Improved prediction of undrained shear strength of clay from CPTU data using an ensemble PSO-MARS model with robustness analysis

Abstract

The undrained shear strength (s_u) is an important parameter for clays. However, current empirical models for predicting s_u are not sufficiently reliable. A novel data-driven ensemble learning method combining the particle swarm optimization (PSO) algorithm and multiple adaptive regression splines (MARS) has been developed to capture the relationships between s_u and piezocone penetration test (CPTU) parameters based on collected datasets. Four combinations of CPTU measurements (cone tip resistance, q_t; sleeve friction resistance, f_s; and excess pore water pressure, Δu; or normalized net cone resistance, Q_t; normalized friction ratio, F_r; and pore pressure parameter B_q) and in-situ stresses (total vertical stress, σ_vo, and effective vertical stress, σ´_vo) are used as input variables to determine the optimal combination of variables. In this novel model, PSO optimizes the hyperparameters in the MARS algorithm to form the PSO-MARS model, which has the advantage of visualizing the model expression. The performance of the PSO-MARS model is specifically compared with existing empirical correlations and other machine learning (ML) models. The robustness of prediction models is analyzed using Monte Carlo simulation. The results show that the PSO-MARS model demonstrates higher accuracy and robustness in s_u prediction compared with other ML models and existing empirical correlations. Additionally, the PSO-MARS model provides intuitive expressions of the predicted outcomes. Among the four tested groups, the q_t-f_s-Δu-σ_v0-σ'_v0 combination is identified as the optimal MARS model and is recommended for s_u prediction in engineering practice.