Design Displacements for BaseIsolators Considering Bidirectional

Seismic Effects

Arturo Tena-Colunga,a M.EERI, and Miguel ngel Prez-Osorniob

Currently, there is not available in the literature a specific recommendationto combine peak displacements in orthogonal directions for the design of baseisolators. The 100% +30% combination rule prescribed by many seismiccodes worldwide to account for orthogonal effects in the design of con-ventional structures is sometimes used for base-isolated structures. Thiscombination rule was formerly proposed to account for lateral forces, but itshould be studied whether or not this rule still applies for the designdisplacements of isolated systems. This paper presents a parametric studywhere it is found that the statistical responses to combine peak displacementsin orthogonal directions are not independent from the effective period for bothlinear and bilinear isolators, so a constant combination rule is somewhatincorrect. DOI: 10.1193/1.2216737

INTRODUCTION

In the seismic design of three-dimensional structures, it is quite common to take intoaccount the simultaneous action of the horizontal ground motions through what it isknown as the 100% +30% combination rule. For instance, in a seismic analysis throughthe static method or response spectrum method, the effects of both horizontal compo-nents of the ground motion are combined taking, for each direction in which the struc-ture is analyzed, 100 percent of the ground component parallel to the main direction ofanalysis and 30 percent of the ground component perpendicular to the main direction ofanalysis, using all sign combinations that would lead to the safest design envelope forthe resisting element. The 100% +30% combination rule is widely used and recom-mended by most seismic design codes worldwide, and it is based on studies conductedalmost 30 years ago Rosenblueth and Contreras 1977, where the 30% was suggested inorder to minimize the errors introduced by the proposed linear approximation when con-sidering the three orthogonal ground components modeled in terms of elastic spectralaccelerations Menun and Der Kiureghian 1998. This 100% +30% combination rule isindependent of the fundamental period for the structure and its dynamic characteristicsof response elastic or nonlinear, soil conditions rock, firm soil, soft soil, etc., corre-lation between ground components, the type of fault mechanism that generates theground motions, etc. This fact makes the 100% +30% combination rule very simple andgeneral, therefore, very attractive to many practicing engineers and even researchers.

a Departamento de Materiales, Universidad Autnoma Metropolitana, Av. San Pablo # 180, 02200 Mxico, DF,Mexico

b Areva, Lago Victoria 74, Col. Granada, 11520, Mxico, DF, Mexico

803

Earthquake Spectra, Volume 22, No. 3, pages 803825, August 2006; 2006, Earthquake Engineering Research Institute

804 A.TENA-COLUNGA AND M. . PREZ-OSORNIORecently, more general procedures to account for orthogonal effects 3-D have beenproposed and compared with the 100% +30% rule Menun and Der Kiureghian 1998,Lpez et al. 2001. Menun and Der Kiureghian 1998 and Lpez et al. 2001 basedtheir methods on the pioneering study of Penzien and Watabe 1975 in which, propos-ing an orthogonal set of principal axes, and using orthogonal transformations identical inform to those used in the transformation of stress, they found that the major principalaxis is horizontal and directed to the epicenter, the intermediate axis is in the transversehorizontal direction, and the minor principal axis is vertical. Penzien and Watabe 1975used 18 acceleration records from six different earthquakes, three in California 1933Long Beach, 1940 El Centro, and 1952 Taft, and three in Japan 1968 Tokachi-Oki,1970 Hiddaka-Sankei, and 1974 Izu-Hanto-Oki. Although the procedures presented byMenun and Der Kiureghian 1998 and Lpez et al. 2001 are very interesting, they arestill based on combinations of elastic response spectrum quantities, mainly spectral ac-celerations; that is, ground motions are still represented in terms of elastic pseudo-acceleration spectra. In fact, Menun and Der Kiureghian 1998 and Lpez et al. 2001illustrate their methods using a single pseudo-acceleration design spectrum.

Surprisingly, most researchers are not utilizing simultaneous orthogonal ground mo-tions recorded in recent earthquakes to study orthogonal effects. It is worth noting thatnowadays there are larger reliable databases available worldwide than the one used byPenzien and Watabe 1975. One exception is the study presented by Burton et al.2002, where they perform a comparison of response values obtained from modalanalyses of bridges using the 100% +30% and the 100% +40% combination rulesthree-directional and from time-history analyses using frequency-scaled records. Theyfound that results obtained for the 100% +30% and the 100% +40% combinations ruleswere conservative with respect to time-history analyses, although they used few records5 for their study.

Therefore, the validity of the 100% +30% rule before the state of current knowledgehas not been fully justified using a reasonable database of simultaneous orthogonalground motions recorded in recent earthquakes, primarily for more recent technologiesas systems for the control of the seismic response of structures, among them, base iso-lation.

The seismic design of isolation systems is accomplished mainly in terms of themaximum displacement that the isolators can sustain for dynamic stability. These peakdesign displacements for isolators are more directly related to the ground displacementsrather than to the ground accelerations. Furthermore, it is common to design isolationsystems to behave inelastically through hysteresis of the material rubber, lead, steel,etc., by friction, damping, combinations, etc.

With respect to structural design with seismic isolation, a specific proposal to com-bine the maximum displacement for isolation systems that occur in orthogonal direc-tions does not exist. Therefore, the 100% +30% combination rule is commonly usedwith little in-depth consideration. To the authors knowledge, few people have evaluatedwhether or not this rule, obtained from the maximum response combinations from

pseudo- acceleration response spectra of a relatively reduced sample, is valid to estimate

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 805the maximum design displacement that could be experienced in the isolation system inany given direction Tena-Colunga and Gmez-Sobern 2002. In this regard, some de-sign recommendations, such as FEMA-273 ATC 1997 in section 9.2.4.5.C, basicallyendorses the 100% +30% combination rule to compute the maximum design displace-ment for the isolation system. Recently, the new AASHTO draft bridge provisions in-corporate a 100% +40% combination rule MCEER/ATC-49, 2003. The 1997 UniformBuilding Code UBC ICBO 1997 establishes that in the design of isolation systemsthrough dynamic analysis, the combination of the two orthogonal components of theground motions in its horizontal direction must exceed 1.3 times the design spectrum.Almost every base isolation project to date as per UBC code has had to use the timehistory method of analysis and the combined response spectra of the two components ofthe time histories should be within 10% of 1.3 times the site specific spectra Reviewer2005. As demonstrated by Naeim and Kelly 1999, the vectorial sum of the 1997 UBCproposal of scaling 1.3 times the design spectrum and the sum of the 100% +30% com-bination rule lead to different results.

It is the opinion of the authors that, with respect to the horizontal ground motions,the following questions must be answered regarding orthogonal effects for the design ofisolation systems: 1 is the 100% +30% combination rule still valid and reasonable tocompute design displacements? and 2 can a rational rule for the combination of or-thogonal effects be independent of the structural period and the characteristics of theground motion?

This paper presents a parametric study where the statistics of the ratio between peakdisplacements of base isolators when subjected to bidirectional seismic input 2D withthose obtained for unidirectional seismic input 1D is computed for base-isolatedstructures within an effective period range between 1.5 and 3.0 seconds 1.5 sTI3.0 s. Both linear and bilinear k2/k1=0.10 isolators were considered. In total, 154pairs of accelerograms recorded in rock or firm soil sites of the Mexican Pacific Coastduring 13 seismic events of Ms6.4 in the last 20 years were used for the parametricstudy. To the authors knowledge, this might be the first study worldwide where a com-prehensive database of acceleration records is used to study orthogonal effects, and thefirst to directly consider the nonlinear behavior of the structural system.

From the simulations done in this study, it is found that the statistical responsesmean, mean plus a standard deviation of the 2D/1D ratio is not independent from theeffective period for both linear and bilinear isolators. Therefore, a constant combinationrule for example, 100% +30%, although practical, is somewhat incorrect. In addition,the 2D/1D ratio also depends on the characteristics of the isolation system, as the ob-tained results varied from linear and nonlinear systems. The obtained amplification fac-tors are also compared with the worldwide accepted 100% +30% combination rule, dis-cussing the advantages and disadvantages of this rule for the seismic design ofelastomeric bearings.

806 A.TENA-COLUNGA AND M. . PREZ-OSORNIOBENCHMARKMODEL CONSIDERED

The subject three-story building for the parametric studies benchmark model is de-picted in Figure 1. The building is regular in elevation and symmetric with respect to twomain orthogonal axes both in mass and stiffness. The building has four frames in eachdirection with a typical bay width of 7 m and a story height of 3 m. Typical RC columnsare of square cross section 5050 cm and typical rectangular RC beams are 3575 cm. The building is supported by 16 cylindrical elastomeric bearings one for eachcolumn line below a rigid floor slab, as depicted in Figure 1. Braces of A-36 steel arelocated as shown in Figure 1 and are of square box section 2525 cm with a platethickness of 0.8 cm. The total weight of the structure above the isolation system is W=991 Ton.

The first six fixed-based periods of vibration for the building model computed withETABS are summarized in Table 1. These structural periods plus their correspondingmode shapes were used in the nonlinear dynamic analysis according to this modelingoption allowed by the 3D-Basis program Nagarajaiah et al. 1991a, b. The mode shapesobtained in ETABS are purely translational and rotational, as the structural model wascompletely symmetric in stiffness and mass. The fundamental fixed-based periods in themain orthogonal directions are Tx=Ty=0.187 s. The ratio between the torsional and lat-eral frequencies for the superstructure is s=1.20. The plan aspect ratio is L/b=1.

Figure 1. Benchmark model: a plan, b elevation, c 3-D layout, and d isolation system.

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 807This model has also been used as symmetric benchmark models in previous studiesdealing with torsional effects for example, Tena-Colunga and Gmez-Sobern 2002,Tena-Colunga and Zambrana-Rojas 2004.

PROPERTIES OFTHE ISOLATION SYSTEMS

In this study, both linear elastic and bilinear cylindrical isolators with a post- to pre-yielding stiffness of 10% k2/k1=0.10 were designed for the following effective periodrange of base-isolated structures TI :1.5 sTI3 s. The isolators were designed fol-lowing some available recommendations of the New Zealand practice Skinner et al.1993 and the 1997 Uniform Building Code UBC-97, as presented in greater detailelsewhere Prez-Osornio 2004. Isolators were modeled in the 3D-Basis software ac-counting for biaxial interaction between the two main orthogonal directions.

The mechanical properties for the bilinear isolation systems were set to comply witha recommendation of the UBC-97 that establishes that the effective stiffness of the iso-lation system at the design displacement keff must be greater than one-third of the ef-fective stiffness at 20% of the maximum design displacement keff2, that is, keff1/3keff2, as depicted in Figure 2. For bilinear systems with k2 /k1=0.10, it can be dem-

Table 1. Periods of vibration for the first six fixed-base mode shapes ofbenchmark structure

Mode Period s Mode Period s

1 Translation X 0.187 4 Translation X 0.0632 Translation Y 0.187 5 Translation Y 0.0633 Rotational 0.156 6 Rotational 0.054Figure 2. Design envelope curve for bilinear isolators that follow the restrictions of the UBC.

808 A.TENA-COLUNGA AND M. . PREZ-OSORNIOonstrated that the maximum ductility demand that can be accepted in order to satisfy thismechanic restriction is 9.0 e.g., Tena-Colunga 1997, 2002; Tena-Colunga andGmez-Sobern 2002.

It is worth noting that this mechanical restriction was added late in the developmentof the UBC in an attempt to prevent the use of very long period isolation systems and isvery rarely used in design in the United States Reviewer 2005. The real limitationswith elastomeric isolators made by quality manufacturers are the buckling and ultimateshear strain limits; some isolators are able to achieve 400% shear strain nowadays Re-viewer 2005.

According to what is outlined in detail in Prez-Osornio 2004 and briefly discussedin the following sections regarding the selected ground motions, five yield strength ra-tios for the isolation system were considered in this study: Vy/W=0.03, 0.05, 0.08,0.10, and 0.12, where W=991 Ton is the total weight for the structure above the isola-tion system. This was done for the effective period range of interest 1.5 sTI3 staking an effective period increment of 0.1 second; that is, there were 16 different de-signs for the isolation system in the considered effective period range. Details on thedesigns of the isolation system are presented in Prez-Osornio 2004.

The yield levels of 10% and 12% are of academic interest since they satisfy the duc-tility limits related to the UBC-97 mechanic restriction described above for seismiczones C and D of the Manual of Civil Structures MOC-93 code Inst. de Invest. Elc-tricas 1993, as it will be evident in following sections. It is worth noting that there areno projects to date that use a yield level beyond 7% Reviewer 2005.

SELECTEDACCELERATION DATA BASE

A comprehensive set of accelerograms typical of subduction earthquakes recorded infirm soil sites or rock during the past two decades in the Mexican Pacific Coast wereused in the present study. These records were obtained from the Strong Motion MexicanData Base Sociedad Mexicana 2000, and were filtered and corrected for baseline errorswith the procedure that is described and illustrated in detail in Prez-Osornio 2004. Inaddition, the seismic zonation of Mexico proposed by the MOC-93 Inst. de Invest. Elc-tricas 1993, where the Mexican Republic is divided in four seismic zones Figure 3,was considered in this study. Some details on the seismic provisions of MOC-93 codeare presented in Tena-Colunga 1999.

GENERAL SELECTION CRITERIA FOR PAIRS OFACCELERATION RECORDS

Recording stations located in seismic zones B, C, and D of the Mexican PacificCoast for firm soils and rock were selected in this study. The selected stations are iden-tified in detail in Prez-Osornio 2004 and the location of some of them is depicted inFigure 4. The selection of recorded accelerograms was made utilizing the following cri-teria:

Only acceleration records of Mexican earthquakes with magnitude M6.4 wereconsidered. The following 13 Mexican earthquakes were then selected: a 19

September 1985 M=8.1, b 21 September 1985 M=7.6, c 30 April 1986

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 809M=7.0, d 25 April 1989 M=6.9, e 24 October 1993 M=6.6, f 14March 1994 M=6.8, g 14 September 1995 M=6.4, h 9 October 1995M=8.0, 21 October 1995 M=6.5, j 15 July 1996 M=6.5, k 11 January1997 M=6.9, l 15 July 1999 M=6.5, and m 30 September 1999 M=7.5.

Selected records must have peak ground accelerations amax10 cm/s2 in bothorthogonal horizontal components.

Figure 3. MOC-93 seismic zone map of Mexico. Courtesy of Servicio Sismolgico NacionalFigure 4. Some of the recording stations in firm soil and rock selected for this study.

810 A.TENA-COLUNGA AND M. . PREZ-OSORNIO The integral curve obtained from calculation from the Arias intensity must showan adequate form for an acceleration record, that is, the curve of such integralshould not be similar to the one which is obtained for a pulse or a noise sign. Forthis purpose, each acceleration record was independently evaluated using theDegtra program Ordaz 2001. These criteria must be simultaneously fulfilled bythe two orthogonal horizontal ground components as well.

As a result, 154 pairs of records 308 individual records in total for the 13 Mexicanearthquakes complied with all the selection criteria described above, as presented in de-tail in Prez-Osornio 2004.

ADDITIONAL SELECTION AND SCALING CRITERIA OF PAIRS OFACCELERATION RECORDS FOR BILINEAR ISOLATORS

It is not important to scale acceleration records to obtain the ratio between peak dis-placements of linear elastic base isolators when subjected to bidirectional seismic input2D with those obtained for unidirectional seismic input 1D. However, it is very im-portant to scale acceleration records for inelastic systems, among other considerations,because the accelerograms should have sufficient energy to cause the isolators to re-spond in the nonlinear range. Therefore, it was necessary to define scaling criteria for theacceleration records that would cause the isolation systems in the study to have a rea-sonable inelastic response, but at the same time would maintain the original intensityrelationship between the two orthogonal horizontal ground components. That is, thescaling factor to use should be the same for the two components E-W and N-S, foreach pair of accelerograms under study.

Thus the original set of 154 pairs of acceleration records previously selected wereindividually scaled in order that the so-called dominant ground component would matchthe spectral acceleration for T=2.24 s of the design spectrum of interest of MOC-93code zones D-I, C-I, and B-I, as illustrated in Figure 5 and presented and discussed ingreater detail in Prez-Osornio 2004. The design spectra specified by MOC-93 can befound in Tena-Colunga 1999. The effective period of the isolated structure T=2.24 swas arbitrarily selected as is an intermediate period in the period range 1.5 sTI3.0 s where it is recognized in the literature that base isolation is most appropriate, ashas been done in previous studies Tena-Colunga 2002.

The final selection criterion for each pair of scaled acceleration records was that bothrecords should simultaneously agree that a the scaled peak ground accelerations wouldnot surpass amax=1.2 g, and b the scaling amplification factor would not surpass 100fsc100. Both orthogonal records should fulfill this criterion in order to be used.Minimum, peak, and average scaling amplification factors used in the selected recordswere, respectively, 0.74, 66.5, and 20.3 for the zone D-I; 0.54, 96.2, and 18.7 for zoneC-I; and 0.21, 45.3, and 9.9 for zone B-I. This criterion, while arbitrary, was taken inorder to avoid amplifying peak ground accelerations of the Mexican earthquakes to un-realistic values, taken as reference peak ground accelerations recorded in firm soils and

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 811rock worldwide during strong earthquakes. After this selection process, 73 pairs of ac-celeration records fulfilled the criteria when scaling to the design spectrum of zone D-I,90 pairs for zone C-I, and 135 pairs for zone B-I.

The mean response spectrum obtained from the SRSS combination of the responsespectrum related to the two orthogonal components of the 73 scaled pairs of time his-tories that fulfilled the criteria for zone D-I is compared with 1.3 times the design spec-trum of zone D-I of MOC-93 code in Figure 6. It can be observed from this figure thatthe average SRSS spectrum compares reasonably well with the scaled MOC-93 D-I de-sign spectrum in the period range of interest of this study 1.5 sTI3 s. For shorterperiods T1 s the resulting SRSS spectrum considerably surpasses the scaled designspectrum, whereas for longer periods the SRSS spectrum T3 s is notably below thescaled design spectrum.

AMPLIFICATION FACTORS FORTHE DISPLACEMENTS OF BASEISOLATORS DUETO ORTHOGONAL EFFECTS

Dynamic analyses linear and nonlinear were conducted for the different base-isolated models using 3D-BASIS program Nagarajaiah et al. 1991a,b, where the su-perstructure is modeled to behave elastically. For each pair of acceleration records thereare 16 different models, as an effective period increment of 0.1 seconds was taken for

Figure 5. Scaling procedure for some selected accelerograms to match the spectral accelerationfor the design spectrum of zone D-I of MOC-93 code for T=2.24 s.the base-isolated structures in the effective period range of interest 1.5 sTI3 s.

812 A.TENA-COLUNGA AND M. . PREZ-OSORNIOAlso, for each one of the 16 models, three different loading cases were considered. Themodels were subjected to the action of 1 the E-W component alone, 2 the N-S com-ponent alone, and 3 both horizontal orthogonal components N-S and E-W, E-W andN-S, Figure 7. Please note that as a consequence of having a completely symmetric sys-tem using cylindrical isolators of circular cross section, peak displacements for the iso-lators for the bidirectional loading conditions depicted in Figures 7c and 7d are exactlythe same, although the specific angle where they occur changes. However, as this studyis only interested in the 2D/1D ratio and not in the angles where they occur, this ob-servation allowed us to reduce the number of required simulations from 64 to 48, as onlythe bidirectional loading depicted in Figure 7c or 7d is needed to compute this ratio.

All told, 48 different analyses were computed for each pair of accelerograms for theeffective period range of interest, giving a total of 7,392 simulations for the linear-elasticisolators. For the bilinear isolators, for each considered yield strength, 6,480 nonlineardynamic simulations were conducted for zone B-I Vy/W=0.03 and Vy/W=0.05,4,320 simulations for zone C-I Vy/W=0.08 and Vy/W=0.10, and 3,504 simulationsfor zone D-I Vy/W=0.08, Vy/W=0.10, and Vy /W=0.12. Thus a total of 39,504simulations were conducted for this parametric study.

The results of the analyses were organized by classifying the data files by event.From the time history results, peak dynamic displacements for the isolators were se-lected. Due to the symmetry of the benchmark model and to the absence of a rotational

Figure 6. Comparison of the mean average spectrum obtained from the SRSS combination ofthe 73 scaled pairs of time histories for zone D-I and 1.3 times the design spectrum of zone D-Iof MOC-93 code.

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 813component of the ground, all 16 isolators Figure 1d experienced the same displace-ment.

An interesting issue was to define what it is called the dominant component for theground motion. Some researchers define the dominant component in terms of the peakground acceleration, while others use spectral ordinates, usually in terms of pseudo-acceleration response spectra or the Fourier Amplitude Spectra. In this work, it was im-portant to define the dominant component for the effective period range of interest1.5 sTI3 s, using a criteria that it should not be based on a single peak responseor a crude average. As discussed in Prez-Osornio 2004, one can assess different op-tions. For example, a possible criterion is to select the smallest amplification ratio2D/1D regardless of the direction of the ground component E-W or N-S, for eachgiven effective period, that is, the dominant ground component can switch directionE-W to N-S or vice versa among the effective period range of interest. This envelopecriterion, though very easy to implement, would yield to the smallest 2D/1D amplifi-

Figure 7. Benchmark symmetrical system: a unidirectional E-W input, b unidirectional N-Sinput, and c and d bidirectional E-W and N-S input.cation ratios. However, it is not conceptually strong, since it does not really define a

814 A.TENA-COLUNGA AND M. . PREZ-OSORNIOdominant ground component. This procedure was not used because the 100% +30%combination rule is based on studies where spectral values have been combined in termsof defining a dominant component.

The criterion used in this study can be illustrated with the help of Table 2. The num-bers distinguished in bold italics in columns 5 and 6 of Table 2 depict the smallest2D/1D amplification ratios for a given effective period TI in the effective period rangeof interest 1.5 sTI3 s. In order to define the dominant ground component column7, it was decided to take an indirect criteria where the dominant ground component inthe effective period range of interest was defined in terms of the smallest total sum of allthe 2D/1D ratios for the E-W component column 5 or N-S component column 6 inthe effective period range of interest. Then, for the example shown in Table 2, the small-est 2D/1D total sum 20.603 is connected to the N-S component column 6, and itwas therefore decided with this criteria that the N-S component of CHIL station is thedominant ground component from a displacement perspective in the effective periodrange of interest. It is obvious that others could consider different procedures.

Table 2. Peak displacements for linear-elastic isolators computed with 3D-BASIS program for the ground records of CHIL station 15 June 1999earthquake

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 815As also illustrated with the help of Table 2, it is not always simple to define thedominant ground component. If one compares the smallest 2D/1D amplification ratiosof columns 5 and 6 for each effective period in the period range of interest, it can beobserved that for some periods the dominant component is the E-W component seven,column 5 and for some others the dominant component is the N-S component nine,column 6, therefore, it is not so clear for this station to define the dominant groundcomponent as it is for other ground motions. In fact, both columns 5 and 6 could rea-sonably be identified as the dominant ground component, so it is difficult to take asimple decision in this regard. It is precisely in cases like this one where the proposedcriterion shows its added value. If in the decision process the smallest sum of the2D/1D ratios of columns 5 and 6 is taken into account, we have an additional param-eter to make a reasonable decision, as can be observed in Table 2, since the smallest sumcorresponds to column 6 20.603. Then, it was decided that the N-S component col-umn 6 represents the dominant ground component for displacements in the period

Figure 8. Histogram that summarizes the statistics of dominant periods E-W vs. N-S in theeffective period range of interest for the 154 pairs of records selected for the linear-elastic iso-lators under study.range of interest and, therefore, it is identified as such in column 7.

816 A.TENA-COLUNGA AND M. . PREZ-OSORNIOFigure 8 is a histogram where the statistics of 2D/E-W vs. 2D/N-S ratios forlinear-elastic isolators in the effective period range of interest for the ground motionrecords used in this study are grouped in terms of similar statistics, that is, the numberof events where a component E-W or N-S dominates in the period range of interest.For example, in Table 2, the E-W component dominated in 7 periods and the N-S domi-nated in 9 periods, so defining the stats in terms of the E-W component vs. the N-Scomponent E-W vs. N-S, the score is 7-9. These histograms were used to help appre-ciate how many cases of a clear dominant component were detected for example, scoresof 16-0, 0-16, 15-1, 1-15, 14-2, 2-14, 13-3, and 3-13 with respect to those where thiswas difficult to assess 8-8, 9-7, 7-9, 10-6, and 6-10, rather than finding if there weremore dominant E-W components than N-S components. From the histogram depicted inFigure 8 one can observe that the cases where a component is clearly dominant are prac-tically equal to the number of cases where a dominant component is difficult to assess.Therefore, the smallest sum of the 2D/1D ratios criterion used in this study was veryimportant in the definition of the dominant ground component and, therefore, in the re-sults presented in this paper.

The same procedure was used for defining the dominant ground component for bi-linear isolators and, as illustrated in the histograms of Figures 9 and 10, the criterion ofthe smallest sum is very useful, since the definition of the dominant ground componentfor nonlinear systems depends also on the yield force of the isolation system, as dis-

Figure 9. Histogram that summarizes the statistics of dominant periods E-W vs. N-S in theeffective period range of interest for the 73 pairs of records selected for the bilinear isolatorsunder study for zone D-I and Vy/W=0.10.cussed and shown in greater detail in Prez-Osornio 2004.

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 817STATISTICAL CRITERION USED

Mean values and the mean plus one standard deviation +Sdev for the2D/1D amplification ratios of all simulations were considered in this study to evaluatebidirectional orthogonal effects for the peak displacements of base isolators. This statis-tical criterion is considered reasonable for many engineering applications.

2D/1D AMPLIFICATION FACTORS FOR LINEAR-ELASTIC ISOLATORS

As mentioned in previous sections, 154 pairs of acceleration records correspondingto 13 different seismic events and a total of 7,392 simulations were considered for thisparametric study. For the parametric study, the 2D/1D ratios for Mexican earthquakesof M6.4 were first classified by event and magnitude, so the statistical response wasfirst computed event by event in order to discern first if there exists a strong correlationbetween the amplification factors and the characteristics of each event for example,magnitude. Based on this extensive study that is shown in Prez-Osornio 2004, it wasfound that the mean values of 2D/1D ratios depend on many factors. Therefore, amore complex study with a considerably larger database is needed in order to discern ifthere is a relationship between 2D/1D ratios and the magnitude for the earthquake,something that is beyond the scope of the present study. Also, a larger database is neededif a dependency on the earthquake source mechanism is to be evaluated subduction,fault normal, fault parallel, strike-slip fault, etc., and to study the impact of near-faultacceleration records with velocity pulses recorded in large magnitude earthquakes suchas Northridge 1994, Kobe 1995, Chi-Chi 1999, and Izmit 1999.

Mean values and the mean plus one standard deviation +Sdev for the

Figure 10. Histogram that summarizes the statistics of dominant periods E-W vs. N-S in theeffective period range of interest for the 73 pairs of records selected for the bilinear isolatorsunder study for zone D-I and Vy/W=0.08.2D/1D amplification factor for linear-elastic isolators were computed for the 154 pairs

818 A.TENA-COLUNGA AND M. . PREZ-OSORNIOof accelerations records and the results plotted in Figure 11, where they are comparedwith the 100% +30% combination rule. It can be observed from Figure 11 that the meanvalues for the 2D/1D ratios vary in the effective period range of interest, that is, theyare not constant. Therefore, it is clear that this amplification factor depends on the pe-riod. Furthermore, it can also be observed that in the period interval between 2.2 and 2.7seconds, where maximum values are obtained, the amplification curve takes a sinusoidalform with two peaks, as well as a higher standard deviation. In general, the mean plusone standard deviation +Sdev surpasses the 100% +30% combination rule for the en-tire period range, so if +Sdev is used as the design criteria for orthogonal effects, thenthe 100% +30% rule is unconservative for linear-elastic isolators subjected to typicalground motions of firm soils and rock of the Mexican Pacific Coast. However, the100% +30% combination rule is quite conservative for the mean results. This relationneeds to be evaluated for near-fault strong motions elsewhere in the world, somethingthat is beyond the scope of the present study.

2D/1D AMPLIFICATION FACTORS FOR BILINEAR ISOLATORS

The parametric study for each zone of MOC-93 code was organized in the followingway. For zone B-I, nonlinear dynamic analyses were conducted for bilinear isolatorswith k2 /k1=0.10 and yield forces Vy/W=0.03 and 0.05; therefore, 12,960 simulationswere needed for this zone. For zone C-I, nonlinear dynamic analyses were conducted forbilinear isolators with k2 /k1=0.10 and yield forces Vy/W=0.08 and 0.10; therefore,8,640 simulations were needed for this zone. For zone D-I, nonlinear dynamic analyseswere conducted for bilinear isolators with k2 /k1=0.10 and yield forces Vy/W=0.08,0.10 and 0.12; therefore, 10,512 simulations were needed for this zone. Therefore, a totalof 32,112 nonlinear dynamic analyses were conducted to study the statistics of 2D/1Dratio for bilinear isolators.

Figure 11. Amplification factors due to orthogonal effects 2D/1D for linear-elastic isola-tion systems.Among the processed results for all the considered zones are curves for the mean

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 819values and the mean plus one standard deviation +Sdev for a the amplificationfactors due to orthogonal effects 2D/1D, and b their corresponding displacementductility demands =2D/y, as shown in detail in Prez-Osornio 2004. The resultsfor the amplification factors due to orthogonal effects 2D/1D are presented in fol-lowing sections for zones B-I, C-I, and D-I. However, because of space constraints, theresults obtained for displacement ductility demands =2D/y are only discussed forzone D-I.

Results for Zone B-I

Mean values and the mean plus one standard deviation +Sdev for the2D/1D amplification factor for bilinear isolators with Vy/W=0.03 and 0.05 computedwith the 135 selected pairs of accelerations records selected for zone B-I are given inFigure 12, where the statistical quantities are also compared with the 100% +30% com-bination rule. The following observations can be made from Figure 12 regarding the2D/1D ratios:

2D/1D ratios are reasonably constant in the effective period range of interest.Results for the mean values are below the line that represents the 100% +30%combination rule. Curves for the mean plus one standard deviation are also be-low the 100% +30% line, except for Vy/W=0.03 for the period range 1.5 sTI1.8 s.

The isolation system has a higher displacement response as the yielding forceVy/W is reduced; therefore, 2D/1D amplification factors increase as the iso-lation system has a higher displacement response. This can be confirmed observ-ing that 2D/1D ratios for Vy/W=0.03 are higher than those computed forVy/W=0.05.

Figure 12. Amplification factors due to orthogonal effects 2D/1D for MOC-93 seismiczone B-I for bilinear isolation systems with k2 /k1=0.10, Vy/W=0.03 and 0.05.

820 A.TENA-COLUNGA AND M. . PREZ-OSORNIOResults for Zone C-I

Mean values and the mean plus one standard deviation +Sdev for the2D/1D amplification factor for bilinear isolators with Vy/W=0.08 and 0.10 computedwith the 90 selected pairs of accelerations records selected for zone C-I are given in Fig-ure 13, where these statistical values are also compared with the 100% +30% combina-tion rule. The results are similar to those obtained for zone B-I regarding 2D/1D ra-tios, but it can be seen that smaller values are obtained for zone C-I Figure 13 withrespect to zone B-I Figure 12, particularly for the period range between 1.5 and 1.9seconds. In fact, the curves for the mean values and the mean plus one standarddeviation +Sdev are both below the line that represents the 100% +30% combinationrule for the entire period range of interest.

Results for Zone D-I

Mean values and the mean plus one standard deviation +Sdev for the2D/1D amplification factor for bilinear isolators with Vy/W=0.08, 0.10, and 0.12computed with the 73 selected pairs of accelerations records selected for zone D-I aregiven in Figure 14, where these statistics are also compared with the 100% +30% com-bination rule. The results are similar to those obtained for zones B-I and C-I regarding2D/1D ratios, but the following additional observations can be made:

1. 2D/1D amplification factors for the considered yield strength ratiosVy/W=0.08, 0.10, and 0.12 approach a similar value when TI2.7 s.

2. The computed 2D/1D amplification factors for zone D-I are greater than thoseobtained for zones B-I and C-I for the period range under consideration.

3. 2D/1D curves for the mean plus one standard deviation are below the100% +30% line in the entire period range of interest only for Vy/W=0.12,and above the 100% +30% line in the entire period range of interest only forVy/W=0.08, and for Vy/W=0.10, the curve is below this 100% +30% line for

Figure 13. Amplification factors due to orthogonal effects 2D/1D for MOC-93 seismiczone C-I for bilinear isolation systems with k2 /k1=0.10, Vy/W=0.08 and 0.10.the period range 1.5 sTI2.1 s and above this line for the period range2.2 sTI3.0 s.

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 821Their corresponding displacement ductility demands for bidirectional input aredepicted in Figure 15. It can be observed for the curves associated with the mean re-sponse that peak displacement ductility demands for the isolators for both Vy/W=0.10 and Vy/W=0.12 do not exceed the limiting value 9.0 associated with the pri-mary curve defined by the 1997 UBC for the entire effective period range of interest.However, for Vy/W=0.08, the curve is above =9 in the period range 1.5 sTI1.7 s. For the plots corresponding to the mean plus one standard deviation +Sdev,peak displacement ductility demands for the isolators do not exceed the limiting value9.0 for Vy/W=0.12 for the entire period range of interest, but for Vy/W=0.10, isexceeded in the period range 1.5 sTI1.8 s and for Vy/W=0.08, is exceeded inthe period range 1.5 sTI2.3 s.

Figure 14. Amplification factors due to orthogonal effects 2D/1D for MOC-93 seismiczone D-I for bilinear isolation systems with k2 /k1=0.10, Vy/W=0.08, 0.10, and 0.12.

Figure 15. Displacement ductility demands =2D/y for bilinear isolation systems with

k2/k1=0.10 and Vy/W=0.08, 0.10, and 0.12, subjected to bidirectional seismic input, forMOC-93 seismic zone D-I.

822 A.TENA-COLUNGA AND M. . PREZ-OSORNIOFrom the viewpoint of an efficient design of bilinear isolators with k2 /k1=0.10 interms of an acceptable displacement ductility demand for a stable behavior 9.0, itcan be deduced from Figure 15 that the optimal design curve for seismic zone D-I ofMOC-93 should be closer to a yielding force for the isolation system Vy/W=0.10 ratherthan Vy/W=0.08 excessive demands for the period range 1.5 sTI1.7 s, if meanvalues are considered.

COMPARISONWITHTHE 100%+30% COMBINATION RULE

As already shown and discussed for linear-elastic and bilinear isolators, the meanvalues obtained for the 2D/1D ratios are not constant, and they depend on the periodand the mechanical characteristics for the isolators.

In general, displacement amplification factors due to orthogonal effects 2D/1Dratios corresponding to mean values are always below the 100% +30% combina-tion rule for the entire period range for both linear-elastic and bilinear isolators. The re-sults for the mean plus one standard deviation +Sdev of the 2D/1D ratios exceedthe 100% +30% combination rule for the entire period range for linear-elastic isolators,and depending on the yield strength Vy/W and the seismic zone under consideration,they can also surpass the 100% +30% combination rule for nonlinear isolators.

Although the observed variations on the 2D/1D ratios can be taken into accountwith a simple straight line, the question is if this line should be a constant, as the onegiven by the 100% +30% combination rule, or if it is more appropriate to provide a lin-ear equation for this rule that will depend on the period. In the opinion of the authors, toprovide a linear equation depending on the period will make the design process moretransparent to the practicing engineers, at minimum additional effort.

CONCLUDING REMARKS

A parametric study devoted to study the statistical response of displacement ampli-fications factors due to orthogonal effects 2D/1D ratios for linear-elastic and bilinearisolation systems was presented. The study considered acceleration records for 13 sub-duction earthquakes M6.4 of the Mexican Pacific Coast recorded in rock or firmsoils during the past 20 years. An effective period range for base-isolated structures be-tween 1.5 and 3.0 seconds 1.5 sTI3.0 s was considered.

The parametric study was rigorous with the selection criteria, filtering, and scaling ofthe acceleration data base, as discussed in detail in the paper. For linear-elastic isolators,a database composed of 154 pairs of acceleration records was used. For bilinear isola-tors, 73 pairs of acceleration records fulfilled the criteria when scaling to the designspectra of zone D-I of MOC-93 code, 90 pairs for zone C-I, and 135 pairs for zone B-I.

It was shown from the results of the parametric study that the mean values for the2D/1D ratios for linear-elastic and bilinear isolators are not constant, and they dependon the period and the mechanical characteristics for the isolators. Also, for bilinear iso-lators it was found that the 2D/1D amplification factors increase as the isolation sys-

tem has a higher displacement response lower yield strength, Vy/W.

DESIGN DISPLACEMENTS FOR BASE ISOLATORS CONSIDERING BIDIRECTIONAL SEISMIC EFFECTS 823In general, displacement amplification factors due to orthogonal effects 2D/1Dratios corresponding to mean values are always below the 100% +30% combina-tion rule for the entire period range for both linear-elastic and bilinear isolators. How-ever, the curves for the mean plus one standard deviation +Sdev of the 2D/1D ra-tios surpass the 100% +30% combination rule for the entire period range for linear-elastic isolators, and depending on the yield strength Vy /W and the seismic zoneunder consideration, they can also surpass the 100% +30% combination rule for bilin-ear isolators.

The authors stated in the introduction of this paper that the questions to answer re-garding orthogonal effects for the design of isolation systems are 1 is the 100%+30% combination rule still valid and reasonable to compute design displacements? and2 can a rational rule for the combination of orthogonal effects be independent of thestructural period and the characteristics of the ground motion?

Assessing results of the parametric study briefly described in this paper, the authorshave the following answers to these questions:

1. The 100% +30% combination rule is a reasonable and conservative method tocompute design displacements, as the 2D/1D ratios obtained in this study forthe mean curves are well covered, and this rule is not exceeded by a large mar-gin even when using the results of the mean plus one standard deviation +Sdev. Nevertheless, this rule should be upgraded.

2. Although the observed variations on the 2D/1D ratios can be taken into ac-count with a simple straight line, the question is if this line should be a constant,as the one given by the 100% +30% combination rule, or if it is more appro-priate to provide a linear equation in terms of the effective base-isolated periodfor the structure. The use of constants in engineering practice has already lead toseveral judgment errors in earthquake-resistant design. In the opinion of the au-thors, to provide a linear equation depending on the period would make the de-sign process more transparent to practicing engineers at a minimum additionaleffort, and would reduce the risk of judgment errors. However, it must also berecognized that adopting such a recommendation would add complexity to ouralready complex design codes. Building officials and code developers shoulddiscuss this issue and take the best decision for engineering practice.

Finally, based on the extensive study presented in Prez-Osornio 2004, it wasfound that the mean values of 2D/1D ratios may depend on other factors such as themagnitude for the earthquake explored or the earthquake source mechanism not ex-plored. Therefore, more extensive studies with considerably larger databases are neededin order to discern if there is a relationship between 2D/1D ratios and the magnitudefor the earthquake or the earthquake source mechanism, and to study the impact of near-fault strong motions of large-magnitude earthquakes. Future research efforts should beconducted in this direction.

824 A.TENA-COLUNGA AND M. . PREZ-OSORNIOACKNOWLEDGMENTS

Financial support of the National Science and Technology Council of Mexico Cona-cyt and Universidad Autnoma Metropolitana Azcapotzalco are gratefully acknowl-edged. Additional comments of anonymous reviewers of the manuscript were helpful inimproving this paper and are gratefully acknowledged.

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Received 20 October 2004; accepted 29 November 2005