Static and dynamic instability of liquefiable soils
The objective of this project is to develop a finite element model for analyzing the problem of dynamic instability and flow liquefaction, including the accompanying lateral flow and large ground movement during and following an earthquake. The model is based on a two-phase mixture theory with the following essential components: (a) a constitutive model that replicates the buildup of excess pore pressure prior to liquefaction; (b) a criterion for the onset of flow liquefaction instability; and (c) a constitutive response at residual state following flow liquefaction. A bounding surface plasticity model developed by the PI and co-workers will be used to model the anisotropic cyclic stress-strain behavior of soils before the onset of flow liquefaction, as well as to predict the accompanying pore pressure buildup. The criterion for the onset of flow liquefaction instability is a generalized flow liquefaction surface in six-dimensional stress space, modeled as a truncated Mohr-Coulomb surface centered with respect to the hydrostatic axis in principal Kirchhoff stress space, which collapses to the steady-state point at residual strength upon strain softening. Large deformation will be employed through the use of a finite deformation theory based on a multiplicative decomposition of the deformation gradient.
A significant part of the studies will be devoted to analyzing the results of monotonic undrained triaxial tests and cyclic undrained simple shear tests as a boundary-value problem. A universal assumption employed in interpreting the results of these tests is that the specimen is deforming homogeneously, suggesting that any measured specimen response may be interpreted as a material response. However, there are strong indications that this is far from being true. Among the issues we want to address by performing boundary-value problem simulations is whether or not the quasi-steady state condition commonly observed in saturated sand specimens of intermediate density is non-local. We will also investigate the effects of imperfections and other perturbations on the response of soil specimens taken as a structural system. Finally, we will devise a systematic methodology for re-calibrating the constitutive model parameters in the finite deformation regime, and use the finite element model to reanalyze the collapse of the Lower San Fernando Dam following the San Fernando earthquake of 1971.