New Particle‐Wise Finite Element Strain Analysis for Discrete Displacement of Fold‐And‐Thrust Belt and Horst‐And‐Graben Models

Abstract

Abstract The granular behaviors of shallow Earth materials are associated with brittle deformations and mass transport along the surface and fault zones. Green strain has been adopted to quantitatively analyze the fold‐and‐thrust belt and horst‐and‐graben discrete element (DE) models driven by contractional and extensional forces, respectively. Deriving Green strain from DE models is challenging because of the need for precise mapping of the discrete particle displacement onto differentiable meshes. Here, we developed a new Green strain calculation methodology, the implicit global‐finite element method (IG‐FEM), which inverts a global matrix to reflect the interconnectivity of all particles. The IG‐FEM obtains strain quantities associated with particles to prevent an information loss, for example, displacement, at particle positions. We validated the accuracy of IG‐FEM compared to the conventional strain analysis scheme for DE model, finite difference method (FDM), by estimating the relative root mean square error from analytical solutions for a given mathematical transformation. On average, the IG‐FEM and the FDM show 2.8% and 17.4% relative root mean square errors, respectively. Furthermore, the strain quantities in the fold‐and‐thrust belt and horst‐and‐graben DE models were computed. The strain patterns of the IG‐FEM are more consistent with the particle spin distribution, which is noninterpolated information of the DE models. We present the potential benefits of the IG‐FEM for assessing strain‐related values such as stress, pore pressure, and seismic velocities within brittle deformation zones. The IG‐FEM is applicable in analog models and geodetic surveys to extract strain from discrete displacement data.

Keywords

• green strain
• discrete element method
• finite element method
• fold‐and‐thrust belt
• horst‐and‐graben
• strain heterogeneity