Solution of stress and deformation field and inversion of material parameter for gravity dams based on physics-informed neural networks

Abstract

The stress and deformation analysis of concrete gravity dams is a core component of evaluating the structural safety of dam bodies. To obtain accurate and efficient solutions for the stressdeformation fields of gravity dams and fast inversion of material parameter, based on physics-informed neural networks (PINNs), we develop a residual minimization-based PINN model and a potential energy minimization-based EPINN model specifically targeted at gravity dams, which are grounded in the elasticity theory of solid mechanics. Through various case studies involving gravity dams, the computational accuracy and efficiency of different PINN models are compared. The results show the following: (1) The EPINN model demonstrates superior solving capability and computational efficiency—it is approximately 20 times faster than the PINN model—when dealing with complex geometries and boundary conditions. Conversely, the PINN model achieves higher computational accuracy for simpler geometries, with its precision being approximately twice that of the EPINN model. (2) Both models exhibit strong capabilities in material parameter inversion. In particular, the PINN model achieves accurate inversion of material properties via extremely limited data samples, with errors of only 0.46 % for the elastic modulus E and 2.32 % for Poisson's ratio μ. (3) The convergence performance of PINNs is influenced by factors such as the number of hidden layers, the number of neurons, and the test displacement functions. Overall, PINNs serve as a machine learning method that enables the direct construction of mechanistic models for gravity dams, contributing to the rapid and intelligent assessment of dam structural safety.