Hydromechanical modeling of an initial boundary value problem: Studies of non-uniqueness with a second gradient continuum

A non-uniqueness study for a hydromechanical boundary value problem is performed. A fully saturated porous medium is considered using two different elasto-plastic constitutive equations to describe the mechanical behavior of the skeleton. Both models are based on the Drucker–Prager yield criterion with a hyperbolic hardening rule for the cohesion and friction angle as a function of an equivalent plastic strain. The two constitutive equations taken into account (Plasol and Aniso-Plasol) differ only for the elastic part of the model: isotropic elasticity or cross anisotropic elasticity respectively. A real hydromechanical experiment which consists in a hollow cylinder test on a Boom Clay sample is modeled in two phases. For the first phase (a hydromechanical unloading) non-uniqueness studies are carried out using both constitutive equations. In the second phase, boundary conditions are kept constant to dissipate the excess water pressure. It is shown in the first phase that the time step discretization of the numerical problem has an effect on the initialization of the Newton–Raphson algorithm on a given time step. Different solutions for the same initial boundary value problem can consequently be found. A convergence study is also presented giving an insight into the behavior of the computation during the iterations.