Second-order analysis method for pile-supported structures using neural-operator element method

The second-order analysis method is extensively employed in structural design practices due to the effectiveness of advanced line finite element methods (LFEMs), which accurately capture structural behavior with one element per pile. However, the application of this approach to pile-supported structures remains limited, primarily due to the computational inefficiency of LFEMs when modeling complex Soil-Pile Interaction (SPI). Although extensive research has explored alternative numerical methods, these existing approaches typically fall in effectively simulate the SPI of pile-supported structures. They either focus solely on single-pile analyses or oversimplify piles as spring elements, neglecting critical pile responses necessary for accurate structural design. This paper implements a novel numerical framework, termed the Neural Operator Element Method (NOEM), for the second-order analysis of pile-supported structures. In the NOEM, the superstructure is modeled using conventional line elements, whereas piles are represented by neural operator elements (NOEs), which are constructed from pre-trained neural operators (NOs). These NOEs effectively capture pile behavior under complex geological conditions using only one element per pile, leading to more than 50 % reduction in computational cost compared to the conventional LFEM. Therefore, this study offers a promising tool to broaden the practical application of second-order analysis methods for pile-supported structures. • Implement Neural Operator Element Method for pile-supported structures. • Accurate capture complex pile response with one-element-per-pile. • Propose a local linearization technique to incorporate nonlinear p-y curves. • Reduce up to 50 % computational costs for pile-supported structure simulations. • Promote second-order analysis for pile-supported structures.