A blended transient/quasistatic Lagrangian framework for salt tectonics simulations with stabilized tetrahedral finite elements

Abstract

We propose a Lagrangian solid mechanics framework for the simulation of salt tectonics and other large‐deformation geomechanics problems at the basin scale. Our approach relies on general elastic‐viscoplastic constitutive models to characterize the deformation of geologic strata, in contrast with the majority of published works on the subject, which utilize nonlinear Stokes flow models. By means of multiscale asymptotics, we also show that the inertia term in the momentum balance equation can be safely neglected, if the goal is to track the Earth's crust deformation over long periods of time. Our time integration strategy is a blended transient/quasistatic approach, in that it consists of a constitutive stress update, subject to the constraint that the stresses must satisfy static equilibrium. In addition, we use stabilized finite element methods specifically built for triangular and tetrahedral grids, which can also perform well under incompressibility constraints. Our approach offers computational geologists the following advantages: (1) improved flexibility in the choice of subsurface constitutive models with respect to the nonlinear Stokes flow; (2) improved efficiency over transient dynamics algorithms used in this context in the past, which are forced to resolve seismic events over geologic time scales; and (3) improved robustness in large strain computations over quadrilateral/hexahedral finite elements. We demonstrate the performance of the proposed approach with simulations of passive diapirism.

Strain Localization Patterns and Thrust Propagation in 3‐D Discrete Element Method (DEM) Models of Accretionary Wedges

“…For example, numerical methods based on the continuum assumption such as the Finite Element Method (FEM) (Bird, 1978; Borja & Dreiss, 1989), Finite Difference (FD) schemes (Gerya & Yuen, 2007; Weiss et al., 2018), or Boundary Element Methods (Del Castello & Cooke, 2007; Madden et al., 2017; McBeck, Cooke, & Renard, 2020; McBeck et al., 2016) permit the easy characterization of strain and stress maps within the accretionary wedge model. The ability of arbitrary Eulerian‐Lagrangian (Fullsack, 1995; Ruh et al., 2012; Simpson, 2011), or pure Lagrangian (Crook et al., 2006; Perić et al., 1999; Scovazzi et al., 2021) FEM implementations to handle large deformations adds to the widespread usage of FEM. Nevertheless, continuum models have a series of disadvantages, most notably that constitutive relations linking stress to strain must be pre‐defined.…”