# Safety of Nuclear Power Plants with Respect to the Fault Displacement Hazard
## 3 Concept Proposed for Definition of Design Basis PGD  
The design basis for PGD is proposed to be developed starting with considerations of whether the design basis earthquake could cause PGD. It is assumed that the site is investigated in accordance with IAEA requirements and guidance [1,2]. The design basis earthquake is defined in terms of the annual probability of the exceedance of maximum horizontal acceleration that is set usually to \(10^{-4}\)/year. The deaggregation of the hazard defines the weights in magnitude-distance bins how the earthquake with magnitude \(Mw\) and at distance \(R\) contributes to the hazard. The deaggregation of hazard can be transformed to a probability density function, \(\wp(Mw,R)\), i.e., the integral for all magnitudes and distances \(\iint\ \wp(\mathrm{Mw},\mathrm{R})dMwdR=1\). It does not seem practicable to assume that the site location can be affected by several sources within the site area. Furthermore, it should be noted that, in case of seismic design basis at hazard levels \(10^{-4}\) to \(10^{-5}\) per annum, the dominating sources are generally close to the site (see, Figure 1) and the magnitudes tend to maximum potential (or cut-off) magnitude \(Mw_{max}\)\({}^{*}\) (see, Figure 2) for the Paks site, Hungary [27]. The first question to be answered is whether permanent ground displacement can happen at the hazard level for the seismic design basis. Considering the fault traces and possible surface ruptures, those distance bins should be taken into account that are within the screening distance, \(R_{scr}\) between the site location and principal fault or between the site location and any Quaternary fault as per ANSI/ANS-2.30-2015 [21]. Let us denote the magnitude probability distribution as \(p(Mw)=\mathrm{C}\int_{0}^{R_{scr}}\wp(Mw,R)dR\), where \(C>1\) is the scaling constant for ensuring that \(\int_{0}^{Mw_{max}}p(Mw)dMw=1\). The \(Mw_{max}\) is the maximum magnitude of the source contributing to the seismic hazard at the level of design basis (\(H_{DBE}\)). The \(Mw_{max}\) should be less or equal to the maximum potential magnitude of the source \(Mw_{max}\)\({}^{*}\) that is defined on the basis of geologic and tectonic considerations for the seismogenic source contributing to the hazard. It is reasonable to assume that a single capable source is in the site area. Figure 1: Deaggregation matrix for 12,642 years return period [28]. Introducing the conditional probability distribution of PGD greater than zero versus magnitude \(P(sr\
eq 0|Mw)\), the probability of PGD greater than zero \(P(sr\
eq 0)\) for the hazard level of design basis earthquake can be calculated as follows:  
\[\int_{Mw_{min}}^{Mw_{max}}p(\mathrm{m})\mathrm{P}[\mathrm{sr}\
eq 0|\mathrm{m} \,]dm=P(sr\
eq 0) \tag{2}\]  
where \(m\) is the running value of \(Mw\), \(Mw_{min}\) is the minimum magnitude that can cause surface rupture, and \(Mw_{max}\) is the maximum potential magnitude of the source that contributes to the hazard and is capable of causing PGD at the site \(Mw_{max}\leq Mw_{max}\)\({}^{*}\). Thus, for the sake of the simplicity of writing the equations, the continuous distribution form is used. The \(\mathrm{P}[\mathrm{sr}\
eq 0|Mw]\) is the conditional distribution for surface rupture (indicated here as \(sr\)) if an earthquake happens with \(M_{w}\). Depending on the fault type, the \(\mathrm{P}[\mathrm{sr}\
eq 0|M_{w}]\) is to be taken into account, for example, from [PERSON] et al. (2003) [5] and [PERSON] et al. (2011) [6], [PERSON] and [PERSON] [7], or from [PERSON] et al. (2015) [8]. Regarding minimum accountable \(Mw_{min}\) and the area of possible distribution faulting, it is advised that [18,19] are taken into account. An estimation of the \(P(sr\
eq 0)\) can be done approximating \(p(Mw)\) by uniform distribution in the interval \([Mw_{min};Mw_{max}]\) and \(\mathrm{P}[\mathrm{sr}\
eq 0|Mw]\leq\mathrm{P}[\mathrm{sr}\
eq 0|Mw_{max}]\).