Author:

Keywords:

eigenfunctions, eigenvalues, neural network, PINNs, soil-pile interaction

Abstract:

This work presents a reference solution for a typical soil-pile interaction problem, by means of a Physics Informed Neural Network (PINN). Advanced elastodynamic solutions for pile response can perform as scoping tools in early design stage and complement finite element simulations serving as “benchmark” solutions to allow the verification of more complex dynamic numerical models. Their intrinsic theoretical interest lies in tackling the Sturm-Liouville (SL) boundary value problem, which in presence of soil inhomogeneity is not straightforward, and can yield solutions only for specific types of soil inhomogeneity. Inspired by the recent advancements in scientific machine learning in a wide range of scientific disciplines, an application of a PINN to Soil-Structure Interaction (SSI) is presented herein. In this respect, eigenvalues and eigenfunctions of a SL operator, which arises in the classic elastic solution of a single axially loaded pile embedded in inhomogeneous soil deposit, are obtained. PINNs are physically motivated neural networks, in the sense that natural constraints such as physical laws, boundary conditions or other physical properties are embedded in either the cost function or the architecture of the network, to form a data-efficient universal function approximator. Moreover, their versatility (high adaptability to a wide range of problems), their straightforward extension to higher dimensions and, their meshfree nature (free from geometrical restrictions imposed by conventional numerical methods), can render them a valuable asset in the SSI toolkit of geotechnical engineers.