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Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients. (English) Zbl 1194.74480

Summary: Finite element simulations of coupled solid-deformation/fluid-diffusion occurring in earthquake fault zones often require high-fidelity descriptions of the spatial and temporal variations of excess pore water pressure. Large-scale calculation of the coupled fault zone process is often inhibited by the high-order interpolation of the displacement field required to overcome unstable tendencies of the finite elements in the incompressible and nearly incompressible limit. In this work we utilize a stabilized formulation in which the balance of mass is augmented with an additional term representing a stabilization to the incremental change in the pressure field. The stabilized formulation permits equal-order interpolation for the displacement and pore pressure fields and suppresses pore pressure oscillations in the incompressible and nearly incompressible limit. The technique is implemented with a recently developed critical state plasticity model to investigate transient fluid-flow/solid-deformation processes arising from slip weakening of a fault segment. The accompanying transient pore pressure development and dissipation can be used to predict fault rupture and directivity where fluid flow is an important driving force.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74L05 Geophysical solid mechanics

Software:

deal.ii; UMFPACK
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References:

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