Evacuation simulation of multi-story buildings during earthquakes based on improved cellular automata model

ABSTRACT The simulation of the authentic evacuation process is conducive to accurately evaluate the casualties of buildings under earthquake. This study improves the traditional cellular automata model to simulate the crowd evacuation process in buildings under earthquake. The modified model simulates the attraction of exits to crowds, herd behavior of crowds, avoidance behavior for obstacles, decision-making behavior for paths/exits selection, and conflict between pedestrians in the evacuation process. Based on the video, which records authentic evacuation under earthquake, the influence coefficients of each factors are determined. In addition, the modified cellular automata model uses the refined cellular space to describe the geometric dimensions of the evacuation environments and obstacles, and therefore it improves the accuracy of the evacuation model. The explicit finite element method is used to simulate the seismic damage process of structural and non-structural components. The judgment criterion of casualties which combines the finite element model with the evacuation model, is proposed. The number and distribution of casualties are predicted based on the criteria. Finally, a seven-story official building with reinforced concrete frame structure located in Dujiangyan City, Sichuan Province, China is considered as example to verify the rationality and applicability of the proposed method.


Introduction
The existing casualty assessment methods are mainly based on empirical formula or probability statistical methodology (Badal, Vázquez-Prada, and González 2005;Shapira, Aharonson-Daniel, and Shohet et al. 2015;Shaohong and Jin 2015;Gul and Guneri 2016). These studies can perform the assessment of casualties on regional scales from macro perspective, and they have an acceptable accuracy. However, they are not suitable for predicting the number of casualties in building scale. In order to satisfy the requirements of accurate rescue plan after earthquake and accurately determine the number of refugees, it is necessary to efficiently assess the number and location distribution of casualties in small-scale. The observations after the earthquakes illustrate that the evacuation process affects the casualties during the earthquake (Shuang, Xiaohui, and Zhang et al. 2018). Considering the influence of the evacuation process is a more accurate approach for the evaluation of casualties in building dimensions under earthquake.
In the emergency evacuation field, several researchers simulate the process of crowd evacuation using computer simulations (Gwynne, Galea, and Lawrence et al. 1999;Lindell 2008). The crowd emergency evacuation models are divided into macro and micro models. The macro model (Henderson 1971) considers the movement of pedestrians as flow. It uses the partial differential equation in fluid dynamics in order to describe the variation trend of pedestrians' speed and density function of time. It has a high computational efficiency. However, it cannot reflect the interaction and heterogeneity between individuals. The micro model considers the pedestrians as individual particles. It can simulate a specific evacuation behavior, interaction and heterogeneity between individuals. The micro model has the advantage of leading to accurate simulation results. Moreover, the descriptions of the pedestrians' movement are accurate and natural. The most common micro models include the social force model (Helbing and Molnar 1995), cellular automata (Burstedde et al. 2001), multi-agent model (Pan, Han, and Dauber et al. 2007), lattice gas model (Muramatsu, Irie, and Nagatani 1999) and RVO model (Wei, Chen, and Jiheng et al. 2010).
The social force model (Helbing, Farkas, and Vicsek 2000) is integrated into the underlying algorithm of Anylogic platform (8.5.0). It has high accuracy and characteristics of continuous micro simulation. However, the simulation efficiency is not ideal. The cellular automata (CA) model is suitable to describe the dynamic process of evacuation, and considers the complex human behavior (Burstedde, Klauck, and Schadschneider et al. 2001). It is a grid dynamics model based on the continuous evolution of the states of adjacent cells in the time dimension and spatial dimension. It can simulate the spatial-temporal evolution of complex systems. It can also simulate the specific evacuation behavior and psychology, including the avoidance (Song, Zhang, and Huo et al. 2020), panic (Varas, Cornejo, and Mainemer et al. 2007), following (Can, Qun, and Chen 2019), herd (Yuan and Tan 2007), helping (Gao and Guan 2018) and inertial (Zhai, Jie, and Hou et al. 2020) behaviors. Therefore, it is widely used to simulate the process of crowd evacuation. Currently, most of the researchers use the cellular automata model to simulate the crowd evacuation under fire (Cao, Song, and Liu et al. 2014), flood (Simonovic and Ahmad 2005;Liu, Okada, and Shen 2009), toxic gas leakage (Cao, Fan, and Shuxia 2016), hurricane (Koshute 2013), terrorist attack (Liu 2018), or without considering the disaster environment (Tan, Mingyuan, and Lin 2015;Ma, Lo, and Song 2012;Zhao, Yang, and Jian 2006). Some researchers introduced the field intensity of fire (Jin, Ruan, and Yue 2018), repulsive force of fire (Meng, Zhou, and Rao 2009) and fire risk, in order to improve the traditional CA model. The calculation formula of movement probability is modified to simulate the pedestrians' avoidance behavior and panic psychology under fire source. However, the evacuation simulation under earthquake based on cellular automata model is rare.
In addition, the cells size in the CA model is too coarse (0.5 m × 0.5 m (Zhao, Yang, and Jian 2008) or 0.4 m × 0.4 m (Chen, Wang, and Heng et al. 2020)), which cannot accurately simulate the authentic size of obstacles. The CA model with more precise cellular space should be further studied. The human behavior and the interaction between human and environment, are critical factors having a crucial influence on the evacuation process and evacuation time. Defining and simulating the human behavior and movement law of pedestrians, are important for evacuation simulation under earthquake. However, the current studies on evacuation behavior mostly concentrate on one or two behavioral characteristics. The studies on coupling multiple behaviors are rare. With the development of the evacuation simulation model and accuracy, studies on multiple evacuation behaviors are crucial.
Combining the crowd emergency evacuation process with the structural damage process, is also crucial for the evacuation model under earthquake. Xiao et al. (2017) perform the evacuation simulation of residential buildings (Xiao, Chen, and Yan et al. 2016) and primary schools during the Ludian earthquake. The required safe evacuation time (REST) is estimated by the nonlinear time history analysis of building structure. The reduction of speed under earthquake is also considered. However, the damage process of building structure is not coupled with the evacuation process. Liu, Jacques, and Szyniszewski et al. (2016) and Cimellaro, Ozzello, and Vallero et al. (2017) assume that the evacuation starts when the vibration induced by the earthquake stops. This assumption does not consider the evacuation behavior in the evacuation simulation model when the building is vibrating. Shuang, Xiaohui, and Zhang et al. (2018), Shuang, Zhai, and Xie (2015) propose a novel evacuation simulation model in order to perform casualty assessment of a teaching building. It is assumed that, when the relative displacement of adjacent floors is less than the critical value, the casualties will occur in this position.
The model combines the collapse process of building structure with the evacuation process. However, it does not consider the influence of the failure of nonstructural components on the evacuation process.
This study aims at improving the traditional CA model, and proposes an approach for casualty assessment in building scale. It solves three existing critical issues: simulation of crowd evacuation behavior under earthquake, establishment of highly refined cellular units, and combining the structural damage process with the evacuation process. The improved CA model under earthquake is proposed to simulate panic psychology, herd behavior and decision-making behavior under multi-exit environment. The model combines the damage process of structural and non-structural components with the crowd evacuation process. It also proposes a refined cellular unit to more accurately simulate the spatial size of obstacles, and improve the simulation accuracy. The model can provide structural designers, architects and rescuers with important information such as the evacuation route, total evacuation time and casualties under earthquake, for example. Based on the provided information, the optimal evacuation paths can be determined on the architectural design stage, or the locations where casualties occurred on existing buildings can be predicted.
The remainder of this paper is organized as follows. In section 2, a seismic evacuation model based on an improved CA model is proposed. According to the coefficient of variation and a video of the evacuation process in authentic earthquake scenarios, the parameters of the evacuation model are calibrated. Section 3 puts forward the coupling rules between the damage process of the structural and nonstructural components with the process of crowd evacuation under earthquake. The judgment criteria of casualties are also developed. In section 4, a 7-story reinforced concrete frame structure in Wenchuan earthquake is considered as an empirical case, in order to verify the efficiency and rationality of the proposed approach. Finally, section 5 summarizes the advantages of the proposed method and concludes the paper.

Evacuation simulation model: improved cellular automata model
The spatial dimensions, time dimensions and state of units in the CA model are discrete. The CA model discretizes the evacuation space into cellular units, where the pedestrians and obstacles occupy one or more cellular units. The state of each cellular unit is determined by the state of its adjacent cellular unit in the last time step and a series of local rules. The evacuation process and complex evacuation behavior can be simulated by establishing the rules for pedestrians in order to move to the surrounding cellular units, the interaction rules between pedestrians, and the interaction rules between the pedestrians and disaster environment. This section proposes an evacuation simulation model based on the improved CA model. The refined cellular space is then developed. The crowd's decision-making behavior for exits and avoidance behavior for obstacles under a multi-exit evacuation scenario, are simulated.

Improving the size of the cellular unit
Typical sizes of the cellular unit are 0.4 m × 0.4 m (Chen, Wang, and Heng et al. 2020) and 0.5 m × 0.5 m (Dewei and Han 2015). The refined cellular unit can more accurately simulate the geometrical dimensions of the evacuation environments and obstacles. In addition, the influence of multiple velocities on the evacuation process can be considered. The evacuation speed under diagonal direction is determined as ffi ffi ffi 2 p m/s. When people move through the horizontal or vertical direction, the evacuation speed is determined as 1 m/s. Compared with the cellular unit of 0.1 m × 0.1 m dimension, the cell having a dimension of 0.2 m × 0.2 m is able to accurately represent the geometric size of obstacles and decrease the computational load. Therefore, the size of the refined cellular unit is determined as 0.2 m × 0 2 m. In order to ensure the space pedestrians need and swing amplitudes of four limbs during evacuation, this study stipulates that one pedestrian should occupy four cellular units. The cellular space occupied by pedestrians is presented in Figure 1, where the blue circle represents one pedestrian, and the grey shaded area denotes the space occupied by the pedestrian, which cannot be occupied by other people.

Simulation of evacuation behavior
In each time step, the pedestrians determine the movement direction and target cell for the next time step, according to the local rules. The influence of the static attraction, dynamic attraction, exit-choice function and falling components (obstacles) during the evacuation process is considered. The static attraction simulates the self-driving behavior that pedestrians move towards the exit. The dynamic attraction simulates the interaction between the pedestrians and herd behavior. The function for exit choice simulates the selective behavior in the multi exit/multi-route evacuation environment. The "risk value" simulates the avoidance behavior for falling components (obstacles).
(1) Static attraction The static attraction represents the attraction from exits to pedestrians. The value of the static attraction does not change with time nor with the pedestrians' movement. It is quantified by the distance from the cellular units to the exits: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ði e À i s Þ 2 þ ðj e À j n Þ 2 q � � À ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ði e À iÞ 2 þ ðj e À jÞ 2 q (1) where (i e , j e ) represents the position coordinates of exit e, (i s , j s ) denotes the position coordinates of all the cellular units, and (i, j) are the location coordinates of a cellular unit. Under multiple-exits environment, the S i,j of each exit should be first calculated separately, and then determined as the maximum value.
Kirchner uses the Euclidean distance to calculate the static attraction (Kirchner and Schadschneider 2002), which is only applicable to simple scenarios with convex boundaries and without obstacles. For the evacuation scenario with obstacles, the following methods are used to determine the static attraction: (1) The static attraction of the cellular unit at the exit is assigned as 0; (2) The static attraction of each cellular unit is calculated from the exits to the inside. The value of the adjacent cellular unit in vertical and horizontal directions increases by 1, while the value in the diagonal direction increases by 1.5; (3) The static attractions of walls and obstacles are determined as the maximum values; (4) When all the cellular units are assigned, the static attraction of each cellular unit is determined by subtracting the value of the current cellular unit from the maximum value.
(2) Dynamic attraction The dynamic attraction determined the interaction between pedestrians and herd behavior. In contrast to the static attraction, the dynamic attraction changes with time and evacuation process. Its initial value D ij is set to zero, and increases with the occupied frequency. When people occupy the cellular unit (i, j) at moment t, and leave at moment t+ Δt, the dynamic attraction increases by 1: The dynamic attraction is related to the evacuation time, and has dynamic characteristics of diffusion and attenuation. This study uses α and β to describe the diffusion characteristics and attenuation characteristics of dynamic attraction (α∈[0,1], β∈[0,1]), respectively. In each time step, the dynamic attraction will spread with probability value α and attenuate with probability value β, which affects the adjacent cellular units. The diffusion phenomenon is considered as: Simultaneously, the attraction of cell (i, j) will decay with time after the pass of occupant. The decay phenomenon is considered as: According to the order that dynamic attraction first diffuses and then attenuates, this section combines equation (3) and (4) to determine the dynamic attraction of cell (i, j) at moment t + 1: (3) Function for exit choice and route choice In a multi-exits evacuation environment, the evacuation route choice is affected by the evacuation distance and population density at the exit (Jia et al. 2018). In the process of choosing exits, the pedestrians estimate the waiting time according to congestions at different exits and evacuation distances, thus constantly adjusting the target exit and evacuation route. This study develops the exit-choice function E in order to simulate the pedestrians' choice of exit during evacuation. For the evacuation environment with two exits, the exit-choice function of each cell at moment t is expressed as: where density A and density B, respectively, represent the population density at exit A and exit B, distance A and distance B represent the distance from cell (i, j) to exit A and exit B, respectively.
(4) Avoidance behavior for obstacles The avoidance and panic psychology for damaged structural or non-structural components, are typical behaviors and psychology in seismic evacuation. The cell where damaged components are located in is referred to as "hazard source". Similar to the original obstacles, the "hazard source" will not be occupied or crossed by pedestrians. The difference between the "hazard source" and the original obstacles is that the "hazard source" will radiate into the surrounding area. Based on the video analysis of evacuation in the classroom (Xiaolin, Zhongliang, and Yingchun 2010), when an earthquake occurs, the distance for pedestrians to avoid obstacles does not exceed three meters. Therefore, the radiation radius of the "hazard source" is determined as 3 m. The radiation intensity of cell (i, j) decreases when the distance from cell (i, j) to the "hazard source" increases. The risk value of the "hazard source" is similar to that of the static attraction of the cell when it is occupied by original obstacle. The risk value of cell (i, j) is given by: where R ij is the risk value of cell (i, j), S i,j denotes the static attraction when cell (i, j) is occupied by the initial obstacles, and r ij represents the distance from the "hazard source" to cell (i, j).
In the refined cellular unit, each person occupies four cellular units: cell (i, j), cell (i + 1, j), cell (i + 1, j-1) and cell (i, j-1), as shown in Figure 3. Based on the traditional Von Neumann neighborhood and Moore neighborhood, an extended Moore neighborhood is proposed. Since all the rules in the CA model are developed for cells rather than lattice points, the improved CA model uses cells to represent pedestrians, and ensures that cell (i, j), cell (i + 1, j), cell (i + 1, j-1) and cell (i, j-1) will not be occupied by other pedestrians.
The people determine the movement probability of eight directions based on the attraction of neighborhood cells, as shown in Figure 2. The target cell in the next time step is determined on the movement probability. The attraction level and movement probability are determined by the static attraction, dynamic attraction, exit choice function, "hazard source" and state of cells (whether cells are occupied or not). The movement probability of eight neighborhood cells is computed as: where S ij , D ij , E ij and R ij , respectively, represent the static attraction, dynamic attraction, exit-choice function and risk value, k s , k d , k e and k r respectively, denote the influence coefficient of the static attraction, dynamic attraction, exit-choice function and risk value, n i,j = 1 indicates that the neighborhood cell is occupied by pedestrians (otherwise, n i,j = 0), and m i,j = 1 indicates that the neighborhood cell is occupied by obstacles (otherwise, m i,j = 0). N is then introduced as a normalized coefficient: If the target cell is not occupied and multiple pedestrians simultaneously compete for one target cell, a collision will occur. In the authentic evacuation process, due to the influence of psychological, physiological and environmental factors, the pedestrians will hesitate or avoid each other when they compete for one target cell. In order to solve the competition and collision during the evacuation process, the friction coefficient µ is introduced. Firstly, a number ranging between 0 and 1, is randomly generated. When the random number is greater than µ, the pedestrians will compare their movement probability with each other. The pedestrian having the highest movement probability can enter the target cell in the next time step. When the random number is less than µ, the pedestrians will not compare the movement probability and remain in their original position in the next step. Therefore, no pedestrians will enter into the target cell. Figure 4 demonstrates the confilict process during evacuation.
In general, figure 5 illustrates the updating rules for cells of the proposed seismic evacuation model include the following steps: (1) Calculate the movement probability to the surrounding eight neighborhood directions; (2) The pedestrians select the target cell in the next time step, based on the movement probability of eight neighborhood directions; (3) In the local area where collision occurs, when multiple pedestrians choose the same target cell in next time step, if the generated random number is greater than µ, the pedestrian having the highest movement probability will enter the target cell. Otherwise, all the pedestrians remain in the original position in the next time step.
(4) The evacuation process uses the synchronous update rule to update the position status of all the pedestrians within the same time step.
(5) While updating the pedestrians' location, the static attraction, dynamic attraction, exit choice function and risk value of each cell are updated. Finally, the model enters the next cycle simulation.

Parameter analysis
In the parameter analysis, a video, which records an authentic evacuation under earthquake (https://m.v. qq.com/z/msite/play-short/index.html?cid=&vid= o08073ef0ll&qqVersion=0) is considered as an empirical case. The size of the double-exit room is 10.0 m × 8.0 m. The number of people is 51 and the width of the exit is 1.2 m, as shown in Figure 6. Due to the model randomness, the evacuation process of each simulation is uncertain and different. Therefore, under the same evacuation environment, the evacuation routes and evacuation time of people are not the same in each simulation. It is deduced that the evacuation time tends to be stable after 30 calculations. When the computation time continues to increase, the average value of the evacuation time is not influenced. Therefore, the average value of the evacuation times after 30 computations is considered as the final evacuation time.
The influence coefficients in equation (11) are determined using three different methods: (1) existing methods of the literature; (2) calibration based on the video, which records the authentic evacuation scenario; (3) evacuation time and its coefficient of variation. The influence coefficients of exit-choice function and risk value are calibrated based on the video of authentic evacuation. In this section, the influence coefficient of static attraction (k s ) and    influence coefficient of dynamic attraction (k d ), are evaluated by parameter analysis. In the latter, α = 0.1, β = 0.3, k e = 1.2, k r = 4 and µ = 0.5 are used as standard parameter sets. Figure 7) illustrates the influence of k s on the evacuation time for values of k D equal to 0, 1, 2, 5 and 10. For k d = 0, the evacuation Fig 8b process is not related to the dynamic attraction, and it is only affected by static attraction. The evacuation time is not affected by the change of k s . In this situation, the pedestrians do not blindly follow the crowd. Therefore, the evacuation time is stable. For values of k D equal to 1, 2, 5 and 10, the influence of the static attraction and dynamic attraction should be simultaneously taken into account. For a small value of k s (such as k s = 0.05), people are familiar with the exits. The influence coefficient of dynamic attraction is relatively large, and the blind conformity is clear, which results in a longer evacuation time. When k s increases, the static attraction has a greater influence on the evacuation process, people are more familiar with the location of exits, and the phenomenon of blind conformity is gradually weakened, which results in a gradual decrease of the evacuation time. When the value of k s is larger than 2.5, the proportion of static attraction increases, and the evacuation time tends to be gradually stable.
In order to reflect the fluctuation of the evacuation time, Figure 8) illustrates the influence of k s on the variable coefficient of evacuation time for values of k d equal to 0, 1, 2, 5 and 10. For k d = 0, because the evacuation process is not related to the dynamic attraction, and the evacuation time is not affected by the change of k s , the coefficient of variation is small and stable. For values of k D equal to 1, 2, 5 and 10, with a small value of k s (such as k s = 0.05), the variation coefficient of evacuation time reaches the highest level. With the increase of k s , the coefficient of variation gradually decreases and tends to be stable. When the value of k s increases to 2.5, the static attraction plays a leading role, and the pedestrians can quickly and orderly find the exits. Figure 9) presents the influence of k D on the evacuation time for values of k S equal to 0.4, 1.0, 2.5 and 5.0. For k s = 5.0 and 2.5, the static attraction plays  a dominant role in the evacuation process. People are familiar with the position of exits. The evacuation time is stable, since is not affected by the change of k d . For k s = 0.4 and 1.0, the pedestrians' familiarity with exits reaches a low level. For a small value of k d , the static attraction still dominates, and the pedestrians are not significantly affected by the surrounding people. With the increase of k D , the influence of the dynamic attraction gradually increases, and the phenomenon of blind conformity becomes clearer, which results in the gradual increase of the evacuation time. When the influence coefficient of dynamic attraction is large (such as k d = 5), the dynamic attraction gradually occupies a dominant position and the evacuation time becomes stable. When the values of k s and k d are, respectively, 1.0 and 5, the evacuation time tends to decrease, which indicates that a certain extent of conformity is conducive to improving the evacuation speed.
In order to reflect the fluctuation of the evacuation time, Figure 9) illustrates the influence of k d on the variable coefficient of evacuation time, for values of k s equal to 0.4, 1.0, 2.5 and 4.0. For k s = 5.0 and 2.5, the variation coefficient of evacuation time is very small. For k s = 0.4 and 1.0, the variation coefficient gradually increases when k d increases. As the value of k d continues to increase, the evacuation time tends to be stable, and the coefficient of variation decreases.

Verification of the evacuation model
Based on the video, which records the authentic evacuation under earthquake, it is deduced that the pedestrians are familiar with the location of exits during the evacuation process. Therefore, the influence coefficient of static attraction k s should not be too small. It can be observed from Figure 8 that, when the value of k s is less than 2.5, the evacuation time rapidly decreases with the increase of k s . When the value of k s is greater than 2.5, the evacuation time becomes stable. Therefore, the influence coefficient of static attraction is determined as 2.5, according to the parameter analysis. Since the teachers and students in the video record are familiar with the exit environments, the blind conformity phenomenon will not occur. Therefore, the influence coefficient of dynamic attraction k d should not be too large, and it is determined as 1.0 in this study (Shuang, Zhai, and Xie 2015).
Based on the video, which records the authentic evacuation process under earthquake (https://m.v.qq. com/z/msite/play-short/index.html?cid=&vid= o08073ef0ll&qqVersion=0), the evacuation simulation model for a double-exit room (cf. Figure 10) is developed to calibrate the influence coefficient of exitchoice function k e . It can be seen from Figure 11 that, for k e = 1.2, the curve showing the relationship between the time and the number of people completing evacuation fits well with the curve of authentic evacuation.
Based on the surveillance video of classroom during Wenchuan earthquake (http://v.youku.com/v_show/ id-XMjk3 NjE40Dg = .html), Xiaolin, Zhongliang, and Yingchun (2010) performed a statistical analysis on the relationship between the evacuation time and the number of pedestrians completing evacuation. For different values of the influence coefficient of risk k r , the curves showing the relationship between the time and the number of people on simulation model are compared with the curve of authentic evacuation. Some curves that are similar to the authentic situation and their corresponding risk values, are shown in Figure 12.
It can be seen from Figure 12 that the value of k r mainly affects the amplitude of avoidance to the "hazard sources". The larger the value of k r , the greater the amplitude of avoidance, which results in a longer evacuation time. In addition, for k r = 4, the evacuation time required by pedestrians is similar to the actual situation. The two reasons for the difference between the simulation model and authentic evacuation scenario are summarized as follows: (1) the behavior pattern of pedestrians is a very complex process. The simulation algorithm cannot consider all the types of behaviors and coupling between different behaviors; (2) the authentic evacuation process in one video record has a certain amount of randomness. The result of the evacuation simulation model is determined as the average value under repeated numerical experiments, which is more stable.
Considering that the probability of whether collision during evacuation is 50%, the value of the friction coefficient µ is determined as 0.5.

Criteria for determining casualties
The casualties during evacuation under earthquake are induced by the overall collapse of the building structure, floor collapse and damage of non-structural components. The evacuation simulation based on the improved CA model is combined with the seismic nonlinear time history analysis of building structures in time dimensions and spatial dimensions, in order to determine the casualties. The evacuation space has two superimposed grid systems: cellular automata grid and finite element grid. The spatial coordinates of damaged components are tracked by a finite element mesh. The cellular automata mesh in the lower floor, overlapped with the vertical projection of damaged components, is then identified. If people are located in the cellular automata grid, which overlaps with the projection of damaged components during evacuation, then casualties will occur, as shown in Figure 13.
Besides acquiring information on casualties, another function of the developed coupling model is to simulate the dynamically changing obstacles. In the process of authentic evacuation, the structural and non-structural components fall down as the time change, which results in casualties and newly generated obstacles during subsequent evacuation. The coupling model simulates the phenomenon that people re-select a reasonable evacuation route after new obstacles exist. If casualties occur, they will stay in place and then become new obstacles for other pedestrians during evacuation.
The criteria of casualties induced by damaged structural components are determined as follows: (1) according to the average height of Chinese people, this study assumes that, when the relative vertical displacement between adjacent floors is less than 1.65 m, the casualties will occur at the corresponding position (Shuang, Zhai, and Xie 2015); (2) when the interstory drift ratio of floor j exceeds the limit value of collapsed state at moment t, pedestrians in floor j, j + 1, j + 2 . . . will stop the evacuation after this moment. Pedestrians who have not completed the evacuation will suffer from casualties.      The evacuation simulation model considers the damage of infilled walls and suspended ceilings. According to the experimental results in (Guoqiang, Zhao, and Sun et al. 2003;Guoqiang, Fang, and Liu et al. 2005;Cheng, Liu, and Liu 2010), when the peak acceleration at the center of the infilled wall reaches 1.0 g, the infilled wall will collapse out of plane. When the infilled wall collapses, it is assumed that the collapse probability on both sides is the same. The range of a collapsed wall is determined using equation (12) (Xinzheng, Yang, and Paolo Cimellaro et al. 2019). The evacuation process based on the CA model is combined with the collapse process of infilled wall in time and spatial dimensions. If an infilled wall collapses at moment t, casualties will occur while the pedestrians simultaneously get through the collapsed area.
where d represents the collapsed area, v i denotes the velocity at floor i + 1, h i is the height of floor i, and g represents the gravitational acceleration. Several researchers proposed different damage indexes and strength parameters to analyze the vulnerability of suspended ceilings (cf. Table 1). Based on ATC specification (cf. Table 2), the damage of suspended ceilings is divided into three states depending on the falling rate: 5% (D1, slight damage), 30% (D2, moderate damage) and 100% (D3, severe damage). This study considers the peak floor acceleration as the strength parameter, and then generates falling suspended ceilings using the stochastic method. For instance, if a room has 100 suspended ceilings, when the falling rate reaches 30%, 30 suspended ceilings are generated by the stochastic method. Based on the approach which combines the evacuation process with the collapse process in time and spatial dimensions, casualties will occur when suspended ceilings are damaged and fall on the ground, and pedestrians simultaneously get through the damaged area. The size of the suspended ceilings is considered as 600 mm × 600 mm (Qiqi, Zhe, and Xie et al. 2019). Figure 14 and figure 15 illustrates the suspended ceiling with a failling rate of 5% and 30% respectively.

Overview of target building
The target building is a seven-story office building of a Power Gas Company located in Dujiangyan, Sichuan Province, China. The structural type is a reinforced concrete frame structure (cf. Figure 16). Although the structure is originally designed based on a seismic intensity of 7 in 1997, it was damaged during the Wenchuan earthquake. The structure has a plan dimension of 50.4 m × 17.4 m (cf. Figure 17). The height of stories 1 to 7 is 4.6 m, 4.2 m, 3 × 3.6 m, 4.2 m and 3.6 m, respectively. The cross sections of frame beams are 350 mm × 600 mm, and those of the columns change along the structural height from 800 mm × 800 mm to 500 mm × 500 mm. The thickness of the slab is 100 mm. All the concrete design grades are C30. The infilled wall is made by air brick with a thickness of 200 mm. An analytical structural model is developed by ABAQUS (cf. Figure 18).

Development of finite element model
This study uses the ABAQUS (Systèmes 2013) software to simulate the building damage under the earthquake excitation. The ABAQUS software includes two algorithms: ABAQUS/implicit and ABAQUS/explicit. Due to the refined division of elements in the finite element model, complexity of material model and contact type, the implicit algorithm leads to a large number of iterative processes. Each iterative process requires to solve a large number of nonlinear equations, which not only decreases the calculation efficiency but also results in a difficult convergence. Therefore, the implicit algorithm for finite element analysis has a high cost. The explicit algorithm uses the central difference method for calculation, which does not require to iterate and solve a large number of equations. In terms of the definition of element mass, the explicit algorithm uses the centralized mass matrix, which reduces the inversion process of mass matrix when calculating the inertial force. Therefore, it has a high calculation efficiency. Therefore, the explicit algorithm is used for calculation. The concrete material uses the concrete damage plastic model, while its constitutive curve follows the uniaxial stress-strain relationship specified in the code for the design of concrete structures (Industry Standard of the People's Republic of China 2010). The reinforcement in the floor slab is determined as a bilinear steel model with a post yielding module ratio of 0.01. The reinforcements in the beam and column are determined as the fourfold line model with negative stiffness and Poisson's ratio of 0.3. The developed finite element model uses the Timoshenko beam element B31 to simulate beam and column members. The floor simulation for floor slab uses the S4R quadrilateral shell element, which considers arbitrary large deformation and effective membrane strain. In the analysis steps, the Rayleigh damping and general contact algorithm are used in the finite element model. The ground is simulated by an analytical rigid body. Finally, the ground and column are consolidated.

Evacuation model under earthquake and prediction for casualties
The number of pedestrians stranded on each floor under different earthquake intensities, distribution of pedestrians at different moments, casualties on different parts of the building and number of people completing evacuation at the end of the earthquake, are studied based on the results of evacuation simulation and nonlinear time history analysis. According to previous analysis, the parameters of the improved CA model are determined as follows: the influence coefficient of static attraction (k s ), influence coefficient of dynamic attraction (k d ), influence coefficient of exit choice function (k e ), influence coefficient of "risk value" (k r ) and friction coefficient (μ) are determined as 2.5, 1.0, 1.2, 4 and 0.5, respectively. The improved CA model proposed in section 2, is used to develop the seismic evacuation model. The number of casualties is determined based on the coupling rules proposed in section 3. Tables 3 and 4 present the damage degree and failure time of the suspended ceilings and partition walls on each floor, for different earthquake intensities. It can be seen that, under a minor earthquake of intensity 8, the overall structure does not collapse, the suspended ceilings do not fall, and the partition walls do not collapse. Under a moderate earthquake of intensity 8, the overall structure does not collapse. However, the suspended ceilings on the 2 nd , 4 th , 5 th and 6 th floors drop out, with a falling rate of 5%. In addition, the partition walls on the 2 nd and 3 rd floors collapse. Under a major earthquake of intensity 8, the inter-story drift ratios of floors 2, 3 and 4 exceed the limit for collapse (1/20), and therefore the whole structure collapses. The partition walls collapse and the suspended ceilings are damaged on each floor. The falling rate of the suspended ceilings on the first floor is 5%. The falling rates of the suspended ceilings from the 2 nd floor to the 6 th floor is 30%.
The initial number of pedestrians inside the building is 1200. Under a minor earthquake of intensity 8, the structural and non-structural components in the target building are not damaged, and no obstacles are newly generated during the evacuation process. All the pedestrians can complete the evacuation. The evacuation process is illustrated in Figure 23. The total evacuation time reaches 528 s. The relationship between the time and the number of people completing evacuation is presented in Figure 24. The congestion mainly occurs in corridors and stairs.
Under a moderate earthquake of intensity 8, the overall structure is not damaged. However, the suspended ceilings and partition walls are damaged. The evacuation process under the moderate earthquake of intensity 8 is illustrated in Figure 25. It can be seen that 55 pedestrians do not complete the evacuation and casualties occur. The overall evacuation time is reached after 570 s. Although the whole structure is not damaged, the casualties induced by the damage of non-structural components account for 4.58% of the total population. The emergent new obstacles obstruct the evacuation routes and exits, which results in the phenomenon that the pedestrians will re-select a reasonable evacuation route in the evacuation process. Therefore, it is necessary to consider the influence of damage on the non-structural components, in seismic evacuation simulation. Figure 25 illustrates that under a major earthquake of intensity 8, the floors of the whole structure that are above the 2 nd floor collapse, the suspended ceilings and partition walls of non-structural components are seriously damaged. At the end of the earthquake, 617 pedestrians are stranded in the damaged structure, 406 pedestrians are injured and killed, while 177 pedestrians complete the evacuation. Most of the pedestrians who successfully escaped are originally located in the first floor. By analyzing the evacuation process, it can be deduced that the areas with high incidence of casualties are concentrated in corridors and staircases. If the pedestrians are anxious to evacuate, they will be crowded in corridors or staircases. Once high population density areas are damaged, the consequences will be very serious. If there is no sufficient evacuation time under strong earthquakes, the pedestrians choose to enter a relatively safe area for emergency shelter, which is an efficient way of self-protection.

Conclusion and discussion
Due to the randomness of the pedestrian evacuation process, a damage of building structure and ground motion occurs, and therefore the evacuation time, evacuation route and casualties under earthquake have indeterminacy. This paper proposes a high-precision model to simulate crowd evacuation under earthquake, and an approach for casualties assessment based on evacuation simulation. In order to perform the assessment of casualties, this paper develops the finite element method to simulate the seismic damage of building structure. In addition, it proposes the improved CA model in order to accurately simulate the evacuation process. Moreover, the criterion for determining casualties, which considers the damage of structural and nonstructural components, is proposed. Based on this criterion, the prediction of casualties is performed by spatial and temporal combination of the finite element model and evacuation simulation model. The crowd evacuation simulation model is an improved CA model, which accurately demonstrates the geometric dimensioning of the evacuation environment and obstacles. The influence of the evacuation distance and crowd density at the exits are considered, when the pedestrians select target exits. The improved CA model also considers the herd behavior, conflict phenomenon and falling non-structural components on