IMPLICIT INTEGRATION ALGORITHM FOR NUMERICAL SOLUTION OF PARTIALLY SATURATED SOILS WITH AN ENHANCED GENERALIZED PLASTICITY CONSTITUTIVE MODEL

The stress update algorithm and the tangent operator for an enhanced generalized plasticity model is investigated within the framework of generalized plasticity. The constitutive model used was developed recently for partially saturated soilsl,2, where on top ofthe hydrostatic and deviatoric components ofthe (effective) stress tensor suction has to be considered as an independent variable. The form of the effective stress tensor chosen is thermodynamically consistent. The enhanced generalized constitutive model is derived from a potential energy function, the Helmholtz ftee energy, and from a dissipation function that has to be positive for every value oftheir independent variables, the plastic components of the volumetric and shear strain rates, and are defined for the case of associative plasticity and non-associative one3. The effective stress o'and the modified suction (scaled by the porosity) ns are work conjugate with the rate of soil skeleton strain i and the rate of degree of saturation - S' , respectively. The suction plays the role of stress, the degree ofwater saturation is a strain-like variable. The rate of input work to the soil is equal to the sum of the products of the stresses with their corresponding strain rates. The Galerkin method is used to obtain a weak form of the governing equations and a "stress-suction coupling matrix" is derived in the discretization in space by the finite element method. The implicit integration algorithm4 is incorporated in a code for partially saturated soil dynamics. Numerical examples are computed to show the effrciency and validity of the algorithm developed.