Risk-targeted maps for Romania

J Seismol https://doi.org/10.1007/s10950-017-9713-x ORIGINAL ARTICLE Risk-targeted maps for Romania Radu Vacareanu & Florin Pavel & Ionut Craciun & Veronica Coliba & Cristian Arion & Alexandru Aldea & Cristian Neagu Received: 14 February 2017 / Accepted: 3 November 2017 # Springer Science+Business Media B.V., part of Springer Nature 2017 Abstract Romania has one of the highest seismic hazard levels in Europe. The seismic hazard is due to a combination of local crustal seismic sources, situated mainly in the western part of the country and the Vrancea intermediate-depth seismic source, which can be found at the bend of the Carpathian Mountains. Recent seismic hazard studies have shown that there are consistent differences between the slopes of the seismic hazard curves for sites situated in the fore-arc and back-arc of the Carpathian Mountains. Consequently, in this study we extend this finding to the evaluation of the probability of collapse of buildings and finally to the development of uniform risk-targeted maps. The main advantage of uniform risk approach is that the target probability of collapse will be uniform throughout the country. Finally, the results obtained are discussed in the light of a recent study with the same focus performed at European level using the hazard data from SHARE project. The analyses performed in this study have pointed out to a dominant influence of the quantile of peak ground acceleration used for anchoring the fragility function. This parameter basically alters the shape of the risk-targeted maps shifting the areas which have higher collapse probabilities from eastern Romania to western Romania, as its exceedance probability R. Vacareanu : F. Pavel (*) : I. Craciun : V. Coliba : C. Arion : A. Aldea : C. Neagu Seismic Risk Assessment Research Center, Technical University of Civil Engineering Bucharest, Bd. LaculTei, no. 122-124, Sector 2, 020396 Bucharest, Romania e-mail: florin.pavel@utcb.ro increases. Consequently, a uniform procedure for deriving risk-targeted maps appears as more than necessary. Keywords Seismic hazard . Fragility curves . Probability of collapse . Share . Uncertainty 1 Introduction The Romanian seismic design code P100-1/2013 (2014), enforced since January 2014, estimates the design peak ground acceleration (for the life safety ultimate limit state—ULS) for a mean return period of 225 years (20% probability of exceedance in 50 years). This mean return period represents an intermediary step before moving to the mean return period of 475 years, recommended by EN 1998-1 (Eurocode 8). It also has to be emphasized the fact that the mean return period associated with the design peak ground acceleration has increased ever since the 1992 version of the Romanian seismic code. The 1992 version of the code had a mean return period of 50 years, which increased to 100 years in the 2006 version of the code before moving to 225 years in the current version. Significant differences in terms of both seismic hazard levels and slopes for the seismic hazard curves (k parameter in Eurocode 8) have been noticed between the study of Pavel et al. (2016), denoted hereinafter as BIGSEES model, and Woessner et al. (2015), denoted hereinafter as SHARE model. The first main reason for the observed differences are the different soil conditions employed in the two models; while SHARE model uses as reference rock conditions, the BIGSEES model J Seismol employs as reference the soil conditions derived through the topographic slope method proposed by Wald and Allen (2007). The second reason is related to the different ground motion prediction equations (GMPEs) used in the two studies. One of the two GMPEs used in the SHARE model, namely the Lin and Lee (2008) GMPE, was tested using a collection of ground motion recordings from Vrancea earthquakes and was found to consistently underestimate the observed ground motions (Vacareanu et al. 2013). A third reason which might also explain the differences is related to the SHARE modeling of the Vrancea subcrustal seismic source, which covers an area roughly 15 times its actual size; in addition, the earthquake occurrence rates used in the SHARE model underestimate the observed seismicity. Concerns regarding the SHARE seismic source models have also been raised by Zimmaro and Stewart (2017). Recently, Silva et al. (2016) have developed risktargeted maps for Europe using the seismic hazard results obtained in the SHARE project. Their analysis shows that most of Romania, namely the southern and eastern parts (which are under the influence of the Vrancea intermediate-depth seismic source), have a quite low probability of collapse, similar with that from countries with low seismicity, such as Sweden, Finland, or Ireland. Consequently, the authors recommend a decrease of the seismic hazard levels for most of southern and eastern Romania and an increase for the sites situated towards the western part of the country. It is not the intention of the authors to compare per se the seismic risk results based on the SHARE and BIGSEES seismic models. The comparison with the results of Siva et al. is made just in broad terms and trends, highlighting opposite general conclusions regarding the seismic risk in the front and in the back of the Carpathian Mountains. In this context, in the present study, risk-targeted maps are developed for Romania using as reference the seismic hazard results obtained by Pavel et al. (2016). Among other studies which have applied the same methodologies (albeit with different input values), one should mention the papers of Luco et al. (2007) for the conterminous US, Douglas et al. (2013) for mainland France, or Vanzi et al. (2015) for Italy. 2 Calculation of risk-targeted maps The most recent probabilistic seismic hazard assessment for Romania performed by Pavel et al. (2016) employed a logic-tree approach in order to account for the epistemic uncertainties. Three GMPEs were used in the logic tree for the crustal seismic sources in Romania and six GMPEs were employed for the Vrancea intermediatedepth seismic source (three for the sites situated in the fore-arc region and three for the sites in the back-arc region). The delineation between the fore-arc and backarc region was considered to be along eastern and southern sides of the Carpathian Mountains. In addition, the uncertainties regarding the focal depths, maximum magnitudes and seismic activities rates were also accounted for. The most important result of this analysis is represented by the uniform seismic hazard map for a mean return period of 475 years, shown in the paper of Pavel et al. (2016). The noticeable difference in terms of slopes of the seismic hazard curves between fore-arc and back-arc sites is highlighted in Fig. 1. The four sites have basically the same peak ground acceleration for a mean return period of 475 years, yet the slope of the hazard curve is totally different. This difference can be attributed to the much higher seismic activity rate of the Vrancea intermediate-depth seismic source which affects mostly fore-arc sites, as compared to the lower seismic activity rates for the crustal seismic sources which affect mainly back-arc sites (situated in the western part of Romania). Consequently, it is to be expected that the seismic risk in terms of failure probabilities will differ significantly between these two zones. The model on which probabilistic seismic hazard analysis (PSHA) was accomplished in BIGSEES model is based on the following assumptions: the seismicity model grounded on the earthquakes catalogs from Romania, Bulgaria, and Serbia, the GMPEs on soil conditions purposely developed for Vrancea intermediate-depth seismic source or tested against the database of strong ground motions recorded in Romania and a logic tree taking into account the epistemic uncertainties in terms of maximum magnitude, focal depth, and goodness-of-fit of GMPEs. Consequently, the results of PSHA in terms of PGAs or spectral accelerations (SAs) are for ground types A, B, and C, as they are defined in EN 1998-1. Because detailed geophysical and geotechnical information, as requested for the definition of ground types in EN 1998-1, are not available for all sites in Romania, the soil conditions in BIGSEES model were largely based on topography and enhanced with local relevant information, where available. The Romanian seismic design code P100-1/2013 defines the local soil conditions in terms of control periods TB and TC of design response J Seismol spectrum. The code-based control periods are obtained from the envelope of values calculated from strong ground motions recorded during large earthquakes in Romania. This decision of the Romanian code drafters is based on the larger reliability of the control periods values arising from actual ground motions than of the values obtained from empirical correlations with geophysical and geotechnical values. There are four input data to be considered in the calculations for risk-targeted maps: the mean return period of the ground motion parameter selected for the analysis, the corresponding value of the quantile of the fragility function of buildings, the standard deviation of the lognormal distribution describing the fragility function, and the target annual probability of collapse/failure. One has to mention that collapse/failure is defined as the exceedance of a given design limit state. Both EN 1998-1 (2004) and Romanian seismic design code P100-1/2013 (2014) consider two performance levels for structural design, namely the damage limitation limit state (which is a serviceability limit state) and the life safety limit state (which is an ultimate limit state). Neither EN 1998-1/2004 nor P100-1/2013 makes an explicit check of the no-collapse performance objective. Thus, the assessment of the associated probability of collapse (collapse means exceedance of a limit state) is one of the key issues of the risk-targeted approach. Luco et al. (2007) have proposed a collapse probability of 10% associated to a ground motion parameter with mean return period of 2475 years. Goulet et al. (2007) has computed failure probabilities in the range 2–7% for the same mean return period of the seismic action as used by Luco et al. (2007).On the contrary, Ulrich et al. (2014) assigned annual failure probabilities of the order 10−5…10−7 depending on the seismic zone in which the structure is situated (lower failure probabilities are assigned to the buildings built in the zones with the lower seismic hazard). Fajfar and Dolšek (2012) have computed annual failure probabilities of the order 10−4…10−5. Vanzi et al. (2015) have used the same failure probability as the one assigned by EN 1990 (Eurocode 0) for gravity loads, namely 1.3·10−6. The second major issue is the assessment of the variability inherent to the fragility curves (logarithmic standard deviation β). In this aspect, too, there are significant differences between the values used by various researchers. For instance, Luco et al. (2007) use a β value of 0.8, while Douglas et al. (2013) employ a value of 0.5. Silva et al. (2016) consider a standard deviation of 0.6, while Vanzi et al. (2015) use a value of 0.2, which is by far the lowest value encountered in all the studies with this focus. With regard to the actual calculation of the mean annual frequency (MAF) of exceeding a given limit state, there are also several approaches. Doulgas et al. (2012) use the classic convolution products for the computation of the annual failure probability, given by Kennedy (2011): þ∞ P F ¼ ∫ H A ðaÞ⋅ 0 þ∞ P F ¼ − ∫ P F ja ⋅ 0 dP F ja da da ð1Þ dHa ðaÞ da da ð2Þ where PFla is the fragility function (conditional cumulative distribution function of the probability of failure given a ground motion value) and Ha(a) is the hazard curve. Silva et al. (2016) have computed the annual failure probability by dividing both the fragility curve and the seismic hazard curve into segments and then numerically integrating the distribution. On the contrary, Vanzi et al. (2015) employed an approach based on the approximation of the seismic hazard curve with a line (in log-log space) and then computing numerically the risk convolution integral. Under the Poisson assumption, there is a negligible difference between the values of annual probability of collapse and MAF, since we are targeting very low values. In this study, the MAF of exceeding the life safety limit state (LS) is obtained in the same manner as in Douglas et al. (2013), through the convolution product between the fragility function (expressed as probability density function, PDF) and the MAF of exceeding various values of peak ground acceleration (representing actually the seismic hazard curve), using Eq. 1. Alternatively, the MAF of exceeding a given LS can be obtained by the convolution product between the fragility function (expressed as cumulative distribution function, CDF) and the first derivative of the seismic hazard curve, using Eq. 2. In both situations, the fragility function is conditional upon the values of PGA, and represents the conditional probability of exceeding the given LS as a function of PGA values. The fragility functions are expressed as lognormal distributions with two parameters: the median value of PGA and the logarithmic J Seismol Fig. 1 Comparison of seismic hazard curves for fore-arc and back-arc sites standard deviation of PGA (parameter β).Subsequently, the peak ground acceleration for various mean return periods are extracted from the seismic hazard curves for the same 200 sites analyzed by Pavel et al. (2016). The extracted peak ground accelerations shall be considered as an inferior fractile (quantile) of the lognormal distribution, say p quantile. This means that there is a p probability that the exceedance of the life safety LS is encountered for PGA values lower than the design value, and 1-p probability that the exceedance will be reached for higher PGA values. Considering the p value of PGA quantile and using the properties of the lognormal distribution, we obtain the median value of PGA for the fragility curve describing the probability of exceedance of life safety LS conditional upon PGA values. Then, we proceed to the calculation of the convolution integral and we obtain the MAF of failure. If one considers that the probability distribution of failure is of Poisson type (and this is reasonable since failure is a rare and independent event for any given year), using the values obtained for MAF we obtain the annual probability of failure. Conversely, one can impose a target MAF of exceedance of life safety limit LS and then use the convolution integral to iterate for the median value of PGA that produce the appropriate fragility function. Once the median value is obtained, using the properties of the lognormal distribution of probability, one can obtain the p quantile value of PGA that becomes the design value for the site given the target MAF of exceedance of life safety LS. The influence of the slope of the seismic hazard curve on the annual probability of collapse is visually represented in Fig. 2. The two cities selected, Bucharest and Timisoara, are mostly influenced by the Vrancea intermediate-depth seismic source, respectively, by local shallow seismic sources, producing more abrupt, respectively, less abrupt slopes. The area under the red curve in Fig. 2 evaluates the annual probability of collapse and one can notice that steeper the slope towards larger PGA values, higher the area enclosed by the risk curve. 3 Results for Romania The risk-targeted maps for Romania are developed taking into consideration the combination of target annual collapse probabilities and standard deviations proposed by both Luco et al. (2007) and Silva et al. (2016). Several sets of maps were created in order to evaluate the influence of three key input parameters, namely the value of peak ground acceleration, the standard deviation β, and the quantile of the lognormal distribution (describing the fragility function) to which the peak ground acceleration was assigned to. The first four maps presented in Fig. 3 (left and right) and Fig. 4 (left and right) show the peak ground accelerations corresponding to a collapse probability of 2·10−4. The accelerations were computed for β = 0.6 and β = 0.8 and using a quantile of either 0.001 or 0.1 as used by Silva et al. (2016) and Luco et al. (2007). The J Seismol Fig. 2 Calculation of convolution integral using relation (2) for Bucharest (left) and Timisoara (right) main observations regarding the four abovementioned figures are: & & & & The overall shape of the map does not appear to change with either of the two variable parameters (β and quantile); The corresponding peak ground accelerations for a given collapse probability increase with the value of the standard deviation (this increase is more visible in the case of 0.1 quantile); Just by changing the quantile from 0.001 to 0.1, the resulting peak ground accelerations increase by at least three times (the change of β produces a variation of less than 20%); The overall shape of the map does appear to resemble that of the uniform hazard map shown in Pavel et al. (2016). In the subsequent step of the analysis, we compute the ratio between the peak ground accelerations for a mean return period of 475 years (uniform hazard values) and those corresponding to a collapse probability of 2·10−4, β = 0.8 and 0.1 or 0.001 quantiles. The resulting maps are shown in Fig. 5 (left and right). It is to be noted that the range of the computed ratios is generally below 0.5–0.6 for the 0.1 quantile, while in the case of the 0.001 quantile, the ratio is above unity, thus meaning that the amplitudes resulting from the seismic hazard analysis are superior to the ones based on the uniform risk approach. The difference between the results produced by employing the two quantiles is again very large. Next, we evaluated the collapse probabilities corresponding to two mean return periods of the PGA, namely 475 and 2475 years. For both return periods, the Fig. 3 Peak ground accelerations corresponding to a collapse probability = 2·10−4, β = 0.6 and 0.001 quantile (left) and PGA corresponding to a collapse probability = 2·10−4, β = 0.8 and 0.001 quantile (right) J Seismol Fig. 4 Peak ground accelerations corresponding to a collapse probability = 2·10−4, β = 0.6 and 0.1 quantile (left) and PGA corresponding to a collapse probability = 2·10−4, β = 0.8 and 0.1 quantile (right) standard deviation was taken as 0.6 and 0.8, while the quantile values considered were 0.1 and 0.001. Figure 6 (left and right) shows the results for the 475 years mean return period, while Fig. 7 (left and right) displays the values obtained for the mean return period of 2475 years. The results obtained show a completely distinct pattern of the computed collapse probability. In the case of the 0.001 quantile, the largest collapse probabilities are encountered for the western part of the country which is not under the direct influence of the Vrancea intermediate-depth seismic source. On the contrary, in the case of the 0.1 quantile, the largest collapse probabilities are encountered in the eastern part of Romania, and more specifically in the area which has the highest level of seismic hazard (area under the direct influence of the Vrancea intermediate-depth seismic source). It is intuitive to assume that the collapse probability is larger for sites situated in the eastern part of the country and thus the opposite results obtained when using a different quantile raise some questions regarding the methodology. Similar contradictory results were also obtained for Romania by Silva et al. (2016); however, this result was not discussed in their paper. The final analysis is performed for the following combination of values of the input parameters: the value of the logarithmic standard deviation β is 0.6, same as in Luco et al. (2007) for conterminous US and in Silva et al. (2016) for Europe; the PGA values from hazard curves with 2% exceedance probability in 50 years (2%/ 50 yrs.) are considered as 0.1 quantile of the lognormal fragility curves. The target annual probability of collapse/failure (i.e., the target annual probability of exceedance of collapse prevention limit state), that is associated with the hazard level expressed as 2%/ Fig. 5 Ratio between PGA for uniform seismic hazard (mean return period of 475 years) and for uniform seismic risk (collapse probability = 2·10−4, β = 0.8 and 0.1 quantile) (left) and ratio between PGA for uniform seismic hazard (mean return period of 475 years) and for uniform seismic risk (collapse probability = 2·10−4, β = 0.8 and 0.001 quantile) (right) J Seismol Fig. 6 Probability of collapse for the PGA corresponding to a mean return period of 475 years, β = 0.6 and 0.001 quantile (left) and probability of collapse for the PGA corresponding to a mean return period of 475 years, β = 0.6 and 0.1 quantile (right) 50 years PGA values, is set to 2·10−4 (as in Luco et al. 2007) and 5·10−4. The reason for targeting 5·10−4annual probability of collapse is to maintain, in the epicentral area of Vrancea intermediate-depth seismic source, design values of PGA equal to the ones corresponding to 2%/50 years (see Fig. 8). The uniform seismic hazard map for a mean return period of 2475 years, corresponding to a probability of exceedance of 2% in 50 years, is displayed in Fig. 8 (left) and that for a uniform risk (for a target annual collapse probability of 5·10−4 associated with PGA values with 2%/50 years) is displayed in Fig. 8 (right). One can notice that the uniform risk based PGA values are lower than the uniform hazard based PGA values, as the influence of Vrancea intermediate-depth seismic source is fading away and the crustal seismic sources control the hazard. In Figs. 9, 10, and 11, the ratios of PGA values with 225, 475, and 2475 years mean return periods to the PGA values targeting either 2·10−4, or 5·10−4 annual probability of collapse are represented for the main cities of the 41 counties of Romania. One has to mention that the PGA values with 225 years mean return period are the ones from the current seismic design code in Romania. Consequently, the values with 225 years mean return period are conventional, since they are assigned based on the zonation map of the code; thus, differences are encountered between the actual values with 225 years mean return period from the hazard curve and the code-based values that are rounded up to the value assigned to the equal hazard lines drawn in the uniform seismic hazard map. The PGA values with 475 and 2475 years mean return periods are extracted from the hazard curves. Looking at the ratios in Figs. 9, 10, Fig. 7 Probability of collapse for the PGA corresponding to a mean return period of 2475 years, β = 0.6 and 0.001 quantile (left) and probability of collapse for the PGA corresponding to a mean return period of 2475 years, β = 0.6 and 0.1 quantile (right) J Seismol Fig. 8 PGA for uniform seismic hazard (mean return period of 2475 years) (left) and for uniform seismic risk (collapse probability = 5·10−4, β = 0.6 and 0.1 quantile) (right) and 11, the patterns of the values are different: higher ratio values on the back-arc sites for mean return periods of PGA of 225 and 2475 years, and higher ratio values on the fore-arc sites for PGA values with 475 years mean return period. The different pattern between the ratios corresponding to 225 and 475 years mean return periods PGA values is attributed mainly to the different ways of obtaining the uniform hazard values (from the seismic hazard map, respectively from the seismic hazard curve). On the other hand, the different pattern between the ratios in Figs. 9 and 10 is due to the very different slopes of the hazard curves (see Fig. 1), showing, for 2475 years mean return period much higher PGA values on the back-arc sites, if compared to the fore-arc sites, provided that the PGA values with 475 years mean return period are quasi-equal. Considering the ratios of Fig. 10 (left), one can notice that targeting a uniform annual risk of 2·10−4 implies the increase of the PGA values with 2475 years, on average, by 30% in the fore-arc regions and by 10% in the backarc regions of Romania. On the other hand, the values in Fig. 10 (right) show almost no increase on the fore-arc sites and an average decrease of 30% on the back-arc sites. Based on the results obtained in this study, it is of paramount importance to establish a general procedure for deriving risk-targeted maps. At this moment, based on the results obtained, there are different opinions in which part of Romania should the peak ground accelerations be increased based on the uniform risk approach. Silva et al. (2016) propose a drastic decrease of seismic hazard levels in the eastern part of the country and an increase in the western part. However, in our opinion, the decrease of seismic hazard in the eastern part of the Fig. 9 Ratio between PGA for uniform seismic hazard (MRP of 225 years) and for uniform seismic risk (Pf = 2·10−4, β = 0.6 and 0.1 quantile) for all 41 counties (left) and ratio between PGA for uniform seismic hazard (MRP of 225 years) and for uniform seismic risk (Pf = 5·10−4, β = 0.6 and 0.1 quantile) for all 41 counties (right) J Seismol Fig. 10 Ratio between PGA for uniform seismic hazard (MRP of 475 years) and for uniform seismic risk (Pf = 2·10−4, β = 0.6 and 0.1 quantile) for all 41 counties (left) and ratio between PGA for uniform seismic hazard (MRP of 475 years) and for uniform seismic risk (Pf = 5·10−4, β = 0.6 and 0.1 quantile) for all 41 counties (right) country cannot be justified since this is the most seismically exposed area of Romania. Another key aspect of this methodology is, in our opinion, the coupling with past or present seismic design maps so as to ensure that a future building will not have a reduced structural safety as compared to a new one (due to proposed reduction of peak ground accelerations obtained through risktargeted approach). Furthermore, one has to take into account the fact that the results obtained by Silva et al. (2016) were derived for rock conditions which can be found only in few areas of Romania. Consequently, from the point of view of structural design and in the absence of site-dependent amplification factors, the results of Silva et al. (2016) are not directly applicable. 4 Conclusions In this study, risk-targeted maps are developed for Romania based on the recent seismic hazard study of Pavel et al. (2016). The approach used implies the evaluation of the mean annual probability of failure by using the convolution product between the seismic hazard and fragility. The same 200 sites whose seismic hazard was evaluated in more detail in the study of Pavel et al. (2016) are also investigated in this study, as well. Both the approach of Luco et al. (2007) and Silva et al. (2016) were considered in the analysis. The study aimed at evaluating the corresponding peak ground accelerations for a given annual collapse probability and to determine the collapse Fig. 11 Ratio between PGA for uniform seismic hazard (MRP of 2475 years) and for uniform seismic risk (Pf = 2·10−4, β = 0.6 and 0.1 quantile) for all 41 counties (left) and ratio between PGA for uniform seismic hazard (MRP of 2475 years) and for uniform seismic risk (Pf = 5·10−4, β = 0.6 and 0.1 quantile) for all 41 counties (right) J Seismol probability for a given peak ground acceleration which corresponds to a specific mean return period of the seismic action. The obtained results have pointed out several main issues raised in the application of the methodology: & & & The influence of the standard deviation parameter β is limited in the sense that it either decreases or increases the values of the corresponding peak ground accelerations or collapse probabilities. The influence of the quantile used for anchoring the fragility function at a specified collapse probability is dominant. By assigning a different value of the quantile, the shape and aspect of the resulting map changes dramatically. It was observed that by changing the quantile values from 0.1 as considered by Luco et al. (2007) to 0.001 as used by Silva et al. (2016), the areas which correspond to the largest collapse probabilities shift from eastern to western Romania. This aspect was also noticed by Silva et al. (2016), although it was not commented. The issue of quantile is confusing since if one interprets the Bp^ quantile value of peak ground acceleration as the value for which the probability of exceeding the life safety limit state is B1-p^, then lower the Bp^ value, more reliable the design seems to be. Nevertheless, as Bp^ is decreasing, the value of associated peak ground acceleration is decreasing as well, reaching the conclusion that you might increase the reliability of the design by decreasing the value of peak ground acceleration. The confusion comes from the different interpretation of the peak ground acceleration. When we search for the probability of failure (direct approach), the peak ground acceleration represents the capacity and the fragility function is the cumulative distribution function of the capacity. Given the fact that peak ground acceleration is the capacity, it is on the safe side to choose a lower Bp^ value to increase the seismic reliability of the structure. On the other hand, when we search for the value of the peak ground acceleration for a target reliability level (indirect approach), the ground motion parameter becomes a demand. In order to be consistent with the direct approach when using the indirect one, the value of peak ground acceleration is associated with low Bp^ values, a very uncommon situation from the structural reliability position. It is the authors’ opinion that the decision of choosing the value of the quantile in indirect approach is rather subjective. Moreover, & & the meaning of the fragility function as a cumulative distribution function of the seismic capacity shall be dropped. The uniform risk-targeted maps are based on the indirect approach. In this situation, there are three knobs to be turned by the analyst: the target probability of failure, the logarithmic standard deviation and the Bp^ values. For the first and second knob, there is a broad consensus in the literature on the values to be used. As for the third knob, the range of Bp^ values used in the literature covers three orders of magnitude. Given this fact, it is the opinion of the authors that the third knob shall be turned until the design values of peak ground acceleration obtained from uniform risk maps equals the values obtained from uniform hazard maps in areas where it is proved that the uncertainties assessed from probabilistic seismic hazard assessment are the lowest. Further on, the results obtained from uniform risk maps are used for fine tuning of the peak ground acceleration values in areas with higher uncertainties associated with probabilistic seismic hazard approach. In the opinion of the authors, the most appropriate and feasible approach for Romania is to use the PGA values with 2% exceedance probability in 50 years as the 10% quantile of the fragility function and to set the target annual probability of failure as 5·10−4 (providing uniform risk PGA values close to PGA values with 2%/50 years, in epicentral area), or 2·10−4 (as for conterminous US, but providing PGA values higher than 2%/50 years PGA). Consequently, based on the abovementioned issues, it is of critical importance to establish a uniform procedure for deriving risk-targeted maps. In addition, the development of risk-targeted maps should be based on seismic hazard results which take into account the actual soil conditions, although in a simplified manner, and not based on uniform soil conditions throughout a country or continent. Moreover, this approach should be coupled also with the previous uniform hazard maps from seismic design codes of a country so that a future building will not have a reduced structural safety as compared to an existing one due to a decrease in the seismic hazard levels obtained through a risk-targeted approach. Acknowledgements The first four authors gratefully acknowledge the financial support of the Romanian National Authority for J Seismol Scientific Research and Innovation, CNCS – UEFISCDI. The first two authors are indebted to John Douglas (University of Strathclyde) for the very fruitful discussions that enabled them to acquire a more comprehensive and in-depth understanding of the uniform seismic risk maps issues and approaches. The authors deeply acknowledge the valuable constructive comments and suggestions from an anonymous reviewer that considerably enhanced the quality of the manuscript. Funding information This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS – UEFISCDI, project number PN-II-RU-TE-2014-40697. References Douglas J, Ulrich T, Negulescu C (2013) Risk-targeted seismic design maps for mainland France. Nat Hazards 65(3):1999– 2013. https://doi.org/10.1007/s11069-012-0460-6 EN 1990:2002 + A1 (2010) Eurocode - Basis of structural design. European Committee for Standardization, Brussels, Belgium EN 1998-1 (2004) Design of structures for earthquake resistance—part 1: general rules, seismic actions and rules for buildings. European Committee for Standardization, Brussels, Belgium Fajfar P, Dolšek M (2012) A practice-oriented estimation of the failure probability of building structures. 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