Hyper-reduced model speeds up simulations of soil and water flow in dams
A hyper-reduction strategy for elastoplastic hydro-mechanical problems in partially saturated soil
Computational Engineering, Finance, and Science
Summary
Simulating how soil and water move and change inside structures like earthfill dams is very slow but important for safety assessments. The authors developed a way to make these simulations much faster by simplifying the calculations without losing much accuracy. They do this by focusing only on crucial parts of the soil where changes matter most. Their approach works well in 2D and 3D tests, cutting computing time dramatically while keeping errors under half a percent.
What this means in practice
- •For geotechnical engineers: Run faster and accurate safety assessments of earthfill dams by simulating soil deformation and water flow under various conditions.
- •For civil infrastructure modelers: Use the hyper-reduced model to speed up scenario analysis and uncertainty quantification in coupled soil-structure-water systems.
Authors
Alba Muixí, Lluís Monforte, Antonio Rodríguez-Ferran, Sergio Zlotnik
Abstract
This work proposes a hyper-reduced order model for coupled hydro-mechanical simulations of elastoplastic deformation and water flow in partially saturated soils. These simulations are used to monitor and assess the safety of geotechnical structures such as earthfill dams, where calibration, uncertainty quantification and scenario analysis require solving the same transient model many times for different parameter values. The displacement and the pore pressure are approximated in a field-split reduced basis obtained by proper orthogonal decomposition, and the Galerkin-projected equations are integrated with decomposed cubature rules, one per balance equation, built with the energy-conserving sampling and weighting (ECSW) method. Each residual is split into an affine part and a nonlinear correction: the affine part is computed exactly, at negligible online cost, so that the cubature rule only needs to approximate the correction, which is localized in space. The construction is independent of the constitutive model choices and is implemented in FEniCSx by assembling the original variational forms on the small set of elements selected by ECSW. The method is tested on two- and three-dimensional dams retaining tailings and water, simulating a raise of the dam and the subsequent consolidation phase, with the friction angle, stiffness and hydraulic conductivity of the dam material and the height of the raise as varying parameters. The hyper-reduced model reproduces the displacement and pressure fields with errors below $0.5\%$ with respect to the finite element solution, achieving speed-ups of up to $43\times$ in two dimensions and $77\times$ in three. These performance gains grow with the extent of the plastic yielding, and the selected elements concentrate in the plastified and unsaturated zones, whose size is set by the physics rather than by the mesh resolution.