## 4 Discussion
### Designing with Load and Resistance Factor Design (LRFD) Codes  
Recent geotechnical design codes (such as Eurocode 7 [32] and AASHTO [4]) aim to achieve geotechnical designs with an appropriate target reliability by applying partial factors to _characteristic_ parameter values. In principle, the _characteristic_ values of geotechnical parameters are selected so as to take account of the inherent variability of the ground, the uncertainty in the determination of the soil parameters and the extent of the relevant failure mechanism. _\"Partial factors\"_ are also applied to actions, material properties, and/or resistances to provide safety and also to account for model uncertainties and dimensional variations [33]. Meanwhile, Eurocode 7 [32] defines the characteristic value of a geotechnical parameter as \"a cautious estimate of... the mean of a range of values covering a large surface or volume of the ground\". In the various codes of North America, the mean value of the measurements is used [4; 34; 35; 36]. Eurocode 7 further notes that \"if statistical methods are used, the characteristic values should be derived such that the calculate probability of a worse value governing the occurrence of the limit state under consideration is not greater than \(5\%\)\". In this respect, the following statistical equation is often used for the calculation of the characteristic value [33; 37]:  
\[X_{k}=X_{m}-\frac{t_{a,y_{k}}\cdot S_{d}}{\sqrt{n}} \tag{4}\]  
where \(X_{m}\) is the sample mean, \(S_{d}\) is the sample standard deviation, \(n\) is the number of samples, \(t_{a,y_{n}}\) is the Student \(t\) factor for a confidence level of \(\alpha\%\) in the case of \(v_{s}\) degrees of freedom, and \(v_{s}\) is equal to \(n-1\), assuming a normal distribution. \(t_{a,y_{s}}\) values for a confidence level of \(95\%\) and various degrees of freedom \(v_{s}\) in tabular form can be found in any statistical book (e.g., [38]).EN 1997-1 [32] dictates that the design values of the geotechnical parameters (\(X_{d}\)) be derived from the respective characteristic values using the following equation:  
\[X_{d}=X_{k}/\gamma_{M} \tag{5}\]  
where \(X_{k}\) is the characteristic value of a material property \(X\) and the symbol \(\gamma_{M}\) denotes the partial material factor. When partial factors are not applied to the material properties (i.e., \(\gamma_{M}=1\)), a model factor \(\gamma_{R}\) greater than \(1\) is applied to the resistances. The discussion on the design of earth-retaining structures based on characteristic soil property values instead of the respective mean values is facilitated by the two example charts in Figure 23. These charts refer to Case #3 presented in the previous paragraph (see also Table 1). This specific case was chosen because of the relatively low \(\theta\) value (i.e., \(\theta/H=0.42\)), which indicates a rather highly spatially variable soil; thus, the use of the characteristic value makes more sense. Two cases are presented, the \(d_{d}/H=1\) and the \(d_{d}/H=0.25\). The figure in question refers to the sliding mode of failure; however, the respective curves for the overturning mode of failure do not differ appreciably. It is also mentioned that, in the example presented here, the partial material factor for the friction angle \(\gamma_{\rm M}=\gamma_{\phi}\) was set equal to unity. From Figure 23, it is clear that the benefit from a targeted field investigation is much greater as compared to the benefit gained using characteristic values. Moreover, despite the conservatism which is inserted in the analysis using the characteristic value concept, the characteristic values alone, as shown, cannot guaranty a conservative enough engineering study. The safety level can be increased by applying a statistical uncertainty partial factor (similar to the model factor \(\gamma_{R}\) used by Eurocode 7) or a unified and more conservative model factor to the resistances, which will absorb the statistical uncertainties related to the soil.