Calcul à la rupture en présence d'un écoulement : formulation cinématique avec un champ de pression approchéYield design formulation for porous media subjected to flow,using approximate pressure field

We attempt here to use the kinematic method of yield design in the case of a porous medium subjected to flow (with or without free surface), without looking for the exact solution of the pressure field. The method proposed here is based on the use of approximate pressure fields. In this paper, we show how, under different conditions concerning the yield criterion and the velocity field, the use of such approximate fields allows one to obtain a necessary condition for stability without having to find the real pressure field. To cite this article: A. Corfdir, C. R. Mecanique 334 (2006).     

Calcul à la rupture en présence d'un écoulement à surface libre : construction de champs de pression approchésYield design for porous media subjected to unconfined flow: construction of approximate pressure fields

We consider the stability of a porous medium submitted to a steady-state flow with free-boundary. Assuming some hypotheses, it is possible to implement the kinematic method by using an approximate pressure field bounding the true pressure field from below. We are interested in finding such approximate pressure fields and in proving that they bound the true pressure field from below without knowing the true pressure field. We use fields which are solutions of a problem with relaxed conditions with regard to the real problem. Under a uniqueness condition of the solution of a weak formulation of the problem, such fields are lower bounds for the true pressure field. Finally, we give the example of a vertical dam. To cite this article: A. Corfdir, C. R. Mecanique 334 (2006).