Effects of engineering geological condition on response of suspensionbridges

Junjie Wang*, Shide Hu, Xiao Wei

National Key Laboratory for Disaster Reduction of Civil Engineering, Tongji University, Shanghai, 200092, China

Abstract

The geological condition may vary largely from one support to another for a long span bridge. The effect of geological variability andspatial variation produced by propagation and coherence loss of seismic ground motion on the response of long span suspension bridges isinvestigated in this article. The case of Jiangyin Yangtse River Bridge, a suspension bridge with a main span of 1385 m, is studied in detail.Numerical results show that the geological difference at the supports has a significant effect on the seismic response of long span suspensionbridges and, that it is unacceptable to neglect the difference. The effect of the propagation of seismic ground motion on the response of longspan suspension bridges is far more important than that of the coherence loss. The response of bridges varies greatly with the horizontalapparent velocity in a very complex way, and there is a critical horizontal velocity for a given response quantity.q 1999 Elsevier ScienceLtd. All rights reserved.

Keywords:Suspension bridge; Geological condition; Spatial variation

1. Introduction

Spatial variation of seismic ground motion (SVSGM)might be important to long span bridges, and its effect onthe seismic response of bridges has been investigated for awhile. In the past decade researchers have paid attention tothe importance of SVSGM to seismic evaluation of bridgestructures, and research results have been reported in theliterature [1–16]. Various methods, structural models andground motion models with various degrees of complexitywere adopted in the contributions. However, all of the afore-mentioned research contributions took the assumption of a‘uniform site condition’, i.e. there is not much geologicaldifference along the longitudinal axis of a bridge. Thereforethe seismic ground motions at different spatial points alongthe longitudinal axis of a bridge are assumed to have thesame intensity, the same frequency contents and the sameduration, but with consideration of propagation effect andcoherence loss. However, the site conditions that the towersand anchor stones lie on might be quite different for a longspan bridge, an example is the Jiangyin Yangtse RiverBridge (JYRB), shown in Fig. 1.

A distinct feature of JYRB is its geological condition. Thenorth anchor stone and the north tower pier lie on a quater-nary surficial deposit, which is 80–120 m in thickness. Bed

rock, which is Triassic lime–rock, is at an elevation of about2 80.0 m under the north anchor stone and in an elevationof 2 85.0 m under the north tower pier. The south anchorstone and the south tower pier lie on a silicarenite rock siteat the ground surface. The rock is solid with a uniaxialcompressive strength of 40–60 MPa and a modulus ofdeformation of 1–3 MPa.

According to the author’s knowledge, so far no researchcontributions have taken the variation of geological condi-tion into account for the prediction of seismic responses oflong span bridges. In fact we have little knowledge about theseismic response characteristics of suspension bridgeslocated at a geological site similar to that of the JYRB.

In this article the seismic response characteristics of longspan suspension bridges are investigated using a randomvibration analysis and a three-dimensional finite elementmodel of the bridge is used. The effects of the site conditions(geological conditions), the propagation effect and thecoherence loss of seismic ground motion on the responseof long span suspension bridges are taken into account.

2. Bridge model

As shown in Fig. 1, the main span of JYRB is flanked bysimply supported side spans. The side spans are separatedfrom the main span at the intersection of the tower and thegirder. Therefore in this article only the main span (towers,

Soil Dynamics and Earthquake Engineering 18 (1999) 297–304

0267-7261/99/$ - see front matterq 1999 Elsevier Science Ltd. All rights reserved.PII: S0267-7261(99)00002-0

* Corresponding author.E-mail address:junjiew@uci.edu (J. Wang)

girder and cables) is modeled and analyzed. The two maincables are assumed to move in tandem as if they wereconnected by horizontal struts, and the cable ends areassumed to be fixed. The two towers are fixed at the levelof the pile cap. The towers, hangers and deck are modeledusing beam elements. The idealized bridge model is shownin Fig. 2.

3. Model of seismic excitations

3.1. Auto power spectral density (APSD)

The artificial accelerations on the ground surface from theseismic hazard analysis at the site of JYRB are shown in Fig.3. The acceleration with high frequency contents at thesouth bank is very different from that with low frequencycontents at the north bank. The APSDs of these accelera-tions are computed and shown in Fig. 4.

3.2. Cross power spectral density (CPSD)

Following the theory of stationary random process, theCPSD, Scr�v; r r ; r s�, between the acceleration�ug�t; r r � atspatial point r r and the acceleration�ug�t; r s� at spatialpoint r s can be expressed as

Scr�v; r r ; r s� ��������������������S�v; r r �S�v; r s�

pg�v; r r ; r s� �1�

in which S�v; r r � is the APSD of�ug�t; r r � andg�v; r r ; r s� isthe coherency function between�ug�t; r r � and �ug�t; r s�, which

is generally separated into two parts,

g�v; r r ; r s� � r�v; r r ; r s� exp 2ivd

c�v�� �

; �2�

wherer�v; r r ; r s� is the absolute coherency;d the distancefrom r r to r s; c(v ) the apparent velocity of seismic groundmotion, which is usually a function of the frequency.Various empirical expressions ofr�v; r r ; r s� (e.g. Refs.[17–21]) have been proposed, the model suggested by Quet al. (1996) [21] was used in this article,

r�v; r r ; r s� � exp{ 2 a�v�db�v�} ; d � ur s 2 r r u �3�in which

a�v� � a1v 1 a2; b�v� � b1v 1 b2; �4�wherea1� 0.00001678;a2� 0.001219;b1� 2 0.005500;b2 � 0.7674, the coherency functions are shown in Fig. 5.

4. The effects of geological conditions

The first 10 modal frequencies of the JYRB are 0.0522,0.0907, 0.1260, 0.1342, 0.1404, 0.1823, 0.2016, 0.2228,0.2310 and 0.2394 Hz. The bridge is a very flexible structurewith a first modal frequency of 0.0522 Hz, and otherfrequencies very closely spaced, i.e. the frequency differ-ence between a mode and its previous or next one is verysmall. In this article the first 90 modes of JYRB are includedin the analysis. A damping ratio of 0.03 was used for allmodes.

The structural responses under various excitations arecalculated and the results are listed in Tables 1 and 2 andFigs. 6–9. An apparent horizontal velocity of 1000 m/s isused in this section. In Tables 1 and 2Rockstands for theAPSD used in the computation from the artificial seismicwave at the south tower;Soilmeans the APSD used from theartificial seismic wave at the north tower; andRock–Soilstands for the APSDs at the bottom of the south tower andthe south anchor stone which are derived from the artificialseismic wave at the south tower and the APSDs at thebottom of the north tower and the north anchor stonewhich are derived from the artificial seismic wave at thenorth tower. In Figs. 6–9,R, S and R–Sstand forRock,Soil andRock–Soil, respectively.

J. Wang et al. / Soil Dynamics and Earthquake Engineering 18 (1999) 297–304298

Fig. 1. General design drawing of JYRB.

Fig. 2. Analytical model of JYRB.

4.1. Response of internal force at the middle of the mainspan

From Table 1 it is observed that the internal forceresponse at the middle of the main span are very differentunder various excitations. The maximum values occur underthe Soil excitation, minimum valves occur under theRockexcitation, and the maximum values are more than threetimes than that of the minimum values. The main reasonfor this is that JYRB is a long period structure (its firstperiod is 1/0.0522� 19.157 s), and strong vibration isgenerated by a low frequency excitation. The responses ofinternal forces underRock–Soilexcitations, which we takeas the practical excitation case, are between the aforemen-tioned maximum and minimum values. Axial forces, shearand moments are similar for the longitudinal excitation andtransverse excitation.

4.2. Response of tower

From Table 2 and Figs. 6–9, it can be seen that the char-acteristics of the tower responses may be divided into twocases, the longitudinal excitation and the transverse excita-tion. For the longitudinal excitation case the observationsare the same as those of internal force responses at themiddle of main span, i.e. the responses of the south towerand the north tower reach their maximum values under theSoil excitation, minimum values under theRockexcitationand take values between the aforementioned maximum andminimum values underRock–Soilexcitations, be it for theresponse of internal force or for the response of the relativedisplacement between the top and the bottom of the towers.

In contrast with the longitudinal excitation case theresponse of JYRB under transverse excitation shows adifferent feature. The response of the south tower under

J. Wang et al. / Soil Dynamics and Earthquake Engineering 18 (1999) 297–304 299

Fig. 3. (a) Artificial seismic wave at south tower and anchor. (b) Artificial seismic wave at north tower and anchor.

Fig. 4. PSDs of artificial waves of ground motion.

Rock–Soilexcitation is nearly the same as that under theRockexcitation, while the response of the north tower undertheRock–Soilexcitation is nearly the same as that under theSoil excitation. This feature can be clearly observed fromTable 2 and Figs. 8 and 9. The reason may be that the cablesand girder take a weak connection between the south towerand the north tower when JYRB vibrates in transverse direc-tion. This feature may be used to simplify the modeling ofthe long span suspension bridges. However it must be keptin mind that the difference of geological conditions at thesouth and north banks is very important to the responses ofJYRB whether for the longitude excitation case or the trans-verse excitation case. It is unacceptable to neglect thedifference.

5. The effect of propagation and coherence loss

According to Eqs. (1) and (2), there are three factors toproduce the spatial variation of seismic ground motion. Thefirst is the difference of site conditions at the supports of abridge, presented byS�v; r r �, which is discussed in theSection 4. The second is the propagation characteristic ofthe seismic wave, expressed byc(v ); the third is the coher-ence loss, expressed byr�v; r r ; r s�. Although the impor-tance of the second and the third factors to long spanbridges has been recognized (e.g. Refs. [10, 16]), the effectof the propagation of seismic waves has not been distin-

guished from that of the coherence loss of seismic groundmotion. In this section the relative importance ofc(v ) andr�v; r r ; r s� is discussed.

To identify the relative importance of coherence loss onthe structural responses, a ratioR is defined as,

R� GT; �5�

whereG is the response under general excitations andT isthe response under travelling excitations. The results ofRare shown in Figs. 10–12.

It is observed thatR varies with apparent velocityc(v)and is different from one response quantity to another. Itmay be larger or less than unity, which means the coherenceloss of the seismic ground motion may increase or decreasethe responses of the structures. A more important observa-tion is thatR of the north tower is obviously less extremethan that of the south tower. This observation may beexplained as follows. The energy of seismic ground motionat the south tower distributes in a wide range of frequency(about 0.0–10.0 Hz, see Fig. 4), but a narrow range offrequency (0.0–3.0 Hz) for the seismic ground motion atthe north tower. Consequently, compared with the responsesof the north tower, more of the responses of the south towerare excited by the high frequency components of seismicground motion. As we know, the spatial coherence function,r�v; r r ; r s�, decreases with frequency, which means lessfrequency components of seismic ground motion can be

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Fig. 5. Coherency function used in this article.

Table 1Response of the internal forces at the mid of the main span (unit: N for axisforces and shears, Nm for moments)

APSD used Longitudinal excitation Transverse excitationN(104) Q(104) M(105) N(103) Q(105) M(107)

Rock 4.120 2.258 9.750 3.054 3.250 2.408Soil 14.091 8.104 34.734 8.585 10.398 7.120Rock–soil 9.808 6.187 24.055 7.551 7.181 5.174

Table 2Responses of the relative displacements between the top and bottom of thetowers (unit – cm)

APSD used Longitudinal excitation Transverse excitationSouth tower North tower South tower North tower

Rock 2.103 2.471 3.632 3.628Soil 6.174 7.056 7.097 7.109Rock–Soil 4.479 6.020 3.615 7.105

taken as travelling seismic waves�r�v; r r ; r s� ; 1 for thetravelling seismic waves) with frequency. The value ofRreflects this fact. This observation means that the coherenceloss of the seismic ground motion may be important to thosestructures with high stiffness. We also observe from Figs.10–12 thatR is not more than 1.15 for the relative displace-ment, 1.06 for the internal forces, that is, the error producedby neglecting the effect of the coherence loss is not morethan 15% for the relative displacement and 6% for the inter-nal forces. Obviously the coherence loss is less importantthan the travelling effect of seismic ground motion. It isreasonable and possible to find a simple way to take thecoherence loss into account in the seismic analysis or aseis-mic design of long span suspension bridges, rather thanusing a complex empirical model ofr�v; r r ; r s�.

6. Conclusions

In this article, the effect of spatial variation of seismicground motion on responses of long span suspension bridgesis investigated with the emphasis on its engineering geolo-gical condition and it is concluded that:

• The large geological difference at the supports of abridge is important to the prediction of seismic responsesof long span suspension bridges and it is unacceptablenot to take this difference into account. The responses ofJYRB are overestimated if the seismic ground motionfrom north bank (soil site) is taken as the excitation,while they are underestimated with the seismic groundmotion from the south bank (rock site).

J. Wang et al. / Soil Dynamics and Earthquake Engineering 18 (1999) 297–304 301

Fig. 6. Responses of internal forces at south tower under longitudinal excitations.

Fig. 7. Responses of internal forces at north tower under longitudinal excitations.

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Fig. 8. Responses of internal forces at south tower under transverse excitations.

Fig. 9. Responses of internal forces at north tower under transverse excitations.

Fig. 10. Relative displacements between the tops and bottoms of the towers.

• The response of a tower is dominated by the excitation atthe bottom of the tower. This may be used to simplify theanalytical model of the long span suspension bridges.

• The error produced by neglecting the effect of coherenceloss is not more than 15%. For engineering application, itis reasonable and possible to find a simple way to takethis effect into account in the seismic analysis or aseismicdesign of long span suspension bridges, rather than usinga complex expression of the coherence function.

This research is partly supported by National ScienceFoundation of China under contract no. 59408006.

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