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A composite quadrature element with unequal order integration for consolidation problems

The weak form quadrature element method is a high-order algorithm which has been applied successfully to consolidation analysis of saturated and unsaturated soils. Its superiority over the conventional finite element method has been verified. However, in consolidation analysis, pore pressure oscillations will appear when small time increments are used due to the very small permeability and near-incompressibility of the pore water. This can produce almost zero values of main diagonal elements in the coefficient matrix. To overcome the pressure oscillations, we propose a coupled composite quadrature element in which different orders of integration are employed for the pore pressure and the displacement. Its performance is evaluated and compared with that of the standard element through 1D and 2D numerical tests. Our results show that pressure oscillations can be effectively alleviated and stability and accuracy can be significantly enhanced by using the proposed element.