Finite element formulation and algorithms for unsaturated soils. Part I: Theory

Abstract

SUMMARYThis paper presents a complete finite-element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress-strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time-stepping scheme which automatically adjusts the time-step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non-linearity caused by suction-dependent plastic yielding, suction-dependent degree of saturation , and saturation-dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress-strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction.

Modelling hydro-mechanical behavior for unsaturated soils

“…The strains and suctions are solved from the displacements and pore pressures, while the degree of saturation is solved in the same way as the stresses at integration points. In this context, the degree of saturation is indeed similar to the stresses, as noted by Sheng et al (2003a;). …”

Finite Element Modeling of Free Surface Flow in Variable Porosity Media

“…The level set function, for a given time instant t, is dened as (51) where d(x) = min|x − x i | being x i is any point on the free surface boundary ∂Ω.…”

“…Many authors during the last decades have proposed numerical models to analyze the eects of seepage ows in deformable or undeformable soils and low permeability porous materials in general. Among others we can mention the work of [2], [42], [51] [50], [24] [58]. Unfortunately these classical approaches are not applicable for the analysis of the water motion within rockll or rocklllike materials (such as concrete tetrapods, cubes or similar coastal structure).…”

A solution to transient seepage in unsaturated porous media

“…One important aspect to be considered when modelling unsaturated porous media is the so-called water retention curve (or liquid retention model -LRM) [15][16][17][18][19][20][21]. This curve represents the link between liquid saturation and capillary pressure hence closing the system of equations in addition to introducing each particular material behaviour into the computational model.…”