78 / 2025-04-24 12:55:44

Numerical Modeling of Surface Erosion in Earthen Dams by Surface-Subsurface Coupled Flow Analysis and Multiscale Space-Time Finite Element Method

Due to climate change, the intensity and frequency of tsunami or storm-induced flooding are likely to increase, which puts geotechnical infrastructure, such as levees, embankment dams, and natural slopes, in severe danger against hydromechanical failures such as overtopping failure. Understanding the characteristics of surface flow (i.e., flow over the ground) and subsurface flow is essential to make geotechnical infrastructures more resilient and adaptable to adverse climatic conditions. However, the numerical solutions of such coupled flow problems suffer from severe numerical oscillations near the soil-water interface.

This study presents a variational multiscale stabilized space-time finite element (VMS-SST/FEM) method for analyzing coupled surface-subsurface flow over the deforming spatial domain. The proposed method is a single domain type method in which the surface and subsurface flow are modeled by Darcy-Brinkman equations (DBE). The space-time finite element method (ST/FEM) is employed to solve DBE, which is stabilized by adding extra terms to the Galerkin form. The stabilization terms are derived from the residual-based variational multiscale method. It is demonstrated that the proposed method circumvents the Babuska-Brezzi condition and allows equal order interpolation for velocity and pressure fields in both soil and fluid domains. The method remains stable against DBE's convection and Darcy's (reaction) terms. The performance of the proposed method is demonstrated by simulating the surface erosion of an earthen dam due to overtopping failure. An elasticity-based automatic mesh moving scheme handles the moving boundaries due to free-surface and surface erosion. This study demonstrates that modeling coupled surface-subsurface by DBE and SST/FEM can be a valuable tool for simulating the hydromechanical failure of earthen structures.