Incompressible or nearly incompressible soil dynamic behaviour—a new staggered algorithm to circumvent restrictions of mixed formulation

Abstract

The restriction of the Babuska–Brezzi stability criteria for the mixed formulation requires non-uniform interpolation of displacement and pore-pressure variables, which complicates the coding in the finite element analysis. This will certainly preclude the use of many otherwise useful elements. A possible solution to overcome this problem introduced earlier by the authors requires a semi-explicit form. However, the effectiveness of the semi-explicit procedure is dependent on the time step length used, which presents difficulties for transient analysis. In this paper, an unconditionally stable staggered implicit-implicit algorithm is developed, which is generalised from the semi-explicit form. For non-uniform mesh configurations, the results indicate a significant improvement compared with those obtained by using the semi-explicit procedure.