Keywords: soil-pile-structure interaction, radiation damping, pile group foundation, Drucker-Prager soil model.

Using a three-dimensional finite element model of a soil-pile foundation system, a nonlinear analysis in the time domain is performed to provide a method for assessing the seismic performance of the soil-pile foundation system. This research focuses on kinematic seismic soil-pile-structure interaction by comparing the results of different pile foundation configurations. Both harmonic and specific seismic excitations are considered.

Material nonlinearity of the soil has significant effects on the seismic response of a soil-pile foundation system, as suggested by Bentley and Naggar [1] and Maheshwari et al. [2]. The Drucker-Prager plastic soil model is employed in this study to represent the nonlinear behavior of the soil. Associated flow rule of the Drucker-Prager model is considered with work-hardening behavior. The piles in the soil-pile system are considered to be linear concrete.

In order to determine an appropriate model dimension, a soil-single pile foundation system with dynamic concentrated loads acting at the pile head is constructed. A comparison of the pile head dynamic responses due to different finite element model dimensions is implemented and this study suggests an analytical model with dimension of 40m30m18m as being computationally efficient and accurate for the considered soil-pile foundation systems. As suggested by Kuhlemeyer and Lysmer [3] and Lysmer et al. [4], the maximum dimension of the finite element mesh depends on the shortest wavelength in the wave propagation problems and should be smaller than . The soil is discretized with differing mesh sizes for near-site soil and far-site soil to enhance the computational efficiency. The soil mesh size in this analysis is 1m1m in plan for elements near the pile. The maximum dimension of the mesh is 3m in plan for finite elements on the boundary between the finite and infinite elements.

Radiation damping is defined as the energy dissipated from the finite element region of a soil-pile system by outwardly propagating waves. Chu and Truman [5] compared the dynamic response of a soil-pile foundation system using a frequency independent viscous dashpot boundary and an infinite element boundary, respectively. It was found that dynamic responses using an infinite element boundary agree with existing results of previous elastic analyses. Thus an infinite element boundary is considered in this study to represent the energy absorption by the far-field soil to avoid reflection of dilatational and shear wave energy back into the finite element model. The infinite elements are assumed to behave linearly.

Natural frequency extraction and dynamic analyses due to harmonic excitation are performed in order to study the dynamic characteristics of both 22 and 33 pile foundation systems. It is found that soil properties affect the natural frequencies of the soil-pile systems greatly and the pile head responses are smaller when the soil is stiffer. The effects of the pile spacing ratios are insignificant, which is due to the small contribution of pile groups to the stiffness of the soil-pile system. It can also be seen that largely spaced pile groups have slightly larger pile head responses (acceleration and displacement) for both the 22 and 33 soil-pile foundation systems, which is attributed to the higher stiffness of the systems with less pile-soil-pile interaction in the largely spaced pile foundation systems.

The seismic soil-pile interaction problem can be explained from the perspective of energy transmission and dissipation as well. Energy from the earthquake is transmitted to the soil-pile system through the base excitation and is considered as external work acting upon the soil-pile system. The external work is transformed into internal energy and kinetic energy of the soil-pile system. The total energy of a soil-pile system is the difference between the external work and the sum of the internal energy and the kinetic energy. Internal energy is transformed into three parts: the energy lost to the quiet boundary, the strain energy and the energy due to plastic dissipation. The present study suggests that the majority of the external work is transformed into internal energy and the majority of internal energy is lost to the quiet boundary, indicating that radiation damping is predominate in the seismic analysis of soil-pile foundation systems.

1

Bentley, K.J., Naggar, M.H. EI., "Numerical analysis of kinematic response of single piles", Canadian Geotechnical Journal, 37, 1368-1382, 2000. doi:10.1139/cgj-37-6-1368

2

Maheshwari, B.K., Truman, K.Z., Gould, P.L., "Nonlinear Kinematic Response of Single Piles", Proceedings 7th National Conference on Earthquake Engineering, Boston, MA. 2002.

3

Kuhlemeyer, R.L. and Lysmer, J., "Finite element method accuracy for wave propagation problems", Journal of Soil Mechanics and Foundation Division, ASCE, 99 (5): 421-427, 1973.

4

Lysmer, J., Udaka, T., Tsai, C.F. and Seed, H.B., "FLUSH: a computer program for approximate 3-D analysis of soil-structure interaction problems", Report EERC 75-30, Earthquake Engineering Research Center, University of California, Berkeley, 1975.

5

Chu, D.M., Truman, K.Z., "Modeling of Unbounded Domain in Seismic Soil-Pile-Structure Interaction", 6th Technical Council on Lifeline Earthquake Engineering, Long Beach, CA, 2003. doi:10.1061/40687(2003)99

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