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The mechanical response of the skeleton of a porous medium is highly dependent on its seepage behaviour as pore pressure modifications affect the in situ stress field. The purpose of this paper is to describe how u‐p formulation is employed using an explicit time integration scheme where fully saturated and single‐phase partially saturated analyse are incorporated for 2D and 3D cases.

Owing to their inherent simplicity, low‐order elements provide an excellent framework in which contact conditions coupled with crack propagation can be dealt with in an effective manner. For linear elements this implies single point integration which, however, can result in spurious zero‐energy modes which necessitates introduction of a stabilization technique to provide reliable results.

The success of the modelling strategy ultimately depends on the inter‐dependence of different phenomena. The linking between the displacements components, network and pore pressures represents an important role in the efficiency of the overall coupling procedure. Therefore, a master‐slave technique is proposed to link seepage and network fields, proving to be particularly attractive from a computational cost point of view. Another development that has provided substantial savings in CPU times is the use of an explicit‐explicit subcycling scheme.

Significant reduction in computational cost is achievable using a master‐slave procedure to link seepage and fracture network‐flows and an explicit‐explicit subcycling scheme. Special attention is focused on the investigation of the influence of plastic zones in oil production problems.