Hydro-mechanical simulation of the saturated and semi-saturated porous soil–rock mixtures using the numerical manifold method

Dynamics of the widespread saturated and semi-saturated soil–rock mixtures (SRMs) are of importance in practical engineering. In this paper, a numerical manifold model is presented for hydro-mechanical simulation of the saturated and semi-saturated SRMs. In the case of the semi-saturated SRMs, the model is based on the generalized Biot theory involving immiscible two-phase wetting and non-wetting fluids in deformable porous media. The wetting, non-wetting fluid pressure and skeleton displacement are chosen to be primary variables which are related to the wetting and non-wetting saturation and permeability by experimental relationships. For the mechanical problem, the material interfaces between soil and rock are deemed discontinuous by imposing a stick–slip contact constraint using an augmented Lagrange multiplier approach. For the hydraulic problem, the material interfaces are continuous for the fluid pressure and flux fields. Within the framework of the numerical manifold method (NMM), the discretized model including the interfacial discontinuities always can be established using the triangular mesh and the lumped mass representation is always available to increase computational efficiency. Besides the benchmark problems of saturated and semi-saturated porous media, two examples of soil–rock foundation and slope are performed to demonstrate the versatility and robustness of the model and to investigate the hydro-mechanical responses of the porous SRMs. •A numerical manifold model is proposed for the semi-saturated porous SRMs.•The displacement discontinuity is modeled using a stick–slip contact model.•The effect of rock blocks on the dynamic responses of SRM is investigated.