A wave propagation algorithm for nonlinear site response analysis of layered soil accounting for liquefaction

Abstract

A constitutive model is developed for the ground response analysis of layered sites. The model is a one-dimensional version of Ta-Ger (2016) and involves critical state compatibility, anisotropic plastic flow rule and Bouc-Wen type hardening law. After being downgraded to the p-q stress space the model is reformulated to provide a unified framework of analysis for both drained and undrained loading conditions and for sand and clay. The calibration of the model parameters for sand is based on a procedure that targets to the optimum performance in both drained and undrained load conditions by simultaneously matching the response in terms of: (a) the cyclic resistance ratio curves as per the NCEER/NSF methodology, and (b) widely-used experimental shear modulus and damping ratio curves available in the literature. For the clay-like soil the calibration involves only the second step under the assumption of fully undrained conditions. The model is implemented through an explicit finite difference algorithm into an in-house computer code which performs integration of the wave equations to obtain the non-linear response of the soil. The accuracy of the algorithm is verified through comparison with analytical solutions for the amplification function of soil deposits with linearly increasing Vs, subjected to vertically propagating shear waves. It is then validated against experimental data from two centrifuge experiments. Finally, the records of the Port Island array from Kobe 1995 earthquake are employed to test the ability of the model to predict the observed response.