| Author: | Ouyang, Weihang |
| Title: | Second-order analysis of pile-supported framed structures by machine learning-enhanced finite-element method |
| Advisors: | Liu, Si-wei (CEE) Chan, Siu-lai (CEE) Chan, Tak-ming (CEE) |
| Degree: | Ph.D. |
| Year: | 2026 |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xxii, 266 pages : color illustrations |
| Language: | English |
| Abstract: | The second-order analysis method, a modern simulation-based design approach, is widely recommended by global design guidelines. This approach requires accurate and efficient numerical methods to evaluate design results for large-scale structural systems. Among various numerical methods, the line finite element method (LFEM) is preferred in current design practices. The advanced LFEMs offer notable advantages: a single element can model an entire structural member and effectively capture critical nonlinear behaviors, streamlining both modeling efforts and computational demands. Despite its proven success in superstructure design, the application of the second-order analysis method to pile-supported framed structures remains underexplored. Current second-order analysis methods often simplify building structures by modeling them as fixed on the ground, neglecting pile foundations due to the complexity of nonlinear Soil-Pile Interaction (SPI). Various soil resistance models, such as p-y curves, have been developed and implemented within the LFEM to model SPI. However, these methods are mainly suited for single piles and are rarely applied to pile-supported structures with multiple piles due to high computational costs. Accurately modeling SPI along piles typically requires a dense mesh, often exceeding 100 elements per pile. For buildings with multiple piles, LFEM requires large degrees of freedom (DOFs), resulting in a tedious analysis process. Therefore, developing an efficient numerical method that accurately captures SPI in pile-supported structures using a coarse mesh, ideally one element per pile, is essential for the broader practical adoption of second-order analysis methods. To enable a more effective SPI analysis, the refined Three-dimensional Pile Element (3DPE) formulation is presented for pile-supported framed structures. The proposed refined 3DPE formulation can efficiently capture the nonlinear SPI that is over-simplified in the conventional analysis method. Compared with the existing LFEM, the proposed refined 3DPE formulation can more accurately capture the structural behaviors of piles under complex loading conditions, including the shear effect and axial-torsional coupled response. Furthermore, three soil stiffness matrices are derived to improve the numerical stability of spatial analysis using the existing pile element formulation. Extensive examples are provided to validate the effectiveness of the refined 3DPE formulation, indicating its capability in accurately modeling three-dimensional SPI with coarse mesh. Nevertheless, this method still cannot efficiently model pile-supported framed structures with one element per pile. In addition to conventional mesh-based numerical methods, machine learning (ML) techniques have significantly transformed structural analysis recently. ML models, trained to predict structural system responses, provide near-instant solutions with negligible computational cost. However, applying ML techniques to large-scale systems remains challenging due to the high costs of training and data collection. Moreover, large-scale structural systems are often project-specific, indicating pre-trained ML models are less reusable for different projects. This lack of reusability significantly limits the practical application of ML techniques. In this thesis, a hybrid numerical framework combining the finite element method (FEM) and ML is proposed for solving general partial differential equation (PDE) problems. The proposed method, named the Neural Operator Element Method (NOEM), utilizes ML models known as neural operators (NOs) to model specific subdomains of the system. This streamlined approach reduces the training process time. These trained NOs are then used as neural-operator elements (NOEs) to model the corresponding subdomains, while other areas are modeled with standard finite elements (FEs). This hybrid modeling approach significantly reduces computational costs by replacing dense meshes in NOE-modeled subdomains with single NOEs, without compromising accuracy. Additionally, the ML models can be reused in different PDE systems without additional training, enhancing their reusability in design practice. As ML models, especially NOs in operator learning, play a vital role in NOEM, this thesis develops a novel sampling method to enhance ML model training processes. The proposed method, called the Residual-based Adversarial-gradient Moving Sample (RAMS) method, demonstrates stable performance across various tasks, including physics-informed neural networks (PINN), physics-informed operator learning, and data-driven operator learning. Notably, RAMS is the first adaptive sampling approach that can be efficiently implemented for operator learning, representing a significant contribution to the field. To implement NOEM for pile-supported framed structures, the governing equations describing the structural responses of single piles are derived. These equations account for the geometric nonlinearity of single piles undergoing large deformations and the nonlinear SPI. In addition, the governing equations derived are then implemented within the PINN, a data-free ML training paradigm, to train models for large deflection analysis of single piles. Finally, the governing equations are integrated into NOEM to provide a practical numerical method for second-order analysis of pile-supported framed structures. To improve training efficiency, the proposed RAMS method is also used to train NOs for single piles within the entire structural system. This numerical method can accurately model the structural behavior of piles in pile-supported structures using one NOE per pile, showcasing its potential for advancing second-order analysis methods. A key feature of this research is the development of a hybrid numerical framework that unifies two distinct methodologies, FEM and ML, to solve PDE problems and then to apply for large-scale pile-supported framed structures. It is believed that this study will not only facilitate the application of the second-order analysis method to pile-supported structures but also demonstrate the potential for efficiently handling large-scale, complex numerical simulations in other challenging engineering analysis problems. |
| Rights: | All rights reserved |
| Access: | open access |
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