Risk assessment of people trapped in earthquake based on km grid: a case study of the 2014 Ludian earthquake, China

ABSTRACT China is one of the most earthquake-prone countries in the world. The highest-priority mission after an earthquake is to rapidly save lives, and to minimize the loss of life. Rapid judgment of the trapped personnel location is the important basis to identify the emergency supply demands and carry out the search and rescue work after the earthquake. Through analyzing the main influencing factors, we constructed an assessment model of people trapped in collapsed buildings caused by the earthquakes. The accuracy of the estimation results from the model was then tested against the actual investigation data in 2014 Ludian earthquake-hit area. Results showed that, the trapped personnel distribution assessed by this model is generally concordant with that obtained by the actual survey in Ludian earthquake. The grid-based assessment of people trapped in earthquakes can meet the requirements of key search and rescue zone identification and rescue forces allocation in the early stage of earthquake emergency. Although there were some limitations in the study, it offers a simple and rapid approach for assessing the trapped people losses based on basic empirical data. The approach can be further improved to provide more information and suggestions for earthquake emergency search and rescue.


Introduction
Earthquakes are among the most feared and destructive of all natural disasters. Unlike many other types of natural disasters, earthquakes pose a significant threat to society because there is no existing warning system available for earthquakes (Geller 1997). The gravity of the hazard presented by earthquakes on the welfare of human society has prompted an earnest concern from governments, as well as scientists. One of the most feasible and effective strategies to reduce social and economic losses caused by earthquakes is to mitigate the vulnerability of society to seismic hazards based on an accurate and scientific risk assessment (Tantala et al. 2008). A primary validation to estimate earthquake risks is the estimation of the spatial distribution of casualties, following which search and rescue (SAR) and other emergency response activities can be prioritized and rationally coordinated (Erdik et al. 2014). This casualty estimation is essential to the entire post-earthquake rescue operation, and it is thus essential to develop methods that can obtain this information as quickly as possible (Feng et al. 2013).
In the last two decades, researchers have attempted to estimate earthquake casualties and losses at local and regional levels and have subsequently proposed various approaches depending upon the CONTACT Benyong Wei bywei1982@163.com type of available data, spatial applicability, and modelling principles (FEMA 2003;Hancilar et al. 2010;Furukawa et al. 2010;Jaiswal et al. 2011;CAPRA 2012;Ara 2014;Su et al. 2015). For instance, Coburn and Spence (2002) considered five factors-the population per building, occupancy time, number of occupants trapped, mortality at collapse, and rescue efficiency-in order to generate a post-earthquake casualty prediction model. Badal et al. (2005) employed a quantitative model that includes a correlation between the earthquake magnitude and the number of lives lost to assess earthquake losses and damages as a function of the population density. Aghamohammadi et al. (2013) proposed a backpropagation neural network method in order to model and estimate the severity and distribution of human loss as a function of building damage during an earthquake disaster. Feng et al. (2013) developed a model that rapidly estimates the number of casualties based upon the attributes of damaged buildings using satellite remote sensing. By relating fatality rates to the damage rates of different classes of buildings present within the local building stock, So and Spence (2013) were able to propose a global casualty estimation model in order to measure shakinginduced casualties and building damage for global earthquake events. Ara (2014) used building-specific human vulnerability curves developed by the Central American Probabilistic Risk Assessment to obtain possible loss of life estimates. Huang et al. (2015) proposed a robust wavelet v-support vector machine earthquake casualty prediction model. By amalgamating remote sensing data and building-relevant local knowledge, Su et al. (2015) was able to propose an integrated method for the largescale estimation of seismic loss hazards to buildings. As part of a miscellaneous research investigation, Shapira et al. (2015) integrated epidemiological with engineering approaches in the assessment of human casualties resulting from earthquake activity and indicated that the integration of demographic and socio-economic characteristics for the population, as well as levels of medical preparedness into casualty estimation models, may improve their accuracy. Park et al. (2016) estimated the number of casualties related to a given earthquake scenario by combining structural damage estimates with spatiotemporal behaviour patterns that were assessed using a daily time-behavioural survey in Ulsan, Korea. Most recently, Corbane et al. (2017) performed a seismic loss risk assessment at a pan-European level with an open access methodology and using open data-sets available across the European Union (EU). On the whole, available earthquake casualty estimations can be classified into three distinct categories based upon their relative approach: empirical, semi-empirical, and analytical. The empirical approach consists primarily of simple correlations of casualties inflicted upon the populace exposed to an earthquake with the estimated seismic ground-shaking intensity. The semiempirical approach estimates damage rates for different building types in the study area and subsequently demonstrates a relationship between the casualty rates and each type of building. Finally, analytical methods predict the behaviour of buildings during earthquake activity, and therein determine the effects of quakes on people who are within those buildings in the course of seismicity. This method does not take into account the behaviour of non-engineered buildings in earthquake-prone areas of the world where the impact of seismic hazards on humans is extensive (Spence and So 2009;Jaiswal et al. 2011).
China is one such region that is frequently affected by detrimental earthquakes, the effects of which carry the potential for devastation across most of its territory. Recently, several destructive earthquakes have struck mainland China and have incurred enormous casualties and losses, including the 2008 Wenchuan earthquake, 2010 Yushu earthquake, 2013 Lushan earthquake, and 2014 Ludian earthquake. Although the available emergency management services during earthquake disasters have improved markedly, the general efficiency and effectiveness of earthquake relief is still relatively low throughout China (Huang et al. 2015). This poor efficacy can be most fundamentally attributed to the difficulty involved in the prediction of the number and specific location of earthquake-related casualties. This represents the foremost and critical issue that results in the delayed reaction of earthquake emergency management. The highest-priority mission during the aftermath of an earthquake is to rapidly save lives, and therein to minimize the loss of life. The reduction of casualties in an area immediately following an earthquake could be improved if the location and number of trapped people in damaged buildings could be rapidly assessed (Erdik et al. 2014).
In the case of China, many studies have been performed to assess the loss of life resulting from an earthquake disaster (Li 1987;Wu et al. 2011;Ma and Xie 2000a). Li et al. (2014) classified the available casualty estimations for earthquakes into three primary approaches: the empirical model, which is based on the simple relationship between earthquake parameters (i.e. magnitude and intensity) and mortality rate; the building damage probability matrix (DPM) model, which is based on damage rates for different building types during historical earthquakes; and the vulnerability model, which is based on anti-seismic performance. Since the rescue of human life is the fundamental obligation of an earthquake emergency management response team, several researchers have begun to provide attention toward the estimation of people who are trapped inside a collapsing or collapsed building caused by an earthquake in China. For example, Xu et al. (2008) predicted the possible number of trapped people during different periods of time within different urban blocks of Zhangzhou city (Fujian Province, China) based on an empirical model of casualty estimation. Xiao et al. (2009) assessed the number of primary and secondary school students trapped during the Wenchuan earthquake based on the rate of indoor occupancy and collapse rate. More recently, Yu et al. (2015) presented an empirical assessment model of people who are trapped during an earthquake disaster that considered specific influencing factors on the trapped rate within the model by providing the influencing coefficients of these factors. However, these previous studies concerning earthquake casualties or the number of people trapped chiefly focused on the estimation of the mortality rate or trapped rate, and they were unable to account for factors related to the human response (e.g. personal protection actions). The estimation of casualties or the number of people trapped as a result of earthquakes also requires the addition of social science contributions that can help to understand and thus constrain casualty outcomes . Additionally, the potential impact of large earthquakes on societies can be reduced by timely and appropriate action following a disastrous earthquake. Earthquake casualties can also be significantly reduced by permitting the rapid and effective deployment of emergency operations (Erdik et al. 2014). However, the actual available information of a disaster is very limited during the early stages of a destructive earthquake, with the exception of the earthquake magnitude, intensity, etc. Therefore, the development of a method established upon these basic hazard parameters and available local social-economic information that can rapidly determine the location and number of people trapped in an earthquake is an essential issue toward improving SAR operations.
Considering all of the aforementioned, this study has constructed an assessment model of people trapped in earthquakes (hereafter known as the PTE model) through an analysis and summary of the main factors affecting the distribution of people trapped by collapsed buildings during earthquakes. As a case study, we assessed the distribution of people trapped during the 2014 Ludian earthquake using the constructed PTE model based on kilometre grid data. Finally, we evaluated the accuracy of the estimation results obtained from the PTE model through a comparison with that from the actual investigation. Finally, we also discussed the limitations of the PTE model employed within this study and stipulated suggestions for future research.

Primary causes for people trapped in earthquakes
It is now widely recognized that the number of deaths related to shaking during an earthquake is closely related to the quantity of buildings that fully or partially collapse during the seismicity (Yin 1996;Ma and Xie 2000b;Lu et al. 2003;Bai 2006;So and Spence 2013). Previous work has established that the collapse of buildings, as well as earthquake-induced secondary geological disasters (e. g. landslides and debris flows), are all significant causes for people to become trapped during earthquakes, but the collapse of building structures during seismic activity is the most important (Wang et al. 2009;Marano et al. 2010). The number of people trapped during earthquakes is decidedly dependent upon such factors as the ground shaking intensity, the number of buildings affected at a particular intensity, the structural damage rate, the occupancy rate, and the response action. Overall, the factors that instigate the trapping of people within collapsed buildings as a consequence of earthquakes can be divided into four aspects: the scale of the earthquake hazard, building vulnerability, population exposure, and human response.

Scale of earthquake hazard
One of the primary descriptors for building damage is the site-specific scale of the earthquake hazard, which indicates the scope of the impact of the earthquake as well as the degree of earthquake damage. It can usually be expressed by a select few parameters, such as the earthquake magnitude, seismic intensity, focal depth and peak ground acceleration (PGA), among others. Because the seismic intensity can more precisely indicate the damage following seismicity than the other parameters, and can be assessed immediately following an earthquake, most estimations regarding earthquake disaster loss and building damage are all based on the shaking intensity.

Building vulnerability
Building vulnerability represents the probability of a specific building's situation (i.e. the amount and type of damage) following the impact of seismic ground acceleration, and is a probability-based method for analyzing structural anti-seismic performance. Whether a building will collapse during an earthquake is highly related to the building vulnerability. Multiple factors, such as the building age, number of floors, seismic protection code, structure type, anti-seismic measures, and occupancy types, all possess an important influence on the building vulnerability. At present, numerous methods have been developed to assess building vulnerability in China (Zhang 2007;Wu et al. 2012;Su et al. 2013). Among these methods, the earthquake damage index (EDI) and building DPM are the two most commonly utilized. The EDI is a non-dimensional index used to assess the degree of damage of an engineering structure or component following an earthquake disaster, and it is typically applied to examine the earthquake disaster loss for a single building. Alternatively, the DPM is an important tool for describing the damage probability distribution of architectural groups under different earthquake intensities, and is based upon previous statistical earthquake disaster data. It generally indicates the comprehensive anti-seismic performance of one structural type of building in a city or region. Due to the concise and practical characteristics of the DPM, increasing amounts of studies have been choosing DPM as the tool to assess the vulnerability of buildings (Yin 1995;Hu 2007;Zhang et al. 2010;Sun and Zhang 2012).

Population exposure
The accurate estimation of population exposure is a key component for the approximation of the human loss of life (Chen et al. 2004;Aubrecht et al. 2012). In a densely populated urban area, the distribution of people depends on the time of day as a consequence of daily human routines (Ara 2014). The population distribution and density are very different during the daytime as opposed to the night-time. Researchers have consequently recognized that it is incredibly important to assess human loss of life throughout the temporal cycles of a day . Alexander (1996) concluded that the risk of injury varies significantly between night and day when an earthquake occurs. Ara (2014) analyzed the impact of the temporal population distribution on earthquake loss estimation in Sylhet, Bangladesh, and discovered that there is a high positive correlation between the spatiotemporal distribution of population and the potential number of casualties. More recently, Park et al. (2016) found that the estimated casualties reach a maximum value when the indoor population is maximized, which usually falls between 2 am and 4 am. Li et al. (2001) divided the occupancy type of buildings into four categories to estimate the number of casualties for an earthquake disaster in China. Cheng (1993) and Xiao et al. (2009) used a probability method to study the effects of a temporal population distribution on earthquake casualties in urban and rural areas of China. To assess the human loss of life due to earthquakes, Tian (2012) studied the changes of population distribution and density at different times of day in the Sichuan and Yunnan Provinces. In summary, factors, including the time of day, presence of a holiday, the occupancy type, weather, population structure, and occupation, influence the population distribution and density, and, therefore, also impact the number of casualties or people trapped in damaged buildings following an earthquake. It is therefore necessary to take these factors into account in order to achieve a realistic assessment of human loss of life as a consequence of an earthquake.

Human response
The human response is an important component for the estimation of casualties resulting from earthquake disasters, as it has to potential to either increase or reduce the loss of life. Numerous societally dependent variables are related to the human response, including personal protection actions and building egress rates, rescue and emergency medical capabilities ). Due to the complexity and limitation of available data, the variables related to the human response were rarely accounted for in previous research regarding casualty estimations. According to statistical data of past earthquakes, roughly 85%-90% of victims who survived an earthquake disaster escaped through self and mutual rescue measures (Xiu 2004;Li 2006;Qu et al. 2010). In fact, it appears that occupants who are trapped under heavily damaged structures are essentially doomed if they cannot otherwise escape by themselves, or if they are not extricated within a narrow time frame (Ohta et al. 2004). Therefore, it is very necessary to take the variables related to the human response into account in order to minimize the loss of life in earthquakes.

PTE model
In this paper, the PTE includes all of the deaths and injuries, as well as the people who are not in immediate danger but cannot readily escape from a collapsed building. Based on the above analysis of the influencing factors for the estimation of the number of people trapped, we construct an assessment model for the trapped personnel distribution in earthquakes (i.e. the PTE model), as follows: where the variables are defined as follows: B peop is the number of trapped people in an earthquake; R d is the average population density per building area in an assessment unit; P(t) is the average occupancy rate (the proportion of the resident populace who are actually inside the building at the time t of the earthquake) in the damaged building; B s is the total area of the s structural-type building exposed to the earthquakes within an assessment unit; L s (I) represents the collapse rate (the proportion of the collapsed buildings) of the s structural-type buildings at a particular shaking intensity I, based on the Chinese Seismic Intensity Scale (SAC 2008); and d is the rate of self-aid and mutual aid (SAMA; i.e. the proportion of the people who can escape from a damaged building by themselves or through mutual aid) following the earthquake.
This model takes into account the effects that earthquakes have on different building structural types as well as people who are trapped according to a scale combining the earthquake intensity or hazard (I), building vulnerability (B s , L s ), population exposure (R d , P(t)) and human response level (d). In this model, we used the ground shaking intensity as the parameter of the seismic hazard based on the Chinese Seismic Intensity Scale (SAC 2008). Because seismic loss assessment practices are either pre-or post-earthquake in mainland China, currently available DPMs are still based on seismic intensity, e.g. the baseline DPMs for different regions developed by Yin (1995). No PGA-based DPMs are currently available to analyze seismic losses of buildings in groups in mainland China (Su et al. 2015). Thus, we additionally used the shaking intensity as an earthquake hazard parameter, and we chose intensity-based DPMs to assess the extent of damage of structural buildings. Generally, building damage grades can be divided into five categories in China: good (including no damage), light damage, moderate damage, heavy damage, and severe damage (Yin 1996). It is difficult to accurately determine the collapse rates among different building damage grades due to the limitation of historical earthquake data. Preliminary investigations have showed that the trapping of people during earthquakes has mainly been caused by severely damaged buildings (Yin 1996;Ma and Xie 2000a). Therefore, the severe damage rate of different structural buildings at a particular intensity can be considered as its collapse rate.
Additionally, earthquakes can potentially occur at any time of day. Due to human activities, the distribution of people substantially depends on the time of day, occupancy rate and type, whether it is a holiday, the weather, population occupation, etc. At present, there are two primary methods employed to determine the occupancy rate: the probability method (Cheng 1993;Xiao et al. 2009) and the field survey method (Li et al. 2001;Xu et al. 2008;Tian 2012;Yan 2013). Probability methods calculate the occupancy rates of people in different regions from the total probability perspective, which is suitable for an assessment at the macro scale. Although the actual occupancy rate and its variability could be obtained from a field survey, the cost of time and labour for such a survey is very high, and is more suitable for studies at the micro level. Lastly, the rate of SAMA is chosen as the indicator with which to estimate the post-earthquake human response in the model. The SAMA rate can be considered as a comprehensive result of the human response (e.g. personal protective actions, etc.) following an earthquake.

Case study of the PTE model
3.2.1. Mw 6.5 Ludian earthquake On 3 August 2014 (at 16:30), an Mw 6.5 earthquake happened in Ludian County (103.3 E, 27.1 N). The epicentre of the Ludian earthquake was near the Xiyuhe-Zhaotong fault, with a focal mechanism of strike-slip rupture and a focal depth of approximately 12 km (Kuang et al. 2014). Figure 1 shows the location of the Mw 6.5 Ludian earthquake and the affected area by this earthquake. Totally 70 townships which are located in Ludian County, Qiaojia County, Zhaoyang District, Yongshan County, and Huize County, respectively, were affected by this earthquake. Ludian County and Qiaojia County were the most seriously affected areas by this earthquake. Statistical data collected before 15:00 on 8 August 2014 show that the Mw 6.5 Ludian earthquake caused 617 deaths; in addition, 112 people went missing and 3143 peoples were injured. The direct economic loss is up to 23.58 billion Chinese Yuan. The most seriously affected areas with a seismic intensity of IX degree based on the Chinese Seismic Intensity Scale (SAC 2008, the same as followed), had a total area of approximately 90 km 2 . And the total area of the affected regions with the seismic intensity from VI to IX degree, reached to approximately 10,350 km 2 .
Corresponding to the distribution of local people and an inventory of buildings, this study would assess the number and distribution of people trapped during the Ludian earthquake using the PTE model. Because the preliminary investigation showed that there were barely collapsed buildings in the areas with a seismic intensity of VI degree, the following analysis of trapped people only focuses on the areas with seismic intensities ranging from VII to IX degrees in this study.

Data
Given the requirements of SAR following an earthquake, a grid-based assessment of trapped people during the earthquake would be greatly beneficial for a comparison of regional differences of trapped people and the subsequent determination of the key SAR area. This is essential in order to provide a scientific basis for the reasonable allocation of rescue forces and resources in the early stages of an earthquake emergency. Therefore, the data used in this study is based on the grid data (km £ km) of the Yunnan region, including a km grid-based population distribution data set and grid-based building inventory (divided by structure type) data 1

Building collapse rate in the Ludian earthquake
To accurately reflect the characteristics of damaged buildings in the Yunnan region, this study used Yunnan building DPMs from a previous study (Zhou et al. 2007) to determine the collapse rate of each structural type resulting from the Ludian earthquake. The Yunnan building DPMs were given by a statistical analysis of structural damage proportions at different seismic intensities (from the Chinese Seismic Intensity Scale) from 50 destructive earthquakes that occurred between 1992 and 2003 year in Yunnan, China (the details can be obtained within Zhou et al. 2003Zhou et al. , 2007. According to the source of the building inventory data, the building structural types were divided into four categories: reinforced concrete structure, multi-story masonry structure, single-story residential structure and other structures. As aforementioned, this study considered the severe damage rates of four structural types at a specific intensity from Yunnan building DPMs as their collapse rates during the Ludian earthquake (Table 1).  According to Table 1, it is apparent that there are almost no collapsed reinforce concrete buildings in the seismic intensity from VI to IX degree regions. Thus, this study did not further analyze the distribution of collapsed reinforced concrete buildings in the area affected by the Ludian earthquake.

Occupancy rate in the Yunnan region
Considering the occupancy rate in the Yunnan area, Xiao et al. (2009) provided a daily routine timetable of people during the workday and holiday using a probability method based on the characteristics of routines in Southwest China (Table 2). Meanwhile, Tian (2012) analyzed the average occupancy rate at different time stages through a field investigation in the Yunnan region (Table 3). The Mw 6.5 Ludian earthquake initiated at 16:40 on 3 August 2014 (Sunday). This study used the average value of indoor rates from probability analysis and field surveys, respectively, at the earthquake time as the occupancy rate of people in the Ludian earthquake-affected area. According to Tables 2 and 3, we can estimate the average occupancy rate in the study area as approximately 0.75.

Rate of self-aid and mutual aid in the Ludian earthquake
Previous studies and investigations have showed that SAMA is an important measure with which to estimate the magnitude of casualties following a disaster. However, due to limitations in the available data, an accurate number of people escaping from collapsed buildings by themselves, as well as mutual rescue measures, were not retrievable for the Ludian earthquake. According to statistical data of past earthquakes, approximately 85% to 90% of victims successfully escaped during an earthquake disaster by themselves or through mutual rescue measures (Xiu 2004;Li 2006;Qu et al. 2010). Consequently, in order to obtain the SAMA rate, we conservatively determined the SAMA rate of victims as 85% during the Ludian earthquake based on the previous work.

Distribution of the collapsed buildings
Figure 2(a) illustrates the collapsed building distribution in the regions characterized by seismic intensities of VII-IX degrees during the Ludian Earthquake. It can be observed that most of the collapsed buildings were mainly distributed in the VIII and IX intensity regions. The area of the collapsed buildings in the IX intensity region reaches up to 112,450.11 m 2 , accounting for 0.67% of the total area of buildings (16.71 km 2 ) in this region. Meanwhile, in the VIII intensity region, the area of the collapsed buildings reaches up to 52,089.48 m 2 , accounting for 0.31% of the total regional area of buildings. In addition, in the VII intensity region, the area of the collapsed buildings reaches up to 16,926.87 m 2 , accounting for 0.10% of the total area of buildings in this region. Different structural types of buildings demonstrate different anti-seismic performances. Generally, reinforced concrete structural buildings have improved anti-seismic performance relative to multi-story masonry structures, single-story buildings and other structures. While suffering from the same intensity of an earthquake, the damage or collapse rate of reinforced concrete structure buildings is relative lower than that of the other 3 structure types. Figure 2(b)-2(d) shows the distribution of the collapsed multi-masonry structures, single-story structures and the other structures in the VII-IX intensity region of the Ludian Earthquake, from which it can be observed that the collapsed multi-masonry structures are mainly concentrated in the IX intensity region with an area of 18,636.52 m 2 , which accounts for 9.20% of the total area of building in this region (Figure 2(b)). The collapsed single-story structure buildings are also primarily concentrated in the IX intensity region with an area of 40,590.55 m 2 , accounting for 10.26% of the total area of buildings in this region. In addition, the single-story structural-type buildings also collapsed heavily in the VIII intensity region to a certain degree, with a collapsed area of 9,552.07 m 2 that accounts for 0.95% of the total area of buildings in the region (Figure 2(c)). In terms of the other structure buildings, the collapsed area reached 53,223.03 m 2 and 38,927.39 m 2 in the IX and VIII intensity regions, respectively, which account for 11.84% and 3.29% of the total area of buildings in this region, respectively (Figure 2(d)). In addition, from Figure 2(b)-2(d), we can observe that the collapsed area of multi-masonry structures, single-story buildings, and other structures gradually increased within the same intensity region. For example, the collapsed area of the three categories of structures was, respectively, 18,636.52 m 2 , 40,590.55 m 2 and 53,223.03 m 2 in the IX intensity region, which is in accordance with the order of their anti-seismic performances. Figure 3 demonstrates the distribution of the occupancy population within the VII-IX intensity regions at the time of the earthquake. The results showed that 308,685 people were inside a room or building in the VII-IX intensity regions when the Ludian earthquake struck, and the average indoor population per building area (km 2 ) was 18,473 people. In particular, 21,435 people were within a room/building in the IX intensity region, accounting for 6.94% of the total indoor population; 56,420 people were within a room/building in the VIII intensity region, accounting for 18.28% of the total indoor population; and 230,830 people were in a room/building in the VII intensity region, accounting for 74.78% of the total indoor population. Figure 4 demonstrates the distribution of people trapped by collapsed buildings in the Ludian earthquake. The assessment results indicated that there were approximately 454 people trapped in the collapsed buildings caused by the Mw 6.5 Ludian earthquake. All of the trapped people were distributed throughout the VII and VIII intensity regions. In particular, there were approximately 310 people trapped in the collapsed buildings of the IX intensity region, accounting for 68.30% of the total trapped population. Meanwhile, there were approximately 144 people trapped in the VIII intensity region, accounting for 31.70% of the total trapped population. In addition, it can be estimated that Longtoushan town represented the concentrated area of trapped people in the IX intensity region, within which the Longquan community, Guangming village, Baobao village, and Cuiping village were the focal points of people who were trapped within the Ludian earthquake-impacted area.

Results from the PTE model and affecting factors
Based on the major influencing factors, we constructed a PTE model to assess the trapped personnel distribution during an earthquake disaster. This model takes into account the effects that earthquakes have on different building structure types as well as trapped people in collapsed buildings as a consequence of earthquake hazards in combination with the building vulnerability, population exposure, and human response levels. The assessment results from the PTE model demonstrated that there were approximately 454 people trapped by the collapsed buildings in the Ludian earthquake, who were also the main targets in need of external SAR. According to previous work regarding historical earthquakes, the rate of trapped people escaping through the assistance of external rescue during an earthquake is only approximately 10% (Qu et al. 2010;Yang 2014). The research conducted by Li (1987) and Xu et al. (2008) showed that the rate of trapped people who are not in immediate danger is approximately 15%. Thus, it can likely be deduced that approximately 10%-25% of trapped people could potentially survive in collapsed buildings. Based on these proportions, we can conclude that deaths caused by being trapped in collapsed buildings might range between 340 and 409 people within the area impacted by the Ludian earthquake. According to our field investigation of the casualties in the Ludian earthquake, there were 526 deaths in Ludian County, 338 of which were caused by collapsed buildings. Given an additional 91 deaths within other Counties of the earthquake-impacted region, it can be calculated that approximately 396 lives were lost in total (based on the proportion obtained for Ludian County) as a consequence of collapsed buildings due to the Ludian earthquake. This value is in general accordance with our estimated results (between 340 and 409 people).
In addition, taking an administrative village as an example, our field investigation (Figure 4) demonstrated the following: Longquan community (136 deaths, 40.24% of the total deaths in Ludian County), Guangming village (43 deaths, 12.72% of the total deaths in Ludian County), Yinping village (42 deaths, 12.43% of the total deaths in Ludian County), and Babao village (31 deaths, 9.17% of the total deaths in Ludian County). These locations represent the primary locales wherein the deaths caused by collapsed buildings are concentrated, and thus the number of trapped people in collapsed buildings was the largest in these places. The trapped personnel distribution from the field investigation is also generally concordant with that obtained from our assessment results from this study (Figure 4). Given the above, it can be suggested that the results retrieved from the PTE model are reasonable within this study.
There are many factors that affect the trapped personnel distribution among collapsed buildings following earthquakes, and these influencing factors are characterized by uncertainties. The collapse of buildings and the presence of people within the room/building are two critical prerequisites. Additionally, the SAMA capability is another important factor that influences the trapped personnel distribution in the disaster area. According to above analysis, it can be implied that the detail and accurate estimate of the population distribution and building data can directly affect the accuracy of assessment results. Generally, high-resolution assessment results could be greatly beneficial to SAR abilities in post-earthquake disasters. However, high-resolution assessments require high-resolution basic data, which are difficult to acquire in reality. Thus, it is unrealistic and unnecessary to strictly emphasize the accuracy of the number of trapped people in an earthquake disaster.

Implications for SAR
Time is of significant essence in a post-earthquake area, and thus any delays toward understanding the scale of a disaster often hamper potential post-disaster responses, which prove to be both socially and economically costly ). Unfortunately, due to the complexity associated with a large earthquake (including its size, location and rupture uncertainties, and spatially variable shaking characteristics), as well as with the structural environment (i.e. the building and infrastructure vulnerability and population exposure characteristics at the time of the earthquake), it can often require days, weeks, or sometime months before the scope and extent of an earthquake disaster is understood sufficiently ). The available actual information of disaster is very limited during the early stages of a destructive earthquake. This limitation can subsequently cause excessively long emergency start-times and delays in the dispatching and allocation of necessary emergency supplies, because it is impossible to identify the structure and volume of emergency supply demand (Huang et al. 2015). Experiences from the Wenchuan earthquake have demonstrated that the scientific judgment and reasonable allocation of rescue resources is essential for the reduction of casualties.
Regional disaster losses and their differences are the major guidelines for identifying the emergency supply demand and allocation of rescue resources, which could improve (SAR) operations in the earthquake aftermath. The preliminary assessment of trapped people can provide the judgment basis for the estimation of regional disaster losses. Moreover, high-resolution assessment units would be more helpful in the comparison of regional differences of disaster losses and the determination of the key SAR area, which can improve rescue efficiency and reduce casualties. Compared with a county-based estimation, a grid-based assessment could provide a more reasonable and specific SAR area, through which emergency management sectors or organizations can more-readily identify emergency supply demands and thus reasonably allocate necessary resources. In this study, we assessed the number and distribution of trapped people in the Ludian earthquake using a gridbased PTE model. The accurate estimation of the results from the PTE model shows that the number and distribution of trapped people assessed by this model are all generally concordant with those from field investigation results. It can be concluded that the grid-based (km £ km) assessment could meet the requirements for evaluating the risk of PTE, and therein provide directional suggestions for the determination of key recue areas and the allocation of rescue forces in order to improve SAR operations in an earthquake aftermath.

Limitations
As mentioned above, there are various factors that affect the distribution of people trapped in collapsed buildings, namely, the population distribution, the structural collapse of buildings and the human response. In this study, the occupancy rate at the time of earthquake was taken into consideration, but due to the limitation of basic data, we only provide an average indoor rate for the whole study area, which cannot accurately reflect the actual population mobility of different assessment units. The differences between the average indoor rate and actual population mobility consequently affect the assessment accuracy of the actual population exposure to earthquakes in the study area. In terms of the building collapse rate, we utilized the severe damage rate of buildings instead of the collapse rate, which is unable to reflect the truth of the study area since the severe damage rate of buildings is generally not equivalent to the building collapse rate, especially for reinforced concrete buildings. However, on the one hand, according to statistical data, there were almost no collapsed reinforced concrete buildings in areas of seismic intensities ranging from IX to IX degrees in the Yunnan region. On the other hand, according to field investigations, the proportion of civil structural buildings reached up to 80% of the total building area in the rural area of the Ludian region, and the severe damage rate of civil structural buildings is generally equivalent to its collapse rate. Overall, there might not be a significant effect on the assessment results from the use of the severe damage rate of buildings rather than the collapse rate in this study. In addition, due to the limitation of basic data, we were unable to take the urban-rural differences of population and the preferences of buildings into consideration in this study, which might affect the accuracy of the final assessment results.
Nevertheless, the main purpose of this study is to construct a method for the rapid assessment of the number and distribution of trapped people in earthquakes based on grid data. The ambition of this method is to constrain regional differences and determine the key SAR area in order to improve emergency operations and reduce casualties in the early stages of an earthquake. Thus, it is not necessary to strictly emphasize the accuracy of the number of trapped people in the earthquake disaster. Through a comparison of the assessment and field work results, it can be suggested that the assessment results from the grid-based PTE model could meet the requirements for SAR operations in an earthquake aftermath.
Ultimately, the applicability of the PTE model requires further examination utilizing additional earthquake case studies. In the future, with a growth in the abundance and completeness of basic data, the PTE assessment model might be further improved to increase the accuracy and application of the assessment results. This model includes the measurement and distinction of urban-rural differences of population and building distributions and accounting for earthquake-induced secondary disasters (e.g. landslides). In addition, investigations of the trapped personnel distribution in earthquakes on a smaller regional scale (e.g. villages and townships) are also significant toward understanding the impacts of different factors on the trapped personnel distribution in collapsed buildings, as well as for improving the application of the PTE assessment model. The model constructed in this paper is preliminary and necessitates further development in many respects, but it offers a simple and rapid calculator for trapped people losses based on direct empirical data.

Conclusions
This study constructed a model for assessing the people trapped in the collapsed buildings due to earthquakes. Then, we assessed the distribution of people trapped in 2014 Ludian earthquake using the constructed PTE model and evaluated the accuracy of the estimation results from the PTE model. Results suggested that, there are various factors affecting the distribution of PTE. The population distribution and the collapse of buildings are the core factors. Additionally, the factors related to human response (e.g. personal protection actions, etc.) also have important effects on the number of PTE. The constructed PTE model takes into account the effects of earthquake hazard, building vulnerability, population exposure, and human response level on the distribution of trapped people in earthquakes. The results of this approach are then tested against actual trapped people data investigated in Ludian earthquake-hit area. The results showed that, the trapped personnel distribution estimated by the PTE model is basically the same with that obtained by the actual survey in Ludian earthquake-hit area. Grid-based assessment results could allowed the emergency management sectors or organizations to identify the emergency supply demands and reasonable allocate the resources. It could also meet the requirements for evaluating the risk of PTE and then provide suggestions for improving the SAR operations in the early stage of earthquake emergency.
There are some limitations in the constructed PTE model, which might cause the uncertainties in the assessment results. The applicability and reliability of the approach needs to be examined by much more earthquake cases. The PTE model described here is preliminary and needs further development in many respects, but it offers a simple and rapid calculator for trapped people losses based on direct empirical data. Improvement in methodological sophistication and reliability for understanding the location and number of trapped people due to earthquakes in at-risk populations is a promising topic for future study. As the abundance and completeness of basic data, it is possible to further improve and optimize the PTE assessment model, to improve the accuracy of the result and its applicability, in order to provide better guidance for SAR operations. Note 1. The data is from the results of the project 'Regional Differences in Earthquake Preparedness and Emergency Response Capabilities in Mainland China,' funded by the Ministry of Finance of the People's Republic of China.