Integrated machine learning for modeling bearing capacity of shallow foundations.

Analyzing the stability of footings is a significant step in civil/geotechnical engineering projects. In this work, two novel predictive tools are suggested based on an artificial neural network (ANN) to analyze the bearing capacity of a footing installed on a two-layered soil mass. To this end, backtracking search algorithm (BSA) and equilibrium optimizer (EO) are employed to train the ANN for approximating the stability value (SV) of the system. After executing a set of finite element analyses, the settlement values lower/higher than 5 cm are considered to indicate the stability/failure of the system. The results demonstrated the efficiency of these algorithms in fulfilling the assigned task. In detail, the training error of the ANN (in terms of root mean square error-RMSE)) dropped from 0.3585 to 0.3165 (11.72%) and 0.2959 (17.46%) by applying the BSA and EO, respectively. Moreover, the prediction accuracy of the ANN climbed from 93.7 to 94.3% and 94.1% (in terms of area under the receiving operating characteristics curve-AUROC). A comparison between the elite complexities of these algorithms showed that the EO enjoys a larger accuracy, while BSA is a more time-effective optimizer. Lastly, an explicit mathematical formula is derived from the EO-ANN model to be conveniently used in predicting the SV.