Dynamic two-phase interaction of soil can be modelled by a displacement-based, two-phase formulation. The finite element method together with a semi-implicit Euler–Cromer time-stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two-phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two-phase formulation is onerous, an analysis is performed on a simplified two-phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second-order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability-dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit.

### Numerical Stability for Modelling Of Dynamic Two-Phase Interaction

#### Abstract

Dynamic two-phase interaction of soil can be modelled by a displacement-based, two-phase formulation. The finite element method together with a semi-implicit Euler–Cromer time-stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two-phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two-phase formulation is onerous, an analysis is performed on a simplified two-phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second-order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability-dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit.
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2015
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11577/3169099`
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