A hyper-reduction strategy for elastoplastic hydro-mechanical problems in partially saturated soil
Alba Muixí, Lluís Monforte, Antonio Rodríguez-Ferran, Sergio Zlotnik
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.
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