vertical seismic effect on the seismic fragility of large

Research ArticleVertical Seismic Effect on the Seismic Fragility of Large-SpaceUnderground Structures

Zhiming He 12 and Qingjun Chen 12

1State Key Laboratory of Disaster Reduction in Civil Engineering Tongji University Shanghai 200092 China2Department of Structural Engineering and Disaster Reduction Tongji University Shanghai 200092 China

Correspondence should be addressed to Qingjun Chen chenqjtongjieducn

Received 18 February 2019 Revised 16 March 2019 Accepted 18 March 2019 Published 7 April 2019

Academic Editor Rosario Montuori

Copyright copy 2019 Zhiming He and Qingjun Chen is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

emeasured vertical peak ground acceleration was larger than the horizontal peak ground acceleration It is essential to considerthe vertical seismic effect in seismic fragility evaluation of large-space underground structures In this research an approach ispresented to construct fragility curves of large-space underground structures considering the vertical seismic effect In seismiccapacity the soil-underground structure pushover analysis method which considers the vertical seismic loading is used to obtainthe capacity curve of central columns e thresholds of performance levels are quantified through a load-drift backbone curvemodel In seismic demand it is evaluated through incremental dynamic analysis (IDA) method under the excitation of horizontaland vertical acceleration and the soil-structure-interaction and ground motion characteristics are also considered e IDAresults are compared in terms of peak ground acceleration and peak ground velocity To construct the fragility curves theevolutions of performance index versus the increasing earthquake intensity are performed considering related uncertainties eresult indicates that if we ignore the vertical seismic effect to the fragility assessment of large-space underground structures theexceedance probabilities of damage of large-space underground structures will be underestimated which will result in anunfavorable assessment result

1 Introduction

Large-space underground structures such as subway sta-tions commercial streets and parking lots are wildly usedurban construction measures ese structures can suffersevere damage under strong ground shaking [1 2] Espe-cially for shallow embedded structures in soft soil theirsusceptibility to damage can be increased due to groundstrain and velocity along with acceleration increase whenapproaching the ground surface [3 4] In addition for someearly built large-space underground structures they arefacing a high potential risk of seismic damage due to withoutproperly considering seismic design Consequently to en-sure the seismic safety of large-space underground struc-tures especially in seismic prone areas the seismic fragilityassessment is introduced to large-space undergroundstructures by different researchers

So far the seismic fragility studies related to large-spaceunderground structures are conducted in different per-spectives Li et al [5] used the pushover analysis methodapplicable for underground structures to investigate thevulnerability of Daikai subway station In this process theseismic demand calculated from pushover analysis methodcannot consider the soil-structure-interaction and the fre-quency characters of ground motion Liu et al [6] in-vestigated the vulnerability of Daikai subway station basedon the full dynamic numerical analysis e performancelevels thresholds of aboveground structures were directlyapplied to underground subway station Due to the geo-metric feature and the character which undergroundstructures are buried and restrained by surrounding soil[7 8] their seismic behavior and performance are highlydistinct en Huh et al [9] investigated the vulnerability ofa shallow double story underground RC box structure based

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 9650294 17 pageshttpsdoiorg10115520199650294

on the ground response acceleration method e perfor-mance levels thresholds of structures were defined throughthe pushover analysis method In addition the studies in-vestigated by Castaldo et al [10 11] have demonstrated thatthe existing underground structure can cause a notneglectable increase in the seismic vulnerability of the nearbyaboveground RC structure due to the deep excavation-induced foundationsrsquo displacement

e present fragility studies of large-space undergroundstructures only consider the horizontal seismic loadingHowever there are sufficient evidences to prove that thevertical seismic effect cannot be neglected For instance themeasured vertical peak ground acceleration was larger thanthe horizontal peak ground acceleration in the 1995 Kobeearthquake [12] In the 1994 Northridge earthquake [13] thepeak vertical acceleration value of near-field motion reached119 g and the ratio of vertical-to-horizontal peak groundacceleration exceeded 15 significantly greater than 23 Inaddition it has been proved that the contribution of verticalearthquake component is one of the major factors to thefailure of the structure [7 8 14ndash16] Both Parra-Montesinos[7] and Iida et al [12] verified that the high axial load in-duced by the vertical component of ground motion canincrease the axial compression ratio and reduce the ductilityof central column of large-space underground structureswhich is one of the most important factors of collapsingStudy of Nakamura et al [16] demonstrated that the verticalground motion caused the compression-bending failure ofcentral columns An et al [8] stated that ductility of centralcolumn under high compression ratio which was induced byvertical vibration can decrease obviously Although thevertical component of ground motion was introduced toseismic analysis of large-space underground structures theexisting studies still have not provide the solutions toconsider the influence of the vertical seismic effect quan-titatively in seismic fragility analysis

Along these lines this paper presents a seismic fragilityanalysis approach for large-space underground structureswhich account for the vertical seismic effect In seismiccapacity the soil-underground structure pushover analysismethod which considers the vertical seismic loading isapplied to obtain the performance index thresholds Inseismic demand it is evaluated through incremental dy-namic analysis method under the excitation of horizontaland vertical acceleration the soil-structure-interaction andground motion characteristics are also considered Toconstruct the fragility curves the evolutions of performanceindex versus the increasing earthquake intensity are per-formed considering related uncertainties

2 Methodology

21 Overview of the Proposed Method for Deriving FragilityCurve e proposed method is based on pushover analysisand incremental dynamic analysis of large-space un-derground structures considering the vertical seismic effectwhich is described in Figure 1 As the performance levelsthresholds of large-space underground structures are not yetdocumented one of the crucial tasks in this study is to obtain

the thresholds e existing seismic damage and failuremechanism of typical large-space underground structuresdemonstrate that central columns are the weakest position ofthe structure [12 17] erefore the seismic capacity of theentire structure can be represented by the seismic capacity ofthe central column In order to obtain the capacity curve ofthe central column which can be used to quantify thethresholds of performance levels the soil-undergroundstructure pushover analysis method [18] is adopted Be-cause the seismic response of the soil-underground structuresystem is mainly controlled by the fundamental mode theinverted triangular distribution that decreases linearly withdepth is used for the distribution of body force [18] isdistribution is easy to obtain without ground responseanalysis so is more practical than the other types of forcedistributions But it should be noted that this pushoveranalysis method only considering the horizontal seismicloading To consider the vertical seismic effect the uniformvertical acceleration distribution [19] is added to the soil-underground structure system as vertical body force dis-tribution as shown in Figure 2 e influence of the verticalcomponent of ground motion is often introduced by theavah ratio (av is the peak vertical acceleration and ah is thepeak horizontal acceleration) As many design codes use anaverage avah ratio of 23 [20] the inputted vertical accel-eration is scaled to 23 to the inputted horizontal acceler-ation and both seismic accelerations are monotonicallyincreasing simultaneously e pushover analysis procedureis presented as the following sequence of steps

(1) Establish the soil-underground structure analysismodel

(2) Gravity response analysis perform the static re-sponse of the soil-underground structure analysismodel according to the gravity load

(3) Pushover analysis based on the gravity responseanalysis result conduct the pushover analysis bymonotonically increasing forces using the invertedtriangular distribution and uniform vertical accel-eration distribution until structure collapse

(4) Record data of each analytical step and obtain thecapacity curves of the central column

To quantify the thresholds of performance levels basedon the obtained capacity curves definition of performanceindex and performance levels is needed As for performanceindex the univariate performance index has been utilized forlong time Recently the bivariate performance index hasbeen applied widely in case-study such as in the probabilisticanalysis of excavation-induced damages to existing struc-tures [10] and in fragility estimation of reinforce concretebuildings [21] due to the advantage which can identify twodamage criteria of structures Since the earthquake damageinvestigations have demonstrated that the seismic failure oflarge-space underground structure is mainly caused by thehorizontal deformation capacity of central columns [15] weselect the univariate performance index in this study Al-though different performance indexes and associated pa-rameters have been proposed regarding to the vulnerability

2 Advances in Civil Engineering

analysis of buildings [22] and bridge [23 24] there is lack ofrelevant information for large-space underground struc-tures erefore in the present method drift ratio is selectedas the performance index due to the significant correlationbetween drift ratio and structural damage [25] Moreoverthis performance index is compatible with the measurementof seismic response and damage analysis of large-spaceunderground structure in the previous studies [7 8] Foraboveground structures SEAOC [26] has proposed variousperformance levels and damage states according to previousexperience of damages in structures For large-space un-derground structures earthquake damage and experimentaldata of structures or components are insufficient to definethe damage state accurately erefore as a preliminaryconclusion the relationships between the performance levelsand damage states can be extended to large-space un-derground structures Four performance levels are takeninto account due to ground shaking in this study which referto fully operational (FO) operational (OP) life safety (LS)and near collapse (NC) e damage description of eachperformance level is described in Table 1

To obtain the seismic demand of soil-undergroundstructure interaction system the incremental dynamicanalysis method [27] is adopted A series of dynamic

response analyses are conducted under the combination ofhorizontal and vertical seismic acceleration for increasinglevels of seismic intensity en a number of curves de-scribing the parameterized response versus the groundmotion intensity level are produced (ie IDA curves)Utilizing the IDA results the parameters deriving for fra-gility curves can be obtained by performing the linear re-gression of the logarithm of demand measure against thelogarithm of intensity measure which will introduce indetail in Section 22 To construct the fragility curves theevolution of performance index versus the increasingearthquake intensity are performed considering relateduncertainties

e proposed method can be applied to evaluate newfragility curves which consider the different features of large-space underground structures geometries the site propertiesand input motion characteristics

22 Approach for Deriving Fragility Curves e seismicfragilities express the conditional probabilities which theseismic demand (D) of the structure reach or exceed thecapacity (C) of the structure is exceedance probability isconditioned on a selected intensity measure (IM) which

Bedrock

Body force

Uniform distribution Inverted triangular distribution Ground surface

Undergroundstructure

Figure 2 e computational model of pushover analysis

Pushover analysis of soil-underground structure

analysis model

Performance index (PI) performance level (pl) and backbone load-drift model

Thresholds of PI for each pl

Seismic input motionintensity levels

Incremental dynamic analysis of

soil-underground structure dynamic interaction model

IDA curves

Regression analysis onIDA results

Fragility curves

Capacity curve

Uncertainties(seismic demand column capacity

definition of PI and pl and modeling)

Site type oftypical site profilesStructure typology

Figure 1 Proposed procedure for deriving analytical fragility curves of large-space underground structures

Advances in Civil Engineering 3

represents the levels of ground shaking e generic ex-pression of this conditional probability is

fragility P(DgtC | IM) (1)

e fragility function given in equation (1) can beevaluated using a probability distribution for the demandconditioned on the IM (ie probabilistic seismic demandmodel (PSDM)) and convolving it through a distribution forthe capacity Cornell et al [28] suggested the estimation ofthe median demand ( 1113954D) follows a power model

1113954D aIMb (2)

where a and b are regression coefficientse Incremental Dynamic Analysis can be used to es-

tablish the PSDM As a number of curves depicting thedemandD versus the groundmotion intensity are producedthen by conducting the linear regression of the logarithm ofD against the logarithm of IM the PSDM parameters (a andb) can be determined

Furthermore the distribution of the demand median isoften assumed following a two-parameter lognormalprobability distribution erefore after estimating thedispersion (βD|IM) of the demand median which is condi-tioned on the IM the fragility can be written as

P(DgtC | IM) 1minusΦln(1113954C)minus ln a middot IMb1113872 1113873

β2D|IM + β2C + β2DS + β2M

1113969⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠ (3)

whereΦ is the standard cumulative probability function 1113954C isthe median of structural capacity associated with the per-formance level βC βDS and βM are the uncertainties incapacity the definition of damage states and modelingrespectively [29] Considering the lack of more rigorousestimation the values of uncertainty βDS and βC are set as 04following HAZUS in building [30] and 03 based on engi-neering judgment [31] e uncertainty related to modelingis assumed to 02 [32]e parameter βD|IM can be calculatedusing

βD|IM

1nminus 2

1113944

n

i1ln Di 1113857minus ln a middot IMb

1113872 11138731113960 11139612

11139741113972

(4)

where n is the number of (D IM) data points

3 Case Study

31 Numerical Models e underground commercial streetstructure which was designed and built in China is taken asthe research background Its cross-sectional dimensions aredepicted in Figure 3 e reinforcement ratios of structuralcomponents are 2 (columns) 1 (wall) and 08 (ceilingand bottom slab) Sites IndashIV are selected according topractical engineering condition and respectively corre-spond to stiff site (site I) medium stiff site (site II) mediumsoft site (site III) and soft site (site IV) based on the code forseismic design of building in China [33] e shear wavevelocity of each site is listed in Figure 4

To obtain the seismic capacity and seismic demand oflarge-space underground structures respectively a detailedsoil-underground structure pushover analysis model andsoil-underground structure interaction analysis model aredeveloped using the finite element code ABAQUS Studieshave demonstrated that the results obtained through finiteelement method are always affected by the epistemic un-certainties (ie the definition of structural model) due to theanalytical model become increasingly simple or increasinglycomplex [34ndash36] erefore to consider the epistemic un-certainties during the finite element analysis differentmethods have been proposed under the framework ofBayesian approach [34ndash36] In these methods the experi-mental data are one of the importance factors in evaluatingthe posterior distribution of the uncertainty As for large-space underground structures the epistemic uncertainty isnot considered in the present analytical model due to thelimited experimental data Depths of the analytical domainare 2265m (site I) 48m (site II) 60m (site III) and 70m(site IV) respectively which is the thickness of the assumedsoil deposit In dynamic analysis the width of the analyticalmodel mainly depends on two factors the distance betweenthe underground structure and free-field zone and thereflection of the lateral boundary Because lateral boundarydoes not absorb energy the distance between undergroundstructure and tied boundary must be sufficiently large so thatthe reflected vibration will not affect the dynamic behavior ofunderground structures A large domain of 2265m (site I)480m (site II) 600m (site III) and 700m (site IV) are usedin this analysis which has been validated as sufficiently largee calculation domain and element mesh of the models aredepicted in Figures 5 and 6

e inelastic response characteristics of the surroundingsoil are simulated through an elastoplastic model [37] ebone curve of this model is established using the isotropichardening law and characterized by the MohrndashCoulombyield criterion [38] e MohrndashCoulomb yield criterionassumes that yield happens when the shear stress in amaterial achieves a value that depends linearly on the normal

Table 1 Division of performance levels for large-space un-derground structures

Performancelevels

Damagestates Description of performance levels

Fullyoperational

Nodamage

Structure components do not sufferdamage Structures can be used

normally

Operational Repairable

Strength and stiffness of structuremaintain the same before and afterthe earthquake Structures can beensured its function with minor

repair

Life safety IrreparableStructure components experience

serious damage and stiffnessdegeneration but are not collapsed

Near collapse Severe

Structure components are destroyedand their strength and stiffness

degenerate greatly Structure nearlycollapses


stress in the same plane e corresponding mechanicalproperties (ie the shear velocity (Vs) the unit weight (c)the Poisson ratio (υ) the cohesion (c) and the frictionangle (φ)) of different soils in each site are listed inTables 2ndash5 During the analyses the elasticity of soil can becalculated through E G times 2 times (1 + υ) while G ρ times V2

s

e plasticity of soil is characterized by the cohesion and thefriction angle e plastic-damage model [39] is used forunderground structure it assumes that the uniaxial tensileand compressive behavior of concrete are characterizedthrough damage plasticity During the mathematic calcula-tion the crucial parameters of the plastic-damage model

6000 6000 6000 6000 6000 6000

650

700700850

4000

36000

Figure 3 Cross section of the selected large-space underground structure

24

20

16

12

8

4

00 300 600 900 1200 1500 1800

Vs (ms)

Dep

th (m

)

(a)

Vs (ms)

60

50

40

30

20

10

00 100 200 300 400 500 600

Dep

th (m

)

(b)

Vs (ms)

Dep

th (m

)

60

50

40

30

20

10

00 100 200 300 400 500 600

(c)

Vs (ms)

Dep

th (m

)

72

60

48

36

24

12

00 50 100 150 200 250 300

(d)

Figure 4 Shear velocity (a) Site I (b) Site II (c) Site III (d) Site IV


(Tables 6 and 7) are adopted to describe the materialproperties and deformation behavior of concrete More-over the idealized elastoplastic model is selected for thesteel bars with the density of 7800 kgm3 and yield stress of300MPa

e interaction between underground structure and thesurrounding soil is related to their interface properties Inthe normal direction of the interface we define a hardcontacte normal contact compressive stress can mutuallytransfer via the contact constraint e element nodes on the

120 m

Soil-structure analysis modelAdditional free field

Mixed lateral boundary

Fixed boundary

Inverted triangular distribution

2 m

70 m

120 m36 m

Uniform vertical distribution

Figure 5 Soil-underground structure pushover analysis model with the additional free field

Soil solid elements

h

l = 20h

Underground structure solid elementsSoil-underground structure interface

Input motion

Figure 6 Soil-underground structure interaction analysis model

Table 2 Soil physical properties for site I

Soil layer ickness (m) Soil type Unit weight(kgmiddotmminus3)

Shear wavevelocity (mmiddotsminus1) Poisson ratio Cohesion (kPa) Friction angle (deg)

1 175 Miscellaneous fill 1750 142 040 100 2382 190 Silty clay 1900 348 035 134 1203 900 Strong weathered granite 2300 695 035 mdash 324 600 Medium weathered granite 2450 1246 025 mdash 325 400 Slightly weathered rock 2500 1578 022 mdash 32

Table 3 Soil physical properties for site II



1 300 Fill 2000 152 030 100 2382 400 Silty clay 2000 170 030 134 1203 900 Clay 2000 258 030 100 2504 600 Silt 2000 300 030 100 2505 400 Silt 2000 320 030 00 3206 300 Clay 2000 400 030 100 2507 200 Round gravel 2000 350 030 00 3508 800 Medium-fine sand 2000 420 030 00 3409 900 Clay 2000 400 030 100 25010 18 Rock 2000 550 030 mdash 32


interface satisfy Hookersquos Law and the Harmonized Condi-tion of Displacement In the tangential direction of theinterface tangential contact shear stress is also transferredand we assume that tangential mechanics behavior of theinterface follows the Coulomb friction law with a frictioncoefficient micro of 04 which corresponds to a frictional angleof 22deg for the soil-underground structure interface iscontact relationship was commonly used by different re-searchers [14 40 41]

In pushover analysis to consider the gravity-load ef-fect an additional free-field model is established emixed lateral boundary condition is used for the lateralsides of the model (ie the displacement boundary con-dition is fixed in the vertical direction and a forcedboundary condition is adopted in the horizontal di-rection) e bottom boundary is fixed in both directionserefore the vertical displacements and horizontal forcesof the lateral boundary are obtained through self-gravityresponse analysis of the additional free-field model andthen subjected to the corresponding lateral boundary ofthe soil-underground structure model e dynamic an-alyses are conducted in two steps First step is a static stepwhich the geostatic stresses are introduced considering

the underground structure in place During this step thebase of the analysis model is fixed in the horizontal andvertical directions e subsequent step is a dynamic an-alyses step the horizontal and vertical seismic accelerationis applied uniformly along the base of the model and the

Table 4 Soil physical properties for site III



1 200 Clay 1940 173 033 100 2502 300 Silty clay 1980 200 032 134 1203 1330 Silty clay 1990 212 032 100 2384 710 Silty clay 2000 244 040 134 1205 1960 Sandy clay 2000 273 030 100 2506 1500 Silty clay 2050 333 026 100 250

Table 5 Soil physical properties for site IV



1 100 Fill 1890 74 040 100 2382 540 Silty clay 1850 87 035 134 1203 1126 Silty clay 1830 110 038 100 2384 2640 Sandy clay 1820 220 035 100 2505 740 Clay 2040 195 035 100 2506 1854 Fine sand 1935 225 030 00 320

Table 6 Material properties of concrete

Parameters ValueDensity ρ(kg middotmminus3) 2400Dilation angleψ(deg) 30ElasticmodulusE(MPa) 32500Poissonrsquos ratio υ 02Initial compressive yield stress σc0(MPa) 955Limited compressive yield stress σcu(MPa) 268Initial tensile yield stress σt0(MPa) 239Tensile stiffness recovery parameterωt 0Compressive stiffness recovery parameterωc 1Damage variable (Table 3)

Table 7 Stress and damage factor versus plastic strain of concrete

Plastic strain Stress (MPa) Damage variableCompression00000E+ 00 18026 00000029233Eminus 05 21576 00143912438Eminus 04 29746 00486420932Eminus 04 32617 00749232177Eminus 04 34594 01066162346Eminus 04 36052 01812483638Eminus 04 35380 02283610796Eminus 03 33723 02783413385Eminus 03 31557 03272718656Eminus 03 26920 04145426240Eminus 03 21018 05149637809Eminus 03 14657 06244762920Eminus 03 9087 07345292686Eminus 03 5002 083782Tensile00000E+ 00 1608 00000013586Eminus 05 3131 00340623198Eminus 05 3215 00553840877Eminus 05 3037 00985762300Eminus 05 2738 01560310436Eminus 04 2165 02814617538Eminus 04 1444 04966326383Eminus 04 0951 06927134435Eminus 04 0716 07963247258Eminus 04 0517 08813459794Eminus 04 0412 09218772209Eminus 04 0346 09443190721Eminus 04 0283 09630310917Eminus 03 0242 097345


bottom and lateral boundary are free in the horizontal andvertical direction

e viscous damping of the soil-underground structuresystem is modeled in the form of Rayleigh type Because thisdamping type is a linear combination of mass as well asstiffness matrix it can incorporate into the analysis pro-cedure efficientlyematerial damping for soil was selectedin different values during dynamic response analysis bydifferent researchers [42ndash44] mainly ranging from 005 to01 In [43] the modeling issues of Rayleigh damping matrixin soil layers are discussed which demonstrate the dampingvalue of 008 for soil can better represent a realistic value ofsoil damping during strong ground motions erefore weutilize a 008 damping in the dynamic analysis for soilSimilarly a widely used 005 damping is selected for un-derground structures

e soil and structure are discretized with 8-node re-duced integration linear solid element (C3D8R) while thereinforcement is modeled with three-node linear beam el-ements (B31) In dynamic analysis the element mesh for soilis based on Liaorsquos study [45] which can ensure the efficientreproduction of all the waveforms of whole frequency rangeunder study and the maximum height of element hmax insoil is determined as

hmax ((175)minus(1160))Vs

fmax (5)

where Vs is the shear and compression motion velocitywhich can be determined through G0 ρV2

s ρ is thedensity of soil and fmax is the maximum vibration fre-quency of the inputted motion erefore the maximumheights of the element are 1m to 3m from the surface tobottom A finer discretization is adopted near the un-derground structure

32 Selection of Input Motions e seismic IMs can beexpressed in terms of PGA PGV or Sa (T1 5) (ie 5damped first-mode spectral acceleration) As for un-derground tunnel structures American Lifelines Alliance[46] produced empirical fragility curves by PGA whileCorigliano [47] proposed empirical fragility curves byPGV Due to no consensus on the IMs required for seismicanalysis of underground structures PGA and PGV areadopted as IMs to investigate the effects of each parameterin the scattering of the engineering demand parameter(EDP) values A total of 15 strong motion records areselected from strong motion database of the United States(PEER) Japan (NRIESDP) and China and Taiwan(SMART-I) for each site respectively exhibiting differentspectral acceleration amplitudes frequency content sig-nificant duration and seismotectonic environment is isconsidered sufficient to capture the randomness of groundmotion and provide sufficient accuracy in estimatingseismic demand [48] ese records are all selected fromdifferent earthquakes with source distances larger than10 km relatively large interpolated earthquakes (MWge 6)and peak ground acceleration of 01 g or more e hori-zontal and vertical acceleration response spectra (damping

ratio 008) of the selected ground motions are plotted inFigures 7 and 8

e selected motion records are ground motionserefore the horizontal and vertical components areinverted to bedrock to obtain the input motions Accordingto the established empirical curves which decrease in shearmodulus and increase in material damping with the in-creasing shear strain amplitude for each soil layer theseprocesses were accomplished through the shake91 codebased on the one-dimensional equivalent-linear wave-propagation analyses For a gradually increasing level ofseismic intensity the horizontal earthquake components arescaled from lower to higher levels of peak acceleration onbedrock (ie 0035 g 01 g 02 g 04 g 06 g 08 g 10 g and12 g) en a series of nonlinear time history analyses ofsoil-underground structure interaction analysis model areconducted

33 Pushover Analysis Results e capacity curves of thecentral column considering the vertical seismic effect areobtained (Figure 9) To investigate the influence of thevertical seismic effect we also present the capacity curveswithout considering the vertical seismic effect (Figure 10)e characteristic points (ie θy (the yield drift ratio) θp (thedrift ratio of peak loading) and θu (the ultimate drift ratio))are shown within the figures We can know the values of θyand θp under considering the vertical seismic loading arealmost the same to the values without considering the verticalseismic effect at is mainly because during the initialloading period the subjected acceleration is small ereforethe vertical seismic effect is not significant compared to self-gravityWith both horizontal and vertical seismic accelerationincreasing the structure gradually enters to the nonlinearstage Under the vertical seismic effect the capacity curvedecreasing rate is faster compared to only consider thehorizontal seismic loadingerefore we can find the value ofθu under the vertical seismic effect is nearly 50 less com-pared to without considering the vertical seismic effect Itdemonstrates the vertical seismic effect can seriously reducethe ductility of the central column is finding is in ac-cordance with the previous studies [7 8 14ndash16] us theseismic capacity of the central column will be overestimated ifthe vertical seismic effect is not considered

349resholds of Performance Levels In order to determinethe thresholds of different performance levels based onpushover analysis results in this study lateral load-driftcurve (Figure 11) is adopted as the backbone curve modelbased on the experimental study [49] is model consistsof four performance levels for the component which are inaccordance with the definition of performance levels inthis study It includes four characteristic points originpoint (A) yield point (B) peak strength point (C) andultimate point (D) e associated drift ratios are θy θpand θu e ultimate point is defined as the force droppedto 85 of the peak force e values of θOP and θLS aredefined as


θOP θy + 05 θp minus θy1113872 1113873

θLS θp + 05 θu minus θp1113872 1113873(6)

e average values of characteristic points of the ca-pacity curves under different site are used to quantify thethresholds of different performance levels e quantifiedthresholds are listed in Table 8 For FO and OP perfor-mance level the thresholds(H+V) (ie thresholds consid-ering the vertical seismic effect) are the same tothresholds(H) (ie thresholds without considering thevertical seismic effect) However for LS and NC perfor-mance level thresholds(H+V) are obviously less thanthresholds(H) is means that the underground structureis easier to reach these two performance levels for the casesconsidering the vertical seismic effect If we ignore thevertical seismic effect to the thresholds of performancelevels the seismic capacity of underground structure canbe overestimated

35 Incremental Dynamic Analysis Results In incrementaldynamic analysis the failure condition of the structure hasbeen considered recently within the numerical analysis bythe mean defining the collapse condition of the structure[50] e failure condition can be reflected in the seismicfragility assessment through the mean of the total

probability theorem As for large-space undergroundstructures they almost reach completely failure conditionduring earthquake due to the surrounding soil ereforethe failure condition is not considered in the present in-cremental dynamic analysis e EDP (ie drift ratio) andIMs (ie PGA and PGV) are set as horizontal and verticalaxis respectively Based on the spline interpolation be-tween discrete points then IDA curves of different seismicmotions under different sites are obtained (Figures 12 and13) Due to various values of the material properties of soilsuch as modulus elasticity Poissonrsquos ratio cohesion andfriction angle as well as the different ground motioncharacteristics each IDA curve shows different developingtendency Unlike aboveground structures the IDA curvesdo not exhibit a noticeable plateau after a certain seismicintensity is phenomenon which is due to the soilprevents structures from reaching the nonlinear stageMoreover the restraint of the surrounding soil results inthe underground structure not reflecting its self-vibrationcharacteristics Consequently the dynamic response be-tween underground structure and aboveground structuresexhibits clear differences

e dispersion of the IDA curves is mainly due todifferent input motions (ie same PGA but differentground motion records) To quantify this dispersion theaverage of the In (EDP)rsquos standard deviation is computedand compared e smaller value of In (EDP)rsquos standard

0 1 2 3 4 5 60

1

2

3

4

5

S a (A

max

)

Average

T (sec)

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

Average

T (sec)0 1 2 3 4 5 6

00

15

30

45

60

75

S a (A

max

)

(c)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

S a (A

max

)

(d)

Figure 7 Acceleration response spectra of the horizontal component (a) Site I (b) Site II (c) Site III (d) Site IV


S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)

Figure 8 Acceleration response spectra of the vertical component (a) Site I (b) Site II (c) Site III (d) Site IV

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)

Dri ratio (10ndash3 rad)

(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)

Figure 9 Capacity curves considering the vertical seismic effect (a) Site I (b) Site II (c) Site III (d) Site IV


deviation represents lower dispersion so the associated IMis more appropriate for IDA curves Table 9 listed theaverage of In (EDP)rsquos standard deviation of the drift ratiowith respective PGV and PGA as the IM of different sites Itis found that PGA is more suitable than PGV as IM in stiffsite and has a relatively large scatter in soft site while PGVshows less scatter as IM in soft site In order to yield theregression coefficient in equation (3) we select PGV as the

representative parameter of seismic IM in the followingfragility curves because its mean In (EDP)rsquos standard de-viation is smaller than PGA

36 Fragility Analysis e derivations of fragility curves arebased on the constructions of diagrams of the obtainedperformance index thresholds (Table 8) versus PGV at theground surface e diagrams are estimated through linearregression analyses In these analyses the natural logarithmof the performance index is set as the dependent variableand the natural logarithm of PGV is set as the independentvariable (Figure 14)

e sets of fragility curves of large-space undergroundstructures derived for each site are given in Figure 15 ecomparison reveals that the vulnerability of the large-spaceunderground structure is increased when it is embedded insofter site conditions ie from site I to site IV ereforein this context the important effect of sites conditions onthe vulnerability of large-space underground structure ishighlighted It is observed that the probability of the NC

0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)

Dri ratio (10ndash3 rad)0 3 6 9 12 15

0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)

Drift ratio (10ndash3 rad)0 3 6 9 12 15

0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)

Figure 10 Capacity curves without considering the vertical seismic effect (a) Site I (b) Site II (c) Site III (d) Site IV

No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP

Figure 11 Backbone load-drift quantization model

Table 8 resholds of performance levels

Performance levels (10minus3 rad)FO OP LS NC

resholds(H+V) 15 22 58 86resholds(H) 15 22 79 128


performance level is very low in site I site II and site IIIese phenomena are in accordance with the obtainedobservations from recent strong earthquakes e sitewhich Daikai subway station located is similar to site IIin this study However the obtained fragility curves oflarge-space underground structure embedded in site IIare less satisfactory in the case of Daikai subway stationis difference may be caused by the difference of thedesign and construction standard of the large-space un-derground structure e current obtained fragility curvesrepresent the underground structures designed and con-structed based on the improved modern seismic codeHowever Daikai station is designed without consideringthe modern seismic codes In addition these fragilitycurves are developed for square section which is not thesame as the vulnerable central columns in Daikai subwaystation

In Figure 16 the fragility curves yielding fromthresholds(H+V) and thresholds(H) are compared As thethresholds(H+V) and thresholds(H) are the same in FO andOP performance levels we only compare the fragilitycurves derived from LS and NC performance levels eexceedance probability of damage in the case of consid-ering the vertical seismic effect is increased from 1 to13 for LS performance level in both site conditions Forthe CP performance level this increase ranges between 1and 15 is demonstrates when considering the vertical

earthquake motion in seismic fragility analyses of large-space underground structures the exceedance probabili-ties will be underestimated if thresholds(H) are adoptedresulting in an unfavorable assessment result

4 Conclusions

An approach is proposed to construct fragility curves forlarge-space underground structures considering the ver-tical seismic effect resholds of performance levels areobtained based on the soil-underground structure push-over analysis method which considers the contribution ofvertical seismic effect to seismic capacity e seismicdemand of the large-space underground structure isevaluated through 3D incremental dynamic analyses ac-counting for soil inelasticity and ground motion charac-teristics Based on a selected typical large-spaceunderground structure this approach is applied to thederivation of seismic fragility curves of different sitesaccounting for soil-underground structure interaction efragility curves are compared highlighting the importantrole of site and the vertical seismic effect in the vulnerabilityof large-space underground structures e main findingsof this study are as follows

(1) For fully operational and operational performancelevel the thresholds are the same whether

00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)

Figure 12 IDA curves in terms of PGA as IM (a) Site I (b) Site II (c) Site III (d) Site IV


00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)

Figure 13 IDA curves in terms of PGV as IM (a) Site I (b) Site II (c) Site III (d) Site IV

Table 9 Average of σln(EDP)

IMsite Site I Site II Site III Site IVPGA 0403 0436 0451 0503PGV 0444 0441 0432 0469

ndash5 ndash4 ndash3 ndash2 ndash1 0 1 2ndash14

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)

ndash4 ndash3 ndash2 ndash1 0 1 2 3ndash14

ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued


considering the vertical seismic effect For life safetyand near collapse performance level the thresholdsconsidering the vertical seismic effect are obviouslyless compare to without considering the vertical

seismic effect If we ignore the vertical seismic effectto the thresholds of performance levels the seismiccapacity of the large-space underground structurewill be overestimated

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)

ndash5 ndash4 ndash3 ndash2 ndash1 0 1 2 3ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)

Figure 14 Linear regression analyses of IDA results (a) Site I (b) Site II (c) Site III (d) Site IV

0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)

Figure 15 Comparison of fragility curves of different sites under different performance levels (a) FO (b) OP (c) LS and (d) NC


(2) e vulnerability of large-space undergroundstructures is increased when the site is getting softerIt also reveals that the exceedance probabilities ofdamage for the thresholds considering the verticalseismic effects are larger than the exceedanceprobabilities of damage for the thresholds withoutconsidering the vertical seismic effect in life safetyand near collapse performance levels

(3) When considering the vertical earthquakemotion in aseismic fragility analysis of large-space undergroundstructures the use of performance level thresholdswithout considering the vertical seismic effect willunderestimate the exceedance probabilities of dam-age which can result in an unfavorable assessmentresult With the proposed fragility analysis approachthe vertical seismic effect can be considered quanti-tatively on obtaining the seismic fragility curves oflarge-space underground structures

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 there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is research was supported by the National Natural ScienceFoundation of China (grant no 51778489) National Scienceamp Technology Pillar Program of China (grant no2015BAK17B04) and the Program for Innovative ResearchTeam in China Earthquake Administration

References

[1] Y M A Hashash J J Hook B Schmidt and J I-Chiang YaoldquoSeismic design and analysis of underground structuresrdquoTunnelling and Underground Space Technology vol 16 no 4pp 247ndash293 2001

[2] S Sharma and W R Judd ldquoUnderground opening damagefrom earthquakesrdquo Engineering Geology vol 30 no 3-4pp 263ndash276 1991

[3] K Pitilakis and G Tsinidis ldquoPerformance and seismic designof underground structuresrdquo in Earthquake Geotechnical

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)

Figure 16 Comparison of fragility curves obtained from thresholds(H+V) and thresholds(H) (a) Site I (b) Site II (c) Site III (d) Site IV


Engineering Design pp 279ndash340 Springer Cham Switzer-land 2014

[4] M Power D Rosidi J Kaneshiro et al ldquoSummary andevaluation of procedures for the seismic design of tunnelsrdquoFinal Report for Task 112-d-53 (c) National Center forEarthquake Engineering Research Buffalo NY USA 1998

[5] W T Li Q J Chen and Y C Wang ldquoA simplified evaluationmethod for the seismic fragility of subway stationsrdquo inProceedings of the 16th World Conference on EarthquakeEngineering (WCEE) Santiago Chile January 2017

[6] T Liu Z Chen Y Yuan and X Shao ldquoFragility analysis of asubway station structure by incremental dynamic analysisrdquoAdvances in Structural Engineering vol 20 no 7 pp 1111ndash1124 2016

[7] G J Parra-Montesinos ldquoEvaluation of soil-structure in-teraction and structural collapse in Daikai subway stationduring Kobe earthquakerdquo ACI Structural Journal vol 103no 1 pp 113ndash122 2006

[8] X An A A Shawky and K Maekawa ldquoe collapsemechanism of a subway station during the Great Hanshinearthquakerdquo Cement and Concrete Composites vol 19 no 3pp 241ndash257 1997

[9] J Huh Q Tran A Haldar I Park and J-H Ahn ldquoSeismicvulnerability assessment of a shallow two-story un-derground RC box structurerdquo Applied Sciences vol 7 no 7p 735 2017

[10] P Castaldo M Calvello and B Palazzo ldquoProbabilisticanalysis of excavation-induced damages to existing struc-turesrdquo Computers and Geotechnics vol 53 pp 17ndash30 2013

[11] P Castaldo and M De Iuliis ldquoEffects of deep excavation onseismic vulnerability of existing reinforced concrete framedstructuresrdquo Soil Dynamics and Earthquake Engineeringvol 64 pp 102ndash112 2014

[12] H Iida T Hiroto N Yoshida and M Iwafuji ldquoDamage toDaikai subway stationrdquo Soils and Foundations vol 36pp 283ndash300 1996

[13] D J Goltz ldquoe Northridge California earthquake of January17 1994 general reconnaissance reportrdquo Technical ReportNCEER NCEER Buffalo NY USA 1994

[14] H Huo A Bobet G Fernandez and J Ramırez ldquoLoadtransfer mechanisms between underground structure andsurrounding ground evaluation of the failure of the Daikaistationrdquo Journal of Geotechnical and Geoenvironmental En-gineering vol 131 no 12 pp 1522ndash1533 2005

[15] W T Li and Q J Chen ldquoSeismic performance and failuremechanism of a subway station based on nonlinear finiteelement analysisrdquo KSCE Journal of Civil Engineering vol 22no 2 pp 765ndash776 2017

[16] S Nakamura N Yoshida and T Iwatate ldquoDamage to Daikaisubway station during the 1995 Hyogoken-Nambu earth-quake and its investigationrdquo in Proceedings of the Conferenceon Earthquake Engineering pp 287ndash295 Japan Society ofCivil Engineers Acapulco Mexico June 1996

[17] C Ma D Lu and X Du ldquoSeismic performance upgrading forunderground structures by introducing sliding isolationbearingsrdquo Tunnelling and Underground Space Technologyvol 74 pp 1ndash9 2018

[18] J Liu W Wang and G Dasgupta ldquoPushover analysis ofunderground structures method and applicationrdquo ScienceChina Technological Sciences vol 57 no 2 pp 423ndash437 2014

[19] Y Gu Q Zhu H Zhong et al ldquoStudy on seismic response ofshield tunnel and its Pushover method considering horizontaland vertical directionrdquo Earthquake Resistant Engineering andRetrofitting vol 39 pp 44ndash51 2017 in Chinese

[20] N M Newmark J A Blume and K K Kapur ldquoSeismicdesign spectra for nuclear power plantsrdquo Report of Consul-ting Engineering Services Consulting Engineering ServicesUrbana IL USA 1973

[21] H Xu and P Gardoni ldquoProbabilistic capacity and seismicdemandmodels and fragility estimates for reinforced concretebuildings based on three-dimensional analysesrdquo EngineeringStructures vol 112 pp 200ndash214 2016

[22] D Vamvatsikos and C A Cornell ldquoIncremental dynamicanalysisrdquo Earthquake Engineering amp Structural Dynamicsvol 31 no 3 pp 491ndash514 2002

[23] A J Kappos G Panagopoulos C Panagiotopoulos andG Penelis ldquoA hybrid method for the vulnerability assessmentof RC and URM buildingsrdquo Bulletin of Earthquake Engi-neering vol 4 no 4 pp 391ndash413 2006

[24] E Choi R DesRoches and B Nielson ldquoSeismic fragility oftypical bridges in moderate seismic zonesrdquo EngineeringStructures vol 26 no 2 pp 187ndash199 2004

[25] I F Moschonas A J Kappos P Panetsos V PapadopoulosT Makarios and Panopoulos ldquoSeismic fragility curves forGreek bridges methodology and case studiesrdquo Bulletin ofEarthquake Engineering vol 7 no 2 pp 439ndash468 2009

[26] B B Algan Drift and damage considerations in earthquake-resistant design of reinforced concrete buildings PhD dis-sertation University of Illinois at Urbana-ChampaignChampaign IL USA 1982

[27] Structural Engineers Association of California Vision 2000Committee and California Office of Emergency ServicesPerformance Based Seismic Engineering of Buildings Pt 3Preliminary Northridge lessons Pt 4 Moving the Blue Booktoward Performance-Based Engineering Structural EngineersAssociation of California Vol 2 Sacramento CA USA 1995

[28] C A Cornell F Jalayer R O Hamburger and D A FoutchldquoProbabilistic basis for 2000 SAC federal emergency man-agement agency steel moment frame guidelinesrdquo Journal ofStructural Engineering vol 128 no 4 pp 526ndash533 2002

[29] O C Celik and B R Ellingwood ldquoSeismic fragilities for non-ductile reinforced concrete framesmdashrole of aleatoric andepistemic uncertaintiesrdquo Structural Safety vol 32 no 1pp 1ndash12 2010

[30] P Rajeev and S Tesfamariam ldquoSeismic fragilities of non-ductile reinforced concrete frames with consideration of soilstructure interactionrdquo Soil Dynamics and Earthquake Engi-neering vol 40 pp 78ndash86 2012

[31] S Argyroudis G Tsinidis F Gatti and K Pitilakis ldquoEffects ofSSI and lining corrosion on the seismic vulnerability ofshallow circular tunnelsrdquo Soil Dynamics and EarthquakeEngineering vol 98 pp 244ndash256 2017

[32] H Fema Multi-Hazard Loss Estimation MethodologyEarthquake Model Federal Emergency Management AgencyWashington DC USA 2003

[33] C Standard Code for Seismic Design of Buildings ChinaArchitectural and Building Press Beijing China 2001

[34] P Castaldo D Gino G Bertagnoli and G Mancini ldquoPartialsafety factor for resistance model uncertainties in 2D non-linear finite element analysis of reinforced concrete struc-turesrdquo Engineering Structures vol 176 pp 746ndash762 2018

[35] T Haukaas and P Gardoni ldquoModel uncertainty in finite-element analysis Bayesian finite elementsrdquo Journal of Engi-neering Mechanics vol 137 no 8 pp 519ndash526 2011

[36] T Most ldquoAssessment of structural simulation models byestimating uncertainties due to model selection and modelsimplificationrdquo Computers amp Structures vol 89 no 17-18pp 1664ndash1672 2011


[37] Y Hui J X Liang and L P Yuan ldquoSeismic response of tunnellining for shallow-bias tunnel with a small clear distanceunder Wenchuan earthquakerdquo Advances in Civil Engineeringvol 2018 Article ID 2578062 10 pages 2018

[38] A J Abbo and S W Sloan ldquoA smooth hyperbolic approx-imation to the Mohr-Coulomb yield criterionrdquo Computers ampStructures vol 54 no 3 pp 427ndash441 1995

[39] J Lee and G L Fenves ldquoPlastic-damage model for cyclicloading of concrete structuresrdquo Journal of Engineering Me-chanics vol 124 no 8 pp 892ndash900 1998

[40] H Zhuang Z Hu X Wang and G Chen ldquoSeismic responsesof a large underground structure in liquefied soils by FEMnumerical modellingrdquo Bulletin of Earthquake Engineeringvol 13 no 12 pp 3645ndash3668 2015

[41] H Liu and E Song ldquoSeismic response of large undergroundstructures in liquefiable soils subjected to horizontal andvertical earthquake excitationsrdquo Computers and Geotechnicsvol 32 no 4 pp 223ndash244 2005

[42] H EI Ganainy and M EI Naggar ldquoSeismic performance ofthree-dimensional frame structures with undergroundstoriesrdquo Soil Dynamics and Earthquake Engineering vol 29no 9 pp 1249ndash1261 2009

[43] M L Lou and X G Shao ldquoDiscussion on modeling issues ofRayleigh damping matrix in soil layers with deep depositrdquoChinese Journal of Geotechnical Engineering vol 35 no 7pp 1272ndash1279 2013 in Chinese

[44] G D Hatzigeorgiou and D E Beskos ldquoSoil-structure in-teraction effects on seismic inelastic analysis of 3-D tunnelsrdquoSoil Dynamics and Earthquake Engineering vol 30 no 9pp 851ndash861 2010

[45] Z Liao 9eories of Wave Motion for Engineering SciencePress of China Beijing China 2002

[46] American Lifelines Alliance Seismic Fragility FormulationsforWater Systems Guideline American Lifelines Alliance SanFrancisco CA USA 2001

[47] I Anastasopoulos N Gerolymos V Drosos R KourkoulisT Georgarakos and G Gazetas ldquoNonlinear response of deepimmersed tunnel to strong seismic shakingrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 133no 9 pp 1067ndash1090 2007

[48] N Shome Probabilistic Seismic Demand Analysis of NonlinearStructures Stanford University Stanford CA USA 1999

[49] J R Qing and B R Feng ldquoExperimental study on seismicbehavior of different seismic grade RC columnsrdquo Journal ofBuilding Structures vol 35 no 7 pp 105ndash114 2014 inChinese

[50] P Castaldo B Palazzo G Alfano and M F PalumboldquoSeismic reliability-based ductility demand for hardening andsoftening structures isolated by friction pendulum bearingsrdquoStructural Control and Health Monitoring vol 25 no 11article e2256 2018


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Submit your manuscripts atwwwhindawicom

on the ground response acceleration method e perfor-mance levels thresholds of structures were defined throughthe pushover analysis method In addition the studies in-vestigated by Castaldo et al [10 11] have demonstrated thatthe existing underground structure can cause a notneglectable increase in the seismic vulnerability of the nearbyaboveground RC structure due to the deep excavation-induced foundationsrsquo displacement

e present fragility studies of large-space undergroundstructures only consider the horizontal seismic loadingHowever there are sufficient evidences to prove that thevertical seismic effect cannot be neglected For instance themeasured vertical peak ground acceleration was larger thanthe horizontal peak ground acceleration in the 1995 Kobeearthquake [12] In the 1994 Northridge earthquake [13] thepeak vertical acceleration value of near-field motion reached119 g and the ratio of vertical-to-horizontal peak groundacceleration exceeded 15 significantly greater than 23 Inaddition it has been proved that the contribution of verticalearthquake component is one of the major factors to thefailure of the structure [7 8 14ndash16] Both Parra-Montesinos[7] and Iida et al [12] verified that the high axial load in-duced by the vertical component of ground motion canincrease the axial compression ratio and reduce the ductilityof central column of large-space underground structureswhich is one of the most important factors of collapsingStudy of Nakamura et al [16] demonstrated that the verticalground motion caused the compression-bending failure ofcentral columns An et al [8] stated that ductility of centralcolumn under high compression ratio which was induced byvertical vibration can decrease obviously Although thevertical component of ground motion was introduced toseismic analysis of large-space underground structures theexisting studies still have not provide the solutions toconsider the influence of the vertical seismic effect quan-titatively in seismic fragility analysis

Along these lines this paper presents a seismic fragilityanalysis approach for large-space underground structureswhich account for the vertical seismic effect In seismiccapacity the soil-underground structure pushover analysismethod which considers the vertical seismic loading isapplied to obtain the performance index thresholds Inseismic demand it is evaluated through incremental dy-namic analysis method under the excitation of horizontaland vertical acceleration the soil-structure-interaction andground motion characteristics are also considered Toconstruct the fragility curves the evolutions of performanceindex versus the increasing earthquake intensity are per-formed considering related uncertainties

2 Methodology

21 Overview of the Proposed Method for Deriving FragilityCurve e proposed method is based on pushover analysisand incremental dynamic analysis of large-space un-derground structures considering the vertical seismic effectwhich is described in Figure 1 As the performance levelsthresholds of large-space underground structures are not yetdocumented one of the crucial tasks in this study is to obtain

the thresholds e existing seismic damage and failuremechanism of typical large-space underground structuresdemonstrate that central columns are the weakest position ofthe structure [12 17] erefore the seismic capacity of theentire structure can be represented by the seismic capacity ofthe central column In order to obtain the capacity curve ofthe central column which can be used to quantify thethresholds of performance levels the soil-undergroundstructure pushover analysis method [18] is adopted Be-cause the seismic response of the soil-underground structuresystem is mainly controlled by the fundamental mode theinverted triangular distribution that decreases linearly withdepth is used for the distribution of body force [18] isdistribution is easy to obtain without ground responseanalysis so is more practical than the other types of forcedistributions But it should be noted that this pushoveranalysis method only considering the horizontal seismicloading To consider the vertical seismic effect the uniformvertical acceleration distribution [19] is added to the soil-underground structure system as vertical body force dis-tribution as shown in Figure 2 e influence of the verticalcomponent of ground motion is often introduced by theavah ratio (av is the peak vertical acceleration and ah is thepeak horizontal acceleration) As many design codes use anaverage avah ratio of 23 [20] the inputted vertical accel-eration is scaled to 23 to the inputted horizontal acceler-ation and both seismic accelerations are monotonicallyincreasing simultaneously e pushover analysis procedureis presented as the following sequence of steps

(1) Establish the soil-underground structure analysismodel

(2) Gravity response analysis perform the static re-sponse of the soil-underground structure analysismodel according to the gravity load

(3) Pushover analysis based on the gravity responseanalysis result conduct the pushover analysis bymonotonically increasing forces using the invertedtriangular distribution and uniform vertical accel-eration distribution until structure collapse

(4) Record data of each analytical step and obtain thecapacity curves of the central column

To quantify the thresholds of performance levels basedon the obtained capacity curves definition of performanceindex and performance levels is needed As for performanceindex the univariate performance index has been utilized forlong time Recently the bivariate performance index hasbeen applied widely in case-study such as in the probabilisticanalysis of excavation-induced damages to existing struc-tures [10] and in fragility estimation of reinforce concretebuildings [21] due to the advantage which can identify twodamage criteria of structures Since the earthquake damageinvestigations have demonstrated that the seismic failure oflarge-space underground structure is mainly caused by thehorizontal deformation capacity of central columns [15] weselect the univariate performance index in this study Al-though different performance indexes and associated pa-rameters have been proposed regarding to the vulnerability







Bedrock

Body force





analysis model






IDA curves


Fragility curves

Capacity curve









1113954D aIMb (2)






1113969⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠ (3)


βD|IM

1nminus 2

1113944

n


1113872 11138731113960 11139612

11139741113972

(4)


3 Case Study





Performancelevels


Fullyoperational

Nodamage


normally



repair








s


6000 6000 6000 6000 6000 6000

650

700700850

4000

36000


24

20

16

12

8

4

00 300 600 900 1200 1500 1800

Vs (ms)

Dep

th (m

)

(a)

Vs (ms)

60

50

40

30

20

10

00 100 200 300 400 500 600

Dep

th (m

)

(b)

Vs (ms)

Dep

th (m

)

60

50

40

30

20

10

00 100 200 300 400 500 600

(c)

Vs (ms)

Dep

th (m

)

72

60

48

36

24

12

00 50 100 150 200 250 300

(d)





120 m



Fixed boundary


2 m

70 m

120 m36 m



Soil solid elements

h

l = 20h


Input motion































fmax (5)









θOP θy + 05 θp minus θy1113872 1113873

θLS θp + 05 θu minus θp1113872 1113873(6)





0 1 2 3 4 5 60

1

2

3

4

5

S a (A

max

)

Average

T (sec)

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

Average

T (sec)0 1 2 3 4 5 6

00

15

30

45

60

75

S a (A

max

)

(c)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

S a (A

max

)

(d)



S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)


0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)


(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)







0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Bedrock

Body force





analysis model






IDA curves


Fragility curves

Capacity curve









1113954D aIMb (2)






1113969⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠ (3)


βD|IM

1nminus 2

1113944

n


1113872 11138731113960 11139612

11139741113972

(4)


3 Case Study





Performancelevels


Fullyoperational

Nodamage


normally



repair








s


6000 6000 6000 6000 6000 6000

650

700700850

4000

36000


24

20

16

12

8

4

00 300 600 900 1200 1500 1800

Vs (ms)

Dep

th (m

)

(a)

Vs (ms)

60

50

40

30

20

10

00 100 200 300 400 500 600

Dep

th (m

)

(b)

Vs (ms)

Dep

th (m

)

60

50

40

30

20

10

00 100 200 300 400 500 600

(c)

Vs (ms)

Dep

th (m

)

72

60

48

36

24

12

00 50 100 150 200 250 300

(d)





120 m



Fixed boundary


2 m

70 m

120 m36 m



Soil solid elements

h

l = 20h


Input motion































fmax (5)









θOP θy + 05 θp minus θy1113872 1113873

θLS θp + 05 θu minus θp1113872 1113873(6)





0 1 2 3 4 5 60

1

2

3

4

5

S a (A

max

)

Average

T (sec)

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

Average

T (sec)0 1 2 3 4 5 6

00

15

30

45

60

75

S a (A

max

)

(c)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

S a (A

max

)

(d)



S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)


0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)


(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)







0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





1113954D aIMb (2)






1113969⎛⎜⎜⎜⎝ ⎞⎟⎟⎟⎠ (3)


βD|IM

1nminus 2

1113944

n


1113872 11138731113960 11139612

11139741113972

(4)


3 Case Study





Performancelevels


Fullyoperational

Nodamage


normally



repair








s


6000 6000 6000 6000 6000 6000

650

700700850

4000

36000


24

20

16

12

8

4

00 300 600 900 1200 1500 1800

Vs (ms)

Dep

th (m

)

(a)

Vs (ms)

60

50

40

30

20

10

00 100 200 300 400 500 600

Dep

th (m

)

(b)

Vs (ms)

Dep

th (m

)

60

50

40

30

20

10

00 100 200 300 400 500 600

(c)

Vs (ms)

Dep

th (m

)

72

60

48

36

24

12

00 50 100 150 200 250 300

(d)





120 m



Fixed boundary


2 m

70 m

120 m36 m



Soil solid elements

h

l = 20h


Input motion































fmax (5)









θOP θy + 05 θp minus θy1113872 1113873

θLS θp + 05 θu minus θp1113872 1113873(6)





0 1 2 3 4 5 60

1

2

3

4

5

S a (A

max

)

Average

T (sec)

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

Average

T (sec)0 1 2 3 4 5 6

00

15

30

45

60

75

S a (A

max

)

(c)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

S a (A

max

)

(d)



S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)


0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)


(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)







0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



s


6000 6000 6000 6000 6000 6000

650

700700850

4000

36000


24

20

16

12

8

4

00 300 600 900 1200 1500 1800

Vs (ms)

Dep

th (m

)

(a)

Vs (ms)

60

50

40

30

20

10

00 100 200 300 400 500 600

Dep

th (m

)

(b)

Vs (ms)

Dep

th (m

)

60

50

40

30

20

10

00 100 200 300 400 500 600

(c)

Vs (ms)

Dep

th (m

)

72

60

48

36

24

12

00 50 100 150 200 250 300

(d)





120 m



Fixed boundary


2 m

70 m

120 m36 m



Soil solid elements

h

l = 20h


Input motion































fmax (5)









θOP θy + 05 θp minus θy1113872 1113873

θLS θp + 05 θu minus θp1113872 1113873(6)





0 1 2 3 4 5 60

1

2

3

4

5

S a (A

max

)

Average

T (sec)

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

Average

T (sec)0 1 2 3 4 5 6

00

15

30

45

60

75

S a (A

max

)

(c)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

S a (A

max

)

(d)



S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)


0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)


(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)







0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




120 m



Fixed boundary


2 m

70 m

120 m36 m



Soil solid elements

h

l = 20h


Input motion































fmax (5)









θOP θy + 05 θp minus θy1113872 1113873

θLS θp + 05 θu minus θp1113872 1113873(6)





0 1 2 3 4 5 60

1

2

3

4

5

S a (A

max

)

Average

T (sec)

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

Average

T (sec)0 1 2 3 4 5 6

00

15

30

45

60

75

S a (A

max

)

(c)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

S a (A

max

)

(d)



S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)


0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)


(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)







0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






















fmax (5)









θOP θy + 05 θp minus θy1113872 1113873

θLS θp + 05 θu minus θp1113872 1113873(6)





0 1 2 3 4 5 60

1

2

3

4

5

S a (A

max

)

Average

T (sec)

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

Average

T (sec)0 1 2 3 4 5 6

00

15

30

45

60

75

S a (A

max

)

(c)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

S a (A

max

)

(d)



S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)


0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)


(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)







0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


θOP θy + 05 θp minus θy1113872 1113873

θLS θp + 05 θu minus θp1113872 1113873(6)





0 1 2 3 4 5 60

1

2

3

4

5

S a (A

max

)

Average

T (sec)

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

Average

T (sec)0 1 2 3 4 5 6

00

15

30

45

60

75

S a (A

max

)

(c)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

S a (A

max

)

(d)



S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)


0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)


(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)







0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(a)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(b)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(c)

S a (A

max

)

Average

T (sec)0 1 2 3 4 5 6

0

1

2

3

4

5

(d)


0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000872

θy = 000148

Shea

r (kN

)


(a)

0 3 6 9 12 150

75

150

225

300θp = 000292

θu = 000877

θy = 000146

Shea

r (kN

)


(b)

0 3 6 9 12 150

75

150

225

300θp = 000300

θu = 000862

θy = 000145

Shea

r (kN

)


(c)

0 3 6 9 12 150

75

150

225

300θp = 000298

θu = 000850

θy = 000145

Shea

r (kN

)


(d)







0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0 3 6 9 12 150

75

150

225

300θp = 000288

θu = 00128Sh

ear (

kN)


θy = 000147

(a)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00127θy = 000157

(b)

Shea

r (kN

)


0

75

150

225

300θp = 000296

θu = 00126θy = 000155

(c)

Shea

r (kN

)


0

75

150

225

300θp = 000298

θu = 00129θy = 000151

(d)


No

dam

age

Min

or d

amag

e

Mod

erat

e dam

age

CD (NC)

FFp

FuFy

θy θP θu θA

B (FO)

Seve

re d

amag

e

θLS

LS

Col

laps

e

OP

θOP









4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





4 Conclusions



00 15 30 45 60 750

2

4

6

8

10

PGA

(g)


(a)

PGA

(g)

00 15 30 45 60 750

1

2

3

4

5


(b)

PGA

(g)

00 15 30 45 60 750

1

2

3

4


(c)

PGA

(g)

0 5 10 15 20 2500

02

04

06

08

10


(d)



00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


00 15 30 45 60 750

1

2

3

4

PGV

(ms

)


(a)

PGV

(ms

)


0

1

2

3

4

(b)

PGV

(ms

)


0

1

2

3

4

(c)

PGV

(ms

)


0

1

2

3

4

(d)





ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

ln(θ

)

ln(PGV)

ln(θ) = 11059 ln(PGV) ndash 68006

(a)

ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 12708 ln(PGV) ndash 65250

(b)

Figure 14 Continued




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




ln(θ

)


ndash12

ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 13801 ln(PGV) ndash 63314

(c)

ln(θ

)


ndash10

ndash8

ndash6

ndash4

ndash2

0

ln(PGV)

ln(θ) = 09941 ln(PGV) ndash 49291

(d)


0 30 60 90 120 15000

02

04

06

08

10

Site I Site II

Site III Site IV

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(a)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(b)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(c)

Site I Site II

Site III Site IV

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

(d)





Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References




0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(a)

0 30 60 90 120 15000

02

04

06

08

10

PGV (cms)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

(b)

0 30 60 90 120 15000

02

04

06

08

10

Exce

edin

g po

ssib

ility

of d

amag

e

PGV (cms)

LS(H)LS(H+V)

NC(H)NC(H+V)

(c)

Exce

edin

g po

ssib

ility

of d

amag

e

LS(H)LS(H+V)

NC(H)NC(H+V)

0 30 60 90 120 150

02

04

06

08

10

PGV (cms)

00

(d)























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


vertical seismic effect on the seismic fragility of large

Documents