Research ArticleNumerical Study on Crack Distributions of the Single-LayerBuilding under Seismic Waves
Fenghui Dong 1 Zhipeng Zhong 2 and Jin Cheng3
1Department of Bridge Engineering Tongji University Shanghai 200092 China2Department of Civil Engineering Shanxi University Taiyuan Shanxi 030013 China3State Key Laboratory for Disaster Reduction in Civil Engineering Tongji University Shanghai 200092 China
Correspondence should be addressed to Zhipeng Zhong zpz 2006sxueducn
Received 20 March 2018 Revised 17 April 2018 Accepted 22 April 2018 Published 15 May 2018
Academic Editor Changzhi Wu
Copyright copy 2018 Fenghui Dong et al This 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
This paper conducts a numerical simulation of the antiseismic performance for single-layer masonry structures completes a studyon crack distributions and detailed characteristics of masonry structures and finally verifies the correctness of the numericalmodel by experimental testsThis paper also provides a reinforced proposal to improve the antiseismic performance of single-layermasonry structures Results prove that the original model suffers more serious damage than the reinforced model in particularlongitudinal cracks appear on bottoms of two longitudinal walls in the original model while these cracks appear later in thereinforcedmodel a lot of cracks appear on the door hole of the original model and no crack appears in the reinforcedmodel till theend of seismic waves seismic damage of walls in the reinforced model is obviously lighter than that in the original model dynamicresponses at all observed points of the reinforcedmasonry are obviously less than those of the original model Strains at all positionsof the reinforcedmodel are obviously smaller than those of the originalmodel Frommacroscopic andmicroscopic perspectives thecomputational results prove that the reinforced proposal proposed in this paper can effectively improve the antiseismic performanceof the masonry structure
1 Introduction
As a traditional structure formmasonry structures arewidelyapplied inmiddle and small citiesMaterials used bymasonrystructures such as clay sand and stones are local materialsTherefore important materials including steel cement andtimber can be saved and engineering cost can be reducedMasonry materials are featured by high durability and highfire resistance and do not require special technical equipmentin construction [1ndash5] Because of these advantages masonrystructures have been applied widely since ancient timesAt present the proportion of masonry structures in wallstructures is more than 90 [6] Masonry structures are themost utilized structure form in construction engineeringHowever the traditional structure form is deficient in poorantiseismic performance high weight bad tension and poorductility When an earthquake takes place the structure isoften damaged due to the serious displacement outside the
complete wall plane [7ndash10] Earthquakes have caused somany tragedies involving house damage wall cracks andresultant living risks as well as large destructions such asdirect collapse economic losses and casualties
Therefore a lot of researches have been conducted onthe antiseismic performance of masonry buildings at presentZheng et al [11] analyzed the mechanical performanceof multilayer masonry structures under horizontal seismicwaves while the mechanical performance included forcebearing characteristics deformations and damage forms aswell as dynamic characteristics and antiseismic capacitiesof the structure under different force stages Jia et al [12]discussed common seismic safety problems ofmasonrywallsanalyzed seismic damage of walls for masonry buildings indifferent intensity regions obtained damage forms of housesin the intensity regions and also proposed some suggestionson reducing seismic damage of masonry buildings Liu andTong [13] studied houses with a frame masonry structure
HindawiComplexityVolume 2018 Article ID 2167326 16 pageshttpsdoiorg10115520182167326
2 Complexity
established a finite element model applied seismic wavesto the structure in order to conduct the elastoplasticityanalysis and analyzed changing trends of structural cracksbefore and after adding antiseismic walls In order to studyimpacts of front longitudinal columns in walls on antiseismicperformance of a multilayer masonry building Liang et al[14] conducted an experimental test on a masonry buildingusing the vibration table and analyzed damage processesof this model as well as parameters including accelerationamplification coefficients and typical position strains Inorder to study and prevent seismic damage of masonrystructures Liu et al [15] used LS-DYNA to simulate collapseprocesses of a masonry structure verified the correctnessof the numerical model by experiments and found weakpositions in this structure under strong seismic waves whichproposed a powerful support to improve the antiseismicperformance of masonry buildings The macroelement tech-nique for modeling the nonlinear response of masonrypanels is particularly efficient and suitable for the analysisof the seismic behavior of complex walls and buildingsTherefore Penna et al [16] have established a macroelementmodel specifically developed for simulating the responseof masonry walls with possible applications in nonlinearstatic and dynamic analysis of masonry structures underseismic waves Betti et al [17] have conducted a comparisonbetween different methods and numerical models to estimatethe seismic behavior of unreinforced masonry buildingsand the model is able to predict the damaged areas andthe incipient collapse mechanism as well as the collapseload
In these reports detailed experimental tests and numer-ical simulation are mainly conducted on the antiseismicperformance of multilayer masonry structures and someachievements are obtained However single-layer masonrystructures in rural regions are rarely reported Single-layermasonry structures are the main buildings in some regionsResidents do not have strong consciousness for antiseismicperformance and prevention of these buildings Therefore itis very necessary to study and design the antiseismic perfor-mance Dong et al [18] conducted the numerical simulationof the antiseismic performance for single-layer masonrystructures and proposed some reinforcedmeasures but failedto report the distribution expanding processes and detailedcharacteristics of building cracks Lou et al [19] completedthe numerical simulation on the collapse of single-layermasonry structures and also conducted comparative verifica-tion between computational results and experimental resultsbut failed to propose any reinforced measure for improv-ing the antiseismic performance of single-layer masonrystructures Aimed at this current status this paper conductsthe numerical simulation of the antiseismic performancefor single-layer masonry structures completes a systematicstudy on crack distribution and detailed characteristics ofmasonry structures and finally verifies the correctness ofthe numerical model by experiments This paper providesa technology support for the antiseismic performance ofsingle-layer masonry structures
2 The Theoretical Basis of theNumerical Computation
21 Modal SolutionTheories Modal analysis is used to deter-mine the natural vibration characteristics of the structurewhich is the natural frequency and mode shape of the struc-ture It is an important parameter to study the elastoplasticanalysis of vertical earthquakes and also the basic premise ofcomputing structural dynamics Under the external load thedynamic equation of the structural system at any moment isas follows
119865119905 + 119865
119863 + 119865
119878 = 119865 (1)
Among them 119865119905 119865119863 119865119878 are the inertial force vector
damping force vector and elastic force vector of the structurerespectively and 119865 is the external load vector acting onthe structure Inertial force vector damping force vectorand elastic force vector can be represented by 119911(119905) and itsreciprocal as follows
Among them [119872] [119862] [119870] are the mass matrix dampingmatrix and stiffness matrix of the structure respectively119911(119905) (119905) (119905) are the displacement velocity and accelerationvectors of the structure respectively The dynamic equationof the structural system at any time becomes as follows ifformula (2) is substituted into formula (1)
[119872] (119905) + [119862] (119905) + [119870] 119911 (119905) = 119865 (3)When the structural system is in the free vibration state thevibration direction of the structural system becomes
[119872] (119905) + [119870] 119911 (119905) = 0 (4)When the structural system is in the free vibration stateassuming that the displacement of the structure in freevibration is 119911(119905) = 119860 sin120596119905 the homogeneous equationscan be obtained as follows when substituting the former intoformula (4)
([119870] minus 1205962 [119872]) 119860 = 0 (5)
Among them 119860 is not all 0 so the value of the determinantof the coefficient matrix must be all 0 that is10038161003816100381610038161003816[119870] minus 1205962 [119872]10038161003816100381610038161003816 = 0 (6)
According to formula (6) the mass matrix and stiffnessmatrix of the structural system at any time can be solved andthen the natural frequency and mode shape of the structurecan be extracted
22 The Constitutive Relation of the Solved Masonry Theconstitutive relation of the solved masonry is one of the mostimportant mechanical properties of the masonry structureand also the basic parameter that the model must inputwhen solving masonry structure At present the constitutiverelations of the solved masonry have mainly the followingthree kinds
Complexity 3
(a) Geometric model (b) Finite element model
Figure 1 Geometric model and finite element model of the masonry structure
221 Single-Segment Constitutive Relations The constitutiverelation of masonry under a short-term load is usually deter-mined by the axial compression test When the stress of themasonry structure reaches a maximum value the masonrystructurewill suddenly collapse under normal circumstancesAccording to a great deal of experience the constitutiverelation of masonry structure material is put forward asfollows [20]
222 Two-Segment Constitutive Relations Based on theexperimental results Zhu and Dong give a constitutiverelationship for the expression of a two-stage full-curve withascending and descending segments [21]
120590119891119898
120576120576002 + 08120576120576
0
120576 le 120576012 minus 02120576120576
0120576 gt 1205760
(8)
Formula (8) is relatively simple although it can reflect themechanical performance of masonry structures in the stressdrop stage the formula is not derivable at 120576 = 1205760 indicatingthat the stress-strain curve is discontinuous Zhuang con-ducted an experimental study of the masonry model and alsogave the ascending anddescending constitutive relations [22]
120590119891119898 =
152 (1205761205760) minus 0279 (120576120576
0)2
1 minus 0483 (1205761205760) + 0724 (120576120576
0)2 120576 le 1205760
34 (1205761205760) minus 113 (120576120576
0)2
1 + 14 (1205761205760) minus 013 (120576120576
0)2 120576 gt 120576
0
(9)
223 Polynomial Constitutive Relations The stress-strainrelation curve proposed by Turnserk and Cacovic is notonly consistent with experimental results but also smoothand continuous Therefore this paper selects the constitutiverelation of the polynomial and its constitutive expression isas follows [23]
120590120590max= 64 ( 120576120576
0
) minus 54 ( 1205761205760
)117
(10)
Among them 120590max is the peak stress and 1205760 is the straincorresponding to the peak stress
3 The Numerical Computation for Dynamicsof Masonry Structures under Seismic Waves
31 The Numerical Computation Model In this paper asingle-layer masonry building with a relatively simple struc-ture is selected Related dimensions of this model areobtained through the real investigation as shown in Fig-ure 1(a) It is shown in this figure that doors and windowsare set on the front longitudinal wall and no hole is seton other three walls Actual dimensions of the window holeare as follows height is 1700mm and width is 2150mmActual dimensions of the door hole are as follows height is2800mm and width is 1320mm No structural antiseismicmeasures including column and beam are applied to thismodel In order to simplify the computation all the surfacesof this model are smooth and even planes Dimensions ofthe experimental model cannot be too large in order toconduct the experimental verification on the correctness ofthe numericalmodel a numericalmodel with scaled ratio 1 2is used for the modeling The finite element model is shownin Figure 1(b) The degree of freedom in the bottom of themasonry structurewas constrained in 6 directions to simulatethe actual condition In order to realize the constraint thedegree of freedom of the element in the bottom of the finiteelement model was constrained In respect of the large sizeof masonry models in this paper if the finite element modelof a masonry structure is established based on a discretemodel it will be limited by the computational software andcomputer performance Besides this paper is focused onthe numerical simulation on a macroscopic damage type ofa masonry structure so that an integral model with easilyestablishing the finite element model is adopted In thismodel the integral modeling is conducted on masonry andconcrete and components are connected by co-nodes [24ndash28] In addition with regard to roofs of rear houses a claylayer will be paved on the roof board In view of features ofthe clay layer its rigidity contribution is not considered in thefinite element model its mass is uniformly distributed on theroof board and reinforced steel bars are simulated using rodelements with dual-directional forces Solid65 elements areused for the masonry structure In view of tension failure andbreakdown failure element size of walls and roofs is 015mAll the materials are deemed as isotropic Parameters of themasonry are as follows compressive strength is 15 times 106 Pa
4 Complexity
10Action time (s)20 30 40 50
1210
86420
0
minus2minus4minus6minus8
minus10
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ic
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(b) Seismic waves in Y direction
Figure 2 Seismic waves in time-domain in X and Y directions
Seism
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15100 5Frequency (Hz)
20 25
(a) Seismic waves in X direction
Seism
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de
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(b) Seismic waves in Y direction
Figure 3 Seismic waves in frequency-domain in X and Y directions
tension strength is 014 times 106 Pa elasticity modulus is 24 times109 Pa Poissonrsquos ratio is 015 and density is 1900 kgm3
Thepaper ismainly focused on the performance of single-layer masonry structures under seismic waves so seismicwaves should be input into the finite element model Localseismic waves of the single-layer masonry structure lackmonitoring and recording so EL-Centro seismic waves areused for the numerical simulation The seismic waves arecomplete seismic wavers which are recorded internationallyfor the first time and also the seismic waves are widely usedto study the seismic waves [29ndash34] Typical EL-Centro waveswith peak acceleration 03 g are selected as loads and appliedto the X direction and Y direction in this model respectivelyIn general seismic energies in the Z direction are very smalland can be neglected Acceleration time history of seismicwaves is shown in Figure 2 It is shown in this figure thatseismic waves in X and Y directions are not completely thesame Vibrations of the seismic waves are relatively weak after30 s Data in frequency-domain can be obtained after Fouriertransform for data in time-domain of EL-Centro seismicwaves as shown in Figure 3Obviously EL-Centro energies inthe two directions are mainly concentrated within 0sim10Hz
During analyzing the antiseismic performance of single-layermasonry structures two steps should be set for the finiteelement model The first step is structural responses underself-weight loads Static problems are solved by dynamicalgorithms so monotone increasing and steady loading areadopted and self-weight loads are input in forms of datasheets in order to avoid impacts caused by sudden addition ofstatic forces on the structure After the first step is completedthe structure stays at a stable status under vertical static
loads and effects of the structure under static loads areintroduced to the second step The second step is the inputand computation of seismic motion In this paper horizontalseismic motion in X direction and Y direction is inputSeismic motion is also input in the form of data sheets
32 Natural Modals of Masonry Structures In the modalanalysis only density elasticity modulus and constraintconditions play an important role while other loads have noimpact on the modal results According to the finite elementmodel and boundary conditions constraint modals of thesingle-layer masonry structure are computed as shown inFigure 4 It is shown in this figure that vibrations of masonrystructures mainly perform bending vibrations of each walland no torsional vibrations are presented The vibrationshape of the masonry structure was not symmetrical becausethe front wall is not symmetrical Vibration shapes at the1st 3rd 4th and 6th orders mainly performed bendingvibrations of doors and windows because holes are set thereand structural rigidity is weak Vibration shapes of top platesat the 2nd and 5th orders are similar while bending vibrationdirections of longitudinal walls on two sides are oppositeNatural frequencies of the single-layer masonry structureare extracted namely 35Hz 41 Hz 49Hz 57Hz 65Hzand 72Hz which satisfied the distribution of modal densityfor large facilities This result also indirectly verifies theeffectiveness of the finite element model in this paper
33 Dynamic Responses of Masonry Structures Based onthe established finite element model its dynamic responsesunder seismic waves can be obtained In order to monitor
Complexity 5
(a) First order (b) Second order
(c) Third order (d) Fourth order
(e) Fifth order (f) Sixth order
Figure 4 The top six vibration shapes of the masonry structure
Observed point 4 Observed point 2Observed point 3Observed point 1
Figure 5 The observed points on the masonry structure
responses of the masonry structure 4 observed points areset at different positions of the walls as shown in Figure 53 additional points are set around each observed point andthe average value of these 4 observed points is taken as aresult of the observed point Observed points 1 and 2 are used
to monitor dynamic responses of front and rear longitudinalwalls and dynamic responses of left and right cross wallsare monitored using observed points 3 and 4 respectivelyDynamic responses of these 4 observed points are extractedin the time-domain as shown in Figure 6Dynamic responses
6 ComplexityVi
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) 0006
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00006
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(d) Point 4
Figure 6 Dynamic responses of observed points on the masonry structure in time-domain
in frequency-domain are obtained through FFT for time-domain results as shown in Figure 7 It is shown in Figure 6that dynamic responses of front and rear longitudinal wallsare similar and numerical results are obviously more thandynamic response results of left and right cross walls Frontand rear longitudinal walls are large in length and low inequivalent stiffness so their dynamic responses are largeunder the same seismic wave Besides dynamic responseamplitudes of front and rear longitudinal walls are at the sametime points caused by local modals of two walls Dynamicresponses of left and right cross walls are obviously differentwhere dynamic responses of the right cross wall are smallerthan those of the left cross wall because the single-layermasonry structure is not a symmetric structure the left crosswall is close to the door hole and the locally structuralstiffness is weak It is shown in Figure 7 that peak frequenciesat different positions are similar and approach 3Hz whichmay be attributed to fundamental frequency of the masonrystructure The computational results of modals prove thatthe minimum natural frequency of the masonry structureis 35Hz and frequencies at different orders are distributeddensely Energies of each observed point are mainly concen-trated within 0ndash6Hz Dynamic responses of observed points
1 and 2 are similar in time-domain but present differencesin the frequency-domain because it represents concentrationof the frequency band energy and is more sensitive to smalldifferences However frequency spectrum peaks of observedpoints 1 and 2 are basically consistent which is also consistentwith computational results in time-domain Computationalresults of observed points 3 and 4 are obviously less than thoseof observed points 1 and 2 in frequency-domain Spectrumpeak regions are wide and dual-peak regions are obviousThereason may be that stiffness difference between left and rightcross walls is obvious and local torsional effects are generatedto the masonry structure
34 Crack Distributions of Masonry Structures Researcheson crack propagation and damage process of a masonrystructure under seismic waves are very important for study-ing the weak parts of the structure as well as the rescuework In finite element analysis cracks are mainly treatedby a discrete crack model and a diffuse crack model In thediscrete crack treatment cracks are formed due to fracturebetween elements The method is similar to the discreteelement method and established based on noncontinuousgeometric conditions However themodeling is complicated
Complexity 7
00006
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00001
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ampl
itude
Frequency (Hz)9630 12
(a) Point 1
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(c) Point 3
Resp
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ampl
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000010
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000000
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(d) Point 4
Figure 7 Dynamic responses of observed points on the masonry structure in frequency-domain
so this method is not suitable for the numerical simulationof large structures In diffuse crack treatment cracks areformed on elements based on material constitution wheregeometric continuity of this model is still maintained aftercrack formationThemodeling of the diffuse crack treatmentis simple and correct results can be obtained through rationalselecting material and constitutive models Therefore thispaper selects the diffuse crack model to simulate the crackpropagation of single-layer masonry structures
Figure 8 presents the crack propagation of the single-layer masonry structure under 20 s seismic waves Cracksstart taking place since the moment 168 s of EL-Centroseismic waves With continuous affecting of seismic wavesthe cracks expand continuously till the moment 598 s whenrear walls and walls of windows and door boundaries arecompletely penetrated During 598 ssim20 s derivation ofcracks is stopped while the cracks get increasingly wider Atthis time the rear wall is completely destroyed Developmentprocesses of cracks are as follows at 168 s cracks based ontension damage begin taking place on the door upper leftcorner of windows turning corners of walls and lower rightcorner of the door as a result the corner of the window anddoor will be damaged firstly because the stiffness in these
positions is relatively weak as the space structure in thesepositions is discontinuous at 198 s cracks around doors andwindows expand continuously a lot of cracks appear on thebottom of front longitudinal walls and cracks also appearon the bottom of rear longitudinal walls at 232 s secondarycracks appear on bottoms of the front and rear longitudinalwalls cracks are continuously widened and large cracksappear at the middle part of rear longitudinal walls and passthroughout the longitudinal direction of masonry structuresat 598 s cracks pass through doors and windows of thefront longitudinal wall and cracks at the middle part of rearlongitudinal walls develop downwards As shown in Figure 8during 598 sndash20 s cracks stop their external expansion andbecome increasinglywider secondary cracks and third cracksappear at original crack positions in succession At thismoment the walls are damaged already and may collapseunder seismic waves Therefore if the time is more than 20 sthe computational results will not have an obvious differencecompared with those results within 20 s
35 Damage Analysis on Masonry Structures Tension dam-age will easily appear in a masonry structure In generalthe damage is caused by cracks of masonry structures It
8 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 8 Crack distributions of the original masonry structure at different moments
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
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00012
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(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
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2 Complexity
established a finite element model applied seismic wavesto the structure in order to conduct the elastoplasticityanalysis and analyzed changing trends of structural cracksbefore and after adding antiseismic walls In order to studyimpacts of front longitudinal columns in walls on antiseismicperformance of a multilayer masonry building Liang et al[14] conducted an experimental test on a masonry buildingusing the vibration table and analyzed damage processesof this model as well as parameters including accelerationamplification coefficients and typical position strains Inorder to study and prevent seismic damage of masonrystructures Liu et al [15] used LS-DYNA to simulate collapseprocesses of a masonry structure verified the correctnessof the numerical model by experiments and found weakpositions in this structure under strong seismic waves whichproposed a powerful support to improve the antiseismicperformance of masonry buildings The macroelement tech-nique for modeling the nonlinear response of masonrypanels is particularly efficient and suitable for the analysisof the seismic behavior of complex walls and buildingsTherefore Penna et al [16] have established a macroelementmodel specifically developed for simulating the responseof masonry walls with possible applications in nonlinearstatic and dynamic analysis of masonry structures underseismic waves Betti et al [17] have conducted a comparisonbetween different methods and numerical models to estimatethe seismic behavior of unreinforced masonry buildingsand the model is able to predict the damaged areas andthe incipient collapse mechanism as well as the collapseload
In these reports detailed experimental tests and numer-ical simulation are mainly conducted on the antiseismicperformance of multilayer masonry structures and someachievements are obtained However single-layer masonrystructures in rural regions are rarely reported Single-layermasonry structures are the main buildings in some regionsResidents do not have strong consciousness for antiseismicperformance and prevention of these buildings Therefore itis very necessary to study and design the antiseismic perfor-mance Dong et al [18] conducted the numerical simulationof the antiseismic performance for single-layer masonrystructures and proposed some reinforcedmeasures but failedto report the distribution expanding processes and detailedcharacteristics of building cracks Lou et al [19] completedthe numerical simulation on the collapse of single-layermasonry structures and also conducted comparative verifica-tion between computational results and experimental resultsbut failed to propose any reinforced measure for improv-ing the antiseismic performance of single-layer masonrystructures Aimed at this current status this paper conductsthe numerical simulation of the antiseismic performancefor single-layer masonry structures completes a systematicstudy on crack distribution and detailed characteristics ofmasonry structures and finally verifies the correctness ofthe numerical model by experiments This paper providesa technology support for the antiseismic performance ofsingle-layer masonry structures
2 The Theoretical Basis of theNumerical Computation
21 Modal SolutionTheories Modal analysis is used to deter-mine the natural vibration characteristics of the structurewhich is the natural frequency and mode shape of the struc-ture It is an important parameter to study the elastoplasticanalysis of vertical earthquakes and also the basic premise ofcomputing structural dynamics Under the external load thedynamic equation of the structural system at any moment isas follows
119865119905 + 119865
119863 + 119865
119878 = 119865 (1)
Among them 119865119905 119865119863 119865119878 are the inertial force vector
damping force vector and elastic force vector of the structurerespectively and 119865 is the external load vector acting onthe structure Inertial force vector damping force vectorand elastic force vector can be represented by 119911(119905) and itsreciprocal as follows
Among them [119872] [119862] [119870] are the mass matrix dampingmatrix and stiffness matrix of the structure respectively119911(119905) (119905) (119905) are the displacement velocity and accelerationvectors of the structure respectively The dynamic equationof the structural system at any time becomes as follows ifformula (2) is substituted into formula (1)
[119872] (119905) + [119862] (119905) + [119870] 119911 (119905) = 119865 (3)When the structural system is in the free vibration state thevibration direction of the structural system becomes
[119872] (119905) + [119870] 119911 (119905) = 0 (4)When the structural system is in the free vibration stateassuming that the displacement of the structure in freevibration is 119911(119905) = 119860 sin120596119905 the homogeneous equationscan be obtained as follows when substituting the former intoformula (4)
([119870] minus 1205962 [119872]) 119860 = 0 (5)
Among them 119860 is not all 0 so the value of the determinantof the coefficient matrix must be all 0 that is10038161003816100381610038161003816[119870] minus 1205962 [119872]10038161003816100381610038161003816 = 0 (6)
According to formula (6) the mass matrix and stiffnessmatrix of the structural system at any time can be solved andthen the natural frequency and mode shape of the structurecan be extracted
22 The Constitutive Relation of the Solved Masonry Theconstitutive relation of the solved masonry is one of the mostimportant mechanical properties of the masonry structureand also the basic parameter that the model must inputwhen solving masonry structure At present the constitutiverelations of the solved masonry have mainly the followingthree kinds
Complexity 3
(a) Geometric model (b) Finite element model
Figure 1 Geometric model and finite element model of the masonry structure
221 Single-Segment Constitutive Relations The constitutiverelation of masonry under a short-term load is usually deter-mined by the axial compression test When the stress of themasonry structure reaches a maximum value the masonrystructurewill suddenly collapse under normal circumstancesAccording to a great deal of experience the constitutiverelation of masonry structure material is put forward asfollows [20]
222 Two-Segment Constitutive Relations Based on theexperimental results Zhu and Dong give a constitutiverelationship for the expression of a two-stage full-curve withascending and descending segments [21]
120590119891119898
120576120576002 + 08120576120576
0
120576 le 120576012 minus 02120576120576
0120576 gt 1205760
(8)
Formula (8) is relatively simple although it can reflect themechanical performance of masonry structures in the stressdrop stage the formula is not derivable at 120576 = 1205760 indicatingthat the stress-strain curve is discontinuous Zhuang con-ducted an experimental study of the masonry model and alsogave the ascending anddescending constitutive relations [22]
120590119891119898 =
152 (1205761205760) minus 0279 (120576120576
0)2
1 minus 0483 (1205761205760) + 0724 (120576120576
0)2 120576 le 1205760
34 (1205761205760) minus 113 (120576120576
0)2
1 + 14 (1205761205760) minus 013 (120576120576
0)2 120576 gt 120576
0
(9)
223 Polynomial Constitutive Relations The stress-strainrelation curve proposed by Turnserk and Cacovic is notonly consistent with experimental results but also smoothand continuous Therefore this paper selects the constitutiverelation of the polynomial and its constitutive expression isas follows [23]
120590120590max= 64 ( 120576120576
0
) minus 54 ( 1205761205760
)117
(10)
Among them 120590max is the peak stress and 1205760 is the straincorresponding to the peak stress
3 The Numerical Computation for Dynamicsof Masonry Structures under Seismic Waves
31 The Numerical Computation Model In this paper asingle-layer masonry building with a relatively simple struc-ture is selected Related dimensions of this model areobtained through the real investigation as shown in Fig-ure 1(a) It is shown in this figure that doors and windowsare set on the front longitudinal wall and no hole is seton other three walls Actual dimensions of the window holeare as follows height is 1700mm and width is 2150mmActual dimensions of the door hole are as follows height is2800mm and width is 1320mm No structural antiseismicmeasures including column and beam are applied to thismodel In order to simplify the computation all the surfacesof this model are smooth and even planes Dimensions ofthe experimental model cannot be too large in order toconduct the experimental verification on the correctness ofthe numericalmodel a numericalmodel with scaled ratio 1 2is used for the modeling The finite element model is shownin Figure 1(b) The degree of freedom in the bottom of themasonry structurewas constrained in 6 directions to simulatethe actual condition In order to realize the constraint thedegree of freedom of the element in the bottom of the finiteelement model was constrained In respect of the large sizeof masonry models in this paper if the finite element modelof a masonry structure is established based on a discretemodel it will be limited by the computational software andcomputer performance Besides this paper is focused onthe numerical simulation on a macroscopic damage type ofa masonry structure so that an integral model with easilyestablishing the finite element model is adopted In thismodel the integral modeling is conducted on masonry andconcrete and components are connected by co-nodes [24ndash28] In addition with regard to roofs of rear houses a claylayer will be paved on the roof board In view of features ofthe clay layer its rigidity contribution is not considered in thefinite element model its mass is uniformly distributed on theroof board and reinforced steel bars are simulated using rodelements with dual-directional forces Solid65 elements areused for the masonry structure In view of tension failure andbreakdown failure element size of walls and roofs is 015mAll the materials are deemed as isotropic Parameters of themasonry are as follows compressive strength is 15 times 106 Pa
4 Complexity
10Action time (s)20 30 40 50
1210
86420
0
minus2minus4minus6minus8
minus10
Seism
ic
acce
lera
tion
(mＭ
2)
(a) Seismic waves in X direction
10Action time (s)20 30 40 50
1210
86420
0
minus2minus4minus6minus8
minus10
Seism
ic
acce
lera
tion
(mＭ
2)
(b) Seismic waves in Y direction
Figure 2 Seismic waves in time-domain in X and Y directions
Seism
ic am
plitu
de
040035030025020015010005000
15100 5Frequency (Hz)
20 25
(a) Seismic waves in X direction
Seism
ic am
plitu
de
035030025020015010005000
15100 5Frequency (Hz)
20 25
(b) Seismic waves in Y direction
Figure 3 Seismic waves in frequency-domain in X and Y directions
tension strength is 014 times 106 Pa elasticity modulus is 24 times109 Pa Poissonrsquos ratio is 015 and density is 1900 kgm3
Thepaper ismainly focused on the performance of single-layer masonry structures under seismic waves so seismicwaves should be input into the finite element model Localseismic waves of the single-layer masonry structure lackmonitoring and recording so EL-Centro seismic waves areused for the numerical simulation The seismic waves arecomplete seismic wavers which are recorded internationallyfor the first time and also the seismic waves are widely usedto study the seismic waves [29ndash34] Typical EL-Centro waveswith peak acceleration 03 g are selected as loads and appliedto the X direction and Y direction in this model respectivelyIn general seismic energies in the Z direction are very smalland can be neglected Acceleration time history of seismicwaves is shown in Figure 2 It is shown in this figure thatseismic waves in X and Y directions are not completely thesame Vibrations of the seismic waves are relatively weak after30 s Data in frequency-domain can be obtained after Fouriertransform for data in time-domain of EL-Centro seismicwaves as shown in Figure 3Obviously EL-Centro energies inthe two directions are mainly concentrated within 0sim10Hz
During analyzing the antiseismic performance of single-layermasonry structures two steps should be set for the finiteelement model The first step is structural responses underself-weight loads Static problems are solved by dynamicalgorithms so monotone increasing and steady loading areadopted and self-weight loads are input in forms of datasheets in order to avoid impacts caused by sudden addition ofstatic forces on the structure After the first step is completedthe structure stays at a stable status under vertical static
loads and effects of the structure under static loads areintroduced to the second step The second step is the inputand computation of seismic motion In this paper horizontalseismic motion in X direction and Y direction is inputSeismic motion is also input in the form of data sheets
32 Natural Modals of Masonry Structures In the modalanalysis only density elasticity modulus and constraintconditions play an important role while other loads have noimpact on the modal results According to the finite elementmodel and boundary conditions constraint modals of thesingle-layer masonry structure are computed as shown inFigure 4 It is shown in this figure that vibrations of masonrystructures mainly perform bending vibrations of each walland no torsional vibrations are presented The vibrationshape of the masonry structure was not symmetrical becausethe front wall is not symmetrical Vibration shapes at the1st 3rd 4th and 6th orders mainly performed bendingvibrations of doors and windows because holes are set thereand structural rigidity is weak Vibration shapes of top platesat the 2nd and 5th orders are similar while bending vibrationdirections of longitudinal walls on two sides are oppositeNatural frequencies of the single-layer masonry structureare extracted namely 35Hz 41 Hz 49Hz 57Hz 65Hzand 72Hz which satisfied the distribution of modal densityfor large facilities This result also indirectly verifies theeffectiveness of the finite element model in this paper
33 Dynamic Responses of Masonry Structures Based onthe established finite element model its dynamic responsesunder seismic waves can be obtained In order to monitor
Complexity 5
(a) First order (b) Second order
(c) Third order (d) Fourth order
(e) Fifth order (f) Sixth order
Figure 4 The top six vibration shapes of the masonry structure
Observed point 4 Observed point 2Observed point 3Observed point 1
Figure 5 The observed points on the masonry structure
responses of the masonry structure 4 observed points areset at different positions of the walls as shown in Figure 53 additional points are set around each observed point andthe average value of these 4 observed points is taken as aresult of the observed point Observed points 1 and 2 are used
to monitor dynamic responses of front and rear longitudinalwalls and dynamic responses of left and right cross wallsare monitored using observed points 3 and 4 respectivelyDynamic responses of these 4 observed points are extractedin the time-domain as shown in Figure 6Dynamic responses
6 ComplexityVi
brat
ion
disp
lace
men
t (m
) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
15100 5 20
Time (s)
(a) Point 1
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
Time (s)15100 5 20
(c) Point 3
Vibr
atio
n di
spla
cem
ent (
m)
00006
00008
00010
00004
00002
00000
minus00002
minus00004
minus00006
Time (s)15100 5 20
(d) Point 4
Figure 6 Dynamic responses of observed points on the masonry structure in time-domain
in frequency-domain are obtained through FFT for time-domain results as shown in Figure 7 It is shown in Figure 6that dynamic responses of front and rear longitudinal wallsare similar and numerical results are obviously more thandynamic response results of left and right cross walls Frontand rear longitudinal walls are large in length and low inequivalent stiffness so their dynamic responses are largeunder the same seismic wave Besides dynamic responseamplitudes of front and rear longitudinal walls are at the sametime points caused by local modals of two walls Dynamicresponses of left and right cross walls are obviously differentwhere dynamic responses of the right cross wall are smallerthan those of the left cross wall because the single-layermasonry structure is not a symmetric structure the left crosswall is close to the door hole and the locally structuralstiffness is weak It is shown in Figure 7 that peak frequenciesat different positions are similar and approach 3Hz whichmay be attributed to fundamental frequency of the masonrystructure The computational results of modals prove thatthe minimum natural frequency of the masonry structureis 35Hz and frequencies at different orders are distributeddensely Energies of each observed point are mainly concen-trated within 0ndash6Hz Dynamic responses of observed points
1 and 2 are similar in time-domain but present differencesin the frequency-domain because it represents concentrationof the frequency band energy and is more sensitive to smalldifferences However frequency spectrum peaks of observedpoints 1 and 2 are basically consistent which is also consistentwith computational results in time-domain Computationalresults of observed points 3 and 4 are obviously less than thoseof observed points 1 and 2 in frequency-domain Spectrumpeak regions are wide and dual-peak regions are obviousThereason may be that stiffness difference between left and rightcross walls is obvious and local torsional effects are generatedto the masonry structure
34 Crack Distributions of Masonry Structures Researcheson crack propagation and damage process of a masonrystructure under seismic waves are very important for study-ing the weak parts of the structure as well as the rescuework In finite element analysis cracks are mainly treatedby a discrete crack model and a diffuse crack model In thediscrete crack treatment cracks are formed due to fracturebetween elements The method is similar to the discreteelement method and established based on noncontinuousgeometric conditions However themodeling is complicated
Complexity 7
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(a) Point 1
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(b) Point 2
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(c) Point 3
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(d) Point 4
Figure 7 Dynamic responses of observed points on the masonry structure in frequency-domain
so this method is not suitable for the numerical simulationof large structures In diffuse crack treatment cracks areformed on elements based on material constitution wheregeometric continuity of this model is still maintained aftercrack formationThemodeling of the diffuse crack treatmentis simple and correct results can be obtained through rationalselecting material and constitutive models Therefore thispaper selects the diffuse crack model to simulate the crackpropagation of single-layer masonry structures
Figure 8 presents the crack propagation of the single-layer masonry structure under 20 s seismic waves Cracksstart taking place since the moment 168 s of EL-Centroseismic waves With continuous affecting of seismic wavesthe cracks expand continuously till the moment 598 s whenrear walls and walls of windows and door boundaries arecompletely penetrated During 598 ssim20 s derivation ofcracks is stopped while the cracks get increasingly wider Atthis time the rear wall is completely destroyed Developmentprocesses of cracks are as follows at 168 s cracks based ontension damage begin taking place on the door upper leftcorner of windows turning corners of walls and lower rightcorner of the door as a result the corner of the window anddoor will be damaged firstly because the stiffness in these
positions is relatively weak as the space structure in thesepositions is discontinuous at 198 s cracks around doors andwindows expand continuously a lot of cracks appear on thebottom of front longitudinal walls and cracks also appearon the bottom of rear longitudinal walls at 232 s secondarycracks appear on bottoms of the front and rear longitudinalwalls cracks are continuously widened and large cracksappear at the middle part of rear longitudinal walls and passthroughout the longitudinal direction of masonry structuresat 598 s cracks pass through doors and windows of thefront longitudinal wall and cracks at the middle part of rearlongitudinal walls develop downwards As shown in Figure 8during 598 sndash20 s cracks stop their external expansion andbecome increasinglywider secondary cracks and third cracksappear at original crack positions in succession At thismoment the walls are damaged already and may collapseunder seismic waves Therefore if the time is more than 20 sthe computational results will not have an obvious differencecompared with those results within 20 s
35 Damage Analysis on Masonry Structures Tension dam-age will easily appear in a masonry structure In generalthe damage is caused by cracks of masonry structures It
8 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 8 Crack distributions of the original masonry structure at different moments
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
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Submit your manuscripts atwwwhindawicom
Complexity 3
(a) Geometric model (b) Finite element model
Figure 1 Geometric model and finite element model of the masonry structure
221 Single-Segment Constitutive Relations The constitutiverelation of masonry under a short-term load is usually deter-mined by the axial compression test When the stress of themasonry structure reaches a maximum value the masonrystructurewill suddenly collapse under normal circumstancesAccording to a great deal of experience the constitutiverelation of masonry structure material is put forward asfollows [20]
222 Two-Segment Constitutive Relations Based on theexperimental results Zhu and Dong give a constitutiverelationship for the expression of a two-stage full-curve withascending and descending segments [21]
120590119891119898
120576120576002 + 08120576120576
0
120576 le 120576012 minus 02120576120576
0120576 gt 1205760
(8)
Formula (8) is relatively simple although it can reflect themechanical performance of masonry structures in the stressdrop stage the formula is not derivable at 120576 = 1205760 indicatingthat the stress-strain curve is discontinuous Zhuang con-ducted an experimental study of the masonry model and alsogave the ascending anddescending constitutive relations [22]
120590119891119898 =
152 (1205761205760) minus 0279 (120576120576
0)2
1 minus 0483 (1205761205760) + 0724 (120576120576
0)2 120576 le 1205760
34 (1205761205760) minus 113 (120576120576
0)2
1 + 14 (1205761205760) minus 013 (120576120576
0)2 120576 gt 120576
0
(9)
223 Polynomial Constitutive Relations The stress-strainrelation curve proposed by Turnserk and Cacovic is notonly consistent with experimental results but also smoothand continuous Therefore this paper selects the constitutiverelation of the polynomial and its constitutive expression isas follows [23]
120590120590max= 64 ( 120576120576
0
) minus 54 ( 1205761205760
)117
(10)
Among them 120590max is the peak stress and 1205760 is the straincorresponding to the peak stress
3 The Numerical Computation for Dynamicsof Masonry Structures under Seismic Waves
31 The Numerical Computation Model In this paper asingle-layer masonry building with a relatively simple struc-ture is selected Related dimensions of this model areobtained through the real investigation as shown in Fig-ure 1(a) It is shown in this figure that doors and windowsare set on the front longitudinal wall and no hole is seton other three walls Actual dimensions of the window holeare as follows height is 1700mm and width is 2150mmActual dimensions of the door hole are as follows height is2800mm and width is 1320mm No structural antiseismicmeasures including column and beam are applied to thismodel In order to simplify the computation all the surfacesof this model are smooth and even planes Dimensions ofthe experimental model cannot be too large in order toconduct the experimental verification on the correctness ofthe numericalmodel a numericalmodel with scaled ratio 1 2is used for the modeling The finite element model is shownin Figure 1(b) The degree of freedom in the bottom of themasonry structurewas constrained in 6 directions to simulatethe actual condition In order to realize the constraint thedegree of freedom of the element in the bottom of the finiteelement model was constrained In respect of the large sizeof masonry models in this paper if the finite element modelof a masonry structure is established based on a discretemodel it will be limited by the computational software andcomputer performance Besides this paper is focused onthe numerical simulation on a macroscopic damage type ofa masonry structure so that an integral model with easilyestablishing the finite element model is adopted In thismodel the integral modeling is conducted on masonry andconcrete and components are connected by co-nodes [24ndash28] In addition with regard to roofs of rear houses a claylayer will be paved on the roof board In view of features ofthe clay layer its rigidity contribution is not considered in thefinite element model its mass is uniformly distributed on theroof board and reinforced steel bars are simulated using rodelements with dual-directional forces Solid65 elements areused for the masonry structure In view of tension failure andbreakdown failure element size of walls and roofs is 015mAll the materials are deemed as isotropic Parameters of themasonry are as follows compressive strength is 15 times 106 Pa
4 Complexity
10Action time (s)20 30 40 50
1210
86420
0
minus2minus4minus6minus8
minus10
Seism
ic
acce
lera
tion
(mＭ
2)
(a) Seismic waves in X direction
10Action time (s)20 30 40 50
1210
86420
0
minus2minus4minus6minus8
minus10
Seism
ic
acce
lera
tion
(mＭ
2)
(b) Seismic waves in Y direction
Figure 2 Seismic waves in time-domain in X and Y directions
Seism
ic am
plitu
de
040035030025020015010005000
15100 5Frequency (Hz)
20 25
(a) Seismic waves in X direction
Seism
ic am
plitu
de
035030025020015010005000
15100 5Frequency (Hz)
20 25
(b) Seismic waves in Y direction
Figure 3 Seismic waves in frequency-domain in X and Y directions
tension strength is 014 times 106 Pa elasticity modulus is 24 times109 Pa Poissonrsquos ratio is 015 and density is 1900 kgm3
Thepaper ismainly focused on the performance of single-layer masonry structures under seismic waves so seismicwaves should be input into the finite element model Localseismic waves of the single-layer masonry structure lackmonitoring and recording so EL-Centro seismic waves areused for the numerical simulation The seismic waves arecomplete seismic wavers which are recorded internationallyfor the first time and also the seismic waves are widely usedto study the seismic waves [29ndash34] Typical EL-Centro waveswith peak acceleration 03 g are selected as loads and appliedto the X direction and Y direction in this model respectivelyIn general seismic energies in the Z direction are very smalland can be neglected Acceleration time history of seismicwaves is shown in Figure 2 It is shown in this figure thatseismic waves in X and Y directions are not completely thesame Vibrations of the seismic waves are relatively weak after30 s Data in frequency-domain can be obtained after Fouriertransform for data in time-domain of EL-Centro seismicwaves as shown in Figure 3Obviously EL-Centro energies inthe two directions are mainly concentrated within 0sim10Hz
During analyzing the antiseismic performance of single-layermasonry structures two steps should be set for the finiteelement model The first step is structural responses underself-weight loads Static problems are solved by dynamicalgorithms so monotone increasing and steady loading areadopted and self-weight loads are input in forms of datasheets in order to avoid impacts caused by sudden addition ofstatic forces on the structure After the first step is completedthe structure stays at a stable status under vertical static
loads and effects of the structure under static loads areintroduced to the second step The second step is the inputand computation of seismic motion In this paper horizontalseismic motion in X direction and Y direction is inputSeismic motion is also input in the form of data sheets
32 Natural Modals of Masonry Structures In the modalanalysis only density elasticity modulus and constraintconditions play an important role while other loads have noimpact on the modal results According to the finite elementmodel and boundary conditions constraint modals of thesingle-layer masonry structure are computed as shown inFigure 4 It is shown in this figure that vibrations of masonrystructures mainly perform bending vibrations of each walland no torsional vibrations are presented The vibrationshape of the masonry structure was not symmetrical becausethe front wall is not symmetrical Vibration shapes at the1st 3rd 4th and 6th orders mainly performed bendingvibrations of doors and windows because holes are set thereand structural rigidity is weak Vibration shapes of top platesat the 2nd and 5th orders are similar while bending vibrationdirections of longitudinal walls on two sides are oppositeNatural frequencies of the single-layer masonry structureare extracted namely 35Hz 41 Hz 49Hz 57Hz 65Hzand 72Hz which satisfied the distribution of modal densityfor large facilities This result also indirectly verifies theeffectiveness of the finite element model in this paper
33 Dynamic Responses of Masonry Structures Based onthe established finite element model its dynamic responsesunder seismic waves can be obtained In order to monitor
Complexity 5
(a) First order (b) Second order
(c) Third order (d) Fourth order
(e) Fifth order (f) Sixth order
Figure 4 The top six vibration shapes of the masonry structure
Observed point 4 Observed point 2Observed point 3Observed point 1
Figure 5 The observed points on the masonry structure
responses of the masonry structure 4 observed points areset at different positions of the walls as shown in Figure 53 additional points are set around each observed point andthe average value of these 4 observed points is taken as aresult of the observed point Observed points 1 and 2 are used
to monitor dynamic responses of front and rear longitudinalwalls and dynamic responses of left and right cross wallsare monitored using observed points 3 and 4 respectivelyDynamic responses of these 4 observed points are extractedin the time-domain as shown in Figure 6Dynamic responses
6 ComplexityVi
brat
ion
disp
lace
men
t (m
) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
15100 5 20
Time (s)
(a) Point 1
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
Time (s)15100 5 20
(c) Point 3
Vibr
atio
n di
spla
cem
ent (
m)
00006
00008
00010
00004
00002
00000
minus00002
minus00004
minus00006
Time (s)15100 5 20
(d) Point 4
Figure 6 Dynamic responses of observed points on the masonry structure in time-domain
in frequency-domain are obtained through FFT for time-domain results as shown in Figure 7 It is shown in Figure 6that dynamic responses of front and rear longitudinal wallsare similar and numerical results are obviously more thandynamic response results of left and right cross walls Frontand rear longitudinal walls are large in length and low inequivalent stiffness so their dynamic responses are largeunder the same seismic wave Besides dynamic responseamplitudes of front and rear longitudinal walls are at the sametime points caused by local modals of two walls Dynamicresponses of left and right cross walls are obviously differentwhere dynamic responses of the right cross wall are smallerthan those of the left cross wall because the single-layermasonry structure is not a symmetric structure the left crosswall is close to the door hole and the locally structuralstiffness is weak It is shown in Figure 7 that peak frequenciesat different positions are similar and approach 3Hz whichmay be attributed to fundamental frequency of the masonrystructure The computational results of modals prove thatthe minimum natural frequency of the masonry structureis 35Hz and frequencies at different orders are distributeddensely Energies of each observed point are mainly concen-trated within 0ndash6Hz Dynamic responses of observed points
1 and 2 are similar in time-domain but present differencesin the frequency-domain because it represents concentrationof the frequency band energy and is more sensitive to smalldifferences However frequency spectrum peaks of observedpoints 1 and 2 are basically consistent which is also consistentwith computational results in time-domain Computationalresults of observed points 3 and 4 are obviously less than thoseof observed points 1 and 2 in frequency-domain Spectrumpeak regions are wide and dual-peak regions are obviousThereason may be that stiffness difference between left and rightcross walls is obvious and local torsional effects are generatedto the masonry structure
34 Crack Distributions of Masonry Structures Researcheson crack propagation and damage process of a masonrystructure under seismic waves are very important for study-ing the weak parts of the structure as well as the rescuework In finite element analysis cracks are mainly treatedby a discrete crack model and a diffuse crack model In thediscrete crack treatment cracks are formed due to fracturebetween elements The method is similar to the discreteelement method and established based on noncontinuousgeometric conditions However themodeling is complicated
Complexity 7
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(a) Point 1
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(b) Point 2
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(c) Point 3
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(d) Point 4
Figure 7 Dynamic responses of observed points on the masonry structure in frequency-domain
so this method is not suitable for the numerical simulationof large structures In diffuse crack treatment cracks areformed on elements based on material constitution wheregeometric continuity of this model is still maintained aftercrack formationThemodeling of the diffuse crack treatmentis simple and correct results can be obtained through rationalselecting material and constitutive models Therefore thispaper selects the diffuse crack model to simulate the crackpropagation of single-layer masonry structures
Figure 8 presents the crack propagation of the single-layer masonry structure under 20 s seismic waves Cracksstart taking place since the moment 168 s of EL-Centroseismic waves With continuous affecting of seismic wavesthe cracks expand continuously till the moment 598 s whenrear walls and walls of windows and door boundaries arecompletely penetrated During 598 ssim20 s derivation ofcracks is stopped while the cracks get increasingly wider Atthis time the rear wall is completely destroyed Developmentprocesses of cracks are as follows at 168 s cracks based ontension damage begin taking place on the door upper leftcorner of windows turning corners of walls and lower rightcorner of the door as a result the corner of the window anddoor will be damaged firstly because the stiffness in these
positions is relatively weak as the space structure in thesepositions is discontinuous at 198 s cracks around doors andwindows expand continuously a lot of cracks appear on thebottom of front longitudinal walls and cracks also appearon the bottom of rear longitudinal walls at 232 s secondarycracks appear on bottoms of the front and rear longitudinalwalls cracks are continuously widened and large cracksappear at the middle part of rear longitudinal walls and passthroughout the longitudinal direction of masonry structuresat 598 s cracks pass through doors and windows of thefront longitudinal wall and cracks at the middle part of rearlongitudinal walls develop downwards As shown in Figure 8during 598 sndash20 s cracks stop their external expansion andbecome increasinglywider secondary cracks and third cracksappear at original crack positions in succession At thismoment the walls are damaged already and may collapseunder seismic waves Therefore if the time is more than 20 sthe computational results will not have an obvious differencecompared with those results within 20 s
35 Damage Analysis on Masonry Structures Tension dam-age will easily appear in a masonry structure In generalthe damage is caused by cracks of masonry structures It
8 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 8 Crack distributions of the original masonry structure at different moments
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
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4 Complexity
10Action time (s)20 30 40 50
1210
86420
0
minus2minus4minus6minus8
minus10
Seism
ic
acce
lera
tion
(mＭ
2)
(a) Seismic waves in X direction
10Action time (s)20 30 40 50
1210
86420
0
minus2minus4minus6minus8
minus10
Seism
ic
acce
lera
tion
(mＭ
2)
(b) Seismic waves in Y direction
Figure 2 Seismic waves in time-domain in X and Y directions
Seism
ic am
plitu
de
040035030025020015010005000
15100 5Frequency (Hz)
20 25
(a) Seismic waves in X direction
Seism
ic am
plitu
de
035030025020015010005000
15100 5Frequency (Hz)
20 25
(b) Seismic waves in Y direction
Figure 3 Seismic waves in frequency-domain in X and Y directions
tension strength is 014 times 106 Pa elasticity modulus is 24 times109 Pa Poissonrsquos ratio is 015 and density is 1900 kgm3
Thepaper ismainly focused on the performance of single-layer masonry structures under seismic waves so seismicwaves should be input into the finite element model Localseismic waves of the single-layer masonry structure lackmonitoring and recording so EL-Centro seismic waves areused for the numerical simulation The seismic waves arecomplete seismic wavers which are recorded internationallyfor the first time and also the seismic waves are widely usedto study the seismic waves [29ndash34] Typical EL-Centro waveswith peak acceleration 03 g are selected as loads and appliedto the X direction and Y direction in this model respectivelyIn general seismic energies in the Z direction are very smalland can be neglected Acceleration time history of seismicwaves is shown in Figure 2 It is shown in this figure thatseismic waves in X and Y directions are not completely thesame Vibrations of the seismic waves are relatively weak after30 s Data in frequency-domain can be obtained after Fouriertransform for data in time-domain of EL-Centro seismicwaves as shown in Figure 3Obviously EL-Centro energies inthe two directions are mainly concentrated within 0sim10Hz
During analyzing the antiseismic performance of single-layermasonry structures two steps should be set for the finiteelement model The first step is structural responses underself-weight loads Static problems are solved by dynamicalgorithms so monotone increasing and steady loading areadopted and self-weight loads are input in forms of datasheets in order to avoid impacts caused by sudden addition ofstatic forces on the structure After the first step is completedthe structure stays at a stable status under vertical static
loads and effects of the structure under static loads areintroduced to the second step The second step is the inputand computation of seismic motion In this paper horizontalseismic motion in X direction and Y direction is inputSeismic motion is also input in the form of data sheets
32 Natural Modals of Masonry Structures In the modalanalysis only density elasticity modulus and constraintconditions play an important role while other loads have noimpact on the modal results According to the finite elementmodel and boundary conditions constraint modals of thesingle-layer masonry structure are computed as shown inFigure 4 It is shown in this figure that vibrations of masonrystructures mainly perform bending vibrations of each walland no torsional vibrations are presented The vibrationshape of the masonry structure was not symmetrical becausethe front wall is not symmetrical Vibration shapes at the1st 3rd 4th and 6th orders mainly performed bendingvibrations of doors and windows because holes are set thereand structural rigidity is weak Vibration shapes of top platesat the 2nd and 5th orders are similar while bending vibrationdirections of longitudinal walls on two sides are oppositeNatural frequencies of the single-layer masonry structureare extracted namely 35Hz 41 Hz 49Hz 57Hz 65Hzand 72Hz which satisfied the distribution of modal densityfor large facilities This result also indirectly verifies theeffectiveness of the finite element model in this paper
33 Dynamic Responses of Masonry Structures Based onthe established finite element model its dynamic responsesunder seismic waves can be obtained In order to monitor
Complexity 5
(a) First order (b) Second order
(c) Third order (d) Fourth order
(e) Fifth order (f) Sixth order
Figure 4 The top six vibration shapes of the masonry structure
Observed point 4 Observed point 2Observed point 3Observed point 1
Figure 5 The observed points on the masonry structure
responses of the masonry structure 4 observed points areset at different positions of the walls as shown in Figure 53 additional points are set around each observed point andthe average value of these 4 observed points is taken as aresult of the observed point Observed points 1 and 2 are used
to monitor dynamic responses of front and rear longitudinalwalls and dynamic responses of left and right cross wallsare monitored using observed points 3 and 4 respectivelyDynamic responses of these 4 observed points are extractedin the time-domain as shown in Figure 6Dynamic responses
6 ComplexityVi
brat
ion
disp
lace
men
t (m
) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
15100 5 20
Time (s)
(a) Point 1
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
Time (s)15100 5 20
(c) Point 3
Vibr
atio
n di
spla
cem
ent (
m)
00006
00008
00010
00004
00002
00000
minus00002
minus00004
minus00006
Time (s)15100 5 20
(d) Point 4
Figure 6 Dynamic responses of observed points on the masonry structure in time-domain
in frequency-domain are obtained through FFT for time-domain results as shown in Figure 7 It is shown in Figure 6that dynamic responses of front and rear longitudinal wallsare similar and numerical results are obviously more thandynamic response results of left and right cross walls Frontand rear longitudinal walls are large in length and low inequivalent stiffness so their dynamic responses are largeunder the same seismic wave Besides dynamic responseamplitudes of front and rear longitudinal walls are at the sametime points caused by local modals of two walls Dynamicresponses of left and right cross walls are obviously differentwhere dynamic responses of the right cross wall are smallerthan those of the left cross wall because the single-layermasonry structure is not a symmetric structure the left crosswall is close to the door hole and the locally structuralstiffness is weak It is shown in Figure 7 that peak frequenciesat different positions are similar and approach 3Hz whichmay be attributed to fundamental frequency of the masonrystructure The computational results of modals prove thatthe minimum natural frequency of the masonry structureis 35Hz and frequencies at different orders are distributeddensely Energies of each observed point are mainly concen-trated within 0ndash6Hz Dynamic responses of observed points
1 and 2 are similar in time-domain but present differencesin the frequency-domain because it represents concentrationof the frequency band energy and is more sensitive to smalldifferences However frequency spectrum peaks of observedpoints 1 and 2 are basically consistent which is also consistentwith computational results in time-domain Computationalresults of observed points 3 and 4 are obviously less than thoseof observed points 1 and 2 in frequency-domain Spectrumpeak regions are wide and dual-peak regions are obviousThereason may be that stiffness difference between left and rightcross walls is obvious and local torsional effects are generatedto the masonry structure
34 Crack Distributions of Masonry Structures Researcheson crack propagation and damage process of a masonrystructure under seismic waves are very important for study-ing the weak parts of the structure as well as the rescuework In finite element analysis cracks are mainly treatedby a discrete crack model and a diffuse crack model In thediscrete crack treatment cracks are formed due to fracturebetween elements The method is similar to the discreteelement method and established based on noncontinuousgeometric conditions However themodeling is complicated
Complexity 7
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(a) Point 1
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(b) Point 2
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(c) Point 3
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(d) Point 4
Figure 7 Dynamic responses of observed points on the masonry structure in frequency-domain
so this method is not suitable for the numerical simulationof large structures In diffuse crack treatment cracks areformed on elements based on material constitution wheregeometric continuity of this model is still maintained aftercrack formationThemodeling of the diffuse crack treatmentis simple and correct results can be obtained through rationalselecting material and constitutive models Therefore thispaper selects the diffuse crack model to simulate the crackpropagation of single-layer masonry structures
Figure 8 presents the crack propagation of the single-layer masonry structure under 20 s seismic waves Cracksstart taking place since the moment 168 s of EL-Centroseismic waves With continuous affecting of seismic wavesthe cracks expand continuously till the moment 598 s whenrear walls and walls of windows and door boundaries arecompletely penetrated During 598 ssim20 s derivation ofcracks is stopped while the cracks get increasingly wider Atthis time the rear wall is completely destroyed Developmentprocesses of cracks are as follows at 168 s cracks based ontension damage begin taking place on the door upper leftcorner of windows turning corners of walls and lower rightcorner of the door as a result the corner of the window anddoor will be damaged firstly because the stiffness in these
positions is relatively weak as the space structure in thesepositions is discontinuous at 198 s cracks around doors andwindows expand continuously a lot of cracks appear on thebottom of front longitudinal walls and cracks also appearon the bottom of rear longitudinal walls at 232 s secondarycracks appear on bottoms of the front and rear longitudinalwalls cracks are continuously widened and large cracksappear at the middle part of rear longitudinal walls and passthroughout the longitudinal direction of masonry structuresat 598 s cracks pass through doors and windows of thefront longitudinal wall and cracks at the middle part of rearlongitudinal walls develop downwards As shown in Figure 8during 598 sndash20 s cracks stop their external expansion andbecome increasinglywider secondary cracks and third cracksappear at original crack positions in succession At thismoment the walls are damaged already and may collapseunder seismic waves Therefore if the time is more than 20 sthe computational results will not have an obvious differencecompared with those results within 20 s
35 Damage Analysis on Masonry Structures Tension dam-age will easily appear in a masonry structure In generalthe damage is caused by cracks of masonry structures It
8 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 8 Crack distributions of the original masonry structure at different moments
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
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Complexity 5
(a) First order (b) Second order
(c) Third order (d) Fourth order
(e) Fifth order (f) Sixth order
Figure 4 The top six vibration shapes of the masonry structure
Observed point 4 Observed point 2Observed point 3Observed point 1
Figure 5 The observed points on the masonry structure
responses of the masonry structure 4 observed points areset at different positions of the walls as shown in Figure 53 additional points are set around each observed point andthe average value of these 4 observed points is taken as aresult of the observed point Observed points 1 and 2 are used
to monitor dynamic responses of front and rear longitudinalwalls and dynamic responses of left and right cross wallsare monitored using observed points 3 and 4 respectivelyDynamic responses of these 4 observed points are extractedin the time-domain as shown in Figure 6Dynamic responses
6 ComplexityVi
brat
ion
disp
lace
men
t (m
) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
15100 5 20
Time (s)
(a) Point 1
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
Time (s)15100 5 20
(c) Point 3
Vibr
atio
n di
spla
cem
ent (
m)
00006
00008
00010
00004
00002
00000
minus00002
minus00004
minus00006
Time (s)15100 5 20
(d) Point 4
Figure 6 Dynamic responses of observed points on the masonry structure in time-domain
in frequency-domain are obtained through FFT for time-domain results as shown in Figure 7 It is shown in Figure 6that dynamic responses of front and rear longitudinal wallsare similar and numerical results are obviously more thandynamic response results of left and right cross walls Frontand rear longitudinal walls are large in length and low inequivalent stiffness so their dynamic responses are largeunder the same seismic wave Besides dynamic responseamplitudes of front and rear longitudinal walls are at the sametime points caused by local modals of two walls Dynamicresponses of left and right cross walls are obviously differentwhere dynamic responses of the right cross wall are smallerthan those of the left cross wall because the single-layermasonry structure is not a symmetric structure the left crosswall is close to the door hole and the locally structuralstiffness is weak It is shown in Figure 7 that peak frequenciesat different positions are similar and approach 3Hz whichmay be attributed to fundamental frequency of the masonrystructure The computational results of modals prove thatthe minimum natural frequency of the masonry structureis 35Hz and frequencies at different orders are distributeddensely Energies of each observed point are mainly concen-trated within 0ndash6Hz Dynamic responses of observed points
1 and 2 are similar in time-domain but present differencesin the frequency-domain because it represents concentrationof the frequency band energy and is more sensitive to smalldifferences However frequency spectrum peaks of observedpoints 1 and 2 are basically consistent which is also consistentwith computational results in time-domain Computationalresults of observed points 3 and 4 are obviously less than thoseof observed points 1 and 2 in frequency-domain Spectrumpeak regions are wide and dual-peak regions are obviousThereason may be that stiffness difference between left and rightcross walls is obvious and local torsional effects are generatedto the masonry structure
34 Crack Distributions of Masonry Structures Researcheson crack propagation and damage process of a masonrystructure under seismic waves are very important for study-ing the weak parts of the structure as well as the rescuework In finite element analysis cracks are mainly treatedby a discrete crack model and a diffuse crack model In thediscrete crack treatment cracks are formed due to fracturebetween elements The method is similar to the discreteelement method and established based on noncontinuousgeometric conditions However themodeling is complicated
Complexity 7
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(a) Point 1
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(b) Point 2
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(c) Point 3
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(d) Point 4
Figure 7 Dynamic responses of observed points on the masonry structure in frequency-domain
so this method is not suitable for the numerical simulationof large structures In diffuse crack treatment cracks areformed on elements based on material constitution wheregeometric continuity of this model is still maintained aftercrack formationThemodeling of the diffuse crack treatmentis simple and correct results can be obtained through rationalselecting material and constitutive models Therefore thispaper selects the diffuse crack model to simulate the crackpropagation of single-layer masonry structures
Figure 8 presents the crack propagation of the single-layer masonry structure under 20 s seismic waves Cracksstart taking place since the moment 168 s of EL-Centroseismic waves With continuous affecting of seismic wavesthe cracks expand continuously till the moment 598 s whenrear walls and walls of windows and door boundaries arecompletely penetrated During 598 ssim20 s derivation ofcracks is stopped while the cracks get increasingly wider Atthis time the rear wall is completely destroyed Developmentprocesses of cracks are as follows at 168 s cracks based ontension damage begin taking place on the door upper leftcorner of windows turning corners of walls and lower rightcorner of the door as a result the corner of the window anddoor will be damaged firstly because the stiffness in these
positions is relatively weak as the space structure in thesepositions is discontinuous at 198 s cracks around doors andwindows expand continuously a lot of cracks appear on thebottom of front longitudinal walls and cracks also appearon the bottom of rear longitudinal walls at 232 s secondarycracks appear on bottoms of the front and rear longitudinalwalls cracks are continuously widened and large cracksappear at the middle part of rear longitudinal walls and passthroughout the longitudinal direction of masonry structuresat 598 s cracks pass through doors and windows of thefront longitudinal wall and cracks at the middle part of rearlongitudinal walls develop downwards As shown in Figure 8during 598 sndash20 s cracks stop their external expansion andbecome increasinglywider secondary cracks and third cracksappear at original crack positions in succession At thismoment the walls are damaged already and may collapseunder seismic waves Therefore if the time is more than 20 sthe computational results will not have an obvious differencecompared with those results within 20 s
35 Damage Analysis on Masonry Structures Tension dam-age will easily appear in a masonry structure In generalthe damage is caused by cracks of masonry structures It
8 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 8 Crack distributions of the original masonry structure at different moments
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
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Submit your manuscripts atwwwhindawicom
6 ComplexityVi
brat
ion
disp
lace
men
t (m
) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
15100 5 20
Time (s)
(a) Point 1
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
Time (s)15100 5 20
(c) Point 3
Vibr
atio
n di
spla
cem
ent (
m)
00006
00008
00010
00004
00002
00000
minus00002
minus00004
minus00006
Time (s)15100 5 20
(d) Point 4
Figure 6 Dynamic responses of observed points on the masonry structure in time-domain
in frequency-domain are obtained through FFT for time-domain results as shown in Figure 7 It is shown in Figure 6that dynamic responses of front and rear longitudinal wallsare similar and numerical results are obviously more thandynamic response results of left and right cross walls Frontand rear longitudinal walls are large in length and low inequivalent stiffness so their dynamic responses are largeunder the same seismic wave Besides dynamic responseamplitudes of front and rear longitudinal walls are at the sametime points caused by local modals of two walls Dynamicresponses of left and right cross walls are obviously differentwhere dynamic responses of the right cross wall are smallerthan those of the left cross wall because the single-layermasonry structure is not a symmetric structure the left crosswall is close to the door hole and the locally structuralstiffness is weak It is shown in Figure 7 that peak frequenciesat different positions are similar and approach 3Hz whichmay be attributed to fundamental frequency of the masonrystructure The computational results of modals prove thatthe minimum natural frequency of the masonry structureis 35Hz and frequencies at different orders are distributeddensely Energies of each observed point are mainly concen-trated within 0ndash6Hz Dynamic responses of observed points
1 and 2 are similar in time-domain but present differencesin the frequency-domain because it represents concentrationof the frequency band energy and is more sensitive to smalldifferences However frequency spectrum peaks of observedpoints 1 and 2 are basically consistent which is also consistentwith computational results in time-domain Computationalresults of observed points 3 and 4 are obviously less than thoseof observed points 1 and 2 in frequency-domain Spectrumpeak regions are wide and dual-peak regions are obviousThereason may be that stiffness difference between left and rightcross walls is obvious and local torsional effects are generatedto the masonry structure
34 Crack Distributions of Masonry Structures Researcheson crack propagation and damage process of a masonrystructure under seismic waves are very important for study-ing the weak parts of the structure as well as the rescuework In finite element analysis cracks are mainly treatedby a discrete crack model and a diffuse crack model In thediscrete crack treatment cracks are formed due to fracturebetween elements The method is similar to the discreteelement method and established based on noncontinuousgeometric conditions However themodeling is complicated
Complexity 7
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(a) Point 1
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(b) Point 2
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(c) Point 3
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(d) Point 4
Figure 7 Dynamic responses of observed points on the masonry structure in frequency-domain
so this method is not suitable for the numerical simulationof large structures In diffuse crack treatment cracks areformed on elements based on material constitution wheregeometric continuity of this model is still maintained aftercrack formationThemodeling of the diffuse crack treatmentis simple and correct results can be obtained through rationalselecting material and constitutive models Therefore thispaper selects the diffuse crack model to simulate the crackpropagation of single-layer masonry structures
Figure 8 presents the crack propagation of the single-layer masonry structure under 20 s seismic waves Cracksstart taking place since the moment 168 s of EL-Centroseismic waves With continuous affecting of seismic wavesthe cracks expand continuously till the moment 598 s whenrear walls and walls of windows and door boundaries arecompletely penetrated During 598 ssim20 s derivation ofcracks is stopped while the cracks get increasingly wider Atthis time the rear wall is completely destroyed Developmentprocesses of cracks are as follows at 168 s cracks based ontension damage begin taking place on the door upper leftcorner of windows turning corners of walls and lower rightcorner of the door as a result the corner of the window anddoor will be damaged firstly because the stiffness in these
positions is relatively weak as the space structure in thesepositions is discontinuous at 198 s cracks around doors andwindows expand continuously a lot of cracks appear on thebottom of front longitudinal walls and cracks also appearon the bottom of rear longitudinal walls at 232 s secondarycracks appear on bottoms of the front and rear longitudinalwalls cracks are continuously widened and large cracksappear at the middle part of rear longitudinal walls and passthroughout the longitudinal direction of masonry structuresat 598 s cracks pass through doors and windows of thefront longitudinal wall and cracks at the middle part of rearlongitudinal walls develop downwards As shown in Figure 8during 598 sndash20 s cracks stop their external expansion andbecome increasinglywider secondary cracks and third cracksappear at original crack positions in succession At thismoment the walls are damaged already and may collapseunder seismic waves Therefore if the time is more than 20 sthe computational results will not have an obvious differencecompared with those results within 20 s
35 Damage Analysis on Masonry Structures Tension dam-age will easily appear in a masonry structure In generalthe damage is caused by cracks of masonry structures It
8 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 8 Crack distributions of the original masonry structure at different moments
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
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Submit your manuscripts atwwwhindawicom
Complexity 7
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(a) Point 1
00006
00005
00004
00002
00003
00000
00001
Resp
onse
ampl
itude
Frequency (Hz)9630 12
(b) Point 2
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(c) Point 3
Resp
onse
ampl
itude
000010
000008
000006
000004
000002
000000
Frequency (Hz)9630 12
(d) Point 4
Figure 7 Dynamic responses of observed points on the masonry structure in frequency-domain
so this method is not suitable for the numerical simulationof large structures In diffuse crack treatment cracks areformed on elements based on material constitution wheregeometric continuity of this model is still maintained aftercrack formationThemodeling of the diffuse crack treatmentis simple and correct results can be obtained through rationalselecting material and constitutive models Therefore thispaper selects the diffuse crack model to simulate the crackpropagation of single-layer masonry structures
Figure 8 presents the crack propagation of the single-layer masonry structure under 20 s seismic waves Cracksstart taking place since the moment 168 s of EL-Centroseismic waves With continuous affecting of seismic wavesthe cracks expand continuously till the moment 598 s whenrear walls and walls of windows and door boundaries arecompletely penetrated During 598 ssim20 s derivation ofcracks is stopped while the cracks get increasingly wider Atthis time the rear wall is completely destroyed Developmentprocesses of cracks are as follows at 168 s cracks based ontension damage begin taking place on the door upper leftcorner of windows turning corners of walls and lower rightcorner of the door as a result the corner of the window anddoor will be damaged firstly because the stiffness in these
positions is relatively weak as the space structure in thesepositions is discontinuous at 198 s cracks around doors andwindows expand continuously a lot of cracks appear on thebottom of front longitudinal walls and cracks also appearon the bottom of rear longitudinal walls at 232 s secondarycracks appear on bottoms of the front and rear longitudinalwalls cracks are continuously widened and large cracksappear at the middle part of rear longitudinal walls and passthroughout the longitudinal direction of masonry structuresat 598 s cracks pass through doors and windows of thefront longitudinal wall and cracks at the middle part of rearlongitudinal walls develop downwards As shown in Figure 8during 598 sndash20 s cracks stop their external expansion andbecome increasinglywider secondary cracks and third cracksappear at original crack positions in succession At thismoment the walls are damaged already and may collapseunder seismic waves Therefore if the time is more than 20 sthe computational results will not have an obvious differencecompared with those results within 20 s
35 Damage Analysis on Masonry Structures Tension dam-age will easily appear in a masonry structure In generalthe damage is caused by cracks of masonry structures It
8 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 8 Crack distributions of the original masonry structure at different moments
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
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Submit your manuscripts atwwwhindawicom
8 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 8 Crack distributions of the original masonry structure at different moments
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 9
is shown in Figure 8 that cracks start appearing on themasonry structure since 168 s but the cracks are very smallAt this moment the masonry structure basically suffers nodamage as shown in Figure 9(a) At 198 s some cracks takeplace on the front longitudinal wall and the bottom so alittle of damage appears around doors and windows of themasonry structure At 232 s the masonry structure beginssuffering serious damage especially the door window andbottom When the loading of seismic waves continues to598 s thewalls begin suffering large-region damageA regionat the middle part of rear longitudinal wall is nearly freeof damage According to crack distributions in Figure 8we can find no obvious crack appearing in this region At598 sndash200 s damage distributions do not change obviouslythe damage-free region is gradually reduced and the damageshapes are kept consistent The analyzed results prove thatthe distribution of cracks and damage on front and rearlongitudinal walls is basically consistent only a few of cracksappear on left and right cross walls but the damage is seriousThe reason is that a lot of cracks appear on the bottom ofmasonry structures which seriously affects the stability ofthe masonry foundation and further intensify damage andinstability of the upper parts of cross walls
4 Experimental Verification of theComputational Model
Boundary conditions and parameters of a simulation modelare very complicated so its correctness should be verified byexperimental tests Before a vibration table test is conducteda masonry structure should bemade Mortar joints should beplump during the wall masonry Constructional columns arepoured after the wall is built During the wall is being builtthe masonry toothing is built at constructional columnsso co-work and coordinated deformation between construc-tional columns and walls can be achieved A reinforcementcage is preset at the constructional column Reinforcementof the constructional column is shown in Figure 10 Thevibration table is 50m times 50m and it is a three-way vibrationtable with electrohydraulic servo Parameters of the vibrationtable are as follows the maximum bearing force is 30 t max-imum overturning moment is 75 tsdotm maximum horizontalacceleration is 100ms2 vertical maximum acceleration is70ms2 maximum velocity is 060ms for single-way inputmaximum velocity is 030ms for three-way input horizontalmaximum displacement is plusmn008m and vertical maximumdisplacement is plusmn005m The vibration table can simulatesine waves sine frequency sweeping waves recorded seismicwaves and artificial seismic waves Experimental data is col-lected by a SigLab data collector FBA-11 force balance sensoris used as the acceleration sensor with the pass band 0ndash80Hzand sensitivity 250V10 g Main parameters of the sensorare listed as follows range is plusmn10 cm and resolution ratio is02mm The range may be more than the limit while otherparameters basically satisfy measurement requirements Inorder to compare numerical simulation results tested pointsshould be arranged according to Figure 5 Experimental datais comparedwith the simulation results as shown in Figure 11
It is shown in this figure that changing trends betweennumerical simulation and experimental test are basicallyconsistent Values of experimental tests are less than those ofthe numerical simulation because the numerical simulationis an ideal condition and has relatively ideal parameters butparameters of the actual masonry structure are very compli-cated while own damp of the experimental table will bringsome attenuation effects on seismic waves Nevertheless themaximum relative errors between numerical simulation andexperimental test are not more than 5 which fully provesthat the numerical model in this paper is reliable and can beused to replace the experimental test
5 Dynamic Responses of the ReinforcedMasonry under Seismic Waves
51 Reinforced Proposal and Model Walls of the model arereinforced using polystyrene packing tapes the masonrytoothing is set at joints and supporting positions of wallsand two supporting columns are set in the masonry spaceas shown in Figure 12(a) The reinforced technology is sim-ple and economic to improve the antiseismic performancePacking tapes are simulated by cable elements which onlybear axial forces and components are connected by co-nodesSolid elements are adopted for the establishedmodel Contactis defined between packing tapes and walls Tie constraintsare applied to joints between components Finally the finiteelement model of the reinforced masonry is obtained asshown in Figure 12(b)
52 Crack Distributions of the Reinforced Masonry Crackanalysis is conducted on the reinforced masonry Analyzedresults are compared with the original model as shown inFigure 13 Damage positions of two kinds of models are basi-cally consistent Seismic damage is mainly concentrated ondoor and window holes bottom and rear longitudinal wallsHowever the original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model tillthe end of seismic waves A lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Stress concentration takes place at this partto cause some cracks easily so cracks expand further withthe increased peaks of input seismic waves However seismicdamage of two walls in the reinforced model is obviouslylighter than that in the original model To a certain extentwe can believe that packing tapes and supporting structurescan improve the integrity of walls and delay propagation ofwall cracks
53 Dynamic Responses of the Reinforced Masonry In orderto present the reinforced effects visually dynamic responsesat observed points in Figure 5 are extracted and comparedwith results in the original model as shown in Figure 14 Itis shown in this figure that dynamic responses at all observed
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
10 Complexity
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 9 Damage distributions of the original masonry structure at different moments
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 11
Figure 10 Experimental test on the dynamic response of the masonry structure
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Numerical computationExperimental test
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Numerical computationExperimental test
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 11 Dynamic responses of tested points on the masonry structure in time-domain
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
12 Complexity
(a) Reinforced proposal (b) Finite element model of the reinforced masonry
Figure 12 Reinforced proposal and finite element model of the masonry structure
points of the reinforcedmasonry are obviously less than thoseof the original model Peak responses of two kinds of modelsappear basically at the same moments Macroscopically theresult proves that the antiseismic performance of themasonrycan be effectively improved by the reinforced proposalMicroscopically equivalent stress and strain at observedpoints of two kinds of models are further computed asshown in Figure 15 It is shown in this figure that under thesame equivalent stress equivalent strains of the reinforcedmasonry are obviously less than those of the original modelIn particular when the equivalent stress is 17MPa theequivalent strain of the reinforced masonry is only half thatof the original model From macroscopic and microscopicperspectives the results prove that the reinforced proposalproposed in this paper can effectively improve the antiseismicperformance of the masonry structure
Strains of two kinds of models under different seismicwaves are computed as shown in Figure 16 It is shown in thisfigure that strains are small when the seismic wave amplitudeis less than 02 g strains are increased rapidly after 02 gbecause themasonry structure stays at an elastic deformationstage when the seismic wave amplitude is less than 02 g andthe structure stays at a cracking stage when the value is morethan 02 g In the original model positions between doorsand windows have the largest strains lower left corner andright corner of the leftwindow rank the second and positionsnear the right window have the smallest strains This result isconsistent with actual situations as positions between doorsand windows must bear dual effects of doors and windowsso that the overall stiffness is small Strain sequence of keypositions in the reinforced model is consistent with thatof the original model but the increased strain magnitudeof the reinforced model is larger when the seismic waveamplitude is more than 02 g Besides strains at all positionsof the reinforced model are obviously smaller than those ofthe original model which also proves that the reinforcedproposal proposed in this paper can reduce strains of wallsand improve the antiseismic performance
6 Conclusions
This paper conducts a numerical simulation of the anti-seismic performance for single-layer masonry structures
completes a study on crack distributions and detailed char-acteristics of masonry structures and finally verifies thecorrectness of the numerical model by experimental testsThis paper also provides a reinforced proposal to improve theantiseismic performance of single-layer masonry structuresand the following conclusions can be achieved
(1) Dynamic responses of front and rear longitudinalwalls are similar and numerical results are obviously morethan dynamic responses of left and right cross walls Peakfrequencies at different positions are similar and approach3Hz Energies of each observed point are concentratedwithin0ndash6Hz Spectrum peak regions are wide and dual-peakregions are obvious
(2) Cracks start taking place since the moment 168 sWith continuous affecting of seismic waves the cracksexpand continuously till the moment 598 s when rear wallswindows and door boundaries are completely penetratedDuring 598 ssim20 s cracks stop their external propagationand become increasingly wider and secondary cracks andthird cracks appear at original crack positions in successionAt this moment the walls are damaged already and maycollapse under seismic waves
(3) The original model suffers more seismic damagethan the reinforced model In particular longitudinal cracksappear on bottoms of two longitudinal walls of the originalmodel while these cracks appear later in the reinforcedmodel A lot of cracks appear on the door hole of the originalmodel and no crack appears in the reinforced model till theend of seismic waves Also a lot of cracks appear on uppermiddle parts of the rear longitudinal walls in two kinds ofmodels indicating that rear longitudinal walls are a weak partin the structure Seismic damage of walls in the reinforcedmodel is obviously lighter than that in the original modelWecan believe that packing tapes and supporting structures canimprove the integrity of walls and delay propagation of wallcracks
(4) Dynamic responses at all observed points of thereinforced masonry are obviously less than those of theoriginal model Strains at all positions of the reinforcedmodel are obviously smaller than those of the original modelFrom macroscopic and microscopic perspectives the resultsprove that the reinforced proposal proposed in this paper
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 13
(a) Time = 168 s
(b) Time = 198 s
(c) Time = 232 s
(d) Time = 598 s
(e) Time = 200 s
Figure 13 Crack distributions of the reinforced masonry structure at different moments
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
14 Complexity
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(a) Point 1
Original modelReinforced model
Vibr
atio
n di
spla
cem
ent (
m) 0006
0008
0004
0002
0000
minus0002
minus0004
minus0006
Time (s)15100 5 20
(b) Point 2
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00015
00010
00005
00000
minus00005
minus00010
minus00015
(c) Point 3
Original modelReinforced model
Time (s)15100 5 20
Vibr
atio
n di
spla
cem
ent (
m)
00012
00010
00008
00000
00002
00004
00006
minus00002
minus00004
minus00006
(d) Point 4
Figure 14 Dynamic responses of observed points on the reinforced masonry in time-domain
00000000050001000015000200002500030
05 07 09 11 13 15 17
Original modelReinforced model
Equi
vale
nt st
rain
(m)
Equivalent stress (MPa)
Figure 15 Equivalent strains of two kinds of masonry structures
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
Complexity 15
0000
0004
0008
0012
0016
0020
01 02 03 04 05 06 07
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
(a) Original model
Locations of doors and windowsLeft corner of the left windowRight corner of the left windowLeft corner of the right windowRight corner of the right window
Stra
in (m
)
Seismic acceleration (g)
0000
0002
0004
0006
0008
0010
01 02 03 04 05 06 07 08 09 10
(b) Reinforced model
Figure 16 Strains of different positions on the masonry structure
can effectively improve the antiseismic performance of themasonry structure
Data Availability
The data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] L Mollo and R Greco ldquoMoisture measurements in masonrymaterials by time domain reflectometryrdquo Journal of Materialsin Civil Engineering vol 23 no 4 pp 441ndash444 2011
[2] M Guizzardi D Derome D Mannes R Vonbank and JCarmeliet ldquoElectrical conductivity sensors for water penetra-tion monitoring in building masonry materialsrdquo Materials andStructuresMateriaux et Constructions vol 49 no 7 pp 2535ndash2547 2016
[3] A DrsquoAmbrisi L Feo and F Focacci ldquoExperimental and ana-lytical investigation on bond between carbon-FRCM materialsand masonryrdquo Composites Part B Engineering vol 46 pp 15ndash20 2013
[4] S A Al-Sanea M F Zedan and S N Al-Hussain ldquoEffect ofmasonry material and surface absorptivity on critical thermalmass in insulated building wallsrdquo Applied Energy vol 102 pp1063ndash1070 2013
[5] B Ghiassi G Marcari D V Oliveira and P B LourencoldquoNumerical analysis of bond behavior between masonry bricksand composite materialsrdquo Engineering Structures vol 43 pp210ndash220 2012
[6] T Suzuki H Choi Y Sanada et al ldquoExperimental evaluationof the in-plane behaviour of masonry wall infilled RC framesrdquo
Bulletin of Earthquake Engineering vol 15 no 10 pp 4245ndash4267 2017
[7] L Redmond P Ezzatfar R Des Roches A Stavridis GOzcebe and O Kurc ldquoFinite element modeling of a reinforcedconcrete frame withmasonry infill andmesh reinforcedmortarsubjected to earthquake loadingrdquo Earthquake Spectra vol 32no 1 pp 393ndash414 2016
[8] H Alwashali Y Torihata K Jin and M Maeda ldquoExperimentalobservations on the in-plane behaviour of masonry wall infilledRC frames focusing on deformation limits and backbonecurverdquo Bulletin of Earthquake Engineering pp 1ndash25 2017
[9] S Nayak and S C Dutta ldquoFailure of masonry structures inearthquake A few simple cost effective techniques as possiblesolutionsrdquo Engineering Structures vol 106 pp 53ndash67 2016
[10] K M Dolatshahi and A J Aref ldquoMulti-directional response ofunreinforced masonry walls experimental and computationalinvestigationsrdquo Earthquake Engineering amp Structural Dynamicsvol 45 no 9 pp 1427ndash1449 2016
[11] S Zheng Y Yang and H T Zhao ldquoExperimental study onaseismic behavior of masonry building with frame-shear wallstructure at lower storiesrdquo China Civil Engineering Journal vol37 no 5 pp 23ndash31 2004
[12] H G Jia H L Zhou and X Z Yuan ldquoStudy on characteristicsand mechanism of seismic damage for walls of rural self-built masonry houserdquo Earthquake Resistant Engineering andRetrofitting vol 33 no 3 pp 127ndash132 2011
[13] S Liu and L P Tong ldquoAnalysis of crack development of bottomframe masonry structure under rare earthquakerdquo StructuralEngineers vol 30 no 5 pp 102ndash109 2014
[14] D Y Liang X Guo Z J Jiang and Y Jiang ldquoSeismic behaviorsof bottom-business multi-story masonry structure with wingedcolumnsrdquoChina Earthquake Engineering vol 39 no 4 pp 623ndash631 2017
[15] H Liu Z Ni and J Ou ldquoSimulation analysis of the collapseresponse of masonry structures subjected to strong groundmotionrdquo Earthquake Engineering and Engineering Vibrationvol 28 no 5 pp 38ndash42 2008
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in
Nature and SocietyHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Dierential EquationsInternational Journal of
Volume 2018
Hindawiwwwhindawicom Volume 2018
Decision SciencesAdvances in
Hindawiwwwhindawicom Volume 2018
AnalysisInternational Journal of
Hindawiwwwhindawicom Volume 2018
Stochastic AnalysisInternational Journal of
Submit your manuscripts atwwwhindawicom
16 Complexity
[16] A Penna S Lagomarsino and A Galasco ldquoA nonlinearmacroelement model for the seismic analysis of masonrybuildingsrdquo Earthquake Engineering amp Structural Dynamics vol43 no 2 pp 159ndash179 2014
[17] M Betti L Galano and A Vignoli ldquoComparative analysis onthe seismic behaviour of unreinforced masonry buildings withflexible diaphragmsrdquo Engineering Structures vol 61 pp 195ndash208 2014
[18] F H Dong C H Lou Y Liu and B J Sun ldquoNumerical analysison dynamic responses of single-storey buildings under seismiceffectsrdquo Journal of Vibroengineering vol 19 no 5 pp 3581ndash35982017
[19] F Y Lou T B Sun X Zhang and H F Chen ldquoThe collapsesimulation of single-storymasonry subjected to seismic groundmotionrdquo Earthquake Engineering and Engineering Dynamicsvol 1 no 2 pp 71ndash77 2015
[20] Y Cai C Shi C Ma and T Bao ldquoStudy of the masonry shearstrength under shear-compression actionrdquo Journal of BuildingStructures vol 25 no 5 pp 118ndash123 2004
[21] L B Zhu and Z X Dong Nonlinear Analysis of ReinforcedConcrete Tongji University Press Shanghai 1985
[22] Z Y Zhuang and C K Huang ldquoExperimental study onmechanical properties of model masonryrdquo Building Structurevol 23 no 2 pp 22ndash25 1997
[23] V Turnserk and F Cacovic ldquoSome experimental results on thestrength of brick masonryrdquo in Proceedings of the SIBMAC 1971
[24] K Cui and T Qin X ldquoVirtual reality research of the dynamiccharacteristics of soft soil under metro vibration loads basedon BP neural networksrdquo Neural Computing amp Applications pp1233ndash1242 2017
[25] A Mohebkhah A A Tasnimi and H A Moghadam ldquoNon-linear analysis of masonry-infilled steel frames with openingsusing discrete element methodrdquo Journal of Constructional SteelResearch vol 64 no 12 pp 1463ndash1472 2008
[26] A Yang Y Han Y Pan H Xing and J Li ldquoOptimum surfaceroughness prediction for titanium alloy by adopting responsesurface methodologyrdquo Results in Physics vol 7 pp 1046ndash10502017
[27] A Cecchi G Milani and A Tralli ldquoValidation of analyti-cal multiparameter homogenization models for out-of-planeloaded masonry walls by means of the finite element methodrdquoJournal of Engineering Mechanics vol 131 no 2 pp 185ndash1982005
[28] K Cui W-H Yang and H-Y Gou ldquoExperimental researchand finite element analysis on the dynamic characteristics ofconcrete steel bridges with multi-cracksrdquo Journal of Vibroengi-neering vol 19 no 6 pp 4198ndash4209 2017
[29] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010
[30] H R Tabatabaiefar B Fatahi and B Samali ldquoSeismic behaviorof building frames considering dynamic soil-structure interac-tionrdquo International Journal of Geomechanics vol 13 no 4 pp409ndash420 2013
[31] M R Kianoush andA R Ghaemmaghami ldquoThe effect of earth-quake frequency content on the seismic behavior of concreterectangular liquid tanks using the finite element method incor-porating soil-structure interactionrdquo Engineering Structures vol33 no 7 pp 2186ndash2200 2011
[32] P Memarzadeh M M Saadatpour and M Azhari ldquoNonlineardynamic response and ductility requirements of a typical steelplate shear wall subjected to el centro earthquakerdquo IranianJournal of Science amp Technology vol 34 no 4 pp 371ndash384 2010
[33] F-G Fan and G Ahmadi ldquoNonstationary Kanai-Tajimi modelsfor El Centro 1940 and Mexico City 1985 earthquakesrdquo Proba-bilistic Engineering Mechanics vol 5 no 4 pp 171ndash181 1990
[34] F-E Udwadia andM-D Trifunac ldquoComparison of earthquakeand micro tremor ground motion in El Centro CaliforniardquoBulletin of the Seismological Society of America vol 63 no 4pp 1227ndash1253 1973
Hindawiwwwhindawicom Volume 2018
MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Mathematical Problems in Engineering
Applied MathematicsJournal of
Hindawiwwwhindawicom Volume 2018
Probability and StatisticsHindawiwwwhindawicom Volume 2018
Journal of
Hindawiwwwhindawicom Volume 2018
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawiwwwhindawicom Volume 2018
OptimizationJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Engineering Mathematics
International Journal of
Hindawiwwwhindawicom Volume 2018
Operations ResearchAdvances in
Journal of
Hindawiwwwhindawicom Volume 2018
Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018
International Journal of Mathematics and Mathematical Sciences
