# Modified, Reliability-Based Robust Geotechnical Design Method, in accordance with Eurocode 7
## 4 Discussion  
This paper presented the modified RGD method, which is used in geotechnical engineering to determine optimal, robust designs which meet the safety and cost requirements. The method is computationally expensive and its application in everyday engineering practice is complex. This fact is mainly the consequence of a large number of reliability analyses within the inner and outer loop of the RGD method, which needs to be performed to calculate the feasibility robustness index \(\beta_{\beta}\). The procedure consists of the FORM method with integrated PEM, as shown in Figure 1. To calculate \(\beta_{\beta}\), we need to know the standard deviations of \"noise factors\". In the RGD method, aside from geotechnical parameters, their standard deviations are also treated as \"noise factors\", so a knowledge of their statistical characteristic is required. In everyday practice we often do not have sufficient data for a quality statistical analysis, so their values can only be roughly estimated. [PERSON] et al. [4] simplify the calculation of \(\beta_{\beta}\) by applying the sensitivity of reliability index. Doing so reduces the number of reliability analyses for \(M\) (the number of designs in the design space), but still uses mathematically complex operations, and input parameters remain unaltered. Different authors introduce changes into the design robustness measure [5; 6; 7; 8; 9; 10], which also greatly reduces the number of reliability analyses for \(M\), and simplifies the input  
Figure 17: The Pareto front, along with the dominated and infeasible designs in objective space (**left**) and decision space (**right**). Figure 18: The projections of the Pareto front, the dominated and infeasible designs onto planes \(\beta_{UILS}-cost\) and \(\beta_{SLS}-cost\). parameters; however, complex mathematical procedures are still applied, unlike the ones used in everyday engineering practice. Unlike previous modifications, we--for the first time--suggest a modification of the RGD method that harmonises the optimisation results with the criteria prescribed in Eurocode 7. By doing so, we eliminated the need for additional assessments of the designs, i.e., the RGD method can be used as an alternative to the traditional geotechnical analysis. As the design robustness measure, we suggest using a generalised reliability index (\(\beta\)), which is traditionally used in engineering practice as the measure for structural reliability. We demonstrated that \(\beta\) by definition fits into the reliability concept, and its relation to \(\beta_{\beta}\) is linear, as shown in Figure 4. Due to the linear relation \(\beta-\beta_{\beta}\), the feasible and infeasible regions, as well as the Pareto fronts yielded from the original and from the modified methods, are similar--as illustrated in Figures 13 and 14. We suggest calculating the generalised reliability index using the modified PEM method (IPEM), which is simpler to use, i.e., it does not include mathematically complex operations, while maintaining a high degree of accuracy--as presented in Tables 2 and 3. We introduce a sensitivity analysis into the RGD method, with the aim of \"freezing\" the random variables whose contribution to system response is negligible. For this purpose, we suggest calculating first order Soboli indices, which can also be estimated using the IPEM method. To further reduce the number of conducted reliability analyses, we suggest conducting them only for the designs chosen via the genetic algorithm NSGA-II. This reduced the number of analyses in the example of a shallow foundation on coherent soil from \(M\) to \(0.5-0.62M\), as presented in Figure 7 and Table 9. The given illustrative example 1 shows a good match of results yielded from the original and modified methods, illustrated in Figures 13 and 14. According to expectations, and due to the introduction of additional constraints, the feasible region of the modified method was moved right in relation to the original method.