# Modified, Reliability-Based Robust Geotechnical Design Method, in accordance with Eurocode 7
## 1 Introduction  
A new geotechnical design approach, called \"reliability-based robust geotechnical design method\" (RGD) was suggested by [PERSON] et al. [1] in 2012. The term \"reliability-based\" stems from the fact that the aim of the method is \"to ensure robustness of reliability-based design even if uncertainties exist in the estimated statistical moments of noise factors\". They prescribed the methodology of defining non-dominated and robust designs of shallow foundations in cohesionless soil. The aim of the RGD method is to calculate a set of non-dominated designs (Pareto from) through multi-objective optimisation, which is conducted using the genetic algorithm NSGA-II. The Pareto front is composed of robust designs that meet the prescribed safety requirements. The final design is chosen from this set, and it is a trade-off between the cost and the robustness of the foundation. The concept of robustness dates from the 1950s, when [PERSON] set the basic principles of the robust method, based on research in Quality engineering [2]. In this context, a robust product is defined as \"a product whose performance is minimally sensitive to factors causing variability (at the lowest possible cost)\" [3]. The application of the robustness concept to the problems in structural and geotechnical engineering has resulted in an adjustment of terminology and methodology, and an array of different definitions connected to the usage of the term itself. A review of relevant literature has shown differing approaches to the structural robustness, with some of them being fundamentally different. In the RGD method, a design is considered robust if the system response is insensitive to the variation of noise factors and the correlations between them [1]. The RGD procedure is generally complex and computationally expensive. Different authors therefore suggest its modifications, most commonly referring to the robustness measure. [PERSON] et al. [4] keep the existing robustness measure (feasibility robustness index \(\beta_{\beta}\)), but suggest its calculation using the sensitivity of reliability index (SRI) incorporated with FORM. The original method uses FORM with integrated PEM. In this case, the total number of analyses is \(n=7 Mn_{c}\), where \(M\) is the number of possible designs, and \(n_{c}\) is the number of noise factors. The modified method has an \(M\) number of analyses, which accelerates the calculation significantly. [PERSON] et al. [5] presume that the existing robustness measure is not fundamentally sound and intuitive, and that it is often isolated from the analysis of design constraints. Consequently, they suggest a gradient-based robust design approach, in which noise factors are treated as random variables, and the design constraints are analysed using advanced First Order Second Moment (AFOSM) method. The design robustness measure is a gradient-based sensitivity index (SI), calculated within probabilistic analyses. Treating noise factors as random variables eliminates standard deviations of their own standard deviations from the procedure, which, in turn, simplifies input parameters significantly. The total number of reliability analyses is reduced to the value of \(M\), which improves the computational efficiency of the method. The sensitivity index, as the design robustness measure in the RGD of soldier-pile-anchor sharing system for deep excavation, is also suggested by [PERSON] et al. [6]. They simplify RGD by reducing multi-objective optimisation to a sequence of single-objective problems. [PERSON] et al. [7] apply the RGD for slope stabilisation using piles. They use signal to noise ratio (SNR) for the design's robustness measure, which is calculated from the standard deviation and the mean value of the factor of safety (FOS). The same robustness measure is applied by [PERSON] et al. [8] in geotechnical slope design. [PERSON] et al. [9] define a new robustness measure for application in the design of rock wedge slopes--the sensitivity index of variability (SIV).