Reliability Analysis of Pile Foundation in Cohesionless Soil Using Machine Learning Techniques

Because of the inherent uncertainty and unpredictability in pile design, a great deal of study has been done to measure the reliability of the structures. This paper offers machine learning (ML)–based prediction method for allowable load carrying capacity of pile foundation and examines and compares the applicability and adaptability of k-nearest neighbor (KNN), deep neural network (DNN), and random forest (RF) in the reliability investigation of pile embedded in cohesionless soil. These three ML models are applied to 150 datasets, considering five important inputs, namely, the diameter of the pile (d), the angle of the internal friction of the soil (φ), the unit weight of the soil (γ), the friction angle between the soil and the pile (δ), and the factor of safety (FOS) for predicting allowable load carrying capacity (Q). A range of performance metrics, including coefficient of determination (R²), variance account factor (VAF), Legate and McCabe’s index (LMI), A-10 index, Willmott’s index of agreement (WI), root mean square error (RMSE), median absolute deviation (MAD), mean absolute error (MAE), mean square error (MSE), and expanded uncertainty (U₉₅), are employed to assess the efficacy of the well-established ML models. Using performance metrics, the results show that, of the three proposed ML models, DNN had the best predictive performance due to its highest value of R² = 0.9678 and the lowest value of RMSE = 0.0306 in the training phase and R² = 0.9853 and RMSE = 0.0145 in the testing phase. The model’s performance is also examined using rank analysis, reliability analysis, regression plot, REC curve, objective function criterion, Akaike information criterion, and error matrix plot. The model’s reliability index (β) is computed using first-order second moment (FOSM) techniques and compared with the actual value. Additionally, to know the effect of each input parameter on the output, a sensitivity analysis is conducted.