NONLINEAR SEISMIC SOIL-STRUCTURE INTERACTION USING SCALED BOUNDARY FINITE ELEMENT METHOD

Abstract

Seismic response of the structures supported on soft soil is a complex process involving inertial interaction between structure and its foundation, kinematic interaction between foundation and the surrounding soil and the nonlinear response of soil to strong earthquake motions. In the present research work, a finite-element code based on the substructure method of analysis in the time domain has been developed in MATLAB for carrying out the dynamic soil-structure interaction (SSI) analysis considering the material nonlinearity of the subsoil. The unbounded foundation media is modeled using the scaled boundary finite element method (SBFEM) whereas the nonlinearity in the near-field region is modeled using the plasticity based advanced nonlinear soil model, namely the hierarchical single surface (HiSS) model. Also, for some of the problems, the pore-water pressure generation for liquefaction is considered by employing Byrne model. The SBFEM rigorously takes into account the radiation condition for the accurate modeling of the unbounded media and is global in time and space. As a result, it exerts tremendous demand on storage requirement as well as high computational effort. To reduce the computational effort, two different approximation techniques namely (1) recursive algorithm for calculation of interaction forces and (2) reduced set of base functions technique have been implemented. The recursive algorithm is an approximation in time, which reduces the computational effort in calculating the unitimpulse response matrices to a linear time-dependency from quadratic timedependency. The reduced set of base functions technique leads to reduction in the DOFs on the interface between near-field and far-field, resulting in reduction in the storage requirements. In order to simulate the nonlinearity of the near-field soil region, the δ0 version of the HiSS model is used. Instead of the commonly used Newton-Raphson procedure, the modified Regula Falsi method is used to solve the contact stress problem before applying the drift correction procedure. Also, the problem arising from the overcorrection of the intermediate stress in the implementation of strain to stress algorithm, has been handled by an efficient method, whereby the stress state is pulled into a valid domain. iv The developed program is sufficiently validated under static, dynamic and nonlinear conditions. The implementation of coupled FEM-SBFEM scheme for both 2D and 3D problems is verified by solving benchmark examples. Also, the efficiency of the FEM-SBFEM scheme with the approximation techniques is demonstrated. The accuracy of the SBFEM over local boundary namely viscous dashpots is shown. For validating the implementation of HiSS-δ0 soil model, the load-displacement behavior for a footing on artificial sand and Tehran sand is analyzed and compared with the results reported in the literature. Also, the dynamic impedance of a single pile calculated for both the linear as well as the nonlinear case is verified with the data from the published literature. The pore-water pressure response obtained using Byrne model is also verified with the result reported in literature. Finally, the developed algorithm is employed to study the effects of nonlinearity on the response of a three-dimensional single pile-soil system by calculating its dynamic impedances. The kinematic interaction factors for the single pile-soil system are evaluated. Further, response of a single pile-soil system for a real earthquake time history under nonlinear soil conditions is also investigated. Also, the developed algorithm is used to investigate the seismic response of a ten-storey building. The effect of linear SSI on the seismic response of the structure is investigated. Also, a parametric study considering the variation in the stiffness of the supporting soil and the height of the building is carried out. The effect of soil plasticity and liquefaction of the soil medium on the response of the building is also studied. It was found that due to nonlinearity both real and imaginary parts of the dynamic stiffness decreases, though effect on real part is more significant. This indicates that the consideration of nonlinearity is important. It is also observed that the nonlinearity of the soil medium (without considering liquefaction) has a definite influence on the response of the structure. However, when liquefaction is considered in the study, the effect on the response of the structure is more pronounced.