Neural networks-based spring element for second-order analysis of pile-supported structures with nonlinear soil- structure interaction

This paper proposes a novel structural analysis approach, the neural networks-based spring element (NNSE) method, to synergize machine learning (ML) techniques with the line finite element method (LFEM) for the second-order analysis method of pile-supported structures. Traditional LFEM, widely used in upper structure design, showcases limitations in efficiently modeling complex Soil-Structure Interaction (SSI) along piles since it requires dense element mesh for accuracy. Conversely, ML offers a mesh-free alternative for analyzing single piles but struggles in simulating pile-supported structures as the training sample collection for large-scale problems might be unbearable. This paper addresses these challenges by proposing a new analysis framework to utilize the neural network (NN) model, which only describes structural responses of single piles, for the simulation of entire pile-supported structures. In the proposed method, the NN model is not directly used for structural analysis but employed to formulate a new spring element named the NNSE to model single piles in pile-supported structures. This NNSE can be seamlessly implemented within the existing LFEM framework to analyze pile-supported structures, eliminating the dense mesh requirement for single piles and thereby significantly improving the computational efficiency. Extensive examples are provided to verify the effectiveness of the proposed method, indicating its potential in promoting the second-order analysis method to the design of pile-supported structures.