Transformation of the Sandler and Rubin Nonsmooth Cap Model to the Pelessone Smooth Cap Model

Abstract

The Sandler and Rubin cap model is the most popular cap model that is able to take account on geomaterial dilation and compaction effects. However, its nonsmooth yielding surface often results in a slow convergent rate or even nonconvergent solution in some numerical simulations. More often, analysts with the Sandler and Rubin model have to switch to a smooth cap model, for example, the Pelessone model, in order to obtain a convergent solution. For cases of original experimental data available direct fitting is the best way for obtaining the required smooth model parameters. For cases of only derived nonsmooth model parameters available, a transformation from nonsmooth models to smooth models is necessary. However, such a transformation is nontrivial. In this paper, we propose two simple and robust methods for transferring the Sandler and Rubin nonsmooth model to the Pelessone smooth model through making a few reasonable assumptions and solving only one nonlinear equation for one primary unknown. Two model examples are presented to demonstrate the good performance of our proposed methods.