Implicit implementation of the Prevost model

The Prevost model for cohesionless soils (Prevost 1985) is currently used for the modelling of their cyclic behaviour, especially in earthquake engineering (Zerfa and Loret 2003) and (Yang and Elgamal 2008). It’s made of conical yield surfaces that allow for plastic deformations in both loading and unloading. Its non-associated volumetric flow rule can roughly take into account pore pressure build-up and cyclic mobility. The method of implementation of a constitutive law is a crucial issue (Montáns and Caminero 2007) and (Mira et al. 2009). On one hand the accuracy of the solution must be ensured, especially when a large number of cycles are considered. But on the other hand, the cost of the computation must be minimized which implies step size as large as possible. In this paper, an implicit implementation of the Prevost model is proposed. The plastic flow rule is computed through a trapezoidal rule, at the time step n + 1/2, in order to increase the accuracy.An iterative process has to be solved, due to the implicit formulation.The Jacobian matrix of the internal Newton-Raphson process is computed analytically to enhance efficiency. The algorithm is implemented in the finite element code LAGAMINE that carries out fully-coupled analysis. Simulations of triaxial tests are compared with “exact” solution.