Numerical manifold method for dynamic consolidation of saturated porous media with three-field formulation

In terms of the three-field formulation of Biot's dynamic consolidation theory, the numerical manifold method (NMM) is developed, where the same approximation to skeleton displacement (u) and fluid velocity (w) is employed and able to reflect incompressible as well as compressible deformation, but the approximation to pore pressure (p) takes two different types, respectively. The first type of approximation to p is continuous piecewise linear interpolation and the second type assumes that p is a constant within each element. It is verified that using the second type of approximation to p naturally satisfies the inf-sup condition even in the limits of rigid skeleton and very low permeability, avoiding the locking problem accordingly. Energy components done by various forces are calculated to verify the accuracy and stability of the time integration scheme. A mass lumping technique in the NMM framework is employed to effectively reduce the unphysical oscillations and increase computational efficiency, which is another unique advantage of NMM over other numerical methods. A number of numerical tests are conducted to demonstrate the robustness and versatility of the proposed mixed NMM models.