# Modified, Reliability-Based Robust Geotechnical Design Method, in accordance with Eurocode 7
## 2 Materials and Methods  
Original Method--Reliability-Based, Robust and Optimal Design (RGD) Method of Shallow Foundations in Cohesionless Soils  
The procedure of applying the RGD method as defined by [PERSON] et al. [1] is shown in Figure 1. The first step requires a characterisation of noise factors, decision variables and the design domain. Since there are uncertainties in the second statistic moment of geotechnical random variables as well, they are considered to be \"noise factors\", i.e., \"hard-to-control\" parameters. Consequently, their standard deviations are treated as random variables, i.e., data on their statistical distributions, mean values and standard deviations is required. Since engineering practice often lacks data for a quality statistical analysis, an estimation is suggested using the statistic bootstrap method. Unlike the statistic characteristics of geotechnical parameters, literature holds no information on typical statistic characteristics of their standard deviations, and their estimation via the bootstrap method is not reliable. This introduces additional uncertainties into the method, which impacts the final results, attained conducting reliability analyses. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Study Authors** & \begin{tabular}{c} **Consideration of** \\ Uncertain Parameters** \\ \end{tabular} & **Robustness Measure** & \begin{tabular}{c} **Geotechnical Problem in** \\ **Consideration** \\ \end{tabular} & \begin{tabular}{c} **The Method for** \\ **Calculating the** \\ **Robustness Measure** \\ \end{tabular} \\ \hline [PERSON] et al. [1] & Noise factors & Feasibility robustness index & Shallow foundations & FORM \\ \hline [PERSON] et al. [4] & Noise factors & Feasibility robustness index & Shallow foundations & FORM \\ \hline [PERSON] et al. [5] & Random variables & Gradient-based sensitivity index (SI) & Shallow foundations & AFOSM \\ \hline [PERSON] et al. [6] & Random variables & \begin{tabular}{c} Gradient-based sensitivity index (SI) \\ \end{tabular} & \begin{tabular}{c} Soldier pile-anchor tieback \\ shoring system for deep \\ excavation \\ \end{tabular} & FEM \\ \hline [PERSON] et al. [7] & Random variables & \begin{tabular}{c} Signal to noise ratio (SNR) \\ of FOS \\ \end{tabular} & Piles for landslide stabilisation & FOSM \\ \hline [PERSON] et al. [8] & Random variables & \begin{tabular}{c} Signal to noise ratio (SNR) \\ of FOS \\ \end{tabular} & Design of the soil slopes & Analytical \\ \hline [PERSON] et al. [9] & Random variables & \begin{tabular}{c} Sensitivity index of \\ variability (SIV) \\ \end{tabular} & Design of the rock wedge slopes & \begin{tabular}{c} N-dimensional equivalent \\ method \\ \end{tabular} \\ \hline [PERSON] and [PERSON] [10] & Random variables & \
\begin{tabular}{c} Standard deviation of \\ differential settlement \\ \end{tabular} & Foundations for wind turbine & Monte Carlo method \\ \hline [PERSON] et al. [11] & Noise factors &
\begin{tabular}{c} Standard deviation of \\ probability of failure \\ \end{tabular} & Design of the rock slope & Monte Carlo method \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The summary of reviewed literature. The middle part of the procedure features an inner and outer loop, which include the calculation of the design robustness measures using the FORM (First Order Reliability Method) with integrated PEM (Point Estimate Method). Design robustness is measured by the index od feasibility robustness (\(\beta_{\beta}\)). Determining \(\beta_{\beta}\) requires the information on the statistical distribution of \(\beta\). The authors of the RGD procedure believe it is reasonable to assume a normally distributed \(\beta\), in which case \(\beta_{\beta}\) can be expressed as follows:  
\[\beta_{\beta}=\frac{\mu_{\beta}-3.8}{\sigma_{\beta}}, \tag{1}\]  
In Equation (1), \(\mu_{\beta}\) and \(\sigma_{\beta}\) are the mean value and the standard deviation of the reliability index.