Boundary element simulation of the normal contact problem with a poroelastic half‐space

Abstract This paper presents a numerical solution procedure to solve quasi‐static normal contact problems between a frictionless indenter of arbitrary shape and a poroelastic half‐space within the framework of Biot's theory of linear poroelasticity. Three types of drainage conditions of the half‐space surface are considered: fully permeable, fully impermeable, and mixed, that is, an impermeable indenter on a completely permeable surface outside the contact area. Using the displacement function method of McNamee and Gibson, a solution in the Fourier space for the displacement of the half‐space surface under the effect of applied normal stress and pore pressure is derived. It is shown how numerical solutions for specific contact problems can be found by rapid evaluation of this “fundamental solution” through successive fast Fourier transforms after discretizing the half‐space surface into boundary elements. Three exemplary contact problems are solved with the newly developed method. A comparison of the results with those from the literature confirms the accuracy of the method.