Nonlinear SSI effect on adjacent bridge structures with pounding

Proceedings of the Ninth Pacific Conference on Earthquake Engineering Building an Earthquake-Resilient Society 14-16 April, 2011, Auckland, New Zealand

Nonlinear SSI effect on adjacent bridge structures with pounding E.M. Behrens Facultad de Ingeniería, Universidad Católica de la Santísima, Concepción, Chile

N. Chouw Department of Civil and Environmental Engineering, University of Auckland, Auckland, New Zealand

ABSTRACT: Past investigations of pounding responses of adjacent bridge decks were performed mainly under the assumption that the considered bridge structures were fixed at their base. If the subsoil was considered at all only linear soil was considered. In this work the nonlinear interaction between adjacent bridge structures and subsoil is incorporated in the numerical analysis. The plastic deformation in the ground with the structural footing is simulated by a macro element and the bridge structures by a lumped mass model. Spatially uniform ground excitation is assumed. The results show that nonlinear structure-foundation-soil interaction can significantly alter the relative response of adjacent structures and consequently the pounding response of bridge girders. 1 INTRODUCTION Damage due to pounding between adjacent structures has been observed in almost all major earthquakes in the past decades, e.g. the Kobe earthquake in 1995 (Kawashima and Unjoh, 1996), the Chi-Chi earthquake in 1999 (JSCE, 1999), the Wenchuan earthquake in 2005 (Lin et al., 2010 and Han et al., 2009) or the recent Maule earthquake in Chile in 2010 (Elnashai et al., 2010). Figure 1 shows a picture of pounding induced damage of the Puente Las Ballenas taken by the authors in a field investigation. The inspected bridges showed all kind of damages related to activated relative movements, e.g. unseating of bridge girders, yielded seismic restrainers and failure of shear keys due to large lateral girder relative displacements. The main causes of structural pounding are large relative responses and insufficient distance between adjacent structures. Relative movements occur when adjacent structures respond to the ground excitation not in phase. These out-of-phase responses strongly reflect the different dynamic properties of the adjacent structures. In current design practice the dynamic structural behaviour is often described by the fundamental frequencies of the structures with an assumed fixed base. The influence of the supporting ground is often considered as negligible. Investigations in the past, however, have shown that the contribution of the supporting ground can be significant. In the case of adjacent buildings it can be assumed that they will experience the same ground excitation. The influence of the supporting soil is also often considered to be negligible, because the ground of the adjacent buildings is likely very similar. If the dynamic properties of the neighbouring buildings are the same theoretically pounding will not take place, since the structure-foundation-soil interaction (SFSI) will be equal and thus will not contribute to a structural relative response. Investigations have shown that the interaction between neighbouring structures through their common ground can have an influence on the structural response (Chouw and Schmid, 1995). The belief, that as long as the dynamic properties of the adjacent structures are similar or the same pounding can be avoided, has been implanted in many design specifications. In the case of long extended structures, e.g. bridge and pipeline, this assumption of spatially uniform ground excitations of adjacent structures may lead to unrealistic prediction of pounding potential. Seismic waves not only need time to travel, but their characteristics also change due to different soil development, i.e. soil

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properties and profile, along the path of wave propagation (Bi et al. 2010a and b; Chouw and Hao, 2008a and b; Sun et al., 2011). Even if the adjacent bridge structures have the same dynamic properties and supported by the same ground, different structural slenderness will cause unequal SFSI and thus will result in relative responses between the adjacent structures (Hao and Chouw, 2008).

Figure 1. Pounding between girders of Puente Las Ballenas in 2010 Chile earthquake Research on bridge girder poundings have been considered by many researchers, e.g. Malhotra (1998) and DesRoches and Muthukumar (2002). Recent investigations have shown, however, that nonlinear soil behaviour can be beneficial to the structures (Deng et al., 2010, Anastasopoulos, 2010, Toh and Pender, 2010). This numerical study addresses the influence of nonlinear SFSI on pounding behaviour of two adjacent bridge segments. 2 BRIGDE STRUCTURES-FOUNDATION-SOIL SYSTEM IN EARTHQUAKES Bridge structure II

Expansion joint

Bridge structure I

Expansion joint

II (a)

I

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Figure 2. Adjacent bridge structures-foundation-soil system. (a) MDOF system and (b) simplified two four DOF systems 2

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Figure 3. El-Centro ground motions Figure 2 shows the considered bridge structures with an equal height of 9 m. The footing is assumed to be rigid with a size of 10 m. It is also assumed that the mass of each bridge structure and its footing are the same and have the values of 1000 t and 500 t, respectively. The corresponding fundamental frequencies of the left and right bridge structures with an assumed fixed base are 1.5 Hz and 1 Hz, respectively. Both fixed-base structures have the same material damping ratio of 5 %. The supporting ground is assumed to be uniform. The dynamic behaviour of soil including plastic deformation is described based on soil constitutive models as a macro element with a lumped mass and three degrees of freedom at the centre of the footing (Toh and Pender, 2010; Pecker, A., C.T. Chatzigogos, 2010). The soil stiffness in the horizontal, vertical and rotational directions is 3.038E5 kN/m, 4.594E5 kN/m and 9.113E6 kNm/rad, respectively. The corresponding damping values are 1.35E4 kNs/m, 2.921E4 kNs/m and 2.44E4 kNms/rad. The bearing strength surface describes the capacity of the soil to bear the combined vertical, horizontal and moment loading. In this study a strain-hardening plasticity model for predicting the settlement of shallow foundation on sand proposed by Nova and Montrasio (1991) is used. The pounding force is assumed to develop linearly, and the contact element has a stiffness of 5E6 kN/m. In order to limit the number of influence factors no energy loss during the pounding is simulated in the investigation and both bridge structures are assumed to experience the same ground motions (Fig. 3). The present study focuses only on the influence of nonlinear SFSI on the linear pounding response of the two adjacent structures. It is therefore assumed that the bridge segments remain linear during the entire earthquake loading, and the adjacent girders have a distance of 5 cm. 3 EFFECT OF NONLINEAR SOIL AND POUNDING Figures 4(a) and (b) show the horizontal displacement of the girders at the expansion joint when the supporting ground is assumed to be linear and to have the ability to behave nonlinearly, respectively. Pounding effect is not considered. The dashed and solid lines are the displacements of the right (uI) and left (uII) bridge structures, respectively. Since both structures experience the same SFSI, as expected the right, more flexible bridge structure has a larger response (Fig. 4(a)). This is also the case when the soil is allowed to behave nonlinearly (Fig. 4(b)). A comparison of these two results clearly shows that nonlinear SFSI has a damping effect on the bridge structural responses. The maximum displacements of the right bridge structure with linear and nonlinear SFSI are 14.51 cm and 12.69 cm, respectively. The corresponding maximum displacements of the left structure are 10.42 cm and 5.9 cm, respectively. From these results one will expect that the relative displacements between the adjacent bridge structures will also reduce when nonlinear SFSI is considered. Figure 5 displays the effect of structural pounding and nonlinear SFSI on the development of the relative displacement urel. As a reference the relative displacement without pounding effect is given as the dashed lines. As previously discussed the maximum relative displacement without pounding effect

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reduces from 15.92 cm to 11.38 cm due to nonlinear SFSI. As expected the closing movement with considering pounding (solid lines) is limited by the gap size of 5 cm. Nonlinear SFSI clearly alters the pounding behaviour of adjacent bridge structures, even though it causes smaller closing relative displacement. While in the considered time window in the case of linear SFSI pounding takes place on eleven occasions, in the case of nonlinear SFSI pounding occurs on 15 occasions. Nonlinear SFSI causes pounding at around 11.7 s. The simultaneous effect of this pounding and nonlinear soil behaviour dampens the subsequent relative displacement between the adjacent bridge girders. This can be clearly observed from a comparison of the relative displacements (solid lines in Figs. 5(a) and (b)) between 12 s and 13 s. The effect of nonlinear SFSI can also be seen in the time window beyond 14 s. Nonlinear soil behaviour causes both bridge girders to stay longer together after each pounding (Fig. 5(b)) which cannot be observed when linear soil behaviour is assumed (Fig. 5(a)).

uI 15 10

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Figure 4. Influence of soil on structural displacement u. (a) Linear and (b) nonlinear soil

Figures 6(a) and (b) show the development of the bending moment at the support of the right bridge structure with linear and nonlinear soil, respectively. The solid and dashed lines are the responses with and without additional pounding effect, respectively. In both soil cases pounding amplifies the bending moment in the early stage of the earthquake loading. However, in the later phase of the loading pounding has an adverse effect. It causes a reduction of the bending moment. In general, as it has been observed in the horizontal displacement of the bridge girders, nonlinear SFSI has a damping effect on the bending moment. In the case of linear soil the maximum bending moment is 77.84 MNm. When nonlinear soil is considered the maximum bending moment is only 51.7 MNm.

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Figure 5. Influence of soil and pounding on relative displacement urel. (a) Linear and (b) nonlinear soil

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Figure 6. Influence of soil and pounding on bending moment. (a) Linear and (b) nonlinear soil

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4 CONCLUSIONS The numerical investigation addressed a simultaneous influence of nonlinear bridge structurefoundation-soil interaction and pounding between adjacent girders on the dynamic response of bridge structures in earthquakes. Each of the adjacent structures is described by a single-degree-of-freedom system, and its footing together with the supporting ground is described by a macro-element consisting of a lumped mass and stiffness of the soil in the horizontal, vertical and rotational directions at the centre of the footing. A uniform El-Centro ground excitation is assumed. The investigation reveals: Nonlinear soil behaviour reduced in the considered case the structural responses. In contrast to the expectation even though because of nonlinear SFSI the relative girder displacement was smaller, larger number of poundings was observed. This outcome indicated that seismic responses of adjacent structures cannot be derived from the analysis with an assumed linear soil, and nonlinear SFSI needs further investigations. 5 ACKNOWLEDGEMENTS The authors would like to thank New Zealand Transport Agency for the support under the grant TAR 08/32 and the reviewer for the useful comments that have improved the clarity of this paper. REFERENCES Anastasopoulos, I. 2010. Beyond conventional capacity design: Towards a new design philosophy. In: SoilFoundation-Structure Interaction, Eds.: Orense, R., Chouw, N., Pender, M., Leiden: CRC Press: 213-220. Bi., K., Hao, H., Chouw, N. 2010a. Required separation distance between decks and at abutments of a bridge crossing a canyon site to avoid seismic pounding. Earthquake Engineering and Structural Dynamics, 39(3): 303-323. Bi., K., Hao, H., Chouw, N. 2010b. Influence of ground motion spatial variation, site condition and SSI on the required separation distances of bridge structures to avoid seismic pounding. Earthquake Engineering and Structural Dynamics, published online. Chouw, N., Hao, H. 2008a. Significance of SSI and non-uniform near-fault ground motions in bridge response I: Effect on response with conventional expansion joint. Engineering Structures, 30(1): 141-153. Chouw, N., Hao, H. 2008b. Significance of SSI and non-uniform near-fault ground motions in bridge response II: Effect on response with modular expansion joint. Engineering Structures, 30(1): 154-162. Chouw, N., Schmid, G. 1995. Influence of soil-structure interaction on pounding between buildings during earthquakes. Proceedings of the 10th European Conference on Earthquake Engineering. Rotterdam: Balkema: 553-558. Deng, L., Kutter, B.L., Kunnath, S., Algie, T.B. 2010. Performance of bridge systems with nonlinear soilfooting-structure interactions. In: Soil-Foundation-Structure Interaction, Eds.: Orense, R., Chouw, N., Pender, M., Leiden: CRC Press: 49-56. DesRoches, R., Muthukumar, S. 2002. Effect of pounding and restrainers on seismic response of multi-frame bridges. ASCE Journal of Structural Engineering, 128(7): 860-869. Elnashai, A.S., Gencturk, B., Kwon, A.-S., Al-Qadi, I.L., Hashash, Y., Roesler, J.R., Kim, S.J., Jeong, S.-H., Duckes, J., Valdivia, A. 2010. The Maule (Chile) earthquake of February 27, 2010: Consequence assessment and case studies. Mid-America Earthquake Centre, Report No. 10-04, 190 pages Han, Q., Du, X., Liu, J., Li, Z., Li, L., Zhao, J. 2009. Seismic damage of highway bridges during the 2008 Wenchuan earthquake. Earthquake Engineering and Engineering Vibration, 8(2): 263-273. Hao, H., Chouw, N. 2008. Seismic design of bridges for prevention of girder pounding. International Journal of Structural Engineering, 8: 133-141. Japan Society of Civil Engineers (JSCE). 1999. The 1999 Ji-Ji earthquake, Taiwan – Investigation into damage to civil engineering structure, Tokyo, Eds.: Hamada, M., Nakamura, S., Ohsumi, T., Megro, K., Wang, E.,

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Tokyo, 160 pages. Kawashima, K., Unjoh, S., 1996. Impact of Hanshin/Awaji earthquake on seismic design and seismic strengthening of highway bridges. JSCE Structural Engineering/Earthquake Engineering, 13(2): 211-240. Lin, C.J., Hung, H., Liu, Y., Chai, J. 2010. Reconnaissance observation on bridge damage caused by the 2008 Wenchuan (China) earthquake. Earthquake Spectra, 26(4): 1057-1083. Malhotra, P.K. 1998. Dynamics of seismic pounding at expansion joints of concrete bridges. ASCE Journal of Engineering Mechanics, 124(7): 794-802. Nova, R., Montrasio, L. 1991. Settlements of shallow foundations on sand. Geotechnique 41(2): 243-256. Pecker, A., C.T. Chatzigogos. 2010. Nonlinear soil structure interaction: impact on the seismic response structures. In: Earthquake Engineering in Europe, Geotechnical, Geological and Earthquake Engineering, Vol. 17, Eds.: M. Garevski, A. Ansal, Heidelberg: Springer: 79-103. Sun, H., Li, B., Bi, K., Chouw, N., Butterworth, J., Hao, H. 2011. Shake table test of three-span bridge model. Proceedings of the 9th Pacific Conference on Earthquake Engineering, 14-16 April, Auckland, New Zealand. Toh, J.C.W., Pender, M.J. 2010. Design approaches and criteria for earthquake-resistant shallow foundation systems. In: Soil-Foundation-Structure Interaction, Eds.: Orense, R., Chouw, N., Pender, M., Leiden: CRC Press: 173-180.

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