Vulnerability is a multidimensional aspect, and it cannot be integrated into a single variable (Cutter and Finch, 2018; Contreras et al., 2020). There are many social vulnerability parameters that determine the impact of natural hazards such as socioeconomic status, geographical features, ethnicity (minority), home ownership/rental status, gender, and age (Burton and Silva, 2016). These intensify the impact of earthquakes; for instance, some people are privileged with social advantages, while some succumb to poverty and discrimination. The households with better economic status can recuperate from disasters better than low-income households (Mileti, 1999). Similarly, there is a lethargic pace in developmental activities, and the situation is aggravated by the centralized development only in the capital city, Kathmandu. As a result, people are obliged to work overseas, especially in Gulf countries, for employment opportunities owing to poverty (Aksha et al., 2019). In addition to it, ethnicity also creates barriers in distribution and access to financial resources after disasters (Cutter et al., 2003). Nepal is home to a wide number of caste and ethnic identity groups facing deep structural marginalization (Pherali, 2016). The diverse indigenous communities experience economic, social, and political marginalization and annexation of infrastructure and financial resources (Mishra et al., 2015). A significant number of minorities, females, and dependent age groups are more vulnerable (Borden et al., 2007). Furthermore, another group of vulnerable populations are renters because, in comparison to the homeowners, renters are financially unprepared for the recovery (Burby et al., 2003). Likewise, the topography of Nepal is also a hindrance to distributing relief materials to the affected regions in time which exacerbates the impact of natural hazards. There are three geographical regions in Nepal: the Terai, hilly, and Himalayan regions covering 24 %, 42 %, and 34 % of the total area, respectively. The flat, arable Terai plain region contains 50 % of the total population. The hilly region is basically situated in the south of the mountain region, which is less developed than the Terai region. However, the densely populated and highly urbanized cities of Kathmandu and Pokhara lie in the hilly region. The mountain region is characterized by severe climatic and rugged topographic conditions with limited economic activities and human habitation.

Earthquake risk assessment is the combination of the exposure model, structural vulnerability, and seismic hazard analysis. Generally, the exposure model represents assets like buildings and population (Silva et al., 2020). In this study, the fundamental exposure data include building typologies and district-wide distribution of buildings. Likewise, the structural vulnerability function resembles expected loss at a given ground motion intensity level which can be derived either by empirical methods or by combining fragility and consequence functions (Martins et al., 2021). Using empirical methods vulnerability is derived in the form of losses from past events at given locations corresponding to the levels of intensity of ground motion. Fragility functions are defined by the probability of exceeding a set of limit states at a given intensity measure level (Gómez Zapata et al., 2021). These functions can be derived empirically or analytically or by modeling the asset behavior at increasing ground motion levels. Likewise, consequence functions are defined by the probability distribution of loss at a given performance level (Pagani et al., 2014).

The seismic hazard curve describes the annual probability of exceeding a specified ground motion level. The probabilistic approach can be used to derive hazard curves. This approach involves (a) delineation of seismic sources and their characteristics, (b) determination of regional seismicity, (c) use of the appropriate ground motion equation, and (d) combination of probability in terms of size, location, and ground motion parameter. There is abundant research on seismic hazard analysis in Nepal which uses various source typologies and characteristics. For instance, Stevens et al. (2018) used a mix of fault and area source models – in total six seismic sources with the Gutenberg a and b values along with maximum magnitude estimated for each source zone. Among the sources used in Stevens et al. (2018), the Main Himalayan Thrust is the principle seismic hazard source in Nepal, which is a huge, shallow-dipping reverse fault capable of producing the largest earthquakes. Similarly, Pandey et al. (2002) divided the whole Nepal region into 10 area sources and 24 fault sources. Thapa and Guoxin (2013) divided the Nepal region into 23 seismic source zones. Chaulagain et al. (2016) also used the same sources to carry out a seismic risk assessment. Similarly, selecting the ground motion prediction equation is one of the important steps in seismic hazard analysis, which governs the propagation of seismic ground motion from seismic source to site in terms of magnitude, distance, depth, and other site parameters (Cornell, 1968). However, in the context of Nepal, there are insufficient strong ground motion records to derive a precise equation capturing the actual response spectrum. On top of that, very little research has been conducted in terms of attenuation relationships in Nepal. Previous studies like Chaulagain et al. (2015) and Stevens et al. (2018) have used a combination of ground motion prediction equations (GMPEs) within the logic tree. The past seismic hazard analyses (Stevens et al., 2018; Chaulagain et al., 2015; Thapa and Guoxin, 2013) have produced a varying range of seismic hazard analyses of Nepal. According to Stevens et al. (2018), in the large part of Nepal, the accelerations in the range of 0.4–0.6 and 1.0–3.0 g may be expected for 10 % and 2 % probability of exceedance over a 50-year period, respectively. Chaulagain et al. (2015) evaluated the estimated PGAs (in g) at 10 % and 2 % probability of exceedance in 50 years in the range of 0.22–0.5 and 0.42–0.85 g, respectively. Thapa and Guoxin (2013) estimated the PGA at 10 % and 2 % probability of exceedance in 50 years in the range of 0.21–0.62 and 0.38–1.1 g, respectively.

The social vulnerability index (SoVI) method was originally formulated by Cutter et al. (2003), and this index provides a comparative metric depicting an area's relative social vulnerability to hazard. Social vulnerability helps to explain the reason behind the difference in consequences in communities even though they are subjected to similar levels of ground shaking (Burton and Silva, 2016). We identified the meaningful variables incorporating the socioeconomic and physical context of Nepal. Moreover, to describe the vulnerability at the municipality and VDC level in Nepal, we computed a modified SoVI.

The classical Probabilistic Seismic Hazard Analysis (PSHA)-based risk calculator was performed to calculate the annual average loss using OpenQuake. This calculator combines numerical integration, physical vulnerability functions of the assets, and seismic hazard curve at the location to calculate the loss distribution for the asset within a specified time period (Pagani et al., 2014). The calculator requires an exposure model describing the distribution of building typologies, physical vulnerability functions for each building type, and hazard curves calculated in the region of interest. The hazard curves required were also calculated using the OpenQuake engine using the classical PSHA approach. For hazard curve derivation, a source model and ground motion prediction were inputted in the OpenQuake engine. Finally, the value of annual average loss (AAL) for each VDC and municipality was rescaled into the range between 0 and 1 using min–max rescaling (Eq. 1).

An integrated risk index was constructed by combining the social vulnerability index and estimates of average annual loss in rescaled metrics. The framework or workflow of the integrated risk assessment is shown in Fig. 8. The first step in Fig. 8, seismic hazard, was evaluated using the probabilistic approach. The geographic features represent exposure modeling for residential buildings and their physical vulnerability. By combining these parameters, seismic risks were evaluated in terms of average annual loss (AAL), which was further recomputed by using the min–max rescaling method. The physical vulnerability and exposure model interact with the social and economic parameters or overall capacity of the population to sustain hazards (Burton and Silva, 2016). The social features define socioeconomic parameters related to the demographic population to prepare for, react to, and recuperate from damaging events (Burton and Silva, 2016). The integrated risk is the combination of physical risk and a set of contextual and social vulnerability conditions (Carreño et al., 2012). In this regard, the integrated risk was evaluated based on direct factors or physical risk and socioeconomic factors. The integrated risk index (RT) was calculated using Eq. (3): 3RT=Rf(1+F). Moncho's equation (Eq. 3) was used to evaluate convoluted risk, where Rf is a physical risk index or average annual loss estimate, and F is a social fragility index or aggravating coefficient (Glorfeld, 1995). This technique and its successful application can be found in numerous studies due to its simplicity and successful applications (Burton and Silva, 2016; Carreño et al., 2012; Khazai et al., 2013; Fernandez et al., 2006). The calculated integrated risk was evaluated using the OpenQuake Integrated Risk Modeling Toolkit (IRMT). The IRMT is a plugin developed by the GEM Foundation and available in the QGIS open-source platform that allows a composite framework to be built to assess physical risk and social characteristics that affect the earthquake risk. The diagrammatic workflow of social and physical risk indicators developed by OpenQuake IRMT is shown in Fig. 9. The integrated toolkit involves details from the selection of indicators to the detailing and mapping of composite risk assessment.

The results of social vulnerability analysis are shown in Fig. 10, which depicts the distribution of total SoVI scores across the country. SoVI scores for each district provide relative comparison within the districts' subdivision units. The districts mapped with darker red shades demonstrate higher rates of social vulnerability. It can be seen in Fig. 10 that there is a higher degree of risk in the far-western region hosting places like Godawari and Deukhuri. This region is one of the most rural areas of Nepal with nominal availability of infrastructure. The results also illustrate that the Terai region with cities like Janakpur and Biratnagar shows a higher level of social vulnerability. These cities may be at greater risk as a result of infrastructure exposure. On the other hand, the central and eastern regions of Nepal with the cities of Kathmandu, Pokhara, and Hetauda are comparatively at lower risk. The social vulnerability map of the country demonstrates higher levels of social vulnerability in rural areas with few exposed assets and industrial areas with exposure of infrastructure, whereas the lowest levels of social vulnerability are in urban and populated cities like Kathmandu, Pokhara, and Hetauda.

To further explore the overall social vulnerability observed in Fig. 10, we generated the maps of sub-components: housing unit, population, health, education, and the economy, as shown in Fig. 11. Figure 11a shows that highly vulnerable areas under the housing unit category are concentrated in the far-western hill and eastern Terai regions. The houses in rural areas are highly vulnerable due to their old age and lack of amenities like retrofitting and repairing. The population component (Fig. 11b) exhibits a high level of vulnerability in Kathmandu, Janakpur, and some parts of the far-western region. There is a dense population and unorganized urbanization in Kathmandu, whereas the far-western region hosts minorities and an old-age population. Under the health component (Fig. 11c), there is an intense degree of vulnerability in the Terai region and the hilly parts of the far-western region. These regions have the least access to health facilities. Similarly, the education component (Fig. 11d) reveals great vulnerability in the eastern Terai region. The economy component (Fig. 11e) shows a very high degree of vulnerability in the mid-part of the far-western region and the Terai region. There is a high level of vulnerability in the far-western region of the country due to the prevalence of a higher number of minorities, illiteracy rate, nominal infrastructural access, and poor economic status.

The probabilistic seismic hazard analysis was carried out, and then the physical risk estimations were made, as shown in Fig. 12. The physical risk in terms of average annual loss (AAL) index obtained from the risk analysis was classified into five quintiles from very low (<-1.5 standard deviation) to very high (>1.5 standard deviations) vulnerability. Figure 12 shows the distribution of AAL per capita in monetary terms, and Fig. 13 shows the distribution of the seismic risk index across the country. The null regions in the maps represent the areas which are national parks and wildlife reserves with nominal population. From Fig. 13, it is observed that the Terai region, especially the eastern Terai and central Terai regions, lies in a higher seismic risk category. Kathmandu Valley also lies in a very high-risk category. Contrary to social vulnerability, the western part of Nepal lies in the lower AAL value region.

Social vulnerability shows the intensity of the impact of any disaster. When combined with the impact of seismic action, the true nature of the distribution of seismic risk becomes evident. As shown in Fig. 14, the integrated risk is higher in the Terai region in cities like Janakpur and Biratnagar. Kathmandu region has a low SoVI index but a high integrated risk index. Similarly, the far-western hills and the mountain region are found to be low-risk regions even though they have a high SoVI index. However, due to their high social vulnerability, these regions should still be depicted as a concern. Despite having a low number of houses, the houses may be of lower quality, which are likely to suffer damage from even low-magnitude earthquakes, and these regions may not have enough resources for mitigation measures. On top of that, even though they are in low-seismic risk-regions, the respective population may be at high risk from other disasters like a landslide, flood, glacier, or other weather conditions.

In this paper, the objective of the social vulnerability assessment was to quantify the vulnerability in Nepal considering socioeconomic parameters at the local level. The results of social vulnerability show that the most socially vulnerable places are located in the far-western, eastern Terai, and western Terai regions of Nepal. Our findings exhibit differences in social vulnerability in areas located in the same ecological region. The main reason behind this could be the pre-existing conditions like infrastructures, education, economy, etc. The population in the far-western region and the eastern Terai region are mostly minorities, Dalits, and marginalized groups who are educationally disadvantaged and developmentally challenged (Gautam, 2017). As for mountainous and hilly areas in the far-western region, the geographical terrain has affected the development path of these areas. Aksha et al. (2019) and Gautam (2017) also found a similar vulnerability in their respective studies. However, Aksha et al. (2019) classified Kathmandu Valley as a high-vulnerability class, while Gautam (2017) classified it as a very low-vulnerability class. Our social vulnerability result agreed with the latter case. This variability in the result is due to differences in variables and hazards considered during the analysis. Moreover, more recent data for SoVI will depict the more exact status of society and its vulnerability to disaster. This study uses census data from 2011. And, the census is done every 10 years in Nepal, and the most recent census was held in 2021. However, data from 2011 were considered due to the unavailability of recent comprehensive data. More recent data can be used in future studies once the 2021 Nepal census is published and made available.

The objective of physical risk assessment in this study was to evaluate the physical risk index using a probabilistic approach. As in Burton and Silva (2016), the classical PSHA risk-based calculator was used to assess loss exceedance curves, risk maps, and average annual loss. In this study, a probabilistic approach and region-specific steps were used to evaluate the seismic hazard curves as in Chaulagian et al. (2015).

The probabilistic method of estimating seismic hazards used in the study utilizes the Poisson distribution model. Although earthquakes are assumed to occur randomly in space and time, the Poisson model assumes that earthquakes make a stochastically independent sequence of events in space and time (Anagnos and Kiremidjian, 1988). Despite such counterintuitive characteristics, the Poisson model is widely used due to its simplicity in the formulation and smaller range of parameters to be estimated. Moreover, recent research (Weatherill et al., 2015; Schiappapietra and Douglas, 2020) in seismic risk assessment has incorporated spatially correlated distribution not only to estimate simultaneous intensity measure levels at locations during a specific earthquake but also to quantify the correlation between locations. The present studies have suggested the modeling of the spatial correlation of earthquake ground motion since attenuation of ground motion is not only period-dependent but also regionally dependent. However, in our study, we have used the conventional method of probabilistic seismic risk assessment due to its simplicity. Nonetheless, a certain standard approach is necessary to evaluate comparable estimates of seismic hazards. Moreover, the authors are aware of the fact that numerous estimations such as casualties, non-structural damage, business interruption loss, and loss of critical infrastructure may improve the indicator of physical risk. However, only the economic losses of buildings were utilized in this study as an initiation for this type of research for Nepal. Similarly, the results of physical risk (average annual loss estimates) were rescaled using the min–max method as mentioned in previous sections. The rescaling is necessary to integrate social vulnerability with physical risk, although the rescaling of the estimates may have resulted in the loss of spatial information of physical damage results.

The integration and mapping of the spatial distribution of average annual losses and social vulnerability are very useful. However, the integrated maps do not reflect the true effect of components inducing seismic risk at a particular location. This can be due to the compounding nature of the spatial risk as the areas of medium to high levels of social vulnerability compound moderate levels of physical risk to generate high levels of integrated risk. The medium level of social vulnerability in the eastern Terai region is compounded with the high level of physical risk to create a higher level of integrated risk, which can be seen in Fig. 14. On the other hand, there is a higher degree of seismic risk and integrated risk in Kathmandu Valley, although the social vulnerability results depict a lower degree of vulnerability. In light of the limitations of this study, it is clear that robust procedures and methods should be used in future analyses of integrated risk assessment. Although this study has certain shortcomings, it is within the context that the inclusion of a higher number of factors that contribute to the mitigation of earthquake risk provides better approaches in the development of policy and plans to reduce overall seismic risk.