High-Order FEM Formulation for 3-D Slope Instability

High-order finite element method (FEM) formulation also referred to as spectral element method (SEM) formulation is currently implemented in this paper for 3-dimensional (3-D) elasto-plastic problems in stability assessment of large- scale slopes (vegetated and barren slopes) in different instability conditions such as seismic and saturation. We have reviewed the SEM formulation, and have sought its applicability for vegetated slopes. Utilizing p (high-order polynomial degree or spectral degrees) and h (mesh operation for quality meshing in required elemental budgets) refining techniques in the existing FEM, the complexity of problem domain can be well addressed in greater numerical stability. Unlike the existing FEM formulation, this high-order FEM employs the same integration and interpolation points to achieve a progressive response of the instability, which drastically reduces the computational costs (formation of diagonalized mass matrix) and offers significant benefits to slope instability computations for serial and parallel implementations. With this formulation, we have achieved the following three qualities in slope instability modeling: 1) geometric flexibility of the finite elements, 2) high computational efficiency, and 3) reliable spectral accuracy. A sample problem has also been presented in this paper, which has accommodated all aforesaid numerical qualities.