## Appendix B Implementation of the Intelligent Computing Methods: Tables and Equations  
* GEP-derived equations  
The parameters characterizing the GEP method for 3D-scour rate predictions are made explicit in Table 12.  
GEP models have been developed via GeneXproTools5 platform. During their development, the values of best-fit function were 1687, 1123, and 1322 for the estimation of \(V_{H}^{*}\), \(V_{R}^{*}\), and \(V_{L}^{*}\), respectively. The best formulations were the following:  
\[ \begin{split} V_{H}^{*}=tanh\Big{(}arctan\ \Big{(}ln\ \Big{(}\min\Bigl{(}-3.8810+KC,\ \bigl{(}1-\frac{\epsilon}{G}\bigr{)}^{2}\Bigr{)}\Bigr{)}\Big{)} \Big{)}+\\ \big{[}-KC-\frac{\epsilon}{G}+sina+\bigl{(}2.3133-\frac{\epsilon}{ D}\bigr{)}\cdot\bigl{(}1-\frac{\epsilon}{D}\bigr{)}\big{]}+min\Big{[}tanh\Big{(}\Big{(}\frac{ \theta_{w}}{1+sina}\Big{)}\Big{)}\cdot\bigl{(}\frac{4.1825+KC}{2}\bigr{)},\frac {3.9524}{(1+sina)^{2}}\Big{]}\end{split}  \tag{1}\]\[ \begin{array}{c}V_{L}^{*}=\left[-\frac{e}{D}+sin\alpha\right.\hskip 56.905512 pt+ \frac{3.5804-sin\alpha}{2}\right]\\ \left.+\left\{arctan\left[\frac{1-0.5\left(2+sin\alpha-\frac{e}{D}\right)+ min\left(8.9196-KC,\theta_{w}-1-sina\right)}{2}\right]\right\}^{2}\\ \hskip 56.905512 pt+\left[1-\left\{tanh\left(1+\frac{e}{D}+sin\alpha-\left(1- \frac{e}{D}\right)^{2}\right)\right\}^{4}\right]\end{array} \right] \tag{10}\]  
\[ \begin{array}{c}V_{R}^{*}=\left[1-\frac{e}{D}+\theta_{w}-\left(1+sin\alpha \right)^{2}\right]\cdot\left(sina-\frac{e}{D}\right)^{\frac{1}{3}}+\left\{ tanh\left[arctan\left(\frac{KC-3.836}{2}\right)\right]+1-\frac{e}{D}\right\}^{2}+1\\ \hskip 56.905512 pt-\left[tanh\left(1-\frac{e}{D}\right)-2-KC+\frac{e}{D} \right]\cdot\theta_{w}^{2}\end{array}  \tag{11}\]  
* EPR-derived equations  EPR models have been developed by EPR MOGA-XL software. The best formulations for the estimation of \(V_{H}^{*}\), \(V_{R}^{*}\), and \(V_{L}^{*}\) were the following: \[ \begin{array}{c}V_{H}^{*}=0.3235\hskip 28.452756 pt\cdot(KC)^{0.5}+0.02161 \cdot\left(1-\frac{e}{D}\right)^{0.5}KC^{0.5}\theta_{w}{}^{2}\cdot ln\left[ \frac{KC^{2}\cdot\theta_{w}{}^{2}}{\left(1-\frac{e}{D}\right)^{2}\cdot\left(1 +sin\alpha\right)^{0.5}}\right]+0.00278\\ \cdot(1+sin\alpha)^{0.5}\left(1-\frac{e}{D}\right)^{0.5}KC^{0.5}\theta_{w}{}^ {0.5}\cdot ln\left[\frac{\left(1-\frac{e}{D}\right)^{0.5}\cdot\theta_{w}{}^ {0.5}}{\left(1+sin\alpha\right)^{2}}\right]+0.01438\cdot(1+sin\alpha)^{2}KC^{0.5}\theta_{w}\\ \hskip 56.905512 pt\cdot ln\left[\left(1-\frac{e}{D}\right)^{0.5}\cdot(1+sin \alpha)^{2}\cdot\theta_{w}^{2}KC^{0.5}\right]\end{array} \] (12) \[ \begin{array}{c}V_{L}^{*}=0.01157\cdot Ln\left[\frac{\theta_{w}}{KC^{2} \cdot\left(1+sin\alpha\right)}\right]+0.001464\cdot ln\left[(1-\frac{e}{D}) \cdot(1+sin\alpha)\cdot\theta_{w}^{0.5}\right]+0.3205\cdot\left(1-\frac{e}{D} \right)+0.01153\\ \hskip 56.905512 pt\cdot ln\left[\frac{\left(1-\frac{e}{D}\right)^{2}\cdot \theta_{w}{}^{2}\cdot KC^{2}}{\left(1+sin\alpha\right)^{0.5}}\right]+0.4768 \cdot(1+sin\alpha)\cdot ln\left[\frac{1}{\left(1+sin\alpha\right)^{1.5}}\right] \end{array} \] (13)
* MARS-derived equations The formulations for the basis functions (BFs) and their weighting coefficients associated with the estimation of 3D- scour rates are listed in Table 11.  
MARS models have been developed by MATLAB2015 software. The best formulations for the estimation of \(V_{H}^{*}\), \(V_{R}^{*}\), and \(V_{L}^{*}\) were the following:  
\[ \begin{array}{c}V_{H}^{*}=3.4903-13.568\cdot BF_{1}+22.259\cdot BF_{2}-4.702 8\cdot BF_{3}-20.026\cdot BF_{4}-3.5962\cdot BF_{5}+4.6579\cdot BF_{6}\\ \hskip 56.905512 ptV_{L}^{*}=3.8165-4.4937\cdot BF_{1}+1.8162\cdot BF_{2}+3.2772 \cdot BF_{3}-4.1566\cdot BF_{4}-0.20284\cdot BF_{5}-0.2084\cdot BF_{6}\\ \hskip 56.905512 pt-7.4663\cdot BF_{7}\end{array}  \tag{14}\]  
\[ \begin{array}{c}V_{R}^{*}=3.3939-0.18259\cdot BF_{1}+4.3799\cdot BF_{2}-8.10 73\cdot BF_{3}-4.2723\cdot BF_{4}\end{array}  \tag{15}\]