A physics-informed machine learning computational framework for solving Mohr-Coulomb plasticity in geomechanics

This paper develops a Physics-Informed Neural Network (PINN) framework for solving Mohr-Coulomb (M-C) plasticity in geomechanics, and the plane strain layered perforated soils subjected to surface compression pressure are employed to validate the PINN solutions, through comparisons with parallel numerical experiments conducted in OptumG2. To incorporate the physical information for the elasto-plastic problem into neural networks (NNs), two modified multi-objective loss functions, respectively known as the collocation loss function and the Least Squares Weighted Residual (LSWR) loss function, are constructed through coarse data-driven information and physical constrains, consisting of M-C constitutive relations, associated/non-associated flow rules, Karush-Kuhn-Tucker (KKT) conditions, equilibrium conditions, and boundary conditions. The total loss function incorporates terms obtained from Finite Element Method (FEM) solutions for a range of elastoplastic field variables, i.e., stress and displacement, to inform the physical knowledge fitting. By employing several independently operating and densely connected artificial neural networks (ANNs), the PINN framework achieves the M-C plastic solutions by minimizing the designed total loss functions. Furthermore, influences of sample size, sampling strategy, and the loss function, on performances of the proposed PINN framework, are investigated for parametric analysis. In all cases, the PINN predictions were compared with finite element solutions at 145,023 mesh points, showing that over 90% of points had relative errors within 10%. The proposed PINN model is effective for data-scarce geotechnical problems, though its performance in regions with significant rates of change in physical quantity still requires further improvement.