## 4 Discussion
### The Importance of Targeted Field Investigation in Practice  
The importance of targeted field investigation, where samples are taken from a priory known optimal locations, is highlighted here. For a random material field referring to a specific RFEM realization (such as the one presented in Figure 1), it can be said that it convincingly represents a real field. For the three examples presented in this paragraph, the reference wall (and the finite element mesh) of Figure 1 will be used, whilst the material properties are given in Table 1. These materials differ from each other, in essence, in the spatial correlation length and only for the first material; in addition to the friction angle of the soil, the unit weight is a random field. Besides, as it is inferred from the present research, the mean and \(COV\) values of \(\phi^{\prime}\) and \(\gamma\) have no effect on the optimal sampling location. The random field of \(\phi^{\prime}\) used in each example is shown in Figures 1, 18 and 19, respectively. It is reminded that the light areas correspond to lower friction angles and vice versa. The \(FS\) value is assumed unity (recall Equation (2)); this factor is discussed in the next paragraph. Figure 17: \(p_{f}\) versus \(d_{d}/H\) example curves for the case of (**a**) sliding and (**b**) overturning wall considering anisotropic soil (\(\theta_{h}/H\) = 20.8 and \(\theta_{v}/H\) = 2.08) and isotropic soil (\(\theta/H\) = 2.08). The _predicted_ resultant driving force (\(F\)) or moment (\(M\)) acting on the wall is compared against the respective \"_actual_\" ones. For each one of the examples presented herein, the latter derives from the respective random field of \(\phi^{\prime}\) using the RFEM method (in Example #1, in addition to \(\phi^{\prime}\), \(\gamma\) is also a random field). The _predicted_\(F\) and \(M\) values derive from a homogenous soil field characterized by the mean of the values sampled from the original (random) field. The results are presented in Figures 20-22 in \(F_{\textit{predicted}}\)/\(F_{\textit{actual}}\)\" or \(M_{\textit{predicted}}\)/\(M_{\textit{actual}}\)\" versus _x/H_ form for various \(d_{d}\)/\(H\) values. The relative difference \(R_{d}\) is also given in each chart (secondary vertical axis; a positive value indicates design on the safe side and vice versa; \(R_{d}\) is equal to \(F_{\textit{predicted}}\)/\(F_{\textit{actual}}\)\"-1 or \(M_{\textit{predicted}}\)/\(M_{\textit{actual}}\)\"-1 for the case of forces and moments respectively). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Example** & **Random Field(s)** & **Distribution** & \(\mu_{\phi^{\prime}}\) & \(\mu_{Y}\) & _COV_ & _0/H_ & **Figure (\({}^{\rm{\bf(1)}}\)** \\ \hline \#1 & \(\phi^{\prime}\), \(\gamma\) & Log-normal & 30\({}^{\circ}\) & 20 kN/m\({}^{3}\) & 0.3 & 8.3 & 1 \\ \#2 & \(\phi^{\prime}\) & Log-normal & 30\({}^{\circ}\) & 20 kN/m\({}^{3}\) & 0.3 & 4.2 & 18 \\ \#3 & \(\phi^{\prime}\) & Log-normal & 30\({}^{\circ}\) & 20 kN/m\({}^{3}\) & 0.3 & 0.42 & 19 \\ \hline \end{tabular} \({}^{\rm{\bf(1)}}\) Figures shown the random fields of \(\phi^{\prime}\).  
\end{table} 
Table 1: Summary of the characteristics of the soils used in the three examples (wall height \(H\) = 2.4 m). Figure 19: Graphical representation of the random field of \(\phi^{\prime}\) of Example #3 (\(\theta/H\) = 0.42; see Table 1). Light areas correspond to lower friction angles and vice versa. Figure 18: Graphical representation of the random field of \(\phi^{\prime}\) of Example #2 (\(\theta/H\) = 4.2; see Table 1). Light areas correspond to lower friction angles and vice versa.