# Use of Evolutionary Computation to Improve Rock Slope Back Analysis
## 8 Conclusions  
Procedures for rock slope back calculation considering material uncertainties were presented using as an example a slope failure in an open mine pit in Turkey as case study 1 and a slope failure induced by an earthquake in China as case study 2. The disturbance factor (\(D\)), geological strength index (\(GSI\)), jointed rock mass (\(m_{i}\)) and unconfined compressive strength (\(\sigma_{ci}\)) are determined to be key parameters in case study 1. Case study 2 involves seismic activity as a result of the parameters considered for back calculation being the horizontal seismic coefficient (\(k_{h}\)), \(GSI\), jointed rock mass (\(m_{i}\)) and the unconfined compressive strength (\(\sigma_{ci}\)) which are determined to be key parameters. It was observed that as the number of uncertainty parameters increase, the results of the back-calculated values obtained from \(PSO\) and \(GA\) become very different. In this study, using upper-bound finite element limit analysis in conjunction with \(PSO\) or \(GA\), back analyses were successfully developed and performed. The two procedures for back calculation yield results that are identical for the single parameter back calculation. Overall, a normal distribution gives better results compared to a uniform distribution in term of accuracy based on the \(COV\) values obtained from the statistical studies. Both approaches of back calculation are easy to implement and require little computational effort and time. In general, for the same population size and number of iterations, the computational time for \(GA\) is 3-5 times less than that of \(PSO\). For case study 1, \(GA\) gave smaller \(COV\) values compared to \(PSO\) but this phenomenon is not repeated in case study 2. As a result, such a phenomenon might be case-specific. Failure mechanisms are not changed with different back-calculated strength parameters. However, parameter distributions can still help us to capture more reasonable strength parameters. This can enhance our knowledge of input parameters for the slope stability assessment or further remediation methods' selection. By comparing the execution time in this study, \(PSO\) is about 3 times slower than \(GA\), and it can be concluded that genetic algorithms are superior to particle swarm optimization for the back analysis problem, at least concerning rock slopes. [PERSON] proposed the idea and conceptualization; [PERSON] performed all numerical analysis; [PERSON] and [PERSON] completed the discussions and prepared the original draft; [PERSON] and [PERSON] gave advice on optimization; All authors have read and agreed to the published version of the manuscript. The authors gratefully acknowledge funding supports from the Ministry of Science and Technology under (Award Number MOST 107-2221-E-011-017) and the Taiwan Building Technology Center from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education in Taiwan. The authors declare no conflict of interest. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline  & \multicolumn{4}{c}{\(GA\)} & \multicolumn{4}{c}{PSO} \\ \cline{2-10}  & \(\sigma_{ci}\) (\(MPa\)) & \(m_{i}\) & \(GSI\) & \(k_{h}\) & \(\sigma_{ci}\) (\(MPa\)) & \(m_{i}\) & \(GSI\) & \(k_{h}\) \\ \hline Material 2 & 11.12 & 11.37 & 6.95 & 43.49 & 19.93 & 11.80 & 6.20 & 44.94 \\ Material 3 & 17.89 & 11.33 & 6.95 & 43.49 & 13.57 & 12.41 & 6.20 & 44.94 \\ \hline \end{tabular}
\end{table} 
Table 26: COVs of back-calculated parameters for \(T/H=\) infinity. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline  & \multicolumn{4}{c}{\(GA\)} & \multicolumn{4}{c}{PSO} \\ \cline{2-10}  & \(\sigma_{ci}\) (\(MPa\)) & \(m_{i}\) & \(GSI\) & \(k_{h}\) & \(\sigma_{ci}\) (\(MPa\)) & \(m_{i}\) & \(GSI\) & \(k_{h}\) \\ \hline Material 2 & 27.46 & 13.29 & 7.83 & 39.75 & 18.68 & 9.94 & 6.84 & 44.98 \\ Material 3 & 18.38 & 9.47 & 7.83 & 39.75 & 23.14 & 14.39 & 6.84 & 44.98 \\ \hline \end{tabular}
\end{table} 
Table 25: COVs of back-calculated parameters for \(T/H=\) 2.5.