# Use of Evolutionary Computation to Improve Rock Slope Back Analysis
## 6 Case Study 1
### Statistical Study on the Distribution and Range of Disturbance Factor (\(D\))  
As shown in the failure surfaces from one, two, three and four uncertainty parameters, the back calculations failure mechanism is almost unchanged. However, it is important to obtain accurate back calculation results in practice. A study was conducted to determine how the mode of distribution and the range chosen for back calculating \(D\) influence the other back calculated parameters. A statistical study was conducted considering both normal and uniform distributions to evaluate how the distribution and range _of_\(D\) influence the coefficients of variation (_COV_s) of the other back-calculated parameters. The range and distribution for \(\sigma_{ci}\), \(m_{i}\) and \(GSI\) are based on the recommendations given by [PERSON]. From the experience of [PERSON] \(\sigma_{ci}\), \(m_{i}\) and \(GSI\) were normally distributed with _COVs_ of 0.25, 0.125 and 0.1 respectively. The original values given by [PERSON] et al. [33] were chosen as the average values in this study as shown in Table 1. Based on the above recommendations the standard deviation and range of the parameters \(\sigma_{ci}\), \(m_{i}\) and \(GSI\) are determined for back analysis as shown in Table 11.  
Since there is no given recommendation on the _COV_ and mode of distribution for \(D\), this study uses different approaches to find a scenario, which could be employed for back calculating \(D\). **Scenario A**: Considering a uniform distribution and a range of 0-1 for back analyzing the disturbance factor (\(D\)). **Scenario B**: Considering a normal distribution and a range of 0-1 for back analyzing the disturbance factor (\(D\)). **Scenario C**: Considering a normal distribution and a range of 0.4-1 for back analyzing disturbance factor. This aims to evaluate the impact of reducing the distributed range of \(D\) on the other back-calculated parameters. In fact, the range of \(D\) can be smaller if the slope surface condition \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Mean Value** & **Standard Deviation (\(\sigma\))** & **Range (\(\pm\)3\(\sigma\))** \\ \hline \(GSI\) & 16 & \(\pm\)1.6 & 11.2–20.8 \\ \(m_{i}\) & 7 & \(\pm\)0.9 & 4.3–9.7 \\ \(\sigma_{ci}\) & 5.2 & \(\pm\)1.3 & 1.3–9.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Standard deviations and ranges for \(\sigma_{ci}\), \(m_{i}\) and \(GSI\). Figure 8: Comparison of original and back-calculated failure mechanism from _PSO_ and _GA_. is judged by experienced engineers. In addition, the study by [PERSON] et al. [37] indicated \(D\) = 0.7 would be reasonable for this case. Therefore, \(D\) = 0.7 is assumed as the mean value herein. For each of the three different scenarios, all four parameters (\(D\), \(GSI\), \(m_{i}\) and \(\sigma_{ci}\)) are back calculated 30 times so as to determine the _COVs_ of all four parameters for all three different scenarios. Table 12 showed the mean values obtained from PSO and GA. While Table 13 showed the comparison of COVs obtained from PSO and GA from the statistical study. The mean value for each parameter is determined for both PSO and \(GA\) for each of the three scenarios taken into consideration for the statistical study, as shown in Table 12. The mean values of the back calculated parameters are close to the original strength parameters in each of the scenarios taken into consideration for both \(PSO\) and \(GA\). For the single and double parameter back calculation, the values of the back-calculated parameters closely match those of the mean values from the statistical study. However, as the number of uncertainty parameters increase to three and four parameters the back-calculated parameters differ from the mean values obtain from the statistical study significantly. Table 13 shows the comparison of COV values for PSO and GA obtained from the statistical study. The COVs obtained from GA are smaller when compared to PSO for all four parameters in all three scenarios.