Earthquake response spectra for seismic design of nuclear power plants in the UK

Nuclear Engineering and Design 241 (2011) 968–977

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Earthquake response spectra for seismic design of nuclear power plants in the UK Julian J. Bommer a,∗ , Myrto Papaspiliou a,b , Warren Price b a b

Civil & Environmental Engineering Department, Imperial College London, London SW7 2AZ, UK National Nuclear Laboratory, Chadwick House, Risley, Birchwood Park, Warrington WA3 6AE, UK

a r t i c l e

i n f o

Article history: Received 17 September 2010 Received in revised form 15 December 2010 Accepted 12 January 2011

a b s t r a c t Earthquake actions for the seismic design of nuclear power plants in the United Kingdom are generally based on spectral shapes anchored to peak ground acceleration (PGA) values obtained from a single predictive equation. Both the spectra and the PGA prediction equation were derived in the 1980s. The technical bases for these formulations of seismic loading are now very dated if compared with the state-ofthe-art in this field. Alternative spectral shapes are explored and the options, and the associated benefits and challenges, for generating uniform hazard response spectra instead of fixed shapes anchored to PGA are discussed. © 2011 Elsevier B.V. All rights reserved.

Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Piecewise-linear response spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. RG 1.60 spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. The PML spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. The EUR spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Eurocode 8 spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Estimates of PGA for anchoring spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uniform hazard spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. PML (1988) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Ground-motion prediction models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. PSHA, conservatism and uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Seismic design of nuclear power plants, in common with most engineering applications, is generally based on the response spectrum, which shows the maximum acceleration experienced by a single-degree-of-freedom (SDOF) oscillator subject to a particular earthquake ground motion. In common with practice in most regulatory environments throughout the world, in the UK the design response spectrum needs to be defined by an annual frequency

∗ Corresponding author at: Civil & Environmental Engineering Department, Imperial College London, Skempton Building, South Kensington Campus, London SW7 2AZ, UK. Tel.: +44 20 7594 5984; fax: +44 20 7594 5934. E-mail address: [email protected] (J.J. Bommer). 0029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2011.01.029

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of exceedance, which is the reciprocal of the return period of the ground motion. In the case of the UK, the specified annual frequency is 10−4 (HSE, 2009), corresponding to a return period of 10,000 years. This requirement implies that the seismic actions for design must be determined through probabilistic seismic hazard analysis (PSHA), as originally formulated by Cornell (1968). PSHA considers all possible earthquake scenarios in terms of location and magnitude, and the resulting levels of ground motion that each earthquake could produce at the site of interest. The frequency of earthquakes of different magnitude is defined by a recurrence relationship, whereas the frequency of exceedance of a specified ground-motion amplitude as a result of a particular earthquake depends on the logarithmic standard deviation of the groundmotion prediction (attenuation) equation. Although this standard

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deviation – often referred to as sigma () – was not included in the original formulation of Cornell (1968), it is now considered an indispensable element in PSHA calculations (Bommer and Abrahamson, 2006). By way of illustration only, the 1,000-year ground motion could result from median levels of shaking (which has a 50% probability of being exceeded) due to an earthquake with a recurrence interval of 500 years (i.e., 500 × 1/0.5); alternatively the 1000-year ground motion could be obtained from the meanplus-two-standard deviations (97.7-percentile) shaking level from an earthquake, of much smaller magnitude, with a recurrence interval of just 23 years (i.e., 23 × 1/0.023). In the UK, seismic design and analysis of nuclear power plants (NPPs) is generally based on standard spectral shapes established in the 1980s. In the decades that have elapsed since these representations of UK design motions were developed, there have been many significant advances in the fields of ground-motion modeling and seismic hazard analysis, which now prompt a re-evaluation of UK design motions. This paper reviews the current UK response spectra, demonstrating that they are significantly out of date, not only justifying their revision and updating, but also in fact warranting the adoption of different approaches that are more aligned with the current state-of-the-practice. Fig. 1. Comparison of RG 1.60 and AP1000 response spectra.

2. Piecewise-linear response spectra The response spectrum plots the maximum acceleration against the natural period, T, of the SDOF system, given by the following equation: T=

1 = 2 f



m k

(1)

where m is the mass of the oscillator and k its flexural stiffness; f is the natural frequency of vibration. The spectral acceleration is the maximum sum of the base acceleration plus the acceleration of the mass relative to the base over the entire interval of the shaking. For a system with natural period T = 0, the oscillator is of infinite stiffness hence the mass does not vibrate relative to the base and the spectral acceleration is equal to the peak ground acceleration (PGA). For this reason, the acceleration response spectrum always anchors at PGA at zero period (or at frequencies somewhere between 30 and 100 Hz if plotted against f rather than T), as can be appreciated from Figs. 1–3. The fact that the acceleration response spectrum, regardless of damping level, anchors to PGA, led to most early formulations of design response spectrum to be based on scaling a spectral shape, related only to the classification of the site in terms of near-surface geology, to the PGA at zero period. An extension of this approach, specifically for nuclear applications, was proposed by Newmark and Hall (1969), in which it was recognized that at intermediate response periods the spectral ordinates are proportional to the peak ground velocity (PGV) and the long-period ordinates to the peak ground displacement (PGD). However, many implementations of this approach used empirical relationships to estimate PGV and PGD from the peak ground acceleration, so in effect the method still consists of anchoring a site-class dependent spectral shape to PGA. This approach to constructing the elastic design response spectrum has been widely used, and continues to be used, in the nuclear industry, as illustrated in the following sections.

order to be scaled to a site-specific PGA. The spectra were defined for a number of damping values ranging from 0.5% to 10% of critical. The records were from sites with a range of near-surface profiles but predominantly from deep soil sites; the spectra, however, were issued as being applicable to all rock and soil sites except “unusually soft sites”. The RG 1.60 spectrum has been applied primarily in Central and Eastern United States (CEUS) since this is where the majority of NPPs in the USA have been located. Ground motions from earthquakes in CEUS tend to be rich in high-frequency radiation as a result of high stress drops and very hard rock sites (e.g., Toro et al., 1997; Atkinson and Boore, 2006), and the RG 1.60 spectrum has been judged to be deficient in the high-frequency range for this reason. The spectrum used for design of the Westinghouse AP1000 reactor (WEC, 2007; HSE, 2008) is actually a modification of the RG 1.60 spectrum specifically intended to correct this shortcoming. The AP1000 spectrum, which is defined for damping ratios

2.1. RG 1.60 spectrum The RG 1.60 spectrum was derived for the design of NPPs in the United States (USAEC, 1973). The spectrum was derived following the Newmark and Hall (1969) approach using a subset of the relatively small database of western US strong-motion recordings available at the time, and was anchored to a nominal PGA of 1.0g in

Fig. 2. The PML spectral shapes for Hard, Medium and Soft sites.

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Although the difference between the two spectra seems modest, at a response frequency of 25 Hz the AP1000 spectrum is actually about 30% greater than the corresponding RG 1.60 ordinate. 2.2. The PML spectra The PML spectral shapes (PML, 1981) were derived essentially following the Newmark and Hall (1969) approach to develop three piecewise-linear spectral shapes for three site classes, defined simply as Hard, Medium and Soft (Fig. 2). The spectral shapes were normalized to a PGA of 1.0g, and although nominally anchored at intermediate and long response periods to PGV and PGD respectively, these latter two quantities are obtained from relationships with PGA. The PML spectral shapes were derived for damping values between 0.5% and 10% of critical. The PML shapes were derived using a total of 49 threecomponent strong-motion accelerograms from around the world, selected to be from free-field recording sites at distance of less than 50 km from earthquakes with magnitude Ms between 4 and 6, and with focal depths of less than 25–30 km. Subsequent re-evaluation of the database used for this study has identified a few minor inconsistencies with regards to the stated selection criteria: • The 1966 Parkfield, California, earthquake (which produced 4 of the records) had a magnitude of Ms 6.1, just beyond the stated upper limit. • The 1967 El Salvador earthquake (responsible for one Hard site record) had a focal depth of 78–100 km, which means that it was associated with the Central American subduction process and therefore not relevant to the UK. • The Temblor-2 recording of the Parkfield earthquake was classified as being from a Hard site, but has since been identified as being of intermediate stiffness (e.g., Boore et al., 1997).

Fig. 3. Comparison of the PML and EUR spectra for Hard, Medium and Soft sites anchored to the same PGA of 0.25g.

from 2% to 7% of critical, was modified from the RG 1.60 spectrum. The modification took into account about 80 strong-motion recordings not considered in the derivation of the earlier RG 1.60 spectrum, ground-motion prediction equations for CEUS, and uniform hazard spectra derived for sites in eastern North America at the 10−4 annual exceedance frequency. The essential difference with the RG 1.60 spectrum was an additional control frequency (at 25 Hz) and higher spectral amplitude than the RG 1.60 spectrum at this frequency. The two spectra are compared in Fig. 1.

With a total of just 49 records distributed among the 3 site classes, the results are likely to have been sensitive to such variations; indeed, the PML (1981) study actually notes that “the number of records in each subset, and in particularly in the hard ground dataset, is small enough for a contribution of a single accelerogram to have an imbalancing effect.” There is now a vastly expanded database available to robustly determine average spectral shapes, and there have been great improvements in the characterization of the factors that influence response spectral amplitudes and shapes. A notable example, which could be easily incorporated into such standard spectra, is the classification of site response effects in terms of the average shear-wave velocity over the uppermost 30 m at the site, Vs30 . There have also been important developments in the processing of strong-motion accelerograms (Boore and Bommer, 2005; Douglas and Boore, in press). However, as well as noting that the derivation of standard spectral shapes for different site classes could be performed more robustly, there are also more fundamental issues to be considered. A particularly important point to note is that the PML spectra were derived using the Newmark–Hall approach developed for application within a framework of deterministic seismic hazard analysis. Therefore, in common with other piecewiselinear spectra from the same era, the shapes were based on the 84-percentile (mean-plus-one-standard deviation) ordinates of the normalized spectra in order to provide a degree of conservatism. Since a probabilistic framework for assessing seismic loads for nuclear facilities in the UK has been adopted, the use of spectral shapes defined in this way could be severely over-conservative since the ground-motion variability will automatically be accounted for in the derivation, through PSHA, of the PGA value to which the shapes will be anchored. Using the 84-percentile spectral ordinates anchored to a probabilistically cal-

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culated PGA effectively means including the effect of this variability twice. In light of the enormous growth of the global databank of strongmotion records in the three decades that have since passed – ground-motion prediction models are now routinely derived using hundreds of accelerograms – the PML spectral shapes are clearly due for revision or updating. 2.3. The EUR spectra The spectral shapes specified by the European Utilities Requirements for the design of Light Water Reactor (LWR) nuclear power plants (EUR, 2001) are another set of piecewise-linear shapes defined for different site classes. The Hard, Medium and Soft site classes are defined in terms of ranges of several parameters, including shear-wave velocity, as follows: Soft 200–500 m/s; Medium 600–1000 m/s; Hard 1200–2500 m/s. As with the PML spectra, the piecewise linear portions of the spectrum are based on PGA, PGV and PGD scaled by frequency-dependent factors (with variations for different damping ratios up to 30% of critical); PGV and PGD are scaled directly from PGA. The basis for the derivation of the EUR spectral shapes is obscure. The authors have been informed that when work began on the EUR spectra there was a desire to make these consistent with the spectral shapes in Eurocode 8 (Labbé, 2010); however, the EUR spectra show little resemblance to the spectra in EC8, which are briefly discussed in the next section. Comparison of the EUR and PML spectral shapes, as shown in Fig. 3, suggests that the EUR spectra were obtained by modification of the PML spectra. Apart from the control frequency B taking a value of 14 Hz for the EUR spectra (as opposed to 12 Hz for the PML spectra) the two shapes are essentially identical apart from the constant acceleration plateau of the EUR being appreciably lower. Since these spectral shapes have been developed more recently than the PML shapes, it is likely that they are intended for application within a probabilistic framework, and therefore the modification to the PML shape may represent an attempt to approximate the mean or median spectral shapes. 2.4. Eurocode 8 spectra The spectral shapes specified in Eurocode 8 (CEN, 2004) are occasionally referred to in the context of nuclear engineering, which is perhaps surprising given that there is a very explicit statement in the code that its provisions do not apply to critical facilities such as nuclear power plants. This is because the code does not provide a complete design methodology for safety and performance issues relevant to nuclear power plants (Booth and Skipp, 2004). However, this does not mean that the spectral shape should not be considered as a basis for defining earthquake loading on nuclear facilities, provided the ordinates are referenced to an appropriate annual exceedance frequency. It should be borne in mind, however, that having been derived primarily for input to the design of buildings, little attention was paid to the high-frequency portion of the spectrum, which is of particular importance for NPPs. For a 3-m high (i.e., single-story) building, the simplified formula in EC8 estimates a natural period between 0.11 and 0.19 s depending on the construction material and structural configuration; for this reason, little attention may have been paid to response frequencies higher than 10 Hz. One refinement of the EC8 spectrum compared to the PML and EUR spectral shapes is that it is defined for 5 different site classes, which are defined in terms of Vs30 ranges (A: Vs30 > 800 m/s, B: Vs30 360–800 m/s; C: Vs30 180–360 m/s; D: Vs30 < 180 m/s; class E corresponds to thin layers of C or D class soil over class A rock). During the process of drafting Eurocode 8, there was extensive debate about the possibility of anchoring the spectral shape to more than a sin-

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gle parameter. In the United States, for example, code spectra in the standard building codes were being anchored to the spectral accelerations at 0.2 and 1.0 s, both of which were mapped separately in order to allow the spectral shape to reflect the influence of other parameters, primarily earthquake magnitude, in addition to site class (e.g., Frankel et al., 2000). Resistance to moving beyond the anchoring of the spectrum to PGA led to the compromise solution of introducing two spectral shapes, Type 1 for regions of high seismicity and Type 2 for regions of low seismicity where controlling earthquake scenarios are unlikely to be of magnitude much larger than Ms 5.5, which is the case for the UK. Booth and Skipp (2008) compare EC8 Type 2 with several other spectra that could be considered for the UK. They observe that for EC8 site class B there is a rather good match with the PML medium spectrum. For hard sites, the PML spectrum exceeds the EC8 ordinates in the constant acceleration plateau. For softer sites the EC8 spectral ordinates are slightly higher than those of the PML spectrum, when both are anchored to the same value of PGA in rock. It is noteworthy that Booth and Skipp (2008) make the comparisons plotting the spectral ordinates against period on a linear axis, which somewhat conceals, or at least distracts from, the rather large differences at very short periods (high response frequencies) that are of relevance to nuclear design. Booth and Skipp (2008) note that one shortcoming of the EC8 spectra is that they do not capture the non-linear response of soils, whereby the amplification of ground shaking by soft soil layers diminishes with increasing amplitude of the motion in the underlying rock. Bommer and Pinho (2006) have highlighted many other issues with the EC8 spectral shapes, the most important for the focus of this review being the use of fixed shapes that scale only with site classification and rock PGA. As Booth and Skipp (2008) note, even within the narrow range of earthquake magnitudes that might be considered for seismic design in the UK, the shape of spectrum can vary appreciably as a function of the size of the earthquake. 2.5. Estimates of PGA for anchoring spectra In order to provide a site-specific elastic response spectrum for design when using standardized spectral shapes such as those proposed by PML, an estimate of the site-specific PGA value is required as the anchor point that scales all the acceleration ordinates. For this purpose, PML (1982) produced an empirical ground-motion prediction equation (GMPE) for PGA using a suite of 113 accelerograms produced by 32 earthquakes; 94 of these records came from events in Italy, Greece, New Zealand, Nicaragua and Yugoslavia (Montenegro), with the remainder from California, the latter being added to capture near-source motions. The data were predominantly from earthquakes with magnitudes in the range from 5 to 6, plus a single, distant recording of an event of magnitude Ms 8.0. The records were obtained at distances ranging from 1 to 330 km, so that a broad range of distances would be covered. The functional form of the equation expressed PGA as a function of magnitude and hypocentral distance only, since no statistically significant dependence on the site conditions was found. Subsequently, a second equation was produced (PML, 1985) based only on records obtained at relatively short distances (<40 km) and limited to a maximum magnitude of Ms 7.0. This study used 203 records, about 60% of which (127) were from western United States, with 67 from the same regions as the data used in the 1982 study, plus another 9 from stable regions of China and Canada. The functional form used was essentially the same except that for this model a term was added to distinguish the stronger motions expected, on average, from reverse-faulting earthquakes compared to those from normal and strike-slip events, which is a consistent feature of most modern GMPEs (Bommer et al., 2003).

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A great deal could be written about these two predictive equations, but for reasons of space the discussion here is limited to some of the more important features. The first is simply that the datasets from which the models were derived were rather small, and the accompanying metadata limited. Using small suites of accelerograms to derive empirical GMPEs can lead to some influences on the ground acceleration not being captured, the clearest example in this case being the influence of the site conditions. A number of the earlier GMPEs (e.g., Joyner and Boore, 1981; Ambraseys and Bommer, 1991) came to the same conclusion that the near-surface geology did not influence the value of PGA, but with the larger datasets used in recent years, and in particular with improved characterization of near-surface soil profiles at accelerograph sites, GMPEs now routinely include terms to account for the influence of site class (e.g., Douglas, 2003). The numbers of records used for both of the PML models are very small by comparison with the databases used to derive modern GMPEs, and for crustal earthquakes predictive equations constrained by so few recordings may not be considered tenable given the state-of-the-art in empirical ground-motion modeling (Bommer et al., 2010). An equally interesting point is that both of the PML studies seem to have used only a selected sub-set of the records available from the earthquakes in their databases: 269 records generated by the 32 earthquakes in the PML (1982) database would have passed the selection criteria presented in the report, although only 113 of these were used; the 203 records used in PML (1985) represent less than half of the 503 records available from the earthquakes considered in that study. The reasons for not using the remaining records are not stated, but it is noteworthy that the standard deviations determined for both equations are rather small. The values in natural logarithms are just 0.553 and 0.490, which correspond to 0.240 and 0.213 in log10 units; these are not exceptionally small values but are towards the lower end of values encountered for published GMPEs (Strasser et al., 2009). The sigma value associated with the PML (1985) equation is among the smallest values associated with published equations, which is perhaps surprising given the simple form of the equation. The small standard deviations may be a fortuitous outcome of the data selection or possibly a consequence of the way the standard deviation is calculated. The coefficients of both PML equations were obtained through one-stage least squares regression, which is generally not considered a suitable approach because it is subject to trade-offs between magnitude and distance dependence as a result of the high degree of correlation between magnitude and distance in most strong-motion datasets, particularly those obtained from analog instruments. For this reason, modern GMPEs almost invariably use two-stage regression or maximum likelihood approaches (e.g., Joyner and Boore, 1993). The PML (1982) equation for PGA has been widely used in seismic hazard analyses for nuclear sites in the UK. A study conducted by PML (1983), using only this equation, determined a PGA value of 0.24g at the Sellafield site for the 10−4 annual exceedance frequency. The latter value was rounded to 0.25g and recommended as the basis for seismic design of NPPs in Britain (Hoy and Colloff, 1983). Interestingly, this is identical to the PGA value recommended for anchoring the EUR spectrum at sites throughout western Europe (EUR, 2001). As discussed in Section 3.2, the endurance of the PML (1982) and PML (1985) equations is exceptional: elsewhere in the world, it is rare to find equations still in use after 15 years, much less 25 or more. It is noteworthy that for the seismic hazard study conducted by the British Geological Survey to provide the seismic zonation map that would accompany the UK National Annex to EC8 (Musson and Sargeant, 2007), the PML equations were not used, but instead the calculations were performed using the European model of Bommer et al. (2007) and an early version of the west-

ern North American model of Campbell and Bozorgnia (2008), with equal weighting. More detailed discussions and analyses of the PGA prediction equations used to obtain the anchor values for the PML, or indeed any other, standard spectral shape, are not considered worthwhile by the authors, since this approach to defining the input to the seismic design and analysis of nuclear power plants is outdated. Rather than improve the specific formulations of this approach it may be preferable to seek entirely new approaches that are more compatible with the global state-of-the-art. 3. Uniform hazard spectrum If the annual frequency (or probability) of exceedance of the design motions is an important consideration, which it must be if one is to adopt a risk-informed approach to seismic safety of nuclear plants, then the accelerations experienced by different structures, systems and components – with different vibration frequencies – should all be at this same target level. Since the shape of the response spectrum is strongly influenced by the magnitude of the earthquake as well as by the nature of the near-surface geology at the site, the use of fixed shapes anchored to PGA is unlikely to produce response spectra having the target exceedance frequency at most response periods, even when the PGA value has been appropriately obtained from a PSHA (McGuire, 1977). A uniform hazard spectrum (UHS) can be obtained by conducting several PSHA calculations, each one using a predictive equation for the spectral acceleration at a different response period. Selecting from each PSHA the spectral acceleration with the target exceedance frequency, and plotting these values against the corresponding response period, a response spectrum is constructed whereby every ordinate has the target annual frequency of exceedance. In some regulatory environments, the UHS has now become the standard approach for defining the seismic design loads (e.g., USNRC, 2007), but many still persist with piecewise linear spectra anchored to PGA. The UK regulator, HMNII (Her Majesty’s Nuclear Installations Inspectorate), has demonstrated resistance to adopting the UHS, although this has been in response to a particular case of a UHS submitted as part of a nuclear safety case rather than the generic concept. In the Technical Assessment Guide (TAG) for external hazards, the annex on Earthquakes states that “HMNII has accepted the principle of the UHS spectra. However, HMNII has not accepted any UHS spectra [sic] for design purposes because of concern about the deliberate avoidance of conservatism” (HSE, 2009). The authors of this paper have not had access to the study presenting the UHS that was judged unsuitable by HMNII, but the wording of this statement in the TAG raises important issues that are discussed in Section 3.3. 3.1. PML (1988) In order to derive UHS, PML (1988) developed GMPEs not only for PGA but also for response spectral ordinates at periods from 0.025 to 1.0 s (response frequencies from 1 to 40 Hz). Strong-motion accelerograms were compiled from around the world and grouped into three separate site class groups for separate regressions performed for Hard, Medium and Soft site classes and for horizontal and vertical components of motion. The division of the data into different site groups for separate regressions, rather than using all the data to constrain magnitude and distance dependence and including additional terms for site effects, is not consistent with current practice in ground-motion modeling. The data were preferentially selected from stable regions (such as eastern North America) but included records from the active parts of Europe and also from California. The resulting datasets were rather small, with the equations

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for horizontal motion being derived from regression on 76 records from Hard sites, 72 from Medium sites, and 70 from Soft sites. The functional form of the equations was simpler than that used for PGA (see Section 2.5) with linear magnitude scaling and magnitude-independent attenuation. Style-of-faulting was not included as a parameter in the models. As for the PGA equations, the study used the larger of the two horizontal components from each accelerogram to determine the spectral ordinate at each response frequency. The larger component was used on the basis that “this is consistent with the requirement that the probability of exceedance of ground motion, independent of orientation, be computed”, although this is actually the argument for the adoption of the geometric mean of the two horizontal components in most modern studies (Beyer and Bommer, 2006; Boore et al., 2006). The simple functional form and very sparse datasets were used to derive the models for the full ranges spanned by the dataset, which in terms of magnitude was from about Ms 3 to 7.7, and distances up to 400 km. 3.2. Ground-motion prediction models The shortcomings of the PML (1988) spectral prediction equations, when judged against the state-of-the-art in ground-motion prediction, are many and serious. However, it is an unusual quirk of the UK environment that GMPEs more than 20 years old are even considered fit for purpose, since in other regions of the world it is customary to update such equations as more data become available and as understanding of generation and propagation of seismic waves improves. For example, a series of equations that were published for use in California in 1997, of which the previously cited equations of Boore et al. (1997) is an example, have now been entirely replaced by the five new models produced as a result of the NGA (Next Generation Attenuation) project (Power et al., 2008; Abrahamson et al., 2008). Similarly, the European spectral prediction equations of Ambraseys et al. (1996) have been entirely superseded by those of Ambraseys et al. (2005) and Akkar and Bommer (2010). Even for smaller areas, such as Italy, equations developed more than 10 years ago (Sabetta and Pugliese, 1996) have more recently been updated (Bindi et al., 2009). The simple fact that the number of records used for PML (1985) was almost twice that in PML (1982) is testimony to the rapid growth of available strong-motion data and the opportunities this provides for the continued evolution of ground-motion modeling. The PML studies identified Britain as an intraplate tectonic region and attempted to use strong-motion records from other intraplate regions in deriving predictive models. Understanding of continental tectonics has matured considerably since then, with a distinction being made between active crustal regions (which are often distributed zones of deformation defining broad areas of plate interaction rather than linear boundaries) and Stable Continental Regions or SCRs (Johnston et al., 1994). The UK has been classified as an SCR (Johnston et al., 1994), but this does not necessarily mean that GMPEs developed for other SCRs, such as Eastern North America (ENA), can be automatically adopted as being applicable to UK hazard assessments since there is uncertainty about the degree to which stable regions are similar in terms of ground-motion generation and propagation. For example, Bakun and McGarr (2002) infer major differences from the examination of intensity data from various SCRs, whereas Allen and Atkinson (2007) find broad similarities in ground motions from stable regions of Australia and North America at distances of less than about 100 km. In addition to this controversial issue, the classification of the UK as an SCR has also been contested: Musson and Sargeant (2007) selected GMPEs for their PSHA study on the premise that observed ground motions in northwestern Europe are

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closer to those from active regions such as California than stable regions such as ENA. Clearly, the best constraints on UK ground motions are accelerograms obtained from local earthquakes, some of which are now available from moderate-sized events (e.g., Ottemöller and Sargeant, 2010). Edwards et al. (2008) performed inversions on a large dataset of recordings from UK earthquakes with moment magnitudes Mw between 2 and 4 to obtain estimates of source, path and site parameters. These small-magnitude recordings can then be used in one of three different ways to obtain ground-motion predictions for the UK: • For direct stochastic simulations (Boore, 2003) to generate models as has been done, for example, for ENA (e.g., Atkinson and Boore, 2006; Toro et al., 1997), using the parameters obtained from inversions. • Using equivalent stochastic parameters from empirical GMPEs from other regions (Scherbaum et al., 2006a) to make hybrid adjustments to UK conditions (Campbell, 2003). • Use the small-magnitude recordings directly to adjust some parameters of an empirical GMPE from another region, creating what is known as a referenced empirical model (Atkinson, 2008). All three approaches suffer from the same limitation, namely that they are attempting to use recordings from small-magnitude earthquakes to predict ground motions from the moderate-tolarge magnitude earthquakes considered in PSHA. Several recent studies have shown that such projections are subject to very large uncertainty (e.g., Bommer et al., 2007; Cotton et al., 2008). Comparing small-magnitude UK motions with small-magnitude recordings from other regions may not reliably indicate similarities or differences in terms of ground motions from larger events. For active crustal areas, a number of studies find no evidence for systematic regional differences in ground motions from moderateto-large magnitude earthquakes (e.g., Stafford et al., 2008; Douglas, 2007), but at smaller magnitudes (Mw < 5.5) differences are sometimes found, for example between southern and central California (Atkinson and Morrison, 2009; Chiou et al., 2010). The bottom line is that in the complete absence of any data, there is no definitive knowledge regarding the nature of expected ground motions from, for example, a magnitude 6 earthquake in the UK. This is highlighted by the differences between the PML prediction equations and models derived using identical data but alternative functional forms, which cannot be demonstrated to be statistically inferior to the originals (Lubkowski et al., 2004). This is a clear example of epistemic uncertainty, which is usually incorporated into seismic hazard assessments using logic-trees with several GMPEs weighted according to the relative confidence that the analyst has in each particular model (Bommer et al., 2005). In low-seismicity regions, such as the UK, uncertainty in the median ground-motion predictions is often found to be the dominant contribution to overall uncertainty in the hazard estimates (Scherbaum et al., 2006b). In view of the very large uncertainty associated with groundmotion predictions in the UK, it is surprising that many, if not most, seismic hazard studies conducted for nuclear sites have been conducted using only the PML equation. When an additional study was conducted to determine confidence intervals on the Sellafield hazard curve (PML, 1987), only variations in the source parameters (activity rate, b-values, focal depth and maximum magnitude) were considered; the sensitivity to the selected GMPE was not explored. In California, where there is abundant strong-motion data from earthquakes covering a range of magnitudes, even PSHA conducted for building code applications considers epistemic uncertainty in the median ground-motion prediction (Petersen et al., 2008). By definition,

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epistemic uncertainty must be much larger where there are no data. 3.3. PSHA, conservatism and uncertainty In UK regulations for nuclear safety, the concept of ‘conservatism’ is mentioned frequently, one example being the following: “for natural hazards, the design basis event should be that which conservatively has a predicted frequency of not being exceeded of 10−4 per year” (HSE, 2009). This position is reflected in the repeated claims in the PML studies that conservative choices were made regarding the input parameters, even though this was never proven for one of the most influential inputs to the PSHA, namely the ground-motion prediction model. The problem with such an approach is that if the hazard analyst makes only one or two conservative choices regarding the inputs, the resulting hazard estimate might not be conservative unless these inputs have a dominant influence. If conservative choices are made for all inputs, then the resulting hazard estimate is likely to be extremely conservative. Only with large numbers of sensitivity analyses can the influence of these choices be ascertained with confidence. The probabilistic framework allows the analyst to avoid such decisions; indeed in PSHA conservative choices should not be made regarding inputs to hazard analysis. Rather, the analysis should only aim to capture both the best estimate of each parameter or model, and the full range of associated epistemic uncertainty. The correct place for conservatism is in the selection of the appropriate exceedance frequency or return period, which directly impacts on the risk level, for the design motions. Since the 10,000-year return period is specified in the UK regulations, this choice has already been made, although it may be noted that in current US specifications for nuclear facilities, the design motions correspond to a return period between 10,000 and 100,000 years (USNRC, 2007). However, direct comparisons of the US and UK regulations would also need to consider design safety factors and load factors given the design motions, which is beyond the scope of this paper. Returning to the definition of the design motions, the associated epistemic uncertainty, as mentioned previously, is generally captured using a logic-tree, which was first applied to PSHA by Kulkarni et al. (1984) and which has become a standard tool in seismic hazard assessments, even if it is often misused (Bommer and Scherbaum, 2008). The use of a logic-tree in PSHA leads to several seismic hazard curves, which could prompt a second opportunity for conservatism in selecting the hazard curve or fractile to form the design basis (Abrahamson and Bommer, 2005); this decision, however, is usually obviated since nuclear regulations are generally based on the mean hazard curve (Fig. 4). The population and weighting of logic-tree branches is essentially an exercise in expert judgment. In order to ensure that the center, the body and the range of legitimate scientific interpretations of the available data are captured, multiple expert assessments are generally used for critical facilities. One of the principles established for seismic hazard analysis by the UK regulator is that “The use of expert judgement should be supported in some way by a solicitation process” (HSE, 2009). Procedures for using multiple-expert assessments in PSHA for nuclear facilities have been developed by Budnitz et al. (1997), in what have become known as the SSHAC (Senior Seismic Hazard Analysis Committee) guidelines. The SSHAC guidelines provide a structured procedure that actually facilitates compliance with all of the principles to which the UK regulator requires adherence (HSE, 2009). The SSHAC guidelines have now been implemented several times in practice, and important lessons have been learnt from those experiences (Hanks et al., 2009). A new document is being drafted that provides detailed guidance on the execution of SSHAC Level 3 and 4 studies (Coppersmith et al., 2010), the highest levels

Fig. 4. Example of seismic hazard curves resulting from a site-specific PSHA using a logic-tree formulation. The PGA value corresponding to a mean annual frequency of exceedance of 10−4 is 0.15g.

and the ones appropriate for safety-critical facilities such as nuclear power plants. Options for applying SSHAC Level 3 processes to PSHA for nuclear sites in the UK are discussed by Bommer (2010). 4. Discussion and conclusions The spectral shapes defined in PML (1981) for seismic design of nuclear facilities in the UK are clearly out of date in every respect. The same statement can be unambiguously made for the PGA prediction equations (PML, 1982, 1985) used to provide the zero-period anchors. The predicted PGA values from the PML equations have been shown to lie within the broad range of predictions from SCR equations (Lubkowski et al., 2004) but such comparisons are not necessarily very informative as they often require several adjustments to be made because of different parameter definitions used for the different models. Moreover, any decision about whether to retain the PML equations should be based not on their degree of agreement or disagreement with other models but rather on their general quality and the degree to which they capture the current state of the art in ground-motion predictions. Even if the PML equations were retained for use in seismic hazard analyses for the UK, other equations would still need to be employed as well since a single model cannot capture the range of epistemic uncertainty. It is worth noting, by way of illustration, that the current national seismic hazard map of the United States (Petersen et al., 2008) employed a logic-tree tree with three groundmotion prediction equations for California (Boore and Atkinson, 2008; Campbell and Bozorgnia, 2008; Chiou and Youngs, 2008). The range of epistemic uncertainty in ground-motion predictions in the UK, where there are almost no recordings of strong ground-motion, cannot be smaller than in California, where there is an extensive strong-motion databank. And the imperative to capture this range of uncertainty is more pronounced for critical facilities such as NPPs than in national hazard maps produced for building codes.

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response frequencies. Although the PML (1988) equations could be used for this purpose, these predictive models clearly do not conform to the state-of-the-art. Moreover, their predictions may be deficient in the high-frequencies of particular interest for the seismic design of NPPs (Fig. 5). In a probabilistic framework, such PSHA should be conducted not by making choices or assumptions that the hazard analyst believes to be conservative but rather in a way that captures the full range of epistemic uncertainty. The use of the PML (1988) equations alone would clearly not be adequate to represent the uncertainty in ground-motion predictions for UK earthquakes. For checking designs and for safety analyses, the representation of the seismic actions as an equivalent static force determined from the response spectrum is not sufficient, and acceleration timehistories are required. Since the preliminary design is always based on the response spectrum, the accelerograms must be consistent, either individually or as an ensemble, with the target response spectrum. Current practice in the UK nuclear industry is to use artificial acceleration time-histories generated from white noise to be consistent with the PML spectra (PML, 1981). The generation of UHS would enable the identification of controlling earthquake scenarios through disaggregation of the PSHA (e.g., McGuire, 1995; Bazzurro and Cornell, 1999); see Musson (2004) for examples of disaggregation of UK hazard estimates. The advantage of performing PSHA for several spectral response periods is that the dominant earthquakes scenarios identified by disaggregation of the hazard in terms of PGA may not be those controlling the hazard at response periods relevant to several structures, systems and components in a plant. These design earthquake scenarios could then provide the basis for selecting real earthquake accelerograms that could then be modified to match the scenario response spectrum, or the conditional mean spectrum (CMS) that accounts for the fact that spectral ordinates are not perfectly correlated across the full period range (Baker and Cornell, 2006). Spectral matching techniques allow records to be adjusted to imitate very closely the target response spectrum while retaining most of the characteristics of real records, thus providing more realistic input to dynamic analyses (Hancock et al., 2006; Al Atik and Abrahamson, 2010).

Acknowledgments

Fig. 5. Comparison of PML (1981) spectral shapes (solid lines) and response spectra predicted by the PML (1988) equations (dashed lines) for a magnitude 6.0 earthquake at 10 km. The PML (1981) spectral shapes are anchored to the PGA predicted by the PML (1988) equations. In the upper plot median predicted values are plotted, in the lower plot 84-percentile values.

A feature of the PML (1981) spectral shapes that discourages their continued use is the fact that they are based on 84-percentiles of the normalized spectral ordinates rather than median values. Fig. 5 shows the PML (1981) spectral shapes anchored to median and 84-percentile PGA values predicted by the PML (1988) equation for an earthquake of magnitude 6.0 at 10 km. In the same plots, the resulting spectra are compared with the median and 84percentile ordinates obtained using the full suite of PML (1988) equations. Although the standard deviations associated with the predictions of spectral accelerations tend to increase slightly with increasing response period (see Fig. 6 of Akkar and Bommer, 2010, for example), the increase is much too small to justify the very large overestimation of the ordinates between 2 and 10 Hz by the PML (1981) spectral shapes. Rather than try to refine or improve the PML spectral shapes, it could be preferable to adopt the approach of generating uniform hazard spectra (UHS) through conducting PSHA at multiple

The authors are very grateful to Dr John Douglas and Dr Robin McGuire for their insightful and constructive reviews that helped us to significantly improve the manuscript.

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