**Published:** Jan 1981

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**Source: **STP740-EB

Soils consist of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled with various fluids. The stresses carried by the soil skeleton are conventionally termed “effective stresses” in the soil mechanics literature, and those in the fluid are called the “pore-fluid pressures”. In cases in which some flow of the pore fluid can take place, there is an interaction between the skeleton strains and the pore-fluid flow. The solution of these problems therefore requires that soil behavior be analyzed by incorporating the effects of the flow (transient or steady) of the pore fluid through the voids, and thus requires that a multiphase continuum formulation be available for soils. Such a theory was first developed by Biot (1955) for an elastic porous skeleton. However, it is observed experimentally that the stress-strain behavior of the soil skeleton is strongly nonlinear, anisotropic, elastoplastic, and path-dependent. An extension of Biot's theory into the nonlinear anelastic range is therefore necessary in order to analyze the transient response of soil deposits. Such an extension of Biot's formulation is proposed herein by viewing soil as a multiphase medium consisting of an anelastic porous skeleton and viscous fluids, and by using the modern theories of mixtures developed by Green and Naghdi (1965) and Eringen and Ingram (1965).

In order to relate the changes in effective stresses carried by the soil skeleton to the solid rate of deformation tensor, a general analytical model is used which describes the nonlinear, anisotropic, elastoplastic, stress and strain dependent, stress-strain-strength properties of the soil skeleton when subjected to complicated three-dimensional and, in particular, cyclic loading paths. The theory falls within the general framework of the formalism of classical plasticity theory. It combines properties of isotropic and kinematic plasticity, and allows for the adjustment of the plastic hardening rate to any kind of experimental hardening law by using a collection of nested yield surfaces. It is shown that the model parameters required to characterize the behavior of any given soil can be derived entirely from the results of conventional soil tests. The model's extreme versatility and accuracy is demonstrated by applying it to represent the behavior of both cohesive and cohesionless soils under both drained and undrained, monotonic and cyclic loading conditions.

The use of the proposed formulation for solving boundary value problems of interest in soil mechanics is illustrated.

**Keywords:**

consolidation, constitutive equations, diffusion, finite elements, geotechnical engineering, plasticity, porous media

**Author Information:**

Prevost, JH *Assistant Professor of Civil Engineering, Princeton University, Princeton, N.J.*

**Committee/Subcommittee:** D18.12

**DOI:** 10.1520/STP28764S