Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method

Abstract

SummaryA finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd.

Low‐order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

“…In this work, the divergence theorem is not applied to the weak forms of the mass balance and Darcy's equations, Equations and . This results in another difference with the work of Markert et al and Sabetamal et al() who apply that theorem and obtain different weak forms. In particular, they arrive to the following mass balance equation(): where the last term appears due to the application of the divergence theorem and represents the imposed normal water flux at the boundary Γ w .…”

“…In the case considered in this section, the soil column is 10 m long and the loading step at the upper boundary is applied over a very small time period ( t 0 = 10 microseconds). This case was also discussed by Sabetamal et al following the analytical solutions proposed by Verruijt and Carter et al The material parameters are listed in Table .…”

“…It is clearly observed that the fast dilatational wave arrives at a time of approximately 90 microseconds, whereas the slower wave arrives after a delay of around 85 microseconds, having about one half of the velocity of the first wave. The solution obtained compares favorably with that presented by Sabetamal et al and, despite some oscillations, shows good agreement with the analytical solution. Further improvement might be achieved exploring different numerical time integration schemes, but this is out of the scope of the present work.…”

“…Sabetamal et al presented a case subject to intermediate frequency loading, given by kPa. It was compared with the analytical solution proposed by De Boer et al, corresponding to incompressible constituents.…”

“…Sabetamal et al() studied the impact of objects into the soil using a formulation. An arbitrary Lagrangian‐Eulerian method with high order elements was used for the solution.…”