1 Introduction

Nepal is situated in the Himalayan region. Geologically, the Himalayan region is divided into higher Himalaya, sub-Himalaya, lesser Himalaya, and Tethyan Himalaya. There are four major structural units in the Himalaya: (a) the Main Frontal Thrust (MFT); (b) the Main Boundary Thrust (MBT); (c) the Main Central Thrust (MCT); and (d) the South Tibet Detachment (STD). The Main Frontal Thrust lies between the sediments of the Indo-Gangetic Plains and outer Himalaya. The border between outer and lesser Himalaya; and lesser and higher Himalaya are known as MBT and MCT, respectively. The South Tibetan Detachment (STD) lies between the higher and Tethys Himalaya. The location of MFT, MBT, MCT, and STD is presented in Fig. 1. Among these, active faults along the MBT and MFT are the most active and have potential to produce large earthquakes in the future (Lava and Avouac 2000).

Fig. 1
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Geological map of Nepal (adapted from Upreti 1999)

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The active faults in and around the Himalayan belt are direct indicators of recent crustal movement as a result of the collision between the Indian and Eurasian plates. Several major earthquakes were reported in 1255, 1810, 1866, 1934, 1980, and 1988 in Nepal (Pandey et al. 1995). Among the major earthquakes recorded in history, the great Bihar–Nepal earthquake of 1934, with a maximum intensity of X (MMI), caused extensive damage in the eastern half of Nepal and resulted in more than 8500 deaths. In addition, about 19 % of the buildings were completely destroyed and 38 % of the buildings were badly damaged (Rana 1935). More recently, the earthquake of August 21, 1988, with a magnitude 6.6 (M w), stroked the eastern part of Nepal and killed 721 people, injured 6553, and damaged or collapsed 66,541 buildings (Thapa 1988).

Despite this worrying scenario, the previous research works conducted by the National Society for Earthquake Technology, Nepal (NSET 2001), and the Japan International Cooperation Agency (JICA 2002) expected that 50 % of the buildings would be damaged and 1.3 % of the population would perish for a large earthquake with a magnitude 8 (M w) occurred 100 km east from the Kathmandu Valley. Afterwards, Wyss (2005) calculated the expected fatalities and injuries in the western part of Nepal. He estimated a minimum death toll of about 15,000 in sparsely populated areas and a maximum of about 150,000 death toll in a populous area for an earthquake of magnitude 8.1 (M w). The number of injuries was expected to range from 40,000 to 250,000. Owing to the poor socioeconomic and uncontrolled building construction, a developing country such as Nepal typically suffers far greater losses from earthquakes than developed countries (Wyss et al. 2012).

In these circumstances, this study tries to explore seismic risk in Nepal by combining probabilistic seismic hazard, structural vulnerability, and exposure data. A probabilistic seismic hazard model is adopted considering a large number of seismic area sources in Nepal. Fundamental exposure data such as type of existing buildings, population, and district-wise distributions of building typologies are estimated from the 2011 national census. The fragility functions used by the National Society for Earthquake Technology (NSET) are adopted for adobe (A), brick/stone buildings with mud mortar (BM/SM), brick/stone buildings with cement mortar (BC/SC), and wooden buildings (W), while recently developed fragility functions are used for the reinforced concrete (RC) building typologies (Chaulagain et al. 2015). A set of fragility functions for each building type is converted into vulnerability functions through consequence models. In this process, the percentage of buildings in each damage state is computed at each intensity level, and multiplied by the respective damage ratio, obtaining in this manner a loss ratio for each level of ground shaking.

2 Seismic risk assessments in Nepal

In this section, the probabilistic seismic hazard analysis (PSHA) model and the selection of ground motion prediction equations in Nepal are discussed. A brief discussion on an exposure model, fragility functions, consequence models, and structural vulnerability are also presented. Moreover, the effect of local site conditions on seismic hazard and loss estimation are addressed.

2.1 Seismic hazard analysis

Earthquake disaster occurs mainly due to collapse of structures triggered by ground shaking. The most effective way to reduce earthquake disaster is to estimate the seismic hazard and disseminate this information for use in improved building design and construction. It is, therefore, important to predict ground-shaking levels in order to determine appropriate building code provisions for earthquake-resistant design of structures. Seismic hazard in the context of engineering design is generally defined as the predicted level of ground acceleration which would be exceeded with a 10 % probability at the site under consideration, owing to the occurrence of an earthquake anywhere in the region, in the next 50 years.

In fact, seismic hazard analysis is the process of evaluating the design motion of the ground during earthquakes. Scenario and probabilistic seismic hazard approaches are used for seismic hazard analysis purposes. A scenario hazard analysis involves a particular seismic event, and thus, it does not use the condition of likelihood of maximum possible ground motion. The ground motion parameters obtained by using a scenario approach of seismic hazard analysis are generally of maximum value, which is rarely used as a seismic input in the analysis of structures. However, in probabilistic seismic hazard analysis, uncertainties in earthquake size, location, and time of occurrence can be considered. Probability of exceedance of some particular value of ground motion parameter (peak ground acceleration/spectral acceleration) is calculated from the attenuation relationships. The application of an appropriate probability method is made from the available seismological and geological data. A complete study is made on selection of the appropriate attenuation and empirical relationships to estimate the ground motion parameter and to compute peak ground acceleration and response spectra. Thus, seismic hazard assessment involves a large spectrum of complex scientific assumptions and analytical modeling. A computational scheme involves (a) identification and characteristics of seismic sources; (b) evaluation of the regional seismicity; (c) use of predictive relationship to find ground motion parameter for any possible size of earthquake; and (d) combination of probability of earthquake location, size, and ground motion parameter to find total probability of exceeding a specified level of ground motion (Kramer 1996). Although these steps are region specific, a certain standardization of the approaches is essential so that reasonably comparable estimates of seismic hazard can be made worldwide, which are consistent across the regional boundaries.

2.1.1 Selection of ground motion prediction equations

Ground motion prediction equations play an important role in seismic hazard assessment for any region. Ground motion attenuation models have the strong influence on seismic hazard as well as the seismic risk (Crowley et al. 2005). The selection of ground motion models is based on the seismotectonic region, distance and magnitude applicability, period range (for spectral ordinates), ability to model site effects, and region wave propagation characteristics, among others (Silva et al. 2014a). Ground motion attenuation relations can generally be categorized into four main groups: (a) stable continental regions; (b) subduction zones; (c) active shallow crustal regions; and (d) volcanic regions. Active shallow crustal regions are characterized by active tectonics with relatively high strain rates, generally close to plate boundaries. Earthquakes occur in the upper 20–30 km of the crust, generally on well-identified mature faults (e.g., California, Italy, Turkey, Greece, and Japan). Subduction zone earthquakes are characterized by significantly different attenuation characteristics compared to shallow crustal earthquakes (Abrahamson and Silva 1997). Since the advent of plate tectonic theory, it has been recognized that subduction zones differ in many aspects relating to their geometry, geology, physics, and chemistry. The ground motion amplitudes owing to in-slab and interface types of subduction zone earthquakes are found to differ significantly. Thus, the ground motion models should address the important features of seismic source properties that characterize each tectonic regime. Youngs et al. (1997) developed separate attenuation relations for the ground motion as a result of in-slab and interface earthquakes, using a global database of about 350 horizontal components. Atkinson and Boore (2003) updated these relationships, using a larger worldwide database of about 1200 horizontal components. Atkinson and Boore relation is based on the assumption that there are no detectable differences between ground motions in different regions of the world, for the same earthquake magnitude and distance. Therefore, the applicability of this model to individual areas needs to be evaluated on a case-by-case basis. The major tectonic regions and corresponding ground motion prediction equations are summarized in Table 1. This selection is based on the recommendations of Douglas et al. (2012) and Steward et al. (2015).

Table 1 List of ground motion prediction equations proposed for various tectonic regimes by Douglas et al. (2012) and Steward et al. (2015)
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Owing to the lack of strong motion data in Nepal from which an attenuation relationship could be derived, the limited research work performed in Nepal has been carried out using some standard ground motion prediction equations. The BECA Worley International Consultants Ltd (BECA 1994) used the Kawashima attenuation model (Kawashima et al. 1984), whereas Pandey et al. (2002) and Maskey (2005) used the attenuation relationship proposed by Youngs et al. (1997) for the seismic hazard assessment in their studies. On the other hand, Parajuli (2009) adopted the model proposed by Atkinson and Boore (2003) in his study. Thapa and Guoxin (2013) used the attenuation relationship developed by the China Earthquake Administration (CEA 2005) for western China for the probabilistic seismic hazard assessment of Nepal.

In the present study, we consider the tectonic region type as active shallow crust and subduction interface. The ground motion prediction equations suggested by Boore and Atkinson (2008), Chiou and Youngs (2008), Campbell and Bozorgnia (2008), Atkinson and Boore (2003), and Youngs et al. (1997) are used within a logic tree for seismic hazard and risk assessment.

2.1.2 Seismic source zones

The study of past earthquakes in and around the Nepal Himalaya shows that the whole area is seismically active. However, the microseismicity activities are particularly intense in the eastern, central, and far-western region (Pandy et al. 1999). In this regard, it is believed that stress accumulation is ongoing in the form of strain at the front of the Himalaya associated with continuous creep at depth beneath the north of the Himalaya. Figure 2 shows the spatial distribution of earthquakes in Nepal and the surrounding regions. The roughly east–west distribution of seismicity shows that the vast majority of earthquakes are located near the Main Central Thrust (MCT) in Nepal. Considering the distribution of earthquakes, fault information, and tectonic features, Pandey et al. (2002) divided the whole region of Nepal into ten area sources and twenty-four linear sources, of approximately 40 km each in length for probabilistic seismic hazard assessment. Their work is limited to peak ground acceleration on bedrock. However, Thapa and Guoxin (2013) divided the region in and around Nepal into twenty-three seismic source zones in their work. In the study presented herein, the same twenty-three seismic source zones are applied for the probabilistic seismic hazard analysis of Nepal.

Fig. 2
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Seismic source zones and spatial distribution of earthquakes in and around Nepal (Thapa and Guoxin 2013)

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The delineated twenty-three seismic source zones are shown in Fig. 2, and each one is considered to be seismically homogenous, so that every point within them is assumed to have an equal possibility of occurrence of an earthquake in the future. These twenty-three seismic source zones differ from one another in dimensions and hazard parameters. The historical earthquake events and the maximum magnitude of earthquakes considered in the selected seismic zones are presented in Table 2.

Table 2 Seismic sources and historical events (Thapa and Guoxin 2013)
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The earthquake catalogue of Nepal (www.seismonepal.gov.np) for the period of 1255–2011 suggests that the database before 1964 is inadequate to delineate earthquakes with a magnitude below 4 (Parajuli 2009; Thapa and Guoxin 2013). The database is more complete from 1964, when many earthquake records become available from modern seismic instruments. Pandey et al. (2002) calculated the annual rate of exceedance, b value, used in the Guttenberg and Richter’s law in the range of 0.75–0.95, for magnitude range of 2.0–5.5. Parajuli (2009) determined b value of 0.76 in his study. Thapa and Guoxin (2013) estimated a b value of 0.85 in their study. The same b value of 0.85 proposed by Thapa and Guoxin (2013) is used in the present study.

2.2 Exposure model

The development of an exposure model for seismic risk assessment at a national scale might be a very challenging task. Information about the location and classification of the existing structures can be achieved through the use of census data (e.g., Erdik et al. 2003 (Turkey); Crowley et al. 2008 (Italy); Silva et al. 2014a (Portugal)), or using other datasets to approximate building distribution, such as population datasets (Jaiswal and Wald 2010). In this research work, the 2011 Building Census data at the district level is used as the main component for the development of exposure model.

2.2.1 Characteristics of the building stock

Nepal is located in the Himalayas, and bordered to the north by China and by India to the south, east, and west. Geographically, Nepal can be divided into three main regions: the Himalaya to the north; the middle hills consisting of the Mahabharat range and the Churia hills; and the Terai to the south. The Himalaya and its foothills make up to the northern border of the country and represent 15 % of the total land area. This is the least inhabited region of Nepal, with <7 % of the population living there. The middle hills cover about 68 % of the total land area and are home to around 43 % of the country’s population. This area is the home of the ancient ethnic hill people of Nepal. The Terai is the southern part of country and is an extension of the Gangetic plains of India. It covers 17 % of the total land area. Today, about 50 % of the population occupies this region. There is a rich diversity of building structures in Nepal, resulting from its geography, ethnic group history, intensity of economic growth, and availability of local building material.

The level of building damage depends on the intensity of ground shaking and seismic performance of the structures. Therefore, a classification of the buildings is conducted as a fundamental step in estimating damage/loss. In this work, the national census data from 2011 for buildings is considered, thus disregarding public infrastructure and exclusively commercial or industrial structures. According to the census survey of 2011, the total number of individual households in the country was 5,423,297. The Terai region hosts 50.27 % of the total population, while hills and mountains comprise 43 and 6.73 %, respectively. The distribution of the buildings in Nepal is also similar to the distribution of the population (see Fig. 3). The data obtained from the National Population and Housing Census (CBS 2012) indicates that mud-bonded brick/stone buildings are more common in Nepal in all the geographical regions, comprising about 44.21 % of the building stock. In the rural region of Terai, wooden buildings are quite popular, comprising about 24.90 % of the building portfolio. Cement-bonded bricks/stones and reinforced concrete buildings have a higher representation in urban areas in most of the Terai region, Kathmandu Valley and some urban areas in the mountainous region of Nepal, constituting 17.57 and 9.94 % of the building stock, respectively. The rest of the buildings have been categorized as ‘Others’. For the sake of simplicity, buildings classified as mixed, others, and not stated in national census survey have been included within the adobe category, since a similar seismic vulnerability is expected. For reinforced concrete buildings, four sub-categories have been defined: (1) current construction practices (CCP), (2) structures according to Nepal building code (NBC), (3) structures according to the modified Nepal building code (NBC+), and (4) well-designed structures (Chaulagain et al. 2013). The amount of CCP, NBC, NBC+, and WDS structures are considered as 76, 8, 8, and 8 %, respectively (Dixit 2004; Shrestha and Dixit 2008). The percentage of each building typology at a national level is described in Table 3.

Fig. 3
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a District-wise distribution of buildings and b building types in Nepal (CBS 2012)

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Table 3 Vulnerability classes for the Nepalese building stock (CBS 2012)
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For the purpose of computing the seismic hazard for each asset, it is assumed that all of the buildings are equally distributed throughout the whole district, which is a common assumption when performing seismic risk assessment on a large scale (e.g., Bommer et al. 2002; Crowley et al. 2008; Silva et al. 2014a).

2.2.2 Estimation of economic value

In this study, the building cost is established as the required monetary value to construct a building with the same characteristics according to present costs, herein termed as the replacement/construction cost. This value naturally depends on the location, types, and total area of the building structure. There is a lack of standard construction cost in various locations in Nepal, so the construction cost for each building type is assumed to be constant at all the districts. Table 4 presents the construction type, area per building type, and corresponding construction cost.

Table 4 Area and corresponding construction cost of existing Nepalese building stock
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2.3 Structural vulnerability model

The concerns over the seismic risk in Nepal are driven not only by the high rate of seismicity but also by the extreme vulnerability of structures and infrastructures. The percentage of building construction that could be considered to be earthquake resistant is negligible, whereas the overwhelming majority of buildings and structures indicate a high vulnerability (Chaulagain et al. 2013). The seismic loss estimation is done using a vulnerability model, which describes the probability distribution of loss ratio for a set of intensity measure levels. In this study, fragility functions used by NSET are adopted for adobe, brick/stone buildings with mud mortar, brick/stone buildings with cement mortar, and wooden buildings, while new fragility functions are used for reinforced concrete buildings (Chaulagain et al. 2015).

A single fragility function was developed during the formulation of Nepal National Building Code for seismic risk assessment in Nepal (BCDP 1994). However, this single fragility function (damage level vs ground acceleration) defining the potential damage did not differentiate different damage states at given of level of shaking. Due to this situation, Guragain (2011) modified the existing fragility functions of Nepalese buildings considering different damage states in the structure.

To this end, fragility functions for adobe and unreinforced masonry buildings in Nepal were developed using extreme loading for structures. The obtained analytical results have a good agreement with the experimental ones. For this, 17 cases of buildings with different configuration, material strength, number of stories, and mortar types were subjected to numerical simulations to calculate the probability of exceeding a number of damage states. The numerical analyses were performed at nine different levels of PGA starting from 0.05 to 1.0 g (Guragain 2011; Guragain and Dixit 2012).

The structural models for RC buildings are created considering the geometrical and material properties of Nepalese RC buildings (Chaulagain et al. 2013). The SPO2IDA framework developed by Vamvatsikos and Cornell (2006) was employed to convert static pushover curves into incremental dynamic analysis. SPO2IDA represents a tool that is capable of recreating the seismic behavior of oscillators with complex multi-linear backbones at almost any period. It provides a direct connection between the static pushover curve and the results of incremental dynamic analysis, a computer-intensive procedure that offers thorough (demand and capacity) prediction by using a series of nonlinear dynamic analyses under a suitably scaled suite of ground motion records. The results of the analysis are summarized into their 16, 50, and 84 % fractile IDA curves. It offers effectively instantaneous estimation of demands and limit-state capacities, in addition to conventional strength reduction R-factor and inelastic displacement ratios, for any SDOF whose SPO curve can be approximated by a quadrilinear backbone. The mean (μ) and standard deviation (σ) per damage state for each building typology are presented in Tables 5 and 6.

Table 5 The mean (μ) and standard deviation (σ) per damage state for each building typology, in terms of spectral acceleration at the yielding period (Ty) (Chaulagain et al. 2015)
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Table 6 The mean (μ) and standard deviation (σ) per damage state for each building typology, in terms of peak ground acceleration
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2.3.1 Consequence model employed to convert fragility curves into vulnerability curves

Vulnerability functions can be derived from fragility functions using consequence models, which describe the percentage of financial loss for a given level of performance or damage state (Silva et al. 2014b). The consequence models developed for Italy, Greece, Turkey, California, and Portugal are different. All these models have different damage scales, and each damage ratio is influenced by the damage level in the structure. In this study, each set of fragility functions is converted into a vulnerability function, through the employment of a consequence model. In this process, the percentage of buildings in each damage state is computed at each intensity measure level and multiplied by the respective damage ratio, thus obtaining a loss ratio for each level of peak ground acceleration or spectral acceleration. The consequence model used in the development of the vulnerability model for the Nepalese building stock is presented in Table 7.

Table 7 Consequence model used in the development of the vulnerability model for the Nepalese building stock
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2.4 Local site effects

Site conditions play a major role in establishing the damage potential of incoming seismic waves from major earthquakes. In the 1985 Michoacan (M s = 8.1) earthquake, only moderate damage was reported in the vicinity of the epicenter, while in Mexico City, located 350 km away, extensive damage was observed (Kramer 1996). In this earthquake, the bedrock outcrop motions were amplified about five times. In the 1989 Loma Prieta earthquake, major damage occurred on soft soil sites in the San Francisco–Oakland region, where the spectral accelerations were amplified two to four times over adjacent rock sites (Housner 1989) and caused severe damage. It shows that surface-level peak ground acceleration and spectral acceleration values can be different from bedrock values, depending on local soil conditions. In fact, shaking is stronger where the shear wave velocity is lower. Amplification of amplitudes of soil particle motion from vertically propagating shear waves occurring from bedrock depends on the type and geotechnical properties of overburdening soil. The soil type, pore water pressure, and the level of the water table are other significant site parameters.

The use of the average velocity of seismic shear waves in the top 30-m layer (Vs30) has become a very common standard to characterize seismic site conditions. The United States design code (BSSC 2001) specifically requires this measurement to represent the local site conditions. Similarly, the European design regulation (EC8—CEN 2004) also provides soil classification using this parameter. Moreover, many ground motion prediction equations (e.g., Atkinson and Boore 2006; Chiou and Youngs 2008), which are fundamental for seismic hazard and risk assessment, have been calibrated against seismic station site conditions, described with Vs30 values (Wald and Allen 2007).

In this study, the OpenQuake-engine (Silva et al. 2014c) uses ground motion prediction equations that require the definition of a Vs30 value for each location where the seismic hazard and risk are going to be computed. If such parameter is not available at a given location, the OpenQuake-engine uses the closest Vs30 value. The site effect in the present study is considered using the Vs30 map downloaded from the USGS Vs30 database. The spatial distribution of Vs30 values is presented in Fig. 4.

Fig. 4
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Vs30 map of Nepal (http://www.usgs.gov)

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3 Results

3.1 Seismic hazard

Probabilistic seismic hazard has been estimated in this study. As presented in Fig. 5, the estimated peak ground acceleration value (PGA in g) at 10, 5, 2, and 1 % probability of exceedance in 50 years is in the range of 0.22–0.50, 0.30–0.64, 0.42–0.85, and 0.51–1.07 g, respectively. In all the cases, the highest ground motions are observed in eastern parts and the mid-western region of the country, and lower values are observed in the southern Nepal.

Fig. 5
figure 5

Seismic hazard maps of Nepal showing the peak ground acceleration distribution with: a 10 % probability of exceedance in 50 years, b 5 % probability of exceedance in 50 years, c 2 % probability of exceedance in 50 years, and d 1 % probability of exceedance in 50 year

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The estimated values are consistent with some recent studies, about 0.50 g for 10 % probability of exceedance in 50 years in far-western Nepal obtained by Mahajan et al. (2010). Nath and Thingbaijam (2012) obtained peak ground acceleration values of 0.35–0.40 and 0.70–0.80 g for 10 and 2 % probability of exceedance in 50 years in eastern Nepal, respectively. However, the value is in the range of 0.70–0.80 g for 2 % probability of exceedance in 50 years in far-western Nepal. The obtained results are also similar to the values obtained by Bhattarai (2010), where PGA at rock and soil sites in the order of 0.29 and 0.39 g was estimated in eastern Nepal, both for 10 % probability of exceedance in 50 years. Pandey et al. (2002) estimated up to 0.50 g peak ground acceleration value in bedrock for 10 % probability of exceedance in 50 years. Parajuli (2009) estimated the peak ground acceleration corresponding to 40, 10, and 5 % probability of exceedances in 50 years. The result showed that eastern and far-western regions may experience bigger peak ground accelerations than in central regions. Moreover, Thapa and Guoxin (2013) calculated peak ground acceleration in bedrock with 63, 10, and 2 % probability of exceedance in 50 years. The estimated PGA values are in the range of 0.07–0.16, 0.21–0.62, and 0.38–1.10 g for 63, 10, and 2 % probability of exceedance in 50 years, respectively.

3.2 Uniform hazard spectra

Traditionally, PGA has been used to characterize ground motion. However, in recent years, the preferred parameter has been the spectral acceleration (S a) for the fundamental period of vibration. For finding uniform hazard spectra (UHS), seismic hazard curves of spectral acceleration are computed for a range of frequency values. From these hazard curves, response spectra for a specified probability of exceedance over the entire frequency range of interest are obtained. The uniform hazard spectra with 10, 5, 2, and 1 % probability of exceedance of earthquakes in 50 years for six different places in Nepal is plotted in Fig. 6. It indicates that the values are higher in mountainous districts. The maximum spectral acceleration for Biratnagar, Kathmandu, and Pokhara sub-metropolitan city are 0.70, 0.67, and 0.66 g, respectively, occurring for 475 years return period. In Lamjung district, the spectral acceleration for 10 % probability of exceedance in 50 year is 0.97 g, which is around 40 % higher than the Kathmandu, Biratnagar, and Pokhara sub-metropolitan city. The expected spectral acceleration value in Kathmandu for the 2475 years return period is 1.38 g. These results are similar to the values proposed by Bhattarai (2010).

Fig. 6
figure 6

Uniform hazard spectra in 5 % damping at different locations in Nepal: a Biratnagar sub-metropolitan city, b Kathmandu metropolitan city, c Pokhara sub-metropolitan city, d Panchthar, e Lamjung, and f Rukum district

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3.3 Seismic risk

Using the set of loss exceedance curves for each asset, a mean loss map for 10, 5, 2, and 1 % probability of exceedance in 50 years is computed and presented in Fig. 7. The estimated economic losses in Nepal are mostly concentrated in the Kathmandu Valley and southeast region of Nepal. Despite the moderate seismic hazard in the Kathmandu Valley and southeast region, significant economic losses are still expected, owing to the presence of large number of brick and stone buildings in medium-to-soft soils. As for example in soft soil, spectral acceleration can be amplified by a factor of 1.5 for short periods and by 2.0 for longer periods (Steward et al. 2015). In the Kathmandu Valley, the losses are 8.3, 8.2, 7.6, and 6.7 billion euro, respectively, which is around 15 % of the total economic value in the whole country. The disaggregation of the economic losses according to the building typology indicates that the brick and stone masonry buildings are responsible for more than 50 % of the losses, which is a predictable scenario considering the large proportion of this type of construction in Nepal (44.21 %), associated with its high seismic vulnerability.

Fig. 7
figure 7

Economic loss map of Nepal: a with 10 % probability of exceedance in 50 years, b with 5 % probability of exceedance in 50 years, c with 2 % probability of exceedance in 50 years, and d with 1 % probability of exceedance in 50 years

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3.4 Earthquake loss estimation for historical earthquake scenario

The distribution of building damage and corresponding economic losses due to the recurrence of the 1934 Bihar–Nepal (8.2 M w) earthquake is presented in this section. The scenario epicenter was assumed in the same location as that of the 1934 earthquake. The damage pattern of each building typology is determined using OpenQuake-engine which is capable of estimating the distribution of buildings in each damage state due to the occurrence of a single event (Silva et al. 2014c). The estimated damage pattern of each building typology in Nepal is tabulated in Table 8.

Table 8 Damage states of buildings in Nepal
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As presented in Fig. 8, it can be seen that about 22 % of adobe, 9 % of BM/SM, 7 % of BC/SC, and 8 % of CCP buildings would collapse due to the recurrence of the 1934 scenario earthquake. The collapse would be limited to 7, 5, 2, and 2 % for NBC, NBC+, WDS, and W buildings, respectively. The result also indicates that about 282,450 masonry buildings would collapse due to the recurrence of 1934 scenario earthquake, which follows the similar trends of Kashmir (M w = 7.6; 2005) and Java (M w = 6.3; 2006) earthquakes (Meguro 2008).

Fig. 8
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Building damages due to earthquake scenario in Nepal

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The structural and financial loss due to the 1934 scenario earthquake are mostly concentrated in the eastern half of the Nepal (see Fig. 9). The total financial loss is about 13 billion euro, which is about 70 % of Nepalese gross domestic product (GDP) in 2013. The economic loss in the Kathmandu Valley is about 2.5 billion euro which is about 20 % of the total loss.

Fig. 9
figure 9

Total building collapse map and economic loss map due to the repetition of the 1934 historical event

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4 Conclusions and recommendations

This study estimates the higher seismic hazard in the mid-western and eastern parts of Nepal, whereas the southern Nepal has the lowest seismic hazard. The expected peak ground acceleration at 10, 5, 2, and 1 % probability of exceedance in 50 years is in the range of 0.22–0.50, 0.30–0.64, 0.42–0.85, and 0.51–1.07 g, respectively. Similarly, the results also indicate that Biratnagar sub-metropolitan city, Kathmandu metropolitan city, and Pokhara sub-metropolitan city have spectral acceleration of 0.70, 0.67, and 0.66 g, respectively (for 475 years returns periods).

About 22 % of adobe, 9 % of BM/SM, 7 % of BC/SC, and 8 % of CCP buildings would be collapsed resulting from the recurrence of 1934 scenario earthquake. From these results, it can be seen that about 14 % of the buildings would experience the extensive damage, whereas the overall collapse of building would be limited to 7 % only. The trends of building damage indicate that the brick and stone masonry buildings are liable for more than 50 % of the losses, which is a predictable scenario considering the large proportion of seismically vulnerable construction in Nepal. The total economic loss would be about 13 billion euro, which is about 70 % of Nepalese gross domestic product (GDP) in 2013. The results are similar to the earthquakes of Haiti (2010), Guatemala (1976), Nicaragua (1972), and El Salvador (1986) that caused economic losses of approximately 120, 98, 82, and 40 % of the normal gross domestic product (GDP) of each country, respectively (Daniell et al. 2010). All the structural and financial losses of the building structures are mostly concentrated in the eastern half of Nepal.

The results of this study are useful for national state, local governments, decision makers, engineers, planners, emergency response organizations, builders, universities, and the general public, who require seismic hazard and risk estimates for land-use planning, improved building design and construction, emergency response preparedness plans, economic forecasts, housing and employment decisions, and many other types of risk mitigation.