Enriched three-field numerical manifold formulation for dynamics of fractured saturated porous media

In terms of the three-field (u-w-p) formulation of Biot’s theory of saturated porous media with incompressible solid and fluid phases, the numerical manifold method (NMM) models are developed to analyze the fully dynamic consolidation of fractured porous media in this study. The same approximation to fluid velocity and skeleton displacement is constructed which is capable of modeling both incompressible and compressible deformation, while two types of approximations to pore pressure field are established. Since the inertial effect of fluid is not neglected, the proposed model can fully capture the dynamic behavior of porous media, especially under the impact or high-frequency loading condition and, accordingly, exhibits apparent superiority in predicting transient and wave propagation responses of cracked porous media. Moreover, low order interpolation functions for primal variables and the most flexible three-node triangular finite element mesh are used, which both are difficult to implement using other partition of unity (PU) based numerical methods in terms of Biot’s two-field formulation. Also, the discontinuities can be modeled more naturally in the NMM framework in comparison with XFEM or PNM. Meanwhile, an augmented Lagrange multiplier method for stick–slip contact model is first incorporated into fully-dynamic three-field Biot’ formulation. In addition, a mass lumping technique within NMM framework, which turns out to be a unique advantage of NMM over other numerical methods, is employed to suppress unphysical oscillations and increase computational efficiency. Energy balance condition is employed to evaluate the stability and accuracy of the time integration scheme. The robustness and versatility of the proposed models are manifested with several typical examples.