Dynamic Theory of Mixtures and Its Finite Element Implementation for Nonlinear Analysis of Ground Motion Induced by Seismic Shaking

Soils exhibit pronounced nonlinear behavior under cyclic loading conditions. For saturated granular soil deposits, the analysis of ground movement due to earthquake shaking is more complicated since it is often followed by the buildup of excess pore water pressure. In this report, a finite-element (FE) model that takes account of soil nonlinearity is developed to analyze the site response of perfectly saturated soils to seismic shaking.

Using theory of mixtures, the wave propagation and diffusion effects are coupled, and the soil is modeled as a two-phase medium composed of interacting solid and fluid phases. The governing equations which describe the motions of the soil-water mixture arc based on the conservation laws of linear momentum and mass. A generalized Galerkin method is used to derive the finite element discretization of the governing equations in u-w-p form, where u is the solid displacement, w is the relative displacement of the fluid phase to that of the solid phase, and p is the pore pressure. The a-method is chosen as the global solution algorithm for solving the general FE equation of motion.

The soil skeleton is modeled as a hyperelast ic-plast.ic material using a reformulated theory of ellipsoidal bounding and loading surfaces, coupled with a hyperelastic model to ensure energy-conserving elastic responses. A return mapping in strain space is used in the integration algorithm, which allows the const.itut ive model to be amenable to fully implicit integration and consistent linearization with Newton's method.

The FE model is implemented into a time-domain FORTRAN code SPECTRA-UWP with "stick" finite elements to accommodate vertically propagating seismic waves. SPECTRA-UWP is based on a fully nonlinear solution algorithm capable of capturing the coupled multidirectional responses of wave motion through an inelastic soil medium. It is also capable of capturing the earthquake-induced pore pressure buildup resulting from the plastic compaction of the soil since it is based on effective stress analysis.

In this report, SPECTRA-UWP is used to analyze the M6.2 earthquake of July 30, 1986 and the M7.0 earthquake of November 15, 1986 at a Large-Scale Seismic Test site in Lot.ung, Taiwan. Predicted responses in t he form of gTound surface accelerations and excess pore pressures are shown to replicate the recorded responses quite well. The report underscores the uncertainties with respect to the chosen values of the coefficient of permeability of the soil, as well as the spatial variabilities of the pore pressure data recorded at the test site. For the ground motions considered the coefficient of permeability and drainage boundaries have a direct impact on t he predicted excess pore pressures, but have little effect on the acceleration-time responses.