Seismic response of bridges on pile foundations considering soil-structure interaction

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1 Tailor Made Concrete Structures Walraven & Stoelhorst (eds) 28 Taylor & Francis Group, London, ISBN Seismic response of bridges on pile foundations considering soil-structure interaction F. Dezi Department of Materials and Environment Engineering and Physics, Università Politecnica delle Marche, Ancona, Italy S. Carbonari Department of Architecture, Constructions, Structures, Università Politecnica delle Marche, Ancona, Italy G. Leoni Department ProCAm, Università di Camerino, Ascoli Piceno, Italy ABSTRACT: This paper attempts to assess the influence of dynamic soil-structure interaction on the behaviour of bridges founded on rigidly capped floating vertical pile groups. A numerical model for the analysis of the soilstructure interaction of generic structures on pile foundations is presented based on a finite element approach for superstructure and pile group whereas the soil is assumed to be a Winkler-type medium. The method is applied to single piers representative for a class of bridges. Varying the soil condition and the foundation geometry, same comparisons are made with respect to the fixed base model. Special issues such as the contribution of the soil profile, of the local amplification and of the rocking at the foundation level are discussed. Soil-structure interaction is found to be essential for effective design of bridges especially for squat piers and soft soil. 1 INTRODUCTION Soil-structure interaction may significantly affect the behaviour of structures founded on piles as demonstrated by field evidences and discussed in several publications (e.g. Dezi 26, Dezi et al. 27, Fan et al. 1991, Kaynia and Kausel 1982, Mylonakis 1995). In order to capture the real dynamic behaviour of the structure, effects of the local site response, which in some cases modifies significantly the structure input motion, and the effects of the soil-foundation interaction must be included in the analyses (Figure 1). In the case of bridges, where the substructures are often constituted by squat abutments and piers, the problem may be extremely significant. Modern seismic codes (pren ) have acknowledged these features and suggest accounting for soil-structure interaction effects in the foundation and superstructure design. Methods for seismic and dynamic analysis of soils and structures are based on analytical and numerical procedures supported by experimental results and by the observation of the effects of past seismic events. There are two main approaches for analyzing soil-structure interaction currently available, namely the direct method and the substructure method (Wolf 1988). Rock outcropping motion Deconvolution Figure 1. Soil-structure interaction problem. Bedrock Surface motion Local site response analysis This paper presents a numerical procedure to perform the whole soil-foundation-structure interaction analysis in the frequency domain. This procedure is used to evaluate the effects of soil-structure interaction in the behaviour of a class of bridges. A parametric analysis is conducted to investigate the importance of the geometry of the pile group, of the soil conditions and of the structural rigidity through 891

2 the comparisons of displacements and base shear forces obtained with compliance-base and fixed-base models. m s, I s 2 PROCEDURE FOR THE SOIL-STRUCTURE INTERACTION ANALYSIS Master node The analysis of soil-structure interaction is performed, by considering the whole structure-foundation system, assuming linear behaviours for the structure, the piles and the soil.the analysis can be divided into two steps: L1 m f, I f Beam element Infinite layer local site response analysis providing the three translational displacement components of the freefield motion at the location of the embedded piles; computation of the seismic response of the whole soil-foundation-structure system subjected to the free-field motion. 2m L2 4m B In the first step, the analysis should be performed with the suitable refinement according to the site configuration. In the simpler case of horizontal layer deposits a one-dimensional analysis is sufficient. For the lack of space, only a brief overview of the procedure used in the second step is presented. 2.1 Numerical model for soil-structure interaction analysis of structures on pile foundation According to a finite element approach, the problem is governed in the frequency domain by the system of complex linear equations The partition of system (1) descends from the separation of the displacement components into those relevant to the structure (S), to the foundation rigid cap (F) and to the embedded piles (E) (Figure 2). The frequency dependent dynamic stiffness matrix is obtained by assembling matrices relevant to the superstructure and to the soil-pile system by imposing the compatibility of the displacements at the node of the cap. With reference to the superstructure, the complex stiffness matrix is constructed starting from the real stiffness, damping and mass matrices Figure 2. Discrete model. In particular the damping matrix is generated according to the Rayleigh method as linear combination of the stiffness and the mass matrices for the fixed base model. The dynamic stiffness matrix for the soil-pile group system is obtained according to Leoni et al. (27). The piles are assumed to be beams and the soil to be a Winkler-type medium constituted by independent infinite layers with uncoupled in-plane and out-plane mechanics. The layer behaviour is governed by simplified elastodynamic Green s functions obtained by simple formulas proposed by Makris and Gazetas (1992). The matrix is constructed by adding the terms relevant to the stiffness and mass of piles (P) and impedances of the soil layers (S) Only the known terms of (1) relevant to the cap (f F ) and to the embedded piles (f E ) are non zero. They are given by the Fourier transform of the forces arising at the model nodes as a result of an incoming free field motion. The model permits to capture the pileto-pile interaction, the radiation and the soil hysteretic damping. 892

3 3 SOIL STRUCTURE INTERACTION OF BRIDGE PIERS The effects of soil-structure-interaction on the seismic response of bridges are studied considering different heights of piers, soil conditions and foundation geometries. The compliance-base model was developed according to the previous formulation and the results obtained were compared with those given by a fixed-base model. Single bridge piers are analyzed. This case is realistic for relatively short bridges, with the deck laying on sliding supports at abutments and fixed supports at the piers, and also for long bridges with a high number of spans and piers of equal height. 3.1 Superstructure system The bridge pier is constituted by a single column and is founded on four piles. The values m s and I s are the lumped masses of the deck and are representative of a steel-concrete composite deck with span of approx. 4 m; similarly, m f and I f are the lumped masses of the foundation cap. The pier has a solid square cross section of edge 2. m and its mass is consistently distributed along the column. Three piers heights equal to 5, 1 and 15 m (labelled by H5, H1 and H15, respectively) are considered in the analyses. The concrete is of grade C3/37 and is considered to be linearly elastic with Young s modulus E c = kn/m 2. Cracking effects are accounted for by considering an effective modulus of elasticity E ceff =.75E c. The pier is discretized by 1 m long beam finite elements. A structural damping is introduced in terms of Rayleigh damping: stiffness and mass proportional terms were evaluated to provide a 5% effective damping for the first and second mode of the fixed-base structures. 3.2 Soil-foundation system The soil profile consists of a 4 m thick deposit overlying a bedrock which is supposed to be elastic. Two different soil profiles, labelled by S1 and S2, having stiffness increasing with depth are considered in the analyses (Table 1). The foundation is on a 2 2 floating pile group and is placed at depth of 2.5 m. The piles have diameter 1 m and length 3 m. Three pile spacings of 3, 4 and 5 diameters (labelled by D3, D4 and D5, respectively) were adopted in the analyses. Each pile is modelled by 1 m long finite elements to provide a suitable level of accuracy. The cap at the top of the pile group is considered to be rigid with a master node placed in correspondence of its centroid. Table 1. Soil properties. Profile S1 Profile S2 V s ρ ξ V s ρ ξ Layer m/s t/m 3 ν % m/s t/m 3 ν % L L B Seismic action The seismic action is defined at the bedrock outcropping with three artificial accelerograms matching the Type 1 elastic response spectrum for soil type A and PGA.25 g of pren (Figure 3a). To predict the free field motion and capturing the effects of the soil profiles, one-dimensional ground response analyses for the two soil profiles were performed by using the computer program EERA (Bardet J.P., Tobita T. 21). The obtained motion, variable with depth, was input at the level of each node of the piles. Furthermore, the motion obtained at the ground surface was used as input motion for the fixed-base model. Figure 3b shows the elastic response spectra for the free field motion obtained at the outcropping soil for the profiles S1 and S2. These are the maximum of the three spectral values obtained for each profile by processing the relevant artificial accelerograms with the local site response analysis. They are superimposed to the Type 1 elastic response spectrum for soil type D and PGA.25 g (pren ) that should be considered in the case examined. It is worth noting that the spectra do not match the one proposed by Eurocode 8 as amplifications are observed for systems with natural period close to the first two fundamental natural periods of the soil deposits (T 1,S1 = 1.1 sec, T 2,S1 =.4 sec, T 1,S2 =.5 sec, T 2,S2 =.21 sec). 4 FOUNDATION-SUPERSTRUCTURE RESPONSE 4.1 Displacements The time histories of the piers horizontal displacements are plotted in Figure 4. The cases of squat and slender piers as well as those with widest and closest spacing between piles are shown for the two soil profiles. The displacement registered at the top of the pier is plotted with a continuous curve whereas that registered at the bottom with a dashed curve. It is evident the different behaviours of the various bridges. In particular, for squat piers the two curves are superimposed and 893

4 pren pren Sa[g] T[sec] 4 (a) T2,S2 (b) T1,S2 T1,S2 T1,S1 S2 S1 2 T[sec] 4 Figure 3. (a) Elastic response spectrum adopted to generate the artificial accelerograms; (b) elastic response spectra at ground surface obtained for the two soil profiles by processing the source accelerograms with a local site response analysis. 5 1 t [sec] 2.35 S1H5D3 5 1 t [sec] 2 S1H5D5 (a) Displ. [m] -.35 bottom top S1H15D3 S1H15D S2H5D3 S2H5D5 Displ. [m] (b) -.35 S2H15D3 S2H15D t [sec] t [sec] 2 Figure 4. Horizontal displacements of the pier: (a) soil profile S1; (b) soil profile S2 (response obtained with the first accelerogram). 894

5 5 1 t [sec] 2 5 S1H5D3 5 1 t [sec] 2 S1H5D5 (a) Rot. [mrad] -5 S1H15D3 S1H15D5-5 5 S2H5D3 S2H5D5 (b) Rot. [mrad] -5 S2H15D3 S2H15D t [sec] t [sec] 2 Figure 5. Rocking of the pier foundation: (a) soil profile S1; (b) soil profile S2 (response obtained with the first accelerogram). cannot be distinguished while for slender piers a great difference is observed. This is due to the foundation rocking and to the elastic deformability of the pier itself. In Figure 5 the time histories of the foundation rocking are reported. As expected, the major rotations are obtained in the case of soft soil, piles spaced of three diameters and slender pier (S1H15D3). This is due to the major deformability of the base degree of restraints against rotation and to the major rotational inertia of the pier-deck system. Also, the frequency content of the responses is strongly affected by the soil profile, the pile spacing and the structure flexibility. 4.2 Forces Figure 6 shows the stress resultants at the pier base obtained in the eighteen cases studied as the maximum values of those obtained with the three accelerograms. They are compared with those obtained by considering fixed base models. In the case of soft soil S1 (diagrams on the left) it is evident that the compliance-base models provide base shears lower than those obtained with the fixed base models in the case of pier with an intermediate height (H1); in the case of a slender pier (H15) the shears are almost the same whereas, for squat piers (H5), shears obtained accounting for soil structure interaction are higher. The pile spacing seems to have not a significant influence on the results. In the case of profile S2 (diagrams on the right), characterised by a higher stiffness, two different behaviours are evident for the squat-medium piers and the slender pier. The results obtained with pile spacing D4 and D5 demonstrate that the foundation can be considered to be rigid while in the case of spacing D3 the soil-structure interaction induces higher stresses than those obtained with the fixed base model. For slender piers the behaviour is strongly affected by the pile spacing in all the cases the fixed base model provides higher stress resultants. In an attempt to understand this complex behaviour, fundamental periods of the structures (Table 2) and the 895

6 6E+3 V [kn] 4E+3 Fixed Fixed 2E+3 S1_D3 S2_D3 S1_D4 S2_D4 S1_D5 S2_D5 H5 H1 H15 H5 H1 H15 (a) (b) Figure 6. Base shear (maximum values obtained with three accelerograms): (a) soil profile S1; (b) soil profile S2. Table 2. Fundamental periods. Profile S1 Profile S2 D3 D4 D5 D3 D4 D5 fixed sec sec sec sec sec sec H H H T/T fixed 2 1 S2_D3 S2_D4 S2_D5 S1_D3 S1_D4 S1_D5 H5 H1 H15 Figure 7. Ratios between the fundamental periods obtained with compliance base models and the relevant fixed base models. response spectra of Figure 3 have to be considered. As expected, the compliance-base models are characterised by the increase of the fundamental period with respect to the fixed-base models (Figure 7). This is due to both soil profile and pile spacing. The major differences are obtained for squat piers in the case of soft soil and with the minor spacing between piles, namely in the case of the maximum superstructure stiffness and the minimum soil foundation stiffness. In the case of slender structures differences are mitigated due to the relevant minor influence of the foundation. In the case of squat piers (H5), the relevant large increase of the fundamental period leads to higher pseudo-accelerations and consequently higher base shear considering both soils. In the case of piers with medium height (H1) and for soil S1, the period obtained with the fixed base model is very close to the first peak of the spectrum (second mode of the soil deposit). The effects of foundation flexibility leads the structure fundamental period to the valley between the two peaks of the spectrum with a consequent reduction of the base shear. For soil S2 this is not evident because the fundamental period of the structures are on the left side of the spectrum peak where there is a short plateau for period comprises between the first and the second period of the deposit. Finally for slender piers (H15) and soil profile S1, both the periods of the fixed-base model and those of the compliance-base model fall between the two peaks with minor variation of the pseudo-acceleration. In the case of soil profile S2, the base shear is very sensitive to the variation of the fundamental period since values fall in the right side of the spectrum peak, relevant to the first period of the soil deposit, characterised by an important slope. 5 CONCLUSIONS A model for the soil-structure interaction of bridges founded on piles was proposed and a parametric analysis was carried out by considering a class of realistic bridges. Based on the results of the analyses, the following conclusions can be drawn: the seismic response of bridges on pile foundation is very sensitive to the soil-structure dynamic interaction and to the site response that amplifies frequency contents close to the first two free vibration frequencies of the deposit; for squat piers the effects of soil structure interaction generally leads to an increase of the base shears; for piers with medium height it is not possible to find trends that could be considered of general 896

7 validity and a site response analysis should always be coupled with a soil-structure interaction one; for slender piers and deposit with medium stiffness, the fixed-base model are conservative and a strong reduction of the base shear can be obtained by considering compliance-base models; rocking is an important component of the foundation motion; compliance-base model should account for it in the case of soft soil and in the case of slender piers even with medium stiffness soils; for squat piers, rocking becomes relatively significant only with very soft soil end piles closely spaced. Finally fixed-base models should be carefully considered since they may be not conservative. Furthermore a preliminary local site response analysis should always be performed in order to catch the effects of local amplifications that sometimes are related even to second vibration modes of the deposit. ACKNOWLEDGEMENTS The authors are grateful to Mr Diego Baldarelli, for his assistance in performing the computer simulations. Dezi F. (26). Soil-Structure Interaction Modelling, PhD Thesis, Università Politecnica delle Marche. Dezi F., Dall AstaA., Leoni G., Scarpelli G. (27) Influence of the soil-structure interaction in the seismic response of a railway bridge, ICEGE 27 4th International Conference on Earthquake Geotechnical Engineering Thessaloniki Greece, paper n Fan K., Gazetas G., Kaynia A., Kausel E., Ahmad. S. (1991). Kinematic seismic response of single piles and pile groups. J. of Geotechnical Engineering 117(12), pp KayniaA.M., Kausel E. (1982) Dynamic stiffness and seismic response of sleeved piles. Rep. R8-12, MIT, Cambridge, Mass. Leoni G., Dezi F., Carbonari S. (27) A model for 3D kinematic interaction analysis of pile groups in layered soils Submitted to Earthquake Engineering and Structural Dynamics. Makris, N., Gazetas, G. (1992). Dynamic Pile-Soil-Pile Interaction Part II: Lateral and Seismic Response. Earthquake Engineering Structural Dynamics, 21(2), pp Mylonakis, G. (1995). Contributions to static and seismic analysis of piles and pile-supported bridge piers, PhDThesis, Faculty of the Graduate School of State University of New York. pren (23). EUROCODE 8: Design of structures for earthquake resistance Part 1: General rules, seismic actions and rules for buildings. Wolf J. P. (1988) Soil-structure Interaction Analysis in Time Domain, Prentice-Hall, Englewood Cliffs, N. REFERENCES Bardet J.P., Ichii K. and Lin C.H. (2). EERA: Equivalentlinear Earthquake site Response Analyses of Layered Soil Deposit. University of Southern California. 897

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