018
[20] R Yao and S N Pakzad ldquoAutoregressive statistical patternrecognition algorithms for damage detection in civil struc-turesrdquo Mechanical Systems and Signal Processing vol 31pp 355ndash368 2012
[21] A Datteo G Busca G Quattromani and A Cigada ldquoOn theuse of AR models for SHM a global sensitivity and un-certainty analysis frameworkrdquo Reliability Engineering ampSystem Safety vol 170 pp 99ndash115 2018
[22] J Hamilton Time Series Analysis Princeton University PressPrinceton NJ USA 1994
[23] P Xu J Liu and C Shi ldquoTotal least squares adjustment inpartial errors-in-variables models algorithm and statisticalanalysisrdquo Journal of Geodesy vol 86 no 8 pp 661ndash675 2012
[24] W E Deming ldquoXI(e application of least squaresrdquo GeLondon Edinburgh and Dublin Philosophical Magazine andJournal of Science vol 11 no 68 pp 146ndash158 1931
[25] W Chen Autoregressive Model Estimation Geory and itsApplication in Deformation Monitoring Data ProcessingWuhan University Wuhan Hubei China 2013
![3C 0.2 0.4 0.6 0.8 1 1.2 1.4 0 5 10 15 20 25 30 35 40 45 Balancing mass [lbm] Maximum shaking force [lbf] Notes_08_04 6 of 20 % shake.m - single cylinder shaking force Notes_08_04](https://static.documents.pub/doc/80x56/5cdb68f688c993a6778cad82/3c-02-04-06-08-1-12-14-0-5-10-15-20-25-30-35-40-45-balancing-mass-lbm-maximum.jpg)
