# Improved Simplified Engineering Fault Displacement Hazard Evaluation Method for On-Fault Sites
## 4 Discussion of the Results  
### Analysis of the Results  
In Figure 6, the hazard's dependence on the site's distance from the end of the fault is apparent. The resulting hazard curves at \(x_{s}=0.1\times FL\), \(x_{s}=0.3\times FL\) and \(x_{s}=0.5\times FL\) complied with the physical considerations. The closer the site was to the middle of the mapped fault, the higher the displacement hazard was. It is remarkable that in the case of \(x_{s}=0.5\times FL\), the most significant contributor to the hazard (Max-dotted black line) was practically equal to the curve obtained for \(D_{ave}\) per Equation (4) and with an annual rate per Equation (7). This can be considered as an empirical justification of the procedure proposed. The hazard curve overestimation obtained by the conservative method in [5] had two essential causes: The dominating cause of over-conservatism was the overestimation of the number of ruptures that intersect the site. The weighted average of six magnitude-displacement scaling relations was slightly more conservative as \(D_{ave}\) per Equation (4) (see Figure 4). It is also remarkable that the method in [5] provides about the same hazard estimation as it is defined assuming \(D_{ave}\) per Equation (4) along the rupture if the intersection probability is calculated according to the procedure in Section 2 above; the red dashed (Dave), the black dashed (Old) and red dotted lines (Old+) were compared. It means that scaling the average displacement versus magnitude is a better estimation for any site position than scaling the displacement per magnitude and associating it to the site with the probability of intersection, which is equal to the ratio of the rupture length (also scaled to the magnitude) to the mapped length of the fault. The basic question for the operators/owners of critical, high-potential-risk facilities is whether the fault displacement hazard is significant for safety. The significance should be assessed at the hazard level prescribed by the regulations and an analysis of the consequences of surface displacements or engineering judgment. In the case of nuclear power plants, as discussed in [3; 4; 5], the hazard can be screened out if the hazard effects at an annual exceedance rate of \(10^{-7}\)/a are negligible for the integrity of the plant structures. Generally, it is assumed that the hazard can be neglected if the surface displacement is less or about 10 cm at \(10^{-7}\)/a. If the hazard is recognised at an operating nuclear power plant, the best estimate displacement can be used to evaluate the safety significance. The mean value of the probability density function for the displacement at the level of \(10^{-7}\)/a should be defined, and the uncertainty should be estimated and considered. It should be proven that the values indicated as \"expected\" are point estimates of the mean displacements at any hazard level, and the maximum and minimum values could be considered the interval where the displacements are likely to fall. Figure 7 shows the annual exceedance rates for displacements at \(x_{s}/FL=0.2\) and \(x_{s}/FL=0.5\) calculated for ruptures with different \(x_{i}\) in the range of \(0\leq x_{i}\leq x_{s}\). These are the possible contributors to the site hazard. The ruptures with \(x_{i}=0\) and \(x_{i}=x_{s}\) are the two extremes contributing to the hazard, giving the largest and smallest possible displacements. The green lines refer to the expected displacement AER, and the dotted lines indicate the AER curves of the maximum and minimum contributors to the displacement hazard. Thus, the minimum and maximum curves bound the possible contributors, including the physically possible largest and lowest contributors with \(x_{i}=0\) and \(x_{i}=x_{s}\), respectively. A minor exception is in the case of \(x_{s}/FL=0.2\), in the interval \(10^{-7}\)/a to \(5\times 10^{-8}\)/a where the contribution to the hazard rupture with \(x_{i}=0\) slightly exceeds the predicted maximum curve.