Numerical Modelling of Saturated Soils
Water plays a fundamental role in soil behaviour and must be explicitly considered in any realistic modelling of geotechnical systems. In many natural and engineered settings, soils are at least partially saturated. In the case of full saturation, water occupies all void spaces, and its interaction with the soil skeleton governs both short- and long-term mechanical response. This chapter focuses on the numerical modelling of fully saturated soils and provides the foundation for more advanced treatments involving partially saturated conditions, which will be addressed later in the course.
It is important to note that the interaction between soil and water is reciprocal: while pore water pressure directly alters the effective stress within the soil skeleton, deformation of the skeleton, in turn, influences pore volume, permeability, and fluid flow. These coupled processes are central to phenomena such as consolidation, slope stability, and liquefaction.
A correct numerical representation of saturated soils within the finite element method hinges on the principle of effective stress, which decomposes total stress into effective stress cariied by the grain skeleton and pore water pressure. A detailed discussion and derivation of the effective stress concept is provided in Section Effective stress in saturated soils, to which reference is made.
To capture the coupled behaviour of the solid and fluid phases, we adopt the Theory of Porous Media (TPM) as a general framework. Based on fundamental balance laws, the TPM provides a consistent formulation for saturated soils and forms the theoretical basis for most finite element and finite difference codes used in geotechnical engineering - commercial or otherwise. Within this framework, we derive the governing equations for momentum and mass conservation, with particular attention given to the mass balance of the pore water phase.
The importance of time integration and numerical stability is illustrated through the classical example of Terzaghi’s one-dimensional consolidation problem. This example highlights how improper time discretisation can lead to instabilities, even in seemingly simple systems. In addition, we discuss the specification of boundary conditions, the selection of relevant material parameters, and the choice of appropriate constitutive models required to simulate saturated soil behaviour.
The following sections introduce the key components: