Applicability of finite difference and finite element methods as a post-processing tool for stran analysis of fold-and-thrust belt model developed with the discrete element method

We develop a fold-and-thrust belts model with extensive brittle-plastic deformations using the discrete element method (DEM), widely adopted for simulating discontinuous granular materials. We confirm that our models are consistent with previous numerical and analog studies in terms of the surface angle, the spacing between two near-thrusts, and the number of thrusts. Furthermore, we build the Python post-processing code for analyzing the strain evolution within the model based on continuum mechanics, i.e., the finite difference method (FDM) and finite element method (FEM). Physical and quantitative analysis such as kinematic sense of fault, the amount of deformation, volumetric strain, and distortion is successfully performed by adopting the finite strain for large geological deformations. The strain calculated based on the FDM is inaccurate at the boundaries but shows a uniform distribution throughout the model, and the FEM shows high accuracy which is comparable with the analytic solution along the boundaries. This suggests that the FEM provides a more efficient tool for analyzing strain fields in geological domains with irregular boundaries such as fold-and-thrust belts. The strain calculation method applied in this study is optimized for the physical analysis of geological structures that have undergone large deviatoric deformations. Moreover, since the DEM inherently includes the frictional granular behaviors of the sediment (e.g., fracture, rotation, disturbance, cementation, and consolidation), our strain analysis method guarantees high feasibility in various cases, such as the observation of the sediments behavior in the surface, the strain analysis of discontinuous structures, and the volume change of sediment layers over time (e.g., settlement and expansion).