Response of Buried Pipelines Under Permanent Ground Movements: Physics-Informed Deep Neural Network Approach

Abstract Long-distance underground pipelines are inexorably constructed over harsh geological fields exposing them to geohazards resulting in both transient and permanent ground movement. The permanent ground movements caused by landslides, liquefaction, ground subsidence, slope failures, fault movement, etc., can result in large deformation threatening the safety and integrity of the pipelines. Therefore, evaluation of the structural response, i.e., displacement and strain fields of the buried pipelines exposed to the permanent ground displacement is a major concern for the industry. The mechanical and physical behavior of the pipelines subjected to ground movement can be described mathematically using nonlinear Partial Differential Equations (PDEs) by adopting the Euler-Bernoulli beam theory with large deformation. The model takes into account the nonlinearities caused by the pipe-soil interaction and pipe geometry. Various methods, including the Finite Element Method (FEM) and Finite Difference Method (FDM), can be used to solve the nonlinear PDEs and thus predict the structural response. However, the FEM usually requires complicated simulation using costly commercial software. Also, both the FE and FD methods are mesh-dependent. On this basis, this research endeavor proposes and utilizes an inexpensive, novel, easy-to-implemented, simulation-free, and meshless method to get the response. As a result, Physics-Informed Neural Networks (PINNs), deep-learning neural networks that consider the underlying law of physics in PDEs, can be a potential strategy to deal with PDEs with high complexity. To this end, the neural networks thoroughly learn based on the incorporated physical laws together with the boundary and/or initial conditions, eliminating the need for large training datasets. The obtained structural response, applicability, and accuracy of the predicted results of the proposed method are assessed by comparison with the obtained results from FEM.