Data-Driven Surrogate Models for Bearing Capacity of Spatially Random Soils

ABSTRACT: Soil properties exhibit inherent spatial variability, which can significantly affect the bearing capacity of foundations. This study conducted two-dimensional stochastic simulations of the bearing capacity of shallow foundations on spatially varying soils, utilizing random field theory and smoothed finite-element limit analysis. Despite the use of low-order elements in the numerical analysis, the node-based smoothed finite element method provides highly accurate bearing capacity estimates through kinematic limit analysis. However, running thousands of stochastic simulations to obtain reliable statistical results of bearing capacity can be computationally expensive and time-consuming. Previous studies have demonstrated that employing data-intelligent surrogate models can effectively eliminate computational bottlenecks while maintaining high-quality numerical results for collapse loads. The motivation of this study is to build deep learning-based surrogate models to overcome computational bottlenecks, leveraging machine learning algorithms inspired by the structure and function of the brain. It is shown that the accuracy of data-intelligent surrogate models in these predictions is improved by using various Kernel functions in Gaussian-based surrogate models. 1. INTRODUCTION Bearing capacity has been estimated using traditionally deterministic analyses, where only average soil properties are considered in the simulations. However, soil exhibits considerable spatial variability due to complex sediment deposition processes (Phoon and Kulhawy, 1999). Ignoring this variability in deterministic calculations can significantly underestimate bearing capacity (Griffiths and Fenton, 2001; Chen et al., 2022, 2023). To overcome this issue, researchers (Griffiths and Fenton, 2001; Griffiths et al., 2002; Fenton and Griffiths, 2002, 2003, 2005; Cheng et al., 2024) applied random field theory to incorporate spatial variability of soil and developed the random finite element method (RFEM) to estimate the probability distribution of bearing capacity. A typical RFEM analysis uses a Monte Carlo method, where random field samples of soil properties are generated and integrated into finite element (FE) models. Numerous random FE simulations are required to obtain statistical estimates of bearing capacity. However, this method is computationally demanding because it requires many samples for accurate statistical results. To address this issue, surrogate models, such as those utilizing machine learning techniques, can replace the time-consuming FE simulations. This updated method involves generating random field samples, running a limited number of FE simulations, training machine learning models, and then performing statistical analysis using the trained models.