Abstract
More accurate and reliable estimation of residual strength friction angle (ϕr) of clay is crucial in many geotechnical engineering applications, including riverbank stability analysis, design, and assessment of earthen dam slope stabilities. However, a general predictive equation for ϕr, with applicability in a wide range of effective parameters, remains an important research gap. The goal of this study is to develop a more accurate equation for ϕr using the Pareto Optimal Multi-gene Genetic Programming (POMGGP) approach by evaluating a comprehensive dataset of 290 experiments compiled from published literature databases worldwide. A new framework for integrated equation derivation proposed that hybridizes the Subset Selection of Maximum Dissimilarity Method (SSMD) with Multi-gene Genetic Programming (MGP) and Pareto-optimality (PO) to find an accurate equation for ϕr with wide range applicability. The final predictive equation resulted from POMGGP modeling was assessed in comparison with some previously published machine learning-based equations using statistical error analysis criteria, Taylor diagram, revised discrepancy ratio (RDR), and scatter plots. Base on the results, the POMGGP has the lowest uncertainty with U95 = 2.25, when compared with Artificial Neural Network (ANN) (U95 = 2.3), Bayesian Regularization Neural Network (BRNN) (U95 = 2.94), Levenberg-Marquardt Neural Network (LMNN) (U95 = 3.3), and Differential Evolution Neural Network (DENN) (U95 = 2.37). The more reliable results in estimation of ϕr derived by POMGGP with reliability 59.3%, and resiliency 60% in comparison with ANN (reliability = 30.23%, resiliency = 28.33%), BRNN (reliability = 10.47%, resiliency = 10.39%), LMNN (reliability = 19.77%, resiliency = 20.29%) and DENN (reliability = 27.91%, resiliency = 24.19%). Besides the simplicity and ease of application of the new POMGGP equation to a broad range of conditions, using the uncertainty, reliability, and resilience analysis confirmed that the derived equation for ϕr significantly outperformed other existing machine learning methods, including the ANN, BRNN, LMNN, and DENN equations.
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