## 5 Conclusions  
The present study focused on the development of an accurate predictive model n for the bearing capacity (\(q_{ns}\)) of composite ground made of geogrid-reinforced sand over geogrid-encased stone columns floating in soft soil using the advanced white-box machine learning technique known as MPR. The MPR system was trained and validated on a comprehensive dataset of 245 experimental tests, using a set of predictors including the ratio of the sandy bed thickness to the foundation diameter (\(t/D\)), the ratio of the geogrid layer diameter to the foundation diameter (\(d/D\)), the ratio of the stone column length to its diameter (\(L/d_{sc}\)), the ratio of the length of the encasement to the diameter of the stone column (\(h/d_{sc}\)), and the shear strength of unreinforced clay soil (\(q_{u}\)). From the results obtained in this research, the following conclusions can be drawn:  
Figure 6: Comparison of the best-fit curves for bearing capacity (\(q_{ns}\)) based on input features: (**a**) \(q_{u}\), (**b**) \(t/D\), (**c**) \(h/d_{sc}\), and (**d**) \(d/D\), with experimental values and the model predictions from MPR. When tested using a cross-validation approach, the MPR model outperformed both the traditional LR (white-box) and RF (black-box) models in terms of \(R^{2}\) and RMSE. The MPR model showed average prediction performances of 0.9850 for \(R^{2}\) and 13.9161 for RMSE, while the RF model showed performances of 0.9820 for \(R^{2}\) and 19.2054 for RMSE. The LR model performed the worst among all the tested models;
* Further, the MPR model was successfully used to predict the bearing capacity (\(q_{\pi s}\)) for the testing dataset, with results closely aligned to the experimental values;
* Comparing new and existing models is important in ML. The MPR model performed well, achieving high accuracy and interpretability when compared to traditional white-box and black-box models, which require specialized knowledge;
* In addition, a parametric analysis was performed to assess the impact of increasing the predictors on \(q_{\pi s}\). The findings revealed that the MPR predictions align well with laboratory results, indicating that an increase in \(q_{u}\) values leads to an increase in \(q_{\pi s}\) values. Similarly, an increase in both \(d/D\) and \(h/d_{\pi s}\) ratios also results in an increase in \(q_{\pi s}\) values. However, an increase in the \(t/D\) ratio shows a different effect on \(q_{u}\) values, which initially increase but then decrease. These findings can help in understanding how different factors impact the bearing capacity of composite foundation systems, such as the one studied in this research. Despite the promising results, the proposed model has some limitations that should be considered in future research. Firstly, the current model does not include water level as an independent parameter, which could play a significant role in the bearing capacity and overall performance of the foundation system. Future studies should investigate the influence of water level on the bearing capacity and consider incorporating it as an input variable in the model. Secondly, the model was developed based on a dataset consisting of 245 experimental results collected from the literature. To further improve the accuracy and generalization performance of the model, it would be beneficial to include additional data points and investigate the influence of other relevant factors on the bearing capacity of the foundation system. Lastly, the performance of the model could be further enhanced by exploring other advanced machine learning techniques, such as deep learning or ensemble methods, which may provide improved predictive capabilities and a better understanding of the complex interactions between the input variables. In conclusion, this study presents a novel approach to predicting the bearing capacity of composite ground using a white-box machine learning model, demonstrating its potential as a valuable tool for geotechnical engineers and researchers.