*4.1. GP Modeling Procedure*

In this study, UC correlates with LOP, PD, IC, Su, and T; therefore, UC = *f* (LOP, IC, PD, Su, and T). GP was implemented to find a function for predicting UC to explore the relationship between UC and the other five input parameters. In this way, an intelligent equation that is easy to implement can be established for predicting pile capacity. The steps to generating the UC prediction formula by GP are as follows:


$$\text{RMSE} = \sqrt{\frac{1}{M} \sum\_{i=1}^{M} \left( \text{UC} - \text{UC}' \right)^2} \tag{2}$$


$$R^2 = 1 - \frac{\sum\_{i=1}^{M} \left( \text{UC} - \text{UC} \right)^2}{\sum\_{i=1}^{M} \left( \text{UC} - \text{UC} \right)^2} \tag{3}$$

where UC represents mean values of the UC. ˆ
