## 6 Results and Discussion
Its MAPE in the low-pressure range (16.45%) was better than that of PhySO and PySR, although very close to PhySO. However, it exhibited high dispersion in the \(>\)200 kPa range (STD = 45.24 kPa) and demonstrated good performance in the 100-200 kPa range. PGSR demonstrated limited strengths compared to the other models. It showed moderate performance in the 100-200 kPa range but performed worst in terms of bias and MAPE in both the low (\(<\)100 kPa) and high (\(>\)200 kPa) ranges. Its lack of consistency made it the least competitive model overall, although its metrics remained good for the analysed case. In conclusion, PhySO was the most balanced model for general use, demonstrating strong performance particularly in low- to medium-pressure predictions. PySR excelled in high-pressure predictions while also maintaining good overall performance. MOSR minimized bias at the extremes and can be suitable for low to medium pressures, whereas PGSR did not exhibit a clear advantage in any specific pressure range. These strengths and weaknesses according to ranges should be considered along with the fact that each equation has parameters that others do not. Only PySR and MOSR share the same input variables (see Table 4), so depending on the available parameters and the intended objective, the most suitable equation can be selected. Figure 7: Scatterplots of real vs. predicted values and prediction residuals with distribution curve for the four SR algorithms analysed. Circles represent individual predictions. The black diagonal line in the scatterplots corresponds to the ideal agreement (1:1 line), while the shaded green and grey bands denote \(\pm 20\%\) and \(\pm 15\%\) error ranges, respectively. In the residual plots, the red horizontal line indicates zero residuals (i.e., perfect prediction), and the green curve illustrates the residual distribution estimated using kernel density estimation (KDE). Figure 8: Radar chart showing the performance metrics of the four SR algorithms analysed. Note that the scale of each axis has been adjusted for better visualization. MAPE is expressed as a percentage (%), MAE and RMSE are in kPa, RMSLE is dimensionless, and R\({}^{2}\) and EVS are unitless coefficients ranging from 0 to 1. Figure 9: Comparative analysis of the four SR algorithms analysed for segmented \(\mathrm{p_{s}}\) data. (**a**) Residual mean, (**b**) residual standard deviation, (**c**) MAPE (%), and (**d**) MAE. Next, a sensitivity analysis of the parameters involved in the four equations proposed was conducted. To this end, [PERSON]'s method [57] was applied. It is commonly used to evaluate the significance of input parameters in computational models with respect to their impact on the output based on the contribution to the output variance. Figure 10 presents the results of this analysis, including the S1 and ST values. In all four models, PI was the dominant factor, with high S1 and ST indices. In PhySO and PySR, PI accounted for almost all of the variability (ST \(\approx\) 0.91 and 0.87; S1 \(\approx\) 0.88 and 0.84, respectively), while the percentage of soil passing #0.075 mm showed moderate contributions, and both LL and \(\gamma_{\mathrm{d}}\) contributed very little. In MOOSR, PI remains crucial (ST \(\approx\) 0.76; S1 \(\approx\) 0.57), but the influence of LL increases (ST \(\approx\) 0.27; S1 \(\approx\) 0.17), suggesting that interactions, deduced from the difference between ST and S1, begin to play a greater role. In PGSR, in addition to the predominance of PI (ST \(\approx\) 0.78; S1 \(\approx\) 0.72), stronger interaction effects are observed, with noticeable contributions from w and \(\gamma_{\mathrm{d}}\) (ST \(\approx\) 0.057 and 0.037). While the individual effects of PI dominate across all models, interaction effects become more relevant in MOOSR and, to a lesser extent, in PGSR. These findings align with the established knowledge in geotechnical engineering regarding expansive soil behaviour.