Physics-based reduced order model for computational geomechanics

Abstract

Numerical models are an essential tool in stability analysis, design, and construction for geotechnical engineering. Yet, numerical modeling is too time-consuming in practical engineering. In this study, a physics-based reduced order model (ROM) was developed to approximate the displacement and stress field of geotechnical structure by combining Latin hypercube sampling (LHS), a numerical method and proper orthogonal decomposition (POD). The set of design variables were constructed using LHS. A numerical model was used to generate the snapshots based on the design variables. POD was used to compute the eigenvalues and eigenvectors of a spatial Gram matrix, which was constructed based on snapshots. The first K eigenfunction vectors were determined based on eigenvalues and eigenvectors of the spatial Gram matrix. The interpolation matrix of elements was computed using a radial basin function (RBF), and then the vector of an element was determined by solving the penalized linear systems. To determine the new design variables, the coefficient of ROM was determined based on the RBF and the vector of elements, and the unknown field variables were predicted based on the ROM. The ROM was illustrated and verified for a circular tunnel. The results showed that the predicted displacement and stress field were in excellent agreement with both the analytical and numerical solutions. The physics-based ROM characterized well the deformation and failure mechanism of the surrounding rock mass and can be used to replace a numerical model for back analysis, optimal design, and uncertainty analysis of geotechnical engineering, thereby eliminating costly repetitive computations.