Influence of local site effects on seismic risk maps and ranking of Italian municipalities

The latest studies concerning seismic risk assessment in Italy were developed without considering the site geo-lithological effects, thus limiting the assessment to rock soil type. In this study, for the evaluation of site amplification effects, we used the results of recent works based on the Italian seismic microzonation data. As this first study is performed for the entire Italian territory at the municipality scale, the site amplification factors (AFs) have been assigned to the chief town of each of the 7715 Italian municipalities, assuming that the building stock is concentrated in that small area. The AFs have been compared with those foreseen by the Italian building code (NTC2018). The PGA amplification with the new AFs ranges from 1 to 2.2 bringing to an average increase of 75% in the hazard, compared to 27% if using the NTC2018 amplification. The seismic risk has been evaluated using the probabilistic hazard assessment adopted in the NTC2018 and recent vulnerability/exposure models developed for Italy. The residential building stock was subdivided into 5 vulnerability classes (3 for masonry and 2 for concrete) derived from the national census data and further refined using the construction age and building height. The results show that, for a rock site condition, the loss estimates are comparable with those of previous works in terms of casualties, homeless, and economic damage. The introduction of the site effects brings to a significant increase in the expected losses resulting higher than the historical data retrieved from a careful analysis of the major Italian earthquakes. This suggests the importance of developing new fragility curves based on updated AFs. To support the implementation of risk reduction programs, a seismic risk index is introduced, allowing a municipality ranking by risk, a cost estimation of the seismic retrofitting in the highest risk municipalities, and an assessment of the consequent risk reduction.


Introduction
Italy is one of the countries with the highest seismic risk in Europe, due to the frequency of earthquakes that have historically affected its territory and to the intensity reached by some of them, causing extensive social and economic losses, mainly due to the high population density and to the considerable fragility of the building stock (Valensise et al. 2017). It follows that the major issue in Italy does not concern the design of new buildings, but rather the high vulnerability of existing ones which may be reduced with appropriate and well-known techniques such as strengthening, retrofitting, and base isolation.
The Italian annual expenditure for the recovery from past seismic events, an average of €3 billion (Camera dei Deputati 2009; Senato della Repubblica 2017), is much larger than that employed for the prevention of losses for future ones. Considering the very large amount of funds required to strengthen/retrofit the whole Italian building stock, it is essential to establish a priority scale of intervention through a well-grounded and reliable seismic risk assessment providing the extent of damage to people and buildings expected for future earthquakes. These are also key factors for insurance and reinsurance companies (Goda et al. 2014).
The first seismic risk maps developed in Italy at national scale date back to 1996 (GNDT-ING-SSN 1996). These maps represented the first attempt to express the seismic risk as a combination of hazard, vulnerability and exposure, even if they had not been included in peer-reviewed journal articles. The exposure model represented the main novelty of that study, and it was based on population and buildings data collected in the 1991 census by ISTAT (Italian National Institute of Statistics). The latest census datasets (ISTAT 2001(ISTAT , 2011 do not differ significantly from the study of 1991 and are still used in recent risk assessments for their homogeneity and completeness over the national territory. Crowley et al. (2009) provided a complete report of the studies on Italian seismic risk maps up to 2009. The report compares several works, such as the risk maps of the Italian Seismic Service (Lucantoni et al. 2001) making use of seismic hazard assessments (Albarello et al. 2000), damage probability matrices and fragility curves (Sabetta et al. 1998;Di Pasquale et al. 2005), the SAVE project (Zuccaro 2004), the risk assessment performed with new analytical vulnerability models (Borzi et al. 2008). More recently, several other studies were published, such as those of Rota et al. (2011), Asprone et al. (2013), Zanini et al. (2019), and the study realized by the Global Earthquake Model (GEM) foundation (GEM 2019; Silva et al. 2020).
The latest comprehensive study concerning Seismic risk studies of Italian residential buildings is provided by Dolce et al. (2020). Six research units, coordinated by the Italian Department of Civil Protection, updated the risk maps of the Italian residential building stock providing six different vulnerability/exposure models (four for masonry buildings and two for RC buildings). The paper describes in detail the adopted methodology and presents the main results in terms of expected damage and impact measures (unusable buildings, homeless, casualties, direct economic losses). As acknowledged by the authors themselves, the study still presents some drawbacks that could underestimate the predicted losses, in particular regarding the consideration of the uncertainties and the reference to a soil of type A only (outcropping rock characterized by flat topography).
The aim of this study is to evaluate the effects on the Italian seismic risk maps of the inclusion of site geo-lithological amplification in the hazard assessment (Falcone et al. 2021;Mendicelli et al. 2022) comparing the results with the work by Dolce et al. (2020) taken as benchmark. Furthermore, an updated analysis of real data from historical earthquakes is presented in terms of casualties, homeless and economic losses. Finally, a seismic risk index is introduced, resulting nearly independent from the site amplification. It allows a ranking by risk of the Italian municipalities, a cost estimation of the seismic retrofitting of the most vulnerable buildings, and an evaluation of the consequent risk reduction.

Methodology
Seismic risk can be defined as a measure of the damage expected at a given region of interest in a certain time interval and it can be represented by the convolution of hazard, vulnerability and exposure (Fig. 1). Seismic hazard expresses the probability of occurrence of a given earthquake or ground motion and it can be obtained by applying the Probabilistic Seismic Hazard Assessment (PSHA, Cornell 1968) which provides seismic hazard curves giving λ IM (frequency of exceedance) as a function of im, (intensity measure of the seismic events, in our case PGA). An example of hazard curves is illustrated in the left plot of Fig. 1 for the Italian municipalities of Firenze, L'Aquila and Napoli. The seismic vulnerability (in our case limited to residential buildings) represents the potential of a structure to undergo a given level of damage and it is generally described through fragility curves, expressing the probability of reaching different levels of damage given the PGA (central plot in Fig. 1). The exposure refers to all the assets which are subjected to the seismic risk in a particular area. In case of the building stock, a building inventory is required providing the number of buildings, dwellings, residents and the percentage distribution in the different vulnerability classes (right plot in Fig. 1).
The mean annual rate λ k of reaching or exceeding a damage state D k may be expressed as: where P(D k |im) is provided by the fragility curve. It expresses the probability of getting a damage state ≥ D k as a consequence of a seismic event with seismic intensity im for buildings of a particular class of vulnerability. λ IM is the mean annual exceedance frequency of the intensity im.
The calculation should be repeated for each vulnerability class of the building inventory and the results should be combined considering the proportion of each class in the considered asset and summed over the different classes to get the mean annual rate of reaching or exceeding a given damage state in a given site or municipality. The λ k can be used to compute the probability p k to reach or exceed the damage state D k in a time interval of t years under the hypothesis that the occurrence of events is a Poisson process: Equation (3) provides the unconditional seismic risk in a time interval t (expressed in years) for a damage state D k . For small values of λ k , as is usually the case, and t = 1 year, p k ≈ λ k . The mean annual probability of reaching or exceeding the different damage states for all the buildings classes can be used to provide an estimate of the consequences of an earthquake in terms of economic, human, and social losses.
In our study, as hazard curves referred to outcropping rock, we used the probabilistic assessment MPS04 (Stucchi et al. 2004) that is the current reference for seismic hazard studies in Italy and is adopted by the Italian building code (NTC2018). For vulnerability we adopted the fragility curves implemented by Rosti et al. (2020a, b). For exposure we used the building and population census dataset (ISTAT 2011) giving information on construction age, building material, and number of storeys of the buildings.

Hazard and site effects
A substantial improvement in the evaluation of the geo-lithological site amplification effects in Italy has been given by the recent works by Mori et al. (2020) and Falcone et al. (2021). The first work, following the methodology suggested by Iwahashi et al. (2018) for a site classification using digital elevation models (DEM), has derived a V S30 map for Italy starting from the geomorphological classes and integrating a large amount of data from the Italian seismic microzonation dataset (DPC 2018, www. webms. it), consisting of 16,000 profiles of shear wave velocity from geophysical surveys and 44,000 logs from continuous coring boreholes. Mori and co-authors found a proxy dependence of V S30 on slope gradient and elevation through a regression model for each geomorphological class. The estimation of V S30 for the Italian territory provided by their study is particularly accurate and provides a good correlation between V S30 , morphological classes and subsoil lithologies.
In Fig. 2 the new V S30 map from the study of Mori and co-workers is compared with that of Michelini et al. (2008), used so far for the implementation of the shakemaps which have been widely used by the Italian engineering community for the evaluation of fragility curves in building vulnerability assessment. It is worth noting that Sardinia is not included in the present work because of its negligible value of seismic hazard (Stucchi et al. 2004). The methodology of Michelini and co-workers is based on soil classification derived from the 1:100,000 geological map of Italy (Amanti et al. 2008) and from the topographic slope (Wald and Allen 2007). The differences between the two maps are substantial. In particular, in the map of Michelini et al. most of the territory is classified as having a V S30 greater or equal to 800 m/s whereas in the new map less than 3% of the territory has a V S30 greater than 760 m/s and about 50% is in the range 360-480 m/s. In the study by Mori et al. (2020) most sites previously considered as rock consists actually of fractured rocks with V S30 < 800 m/s. The works by Falcone et al. (2021) and Mendicelli et al. (2022) introduced new geolithological amplification factors. They are based on the equivalent visco-elastic method allowing to perform 30 million one-dimensional local site response coming from 2 million soil columns (varying V S profile, depth to the seismic bedrock and nonlinear behavior of soils) times 15 input motions. Such input motions were determined in terms of response spectra, with return period of 475 years, selected according to the Italian seismic hazard (Stucchi et al. 2004) and applied to 42 geomorphological clusters resulting in a set of 630 response spectra. The V S profiles were stochastically obtained from the microzonation studies (DPC 2018) with the procedure described in Romagnoli et al. (2022). The Amplification Factors (AFs) obtained with that procedure allow to account for the nonlinear response of soils, the V S profile, the depth to seismic bedrock and the sitespecific seismic hazard.  Figure 3a shows the distribution of the AFs of the PGA, for a 475 years return period (Tr), assigned to the chief town of each of the 7715 Italian municipalities excluding Sardinia (ISTAT 2011). The PGA value at the municipality is derived, as for the Italian building code (NTC2018), with an interpolation of the four grid points of the MPS04 map (Stucchi et al. 2004) closest to the coordinates of the chief town. The assumption of a single AF for the entire municipality represents a rough approximation, and it will be applied also to the exposure and risk. This is unavoidable at the scale adopted in this study and justified by the fact that the building stock data are concentrated in the relatively small area of the chief town. For the sake of simplicity, in these maps we refer only to Tr = 475 years. Different return periods have been considered when using the hazard curves for the risk assessment, as shown in Fig. 6b. Only 16 municipalities (i.e. 0.19% of the total) have an AF slightly lower than 1. The PGA amplification factor ranges from 1 to 2.2, with the highest values in Northwestern Italy and the lowest in the eastern parts of the Po Plain and Puglia region. The low AFs in the Po plain, where the V S is very low (Fig. 2), are due to the high thickness of the deposits that, according to the simplified rule f 0 = V S /(4·H), amplify lower frequencies with respect to those associated to PGA. Figure 3b shows the AFs calculated with the formula foreseen by the NTC2018 and the V S30 values provided by Mori et al. (2020), as illustrated in Table 1. The difference with Fig. 3a is substantial because 76% of the municipalities fall in the soil class B (360 ≤ V S30 ≤ 800 m/s) and the upper limit of amplification imposed by NTC2018 for that class is 1.2. In the AF range 1.6-1.7 there are no municipalities because belonging to soil class C where the upper limit of NTC2018 is 1.5. It follows that the AF averaged over all the municipalities of the NTC2018 is 1.27, compared to 1.75 of this study adopting the AFs proposed by Mendicelli et al. (2022). The low AF values for the soil class D (1.34 in the last column of Table 1) are justified by the trend of the AF-V S30 curve shown in Fig. 4a. In this study the AFs have been calculated for each of the 9 earthquake return periods (Tr) given in Stucchi et al. (2011) and in the NTC2018. Figure 4 shows the plots of AF versus V S30 from different sources. In Fig. 4a, the PGA-AFs of the Italian municipalities resulting from the study by Mendicelli et al. (2022) are plotted for the hazard levels corresponding to three return periods. The plots show a linear increase up to about 300-400 m/s, while they become scattered and decreasing at lower V S30 values due to the nonlinear soil behavior. This effect is more pronounced for a Tr of 2475 years due to its greater PGA as shown by the interpolating functions. Figure 4b shows the AF versus V S30 trend provided by the NTC2018 in case of two cities, Milano and L'Aquila, characterized by low and high seismic hazard, respectively. The four soil classes considered by the code have been assigned to the following V S30 reference values: (A) 900 m/s; (B) 600 m/s; (C) 300 m/s; (D) 150 m/s. In addition, Fig. 4b also reports the AFs proposed by Michelini et al. (2008), used for the implementation of the shakemaps and fragility curves. It is evident that, in particular for high accelerations, the AFs used in the shakemaps (Michelini et al. 2008) are significantly lower than those adopted in this study. This brings to a large increase of the damage Table 1 Breakdown of the Italian municipalities in the different soil classes foreseen by the Italian building code (NTC2018) The amplification factors calculated with the NTC2018 formula are compared, in the last two columns, to those adopted in this study (Mendicelli et al. 2022 Mendicelli et al. (2022) with different return periods; solid lines are the interpolation with a fourth order polynomial; b AF of PGA versus the four soil classes (A, B, C, D) foreseen by the Italian building code at 475 years return period, for three Italian cities (number in parenthesis refer to PGA with 10% exceedance probability in 50 years); the AFs used in the Italian shakemaps (Michelini et al. 2008) are reported (triangles) for low and high acceleration input; the AFs of the GMPE by Bindi et al. (2014) are shown with orange square markers probability in the fragility curves as described in the following sections. It is worth noting that, in the cited papers by Falcone and Mendicelli, the AFs deriving from the GMPE by Bindi et al. (2014), have been compared with those resulting from site-specific 1D simulations for a testing dataset of about 4500 Italian locations. The AFs used in that studies proved to be consistent with the dataset, while the GMPE has limited information about the geophysical characteristics of the strong motion stations and does not consider the nonlinear soil response and the effective depth to the seismic bedrock. Figure 4b shows that the AFs foreseen by the GMPE of Bindi et al. (2014) are lower than those of the NTC2018 code and of this study. Figure 5 shows the effects of the introduction of the site amplification in the hazard map MPS04 (Stucchi et al. 2004), with PGA values assigned to the chief town of each of 7715 municipalities (Sabetta 2021). The maximum PGA increases from 0.28 g (municipality of Ferla in Eastern Sicily) to 0.47 g (municipality of Scigliano in Calabria). The average increase due to the geo-lithological amplification over the national territory is 75%.
The estimation of the risk requires to use the hazard curves with the relative epistemic uncertainty (Meletti and Montaldo 2007) as shown in Fig. 6a for the cities of Biella and L'Aquila. The nine points for which the curves are plotted have been interpolated, at a step of 0.001 g, with a best fit function as shown by the correlation index R 2 reported in Fig. 6a. To avoid unrealistic high values of the losses due to very low levels of ground shaking associated with high probability of exceedance and non-zero damage probability (Dolce et al. 2020), the hazard curves were truncated at values lower than 0.03 g (red line in Fig. 6a). Considering the limited proportion of municipalities with PGA < 0.03 g at the lower value of the hazard curves (38% without site amplification and 8% when amplification is considered), the decrease in losses due to the truncation was less than 10%. The uncertainty in the median hazard, represented by the ± σ dashed lines, is in the order of 10-15% for high hazard municipalities and 20-25% for low hazard ones. It results rather  Mendicelli et al. (2022) low, e.g. compared to the European map ESHM20 (Danciu et al. 2021), probably due to the only sixteen branches logic tree used in the implementation of the MPS04 map (Stucchi et al. 2004). To include the site effects, the hazard values for rock have been multiplied by the AF varying with Tr, as shown in Fig. 6b for some representative cities. Even if more advanced approaches could be used for including nonlinear soil-site effects in probabilistic seismic-hazard (Bazzurro and Cornell 2004) in this study, for the sake of conciseness, we have not considered the uncertainty related to the geo-lithological site amplification, hence, only the 50th percentile of the AFs distribution was retrieved from the study of Mendicelli et al. (2022).

Exposure: building inventory and vulnerability classes
According to the 15th ISTAT Census of population and housing (ISTAT 2011), in 2011 there were 12,187,698 residential buildings for a total of 31,208,161 dwellings. With respect to the age of the housing stock, it emerges that 53.7% of dwellings have been built before 1970, a further 31% was built in 1971-1990 and 7.4% in the period 1991-2000. The remaining 7.9% of the housing stock was built between 2001 and 2011. The homes occupied by resident people are 24.1 million (23.4 million without Sardinia), equal to 77.3% of the total, while seven million are unoccupied (holiday homes, homes occupied by non-residents, empty homes). For evaluating the exposure, we considered the census data concerning the construction age, number of storeys, and building material (masonry M, reinforced concrete RC, other O). As the adopted fragility curves (Rosti et al. 2020a, b) are relative only to M and RC, it was necessary to subdivide the category that ISTAT indicates as O, i.e., all the buildings with a mixed load-bearing structure and a small percentage of steel and timber buildings, between the M and RC classes. To do this, it has been used the criterion suggested by Dolce et al. (2020) based on the percentage of O in each town, the period of construction and the number of floors. Using the classification criteria reported by Rosti et al. (2020a, b), the residential buildings have been divided into twelve vulnerability classes, three for masonry (A, B, C1) further subdivided in two height classes, and two Fig. 6 a Hazard curves for the cities of Biella and L'Aquila with the relative uncertainty (±σ, dotted lines); the analytical functions adopted to interpolate the data are reported in the plot with their corresponding correlation index R 2 ; b AF as a function of the earthquake return period for some cities for reinforced concrete (C2, D) further subdivided in three height classes. Regarding the masonry, the breakdown into classes is based on the building age and number of floors, as illustrated in Table 2, where L and MH are the classes of height considered (1-2 floors and 3 or more floors respectively).
The RC, according to Rosti et al. (2020b), has been divided in two classes assuming the year 1981 as a turning point in the application of the Italian seismic legislation. The vulnerability class C2 includes buildings designed essentially for gravitational loads (≤ 1981) while the vulnerability class D includes buildings with seismic design (> 1981) as illustrated in Table 3.
Each vulnerability class has been further refined based on the height of the building (L = 1-2 floors, M = 3 floors, H = 4 or more floors). Classes A, B, C1 correspond to masonry of poor, average, and good quality, respectively. Classes C2, D correspond to RC building without and with seismic design, respectively. For the risk assessment, given that the population exposure is relevant, the same class breakdown has been applied to the dwellings belonging to each building, because the ISTAT census database distinguishes between inhabited and non-inhabited buildings in terms of dwellings. Since the number of dwellings in a building is highly variable, with typically more dwellings in a RC building with respect to a M building, the classification in terms of dwellings is more appropriate to provide a clearer picture of the actual vulnerability distribution and it has been used in the loss assessment. Figure 7 shows the distribution of the residential dwellings in the vulnerability classes regardless of the building height. The masonry dwellings represent 46% of the total and the largest vulnerability class (32%) is C2 (RC built before 1981). Figure 8 shows the percentage distribution of the dwellings belonging to the highest and lowest vulnerability classes regardless of the building height, respectively class A (masonry built mostly before 1945) and class D (RC built after 1981).
The most vulnerable masonry houses are concentrated in North-Western and Central Italy (Fig. 8a). In Fig. 8b, it can be observed (large number of seismically designed buildings -class D) the effect of the reconstruction after the Irpinia 1980 earthquake (south-east of Naples) and the Belice 1968 earthquake (south of Palermo) which after 1981 was still in progress. The census data refer to 2011, so the beneficial effects given by the reconstruction after the 2009 L'Aquila earthquake are limited.

Fragility curves
Fragility curves represent a fundamental tool for estimating the possible damage resulting from seismic events. With reference to a certain type of building, they express the probability of reaching or exceeding the different Damage States (DS) as a function of the intensity of the earthquake shaking. In the last years, many authors have proposed fragility curves for Italy, both for reinforced concrete and masonry buildings. An exhaustive review of all the studies on fragility curves is beyond the scope of this work. The work by da  provides an overview of the fragility models used by the Italian Department of Civil Protection (IDPC) in the updated version of the National Risk Assessment (IDPC 2018). The seismic risk evaluation was carried out with the IRMA platform (Borzi et al. 2021), implementing six different vulnerability models. Among the four models for masonry buildings, three used empirical or semi-empirical methods , Rosti et al. 2020a, Zuccaro et al. 2021) and one adopted a mechanical approach . Two models were used for RC buildings, one empirical (Rosti et al. 2020b) and one mechanical . Other recent models are those by Del Gaudio et al. (2020), based on a dataset taken from the platform Da.D.O., and the works by Zucconi et al. (2022a, b). It is worth noting that most of the fragility models adopted in Italy use the PGA taken from the shakemaps by Michelini et al. (2008) as input ground motion.
In this study we adopted the fragility curves proposed by Rosti et al. (2020a, b). These two studies implement an empirical model of fragility obtained by statistically processing the damage data of Irpinia 1980 and L'Aquila 2009 earthquakes which were selected for the availability of complete post-earthquake field surveys (Dolce et al. 2019) including  undamaged buildings, and for the lack of significant aftershocks avoiding the problem of the cumulated damage. Furthermore, the cited works adopt empirical models that are more suitable for masonry buildings representing almost half of the building stock in Italy. The curves are described by a cumulative lognormal distribution and DS are taken from the five damage states (from DS1 slight or negligible damage to DS5 collapse) of the European Macroseismic Scale (EMS-98, Grünthal 1998). The comparison of the site AFs used in this work (Fig. 4a) with those of Michelini 2008 (Fig. 4b) reveals that the latter provide significantly lower values, thus leading to a significant increase of the damage probability as it will be shown later. Figure 9 compares the fragility curves for some DS and vulnerability classes previously described. It is worth noting that in some cases the curves intersect, e.g., the curves C2-H (concrete without seismic design, 4 or more floors) at high PGAs and for damage states 3 and 5, exceed the values of poor-quality masonry A-MH.

Seismic risk and damage states
The risk calculation has been performed for each of the 7715 Italian municipalities according to Eqs. (2) and (3) and considering the dwellings distribution in the different vulnerability classes described in Sect. 4. Table 4 shows the resulting estimates in terms of the number of dwellings (thousands) affected by each damage state in a time frame of 1 and 50 years. The results, if the site amplification is not considered, are comparable with those provided in the study of Dolce et al. (2020) which considered only rock sites. Figure 10 shows the unconditional risk in a period of one year corresponding to the average expected probability of damage states DS1 and DS5 including the site amplification with the AFs of Mendicelli et al. (2022). The risk of collapse (DS5) has obviously lower values with

Impact indicators
The definition of specific impact indicators based on seismic risk assessment can be convenient in the field of civil protection, with possible application to response and mitigation strategies, as well as for emergency planning. In this study, we estimated the number of dwellings resulting unusable based on existing risk studies for Italy (Lucantoni et al. 2001;Bramerini and Di Pasquale 2008;Zuccaro and Cacace 2011;Dolce et al. 2020). In particular, for the unusable dwellings, we adopted the formulation given by Dolce et al. (2020) for the long-term unavailability which gives values that are closer to field surveys data. The number of homeless was derived from the resident people in the unusable dwellings also considering the people not counted as victims (99% DS4, 90% DS5). The probability of injury or death of the building occupants has been calculated as a function of dwelling damage states DS4 and DS5, as proposed by Lucantoni et al. (2001) and subsequently developed by Zuccaro and Cacace (2011) and Dolce et al. (2020).
The following impact indicators have been defined for each Italian municipality considering the number of dwellings and resident people belonging to each damage state, indicated by Dw_DSi and Res_DSi, respectively, for the ith damage state:   Figure 11 shows the percentage of dwellings of each municipality expected to become unusable in a period of 1 year. If the site amplification is not included, the maximum values are 0.4-0.7%; when site effects are considered, the percentage of unusable dwellings reaches values higher than 1% per year in some municipalities of Central Italy. Table 5 reports the expected losses over the national territory in a time frame of 1 year obtained averaging (probability of damage state) or summing (losses) the values relative to the single municipalities.
If the site amplification is not included, the estimated losses are comparable with those given by Dolce et al. (2020) except for the number of homeless people, particularly high in that work because they were calculated considering the inhabitants of the unusable dwellings expected both in the long term (0.6•DS3 + DS4) and short term (0.4•DS2 + 0.4•DS3). In Table 5 are reported the loss estimations obtained both with the AFs of Mendicelli et al. (2022) and with those of the NTC2018. As expected, considering the average AF of 1.75 for Mendicelli and 1.27 for NTC2018 discussed in Sect. 3, the losses estimated with the latter are closer to those of rock site condition. As shown in Fig. 3 and Table 1, the AFs of the NTC2018 group most of the municipalities in few classes not catching adequately the spatial variability of the site amplification. Furthermore, as discussed in Sect. 3, the AFs used in this study proved to be consistent with the site-specific data. Therefore, in the following we will refer only to the AFs of Mendicelli et al. (2022), using the term "soil". It is worth noting that, due to the shape of the fragility curves, the increase in damage estimation, going from 116% for DS1 to 307% for DS5 if the site amplification of Mendicelli et al. is included, is larger than the average increase in PGA (75%). When the site effects are incorporated, the loss estimates increase significantly both with respect to previous studies (Zanini et al. 2019;Dolce et al. 2020) and in comparison with the historical data (see following section). As discussed previously, this is mainly due to the fragility curves built using low PGA values taken from shakemaps which adopt a simplified approach for the site amplification. This underlines the need of a re-evaluation of fragility curves with the new site amplification factors provided by Mendicelli et al. (2022) and also adopting, besides PGA, response spectral values as intensity measure.

Comparison with historical earthquakes
A crucial element for the assessment of the reliability of the loss estimates is the comparison with the real values surveyed in Italian earthquakes. Table 6 shows information about medium-strong earthquakes of the last 54 years, which is the only period for which reliable data about homeless and economic damage are available. The last column of the table reports the total cost in Million €, discounted to 2014, incurred by the Italian government for the emergency management and the reconstruction of structures, infrastructures and cultural heritage.
Cost data up to 2002 are taken from a report of the Italian House of Representatives (Camera dei Deputati 2009). Data in italic are estimated from a linear regression with the number of homeless for the 8 earthquakes for which the cost is available. Data relative to the last three earthquakes, since 2009, come from a report of the Italian Senate (Senato  della Repubblica 2017). A more in-depth analysis of these data (not final because the reconstructions are still in progress) reveals that 85% of the resources were destined to the reconstruction of damaged or collapsed buildings, 8% to productive activities, 4% to public administrations and 3% to emergency management. The count of the victims, which should be more reliably reported in the historical chronicles with respect to homeless and economical losses, is highly variable depending on the period considered. The number of victims per year, which is 92 for the last 54 years, increases up to 994 if counting since the beginning of XX century because in that case are included Messina 1908 and Avezzano 1915 earthquakes summing up 113,000 victims, about 94% of the total. Table 7 shows the victims of destructive earthquakes (intensity ≥ X degree of MCS scale) considering the entire catalogue (Guidoboni et al. 2019) since 1169. It is interesting to note that, as shown in Fig. 12a, these destructive earthquakes are concentrated essentially in Southern Italy. Considering that the Italian seismicity does not seem to have had large modifications in the last 1000 years, as illustrated in Fig. 12b, the variation is mostly due to the social, demographic, and building characteristics of the historical period considered and to the site where the earthquake happened (country or city). The most reliable value is probably that reported in Table 7, averaging the short period variation, and giving 407 victims/year. Table 6 Victims, homeless and economic cost relative to 16 earthquakes of the last 54 years with an intensity ≥ VII degree of MCS scale Source: *catalog CFTI5Med Guidoboni et al. (2019); **Web; ***specific study; ****Italian civil protection. The last column reports the total cost, in Million € discounted to 2014, incurred by the Italian government for the reconstruction and the emergency management. Data in italic are estimated from a linear regression with the number of homeless 1 3

Economic losses
The total direct economic losses may be computed based on loss parameters related to damage repair and to the building surface reported in the inventory data. The cost parameters are calibrated as the percentage cost of repair or replacement for each structural damage state and equal to 0.02, 0.1, 0.3, 0.6, 1, for DS1, DS2, DS3, DS4, and DS5, respectively, with a unit cost of € 1350/m 2 including technical expenses and VAT (Di Ludovico et al. 2017;Dolce et al. 2020). If the site amplification is not considered, the estimated cost/year for repair/reconstruction of damaged buildings, is € 2.43 billion, similar to that provided in the work of Dolce and co-workers summing up to € 2.13 billion/year. If site effects are considered the cost increases up to € 7.3 billion/year, resulting higher but to a lesser extent compared to victims and homeless. Figure 13 shows the mean annual expected economic losses (Million €) over the national territory with and without considering the site amplification effect. Being absolute and not percentage values as in the previous maps, the effect of the population exposure becomes prevalent and the higher values correspond to the largest cities as Naples, Rome, Palermo, Catania, Messina. To this end, Table 8 shows, for three Italian cities, the effect of the exposure in terms of inhabitants and dwellings on the absolute values of economic losses and victims compared with hazard (probability of exceeding a PGA of 0.2 g) and risk (risk index as defined in Sect. 10). Rome and Naples, even if affected by a rather low hazard, have the highest values of economic losses and victims, both with and without site amplification, because of their large exposure values. Campobasso, a smallsized city (around 50,000 inhabitants) northeast of Naples, has a definitely higher hazard and risk (columns 2 and 5 in Table 8) but a much lower number of victims and damages expected per year. Table 9 presents a comparison between the estimated losses obtained in this study with those derived from historical surveyed data shown in Tables 6 and 7. The loss estimates have been calculated also considering the epistemic uncertainties in the hazard curves: 50°, 16° and 84° percentiles Meletti and Montaldo 2007). The values including site amplification are higher due to the reasons discussed previously, whereas  (Rovida et al. 2011). The red line is a moving average calculated every 20 points those without amplification are comparable, as order of magnitude, with the historical data. In fact, considering the large uncertainties in the data used for risk assessments and even in the historical ones, the real goal of any risk evaluation is the estimate of the order of magnitude of the expected losses (in our case hundreds of victims, tens thousands of homeless and some billion € per year). The loss estimates referring to rock site condition are also in line with those of previous studies, both in terms of absolute values and territorial distribution (Lucantoni et al. 2001;Rota et al. 2011;Zanini et al. 2019;Dolce et al. 2020).

Risk index for prevention planning
Although the absolute values of losses are affected by considerable uncertainties, the relative ranking of different sites and municipalities is still valid and it is particularly important to have a clear perception of the seismic risk at the national scale and to rationally implement risk reduction programs (Zanini et al. 2019). To this end, in this study we introduce a risk index calculated, for each municipality, by weighting by 2/3 the so-called life-risk (i.e., the annual percentage of homes suffering collapse) and by 1/3 the damage-risk (i.e. the annual percentage of homes suffering damage): where PD is given, for each municipality, by the sum of the annual probability of damage states DS2 and DS3 and PD max is the maximum value among the 7715 municipalities considered. PC and PC max have been calculated in the same way considering the probability of damage states DS4 and DS5. In this way the risk index is normalized to 1. Figure 14 displays the ranking of the Italian municipalities sorted by the seismic risk index, highlighting with different colors the first 100, 200 and 1000 municipalities that are concentrated in Northeastern Alps, in Central Italy, in Calabria and in Eastern Sicily. It is worth noting that the spatial distribution of the highest risk municipalities does not depend much on the introduction of site amplification effects. Table 10 shows the first ten municipalities sorted by seismic risk index and compared with the corresponding ranking in terms of vulnerability and hazard. They are small villages with a population lower than 1000 inhabitants, as the majority of the first 100 municipalities except for Reggio di Calabria, Cosenza, Sulmona, and Campobasso (Table 11). Densely populated cities such as Bologna, Napoli, Messina, Catania are instead included in the first thousand municipalities sorted by risk index. The effect of the site amplification is not relevant for the risk ranking (columns 4 and 5) as the maximum difference is for the city of Caporciano, found in the seventh position in case of rock site conditions and in the 23rd position in case of soil. The influence of vulnerability (represented in column 6 by the ranking in terms of percentage of dwellings belonging to class A) is higher than that of hazard (column 7, ranking in terms of PGA). Seven out of the ten highest 1 3 risk municipalities are in L'Aquila province, remembering that the 2011 ISTAT census did not consider the reconstruction after the 2009 L'Aquila earthquake that is still in progress. Table 11 shows the largest cities, in terms of population, among the first 200 municipalities with the highest seismic risk index.
In Table 12 are illustrated the costs of a hypothetical seismic retrofitting applied to the first 100, 200 and 1000 municipalities sorted by risk index. The costs have been estimated considering an amount of 600 €/m 2 applied only to buildings of the three highest vulnerability classes, namely A and B for masonry and C2 for reinforced concrete, representing about 70% of the total dwelling surface. As a result, about 4 billion € would be necessary to seismically retrofit the first 100 Italian municipalities at risk, € 20 billion for the first 200, and about 140 billion € for the first 1000 municipalities. It is interesting to calculate the risk reduction that can be obtained adopting this kind of intervention. For example, if the retrofit cost of 20 billion € (corresponding to about 7 years of the global expenditure normally granted by the Government for the reconstruction) was applied to upgrade the 479,614 dwellings of the first 200 municipalities at risk by one vulnerability class (A to B, B to C1, etc.) the achieved risk reduction, in terms of expected values of homeless, victims and economic loss, would be of about 57%.

Conclusions
In this study we propose a novel approach to assess the Italian seismic risk considering the geo-lithological site amplification effect derived from numerical simulations based on seismic microzonation data. The amplification factors were assigned to the chief town of each of the 7715 Italian municipalities, assuming the building stock concentrated in that small area. The PGA amplification ranges from 1 to 2.2, with an average value of 1.75, with site effects retrieved from the recent papers by Falcone et al. (2021) and Mendicelli et al. (2022). If the site amplification foreseen by the Italian building code is considered, adopting the V S30 values from Mori et al. (2020), the increase in PGA is between 1 and 1.8, with average value of 1.27. To validate the achieved results, a careful analysis of the historical data relative to the major Italian earthquakes in terms of casualties, homeless, and economic damage has been performed. If a rock site condition is considered for the entire territory, the loss estimates are comparable with those of previous works and with the historical data, both in terms of absolute values and in territorial distribution. The introduction of the site amplification effects yields a significant increase in the expected losses mainly because the adopted fragility curves use low PGA values taken from shakemaps using a simplified approach to consider the site amplification. A seismic risk index has been defined allowing a ranking of the Italian municipalities useful for the implementation of prevention strategies and for the risk communication to different stakeholders both in the private and public sector, such as governments, association of citizens, insurance and reinsurance companies. The first thousand municipalities at risk, regardless of the introduction of the site amplification, are mainly concentrated in Central and Southern Italy and in Northeastern Alps, roughly reflecting the hazard distribution, with significant differences because of buildings' vulnerability and exposure. Even if the absolute loss values may only be considered in terms of order of magnitude, due to the large uncertainties in hazard vulnerability and exposure, the relative ranking of different sites and municipalities is essential to implement seismic risk reduction programs, comparing resulting benefits with costs of seismic retrofitting schemes. It has been verified that, if the retrofitting cost corresponding to about 7 years of the global expenditure normally granted by the Government for the reconstruction was applied to move the dwellings of the first 200 municipalities at risk by one vulnerability class, the achieved risk reduction would be of about 57%. This study represents a first step in considering the new achievements in terms of site amplification effects for the improvement of the seismic risk assessment in Italy. Future works need to: (a) update the hazard, e.g. considering the results of the European map ESHM20 (Danciu et al. 2021); (b) revise the fragility curves introducing the new site effects and adopting, besides PGA, response spectral values as intensity measure; (c) include the aleatory uncertainty of the amplification effects and fragility curves; (d) consider the asset location and the uncertainty in the exposure model; (e) develop a complete logic tree taking into account all the epistemic uncertainties,