Stability investigation of the Generalised-α time integration method for dynamic coupled consolidation analysis

Abstract In this paper, the stability of the Generalised-α time integration method (the CH method) for a fully coupled solid-pore fluid formulation is analytically investigated for the first time and the corresponding theoretical stability conditions are proposed based on a rigorous mathematical derivation process. The proposed stability conditions simplify to the existing ones of the CH method for the one-phase formulation when the solid–fluid coupling is ignored. Furthermore, by degrading the CH method to the Newmark method, the stability conditions are in agreement with the ones proposed in previous stability investigations on coupled formulation for the Newmark method. The analytically derived stability conditions are validated with finite element (FE) analyses considering a range of loading conditions and for various soil permeability values, showing that the numerical results are in agreement with the theoretical investigation. Then, the stability characteristics of the CH method are explored beyond the limits of the theoretical investigation, assuming elasto-plastic soil behaviour which is prescribed with a bounding surface plasticity constitutive model. Since the CH method is a generalisation of a number of other time integration methods, the derived stability conditions are relevant for most of the commonly utilised time integration methods for the two-phase coupled formulation.

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