1 Introduction

The region of Sofia, the main Bulgarian city, is among the areas exposed to the highest earthquake danger in the country. Although the historical earthquake record reports data on several strong damaging earthquakes that have occurred in this region, there are no instrumental records of seismic strong ground motion available for this region.

The city of Sofia extends over 1,315 km2 with an urbanized territory of 242 km2 and a population of about 1,397,000 (~2 million during the day). It is the major political, economic, scientific, culture, and transport centre of the country. Sofia is an industrial centre (800 large enterprises) yielding 50% of overall national industrial production, and a great number of industrial facilities of national importance form the infrastructure of the city. The high concentration of population and various activities of national importance, the variety of elements exposed to risk, and the high seismicity of the region make the problems of earthquake risk evaluation and mitigation of great importance. It is obvious that a strong earthquake could strike the city, and that the damage caused and co-seismic effects could result in a national disaster.

In the context of the state of the art, the major objectives of this paper are to contribute to seismic hazard assessment for Sofia, provide further validation of the neo-deterministic seismic hazard assessment, NDSHA, for the city of Sofia, and to illustrate the direct application of the outcome of NDSHA procedure to earthquake engineering purposes.

2 The Earthquake Record

The available information about ancient events is incomplete and uncertain and only approximate estimation of their location is possible. Published historical documents prove the occurrence of destructive earthquakes during the fifteenth to eighteenth centuries in the Sofia region (Watzov, 1902) and the largest earthquakes are those which occurred in 1818 with epicentral intensity I o = VIII–IX MSK-64, in 1858 with I o = IX–X (near Sofia), and in 1905 with M ~6.5 (near the town of Trun in the western marginal part of the Sofia region). The epicentral macroseismic intensity, I o ~ X, summarising the heavy destruction in the town of Sofia in 1858, was first evaluated on the MSK64 scale (Petkov and Christoskov, 1965a, b) and updated later on the EMS98 scale (Paskaleva et al., 2007). Here and in the following text, when non-integer values for the epicentral intensity are reported in the literature we use the symbol ~ followed by an integer. In fact, any macroseismic intensity scale by its nature is a discrete scale of integer values. To be conservative, we round off by excess the non-integer values given in the literature. The scarcity of the data makes interpretation of that earthquake still disputable; moreover at that time (1858) Sofia was a small town with an urbanized area of ~2.8 km2 and population less than 15,000 inhabitants. The strongest earthquake which has occurred in Sofia so far is the earthquake of October 18, 1917 with magnitude M = 5.2 (Kirov, 1952; Petkov and Christoskov 1965a, b) and reported epicentral intensity I o ~ VIII, MSK-64 (Petkov and Christoskov 1965a, b). Since 1917 strong earthquakes, magnitude M > 5.0, have not occurred in this region. Recently, in 15, November 2008, an earthquake of magnitude 4.0 hit Sofia without reported damage.

3 Seismic Hazard Assessment (SHA) and Seismic Microzonation Studies

In the last 15 years several studies on seismic hazard in Bulgaria (Bonchev et al., 1982; Orozova-Stanishkova et al., 1994, 1996; Simeonova et al., 2006) have been published. These studies and particularly the investigation targeted on the Sofia region (Petkov and Christoskov 1965a, b; Christoskov et al., 1989; Stanishkova and Slejko, 1991; Ranguelov, 1996; Ranguelov and Toteva, 1998; Solakov and Christoskov 2001), although based on different approaches, call the public’s attention to the high earthquake danger within the Sofia region. Maximum macroseismic intensity at Sofia, I = IX (MSK), already observed in 1858 (Bonchev et al., 1982) and, possibly, locally exceeded, can be expected to occur within a period of 150 years (Christoskov et al., 1989). According to the seismic zoning map for 1,000-year return period, given in the Bulgarian Code for Design of Buildings and Structures in Seismic Regions (1987), Sofia belongs to a region of expected intensity IX on the MSK-64 scale.

Different seismic zones are considered to determine the earthquake hazard of Sofia and its vicinity. In general the seismogenic zones Kresna, Plovdiv, Negotinska Krayna, and Gorna Orjahovitza are considered to make the major contribution to the seismic hazard of Sofia. The city is also prone to the remote Vrancea seismic zone (Romania), the long-period elements of the built environment being particularly vulnerable to these events, for example the Vrancea quake of March 4, 1977 (VV AA, Brankov, 1983). The recent seismic hazard maps of the Circum–Panonian region (Panza and Vaccari, 2000) show that Sofia could suffer peak design acceleration DGA up to 0.6g, peak ground velocities (PGV) = 60–120 m/s, and peak ground displacements (PGD) = 15–30 cm, which correspond to macroseismic intensity from VIII to X (MSK-76) (Medvedev, 1977). In these maps, usually, shallow seismicity is considered (the hypocentral depth considered is 10 km for events with magnitude less than 7, and 15 km for larger events) and the computations are limited to epicentral distances shorter than 90 km. In the case of Vrancea events the computation has been performed over Romanian, Northeastern Croatian, and Hungarian territory and within a circle of 350 km radius centred on the Vrancea region. The hypocentral depth considered for Vrancea events is 90 km for magnitude less than 7.4, and 150 km for larger events.

The first attempt at seismic microzonation for Sofia is the map in terms of macroseismic intensity, MSK, published in 1965 by Petkov and Christoskov (1965a, b). This map was prepared by making use of the Medvedev’s (1960) method and distinguishes the micro zones on the base of their rigidity coupled with the information available about the water table level. The Petkov and Christoskov (1965a, b) map is redrawn in Fig. 1a (B), where, within the territory of the city of Sofia, three zones with different macroseismic intensity, MSK, are distinguished. Some later studies (Paskaleva, 2002) show that, considering, in addition, the coseismic effects (e.g. land-sliding, liquefaction), the intensity still varies within the same interval ΔI = 2, even if the intensity distribution within the investigated territory changes visibly, particularly in the south-western part of the region.

Fig. 1
figure 1

a Site response estimation at Sofia: distribution of the fundamental free period, Model30 (30 m depth). b Site response estimation at Sofia: distribution of the fundamental free period, Model50 (50 m depth)

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A further development in the SHA targeted at the city of Sofia seismic microzonation is the probabilistic SHA (PSHA), published by Solakov and Christoskov (2001). In this study the results, obtained from a sensitivity analysis of the PGA, keeping the same seismic source model and the same seismicity characteristics, and varying the standard deviations in the PGA attenuation mode, are discussed. A difference of up to 200% in the PGA value for a 1,000-year period was obtained, and this result has been related to the fact that regional, but not local, attenuation functions were used. A doubt comes from the fact that, in general, the regional data sets are not statistically significant; they are, therefore, unsuitable for representing very different seismotectonic styles that are not mixable, and usually attenuation functions are derived with the assumption of the same propagation model for all the events considered (Decanini et al., 2001). The preliminary computations of the b value for the seismic zones, which can potentially affect the seismic hazard at Sofia, carried out by applying a maximum likelihood procedure (Molchan et al., 1997), supply an explanation for the failure of PSHA application to Sofia region. To perform the computations, the Earthquake Catalogue for East and South-east Europe (Shebalin et al., 1999) for the Bulgarian territory, the Romanian earthquake catalogue for Vrancea zone in Romania, ROMPLUS (Oncescu et al., 1999; http://www.infp.infp.ro), and two tectonic models (Todorovska et al., 1995; Paskaleva et al., 2001) were considered. The preliminary estimates of these coefficients listed in Table 1 (taken from Slavov et al., 2004) show quite large confidence intervals for the b value. The available data are rather limited and the statistical determination of the coefficients of the frequency–magnitude relationships (FMR) for these zones is affected by large uncertainties (Molchan et al., 1997). More detailed analysis of the pitfalls of PSHA have recently been discussed and published by Klügel (2005), Wang (2005), Klügel et al. (2006) and Klügel (2007a, b). A brief comparative analysis of the classical SHA procedure with the neo-deterministic SHA (NDSHA), scenario-based, procedure, summarising the NDSHA limits and possibilities compared with the other two approaches, was published by Panza et al. (2008).

Table 1 Estimates of the b coefficient of the FMR (taken from Slavov et al., 2004)
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A preliminary analysis of the site response in the Sofia region based on the definition of the elastic eigenfrequencies of the site, defined using the data obtained from 14 boreholes, reaching depths up to 600 m, has been performed by Paskaleva (2002). Three models extending to different depths are used to perform these analyses: models M30 (30 m deep) and M50 (50 m deep) are based on the Eurocode 8 ground type classification and model M& (reaching the depth of the bedrock identified with a shear velocity V s > 750 m/s) is built by following the soil classification provided in the Bulgarian Code’87. The computations are performed applying the finite-element approach and the soil is discretised into one-dimensional finite shear elements, with viscous damping and lumped mass system. Maps of the first four free periods are obtained. The map of the fundamental free period for models M30 and M50 over the territory of the city are shown in Figs. 1a and b, respectively. The values of the fundamental natural period for the M30 model, shown in Fig. 1a are in the range 0.30–1.04 s, and for the M50 these values are in the range 0.90–1.40 s (Fig. 1b). The free periods obtained for the M50 model are 1.4–2 times larger than the corresponding M30 periods. These maps can be used only for preliminary practical preventive purposes, e.g. to keep the designers aware of the types of structural systems that should be avoided for a given location (Paskaleva et al., 2004a).

The last attempts at a SHA via seismic wave propagation modelling for the purpose of seismic microzonation of Sofia and vulnerability estimation of the built stock (Paskaleva, 2002; Slavov et al., 2004; Paskaleva, 2003; Paskaleva et al., 2007, 2008; Dineva et al., 2008 ) made use of an advanced innovative, scenario based NDSHA procedure (Panza et al., 2001). Dineva and Paskaleva (2008) present a hybrid method, combining modal summation and boundary integral equations (MS-BIEM) for site-response estimation, using idealized 2D symmetric models. The results’ validation in this study relies mainly on the comparative analyses of test examples considering both, MS-BIEM and MS-FD hybrid approaches (Dineva et al., 2003), but no further validation on the case study of Sofia has been supplied. The other quoted studies (Slavov et al., 2004; Paskaleva 2002; Paskaleva et al., 2008) rely on a hybrid approach (Fäh et al., 1993, 1994a, b) that combines MS, applied for the seismic wave propagation modelling through the anelastic bedrock, representative of the wave travelling path from the source to the target site (Panza, 1985; Panza and Suhadolc, 1987; Panza et al., 2001), and finite differences (FD) techniques (Virieux, 1984, 1986; Levander, 1988), applied to the anelastic, laterally inhomogeneous local medium around the site of interest, composed of sediments. The NDSHA hybrid procedure used for ground-motion modelling is capable of synthesising seismic ground motion from basic understanding of fault mechanism and seismic wave propagation. The capability of the procedure has already been proved, in the framework of UNESCO-IUGS-IGCP project 414, in several major cities in different regions: Bucharest (Panza et al., 2002; Cioflan et al., 2004), Thessaloniki (Triantafyllidis et al., 1998), Zagreb (Lokmer et al., 2002), Rome and Naples, Italy (Fäh et al., 1995a; Vaccari et al., 1995), Mexico City (Fäh et al., 1995b), Beijing (Sun et al., 1998; Ding et al., 2004a, b). Despite the difficult verification of the synthetic strong motion database obtained, because of the lack of strong motion records in Sofia, some encouraging validation regarding the macroseismic intensity variation (Slavov et al., 2004) and the seismic regulation prescriptions (Paskaleva et al., 2008) have been performed. The hybrid approach is being increasingly used to constrain those aspects of ground motion prediction that are not constrained by recorded strong motion data, as in the case of Sofia City (Nenov et al., 1990).

4 The NDSHA Procedure: Construction of the Synthetic Strong-Motion Database for the City of Sofia

To compute the synthetic seismic input, applying the NDSHA procedure (NDSHAP), it is necessary to:

  1. 1.

    Choose the controlling scenario earthquakes that are consistent with the seismicity, seismic regime, and seismic source mechanisms relevant for the target sites;

  2. 2.

    Define geophysical and geological properties along the path between the seismic sources and the target sites; and

  3. 3.

    Define as much as possible in detail the local geology of the target sites.

Therefore, the first step in the NDSHA is the choice of earthquake scenarios and the second step is to systemize the available geotechnical and geological information in order to construct the velocity model(s) for the bedrock structure, representative for the seismic wave propagation path from the seismic source to the target site and the local model(s), representative of the investigated site(s).

The available information on the earthquakes record has shown that two-thirds of the earthquakes had hypocentres no deeper than 10 km (Glavcheva et al., 1996; Solakov et al., 2001). Within this depth the whole energetic variety of the seismic sources is present, including the strongest known earthquake of 1858, I o ~ X and M = 6.5). One-sixth of the hypocentres occupy the depth range 10 < H < 25 km, where it seems earthquakes with magnitude not larger than M = 5 occurred. The deepest seismic sources have been localized at depths of 30 km, where, again, mainly earthquakes with magnitude less than M = 5 occur. Following the empirical relationship available for the epicentral intensity versus magnitude (Lee et al., 1990; Glavcheva, 1990) I o = IX and M = 6.5 correspond to an earthquake with focal depth h = 10 km while I o = X and M = 6.5 correspond to h = 5 m. Some other investigations estimate magnitude 7.0 for the 1858 earthquake (Christoskov and Sokerova 1987) and this value seems fully consistent with I o = X, rather than IX. The earthquake scenarios considered to produce the database (Paskaleva et al. 2004a, b) correspond to a seismic source located 10 km west or southwards from the city centre (Christoskov et al., 1987; Alexiev and Gerogiev 1997; Slavov, 2000, Matova, 2001; Solakov and Christoskov 2001). To construct the comprehensive earthquake scenarios, listed in Table 2, conservative combinations of information available in the literature (Alexiev 1997; Shanov et al., 1998; Slavov, 2000) are considered. The computations for Sce1 (M w = 3.7) and Sce2 (M w = 6.3) consider the frequency-dependent response for point seismic source (Gusev, 1983). For the Sce3 and Sce3a (M w = 7.0) the extended source with bilateral rupture propagation is considered, and the observation point is on a line at 90° from the rupture-propagation direction (Gusev and Pavlov, 2006).

Table 2 Scenario earthquakes used for the computations
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The bedrock is represented by heterogeneous (in composition) and different (in age) rocks, which outcrop within the depression, because the city of Sofia is situated in the central southern part of the Sofia kettle, a continental basin in southern Bulgaria filled with Miocene–Pliocene sediments. The considered velocities of the longitudinal seismic waves in the Neogene sediments are of the order of 1,500–2,000 m/s, and for the basement are in the range 4,000–5,600 m/s. The documented significant lateral and vertical velocity heterogeneities are incorporated in the considered models. The Quaternary sediments, representing the uppermost part of the geological sequence in the Sofia kettle region, are thick, from 3 to 100 m and more (Frangov and Ivanov, 1999). The three velocity layers that are distinguished in the sedimentary complex (Neogene and Quaternary sediments) on the territory of the town of Sofia (Ivanov, 1997), a top one with depth of 3–4 m (depending on the ground water level) with velocity of the longitudinal waves of 300–400 m/s; an intermediate one at a depth of 15–90 m and a velocity of 1,300–1,800 m/s, and a lower one with a velocity of 1,850–2,100 m/s were used to construct the local models. These models also take into account the fact that the velocity of the longitudinal seismic wave distribution sharply increases from 1,850–2,100 to 4,800–5,200 m/s at the boundary between the Neogene sediments and the basement. The man-made fill deposit layer is composed of old structures, technogenic soils, and industrial and household waste. This layer reaches its maximum thickness (up to 10 m) in the central parts of the town. The bulk density of the Quaternary sediments is about 1,840–2,070 kg/m3. The unconsolidated Neogene sediments (sands, clays, clay sands, alevrolites, etc.) are characterized by a density not surpassing 2,000 kg/m3. The density of the basement rocks (limestones, marls, sandstones, andesites, etc.) varies from 2,500 to 2,600 kg/m3. Mean values of the geophysical properties of the geological strata representative for the Sofia kettle are given in Table 3. More details on the local site model used in computation of the seismic waveforms have recently been published by Paskaleva et al. (2004a, b, 2007).

Table 3 Mean values of the geophysical properties of the geological strata representative for the Sofia Kettle
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A generalised scheme of the model adopted for the numerical experiments is drawn in Fig. 2a. Synthetic ground motions along three geological cross sections, M1, M2, and M3, described by different geometry of the representative geological strata were computed by Paskaleva  et al. (2004b). These models correspond to the profiles 1A–1B, 2C–2D, and 3E–3F, respectively, and are shown schematically in Fig. 2b (C).

Fig. 2
figure 2

a A generalised scheme of the model adopted for the numerical experiments. b (A): geographic location of the City of Sofia; (B): Redrawn Petkov and Christoskov (1965a, b) map; (C): city sketch with the location of the profiles used in the numerical simulations: 1A–1B and 2C–2D are parallel and are about 3.5 km apart. The ticks on the frame of the figure are: locations of the epicentre for the scenario M = 7.0; - location of the epicentre for the scenario M = 3.7 (preliminary assessment) -location of the epicentre ML = 4.1 (preliminary assessment)

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Several sets of synthetic accelerograms, velocigrams, and seismograms corresponding to sites 100 m apart along the considered geological cross sections, have been computed. The synthetic ground motion database (Paskaleva et al., 2007) contains more than 2,700 signals, which have been grouped in three ranges of epicentral distances: 10–12, 12–16, and 16–20 km. For each group, mean ground motion spectral quantities are computed. Some validation via comparisons of the spectral quantities of the computed signals and the prescribed corresponding values in the acting seismic regulations is supplied by Slavov et al., (2004) and by Paskaleva et al. (2008). Some additional considerations on the validation of the seismic input are given hereinafter.

4.1 Validation of the Bedrock Signal

The “worst” peak ground acceleration (PGA) distribution, obtained for the M w = 7 scenario (Scenario 3a, model M3, Table 2), is shown in Fig. 3. In the same figure, the horizontal and vertical acceleration limits, according to the present Bulgarian code for design of buildings and structures in seismic regions, are shown as straight lines. The PGA values prescribed in the Bulgarian Code’87 are regarded as normative values. According to this figure, for epicentral distances less than 15 km the PGA does not exceed the normative acceleration values (K c = 0.27g for horizontal components, PGATRA and PGARAD, and PGAV = 0.9 × 0.27g = 0.24g, for the vertical). Some statistical estimates of the PGA distribution versus epicentral distance are given in Figs. 4a–c. For epicentral distances above 16 km, the PGA values, mean and mean +1 standard deviation, exceed the normative acceleration values. For the vertical component, the PGA values, mean and mean +1 standard deviation, become smaller than the normative ones for epicentral distances larger than 12 km.

Fig. 3
figure 3

PGA resultant vector distribution along the profile, M = 7 scenario earthquake, \( {\text{PGA}}_{\text{REZ}} { = }\sqrt {{\text{PGA}}_{\text{TRA}}^{ 2} {\text{ + PGA}}_{\text{RAD}}^{ 2} } . \)

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Fig. 4
figure 4

a PGA statistics versus epicentral distance, M = 7 scenario earthquake, \( {\text{PGA}}_{\text{REZ}} { = }\sqrt {{\text{PGA}}_{\text{TRA}}^{ 2} {\text{ + PGA}}_{\text{RAD}}^{ 2} } , \) epicentral distances 0–12 km. b PGA statistics versus epicentral distance, M = 7 scenario earthquake, \( {\text{PGA}}_{\text{REZ}} { = }\sqrt {{\text{PGA}}_{\text{TRA}}^{ 2} {\text{ + PGA}}_{\text{RAD}}^{ 2} } , \) epicentral distances 12–14 km. c PGA statistics versus epicentral distance, M = 7 scenario earthquake, \( {\text{PGA}}_{\text{REZ}} { = }\sqrt {{\text{PGA}}_{\text{TRA}}^{ 2} {\text{ + PGA}}_{\text{RAD}}^{ 2} } , \) epicentral distances 14–16 km

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The synthetic seismic signals are computed for the period range 0–10 s. The period interval 0–4 s has been chosen as the most interesting for engineering practice, and comparison of the computed displacements response spectra with the EC 8 ones has been performed over this period. The comparison of the computed displacement design spectra (SDD (T)) with the recommended EC8 design spectra (Fig. 5a, b) show that the synthetic spectral values for all models follow the EC8 amplitudes for the period range T = 0.05–1 s. The synthetic amplitudes are larger than the EC8 ones for periods T = 1–2 s.

Fig. 5
figure 5

a Comparison of the computed dynamic coefficients (SA(T)/PGA mean values) for magnitude M w = 7.0 for all considered models M1, M2, and M3 and the design values recommended by the EC8. The dashed line graphs correspond to soil conditions class A (rock), class B (stiff soil), and class C (soft soil), respectively. b Comparison between the computed elastic displacement spectra (mean values of the elastic displacement response spectrum, 5% damping) for magnitude M w = 7.0 for all considered models M1, M2, M3 and the design displacement spectra, recommended by the EC8. The dashed line graphs correspond to peak ground acceleration 270 cm/s2 (BG code 1987) and soil conditions class A (rock), class B (stiff soil) and class C (soft soil)

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Going further with the processing of the computed synthetic data, elastic displacement and acceleration response spectra for 5% damping have been determined from the synthetic accelerograms. Generalized resultant horizontal response spectra have been computed as the square root of the sum of the squares of the two horizontal components, \( {\text{SA}}_{\text{REZ}} \left( T \right) = \sqrt {{\text{SA}}_{\text{TRA}} \left( T \right)^{2}\,+\,{\text{SA}}_{\text{rad}} \left( T \right)^{2} .} \) The important effect of the source-to-site distance, d s, the magnitude, and the local geological conditions on the spectral displacements is shown in Fig. 6, where the mean elastic displacement spectra along the three investigated models M1, M2, and M3, considering the scenario earthquakes given in Table 2, are plotted for the period range 0–2.5 s.

Fig. 6
figure 6

a Mean elastic displacement spectra computed for all considered models M1, M2, and M3 according to the scenario earthquakes listed in Table 2 (Sce 1, Sce 2, Sce 3). b Mean elastic displacement spectra computed for all considered model M3 according to the scenario earthquakes listed in Table 2. Left Sce 3 (solid lines), right Sce3a (dashed lines)

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The elastic displacement spectral amplitudes in the near field (d s = 10–12 km) are larger than those obtained for the far field for the three models, when considering earthquake scenarios Sce 1 (M w = 3.7) and Sce 2 (M w = 6.3). A similar trend is observed for model M1, Sce 3 (M w = 7.0). The results obtained for model M2, Sce 3 (M w = 7.0) and model M3, Sce 3 and Sce 3a (M w = 7.0) show that the local geological conditions determine the seismic input (Fig. 6a). The graph in Fig. 6b shows the relevant effect of the seismic source mechanism on the spectral amplitudes, particularly at periods T > 1.25 s.

Comparison of the maximum displacement d s and the corresponding corner period T c, obtained in this study and the results of Decanini et al. (2003) for stiff soil (S1), at distances from the source less than 5 km and larger than 30 km, magnitude 6.5 < M < 7.1, is shown in Fig. 7a, b. The agreement between the results derived from the data bank of recorded signals (Decanini et al., 2003) and the results obtained from the synthetic database compiled using the neo-deterministic approach is fully satisfactory for displacements and corner periods also.

Fig. 7
figure 7

a Comparison of the maximum spectral displacement SD (models M1, M2, and M3) with the data of Decanini et al. (2003) for stiff soil (S1), magnitude range 6.5 < M < 7.1. b Comparison of the corner period Tc corresponding to the maximum spectral displacement SD (models M1, M2, and M3) with the data of Decanini et al. (2003) for stiff soil (S1), magnitude range 6.5 < M < 7.1

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4.1.1 Relative Displacement Spectra Attenuation

The concept of the displacement relative attenuation, expressed by Att, was introduced by Decanini et al. (2003) to evaluate the effect of the distance from the source to the particular site. For the spectral displacement SD, Att (relative attenuation) is given by the ratio: Att = {Sdsi (T)}/{Sds0 (T)}, where Sdsi (T) represents the spectral displacement value d s considering intervals of distance (10 < d s < 12 km, 12 < d s < 16 km, 16 < d s < 20 km) to the source; Sds0 (T) is the spectral displacement for the shortest distance (d s = 10 km). Obviously, low Att values indicate fast attenuation and high Att values denote slow attenuation with distance. The effect of the magnitude, geological conditions along the profiles, and the seismic source mechanism on the relative displacement attenuation is illustrated in Fig. 8.

Fig. 8
figure 8

a Relative displacement spectra attenuation, computed along all investigated models M1, M2, and M3 considering scenarios Sce1, Sce2, and Sce3. b Relative displacement spectra attenuation, computed along investigated model M3 considering scenario Sce3a

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Generally, the displacement relative attenuation in the far field along all investigated models, considering all scenarios, is visibly faster than the attenuation in the near field. The fastest displacement relative attenuation has been observed for model M3 and the slowest for model M2. Analysing the relative displacement spectra along Model M1 (the left column in Fig. 8a), values of Att increase with increasing magnitude, more visibly at periods T > 1 s. The far field attenuation, d s > 16 km, is visibly faster than the near field one. The significant contribution of the geological conditions to the earthquake site response and to the relative displacement attenuation at the site is illustrated by the comparison between the plotted displacement relative attenuation for model M1 (left columns in Fig. 6a), model M2 (middle column) and model M3 (right column). The last graph in Fig. 8b (lower right corner) shows the effect of the seismic source mechanism on the displacement relative attenuation for model M3—the displacement relative attenuation follows the same trend, but with larger amplitudes.

Figure 9 shows the comparison of the design displacements relative attenuation Att obtained from the synthetic database (computed for Sofia) with the Att values extracted from observations, e.g. as supplied by Decanini et al. (2003) and Bommer and Elnashai (1999). The attenuation coefficient obtained in this study, using the computed seismic input, shows visibly higher Att values, which indicate faster attenuation along the investigated site. This result calls our attention to the need to perform more parametric analyses in order to clarify the contribution of the different characteristics of the computation model and the input information to Att.

Fig. 9
figure 9

Relative attenuation coefficient Att. Comparison of the results obtained in this study for the generalized horizontal component (median values) with the data of Decanini et al. (2003) (6.5 < M < 7.1) and Bommer (1999) (magnitude-independent)

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An extensive numerical analysis has been carried out on SDOF systems for natural periods T in the range 0–2 s. The elastic spectral displacement S d and strength demand S a, which represent the structural performance, have been extracted from all the computed accelerograms assuming a constant damping ratio of 5%. The results for earthquake scenarios M = 7.0 are plotted in S a – S d format in Fig. 10. The same figure shows the comparison of the mean elastic acceleration–displacement diagram with the S a − S d diagram, recommended in EC8, corresponding to the case-study of Sofia City—design acceleration 0.27g “B” soil conditions. The plot in Fig. 10 shows a good correlation between the compared data in the period range 0.4 < T < 0.8 s, whereas for longer periods (0.8 < T < 2.0 s) the synthetic signals are dominant at all considered distances.

Fig. 10
figure 10

Elastic demand diagram. Comparison of the synthetics and the Eurocode 8 values

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5 NDSHA: Engineering Applications

The NDSHA procedure supplies realistic waveforms of acceleration, velocities, and displacement of the free ground surface and thus it is possible to estimate from these signals, in a reliable way, any relevant variable used to characterize the ground motion for risk mitigation purposes. Obviously a similar wealth of information cannot supplied by PSHA. The synthetic data base, can be directly used for different engineering purposes, for example:

  • provide seismic loading in terms of time series, consistent with both National Code and Eurocode 8 (2002) requirements;

  • provide alternative definition of the seismic input, and particularly of the dynamic coefficient, for the National application of Eurocode 8;

  • perform seismic microzonation and vulnerability estimates in terms of elastic and non-elastic quantities (only elastic quantities considered in this paper, non-elastic estimates will be the subject of another paper);

  • perform surface strain and ground failure estimates, and preliminary liquefaction susceptibility estimates;

  • proceed with capacitive and performance-based design;

  • map space distribution of the damage index.

5.1 Seismic Loading and Code Provisions

The validation of the computed seismic demand against the seismic input, prescribed by the EC8, shown in Figs. 4, 5, 6, 7, 8 and 9 has shown the consistency of the computed seismic signals with the Code. Therefore this procedure is able to meet the requirements of the EC8 regarding the use of artificial accelerograms for description of the seismic motion and can be used as an optional independent generator of seismic input for earthquake engineering purposes. When strong motion instrumental records are lacking the NDSHA procedure can also be used as an optional independent procedure for definition of the seismic input in EC8 National Applications (e.g. considering an earthquake scenario with return period of 475 years).

The NDSHA procedure supplies site response estimates simultaneously in the frequency and space domains. The irregular pattern of the site amplification in the frequency–space domain, obtained even when considering rather simplified geological settings, as for the Russe case study, e.g. Kouteva et al. (2004), confirms the complicated properties of the so-called “site effect”. The site response is because of the complex evolution of the seismic wave field (while it propagates through the laterally heterogeneous, geological media) that cannot be captured by standard convolutive methods as described for instance by Reiter (1990). In cases when the investor’s technical specification requires, particularly, the use of software, based on the traditional PSHA or DSHA and the signal convolution, the NDSHA result pertinent to the bedrock should be used for “calibrating” or scaling the (bedrock) signal, that will have to be propagated through the model representing the local site conditions.

5.2 Seismic Microzoning and Vulnerability

The NDSHA can be used directly for seismic microzoning purposes. The seismic microzoning assigns the obtained seismic input, in terms of spectral acceleration (S a), spectral displacement (S d), or capacity diagram (S a − S d), to the area characterized by the corresponding local geological conditions (Paskaleva et al., 2004b). For the discussed earthquake scenario Sce2, six homogeneous zones, shown in Fig. 10, can be identified. Average and maximum response spectra have been computed for each zone. The maximum response spectra, computed for 5% damping, for each of these zones are shown in Fig. 11 by solid lines whereas the thin line represents the BG code’87 design spectrum. For each spectrum the distance range R (km), measured from the beginning of the profile, where the spectrum is applicable, is specified. The maximum particle velocity for the zone is given as an indicator of the strain.

Fig. 11
figure 11

Maximum acceleration response spectra for the zones defined (left corner of the figure) for 5% damping. The lines solid, this study; thin, BG code’87 design spectrum; R, distance range, from the beginning of the profile, where spectrum is applicable

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The available synthetic strong motion database can be readily applied to define site-specific design spectra based on average or maximum amplification. Such results have to be accounted for in site-specific design procedures, especially for underground lifeline systems, which are more sensitive to near surface strains than to maximum peak ground acceleration. This is a good starting point for the microzonation of Sofia. Many more cross-sections will be required to cover the whole city, for better understanding and estimation of the maximum expected risk (Paskaleva et al., 2007). The NDSHA can be also used for estimation of the vulnerability of different elements of the built environment (Paskaleva et al., 2007). The method can be used for the purpose of preliminary qualitative and detailed quantitative vulnerability assessments. In fact, all the performed validation of the theoretically obtained seismic input (S a, S d, S a − S d) has shown that the computed seismic demand is consistent with the Code prescriptions in the short period range, 0.05 > T > 1.0 s, whereas it is characterized by visibly higher values of the variables considered for the longer periods 1 > T > 2.5 s.

5.3 Surface Strain and Ground Failure Estimates

When records are scarce or non-existent as in the case of Sofia city, the synthetically generated database, containing waveforms and time histories, can be directly used for prognostic estimates of the distribution of different data useful for design practice, urban planning, and earthquake preparedness. The computed velocities can be used to estimate the surface strain field and thus to make enable assessment of the expected number of red-tagged buildings and mean number of expected pipe breaks/km2 as it has been done by Paskaleva et al. (2004b). The map of the number of pipe breaks per km2 for the city of Sofia, redrawn from Paskaleva et al. (2004b), is shown in Fig. 12.

Fig. 12
figure 12

Sofia map of number of pipe breaks per km2 compiled from synthetic velocigrams. The solid line indicates intensity higher than VIII (I MM) (data from Trifunac and Todorovska, 1997)

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When considering long structures and their nonlinear response analysis, the designers have to pay particular attention to the representative surface strain and to the number of stress reversals that are related to the duration of the ground motion. The practice shows that for long in-plan structures (life-line systems, bridges, dams, etc.) the quasi-static deformation of the complete structure may contribute to the largest levels of the design loading. Therefore, every sound design approach has to consider all the relevant scaling data. The outcome of the NDSHA procedure in terms of ground surface velocities computed for the target sites allows us to estimate the peaks of the horizontal strain (ε) components, associated with the propagation of earthquake waves (Paskaleva, 2002). The horizontal strain factor Log10 ε distribution, obtained as a result of the zonation of Sofia as computed by Paskaleva (2002) is shown in Fig. 13, where the solid isoline −3.0 corresponds to the strain factor 10−3 beyond which a ground failure might be expected.

Fig. 13
figure 13

Horizontal strain factor Log10 ε distribution, obtained as a result of the zonation of the city of Sofia. The solid isoline −3.0 corresponds to the strain factor 10−3 beyond which a ground failure might be expected

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5.4 Liquefaction Susceptibility

The synthetic database based on the NDSHA procedure provides reliable values of all ground motion variables necessary for assessment of the liquefaction susceptibility, a very important aspect of the vulnerability (Romanelli et al., 1998). An example dedicated to the city of Sofia, is given by Paskaleva (2002, 2008). The performed assessment, as shown in Fig. 14, should be treated as a general guide for the minimum level of liquefaction in Sofia city. Full liquefaction hazard assessment requires substantial engineering and professional judgment, looking site by site. The liquefaction analyses deal either with estimation of the shear stress expected during design earthquake motion or with assessment of the soil strength capacity in terms of the standard penetration tests, SPT, making use of different possible approaches (Berrill and Davis, 1985; Trifunac, 1995). Paskaleva (2002) provides SPT estimates for the city of Sofia, shown in Fig. 14, that can be useful for various engineering and managing purposes concerning urban planning and earthquake preparedness.

Fig. 14
figure 14

Maximum SPT, \( \overline{N} \) values for Sofia supposing overburden pressure σ 0 = 25 kPa (Paskaleva 2002, 2008)

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5.5 Seismic Demand and Capacitive Design Method

Another aspect of the engineering application of the outcome of the NDSHA is related to its explicit representation of the seismic demand by an S a − S d capacity diagram that can be the direct input for the capacitive design method. Dealing with the capacity design method, the representation of both the capacity (pushover) curve and the demand spectrum is made in the spectral acceleration (S a, ordinate), spectral displacement (S d, abscissa) coordinate system. Capacity curves are based on engineering data (design, yield, and ultimate structural strength levels) characterizing the nonlinear behaviour of different classes of model building. They distinguish between construction materials, construction tradition, experience and technology used, and prescribed (by code) and achieved (in practice) levels of seismic protection. Further the capacity models are converted in capacity spectra and thus they can be overlapped with the seismic demand capacity diagram in order to define the performance point of the selected structure. Recently, in 2004, the conclusion of the RISK-EU Project (2004) made available for the public capacity models and capacity spectra for a large set of structures, representative of different typologies, time of design and construction, and number of storeys. Fragility curves are also supplied. Coupling the seismic demand capacity, computed for the city of Sofia with the information on the capacity spectra and the fragility curves for the set of structures considered by the RISK-EU Project enable estimation of the vulnerability of the existing built stock. Such analysis should be targeted by a separate study. It can provide very useful results that can be used for retrofit planning or insurance purposes and will be the subject of a separate study.

5.6 Space Distribution of the Damage Index

The synthetic seismic input, supplied by the NDSHA for the city of Sofia, is used for engineering purposes to assess the distribution of the damage index over the territory of the city, which is useful for urban planning, retrofitting of the built environment, the insurance industry, earthquake preparedness, earthquake risk reduction and earthquake risk management (Paskaleva et al., 2007). These results are based on the seismic vulnerability analysis of a cast-in-situ single-storey industrial reinforced concrete (RC) frame that is designed and tested in the European Laboratory for Structural Assessment (ELSA) of the Joint Research Centre (JRC) of the European Commission at Ispra in the framework of the research project ‘‘Seismic behaviour of reinforced concrete industrial buildings’’ (Dimova and Negro, 2005a, b) The results, obtained in this study, have shown that even for relatively small changes in the source mechanism different values of the damage index (DI), are to be expected.

6 Conclusion

The city of Sofia is a typical example of a large city that is located in a seismic area and can suffer serious damage because of soil conditions, with deep soil deposits and severe local site amplification (Paskaleva et al., 2007). Sofia is exposed to a high seismic risk, because macroseismic intensities up to X (MSK-76) can be expected in the city. For this reason prediction of ground motion from large future earthquakes is very important for hazard mitigation. Sofia is located on thick sedimentary basins, and taking site response into account is essential for realistic predictions of ground motion. The lack of instrumental strong motion records and the high earthquake risk, made evident by the available published reviews of the regional and local seismicity, requires the use of an appropriate scenario-based approach for seismic hazard assessment and advanced ground motion modelling procedures for definition of the seismic input for the city. Currently, uncertainties exist regarding the methodology employed and the level of sophistication required, which determines the number of input data, and the development of these data for implementation. The NDSHA is applied in the case study of Sofia City to cope with the scarcity of data, which will not be overcome in the near future, because of the absence of a relatively dense accelerographs array. The verification of the results obtained and the validation (some with real strong ground records) that has been done for several major cities in different regions (Mexico City, Rome and Naples, Italy, Bucharest, Thessaloniki, Beijing, Zagreb, Russe and Sofia; references have already been given in this paper) allow us to recognize that ground motion prediction using the described NDSHA approach is particularly suitable for all the cases poorly constrained by recorded strong motion data and can be used to make denser (interpolate) the local ground motion information supplied by the instrument.

The capability of demand estimations for buildings exposed to seismic loading is a major challenge for the prognostic estimates of seismic building behaviour. The elastic demand information is very useful for the further development of the design procedures, incorporating different advanced sub-procedures, for example

  1. 1.

    specific serviceability level performance evaluation procedure; and

  2. 2.

    verification of the reliability of the buildings

representative of different structural systems, the reliability of which must be consistent with both the code provisions and developing analytical evaluation procedures capable of predicting building performance with reduced uncertainty. The challenge of urban hazard mapping is to predict the ground motion effects related to various sources, path, and site characteristics not just at a single site but also over an extended region, and to do so with an acceptable level of well placed confidence (reliability). Seismic zoning then consists of linking together site-by-site estimates of site response. SHA practice, either PSHA or DSHA, has shown that such an approach may significantly underestimate the amplitudes and durations of strong ground motion, with energy being trapped within sedimentary basins because of critical reflections and generation of surface waves at the edges of the basin. This shortcoming is not surprising if the poor physical foundations of both PSHA and DSHA are considered. The rapid increase in the development of efficient computational methods and procedures for modelling seismic wave propagation in laterally varying geological structures, combined with increased knowledge of earthquake sources, enables realistic modelling of local site (usually sedimentary basins) effects on the ground motion generated by scenario earthquakes. Analysis of well-recorded data from dense seismograph arrays, when available, can improve the quality of the results of NDSHA by reducing its uncertainties.

Site-specific ground response analyses of strong seismic motion, for example the computed ones making use of the NDSHA procedure, are currently required for the design of new components of civil infrastructure on deep and/or soft sedimentary deposits, and for the revision of seismic code provisions.

In this work it was shown that the NDSHA approach can be used for practical applications in the situation of extreme scarcity of strong motion seismic data, because it enables use of simulated ground motion time-histories, with solid physical roots, for generation of a statistically significant number of input data, adequate to define the validity of the uncertainty assessment analyses.

The analysed synthetic seismic signals are computed using available source and structural models; the provided site response estimates and seismic demand at Sofia because of the chosen earthquake scenarios can be directly applied to assessment of the vulnerability of structures. By means of parametric studies of the source focal mechanism and of the velocity model, it is shown that NDSHA is a powerful approach that may be regarded as fundamental when adding information to the multidisciplinary ‘‘database’’ that must be defined for microzonation purposes. Given a certain earthquake scenario, and an appropriate structural model based on detailed geological, geophysical and geotechnical data, it is possible to evaluate, reliably, the local amplification in the frequency range of interest for civil engineering, and to obtain valuable data for the seismic microzonation.

The seismic demand supplied by the NDSHA application to the city of Sofia, together with the discussed engineering application, show that broadband ground motion simulations for different earthquake scenarios strongly contributes to reliable assessment of the earthquake-induced hazard in the Sofia urban area.

It is obvious that earthquakes will continue to occur and, if we are not prepared, to cause disasters. Assessing earthquake risk and improving engineering strategies to mitigate damage are the only viable options. The future availability of records of even moderate earthquakes will enable immediate validation and, when necessary, second-order revision of the first-order results obtained so far and already applicable to practice. The existence of the first-order reliable estimate of hazard given here enables timely updating of the estimate as new data become available.