Finite element numerical implementation for simulation of deformation band in saturated sand

The matrix form of Newton-Raphson incremental solution at the k+1 iteration is updated based on the finite deformation theory, leading the finite element implementation to the simulation of the deformation band in the fluid-saturated sand, and the criteria for localized deformation under drained and undrained conditions are derived and utilized to detect instabilities. The spatial discretization of the displacements and the pressure fields are furnished by the classical Galerkin method; according to the continuity of tractions across the deformation band, the necessary condition for localization is obtained by introducing the first tangent operator. Based on the algebraic manipulation above, a finite element numerical computational program is coded by FORTRAN; and then numerical simulations on saturated sand under undrained condition is performed to study the onset and development of the shear band. Also, the mesh sensitivity is studied; and the results show that the pathological mesh dependence is mild, which is related to the apparent width of the shear band, while the different meshes display the same overall mechanical behavior.