Wave propagation and localization problems in saturated viscoplastic geomaterials

Abstract

SUMMARYThis paper presents an improved algorithm to deal with wave propagation and localization problems in saturated viscoplastic geomaterials. It consists of a mixed formulation in terms of effective stress, velocity and pore pressure that uses a fractional step algorithm allowing the use of equal order of interpolation for the three variables and the simplest element such as the linear triangle. The viscoplastic model used is of modified cam-clay type. Viscoplasticity results in a strong source term that deteriorates the accuracy of the two-step Taylor-Galerkin algorithm. Therefore a Runge-Kutta splitting scheme has been used to deal with the source terms, resulting in a better accuracy of the method.

Mixed stabilized finite element methods in nonlinear solid mechanics

“…This translates in the achievement of two important goals: (a) the position and orientation of the localization band is independent of the directional bias of the finite element mesh and (b) the global post-peak load-deflection curves are independent of the size of the elements in the localization band. Similar ideas have been used in [37][38][39].…”

“…With the definition in Eq. (38), the subscale ε̃is discontinuous across element boundaries. For linear elements, ε̃is piece-wise linear.…”

“…(38) does not need to be interpreted point-wise, as the values of ε̃are not used in the stabilization procedure; only the integral S 2 in Eq. (35c) is needed.…”

An anisotropic elastic–viscoplastic model for soft clays

“…Extended overstress models [Adachi & Oka 1982, Kutter & Sathialingam 1992, Vermeer & Neher 1999, Yin et al 2002 Conventional overstress models [Shahrour & Meimon 1995, Fodil et al 1997, Hinchberger & Rowe 2005, Yin & Hicher 2008, Mabssout et al, 2006 24h oedometer test…”

“…(1) Conventional overstress models, assuming a static yield surface for stress state within which only elastic strains occur (e.g., Adachi and Oka, 1982;Shahrour and Meimon, 1995;Fodil et al, 1997;Rowe and Hinchberger, 1998;Hinchberger and Rowe, 2005;Mabssout et al, 2006;Yin and Hicher, 2008). In order to determine the viscosity parameters, laboratory tests at very low loading rates are required.…”