Effect of Soil-Structure Interaction on Seismic ...

Research ArticleEffect of Soil-Structure Interaction on Seismic Performance ofLong-Span Bridge Tested by Dynamic Substructuring Method

Zhenyun Tang, HuaMa, Jun Guo, and Zhenbao Li

The Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education,Beijing University of Technology, Beijing 100124, China

Correspondence should be addressed to Hua Ma; [email protected]

Received 9 October 2016; Revised 13 December 2016; Accepted 19 January 2017; Published 8 March 2017

Academic Editor: Salvatore Strano

Copyright © 2017 Zhenyun Tang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Because of the limitations of testing facilities and techniques, the seismic performance of soil-structure interaction (SSI) system canonly be tested in a quite small scale model in laboratory. Especially for long-span bridge, a smaller tested model is required whenSSI phenomenon is considered in the physical test. The scale effect resulting from the small scale model is always coupled withthe dynamic performance, so that the seismic performance of bridge considering SSI effect cannot be uncovered accurately by thetraditional testing method. This paper presented the implementation of real-time dynamic substructuring (RTDS), involving thecombined use of shake table array and computational engines for the seismic simulation of SSI. In RTDS system, the bridge withsoil-foundation system is divided into physical and numerical substructures, in which the bridge is seen as physical substructuresand the remaining part is seen as numerical substructures.The interface response between the physical and numerical substructuresis imposed by shake table and resulting reaction force is fed back to the computational engine. The unique aspect of the methodis to simulate the SSI systems subjected to multisupport excitation in terms of a larger physical model. The substructuring strategyand the control performance associated with the real-time substructuring testing for SSI were performed. And the influence of SSIon a long-span bridge was tested by this novel testing method.

1. Introduction

In the seismic analysis of a structure founded on ground, theground motion passes to the base of structure and then loadson structure. The response of the foundation system affectsthe response of the structure and vice versa, which is calleddynamical soil-structure interaction (SSI).Theoretical results[1, 2] indicate that SSI is sometimes beneficial and sometimesdetrimental to structural performance. Therefore, the effectof soil cannot be neglected, because SSI phenomenon isclosely related to its dynamic characteristics [3], especiallythe damping [4] of the whole system. To explore the effectof SSI on the seismic performance of engineering structures,the finite element methods [5] and theoretical analysis [6] areoften used. However, the uncertainties [7, 8] and boundarycondition [9] existing in SSI system have not been simulatedproperly by thesemethods.At present, experimental evidencerelating to SSI system is scarce. The SSI system is difficult tobe investigated by testing full-size specimen (including both

structure and soil-foundation systems) under earthquakeloading because of the size and power of the testing facil-ities, especially, for the structures with large spatial extent.In current testing of SSI, the soil-foundation systems arereplaced by laminar shear box with soil [10–12], and thestructures are usually scaled down to small size (often scaledto 1/30 or even smaller) or a simple cantilevered mass [10, 11],which results in the inevitable possibility of size effects. Inaddition, time must be scaled, accompanying with frequencyscaled up, in test to provide rapid shaking, often preventedby the frequency bandwidth of shaking table. SSI plays amore important role in the seismic performance of long-spanbridge [13]. However, the smaller specimen is required in thelaboratory experiment because of its dimension. As a result,simplified models are tested at reduced scales making theinterpretation and application of results challenging.

The method of real-time substructuring derived fromhardware-in-the-loop test [14] has been paid close attentionsince the first real-time substructuring test was reported by

HindawiShock and VibrationVolume 2017, Article ID 4358081, 12 pageshttps://doi.org/10.1155/2017/4358081

https://doi.org/10.1155/2017/4358081

2 Shock and Vibration

Numerical modelEarthquake

loading Shaking tableInterface response

Physical model Interface response

Interface reaction

Figure 1: Generally schematic representation of RTDS using shaking table.

Nakashima et al. [15], which is a method of dynamicallytesting a structure without experimentally testing a physicalmodel of the entire system; instead the structure can besplit into two coupled parts, the region of particular interest,which is tested experimentally, and the remainder which istested numerically. It also received interest in SSI systems.To simulate the soil medium numerically in a shakingtable substructuring test where the superstructure is testedexperimentally, Konagai et al. [16, 17] used analogue electriccircuits to generate the transient response of both linearand nonlinear soils. Heath et al. [18] and Wang et al. [19]investigated an inverted substructuring system by modellingthe superstructure numerically. However, only very simplesoil model and superstructures were adopted in these works.To simulate the SSI phenomenon with bridge experimentallyusing RTDS, further validation is required involving morecomplex structures and more complex interactions.

In the research presented in this paper, a framework ofsubstructuring for SSI system with bridge was establishedfirstly; after that the control strategies for the real-timedynamic substructuring testing were analysed. Finally, theinfluence of SSI on a long-span bridge was tested through thisnovel testing method.

2. Modelling of RTDS Systemsfor SSI Simulation

2.1. RTDS Scheme Based on Shaking Table Array. The devel-opment of advanced computation and control techniquesresulted in the great progress of real-time substructure[20, 21]. The basis of such tests is to divide the overallsystem into experimental test specimen and the numericalmodel. Typically the experimental test specimen containsthe area of particular interest which behaves nonlinearly anduncertainly; the numerical model contains the remainderof the system which behaves linearly or can be modelledadequately. These two parts are tested in parallel and inreal-time with information relating to the interface betweenthe two parts being exchanged between them, allowing thetwo parts to emulate the whole system. Figure 1 shows thegenerally schematic representation of substructuring used toemulate dynamics of structures in earthquake engineering.Interface responses are passed from the numerical model toshaking table, which reproduces accurately the responses atthe interface of the test specimen.The interface reaction force

measured from test specimen then feed back to the numericalmodel.

Importantly, the most significant advantage of real-timesubstructuring is that the process is implemented as a time-stepping routine in real-time, which allows that not onlycan the nonlinear and uncertain behaviour of physical sub-structure be accurately tested, but also the time-dependentnonlinearity of numerical substructure can be adopted in thetesting. The test method mentioned above supplies a novelsolution for the SSI testing. As known, compared with soil-foundation system, the behaviour of structure is relativelyeasily modelled, especially, the nonlinearity including gap-ping between the foundations and soil and nonlinear stress-strain response of the soil, and so on. However, the realinterest in SSI is the response of structure under earthquakeloading; meanwhile, the complexity of structural form andmaterial, geometrical, and contacting nonlinearity of struc-ture are also not well described theoretically. Therefore, boththe two kinds of substructuring (soil-foundation system orstructure modelled numerically) for SSI need to be devel-oped. In this work, the soil-foundation system is treated asnumerical substructure and simulated in computer, while thebridge seems as the physical substructure and tested in thelaboratory. A diagrammatic representation of RTDS for abridge is shown in Figure 2. The emulated SSI system shownin Figure 2(a) can be tested by the RTDS strategy shown inFigure 2(b). Unlike other building structures, a single shakingtable is enough to carry out the test; the length of bridgeis quite large, even the scale model is often more than tenmeters long. To overcome this drawback, the shaking tablearray composed of multishaking tables was constructed andused to test the seismic performance of bridge [22].Therefore,the shaking table array is adopted to reproduce the interfaceresponse of each bridge pier and foundation.

2.2. Numerical Model of Soil-Foundation System. The groundmotion imposing on superstructure caused by earthquakeincludes three portions (as illustrated in Figure 3(a)): themovement of free-field soil resulting from earthquake (𝑢g),the deviation of the foundation movement resulting fromthe free-field soil motion (𝑢gs), and the deformation offoundation produced by the reaction force from superstruc-ture (inertia interaction: 𝛿 and 𝜃). This work focuses onthe interaction between soil and structure; consequently,the foundation movement is identical to the free-field soilmovement (𝑢gs = 0). In the seismic analysis for SSI, the

Shock and Vibration 3

(a) Whole soil-structure system under multisupport excitation

Reaction force: F, M

Physical substructure

Numerical substructure

Interface responses: �훿, �휃

kh, ch

kr, cr

(b) Substructured system:soil-foundation system represented as numerical substructure

Figure 2: Substructuring system for bridge subject to earthquake excitation.

Semi-infinite

FM

�훿

�휃

ug + ugs

ug

(a) Deformation of soil-pile-foundation

FoundationFd

Kb Cb

(b) Time-domain difference model

Figure 3: Numerical model of soil-pile-foundation system.

substructure method is cost-effective, comparing with thedirect integrity approach, in which the behaviour of the soil-foundation system (see in Figure 3(a)) was described as animpedance function (also shown in Figure 3(b)):

𝐾h = 𝑘h (𝜔) + 𝑖𝜔𝑐h (𝜔) , (1)

where 𝑘h is horizontal stiffness, 𝑐h is horizontal damping, 𝜔is circular frequency, and 𝑖 is imaginary unit. However, theimpedance function is frequency-dependent, which cannotbe used to represent the nonlinear effect of dynamic interac-tion between soil and structure.

In order to overcome this disadvantage, two main meth-ods [23–25] were developed to transform the frequency-dependent impedance function to time-domain: lumpedparameter model approximately fitting to impedance func-tions using different mass-spring-damping systems and fastintegral algorithms (also referred to as recursivemodel) basedon the properties of Fourier inverse transform. Nevertheless,the two methods have their own defects: lumped parametermodel [23, 24] can only fit the actual impedance functions

in narrow frequency band accurately but cannot reflect theregular component, which corresponds to time-delay effect;meanwhile, recursive model [25] has intrinsically limitationat Nyquist frequency; namely, the imaginary part of filtermust be zero at Nyquist frequency.

So as to take the full advantage of the two models andmake up for their deficiency as well, a time-domain differencemodel (TDDM) for soil-foundation system was proposed byDu and Zhao [26], combining lumped parameter model andtime-domain recursive model, which can take into accountboth the singular and regular component of foundationimpedance comprehensively.Themechanicalmodel is shownin Figure 3(b), where

𝐾𝑏 = 𝑛𝐾𝑠𝑘1,𝐶𝑏 = 𝑛𝐾𝑠𝑐1,

𝐹𝑑 =𝑛

∑𝑖=1

𝑏𝑖𝑦𝑏 (𝑡 − 𝑖Δ𝑡) +𝑚

∑𝑖=1

𝑎𝑖𝐹𝑑 (𝑡 − 𝑖Δ𝑡)(2)


Table 1: Parameters of the used TDD model.

𝑎1 𝑎2 𝑎3 𝑎4 𝑎5 𝑎6 𝑘1 𝑐11.198 −0.013 −0.415 −0.127 0.02 0.004 0.659 0.011𝑏1 𝑏2 𝑏3 𝑏4 𝑏5 𝑏6 — —−0.681 −0.205 0.433 0.028 −0.029 −0.003 — —

with 𝑛 being numbers of piles, 𝐾𝑠 static stiffness of singlepile, 𝑘1 normalized stiffness, 𝑐1 normalized damping, 𝐹𝑑(𝑡)pseudo-force, 𝑦𝑏(𝑡) displacement of foundation, Δ𝑡 integra-tion time step, and 𝑎𝑖, 𝑏𝑖 the coefficients of pseudo-force anddisplacement. From (2) we can see that the determinationof parameters 𝑘1, 𝑐1, 𝑎𝑖, 𝑏𝑖 is the key point for the time-domain differencemodel, the best values of which are derivedusing hybrid optimization based on the theory or numericalsolution of impedance function.

Herein, we assume that the bridge pier is constructed on a3× 3 pile group foundation, and the parameters are as follows:damping ratio of soil is 0.05, Poisson’s ratio of soil is 0.4, ratioof pile spacing and diameter is 5, YoungModulus ratio of pileto soil is 1000, mass density ratio of pile to soil is 1.42, andratio of pile length and diameter is 15. Normalized by singlepile static stiffness, the impedance function of the pile groupfoundation can be expressed as

𝐾h (𝑎0) = 9𝑘sh [𝑘h (𝑎0) + 𝑖𝑐h (𝑎0)] , (3)

where 𝑎0 = 𝜔𝑑/V𝑠 is dimensionless frequency, 𝑘sh is singlepile horizontal static stiffness, V𝑠 is shear wave velocity of soil,𝑑 is pile diameter. Using the dynamic impedance functiondeveloped by Makris and Gazetas [27, 28] for the pile groupfoundation, the parameters of TDDM were estimated bymultiple regression analysis. The evaluated values of allparameters for this model are shown in Table 1. The com-parative results of the TDDM and Markris’s analytical modelpresented in Figure 4 show that TDDMis suitable to representthe soil-foundation system in RTDS.

3. Control Strategies for RTDS

3.1. RTDS Controller Design. In commonly used RTDS sys-tem, displacement or force was used to be target signalto drive transfer system; however in some SSI systems,such as sandy soil, the effect of SSI on the accelerationof structure is noticeable, but the effect on displacementis inconspicuous. In that case, the acceleration of interfacecannot be reproduced well by using displacement control. Inthis work, the acceleration driving was attempted to be usedin the RTDS for SSI of this work. In this RTDS system,shaking table array was used as the transfer system toproduce the interface response of foundation, resulting fromthe dynamics of which, the response between physical andnumerical substructure is always asynchronous, even causingthe instability, especially for the low damping system [29].In standard earthquake testing, the shaking table is drivenby a conventional controller, such as PID or three-variablecontroller. These controllers cannot give a perfect control.Phase lag and magnitude error always exist. In order to

Real part (Makris’s result)Imaginary part (Makris’s result)

Real part (TDDM)Imaginary part (TDDM)

Kh/9k

sh

a0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.2 0.4 0.6 0.8

Figure 4: Normalized dynamic stiffness of pile group foundationreported by Du and Zhao [34].

impose the interface response calculated from numericalsubstructure on the physical substructure through shakingtable synchronously, an additional controller is necessary tocancel the shaking table dynamics.

Based on TDDM presented in Section 2.2, the emulatedsystem shown in Figure 5(a) can be substructured as theRTDS system shown in Figure 5(b). TDDMmodel representsthe soil-foundation system.The bridge is installed on shakingtable array, which is used as the transfer system to simulate theinterface acceleration (𝑎𝑛). As can be seen in Figure 5(b), theinterface acceleration resulted from external excitation (𝑢g)and reaction force of superstructure (𝑓):

𝑎𝑛 = 𝐺𝑓𝑟𝑢g + 𝐺𝑓𝑓𝑓. (4)

From Figure 5(b), the transfer function models for thedifferent parts can be determined.

𝐺𝑓𝑟 (𝑠)

= 𝑠2𝑚𝑏𝑚𝑏𝑠2 + 𝑛𝑘𝑠ℎ (𝑐1𝑠 + 𝑘1 + ∑6𝑖=1 𝑏𝑖𝑧−𝑖/ (1 + ∑6𝑖=1 𝑎𝑖𝑧−𝑖))

,

𝐺𝑓𝑓 (𝑠)

= 𝑠2𝑚𝑏𝑠2 + 𝑛𝑘𝑠ℎ (𝑐1𝑠 + 𝑘1 + ∑6𝑖=1 𝑏𝑖𝑧−𝑖/ (1 + ∑6𝑖=1 𝑎𝑖𝑧−𝑖))

,

(5)


Shaking tableactuator

Ground motion

Bridge

Soilbox

ug

(a) Emulated system

Inner-loopcontroller Shaking table

actuator

RTDScontroller

u

eKb

Cb

Mp

Mb

ap

an

an

Kp , Cp

−

+

f

Σp

ΣNug

(b) Substructured system

Figure 5: Framework of RTDS for SSI simulation.

where 𝑧 = 𝑒𝑖𝜔Δ𝑡, Δ𝑡 is integration time step. Normally, theachieved value of interface acceleration is not 𝑎𝑛 but 𝑎𝑝 aftergoing through shaking table because of its dynamics. Thatleads to the needs of RTDS controller. As reference [30]mentioned, the shaking table can be approximated to a first-order system such that

𝐺𝑠 (𝑠) = 𝑎𝑠 + 𝑎 , (6)

where 𝑎 is the product of the time constant and the propor-tional gain of shaking table. And then the reaction force isformulated as

𝑓 = 𝐺𝑓𝑎𝑝. (7)

𝐺𝑓 represents the transfer function of the total shear force (𝑓)of superstructure from excitation (𝑎𝑝), which is determinedby the dynamic parameters. From Figure 5(b), 𝐺𝑓 can beexpressed as

𝐺𝑓 =𝐶𝑝𝑠 + 𝐾𝑝

𝑀𝑝𝑠2 + 𝐶𝑝𝑠 + 𝐾𝑝 , (8)

where M𝑝, C𝑝, and K𝑝 are the mass, damping, and stiffnessof bridge, respectively.

To formulate the synthesis procedure of RTDS dynamicsand control, a framework of linear substructuring controller(LSC) [31] together with the minimal control synthesis witherror feedback (MCSEF) algorithm [32] was proposed. Tosimplify the LSC for multidegree of freedom system, a mod-ified linear substructuring controller (MLSC) together withMCSEF was developed by Guo et al. [33]. As illustrated inFigure 6, an emulated system is conceptually decomposedinto at least two substructures, Σ𝑛 and Σ𝑝. For practical casesΣ𝑛 represents the numerical model and Σ𝑝 represents the

+

+

+

+

MCSEF

ug

ap

an

u

e

−

−

Kr

Ke

G1

G2

G

Σp

ΣN

Figure 6: MLSC-MCSEF controlled RTDS system.

physical model. Control and excitation signals are denoted by𝑢 and 𝑟, respectively. Here, the RTDS dynamics are rep-resented by three generalized blocks, 𝐺, constraint; 𝐺1,excitation; and 𝐺2, transfer system dynamics. 𝐺1(𝑠) is therelationship between the displacements of the top of thefoundation (𝑎𝑛𝑟) and the ground motion (𝑢g); 𝐺(𝑠) is therelationship between the control signals (𝑢) and the accel-eration of the top of the foundation (𝑎𝑛𝑓) from the reactionforce, including the TS dynamics 𝐺𝑠(𝑠), the reaction forcedynamics 𝐺𝑓(𝑠), and the numerical substructure dynamics𝐺𝑓𝑓(𝑠); 𝐺2(𝑠) is the TS dynamics; thus

𝐺1 (𝑠) = 𝐺𝑓𝑟 (𝑠) ,𝐺 (𝑠) = 𝐺𝑠 (𝑠) 𝐺𝑓 (𝑠) 𝐺𝑓𝑓 (𝑠) ,𝐺2 (𝑠) = 𝐺𝑠 (𝑠) .

(9)


With reference to [31], the error dynamics (𝑒 = 𝑎𝑛 − 𝑎𝑝) of anLSC-controlled DSS can be written as

𝐺err (𝑠) = 𝐺1 (𝑠) − [𝐺 (𝑠) + 𝐺2 (𝑠)]𝐾𝑟 (𝑠)1 + [𝐺 (𝑠) + 𝐺2 (𝑠)]𝐾𝑒 . (10)

To synchronize the two outputs {𝑎𝑛, 𝑎𝑝}, the substructuringerror is expected to equal zero, the numerator of (10) is setequal to zero, and then

𝐾𝑟 (𝑠) = 𝐺1 (𝑠)𝐺 (𝑠) + 𝐺2 (𝑠) . (11)

The control signal and adaptive gains of MCSEF in Figure 6are generated from (12), where {𝛼, 𝛽} are adaptive weights;the ratio 𝛼 = 10𝛽, which has been shown to work wellempirically [29], is used here.The term 𝑦𝑒 is the output error,generated directly from 𝑒, according to 𝑦𝑒(𝑡) = 𝐶𝑒𝑒(𝑡), where𝐶𝑒 is selected to ensure a strictly positive real dynamic in thehyperstability proof for the MCSEF controller [29]; for first-order control,𝐶𝑒 is normally defined as [29]:𝐶𝑒 = 4/𝑡𝑠, where𝑡𝑠 is the step response time of the implicit reference model.

𝑢 (𝑡) = 𝐾𝑟 (𝑠) ��g (𝑡) + 𝐾𝑒 (𝑠) 𝑒 (𝑠) + 𝐾𝑟𝑎 (𝑡) ��g (𝑡)+ 𝐾𝑒𝑎 (𝑡) 𝑒 (𝑡) ,

𝐾𝑟𝑎 (𝑡) = 𝛼∫𝑡

0𝑦𝑒 (𝑡) 𝑟𝑇 (𝑡) 𝑑𝑡 + 𝛽𝑦𝑒 (𝑡) 𝑟𝑇 (𝑡) 𝑑𝑡,

𝐾𝑒𝑎 (𝑡) = 𝛼∫𝑡

0𝑦𝑒 (𝑡) 𝑒𝑇 (𝑡) 𝑑𝑡 + 𝛽𝑦𝑒 (𝑡) 𝑒𝑇 (𝑡) 𝑑𝑡.

(12)

3.2. Validation of RTDSController Performance. For verifyingthe validity of the RTDS for SSI simulation, further tests ofa one-story steel frame including SSI considerations wereperformed. The parameters for the soil model are shown inTable 1, and 𝑘sh = 62600N/m.The parameters of the physicalsubstructure are as follows: 𝑀𝑝 = 115 kg, 𝐶𝑝 = 17.67N/ms,and 𝐾𝑝 = 7.56 × 104N/m. The shaking table used here is ashake table array including nine shaking tables (shown in Fig-ure 7) fromBeijing University of Technology (BJUT), and thespecifications are shown in Table 2. The estimated parameterof the shaking table used in MLSC design was 𝑎 = 16Hz. Theacceleration record of El Centro earthquake (NS componentof the 1940 El Centro, Station: 117 El Centro Array #9,Component 270∘) was chosen as the ground motion. Exper-iment and simulation results are shown in Figure 8, whichdemonstrate that the RTDS method emulates dynamic soil-structure interaction effectively. That means the MLSC-MCSEF controller compensated the dynamics of shakingtable successfully.

4. The Effect of SSI on Seismic Performance ofa Long-Span Bridge

4.1. Test Design. Thedynamic response of a large-span bridgewith the considerations of SSI subjected to earthquake excita-tion was tested using RTDS method developed in this work.

Table 2: Specifications of shake table array in BJUT.

Table size 1m × 1m (𝑋/𝑌),B600 (𝑍)Operation mode 𝑋/𝑌/𝑍Maximum specimen mass 5 tonVelocity ±80 cm/sFrequency of operation 0.1∼50HzTable mass 1 tonNumber 9Displacement ±7.5 cmAcceleration (full load) ±1.5 g (𝑋/𝑌), 0.8 g (𝑍)Control mode TVC

Figure 7: Shake table array in BJUT.

In this RTDS test, the specimen (see in Figure 9) was takenas physical substructure.The parameters of this specimen aremass 4500 kg, length 13.84m, and height 1.2m. The time-domain difference model described in Section 2 was chosenas numerical substructure. The parameters of soil model arelisted in Table 1. And the Young modulus of pile is 113.4Gpa,the density of soil is 2000 kg/m3, and diameter of pile is 0.4m.The photo of the specimen is shown in Figure 10. Herein, fourshaking tables are used to produce the interface response ofeach foundation under piper. The acceleration record of ElCentro (See in Figure 11(a)) and Wenchuan earthquake (Seein Figure 11(b)) was chosen as the ground motion.

Before conducting RTDS test, a conventional shakingtable test with white noise excitation was carried on toidentify the dynamic parameters of the physical substructure.The Fourier spectrums of the acceleration measured at pier2were shown in Figure 12. As can be seen, the frequencies of thefirst and second mode were 4.76Hz and 9.58Hz, and thefirst mode is the dominated mode. For the design of MLSCcontroller in this test, the physical substructure still can betreated as a single degree-of-freedom system. The dampingratio of the first mode obtained from Figure 12 is 2.6%.

4.2. Effect of SSI on the Response of the Long-Span Bridge. Toevaluate the effect of SSI on the dynamic response of long-span bridge, the soft soil-foundation system with the shearwave velocity V𝑠 = 100m/s, 200m/s, and 400m/s was testedusing the MLSC-MCSEF controlled RTDS. For comparison,


0 1 2 3 4 5 6 7 8 9

0

1

2

Time (sec.)

TestingSimulation

−1

−2

Acc.(m

2/s)

Figure 8: Acceleration of physical substructure measured from the RTDS for one-story frame.

Table1 Table2 Table3 Table4

Pier1 Pier2 Pier3 Pier4

3.68m 6.48m 3.68m

1.2mug

Figure 9: Dimensions of specimen.

Figure 10: Photo of specimen.

the hard soil-foundation system was also tested using theconventional shaking table test without the consideration ofSSI.

In the experiment, the MLSC-MCSEF strategy wasadopted. Figure 13 displayed the desired and achieved accel-eration of shaking table in the form of synchronization sub-plots. It was seen that MLSC-MCSEF supplied an acceptableaccuracy for RTDS-SSI test.

The tested results of acceleration and strain responseexcited by Wenchuan earthquake were presented in Figures14(a) and 14(b), respectively. As can be seen from Figure 14,the SSI effect enlarged the dynamic response of bridge whenthe shear wave velocity of soil is 400m/s and 200m/s. Theamplification ratios of acceleration for V𝑠 = 400m/s and200m/s were around 45% and 30%, respectively, while thecorresponding value of strain was around 106% and 86%.However, when the shear wave velocity of soil is too low (e.g.,V𝑠 = 100m/s), the SSI effect reduced the dynamic response ofbridge in this case. The acceleration and strain were bothreduced to 50% of hard soil case (V𝑠 = infinity). The clearevidence can be obtained from the acceleration measured on

the shaking table shown in Figure 15. Compared with thehard soil case (V𝑠 = infinity), the excitation imposed on thebridge was changed significantly by soil. Generally, the highfrequency components of the seismic wave were filtered bysoil, while the low frequency components were amplified.Thecan be seen clearly from the time history (see Figure 15(a))and Fourier spectrum (see Figure 15(b)). In the hard soil case,the seismic wave used in this test has abundant componentsfrom 4Hz to 16Hz. After considering SSI, the componentsof the frequency more than 10Hz were lessened, and thecomponents of the frequency less than 8Hz were enhancedin the cases of V𝑠 = 400m/s and 200m/s. However, the com-ponents of the low and high frequency were both filtered inthe case of V𝑠 = 100m/s. In this case, the soil is too soft andequivalent to an isolator.When V𝑠 = 400m/s and 200m/s, theamplified components were close to the frequency of the firstmode of the bridge; hence, the acceleration and the strain ofthe bridge were enlarged.

Table 3 summarized themaximum strain at the bottom ofPier2 and Pier3 measured from El Centro and Wenchuanearthquake. It can be seen that Pier2 and Pier3 gave the


0 10 20 30 40

0

0.05

0.1

0.15

Time (sec.)

Acc.

(g)

−0.05

−0.1

−0.15

−0.2

(a) El Centro

Time (sec.)

Acc.

(g)

0 10 20 30 40 50 60

0

0.05

0.1

0.15

−0.05

−0.1

−0.15

−0.2

(b) Wenchuan

Figure 11: Seismic wave used in the test.

0 5 10 15 200

0.5

1

1.5

2

2.5

3

3.5

Frequency (Hz)

×10−4

4.76Hz

9.58HzFour

ier s

pect

rum

(g·s)

Figure 12: Flourier spectrum of the acceleration at the top of pier2.

0.05 0.15 0.25

0.05

0.15

0.25

−0.05

−0.15

−0.25−0.05−0.15−0.25

an (g)

a p(g

)

Figure 13: Control performance of the table below pier2.


0

0.5

1

Acc.

(g)

0

0.5

1

Acc.

(g)

0

0.5

1

Acc.

(g)

0 5 10 15

0

0.5

1

Acc.

(g)

Time (sec.)

0 5 10 15Time (sec.)

0 5 10 15Time (sec.)

0 5 10 15Time (sec.)

�s = infinity

�s = 400 m/s

�s = 200 m/s

�s = 100 m/s

−0.5

−1

−0.5

−1

−0.5

−1

−0.5

−1

(a) Acceleration at the top of pier2

0

400

800

0

400

800

0

400

800

0 5 10 15

0

400

800

Time (sec.)

0 5 10 15Time (sec.)

0 5 10 15Time (sec.)

0 5 10 15Time (sec.)

�s = infinity

�s = 400 m/s

�s = 200 m/s

�s = 100 m/s

Stra

in (�휇

�휀)St

rain

(�휇�휀)

Stra

in (�휇

�휀)St

rain

(�휇�휀)

−400

−800

−400

−800

−400

−800

−400

−800

(b) Strain at the bottom of pier2

Figure 14: Dynamic response of bridge.

Table 3: Maximum strain at the bottom of Pier2 and Pier3.

V𝑠 (m/s) Infinity 400 200 100

El Centro Pier2 (𝜇𝜀) 269 559 601 272Pier3 (𝜇𝜀) 193 416 505 216

Wenchuan Pier2 (𝜇𝜀) 345 710 643 185Pier3 (𝜇𝜀) 289 725 513 118

similar conclusion. Whereas almost the same reductionratio was measured from El Centro excitation when V𝑠 =100m/s, the amplification ratio is smaller than Wenchuan

excitation when V𝑠 = 200m/s and 400m/s. This resultedfrom the frequency characteristics of the two excitations.TheFlourier spectrum plotted in Figure 16 demonstrated that ElCentro excitation (see Figure 16(a)) has different frequencycomponents with Wenchuan excitation (see Figure 16(b)). Itshowed that the characteristics of excitation determined theresponse of bridge together with the soil properties in SSIsystem.

5. Conclusions

The purpose of this work is to establish a potential test-ing method for the simulation of soil-structure interaction


0 5 10 15 20Time (sec.)

0 5 10 15 20Time (sec.)

0 5 10 15 20Time (sec.)

0 5 10 15 20Time (sec.)

�s = infinity

�s = 400 m/s

�s = 200 m/s

�s = 100 m/s

0

0.15

0.3

−0.15

−0.3

Acc.

(g)

0

0.15

0.3

−0.15

−0.3

Acc.

(g)

0

0.15

0.3

−0.15

−0.3

Acc.

(g)

0

0.15

0.3

−0.15

−0.3

Acc.

(g)

(a) Time history

0 5 10 15 20 25Frequency (Hz)

0 5 10 15 20 25Frequency (Hz)

0 5 10 15 20 25Frequency (Hz)

0 5 10 15 20 25Frequency (Hz)

�s = infinity

�s = 400 m/s

�s = 200 m/s

�s = 100 m/s

0

1

2

Four

ier s

pec.

×10−3

0

1

2

Four

ier s

pec.

×10−3

0

1

2Fo

urie

r spe

c.×10−3

0

1

2

Four

ier s

pec.

×10−3

(b) Fourier spectrum

Figure 15: Acceleration response of the table below pier2.

based on real-time dynamic substructuring (RTDS), testingbridge experimentally and modelling the remainder partnumerically, which make the long-span bridge testing withconsideration of SSI possible. The “size effect” resulting fromthe scaled model in whole system tests because of the sizeand power of the testing facilities is weakened; meanwhilethe nonlinear dynamics of the SSI system can be investigatedusing this method. The feasibility of this method has beenverified experimentally.

The influence of SSI on a long-span bridge was testedthrough RTDS method. The SSI effect enlarged the dynamicresponse of bridge when the shear wave velocity of soil is400m/s and 200m/s, while the SSI effect reduced thedynamic response of bridge when the shear wave velocity of

soil is too low (e.g., V𝑠 = 100m/s). In other words, themediumsoft soil-foundation may be detrimental to the seismicperformance of bridge, and the soft soil may be beneficialto the seismic performance based on the test results of thiswork.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors gratefully acknowledge the support of theNational Science Foundation of China, Grant no. 51608016,


0 5 10 15 20 250

0.5

1

1.5

2

2.5

3

3.5

Frequency (Hz)

×10−4Fo

urie

r spe

ctru

m (g

·s)

(a) El Centro

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2

1.4

Frequency (Hz)

×10−4

Four

ier s

pect

rum

(g·s)

(b) Wenchuan

Figure 16: Flourier spectrum of the seismic wave used in the test.

and the support of the Beijing Natural Science Foundation(8164050) in the pursuance of this work.

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