multihazardresponsecontrolofbase-isolated

Research ArticleMultihazard Response Control of Base-IsolatedBuildings under Bidirectional Dynamic Excitation

Daniel H Zelleke 1 Sandip K Saha 2 and Vasant A Matsagar 1

1Multi-Hazard Protective Structures (MHPS) Laboratory Department of Civil EngineeringIndian Institute of Technology (IIT) Delhi Hauz Khas New Delhi 110016 India2School of Engineering Indian Institute of Technology (IIT) Mandi Kamand Mandi 175005 India

Correspondence should be addressed to Vasant A Matsagar matsagarciviliitdacin

Received 21 June 2020 Revised 7 September 2020 Accepted 4 November 2020 Published 21 December 2020

Academic Editor Franck Poisson

Copyright copy 2020 Daniel H Zelleke et al -is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

-e issues of safety and posthazard functionality of structures under multihazard scenarios are some of the significant challengesin the current dynamic and rapidly growing urban environment In this paper multistory base-isolated buildings are investigatedunder the independent multihazard scenario of earthquake and blast-induced ground motion (BIGM) Multistory buildingmodels equipped with five different types of isolation systems namely the laminated rubber bearing (LRB) lead-rubber bearing(N-Z system) pure friction (PF) system friction pendulum system (FPS) and resilient-friction base isolator (R-FBI) are assessedunder bidirectional multihazard excitations -e suitability of the isolation systems and their key parameters in protectingmultistory buildings is evaluated Furthermore the influence of the superstructure characteristics such as the superstructuredamping and the number of stories is also assessed-e effect of bidirectional hazards on fixed-base buildings is also presented forcomparison -e key response quantities of base-isolated buildings are presented and compared for different isolation systemsParametric investigations are also conducted and the trends of the response quantities are presented to study the influence ofimportant parameters of isolation systems in protecting the buildings under the multihazard scenario of earthquake and BIGM-e results of the investigation show that the behaviors of the buildings equipped with various isolation systems are different forthe two hazards Moreover the influences of the key parameters of the isolation systems are found to be different for varioushazards-erefore the selection of design parameters of isolation systems shall be made with due consideration of the influence ofmultiple hazards Additionally the influence of the properties of the superstructure such as the number of stories and thedamping of the superstructure on the behavior of the base-isolated buildings under the multihazard loading is presented

1 Introduction

Earthquakes have been and remain to be one of theprominent threats to the safety and serviceability of civilengineering structures and infrastructure systems Numer-ous strategies have been proposed researched and imple-mented for seismic protection of structures [1ndash4] -e use ofstructural response control strategies has been proven to bean effective approach Base isolation is an effective strategy toprotect structures the inhabitants of the structures and thecontents housed within the structures against the undesir-able effects of earthquakes It reduces the earthquake forceimparted on the superstructure by increasing the

fundamental time period of the structure and dissipating theearthquake energy [5 6] Various types of base isolationstrategies such as the elastomeric type bearings slidingbearings and rolling bearings have been proposed [6] Alsodifferent active and semiactive seismic isolation strategieshave attracted researchersrsquo attention in recent years [7ndash10]

Structures including those equipped with base isolationsystems are also likely to be subjected to other hazards intheir service life which necessitates the consideration ofvarious types of loadings in the design of structures Despitethe significant socioeconomic impact caused by variousnatural and human-made hazards [11 12] such as blastimpact earthquake tsunami and wind less attention is

HindawiShock and VibrationVolume 2020 Article ID 8830460 24 pageshttpsdoiorg10115520208830460

devoted on research and development to understand thebehavior of structures under multiple hazards and to devisedesign strategies thereof Additionally the risk associatedwith the reduced safety and serviceability of key infra-structures categorized as lifeline structures such as hos-pitals bridges power plants data centers andcommunication centers is paramount -erefore it iscrucial to design structures especially the critical infra-structures by considering all the hazards likely to affectsafety and serviceability -ere is limited research on the useof the multihazard approach in the performance assessmentand design of structures For instance Messervey et al [13]Gardoni and LaFave [12] Mahmoud and Chulahwat [14]Venanzi et al [15] and Roy and Matsagar [16 17] haveconducted studies on the multihazard protection ofstructures

Although base isolation is an effective strategy to miti-gate the adverse effects of earthquakes its efficacy in pro-tecting structures under multihazard loading is not exploredadequately Most of the studies on the base-isolated struc-tures also focus on earthquake protection and thereforethere are limited studies that are conducted on the per-formance assessment of base-isolated structures under otherhazards such as wind and blast Some of the attempts toinvestigate the behavior of base-isolated structures underwind loading include the studies conducted by Hendersonand Novak [18 19] -ey have conducted theoretical andexperimental studies to assess the response of the base-isolated buildings under wind loading wherein the theo-retical and experimental results are compared Chen andAhmadi [20] have evaluated the sensitivity of structuresisolated by the laminated rubber bearing (LRB) highdamping rubber bearing (HDRB) and resilient-rubberbearing (R-FBI) to wind loading Furthermore Kareem [21]has studied the dynamic response of base-isolated buildingswith passive dampers under wind loading Later Liang et al[22] have assessed the habitability of base-isolated buildingsunder fluctuating wind load Recently a probabilistic in-vestigation on the response of tall base-isolated buildingsunder wind loading has been reported by Feng and Chen[23]

-e response of base-isolated structures under surfaceblast has been assessed by some researchers Zhang andPhillips [24 25] have studied the performance of amultistory base-isolated building with and withoutpassive supplemental dampers in suppressing the vi-bration response of the building exposed to blast loadingAlso Kangda and Bakre [26] have assessed the responseof base-isolated structures subjected to surface blast andconcluded that base isolation could be effective inmitigating the blast response quantities such as the peakstory displacement story drift and root mean square(RMS) absolute acceleration -e performance of base-isolated buildings under blast-induced ground motion(BIGM) has also captured attention in the recent timesMondal et al [27 28] have studied the response ofbuildings isolated by lead-rubber bearing (N-Z system)under BIGM Further the performance of a base isolationsystem equipped with shape-memory alloy in protecting

buildings under BIGM has been studied by Mondal et al[29] Furthermore the use of various base isolationsystems in protecting buildings against blast-inducedground motions has been discussed by Mondal et al [30]-e findings of the investigations reveal that base iso-lation can be beneficial to control the vibration responseof buildings under blast-induced ground motions -eperformance of base isolation strategies for the vibrationresponse control of buildings under other nonseismichazards such as train-induced vibrations has also beenexplored [31ndash33] -e available limited literature on theimplementation of base isolation for the vibration re-sponse control of buildings under different types of ex-citations indicate the potential benefit of the strategy inmitigating the adverse effects of various types of hazardsNotwithstanding the vibration protection potential ofbase isolation systems base-isolated buildings could beinfluenced differently under distinct types of hazards-erefore it is necessary to consider the multihazardapproach to satisfy safety and serviceability design re-quirements for base-isolated buildings that are likely tobe subjected to different types of loading However thereare no studies which investigate the behavior of base-isolated buildings subjected to both earthquakes andblast-induced ground motions In addition the influenceof the key parameters of the base isolation systems on theefficacy of the response mitigation under the multihazardscenario of earthquake and BIGM has not been explored

-erefore it would be essential to investigate and unveilthe performance of buildings equipped with the laminatedrubber bearing (LRB) lead-rubber bearing (N-Z system)pure friction (PF) system friction pendulum system (FPS)and resilient-friction base isolator (R-FBI) under the mul-tihazard scenario of earthquake and blast-induced groundmotion Consequently the behavior of buildings equippedwith various base isolation systems is assessed under mul-tihazard loading in this paper -e main objectives of thisstudy include the following (a) to assess the performance ofbase-isolated buildings under bidirectional near-fault (NF)earthquake ground motions far-fault (FF) earthquakeground motions and blast-induced ground motions(BIGMs) (b) to evaluate the effect of the characteristicparameters of the five base isolation systems consideredherein on the behavior of base-isolated buildings underdifferent hazards and (c) to study the effect of the propertiesof the superstructure on the multihazard response of base-isolated buildings

2 Modeling of a Base-Isolated Building underBidirectional Excitation

-e schematic diagram and idealized model of the base-isolated building considered in this investigation aredepicted in Figure 1 -e three-dimensional model of thebase-isolated building portrayed in the figure shows theorientation of the building the location of the isolatorsthe superstructure properties and the base excitation-e mathematical modeling of the base-isolated building

2 Shock and Vibration

under bidirectional base excitation is described asfollows

21 Governing Equations of Motion -e governing equa-tions of motion of the base-isolated building subjected toground acceleration are derived under the assumption thatthe superstructure remains in the elastic range Furthermoreit is considered that the floors are infinitely rigid the beamsand columns are axially inextensible the building is sym-metric in bothX and Y directions and the torsional responseof the building is neglected Accordingly two degrees offreedom lateral displacements in X and Y directions at eachfloor and base mass levels are considered in the formulationof the equations of motion -e matrix form of the gov-erning equations of motion of the base-isolated buildingunder bidirectional base excitation is given as

M euroX + C _X + KX + f minusMr euroUg (1)

whereM C and K respectively are the mass damping andstiffness matrices of the base-isolated building -esestructural property matrices are given as

M

mb 0 0 0

0T Ms 0T 0

0 0 mb 0

0T 0 0T Ms

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

0 c1xrb 0 0

0T Csx 0T 0

0 0 0 c1yrb

0T 0 0T Csy

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

K

0 k1xrb 0 0

0T Ksx 0T 0

0 0 0 k1yrb

0T 0 0T Ksy

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)

where Ms diag[m1 m2 mj mN] is the super-structure mass matrix of size N N is the number ofstories mj is the mass of the jth floor mb is the base massCsx and Ksx respectively are the damping and thestiffness matrices of the superstructure in the X directionCsy and Ksy respectively are the damping and thestiffness matrices of the superstructure in the Y directionc1x and c1y are the damping constants of the first story ofthe building in X and Y directions respectively k1x andk1y are the stiffnesses of the first story of the building in Xand Y directions respectively rb 1 0 0 0 is a rowvector of size N 0 0 0 0 is a row vector of size Nand 0 is a null matrix of size N times N

Furthermore the vectors of displacements velocitiesand accelerations of the base-isolated building X _X and euroXrespectively the vector of the restoring forces in the isolator

f the vector of ground accelerations euroUg and the matrix ofinfluence coefficients r are given as follows

X xbXTs ybYT

s1113966 1113967T

_X _xb _XT

s _yb _YT

s1113882 1113883T

euroX euroxb euroXT

s euroyb euroYT

s1113882 1113883T

f minusfbx 0 minusfby 01113966 1113967T

euroUg euroxg euroxg + euroxb1113872 1113873 euroyg euroyg + euroyb1113872 11138731113966 1113967T

r

1 0 0 0

0T r 0T 0T

0 0 1 0

0T 0T 0T r

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)

where xb and yb respectively are the displacements of the basemass relative to the ground in X and Y directions _xb and _ybrespectively are the velocities of the base mass relative to theground in X and Y directions euroxb and euroyb respectively are theaccelerations of the base mass relative to the ground inX and Ydirections Xs x1 x2 xN1113864 1113865

T and Ys y1 y2 1113864

yNT respectively are the vectors of floor displacements in Xand Y directions _Xs and _Ys respectively are the vectors offloor velocities in X and Y directions euroXs and euroYs respectivelyare the vectors of floor accelerations in X and Y directions fbx

and fby respectively are the X and Y components of the forceacting on the base isolators euroxg and euroyg are the ground ac-celerations in X and Y directions respectively andr 1 1 1 T is a column vector of influence coefficients ofsize N -e solution of the governing equations of motion isobtained numerically using state-space formulation

22 Mathematical Modeling of Base Isolators under Bidirec-tional Excitation In this study the multihazard response ofmultistory buildings isolated by elastomeric and slidingbearings are studied Two elastomeric bearings the lami-nated rubber bearing (LRB) and lead-rubber bearing (N-Zsystem) are used whereas the three types of sliding bearingsinvestigated are the pure friction (PF) system frictionpendulum system (FPS) and resilient-friction base isolator(R-FBI) -e mathematical modeling of the base isolationbearings is realized by considering their characteristic pa-rameters -e LRB is mathematically represented using theisolation time period (Tb) and the isolation damping ratio(ξb) whereas the N-Z system is modeled using the isolationtime period (Tb) the isolation damping ratio (ξb) the yielddisplacement (q) and normalized yield strength (F0) -ePF system is characterized using the friction coefficient (μb)and the isolation time period (Tb) and the friction coefficient(μb) are used to model the FPS Furthermore the isolationtime period (Tb) the friction coefficient (μb) and theisolation damping ratio (ξb) are used to model the R-FBI-e LRB is a linear isolation system and the restoring forcesof the bearing in X and Y directions can be obtained as

Shock and Vibration 3

fbx cb _xb + kbxb

fby cb _yb + kbyb(4)

where cb 2ξbMtωb is the isolation damping coefficientkb Mt(2πTb)2 is the isolation stiffness ωb is the angularfrequency of the isolation system and Mt mb + 1113936

Nj1 mj is

the total mass of the base-isolated building-e N-Z system PF system FPS and R-FBI are non-

linear isolators and their force-deformation behaviors aremathematically modeled with and without considering thebidirectional interaction-e restoring forces in the isolationsystem acting in X and Y directions respectively can beobtained as

fbx cb _xb + αkixb +(1 minus α)Fyhx (5a)

fby cb _yb + αkiyb +(1 minus α)Fyhy (5b)

where ki Fyq is the initial stiffness of the isolator and α

kbki is the postyield to preyield stiffness ratio of the isolatorFurthermore the nondimensional hysteretic displacementcomponents hx and hy are evaluated using a set of non-linear differential equations proposed by Wen [34 35] andPark et al [36] respectively for hysteretic behavior withoutand with bidirectional interaction Without accounting forthe bidirectional interaction the values of hx and hy can beobtained using the following equations

q _hx A _xb + β _xb

11138681113868111386811138681113868111386811138681113868hx hx

11138681113868111386811138681113868111386811138681113868nminus1

minus τ _xb hx

11138681113868111386811138681113868111386811138681113868n (6a)

q _hy A _yb + β _yb

11138681113868111386811138681113868111386811138681113868hy hy

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τ _yb hy

11138681113868111386811138681113868

11138681113868111386811138681113868n (6b)

On the contrary considering the bidirectional interac-tion hx and hy can be evaluated based on the followingequation

q_hx

_hy

⎧⎨

⎩

⎫⎬

⎭ A minus βsgn _xb( 1113857hx hx

11138681113868111386811138681113868111386811138681113868nminus1

minus τ hx

11138681113868111386811138681113868111386811138681113868n

minusβsgn _yb( 1113857hx hy

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τhxhy

minusβsgn _xb( 1113857hy hx

11138681113868111386811138681113868111386811138681113868nminus1

minus τhxhy A minus βsgn _yb( 1113857hy hy

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τ hy

11138681113868111386811138681113868

11138681113868111386811138681113868n

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

_xb

_yb

1113896 1113897 (7)

where n 2 is a parameter used to characterize thesmoothness of the nonlinear force-deformation curve of the

isolation system and sgn() represents the signum function-e values of the dimensionless parameters A β and τ

Column

Base isolator

Floor slab

Base mass

Seismic moatxgmiddotmiddotyg

middot middot

ZXY

(a)

x gmiddotmiddotygmiddotmiddot

ZXY

x b m b

x 1 m1

c 1x k 1x

x 2 m2

c 2x k 2x

x N m N

c Nx k NxyN m

N cNy kNy

y2 m2 c2y k2y

y1 m1

yb mb

c1y k1y

(b)

Z XY

Blast-induced ground motionUnderground blast Angle of attack (θ)

(c)

Figure 1 Base-isolated building subjected to bidirectional base excitation (a) schematic diagram (b) idealized model and (c) blast-inducedground motion (BIGM)


respectively are given as 1 05 and 05 for the N-Z system[37] whereas the values ofA β and τ respectively are givenas 1 01 and 09 for the PF system FPS and R-FBI [38]Also the value of the yield displacement q is taken as 25 cmfor the N-Z system [39] whereas q 025mm is used forsliding isolation systems Additionally the damping ratio ofthe PF system the postyield stiffness of the PF system andthe damping ratio of the FPS are taken as 0 -e yieldstrength of the N-Z system is evaluated as Fy F0Wt whereF0 and Wt respectively are the normalized yield strength ofthe isolation bearing and the total weight of the base-isolatedbuilding-e yield strength of the PF system FPS and R-FBIis evaluated as Fy μbWt where μb is the friction coefficientof the isolation system

3 Numerical Study

Base-isolated buildings are studied under bidirectionalmultihazard excitations -e buildings are isolated using fivetypes of base isolation systems and the behavior of theisolated buildings is assessed under near-fault (NF) earth-quakes far-fault (FF) earthquakes and blast-inducedground motion (BIGM) -e schematic diagram and theidealized model of the base-isolated building studied in thispaper are portrayed in Figures 1(a) and 1(b) -e masses ofall the floors of the building and the basemass are consideredto be equal (mj mb m) Also the lateral stiffnesses of allstories are equal for both X and Y directions -e Rayleighmethod is used to construct the damping matrix of thesuperstructure where the damping ratio of the superstruc-ture (ξs) is considered to be 5 Five building models havingdifferent number of stories are studied -e different valuesof the number of stories of the five buildings are 1 2 4 6 and8 whereas the fundamental time period (T) values for fixed-base buildings are 01 s 02 s 04 s 06 s and 08 s

respectively Furthermore the story height (H) of 35m isconsidered for all the buildings A summary of the propertiesof the superstructure and five base isolation systems used inthis study is presented in Table 1

In numerical investigations the performances of thebuildings equipped with five base isolation systems areassessed by studying different response quantities under NFearthquakes FF earthquakes and BIGMs -e responsequantities in X and Y directions that are evaluated andstudied include the absolute top floor accelerations (euroxN andeuroyN respectively) top floor displacements (xN and yN re-spectively) relative to the ground isolator displacements (xb

and yb respectively) relative to the ground normalized baseshears (Vn

x and Vny respectively) total superstructure drift

ratio (Δxtotal andΔ

y

total respectively) andmaximum interstorydrift ratio (Max(Δx

j ) and Max(Δyj ) respectively) -e total

superstructure drift ratio is obtained as the ratio of the totaldrift of the superstructure to the total height of the super-structure Furthermore the maximum interstory drift ratiois obtained as the maximum of the peak values of theinterstory drift ratios of all the stories of the building Inaddition resultant top floor acceleration (euroσN) resultant topfloor displacement (σN) resultant isolator displacement(σb) resultant normalized base shear (Vn

σ) resultant totalsuperstructure drift ratio (Δσtotal) and resultant maximuminterstory drift ratio (Max(Δσj )) are also studied

31 Bidirectional Multihazard Condition Considered in theStudy -e current study focuses on the investigation of themultihazard behavior of base-isolated buildings under bi-directional base excitations of different types -e near-fault(NF) earthquake ground motions far-fault (FF) earthquakeground motions and blast-induced ground motions(BIGMs) are imparted on buildings isolated using various

Table 1 Properties of the superstructure and isolation systems of base-isolated buildings

Component of base-isolated buildings Parameter Unit Valuesrange of the parameter used in the study

Superstructure

Mass of each floor mj kg 1427100Base mass mb kg 1427100

Damping ratio ξs mdash 002ndash008Fundamental time period Tlowast s 01 02 04 06 and 08

Height of each story H m 35

Base isolation system

N-Z system

Isolation time period Tb s 25Isolation damping ratio ξb mdash 005ndash015

Normalized yield strength F0 mdash 0025ndash02Yield displacement q cm 25

LRB Isolation time period Tb s 2 25 3 and 35Isolation damping ratio ξb mdash 0025ndash025

PF system Friction coefficient μb mdash 0025ndash02Yield displacement q cm 0025

FPSIsolation time period Tb s 2 25 3 and 35Friction coefficient μb mdash 0025ndash025Yield displacement q cm 0025

R-FBI

Isolation time period Tb s 25Isolation damping ratio ξb mdash 005ndash015Friction coefficient μb mdash 0025ndash02Yield displacement q cm 0025

lowast-e values are given for the fixed-base models of 1 2 4 6 and 8 story buildings respectively


base isolation systems Six recorded bidirectional earthquakeground motion records are used in this investigation -reeof the six earthquake ground motion records (a) the 1979Imperial Valley with the closest distance to rupture planeRrup of 395 km (IV1979) (b) the 1989 Loma Prieta Rrup

388 km (LP1989) and (c) the 1994 NorthridgeRrup 53 km (NR1994) are near-fault earthquake groundmotions -e remaining three earthquake ground motionrecords (a) the 1979 Imperial Valley Rrup 2203 km(IV1979F) (b) the 1989 Loma Prieta Rrup 2482 km(LP1989F) and (c) the 1994 Northridge Rrup 2341 km(NR1994F) are far-fault earthquake ground motions Table 2provides the date of the event the recording station theclosest distance to rupture plane the peak ground accel-eration (PGA) in gravitation acceleration (g) unit and otherrelevant details of the earthquake groundmotion data In thetable the two components of each of the six earthquakeevents are presented which are applied as base excitations inthe X direction ( euroxg) and Y direction ( euroyg) simultaneously

-e extent of ground vibration due to blast is influencedby various parameters such as the type of the explosive theweight of the explosive the type of the ground medium andthe distance to the charge In this study the blast-inducedground motion is represented mathematically using thefunction proposed by Carvalho and Battista [40] -e ex-ponentially decaying BIGM acceleration euroUg(t) that isimparted on the base-isolated buildings with an angle ofattack (θ) measured from the X-axis (Figure 1(c)) can beevaluated as

euroUg (t) minus1td

1113888 1113889 _ug eminus ttd( ) (8)

where t is the time instant td RCp is the arrival time R isthe distance to the charge _ug 03607(QV)02872(RQ(13))minus13375 is the peak particle velocity (PPV) [41]Cp

Eρ

1113968is the velocity of wave propagation through the

soil medium E and ρ respectively are Youngrsquos modulus andthe average density of the soil medium V is the chargechamber volume in m3 andQ is the weight of the equivalenttrinitrotoluene (TNT) charge in kg

-e values of Cp R andV used in this study are 5280ms50m and 1000m3 respectively whereas the TNT charge

weight (Q) values of 50 t 75 t and 100 t are considered toevaluate BIGM acceleration Additionally the obtainedBIGM acceleration is applied to the base-isolated buildingswith angle of attack (θ) values of 0deg 15deg 30deg and 45deg ForBIGM acceleration acting with an angle of attack θ from theX-axis the X component of BIGM can be obtained aseuroxg euroUg cos(θ) whereas the Y component can be computedas euroyg euroUg sin(θ) -e time histories of the near-faultearthquakes far-fault earthquakes and BIGMs used in thestudy are presented in Figure 2 whereas the Fourier spectra ofthe three types of excitations are given in Figure 3

32 Effect of Bidirectional Interaction -e two componentsof the considered earthquake ground motions and BIGMsare applied to the building as base excitations acting in X andY directions simultaneously -e resultant response quantitycan then be evaluated as ψr

ψ2X + ψ2

Y

1113969

where ψr is theresultant value of any response quantity ψX is the value ofthe response quantity in the X direction and ψY is the valueof the response quantity in the Y direction

For the linear base isolation system laminated rubberbearing (LRB) the response of the building under bidi-rectional excitations can be obtained by evaluating the re-sponse of the building under the two components of theexcitations applied in X and Y directions without specialconsideration of the bidirectional interaction at the isolationlevel However this approach may lead to incorrect resultsfor the buildings isolated by nonlinear base isolation sys-tems When buildings isolated by nonlinear base isolatorsare subjected to bidirectional excitations the force that isacting on the base isolators is derived from the excitationsacting in both X and Y directions -erefore when theresultant force in the isolator equals the yield force thepostyield behavior of the isolation system is activated

-eX andY components of the yield strength of the isolatorare influenced by relative magnitudes of the isolator forces in Xand Y directions-e relationship between the normalized yieldstrength (F0) the normalized yield strength in the X direction(FX

0 ) and the normalized yield strength in theY direction (FY0 )

is given as (F0)2 (FX

0 )2 + (FY0 )2 -e graphical representa-

tion of relationship between FX0 FY

0 and F0 is depicted inFigure 4 as a function of the angle (direction) of the resultantisolator force measured from the X-axis (φ)

Table 2 Details of the six bidirectional earthquake ground motions used in the study

Sl no Earthquake event Date of event Rrup (km) Record (NFFF) Notation Component Direction PGA (g)

1 Imperial Valley Oct 15 1979 395 Array 5 (NF) IV1979 Normal (N) X 037Parallel (P) Y 055

2 Loma Prieta Oct 18 1989 388 LGPC (NF) LP1989 Normal (N) X 057Parallel (P) Y 061

3 Northridge Jan 17 1994 530 Sylmar (NF) NR1994 Normal (N) X 073Parallel (P) Y 059

4 Imperial Valley Oct 15 1979 2203 Delta (FF) IV1979F Normal (N) X 024Parallel (P) Y 035

5 Loma Prieta Oct 18 1989 2482 HDA (FF) LP1989F Normal (N) X 027Parallel (P) Y 028

6 Northridge Jan 17 1994 2341 Century City (FF) NR1994F Normal (N) X 026Parallel (P) Y 022


0 5 10 15 20 25

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)

BIGM Q = 75t θ = 30degBIGM Q = 75t θ = 45deg

000 003 006 009 012 015


Time (s)

BIGM

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40

0 5 10 15 20 25

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

000 003 006 009 012 0150

5

10

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)

BIGM

Time (s)

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40Time (s) Time (s)

Gro

und

acce

lera

tion

in th

e X d

irect

ion

xg (g)

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

0

5

10

Gro

und

acce

lera

tion

in th

e Y d

irect

ion

y g (g

)

Figure 2 Time histories of NF earthquakes FF earthquakes and BIGMs used in the study


If the response of the building is evaluated inde-pendently for excitations acting in X and Y directions itresults in neglecting the effect of the bidirectional in-teraction For example the response of a four-storybuilding with a fixed-base fundamental time period (T) of04 s and a superstructure damping ratio (ξs) of 005isolated by the FPS is presented in Figures 5 and 6 InFigure 5 the time histories of the top floor acceleration ofthe four-story building isolated by the FPS (Tb 25 s andμb 01) with and without the consideration of bidirec-tional interaction are presented Furthermore the force-deformation plots of the FPS with and without theconsideration of bidirectional interaction under (a)LP1989 (b) LP1989F and (c) BIGM Q 75 t and θ 30degare shown in Figure 6 -e time history plots and theforce-deformation behavior depicted in Figures 5 and 6

show that the response obtained with and without theconsideration of the bidirectional interaction are sig-nificantly different

-erefore a detailed comparative study is conducted fordetermining the degree to which the values of the differentresponse quantities of base-isolated buildings are influenced dueto the bidirectional interaction -e response quantities of thebuildings isolated by theN-Z system PF system FPS andR-FBIare studied under various bidirectional base excitationswith andwithout the consideration of the bidirectional interaction -epercentage variation between the response quantities of thebuilding with and without the consideration of the bidirectionalinteraction is evaluated as

Δψ ψInt minus ψNoInt( 1113857

ψNoInttimes 100 (9)

0 5 10 15 20 250000

0025

0050

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

Four

ier a

mpl

itude

(g)

X direction

Frequency (Hz)0 5 10 15 20 25

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

0000

0025

0050

Four

ier a

mpl

itude

(g)

Y direction

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25

IV1979F (FF)LP1989F (FF)

NR1994F (FF)

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

Figure 3 Fourier spectra of NF earthquakes FF earthquakes and BIGMs used in the study


where Δψ is the percentage difference in a response quantityψNoInt is the peak value of the resultant response quantitywhen the bidirectional interaction is not considered and ψIntis the peak value of the resultant response quantity when thebidirectional interaction is considered

-e values of Δψ corresponding to the resultant top flooracceleration resultant isolator displacement and resultant baseshear of the four-story building equipped with four nonlinearisolators underNF earthquakes FF earthquakes andBIGMs arepresented in Figure 7 It is shown in the figure that for all casesthe resultant top floor acceleration and the resultant base shearare overestimated if the bidirectional interaction is neglectedOn the contrary the neglection of the bidirectional interaction isobserved to result in the underestimation of the resultantisolator displacement response -e underestimation andoverestimation of the response quantities arise because of themodeling approach that neglects the bidirectional interactionWhen the bidirectional interaction is neglected the isolationsystem is modeled in a way such that the postyield behavior isexhibited at a larger value of the normalized resultant isolatorforce than that of the case where the bidirectional interaction isconsidered -is results in the modeling of the isolation systemwith increased initial stiffness and reduced flexibility underbidirectional excitations Consequently a smaller value of re-sultant isolator displacement and larger values of resultant topfloor acceleration and resultant base shear are obtained for thecase where the bidirectional interaction is not considered

-e extent of the overestimation and underestimation ofthe response quantities varies depending on the excitationand the isolation system For NF earthquake ground mo-tions the neglection of the bidirectional interaction resultsin the overestimation of the resultant top floor acceleration

and the resultant base shear by up to 445 and 319respectively On the contrary the resultant isolator dis-placement is underestimated by up to 32 For FF earth-quakes the neglection of the bidirectional interactionresulted in the overestimation of the resultant top flooracceleration and the resultant base shear by up to 316 and335 respectively Also the resultant isolator displacementis underestimated by up to 812 -e resultant top flooracceleration and the resultant base shear are overestimatedby up to 293 due to the neglection of the bidirectionalinteraction for the base-isolated buildings exposed toBIGMs Furthermore the resultant isolator displacement isunderestimated by up to 276 Consequently it can beconcluded that when the bidirectional interaction isneglected the resultant top floor acceleration and resultantbase shear are overestimated and the resultant isolatordisplacement is underestimated considerably under all threetypes of excitations -is influences the multihazard re-sponse of the base-isolated buildings significantly-ereforethe bidirectional interaction should be considered to capturethe behavior of base-isolated buildings under bidirectionalNF earthquakes FF earthquakes and BIGMs with adequateaccuracy

33 Multihazard Response of Base-Isolated Buildings underBidirectional Excitations Four-story base-isolated buildingsare studied under NF earthquakes FF earthquakes andBIGMs to understand the effect of the various base isolationsystems on the behavior of the buildings under multihazardloading -e base-isolated buildings are subjected to bidi-rectional excitations and their response quantities in X and

X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg

Figure 4-e relationship between the normalized yield strength of the isolator (F0) and its components in X and Y directions (FX0 and FY

0 respectively) for different directions (angle φ measured from the X-axis) of the resultant isolator force


Y directions and the resultant response quantities are in-vestigated considering the bidirectional interaction

331 Response of the Building Isolated by the N-Z System-e trends of the peak values of the X component Ycomponent and resultant response quantities (top flooracceleration and isolator displacement) of a four-storybuilding equipped with the N-Z system are presented inFigure 8 -e fixed-base fundamental time period (T) of thefour-story building used in this investigation is 04 s whereasa superstructure damping ratio (ξs) of 005 is considered-e isolation time period (Tb) of 25 s yield displacement(q) of 25 cm and isolation damping ratio (ξb) of 0075 areused Moreover the normalized yield strength (F0) of theN-Z system varied from 0025 to 02

-e results presented in Figure 8 depict the influence ofthe normalized yield strength (F0) of the N-Z system on theresponse quantities of the base-isolated building under NFearthquakes FF earthquakes and BIGMs For NF earth-quakes and FF earthquakes the average trends of the

absolute top floor acceleration and the isolator displacementare also presented in the figure -e values of the responsequantities for the fixed-base building are also presented forcomparison For all three types of excitations the absolutetop floor acceleration response of the building in X Y andresultant directions show a considerable reduction ascompared to the fixed-base response (FBR) -is reductionhighlights the benefit of base isolation in suppressing theundesirable effect of NF earthquakes FF earthquakes andBIGMs

-e bidirectional response of the base-isolatedbuilding under BIGMs with different values of equivalentTNT charge weight (Q) and the angle of attack (θ) is alsopresented -e influence of Q on the response quantitiesis observed from the results obtained for BIGMs with a30deg angle of attack and equivalent TNT charge weight (Q)values of 50 t 75 t and 100 t As expected the responsequantities are observed to be more for the higher value ofTNTcharge weight In addition the influence of the angleof attack is studied by taking BIGMs with 75 t equivalent

ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )

With bidirectional interactionWithout bidirectional interaction

0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4

BIGM Q = 75t θ = 30deg

0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )

FPS Tb = 25s microb = 01


Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4

Figure 5 Top floor acceleration response history of a four-story base-isolated building with and without the consideration of bidirectionalinteraction


TNTcharge weight and angle of attack (θ) values of 0deg 15deg30deg and 45deg As the angle of attack increases the responsein the Y direction is observed to be increasing and thesame in the X direction is observed to be decreasing -isis primarily because the building is symmetrical about Xand Y axes and the component of BIGM along the Ydirection increases with an increasing angle of attack -eresults presented in Figure 8 show that the top flooracceleration and isolator displacement response

quantities show a similar trend for different values ofequivalent the TNT charge weight and angle of attackAlso for the four-story building with similar propertiesin the X and Y directions the resultant value of the re-sponse quantities under BIGMs having different values ofthe angle of attack are found to be the same In additionan increase in the normalized yield strength results in adecreasing trend of the resultant isolator displacementfor the base-isolated buildings under all three types of

ndash24 ndash12 0 12 24

ndash02

ndash01

00

01

02

With bidirectional interactionWithout interaction

FX bW

t

xb (cm)ndash24 ndash12 0 12 24



ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)

FPS Tb = 25s μb = 01

LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)

Figure 6 Force-deformation curve of the FPS system with and without the consideration of bidirectional interaction


excitations On the contrary the resultant top floor ac-celeration increases with the normalized yield strengthfor the base-isolated buildings under FF earthquake andBIGM Furthermore NF earthquakes result in an initialreduction of the resultant top floor acceleration up to acertain value of the normalized yield strength of theisolator and further increment of the normalized yieldstrength results in an increasing trend of the top flooracceleration

To investigate the behavior of the base-isolated buildingsfurther under the multihazard scenario of earthquake andBIGM the top floor acceleration top floor displacementisolator displacement normalized base shear total super-structure drift ratio and maximum interstory drift ratio areevaluated under bidirectional NF earthquakes FF earth-quakes and BIGMs -e X Y and resultant components ofthe response quantities are assessed for the buildingsequipped with the N-Z system LRB PF system FPS and

Top floor absolute accelerationIsolator displacementBase shear

ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3

IV1979 LP1989 NR1994 IV1979 LP1989 NR1994 IV1979 LP1989 NR1994 IV1979 LP1989 NR1994ndash60

ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF

IV1979F LP1989F NR1994F IV1979F LP1989F NR1994F IV1979F LP1989F NR1994F IV1979F LP1989F NR1994FR-FBIFPS

FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40

60 PF μb = 0075N-Z Ts = 25s q = 25cm FPS Tb = 25s μb = 01 R-FBI Tb = 25s μb = 01ξb = 005F0 = 01 q = 0075

BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF

Isolation system and ground motion

Figure 7 -e effect of bidirectional interaction on the top floor acceleration isolator displacement and base shear response underearthquake and blast-induced ground motions


2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45

X direction Y direction Resultant

FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued


R-FBI under multiple hazards -e average values of theresponse quantities obtained under IV1979 LP1989 andNR1994 earthquake ground motions are taken to obtainrepresentative trends for the NF earthquake case Similarlythe average values of the response quantities obtained underIV1979F LP1989F and NR1994F earthquake ground mo-tions are taken to obtain representative trends for the FFearthquake case -e average response trends are obtainedfor the buildings isolated by the five base isolation systemsunder NF and FF earthquakes which are then comparedwith the response trends obtained for the base-isolatedbuildings subjected to BIGM

-e comparison of the performance of the N-Z system(Tb 25 s and q 25 cm) under NF earthquake FF earth-quake and BIGM is depicted in Figure 9 for the four-storybuilding (T 04 s and ξs 005) -e effect of the normalizedyield strength (F0) of the N-Z system on the resultant top flooracceleration (euroσN) resultant top floor displacement (σN) re-sultant isolator displacement (σb) resultant normalized baseshear (Vn

σ) resultant total superstructure drift ratio (Δσtotal) andresultant maximum interstory drift ratio (Max(Δσj )) is pre-sented-e trends of the six response quantities obtained for theN-Z system with different isolation damping ratio (ξb) valuesare similar For all three types of excitations the resultant topfloor displacement and resultant isolator displacement areobserved to show reduction as the value of the normalized yieldstrength of the N-Z system (F0) increases On the contrary theinfluence of the normalized yield strength on the resultant topfloor acceleration resultant normalized base shear resultanttotal superstructure drift ratio and resultant maximum inter-story drift ratio is found to be different under NF earthquakesFF earthquakes and BIGMs For the base-isolated buildingunder NF earthquakes an increase in the normalized yieldstrength of the N-Z system results in an initial reduction of thefour response quantities However an increase inF0 beyond the

value of about 013 results in an upsurge of the values of theresultant top floor acceleration resultant normalized base shearresultant total superstructure drift ratio and resultant maxi-mum interstory drift ratio For the base-isolated buildingsubjected to FF earthquake ground motions an increase in theF0 typically results in an increment of euroσN Vn

σ Δσtotal and

Max(Δσj ) except for a relatively flat trend for small values of F0(up to 0065) with isolation damping ratio ξb of 005 and 0075Furthermore BIGM results in consistent increasing trends ofeuroσN Vn

σ Δσtotal and Max(Δσj ) for an increase in F0

332 Response of the Building Isolated by LRB -e behaviorof the building isolated by LRB under the three types ofexcitations is assessed considering different values of theisolation time period (Tb) and isolation damping ratio (ξb)-e isolation damping ratio varied from 0025 to 025whereas four different values of the isolation time period (2 s25 s 3 s and 35 s) are considered -e influence of theisolation damping ratio on the response quantities of thefour-story base-isolated building for the three types of ex-citations is depicted in Figure 10 -e trends of the resultanttop floor acceleration resultant top floor displacementresultant isolator displacement resultant normalized baseshear resultant total superstructure drift ratio and resultantmaximum interstory drift ratio observed under earthquakeexcitation for an increase in the isolation damping ratio aresimilar -e values of the six response quantities reduce withan increase in the isolation damping ratio both under NFand FF earthquakes For the building subjected to BIGM theresultant normalized base shear resultant total super-structure drift ratio and resultant maximum interstory driftratio show a relatively flat trend with an increase in theisolation damping ratio On the contrary an increase in theisolation damping ratio results in the reduction of the

2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 30degθ = 45deg



005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)

θ = 0deg | θ = 15deg | θ = 30deg | θ = 45deg

Figure 8 -e response of a four-story building isolated by the N-Z system under NF earthquakes FF earthquakes and BIGMs


resultant top floor displacement and resultant isolator dis-placement whereas the resultant top floor acceleration in-creases with an increase in the isolation damping ratio

333 Response of the Building Isolated by the PF System-e performance of the PF system under NF earthquakeFF earthquake and BIGM is evaluated by varying thefriction coefficient of the isolation system (μb) from 0025to 025 -e influence of the friction coefficient of theisolation system on the response quantities of the four-story base-isolated building under the three types ofexcitations is presented in Figure 11 -e results plotted

in the figure show that the trends of the six responsequantities are similar for NF earthquakes FF earth-quakes and BIGMs For all the three types of excitationsthe top floor displacement and isolator displacementshow a decreasing trend for an increase in the frictioncoefficient Moreover as the friction coefficient of the PFsystem increases the top floor acceleration base sheartotal superstructure drift ratio and maximum interstorydrift ratio increase Also the comparison of the residualresultant isolator displacements of the building equippedwith the PF system to that of the other isolation systems ispresented in Table 3 Because the pure friction systemlacks restoring capacity the building isolated by the PF

2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472

BIGM (Q = 75 t θ = 30deg)FF earthquake (average)NF earthquake (average)

FBR 859 FBR 3208 N-Z

Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125

Figure 9 -e effect of the normalized yield strength (F0) and the isolation damping ratio (ξb) on the response of a four-story buildingisolated by the N-Z system under earthquake and BIGM


system is observed to be prone to large residual dis-placements under the three types of excitations

334 Response of the Building Isolated by the FPS -ebehavior of the four-story building isolated by the FPSunder the independent multihazard scenario of earth-quake and BIGM is presented in Figure 12 -e isolationtime period (Tb) values of 2 s 25 s 3 s and 35 s areconsidered for the FPS whereas the coefficient of frictionof the isolation system (μb) is varied from 0025 to 025For small values of the friction coefficient of the FPS (ieapproximately up to μb 0075) the resultant top flooracceleration shows small reduction for an increase in μb

under NF earthquakes whereas the resultant top flooracceleration exhibits an increasing trend for an increase

in the friction coefficient of the FPS beyond 0075 UnderFF earthquake and BIGM the resultant top floor accel-eration shows a steady increase with an increase in μb Anincrease in the friction coefficient of the FPS affects theresultant top floor displacement and resultant isolatordisplacement similarly Both the response quantitiesreduce with an increase in the friction coefficient underNF earthquake FF earthquake and BIGM Under NFearthquake the resultant normalized base shear resul-tant total superstructure drift ratio and resultant max-imum interstory drift ratio initially reduce with anincrease in the friction coefficient of the isolator and aftera certain value of μb the three response quantities start toshow an increasing trend For FF earthquake the threeresponse quantities show a small reduction for smallvalues of the friction coefficient of the FPS (μb le 005) For

2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03

BIGM (Q = 75t θ = 30deg)FF earthquake (average)

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

NF earthquake (average)

FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ

Figure 10-e effect of the isolation damping ratio (ξb) and the isolation time period (Tb) on the response of a four-story building isolatedby LRB under earthquake and BIGM


friction coefficient values beyond 005 the trends arereversed and the three response quantities increase withan increase in μb Moreover an increase in μb results in aconsistent increment of the resultant normalized baseshear resultant total superstructure drift ratio andresultant maximum interstory drift ratio of thebase-isolated building under BIGM

335 Response of the Building Isolated by the R-FBI -eperformance of the four-story building equippedwith the R-FBIunderNF earthquake FF earthquake and BIGM is portrayed inFigure 13 -e isolation time period (Tb) of the R-FBI is takenas 25 s the isolation damping ratio (ξb) values of 005 007501 0125 and 015 are considered and the coefficient of frictionof the isolation system (μb) is varied from 0025 to 02 -eoverall behavior of the building isolated by the R-FBI is similarto that of the building equipped with the FPS except for a smalldifference in the trends of the resultant normalized base shearresultant total superstructure drift ratio and resultant

maximum interstory drift ratio under FF earthquakes For thebuilding equipped with the R-FBI subjected to FF earthquakesan increase in the friction coefficient of the isolation systemresults in a consistent increment of the resultant normalizedbase shear resultant total superstructure drift ratio and re-sultant maximum interstory drift ratio

For the building subjected to NF earthquakes the topfloor displacement isolator displacement normalizedbase shear total superstructure drift ratio and maximuminterstory drift ratio are influenced significantly by thedamping ratio of the R-FBI For small values of thefriction coefficient of the isolator a larger isolationdamping ratio results in smaller values of the five re-sponse quantities However as the friction coefficient ofthe R-FBI increases the influence of the damping ratio ofthe isolation system diminishes Moreover the effect ofthe damping ratio of the R-FBI on the top floor accel-eration is less under NF earthquakes irrespective of thevalue of the friction coefficient Under FF earthquakesthe top floor acceleration normalized base shear total

0

5

10

0

5

10

0

5

10

BIGM (Q = 75t θ = 30deg)FF earthquake (average)NF earthquake (average)

FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02

FBR 097 FBR 035 FBR 065Max

(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb

Figure 11 -e response of a four-story building T 04 s ξs 005 isolated by the PF system under NF earthquake FF earthquake andBIGM


4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065

FBR 056FBR 025FBR 069

FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)

Figure 12-e effect of the friction coefficient of the isolator (μb) and the isolation time period (Tb) on the response of a four-story buildingisolated by the FPS under earthquake and BIGM

Table 3 Residual resultant isolator displacements of four-story base-isolated buildings under NF earthquakes FF earthquakes and BIGMs

Excitation

Residual resultant isolator displacement for buildings (Ts 04 s ξs 005)equipped with different isolation systems (cm)

LRB (Tb 2 s andξb 01)

N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)

FPS (Tb 2 s andμb 005)

R-FBI (Tb 2 s μb 005and ξb 01)

NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188


superstructure drift ratio and maximum interstory driftratio are not influenced significantly by the damping ratioof the R-FBI Similarly the influence of the isolationdamping on the normalized base shear and the maximuminterstory drift ratio is small for the base-isolatedbuilding under BIGM For the base-isolated building withsmall values of the friction coefficient of the R-FBI that issubjected to FF earthquakes and BIGMs the top floordisplacement and isolator displacement reduce as thedamping ratio of the isolation system increase On thecontrary the top floor acceleration and total super-structure drift ratio increase as the damping ratio in-creases for the base-isolated building under BIGM

34 Influence of Superstructure Characteristics on Perfor-mance under Multihazard Scenario -e behavior of base-isolated buildings can be influenced by the characteristics of

the superstructure such as the flexibility and damping of thesuperstructure -erefore the effect of the characteristics ofthe superstructure on the response of base-isolated buildingsis assessed under NF earthquake FF earthquake and BIGMconsidering the bidirectional interaction -e influence ofthe flexibility of the superstructure is studied by quantifyingthe different response quantities of base-isolated buildingswith different number of stories (N) ie 1 2 4 6 and 8stories-e values of the fundamental time period (T) for thefixed-base models of the buildings with 1 2 4 6 and 8stories respectively are considered as 01 s 02 s 04 s 06 sand 08 s whereas the superstructure damping ratio for allthe building models is considered to be 005 Five types ofbase isolation systems the LRB (Tb 25 s) N-Z system(Tb 25 s ξb 005 and q 25 cm) PF FPS (Tb 25 s)and R-FBI (Tb 25 s and ξb 005) are used to isolate thebuildings having different number of stories -e effect ofthe number of stories on the trends of the resultant top floor

0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020

BIGM (Q = 75t θ = 30)FF earthquake (average)NF earthquake (average)

FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005

microb microb microb

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()

Figure 13 -e effect of the friction coefficient of the isolator (μb) and the isolation damping ratio (ξb) on the response of a four-storybuilding isolated by the R-FBI system under earthquake and BIGM


acceleration and resultant isolator displacement of the base-isolated buildings under NF earthquake FF earthquake andBIGM is presented in Figure 14 Under the three types ofexcitations the trends of the resultant isolator displacementsof the buildings equipped with five base isolators are ob-served to be identical for buildings having different numberof stories Additionally similar trends of the resultant topfloor acceleration are exhibited by base-isolated buildingshaving different number of stories -ough the number ofstories of the base-isolated buildings significantly influ-ences the value of the top floor acceleration of the buildingunder NF earthquake FF earthquake and BIGM For allbase-isolated buildings under all three types of excitationsthe top floor acceleration increases with an increase in thenumber of stories Moreover the influence of the numberof stories on the top floor acceleration is found to beprominent for larger values of the damping ratio of LRBlarger values of the normalized yield strength of the N-Zsystem and larger values of the friction coefficients of thePF system FPS and R-FBI On the contrary it is observedthat the number of stories of the building typically has less

influence on the values of the isolator displacements of thebuildings isolated by the LRB N-Z system PF system FPSand R-FBI under three types of excitations

-e influence of the relative flexibility of the super-structure in X and Y directions is also studied -e ratio ofthe lateral stiffness of the columns of each story of thebuilding in the Y direction to that of the X direction(kjYkjX) values of 1 12 14 16 and 18 is considered Afour-story base-isolated building with a fixed-base funda-mental time period of 04 s in the X direction is studied byusing the different values of kjYkjX under the multihazardscenario of earthquakes (NF earthquake and FF earthquake)and BIGMs-e trends of the resultant top floor accelerationand resultant isolator displacement of four-story base-iso-lated buildings with different values of kjYkjX are depictedin Figure 15-e figure shows that the values of the resultantisolator displacements are not influenced significantly bykjYkjX for the buildings isolated by the LRB N-Z systemPF system FPS and R-FBI under three types of excitationsAlso a larger value of kjYkjX is observed to result in areduced value of resultant top floor acceleration especially

0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s

R-FBI Tb = 25sξb = 005

ξb F0 μb μb μb

Figure 14 -e effect of the number of stories on the top floor acceleration and isolator displacement of base-isolated buildings under NFearthquake FF earthquake and BIGM


for the buildings subjected to BIGM However the trends ofthe resultant top floor acceleration and the resultant isolatordisplacement obtained for different values of kjYkjX are thesame -erefore it can be concluded that the relative flex-ibility of the superstructure in X and Y directions does notinfluence the behavior of the symmetrical building under NFearthquakes FF earthquakes and BIGMs

-e effect of the damping of the superstructure isevaluated by investigating the response of the four-storybase-isolated building considering ξs values of 2 355 65 and 8 It may be worth mentioning that smallstructural damping ratio (ie 2 or 35) may not befeasible for fixed-base multistory buildings when nonlineardeformation is considered However for base-isolatedbuildings small values of superstructure damping canreasonably be considered because the superstructure is

prominently expected to behave elastically -e resultanttop floor acceleration and resultant isolator displacementof the building isolated by the LRB N-Z system PF systemFPS and R-FBI under NF earthquake FF earthquake andBIGM are obtained and the trends are plotted in Figure 16It is observed that superstructure damping does not affectthe trends of the resultant top floor acceleration and re-sultant isolator displacement of the buildings isolated byfour base isolation systems Additionally it is observed thatthe superstructure damping ratio does not influence thevalue of the isolator displacement for the buildings isolatedby five base isolation systems under all three types ofdynamic base excitations However although the trends ofthe top floor acceleration are the same the results presentedin Figure 16 show that a larger superstructure dampingratio typically results in a smaller value of top floor

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t

kjYkjX = 1kjYkjX = 12kjYkjX = 14

kjYkjX = 16kjYkjX = 18

4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s

R-FBITb = 25sξb = 005

ξb F0 μb μb μb

Figure 15 -e effect of kjYkjX on the response of four-story base-isolated buildings under NF earthquake FF earthquake and BIGM


acceleration-erefore based on the observations it can beconcluded that the superstructure characteristics have lessinfluence on the behavior of the base-isolated buildingsunder the multihazard loading scenario of earthquakes (NFearthquakes and FF earthquakes) and BIGMs as comparedto the properties of the base isolators

4 Conclusions

-is study presents an investigation of the behavior of multi-story buildings isolated by various types of elastomeric andsliding base isolation systems under multihazard loading -emultihazard scenario of earthquakes (near-fault and far-faultearthquake) and blast-induced ground motion (BIGM) isconsidered wherein the bidirectional effects of the hazards aretaken into account -e influence of the selection of differentvalues of the parameters of isolators on the key responsequantities of the buildings such as the top floor acceleration topfloor displacement isolator displacement base shear interstorydrift ratio and total superstructure drift ratio are assessed underthe multihazard scenario Furthermore the influence of the

properties of the superstructure (superstructure flexibility andsuperstructure damping ratio) on the behavior of the base-isolated buildings under multihazard loading is assessed Basedon the findings of the extensive numerical studies it is con-cluded that base-isolated buildings behave differently under thenear-fault earthquake far-fault earthquake and blast-inducedground motion Consequently the design of the isolationsystems and the selection of suitable parameters thereof shall bedone cautiously accounting for the effects of both types ofhazards considered on the buildings-e specific conclusions ofthe study are listed as follows

(1) Although the base isolation technology can help inprotecting buildings from three types of dynamicbase excitations (NF earthquakes FF earthquakesand BIGMs) the base-isolated buildings behavedifferently under different multiple hazards

(2) -e response quantities of the base-isolated build-ings obtained with and without the consideration ofbidirectional interaction are significantly different-e resultant isolator displacement is

1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake

LRB Tb = 25s N-Z q = 25cmTb = 25s ξb = 005

PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100

Figure 16 -e effect of the superstructure damping on the response of the four-story base-isolated buildings under NF earthquake FFearthquake and BIGM


underestimated and the resultant top floor accel-eration and resultant base shear are overestimatedwhen the bidirectional interaction is neglected

(3) For the building isolated by LRB an increase in ξb

results in the reduction of all the six responsequantities of the building under NF and FF earth-quakes However the acceleration response increaseswith ξb for the building subjected to BIGM

(4) For the N-Z system an increase in F0 results in aninitial reduction followed by an increase in the topfloor acceleration base shear interstory drift andtotal superstructure drift of the base-isolatedbuilding under NF earthquakes On the contrary allthe four response quantities consistently increasewith F0 for BIGM

(5) -e trends of the response quantities of the buildingisolated by the PF system observed under NFearthquakes FF earthquakes and BIGMs are similar

(6) For the buildings isolated by the FPS and R-FBI thetrends of the top floor displacement and the isolatordisplacement show a reducing trend for an increasein the value of μb under NF earthquakes FFearthquakes and BIGMs However the influence ofthe friction coefficient of the FPS on the trends of thetop floor acceleration base shear interstory driftand total superstructure drift is different for the threetypes of excitations

(7) Under NF earthquakes FF earthquakes and BIGMsthe trends of the top floor acceleration and theisolator displacement are similar for the base-iso-lated buildings with different number of stories (ieN 1 2 4 6 8) Furthermore the relative flexibilityof the superstructure in X and Y directions does notinfluence the behavior of the building for all threetypes of dynamic base excitations NF earthquakesFF earthquakes and BIGMs

(8) Superstructure damping does not influence thetrends of the top floor acceleration and the isolatordisplacement under NF earthquakes FF earth-quakes and BIGMs for the considered range ofisolator parameters

(9) -e behavior of base-isolated buildings undermultihazard loading scenario of earthquakes andBIGMs is influenced more by the properties of baseisolators as compared to that of the superstructure

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

References

[1] V A Zayas S S Low and S A Mahin ldquoA simple pendulumtechnique for achieving seismic isolationrdquo EarthquakeSpectra vol 6 no 2 pp 317ndash333 1990

[2] T T Soong and B F Spencer Jr ldquoActive semi-active andhybrid control of structuresrdquo in Proceedings of the TwelfthWorld Conference on Earthquake Engineering Auckland NewZealand February 2000

[3] M H Stanikzai S Elias V A Matsagar and A K JainldquoSeismic response control of base-isolated buildings usingmultiple tuned mass dampersrdquo Le Structural Design Of TallAnd Special Buildings vol 28 p e1576 2018

[4] R Rupakhety S Elias and S Olafsson ldquoShared tuned massdampers for mitigation of seismic poundingrdquo Applied Sci-ences vol 10 no 6 p 1918 2020

[5] J M Kelly ldquoAseismic base isolation review and bibliogra-phyrdquo Soil Dynamics and Earthquake Engineering vol 5 no 3pp 202ndash216 1986

[6] R S Jangid and T K Datta ldquoSeismic behaviour of base-isolated buildings a state-of-the art reviewrdquo inProceedings ofthe Institution of Civil Engineers-Structures and Buildingsvol 110 no 2 pp 186ndash203 1995

[7] C-M Chang and B F Spencer ldquoActive base isolation ofbuildings subjected to seismic excitationsrdquo Earthquake En-gineering amp Structural Dynamics vol 39 no 13 pp 1493ndash1512 2010

[8] Y Peng L Ding and J Chen ldquoPerformance evaluation ofbase-isolated structures with sliding hydromagnetic bear-ingsrdquo Structural Control and Health Monitoring vol 26 no 1p e2278 2018

[9] R Rabiee and Y Chae ldquoAdaptive base isolation system toachieve structural resiliency under both short- and long-periodearthquake ground motionsrdquo Journal of Intelligent MaterialSystems and Structures vol 30 no 1 pp 16ndash31 2018

[10] Y Peng and T Huang ldquoSliding implant-magnetic bearing foradaptive seismic mitigation of base-isolated structuresrdquoStructural Control and Health Monitoring vol 26 no 102019

[11] P Gardoni C Murphy and A Rowell Risk Analysis ofNatural Hazards Interdisciplinary Challenges and IntegratedSolutions Springer Berlin Germany 2016

[12] P Gardoni and J M LaFave Multi-Hazard Approaches toCivil Infrastructure Engineering Springer Berlin Germany2016

[13] T B Messervey D Zangani and S Casciati ldquoSmart high-performance materials for the multi-hazard protection of civilinfrastructurerdquo Safety And Security Engineering III vol 1082009

[14] H Mahmoud and A Chulahwat ldquoMulti-hazard multi-ob-jective optimization of building systems with isolated floorsunder seismic and wind demandsrdquo In P Gardoni J LaFave(eds) Multi-hazard Approaches to Civil Infrastructure En-gineering Springer Cham Switzerland 2016

[15] I Venanzi O Lavan L Ierimonti and S Fabrizi ldquoMulti-hazard loss analysis of tall buildings under wind and seismicloadsrdquo Structure and Infrastructure Engineering vol 14no 10 pp 1295ndash1311 2018

[16] T Roy and V Matsagar ldquoEffectiveness of passive responsecontrol devices in buildings under earthquake and windduring design liferdquo Structure and Infrastructure Engineeringvol 15 no 2 pp 252ndash268 2019


[17] T Roy and V Matsagar ldquoProbabilistic assessment of steelbuildings installed with passive control devices under multi-hazard scenario of earthquake and windrdquo Structural Safetyvol 85 p 101955 2020

[18] P Henderson and M Novak ldquoResponse of base-isolatedbuildings to wind loadingrdquo Earthquake Engineering ampStructural Dynamics vol 18 no 8 pp 1201ndash1217 1989

[19] P Henderson and M Novak ldquoWind effects on base isolatedbuildingsrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 36 no 1ndash3 pp 559ndash569 1990

[20] Y Chen and G Ahmadi ldquoWind effects on base-isolatedstructuresrdquo Journal of Engineering Mechanics vol 118 no 8pp 1708ndash1727 1992

[21] A Kareem ldquoModelling of base-isolated buildings with passivedampers under windsrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 72 pp 323ndash333 1997

[22] B Liang X Shishu and T Jiaxiang ldquoWind effects on hab-itability of base-isolated buildingsrdquo Journal of Wind Engi-neering and Industrial Aerodynamics vol 90 no 12ndash15pp 1951ndash1958 2002

[23] C Feng and X Chen ldquoEvaluation and characterization ofprobabilistic alongwind and crosswind responses of base-isolated tall buildingsrdquo Journal of Engineering Mechanicsvol 145 no 12 Article ID 04019097 2019

[24] R Zhang and B M Phillips ldquoNumerical study on the benefitsof base isolation for blast loadingrdquo in Joint 6th InternationalConference on Advances in Experimental Structural Engi-neering (6AESE) and 11th International Workshop on Ad-vanced Smart Materials and Smart Structures Technology(11ANCRiSST) Champaign IL USA August 2015

[25] R Zhang and B M Phillips ldquoPerformance and protection ofbase-isolated structures under blast loadingrdquo Journal of En-gineeringMechanics vol 142 no 1 Article ID 04015063 2016

[26] M Z Kangda and S Bakre ldquoPositive-phase blast effects onbase-isolated structuresrdquo Arabian Journal for Science andEngineering vol 44 no 5 pp 4971ndash4992 2018

[27] P D Mondal A D Ghosh and S Chakraborty ldquoPerfor-mance of N-Z base isolation system for structures subject tounderground blastrdquo inProceedings Of the InternationalSymposium On Engineering under Uncertainty Safety As-sessment And Management (ISEUSAM-2012) Springer Ber-lin Germany pp 1007ndash1020 2012

[28] P D Mondal A D Ghosh and S Chakraborty ldquoPerfor-mance of N-Z systems in the mitigation of underground blastinduced vibration of structuresrdquo Journal of Vibration andControl vol 20 no 13 pp 2019ndash2031 2013

[29] P D Mondal A D Ghosh and S Chakraborty ldquoControl ofunderground blast-induced building vibration by shape-memory-alloy rubber bearing (SMARB)rdquo Structural Controland Health Monitoring vol 24 no 10 p e1983 2017

[30] P D Mondal A D Ghosh and S Chakraborty ldquoPerfor-mances of various base isolation systems in mitigation ofstructural vibration due to underground blast induced groundmotionrdquo International Journal of Structural Stability andDynamics vol 17 no 4 p 1750043 2017

[31] J P Talbot and H E M Hunt ldquoIsolation of buildings fromrail-tunnel vibration a reviewrdquo Building Acoustics vol 10no 3 pp 177ndash192 2003

[32] L S Wei and F L Zhou ldquoVibration and seismic isolationdesign for buildings on subway platformrdquo in Proceedings ofthe Fourteenth World Conference on Earthquake EngineeringBeijing China October 2008

[33] DMakovicka andDMakovicka ldquoStructure isolation in orderto reduce vibration transfer from the subsoilrdquo International

Journal of Computational Methods and Experimental Mea-surements vol 2 no 1 pp 1ndash13 2014

[34] Y K Wen ldquoMethod for random vibrations of hystereticsystemsrdquo Journal of the Engineering Mechanics Divisionvol 102 no 2 pp 249ndash263 1976

[35] Y K Wen ldquoMethods of random vibration for inelasticstructuresrdquo Applied Mechanics Reviews vol 42 no 2pp 39ndash52 1989

[36] Y J Park Y K Wen and A H-S Ang ldquoRandom vibration ofhysteretic systems under Bi-directional ground motionsrdquoEarthquake Engineering amp Structural Dynamics vol 14 no 4pp 543ndash557 1986

[37] V A Matsagar and R S Jangid ldquoViscoelastic damper con-nected to adjacent structures involving seismic isolationrdquoJournal of Civil Engineering and Management vol 11 no 4pp 309ndash322 2005

[38] R S Jangid ldquoComputational numerical models for seismicresponse of structures isolated by sliding systemsrdquo StructuralControl and Health Monitoring vol 12 no 1 pp 117ndash1372005

[39] R S Jangid ldquoOptimum lead-rubber isolation bearings fornear-fault motionsrdquo Engineering Structures vol 29 no 10pp 2503ndash2513 2007

[40] E M L Carvalho and R C Battista ldquoBlast-induced vibrationsin urban residential buildingsrdquo inProceedings of the Institutionof Civil Engineers-Structures and Buildings vol 156 no 3pp 243ndash253 2003

[41] C Wu and H Hao ldquoNumerical study of characteristics ofunderground blast induced surface ground motion and theireffect on above-ground structures Part I Ground motioncharacteristicsrdquo Soil Dynamics and Earthquake Engineeringvol 25 no 1 pp 39ndash53 2005


devoted on research and development to understand thebehavior of structures under multiple hazards and to devisedesign strategies thereof Additionally the risk associatedwith the reduced safety and serviceability of key infra-structures categorized as lifeline structures such as hos-pitals bridges power plants data centers andcommunication centers is paramount -erefore it iscrucial to design structures especially the critical infra-structures by considering all the hazards likely to affectsafety and serviceability -ere is limited research on the useof the multihazard approach in the performance assessmentand design of structures For instance Messervey et al [13]Gardoni and LaFave [12] Mahmoud and Chulahwat [14]Venanzi et al [15] and Roy and Matsagar [16 17] haveconducted studies on the multihazard protection ofstructures

Although base isolation is an effective strategy to miti-gate the adverse effects of earthquakes its efficacy in pro-tecting structures under multihazard loading is not exploredadequately Most of the studies on the base-isolated struc-tures also focus on earthquake protection and thereforethere are limited studies that are conducted on the per-formance assessment of base-isolated structures under otherhazards such as wind and blast Some of the attempts toinvestigate the behavior of base-isolated structures underwind loading include the studies conducted by Hendersonand Novak [18 19] -ey have conducted theoretical andexperimental studies to assess the response of the base-isolated buildings under wind loading wherein the theo-retical and experimental results are compared Chen andAhmadi [20] have evaluated the sensitivity of structuresisolated by the laminated rubber bearing (LRB) highdamping rubber bearing (HDRB) and resilient-rubberbearing (R-FBI) to wind loading Furthermore Kareem [21]has studied the dynamic response of base-isolated buildingswith passive dampers under wind loading Later Liang et al[22] have assessed the habitability of base-isolated buildingsunder fluctuating wind load Recently a probabilistic in-vestigation on the response of tall base-isolated buildingsunder wind loading has been reported by Feng and Chen[23]

-e response of base-isolated structures under surfaceblast has been assessed by some researchers Zhang andPhillips [24 25] have studied the performance of amultistory base-isolated building with and withoutpassive supplemental dampers in suppressing the vi-bration response of the building exposed to blast loadingAlso Kangda and Bakre [26] have assessed the responseof base-isolated structures subjected to surface blast andconcluded that base isolation could be effective inmitigating the blast response quantities such as the peakstory displacement story drift and root mean square(RMS) absolute acceleration -e performance of base-isolated buildings under blast-induced ground motion(BIGM) has also captured attention in the recent timesMondal et al [27 28] have studied the response ofbuildings isolated by lead-rubber bearing (N-Z system)under BIGM Further the performance of a base isolationsystem equipped with shape-memory alloy in protecting

buildings under BIGM has been studied by Mondal et al[29] Furthermore the use of various base isolationsystems in protecting buildings against blast-inducedground motions has been discussed by Mondal et al [30]-e findings of the investigations reveal that base iso-lation can be beneficial to control the vibration responseof buildings under blast-induced ground motions -eperformance of base isolation strategies for the vibrationresponse control of buildings under other nonseismichazards such as train-induced vibrations has also beenexplored [31ndash33] -e available limited literature on theimplementation of base isolation for the vibration re-sponse control of buildings under different types of ex-citations indicate the potential benefit of the strategy inmitigating the adverse effects of various types of hazardsNotwithstanding the vibration protection potential ofbase isolation systems base-isolated buildings could beinfluenced differently under distinct types of hazards-erefore it is necessary to consider the multihazardapproach to satisfy safety and serviceability design re-quirements for base-isolated buildings that are likely tobe subjected to different types of loading However thereare no studies which investigate the behavior of base-isolated buildings subjected to both earthquakes andblast-induced ground motions In addition the influenceof the key parameters of the base isolation systems on theefficacy of the response mitigation under the multihazardscenario of earthquake and BIGM has not been explored

-erefore it would be essential to investigate and unveilthe performance of buildings equipped with the laminatedrubber bearing (LRB) lead-rubber bearing (N-Z system)pure friction (PF) system friction pendulum system (FPS)and resilient-friction base isolator (R-FBI) under the mul-tihazard scenario of earthquake and blast-induced groundmotion Consequently the behavior of buildings equippedwith various base isolation systems is assessed under mul-tihazard loading in this paper -e main objectives of thisstudy include the following (a) to assess the performance ofbase-isolated buildings under bidirectional near-fault (NF)earthquake ground motions far-fault (FF) earthquakeground motions and blast-induced ground motions(BIGMs) (b) to evaluate the effect of the characteristicparameters of the five base isolation systems consideredherein on the behavior of base-isolated buildings underdifferent hazards and (c) to study the effect of the propertiesof the superstructure on the multihazard response of base-isolated buildings

2 Modeling of a Base-Isolated Building underBidirectional Excitation

-e schematic diagram and idealized model of the base-isolated building considered in this investigation aredepicted in Figure 1 -e three-dimensional model of thebase-isolated building portrayed in the figure shows theorientation of the building the location of the isolatorsthe superstructure properties and the base excitation-e mathematical modeling of the base-isolated building






M

mb 0 0 0

0T Ms 0T 0

0 0 mb 0

0T 0 0T Ms

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

0 c1xrb 0 0

0T Csx 0T 0

0 0 0 c1yrb

0T 0 0T Csy

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

K

0 k1xrb 0 0

0T Ksx 0T 0

0 0 0 k1yrb

0T 0 0T Ksy

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)




X xbXTs ybYT

s1113966 1113967T

_X _xb _XT

s _yb _YT

s1113882 1113883T

euroX euroxb euroXT

s euroyb euroYT

s1113882 1113883T



r

1 0 0 0

0T r 0T 0T

0 0 1 0

0T 0T 0T r

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)


T and Ys y1 y2 1113864





fbx cb _xb + kbxb



Nj1 mj is








11138681113868111386811138681113868111386811138681113868hx hx

11138681113868111386811138681113868111386811138681113868nminus1

minus τ _xb hx

11138681113868111386811138681113868111386811138681113868n (6a)


11138681113868111386811138681113868111386811138681113868hy hy

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τ _yb hy

11138681113868111386811138681113868

11138681113868111386811138681113868n (6b)


q_hx

_hy

⎧⎨

⎩

⎫⎬


11138681113868111386811138681113868111386811138681113868nminus1

minus τ hx

11138681113868111386811138681113868111386811138681113868n


11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τhxhy


11138681113868111386811138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τ hy

11138681113868111386811138681113868

11138681113868111386811138681113868n

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

_xb

_yb

1113896 1113897 (7)



Column

Base isolator

Floor slab

Base mass


middot middot

ZXY

(a)


ZXY

x b m b

x 1 m1

c 1x k 1x

x 2 m2

c 2x k 2x

x N m N

c Nx k NxyN m

N cNy kNy

y2 m2 c2y k2y

y1 m1

yb mb

c1y k1y

(b)

Z XY


(c)




3 Numerical Study







y








Superstructure





N-Z system






R-FBI







euroUg (t) minus1td

1113888 1113889 _ug eminus ttd( ) (8)


Eρ






ψ2X + ψ2

Y

1113969


















0 5 10 15 20 25

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)


000 003 006 009 012 015


Time (s)

BIGM

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40

0 5 10 15 20 25

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

000 003 006 009 012 0150

5

10

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)

BIGM

Time (s)

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40Time (s) Time (s)

Gro

und

acce

lera

tion

in th

e X d

irect

ion

xg (g)

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

0

5

10

Gro

und

acce

lera

tion

in th

e Y d

irect

ion

y g (g

)








0 5 10 15 20 250000

0025

0050

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

Four

ier a

mpl

itude

(g)

X direction

Frequency (Hz)0 5 10 15 20 25

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

0000

0025

0050

Four

ier a

mpl

itude

(g)

Y direction

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)








X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg









ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References

















































M

mb 0 0 0

0T Ms 0T 0

0 0 mb 0

0T 0 0T Ms

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

C

0 c1xrb 0 0

0T Csx 0T 0

0 0 0 c1yrb

0T 0 0T Csy

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

K

0 k1xrb 0 0

0T Ksx 0T 0

0 0 0 k1yrb

0T 0 0T Ksy

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)




X xbXTs ybYT

s1113966 1113967T

_X _xb _XT

s _yb _YT

s1113882 1113883T

euroX euroxb euroXT

s euroyb euroYT

s1113882 1113883T



r

1 0 0 0

0T r 0T 0T

0 0 1 0

0T 0T 0T r

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)


T and Ys y1 y2 1113864





fbx cb _xb + kbxb



Nj1 mj is








11138681113868111386811138681113868111386811138681113868hx hx

11138681113868111386811138681113868111386811138681113868nminus1

minus τ _xb hx

11138681113868111386811138681113868111386811138681113868n (6a)


11138681113868111386811138681113868111386811138681113868hy hy

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τ _yb hy

11138681113868111386811138681113868

11138681113868111386811138681113868n (6b)


q_hx

_hy

⎧⎨

⎩

⎫⎬


11138681113868111386811138681113868111386811138681113868nminus1

minus τ hx

11138681113868111386811138681113868111386811138681113868n


11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τhxhy


11138681113868111386811138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τ hy

11138681113868111386811138681113868

11138681113868111386811138681113868n

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

_xb

_yb

1113896 1113897 (7)



Column

Base isolator

Floor slab

Base mass


middot middot

ZXY

(a)


ZXY

x b m b

x 1 m1

c 1x k 1x

x 2 m2

c 2x k 2x

x N m N

c Nx k NxyN m

N cNy kNy

y2 m2 c2y k2y

y1 m1

yb mb

c1y k1y

(b)

Z XY


(c)




3 Numerical Study







y








Superstructure





N-Z system






R-FBI







euroUg (t) minus1td

1113888 1113889 _ug eminus ttd( ) (8)


Eρ






ψ2X + ψ2

Y

1113969


















0 5 10 15 20 25

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)


000 003 006 009 012 015


Time (s)

BIGM

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40

0 5 10 15 20 25

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

000 003 006 009 012 0150

5

10

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)

BIGM

Time (s)

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40Time (s) Time (s)

Gro

und

acce

lera

tion

in th

e X d

irect

ion

xg (g)

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

0

5

10

Gro

und

acce

lera

tion

in th

e Y d

irect

ion

y g (g

)








0 5 10 15 20 250000

0025

0050

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

Four

ier a

mpl

itude

(g)

X direction

Frequency (Hz)0 5 10 15 20 25

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

0000

0025

0050

Four

ier a

mpl

itude

(g)

Y direction

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)








X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg









ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References













































fbx cb _xb + kbxb



Nj1 mj is








11138681113868111386811138681113868111386811138681113868hx hx

11138681113868111386811138681113868111386811138681113868nminus1

minus τ _xb hx

11138681113868111386811138681113868111386811138681113868n (6a)


11138681113868111386811138681113868111386811138681113868hy hy

11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τ _yb hy

11138681113868111386811138681113868

11138681113868111386811138681113868n (6b)


q_hx

_hy

⎧⎨

⎩

⎫⎬


11138681113868111386811138681113868111386811138681113868nminus1

minus τ hx

11138681113868111386811138681113868111386811138681113868n


11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τhxhy


11138681113868111386811138681113868111386811138681113868nminus1


11138681113868111386811138681113868

11138681113868111386811138681113868nminus1

minus τ hy

11138681113868111386811138681113868

11138681113868111386811138681113868n

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

_xb

_yb

1113896 1113897 (7)



Column

Base isolator

Floor slab

Base mass


middot middot

ZXY

(a)


ZXY

x b m b

x 1 m1

c 1x k 1x

x 2 m2

c 2x k 2x

x N m N

c Nx k NxyN m

N cNy kNy

y2 m2 c2y k2y

y1 m1

yb mb

c1y k1y

(b)

Z XY


(c)




3 Numerical Study







y








Superstructure





N-Z system






R-FBI







euroUg (t) minus1td

1113888 1113889 _ug eminus ttd( ) (8)


Eρ






ψ2X + ψ2

Y

1113969


















0 5 10 15 20 25

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)


000 003 006 009 012 015


Time (s)

BIGM

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40

0 5 10 15 20 25

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

000 003 006 009 012 0150

5

10

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)

BIGM

Time (s)

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40Time (s) Time (s)

Gro

und

acce

lera

tion

in th

e X d

irect

ion

xg (g)

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

0

5

10

Gro

und

acce

lera

tion

in th

e Y d

irect

ion

y g (g

)








0 5 10 15 20 250000

0025

0050

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

Four

ier a

mpl

itude

(g)

X direction

Frequency (Hz)0 5 10 15 20 25

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

0000

0025

0050

Four

ier a

mpl

itude

(g)

Y direction

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)








X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg









ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References














































3 Numerical Study







y








Superstructure





N-Z system






R-FBI







euroUg (t) minus1td

1113888 1113889 _ug eminus ttd( ) (8)


Eρ






ψ2X + ψ2

Y

1113969


















0 5 10 15 20 25

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)


000 003 006 009 012 015


Time (s)

BIGM

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40

0 5 10 15 20 25

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

000 003 006 009 012 0150

5

10

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)

BIGM

Time (s)

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40Time (s) Time (s)

Gro

und

acce

lera

tion

in th

e X d

irect

ion

xg (g)

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

0

5

10

Gro

und

acce

lera

tion

in th

e Y d

irect

ion

y g (g

)








0 5 10 15 20 250000

0025

0050

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

Four

ier a

mpl

itude

(g)

X direction

Frequency (Hz)0 5 10 15 20 25

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

0000

0025

0050

Four

ier a

mpl

itude

(g)

Y direction

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)








X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg









ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References
















































euroUg (t) minus1td

1113888 1113889 _ug eminus ttd( ) (8)


Eρ






ψ2X + ψ2

Y

1113969


















0 5 10 15 20 25

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)


000 003 006 009 012 015


Time (s)

BIGM

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40

0 5 10 15 20 25

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

000 003 006 009 012 0150

5

10

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)

BIGM

Time (s)

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40Time (s) Time (s)

Gro

und

acce

lera

tion

in th

e X d

irect

ion

xg (g)

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

0

5

10

Gro

und

acce

lera

tion

in th

e Y d

irect

ion

y g (g

)








0 5 10 15 20 250000

0025

0050

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

Four

ier a

mpl

itude

(g)

X direction

Frequency (Hz)0 5 10 15 20 25

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

0000

0025

0050

Four

ier a

mpl

itude

(g)

Y direction

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)








X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg









ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References













































0 5 10 15 20 25

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)


000 003 006 009 012 015


Time (s)

BIGM

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40

0 5 10 15 20 25

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

000 003 006 009 012 0150

5

10

IV1979 (NF)

LP1989 (NF)

NR1994 (NF)

IV1979F (FF)

LP1989F (FF)

NR1994F (FF)

BIGM

Time (s)

Time (s)

0 5 10 15 20 25Time (s)

0 5 10 15 20 25Time (s)

0 20 40 60 80 100Time (s)

0 8 16 24 32 40Time (s)

0 8 16 24 32 40Time (s) Time (s)

Gro

und

acce

lera

tion

in th

e X d

irect

ion

xg (g)

ndash05

00

05

ndash05

00

05

ndash05

00

05

ndash03

00

03

ndash03

00

03

ndash02

00

02

0

5

10

Gro

und

acce

lera

tion

in th

e Y d

irect

ion

y g (g

)








0 5 10 15 20 250000

0025

0050

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

Four

ier a

mpl

itude

(g)

X direction

Frequency (Hz)0 5 10 15 20 25

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

0000

0025

0050

Four

ier a

mpl

itude

(g)

Y direction

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)








X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg









ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References


















































0 5 10 15 20 250000

0025

0050

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

Four

ier a

mpl

itude

(g)

X direction

Frequency (Hz)0 5 10 15 20 25

IV1979 (NF)LP1989 (NF)

NR1994 (NF)

0000

0025

0050

Four

ier a

mpl

itude

(g)

Y direction

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

0000

0005

0010

Four

ier a

mpl

itude

(g)

0 5 10 15 20 25


NR1994F (FF)

Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)

000

002

004

Four

ier a

mpl

itude

(g)

0 50 100 150 200 250


Frequency (Hz)








X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg









ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References


















































X

Yndash05ndash1

005

115

F0X

F0Y

F0

φ

330deg

300deg270deg

240deg

210deg

180deg

150deg

120deg90deg

60deg

30deg

0deg









ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References


















































ndash4

0

4

LP1989

T = 04s ξs= 005

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values361530

Time (s)


0 5 10 15 20

Peak values487551

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash4

0

4

LP1989F

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )


0 5 10 15 20

Peak values343352

Time (s)


0 5 10 15 20

Peak values405521

Time (s)

Top

floor

acce

lerat

ion

inth

e Y d

irect

ion

y N (m

s2 )

ndash4

0

4

ndash2

0

2

4


0 1 2 3 4Time (s)

Top

floor

acce

lera

tion

inth

e X d

irect

ion

xN

(ms

2 )



Peak values364411


Peak values210385

Time (s)0 1 2 3 4To

p flo

or ac

celer

atio

n in

the Y

dire

ctio

n y N

(ms2 )

ndash2

0

2

4






ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References
















































ndash02

ndash01

00

01

02


FX bW

t




ndash02

ndash01

00

01

02

FY bW

t

yb (cm)

ndash02

ndash01

00

01

02

FX bW

t



xb (cm)

LP1989Fndash02

ndash01

00

01

02

FY bW

t



yb (cm)

ndash04

ndash02

00

02

04T = 04s ξs = 005

FX bW

t



xb (cm)


LP1989ndash04

ndash02

00

02

04

FY bW

t



yb (cm)






ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References
















































ndash66

ndash16

3 ndash42

ndash16

7

ndash12

2

ndash97

ndash12

4

ndash27

8

ndash38

6

ndash11

6

ndash27

2

ndash44

5

96

10 19 10

1 146 20

5 320

140

154 22

7

144

148

ndash68

ndash75 ndash3

1

ndash26

7

ndash31

9

ndash24

7

ndash54

ndash12

6

19

ndash92

ndash12

3 ndash37

08

ndash16

2

ndash21

6

ndash16

8

ndash23

2 ndash67

ndash13

1

ndash31

6

ndash41

ndash14

0

ndash30

6

ndash36

05 16

8

ndash83

37

746 812

182

482 551

181

501 538

05

ndash85

ndash22

1

ndash16

1

ndash33

5 ndash14

9

ndash13

5

ndash16

0

ndash14

3

ndash13

8

ndash10

4

ndash14

6

ndash93

ndash10

6

ndash11

2

ndash29

3

ndash29

3

ndash29

3

ndash26

3

ndash25

3

ndash24

4

ndash29

3

ndash29

3

ndash29

3

108

89

75

276

271

271

166

129

106

276

271

271

ndash90

ndash79

ndash71

ndash29

3

ndash29

3

ndash29

3

ndash85

ndash12

9 -80

ndash29

3

ndash29

3

ndash29

3


ndash30

0

30

60

R-FBIFPS

NF earthquake

Ts = 04s ξs = 005

N-Z PF


FPS R-FBI

N-Z PF

ndash60

ndash30

0

30

60

90

FF earthquake

50t 75t 100t

ndash40

ndash20

0

20

40


BIGM

Chan

ge in

resp

onse

due

to b

idire

ctio

nal i

nter

actio

n∆ψ

()

N-Z50t 75t 100t 50t 75t 100t 50t 75t 100t

PF




2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References













































2

4

6

25

50

75

1

2

3

8

16

24

2468

1

2

3

4

246

8

15

30

45

0

10

20

15

30

45


FBR 1090 | 1656 | 2696Tb = 25s ξb= 0075 q = 25cm

FBR 1575 | 1725 | 2418T = 04s ξb = 005

NF earthquake

FBR 1820 | 2083 | 3514

FBRIV1979 | LP1989 | NR1992

N-Z

NF earthquake

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

FBR 769 | 690 | 612 FBR 719 | 974 | 543 FBR 925 | 1006 | 646

FF earthquakeFBR

IV1979F | LP1989F | NR1994F

FF earthquake

FBR 2064 | 2778 | 3430 FBR 1191 | 1604 | 1980

BIGM θ = 30deg

BIGM θ = 30deg

FBR 2383 | 3208 | 3961

FBR

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979LP1989

NR1994Average

IV1979LP1989

IV1979LP1989

NR1994Average

NR1994Average

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

Q = 50tQ = 75t

Q = 100t Q = 50tQ = 75t

Q = 50tQ = 75t

Q = 100t Q = 100t

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

IV1979FLP1989F

IV1979FLP1989F

IV1979FLP1989F

NR1994FAverage

NR1994FAverage

NR1994FAverage

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

x N (m

s2 )

x N (m

s2 )

1

2

3

y N (m

s2 )

y N (m

s2 )

1

2

3

σ N (m

s2 )

σ N (m

s2 )

x b (cm

)x b (

cm)

x b (cm

)

8

16

24

y b (cm

)y b (

cm)

8

16

24

σ b (cm

)σ b (

cm)

25

50

75

y b (cm

)

25

50

75

σ b (cm

)

2

4

6

y N (m

s2 )

2

4

6

σ N (m

s2 )

Q = 50t | Q = 75t | Q = 100t

FIGURE 8 Continued






σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References

















































σ Δσtotal and




2468

0246

10

20

30

0

10

20

30

FBR 3208 | 3098 | 2778 | 2268 FBR 0 | 830 | 1604 | 2268

BIGM Q = 75t

FBR 3208 | 3208 | 3208 | 3208

FBR

BIGM Q = 75 t

θ = 0degθ = 15deg

θ = 0degθ = 15deg

θ = 0degθ = 15deg




005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 0deg

θ = 15deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

θ = 30deg

θ = 45deg

005 010 015 020 005 010 015 020 005 010 015 020F0 F0 F0

x N (m

s2 )

y N (m

s2 )

x b (cm

)2468

10

20

30

σ N (m

s2 )

σ b (cm

)

y b (cm

)







2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References
















































2

4

6

0

2

4

0

5

10

25

50

75

0

10

20

0

25

50

25

50

75

0

10

20

0

25

50

02

03

04

00

01

02

02

03

04

01

02

003

006

009

010

015

020

005 010 015 020 005 010 015 020 005 010 015 02001

02

03

005

010

015

01

02

03

FBR 2472



Tb = 25s q = 0025mT = 04s ξs = 005

FBR 972

FBR 345 FBR 784

FBR 178

Vnσ

FBR 064

FBR 123

FBR 069

∆σto

tal (

)

FBR 025

FBR 056

FBR 097

Max

(∆jσ )

()

F0

FBR 035

F0

FBR 065

F0

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

ξb = 005ξb = 01ξb = 015

ξb = 0075ξb = 0125







2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References

















































2

4

6

1

2

3

2

4

6

40

80

120

15

30

45

20

40

60

40

80

120

15

30

45

20

40

60

02

04

06

00

01

02

01

02

01

02

003

006

009

004

008

012

005 010 015 020 025

01

02

03

005

010

015

000

015

030

03


σ N (m

s2 )

σ N (c

m)

σ b (c

m)


FBR 2472

FBR 972

FBR 069

FBR 097 FBR 035

FBR 025

FBR 178 FBR 064

FBR 345

FBR 859 FBR 3208

FBR 784

FBR 056

FBR 065

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

FBR 123

LRB

T = 04s ξs = 005

∆σ tota

l (

)M

ax(∆

σ j ) (

)

ξb005 010 015 020 025

ξb005 010 015 020 025

ξb

Vnσ







0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References

















































0

5

10

0

5

10

0

5

10


FBR 2472

FBR 859 FBR 3208

PF

T = 04s ξs = 005

σ N (m

s2 )

0

50

100

0

25

50

0

100

200FBR 972 FBR 345 FBR 784

σ N (c

m)

0

50

100

0

25

50

0

100

200

σ b (c

m)

00

01

02

03

00

01

02

03

00

01

02

03

FBR 178 FBR 064 FBR 123

Vn σ

00

01

02

00

01

02

00

01

02

FBR 069 FBR 025 FBR 056

∆σ tota

l (

)

00

01

02

00

01

02

00

01

02


(∆σ j )

()

005 010 015 020microb

005 010 015 020microb

005 010 015 020microb



4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References













































4

8

12

4

8

12

4

8

12

0

50

100

0

10

20

15

30

45

0

50

100

0

10

20

15

30

45

00

02

04

00

02

04

00

02

04

00

01

02

00

01

02

00

01

02

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04

005 010 015 020 02500

02

04


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859

FBR 3208

FPS

μb μb μb

Tb = 2s

Tb = 25s

Tb = 3s

Tb = 35s

T = 04s ξs = 005

σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vnσ

∆σ tota

l (

)M

ax(∆

σ j ) (

)



Excitation



N-Z (Tb 2 s F0 005and ξb 01)

PF(μb 005)



NFearthquake

IV1979 124 061 10250 041 056LP1989 121 091 4174 024 023NR1994 048 019 1698 038 013

FFearthquake

IV1979F 062 012 1163 062 060LP1989F 282 059 3389 007 010NR1994F 066 051 519 055 053

BIGM

Q 75 tθ 30deg 006 002 10132 226 188

Q 75 tθ 45deg 006 002 10132 226 188





0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References
















































0

5

10

25

50

75

25

50

75

01

02

03

00

01

02

005 010 015 020

01

02

03

0

5

10

0

8

16

0

8

16

01

02

03

00

01

02

01

02

03

0

5

10

15

30

45

15

30

45

01

02

03

00

01

02

01

02

03

005 010 015 020 005 010 015 020


FBR 097 FBR 035 FBR 065


FBR 178 FBR 064 FBR 123


FBR 2472 FBR 859 FBR 3208

ξb = 0075ξb = 0125

ξb = 005ξb = 01ξb = 015

R-FBI

Tb = 25sT = 04s ξs = 005


σ N (m

s2 )

σ N (c

m)

σ b (c

m)

Vn σ∆σ to

tal (

)

Max

(∆σ j )

()






0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References
















































0

5

10

0

5

10

0

5

10

0

5

10

0

5

10

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

25

50

75

100

08

16

24

0

3

6

0

3

6

0

3

6

0

3

6

0

20

40

0

15

30

0

15

30

0

15

30

0

15

30

2

4

6

0

4

8

12

0

4

8

12

0

4

8

12

0

4

8

12

005 010 015 02015

30

45

005 010 015 02015

30

45

005 010 015 0200

100

200

005 010 015 02015

30

45

005 010 015 02015

30

45

NF earthquake

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 1N = 2N = 4

N = 6N = 8

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

LRBTb = 25s

N-Z q = 25cmTb = 25s ξb = 005

FPSTb = 25s


ξb F0 μb μb μb






005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References
















































005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

NF earthquake

LRBTb = 25s

PF

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

N = 4

BIGM Q = 75t



4

6

8

50

75

100

1

2

3

10

20

30

40

2

3

4

15

30

45

σ b (c

m)

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ N (m

s2 )

4

6

8

50

75

1

2

3

0

20

0

4

8

0

4

8

0

4

8

0

4

8

15

30

45

4

6

8

50

75

2

4

6

2

4

6

2

4

6

0

20

0

100

200

4

6

8

50

75

0

20

15

30

45

4

6

8

50

25 25 25 25

75

0

10 10 10 10

20

15

30

45

N-ZTb = 25s ξb = 005q = 25cm

FPSTb = 25s


ξb F0 μb μb μb




4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References














































4 Conclusions





1

2

3

1

2

3

2

4

6

2

4

6

2

4

6

10

20

30

40

15

30

45

005 010 015 02015

30

45

005 010 015 020 005 010 015 020 005 010 015 020 005 010 015 020

σ N (m

s2 )

NF earthquake


PF FPSTb = 25s

R-FBI

Tb = 25s ξb = 005

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

σ N (m

s2 )

σ b (c

m)

NF earthquake

FF earthquake

FF earthquake

BIGM Q = 75t

BIGM Q = 75t

N = 4

ξb F0 μb μb

ξs = 2ξs = 35ξs = 5

ξs = 65ξs = 8

μb

30

45

60

25

50

75

100

0

20

0

3

6

9

0

3

6

9

0

3

6

9

0

3

6

9

15

30

45

30

45

60

25

50

75

100

0

20

0

100

200

3

6

9

25

50

75

100

0

20

15

30

45

3

6

9

25

50

75

100

0

10 10 10 10

20

15

30

45

3

6

9

25

50

75

100












Data Availability




References






















































Data Availability




References













































multihazardresponsecontrolofbase-isolated

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