Piecewise-Linear Formulation of Coupled Large-Strain Consolidation and Unsaturated Flow. I: Model Development and Implementation

Abstract

A mass-conservative formulation of one-dimensional (1D) coupled large-strain consolidation and unsaturated flow using a piecewise-linear formulation is developed. The volume and water-content changes in the unsaturated zone are described using three-dimensional (3D) constitutive surfaces of void ratio and gravimetric water content as functions of net stress and matric suction, whereas the volume change in the saturated zone is described using a two-dimensional (2D) curve relating void ratio to Terzaghi effective stress. The hydraulic conductivity varies with both void ratio and suction in the unsaturated zone, and with void ratio only in the saturated zone. The associated nonlinearities are addressed by solving the flow-continuity equation for water mass conservation through a finite-difference scheme in a piecewise-linear manner. The unknowns are calculated from variables in the previous time step without requiring iteration. A novel algorithm is developed to smoothly model transition between the saturated and unsaturated zones. Four types of top boundary conditions are formulated to account for complex soil–atmosphere hydraulic interactions. The developed program is also capable of performing a quasi-unsaturated analysis, which uses the saturated soil’s constitutive relationships in the unsaturated zone, similar to the approach of several models currently used in practice. The theoretical and numerical development of the model is described in this paper, and is followed by verifications of the program’s implementation using a numerical example of saturated large-strain consolidation and an analytical solution to unsaturated flow. Validation of the quasi-unsaturated and unsaturated formulations is presented in the companion paper, using comparisons with numerical cases as well as laboratory and field data.