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

Evacuation simulation of multi-story buildings during earthquakes based on improved cellular... JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING https://doi.org/10.1080/13467581.2022.2070491 Evacuation simulation of multi-story buildings during earthquakes based on improved cellular automata model a a b Guangchun Zhong , Guofang Zhai and Wei Chen a b School of Architecture and Planning, Nanjing University, Nanjing, PR China; School of Geographic and Biologic Information, Nanjing University of Posts and Telecommunications, Nanjing, PR China ABSTRACT ARTICLE HISTORY Received 28 January 2022 The simulation of the authentic evacuation process is conducive to accurately evaluate the Accepted 22 April 2022 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 KEYWORDS model simulates the attraction of exits to crowds, herd behavior of crowds, avoidance behavior Earthquake; evacuation for obstacles, decision-making behavior for paths/exits selection, and conflict between pedes- simulation; modified cellular trians in the evacuation process. Based on the video, which records authentic evacuation under automata model; non- earthquake, the influence coefficients of each factors are determined. In addition, the modified structural components; casualty prediction 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. 1. Introduction 2005; Shapira, Aharonson-Daniel, and Shohet et al. 2015; Shaohong and Jin 2015; Gul and Guneri 2016). The existing casualty assessment methods are mainly These studies can perform the assessment of casualties based on empirical formula or probability statistical on regional scales from macro perspective, and they methodology (Badal, Vázquez-Prada, and González CONTACT Wei Chen chen_wei@njupt.edu.cn School of Geographic and Biologic Information, Nanjing University of Posts and Telecommunications, Nanjing, PR China © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 G. ZHONG ET AL. have an acceptable accuracy. However, they are not evacuation. Currently, most of the researchers use the suitable for predicting the number of casualties in cellular automata model to simulate the crowd evacua- building scale. In order to satisfy the requirements of tion under fire (Cao, Song, and Liu et al. 2014), flood accurate rescue plan after earthquake and accurately (Simonovic and Ahmad 2005; Liu, Okada, and Shen determine the number of refugees, it is necessary to 2009), toxic gas leakage (Cao, Fan, and Shuxia 2016), efficiently assess the number and location distribution hurricane (Koshute 2013), terrorist attack (Liu 2018), or of casualties in small-scale. The observations after the without considering the disaster environment (Tan, earthquakes illustrate that the evacuation process Mingyuan, and Lin 2015; Ma, Lo, and Song 2012; affects the casualties during the earthquake (Shuang, Zhao, Yang, and Jian 2006). Some researchers intro- Xiaohui, and Zhang et al. 2018). Considering the influ - duced the field intensity of fire (Jin, Ruan, and Yue ence of the evacuation process is a more accurate 2018), repulsive force of fire (Meng, Zhou, and Rao approach for the evaluation of casualties in building 2009) and fire risk, in order to improve the traditional dimensions under earthquake. CA model. The calculation formula of movement prob- In the emergency evacuation field, several research- ability is modified to simulate the pedestrians’ avoid- ers simulate the process of crowd evacuation using ance behavior and panic psychology under fire source. computer simulations (Gwynne, Galea, and Lawrence However, the evacuation simulation under earthquake et al. 1999; Lindell 2008). The crowd emergency eva- based on cellular automata model is rare. cuation models are divided into macro and micro In addition, the cells size in the CA model is too models. The macro model (Henderson 1971) considers coarse (0.5 m × 0.5 m (Zhao, Yang, and Jian 2008) or the movement of pedestrians as flow. It uses the partial 0.4 m × 0.4 m (Chen, Wang, and Heng et al. 2020)), differential equation in fluid dynamics in order to which cannot accurately simulate the authentic size of describe the variation trend of pedestrians’ speed obstacles. The CA model with more precise cellular and density function of time. It has a high computa- space should be further studied. The human behavior tional efficiency. However, it cannot reflect the inter- and the interaction between human and environment, action and heterogeneity between individuals. The are critical factors having a crucial influence on the micro model considers the pedestrians as individual evacuation process and evacuation time. Defining particles. It can simulate a specific evacuation beha- and simulating the human behavior and movement vior, interaction and heterogeneity between indivi- law of pedestrians, are important for evacuation simu- duals. The micro model has the advantage of leading lation under earthquake. However, the current studies to accurate simulation results. Moreover, the descrip- on evacuation behavior mostly concentrate on one or tions of the pedestrians’ movement are accurate and two behavioral characteristics. The studies on coupling natural. The most common micro models include the multiple behaviors are rare. With the development of social force model (Helbing and Molnar 1995), cellular the evacuation simulation model and accuracy, studies automata (Burstedde et al. 2001), multi-agent model on multiple evacuation behaviors are crucial. (Pan, Han, and Dauber et al. 2007), lattice gas model Combining the crowd emergency evacuation pro- (Muramatsu, Irie, and Nagatani 1999) and RVO model cess with the structural damage process, is also crucial (Wei, Chen, and Jiheng et al. 2010). for the evacuation model under earthquake. Xiao et al. The social force model (Helbing, Farkas, and Vicsek (2017) perform the evacuation simulation of residential 2000) is integrated into the underlying algorithm of buildings (Xiao, Chen, and Yan et al. 2016) and primary Anylogic platform (8.5.0). It has high accuracy and schools during the Ludian earthquake. The required characteristics of continuous micro simulation. safe evacuation time (REST) is estimated by the non- However, the simulation efficiency is not ideal. The linear time history analysis of building structure. The cellular automata (CA) model is suitable to describe reduction of speed under earthquake is also consid- the dynamic process of evacuation, and considers the ered. However, the damage process of building struc- complex human behavior (Burstedde, Klauck, and ture is not coupled with the evacuation process. Liu, Schadschneider et al. 2001). It is a grid dynamics Jacques, and Szyniszewski et al. (2016) and Cimellaro, model based on the continuous evolution of the states Ozzello, and Vallero et al. (2017) assume that the eva- of adjacent cells in the time dimension and spatial cuation starts when the vibration induced by the earth- dimension. It can simulate the spatial-temporal evolu- quake stops. This assumption does not consider the tion of complex systems. It can also simulate the spe- evacuation behavior in the evacuation simulation cific evacuation behavior and psychology, including model when the building is vibrating. Shuang, the avoidance (Song, Zhang, and Huo et al. 2020), Xiaohui, and Zhang et al. (2018), Shuang, Zhai, and panic (Varas, Cornejo, and Mainemer et al. 2007), fol- Xie (2015) propose a novel evacuation simulation lowing (Can, Qun, and Chen 2019), herd (Yuan and Tan model in order to perform casualty assessment of 2007), helping (Gao and Guan 2018) and inertial (Zhai, a teaching building. It is assumed that, when the rela- Jie, and Hou et al. 2020) behaviors. Therefore, it is tive displacement of adjacent floors is less than the widely used to simulate the process of crowd critical value, the casualties will occur in this position. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 3 The model combines the collapse process of building evacuation process and complex evacuation behavior structure with the evacuation process. However, it can be simulated by establishing the rules for pedes- does not consider the influence of the failure of non- trians in order to move to the surrounding cellular structural components on the evacuation process. units, the interaction rules between pedestrians, and This study aims at improving the traditional CA the interaction rules between the pedestrians and dis- model, and proposes an approach for casualty assess- aster environment. This section proposes an evacua- ment in building scale. It solves three existing critical tion simulation model based on the improved CA issues: simulation of crowd evacuation behavior under model. The refined cellular space is then developed. earthquake, establishment of highly refined cellular The crowd’s decision-making behavior for exits and units, and combining the structural damage process avoidance behavior for obstacles under a multi-exit with the evacuation process. The improved CA model evacuation scenario, are simulated. under earthquake is proposed to simulate panic psy- chology, herd behavior and decision-making behavior 2.1.1. Improving the size of the cellular unit under multi-exit environment. The model combines Typical sizes of the cellular unit are 0.4 m × 0.4 m (Chen, the damage process of structural and non-structural Wang, and Heng et al. 2020) and 0.5 m × 0.5 m (Dewei components with the crowd evacuation process. It also and Han 2015). The refined cellular unit can more accu- proposes a refined cellular unit to more accurately rately simulate the geometrical dimensions of the eva- simulate the spatial size of obstacles, and improve cuation environments and obstacles. In addition, the the simulation accuracy. The model can provide struc- influence of multiple velocities on the evacuation pro- tural designers, architects and rescuers with important cess can be considered. The evacuation speed under pffiffiffi information such as the evacuation route, total evacua- diagonal direction is determined as 2 m/s. When peo- tion time and casualties under earthquake, for exam- ple move through the horizontal or vertical direction, ple. Based on the provided information, the optimal the evacuation speed is determined as 1 m/s. Compared evacuation paths can be determined on the architec- with the cellular unit of 0.1 m × 0.1 m dimension, the cell tural design stage, or the locations where casualties having a dimension of 0.2 m × 0.2 m is able to accurately occurred on existing buildings can be predicted. represent the geometric size of obstacles and decrease The remainder of this paper is organized as follows. the computational load. Therefore, the size of the In section 2, a seismic evacuation model based on an refined cellular unit is determined as 0.2 m × 0 2 m. In improved CA model is proposed. According to the order to ensure the space pedestrians need and swing coefficient of variation and a video of the evacuation amplitudes of four limbs during evacuation, this study process in authentic earthquake scenarios, the para- stipulates that one pedestrian should occupy four cel- meters of the evacuation model are calibrated. lular units. The cellular space occupied by pedestrians is Section 3 puts forward the coupling rules between presented in Figure 1, where the blue circle represents the damage process of the structural and non- one pedestrian, and the grey shaded area denotes the structural components with the process of crowd eva- space occupied by the pedestrian, which cannot be cuation under earthquake. The judgment criteria of occupied by other people. casualties are also developed. In section 4, a 7-story reinforced concrete frame structure in Wenchuan 2.1.2. Simulation of evacuation behavior earthquake is considered as an empirical case, in In each time step, the pedestrians determine the order to verify the efficiency and rationality of the movement direction and target cell for the next time proposed approach. Finally, section 5 summarizes the step, according to the local rules. The influence of the advantages of the proposed method and concludes static attraction, dynamic attraction, exit-choice func- the paper. tion and falling components (obstacles) during the evacuation process is considered. The static attraction simulates the self-driving behavior that pedestrians 2. Development of the evacuation model move towards the exit. The dynamic attraction simu- under earthquake lates the interaction between the pedestrians and herd behavior. The function for exit choice simulates the 2.1. Evacuation simulation model: improved selective behavior in the multi exit/multi-route evacua- cellular automata model tion environment. The “risk value” simulates the avoid- The spatial dimensions, time dimensions and state of ance behavior for falling components (obstacles). units in the CA model are discrete. The CA model (1) Static attraction discretizes the evacuation space into cellular units, The static attraction represents the attraction from where the pedestrians and obstacles occupy one or exits to pedestrians. The value of the static attraction more cellular units. The state of each cellular unit is does not change with time nor with the pedestrians’ determined by the state of its adjacent cellular unit in movement. It is quantified by the distance from the the last time step and a series of local rules. The cellular units to the exits: 4 G. ZHONG ET AL. Figure 1. Cellular space occupied by pedestrians. � � qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of dynamic attraction (α∈[0,1], β∈[0,1]), respectively. 2 2 S ¼ max ði i Þ þðj j Þ i;j e s e n In each time step, the dynamic attraction will spread ði ;j Þ s s qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi with probability value α and attenuate with probability 2 2 ði iÞ þðj jÞ (1) value β, which affects the adjacent cellular units. The diffusion phenomenon is considered as: where (i , j ) represents the position coordinates of exit e e e, (i , j ) denotes the position coordinates of all the s s tþΔt t D ¼ ð1 αÞD cellular units, and (i, j) are the location coordinates of i;j i;j t t t t t a cellular unit. D D D D D iþ1;j i 1;j i;jþ1 i;j 1 i 1;j 1 þ αð þ þ þ þ Under multiple-exits environment, the S of each i,j 8 8 8 8 8 t t t D D D exit should be first calculated separately, and then i 1;jþ1 iþ1;j 1 iþ1;jþ1 þ þ þ Þ determined as the maximum value. 8 8 8 (3) Kirchner uses the Euclidean distance to calculate the static attraction (Kirchner and Schadschneider Simultaneously, the attraction of cell (i, j) will decay 2002), which is only applicable to simple scenarios with time after the pass of occupant. The decay phe- with convex boundaries and without obstacles. For nomenon is considered as: the evacuation scenario with obstacles, the following methods are used to determine the static attraction: (1) tþΔt tþΔt D ¼ ð1 βÞD (4) The static attraction of the cellular unit at the exit is i;j i;j assigned as 0; (2) The static attraction of each cellular According to the order that dynamic attraction first unit is calculated from the exits to the inside. The value diffuses and then attenuates, this section combines of the adjacent cellular unit in vertical and horizontal equation (3) and (4) to determine the dynamic attrac- directions increases by 1, while the value in the diag- tion of cell (i, j) at moment t + 1: onal direction increases by 1.5; (3) The static attractions of walls and obstacles are determined as the maximum tþΔt t D ¼ ð1 αÞð1 βÞD values; (4) When all the cellular units are assigned, the i;j i;j t t t t D D D D static attraction of each cellular unit is determined by iþ1;j i 1;j i;jþ1 i;j 1 þ αð1 βÞð þ þ þ subtracting the value of the current cellular unit from 8 8 8 8 t t t t D D D D i 1;j 1 i 1;jþ1 iþ1;j 1 iþ1;jþ1 the maximum value. þ þ þ þ Þ (5) 8 8 8 8 (2) Dynamic attraction The dynamic attraction determined the interaction (3) Function for exit choice and route choice between pedestrians and herd behavior. In contrast to In a multi-exits evacuation environment, the eva- the static attraction, the dynamic attraction changes cuation route choice is affected by the evacuation with time and evacuation process. Its initial value D is ij distance and population density at the exit (Jia et al. set to zero, and increases with the occupied frequency. 2018). In the process of choosing exits, the pedestrians When people occupy the cellular unit (i, j) at moment t, estimate the waiting time according to congestions at and leave at moment t+ Δt, the dynamic attraction different exits and evacuation distances, thus con- increases by 1: stantly adjusting the target exit and evacuation route. D ¼ D þ 1 (2) ij;tþΔ t ij;t This study develops the exit-choice function E in order to simulate the pedestrians’ choice of exit during eva- The dynamic attraction is related to the evacuation cuation. For the evacuation environment with two time, and has dynamic characteristics of diffusion and exits, the exit-choice function of each cell at moment attenuation. This study uses α and β to describe the diffusion characteristics and attenuation characteristics t is expressed as: JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 5 Figure 2. Extended Moorish domain. density Aþdensity B S � ðd r Þ=d r � d > ij ij ij E ðAÞ ¼ < i;j density A R ¼ (9) ij distance to Aþ distance to B þ (6) : distance to A 0 r > d ij where R is the risk value of cell (i, j), S denotes the ij i,j density Aþdensity B static attraction when cell (i, j) is occupied by the initial E ðBÞ ¼ i;j density B obstacles, and r represents the distance from the ij distance to Aþ distance to B “hazard source” to cell (i, j). þ (7) distance to B 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 E ¼ max½E ðAÞ; E ðBÞ� (8) i;j i;j i;j traditional Von Neumann neighborhood and Moore neighborhood, an extended Moore neighborhood is where density A and density B, respectively, represent proposed. Since all the rules in the CA model are the population density at exit A and exit B, distance developed for cells rather than lattice points, the A and distance B represent the distance from cell (i, j) improved CA model uses cells to represent pedes- to exit A and exit B, respectively. trians, and ensures that cell (i, j), cell (i + 1, j), cell (4) Avoidance behavior for obstacles (i + 1, j-1) and cell (i, j-1) will not be occupied by The avoidance and panic psychology for other pedestrians. damaged structural or non-structural components, The people determine the movement probability of are typical behaviors and psychology in seismic eight directions based on the attraction of neighbor- evacuation. The cell where damaged components hood cells, as shown in Figure 2. The target cell in the are located in is referred to as “hazard source”. next time step is determined on the movement prob- Similar to the original obstacles, the “hazard source” ability. The attraction level and movement probability will not be occupied or crossed by pedestrians. The are determined by the static attraction, dynamic attrac- difference between the “hazard source” and the tion, exit choice function, “hazard source” and state of original obstacles is that the “hazard source” will cells (whether cells are occupied or not). The move- radiate into the surrounding area. Based on the video analysis of evacuation in the classroom ment probability of eight neighborhood cells is com- (Xiaolin, Zhongliang, and Yingchun 2010), when an puted as: earthquake occurs, the distance for pedestrians to P ¼ N exp ½k S þ k D þ k E k R �ð1 n Þð1 m Þ avoid obstacles does not exceed three meters. ij s ij d ij e ij r ij ij ij Therefore, the radiation radius of the “hazard (10) source” is determined as 3 m. The radiation inten- where S , D , E and R , respectively, represent the sity of cell (i, j) decreases when the distance from ij ij ij ij static attraction, dynamic attraction, exit-choice func- cell (i, j) to the “hazard source” increases. The risk tion and risk value, k , k , k and k respectively, denote value of the “hazard source” is similar to that of the s d e r the influence coefficient of the static attraction, static attraction of the cell when it is occupied by dynamic attraction, exit-choice function and risk value, original obstacle. The risk value of cell (i, j) is n = 1 indicates that the neighborhood cell is occupied given by: i,j 6 G. ZHONG ET AL. Figure 3. Diagram of conflict during evacuation. by pedestrians (otherwise, n = 0), and m = 1 indi- greater than µ , the pedestrian having the highest i,j i,j cates that the neighborhood cell is occupied by obsta- movement probability will enter the target cell. cles (otherwise, m = 0). Otherwise, all the pedestrians remain in the original i,j N is then introduced as a normalized coefficient: position in the next time step. (4) The evacuation process uses the synchronous update rule to update the position status of all the N ¼ (11) ð1 n Þ exp½k S þ k D i;j s ij d ij pedestrians within the same time step. ði;jÞ (5) While updating the pedestrians’ location, the þk E k R �ð1 n Þð1 m Þ e ij r ij ij ij static attraction, dynamic attraction, exit choice func- tion and risk value of each cell are updated. Finally, the If the target cell is not occupied and multiple pedes- model enters the next cycle simulation. trians simultaneously compete for one target cell, a collision will occur. In the authentic evacuation pro- cess, due to the influence of psychological, physiologi- 2.2. Parameter analysis cal and environmental factors, the pedestrians will In the parameter analysis, a video, which records an hesitate or avoid each other when they compete for authentic evacuation under earthquake (https://m.v. one target cell. In order to solve the competition and qq.com/z/msite/play-short/index.html?cid=&vid= collision during the evacuation process, the friction o08073ef0ll&qqVersion=0) is considered as an empirical coefficient µ is introduced. Firstly, a number ranging case. The size of the double-exit room is 10.0 m × 8.0 m. between 0 and 1, is randomly generated. When the The number of people is 51 and the width of the exit is random number is greater than µ , the pedestrians will 1.2 m, as shown in Figure 6. Due to the model random- compare their movement probability with each other. ness, the evacuation process of each simulation is uncer- The pedestrian having the highest movement prob- tain and different. Therefore, under the same evacuation ability can enter the target cell in the next time step. environment, the evacuation routes and evacuation When the random number is less than µ , the pedes- time of people are not the same in each simulation. It trians will not compare the movement probability and is deduced that the evacuation time tends to be stable remain in their original position in the next step. after 30 calculations. When the computation time con- Therefore, no pedestrians will enter into the target tinues to increase, the average value of the evacuation cell. Figure 4 demonstrates the confilict process during time is not influenced. Therefore, the average value of evacuation. the evacuation times after 30 computations is consid- In general, figure 5 illustrates the updating rules for ered as the final evacuation time. cells of the proposed seismic evacuation model The influence coefficients in equation (11) are include the following steps: determined using three different methods: (1) exist- (1) Calculate the movement probability to the sur- ing methods of the literature; (2) calibration based rounding eight neighborhood directions; on the video, which records the authentic evacua- (2) The pedestrians select the target cell in the next tion scenario; (3) evacuation time and its coefficient time step, based on the movement probability of eight of variation. The influence coefficients of exit-choice neighborhood directions; function and risk value are calibrated based on the (3) In the local area where collision occurs, when video of authentic evacuation. In this section, the multiple pedestrians choose the same target cell in influence coefficient of static attraction (k ) and next time step, if the generated random number is s JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 7 Figure 4. Procedures of the evacuation simulation. Figure 5. Evacuation process in a real earthquake scenario. Figure 6. Evacuation model based on aacuation model based on a real evacuation scenario. 8 G. ZHONG ET AL. Figure 7. Influence of k on the evacuation time and coefficient of variation. (a) Influence of k on the evacuation time (b) Influence s s of k on the coefficient of variation. Figure 8. Influence of k on the evacuation time and coefficient of variation. (a) Influence of k on the evacuation time (b) Influence d d of k on the coefficient of variation. influence coefficient of dynamic attraction (k ), are weakened, which results in a gradual decrease of the evaluated by parameter analysis. In the latter, evacuation time. When the value of k is larger than 2.5, α = 0.1, β = 0.3, k = 1.2, k = 4 and µ = 0.5 are the proportion of static attraction increases, and the e r used as standard parameter sets. evacuation time tends to be gradually stable. Figure 7) illustrates the influence of k on the eva- In order to reflect the fluctuation of the evacuation cuation time for values of k equal to 0, 1, 2, 5 and 10. time, Figure 8) illustrates the influence of k on the D s For k = 0, the evacuation Fig 8b process is not related variable coefficient of evacuation time for values of k d d to the dynamic attraction, and it is only affected by equal to 0, 1, 2, 5 and 10. For k = 0, because the static attraction. The evacuation time is not affected by evacuation process is not related to the dynamic the change of k . In this situation, the pedestrians do attraction, and the evacuation time is not affected by not blindly follow the crowd. Therefore, the evacuation the change of k , the coefficient of variation is small time is stable. For values of k equal to 1, 2, 5 and 10, and stable. For values of k equal to 1, 2, 5 and 10, with D D the influence of the static attraction and dynamic a small value of k (such as k = 0.05), the variation s s attraction should be simultaneously taken into coefficient of evacuation time reaches the highest account. For a small value of k (such as k = 0.05), level. With the increase of k , the coefficient of variation s s s people are familiar with the exits. The influence coeffi - gradually decreases and tends to be stable. When the cient of dynamic attraction is relatively large, and the value of k increases to 2.5, the static attraction plays blind conformity is clear, which results in a longer a leading role, and the pedestrians can quickly and evacuation time. When k increases, the static attrac- orderly find the exits. tion has a greater influence on the evacuation process, Figure 9) presents the influence of k on the eva- people are more familiar with the location of exits, and cuation time for values of k equal to 0.4, 1.0, 2.5 and the phenomenon of blind conformity is gradually 5.0. For k = 5.0 and 2.5, the static attraction plays s JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 9 a dominant role in the evacuation process. People are for k = 1.2, the curve showing the relationship familiar with the position of exits. The evacuation time between the time and the number of people complet- is stable, since is not affected by the change of k . For ing evacuation fits well with the curve of authentic k = 0.4 and 1.0, the pedestrians’ familiarity with exits evacuation. reaches a low level. For a small value of k , the static Based on the surveillance video of classroom during Wenchuan earthquake (http://v.youku.com/v_show/ attraction still dominates, and the pedestrians are not id-XMjk3 NjE40Dg = .html), Xiaolin, Zhongliang, and significantly affected by the surrounding people. With Yingchun (2010) performed a statistical analysis on the the increase of k , the influence of the dynamic attrac- relationship between the evacuation time and the tion gradually increases, and the phenomenon of blind number of pedestrians completing evacuation. For dif- conformity becomes clearer, which results in the gra- ferent values of the influence coefficient of risk k , the dual increase of the evacuation time. When the influ - curves showing the relationship between the time and ence coefficient of dynamic attraction is large (such as the number of people on simulation model are com- k = 5), the dynamic attraction gradually occupies pared with the curve of authentic evacuation. Some a dominant position and the evacuation time becomes curves that are similar to the authentic situation and their corresponding risk values, are shown in Figure 12. stable. When the values of k and k are, respectively, s d It can be seen from Figure 12 that the value of k 1.0 and 5, the evacuation time tends to decrease, mainly affects the amplitude of avoidance to the which indicates that a certain extent of conformity is “hazard sources”. The larger the value of k , the greater conducive to improving the evacuation speed. the amplitude of avoidance, which results in a longer In order to reflect the fluctuation of the evacuation evacuation time. In addition, for k = 4, the evacuation time, Figure 9) illustrates the influence of k on the time required by pedestrians is similar to the actual variable coefficient of evacuation time, for values of k situation. The two reasons for the difference between equal to 0.4, 1.0, 2.5 and 4.0. For k = 5.0 and 2.5, the the simulation model and authentic evacuation sce- variation coefficient of evacuation time is very small. nario are summarized as follows: (1) the behavior pat- For k = 0.4 and 1.0, the variation coefficient gradually tern of pedestrians is a very complex process. The increases when k increases. As the value of k con- d d simulation algorithm cannot consider all the types of tinues to increase, the evacuation time tends to be behaviors and coupling between different behaviors; stable, and the coefficient of variation decreases. (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 2.3. Verification of the evacuation model the average value under repeated numerical experi- Based on the video, which records the authentic evacua- ments, which is more stable. tion under earthquake, it is deduced that the pedes- Considering that the probability of whether colli- trians are familiar with the location of exits during the sion during evacuation is 50%, the value of the friction evacuation process. Therefore, the influence coefficient coefficient µ is determined as 0.5. of static attraction k should not be too small. It can be observed from Figure 8 that, when the value of k is less 3. Criteria for determining casualties than 2.5, the evacuation time rapidly decreases with the increase of k . When the value of k is greater than 2.5, s s The casualties during evacuation under earthquake are the evacuation time becomes stable. Therefore, the induced by the overall collapse of the building structure, influence coefficient of static attraction is determined floor collapse and damage of non-structural compo- as 2.5, according to the parameter analysis. Since the nents. The evacuation simulation based on the teachers and students in the video record are familiar improved CA model is combined with the seismic non- with the exit environments, the blind conformity phe- linear time history analysis of building structures in time nomenon will not occur. Therefore, the influence coeffi - dimensions and spatial dimensions, in order to deter- mine the casualties. The evacuation space has two cient of dynamic attraction k should not be too large, superimposed grid systems: cellular automata grid and and it is determined as 1.0 in this study (Shuang, Zhai, finite element grid. The spatial coordinates of damaged and Xie 2015). components are tracked by a finite element mesh. The Based on the video, which records the authentic cellular automata mesh in the lower floor, overlapped evacuation process under earthquake (https://m.v.qq. with the vertical projection of damaged components, is com/z/msite/play-short/index.html?cid=&vid= then identified. If people are located in the cellular o08073ef0ll&qqVersion=0), the evacuation simulation automata grid, which overlaps with the projection of model for a double-exit room (cf. Figure 10) is devel- damaged components during evacuation, then casual- oped to calibrate the influence coefficient of exit- choice function k . It can be seen from Figure 11 that, ties will occur, as shown in Figure 13. e 10 G. ZHONG ET AL. Figure 9. Evacuation simulation model for a double-exit room. Figure 10. Relationship between the time and the number of people completing evacuation. Besides acquiring information on casualties, The criteria of casualties induced by damaged struc- another function of the developed coupling model is tural components are determined as follows: (1) to simulate the dynamically changing obstacles. In the according to the average height of Chinese people, process of authentic evacuation, the structural and this study assumes that, when the relative vertical non-structural components fall down as the time displacement between adjacent floors is less than change, which results in casualties and newly gener- 1.65 m, the casualties will occur at the corresponding ated obstacles during subsequent evacuation. The position (Shuang, Zhai, and Xie 2015); (2) when the coupling model simulates the phenomenon that peo- interstory drift ratio of floor j exceeds the limit value ple re-select a reasonable evacuation route after new of collapsed state at moment t, pedestrians in floor j, obstacles exist. If casualties occur, they will stay in j + 1, j + 2 . . . will stop the evacuation after this place and then become new obstacles for other pedes- moment. Pedestrians who have not completed the trians during evacuation. evacuation will suffer from casualties. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 11 Figure 11. The relationship between the time and the number of people completing evacuation, for different k values. Figure 12. Schematic diagram of the spatio-temporal coupling of crowd evacuation model, and nonlinear time history analysis under earthquake. Figure 13. Suspended ceiling falling scenario, with a falling rate of 5% by random number generation. Figure 14. Suspended ceiling falling scenario, with a falling rate of 30% by random number generation. 12 G. ZHONG ET AL. The evacuation simulation model considers the 1997, it was damaged during the Wenchuan earth- damage of infilled walls and suspended ceilings. quake. The structure has a plan dimension of According to the experimental results in (Guoqiang, 50.4 m × 17.4 m (cf. Figure 17). The height of stories Zhao, and Sun et al. 2003; Guoqiang, Fang, and Liu 1 to 7 is 4.6 m, 4.2 m, 3 × 3.6 m, 4.2 m and 3.6 m, et al. 2005; Cheng, Liu, and Liu 2010), when the peak respectively. The cross sections of frame beams are acceleration at the center of the infilled wall reaches 350 mm × 600 mm, and those of the columns 1.0 g, the infilled wall will collapse out of plane. When change along the structural height from 800 mm the infilled wall collapses, it is assumed that the col- × 800 mm to 500 mm × 500 mm. The thickness of lapse probability on both sides is the same. The range the slab is 100 mm. All the concrete design grades of a collapsed wall is determined using equation (12) are C30. The infilled wall is made by air brick with (Xinzheng, Yang, and Paolo Cimellaro et al. 2019). The a thickness of 200 mm. An analytical structural evacuation process based on the CA model is com- model is developed by ABAQUS (cf. Figure 18). bined with the collapse process of infilled wall in time and spatial dimensions. If an infilled wall collapses at 4.1.2. Development of finite element model moment t, casualties will occur while the pedestrians This study uses the ABAQUS (Systèmes 2013) soft- simultaneously get through the collapsed area. ware to simulate the building damage under the pffiffiffiffiffiffiffiffiffiffiffiffi earthquake excitation. The ABAQUS software d¼v 2h =g (12) i i i includes two algorithms: ABAQUS/implicit and where d represents the collapsed area, v denotes the ABAQUS/explicit. Due to the refined division of velocity at floor i + 1, h is the height of floor i, and elements in the finite element model, complexity g represents the gravitational acceleration. of material model and contact type, the implicit Several researchers proposed different damage algorithm leads to a large number of iterative pro- indexes and strength parameters to analyze the vul- cesses. Each iterative process requires to solve nerability of suspended ceilings (cf. Table 1). Based on a large number of nonlinear equations, which not ATC specification (cf. Table 2), the damage of sus- only decreases the calculation efficiency but also pended ceilings is divided into three states depend- results in a difficult convergence. Therefore, the ing on the falling rate: 5% (D1, slight damage), 30% implicit algorithm for finite element analysis has (D2, moderate damage) and 100% (D3, severe a high cost. The explicit algorithm uses the central damage). This study considers the peak floor accel- difference method for calculation, which does not eration as the strength parameter, and then gener- require to iterate and solve a large number of ates falling suspended ceilings using the stochastic equations. In terms of the definition of element method. For instance, if a room has 100 suspended mass, the explicit algorithm uses the centralized ceilings, when the falling rate reaches 30%, 30 sus- mass matrix, which reduces the inversion process pended ceilings are generated by the stochastic of mass matrix when calculating the inertial force. method. Based on the approach which combines the Therefore, it has a high calculation efficiency. evacuation process with the collapse process in time Therefore, the explicit algorithm is used for calcu- and spatial dimensions, casualties will occur when lation. The concrete material uses the concrete suspended ceilings are damaged and fall on the damage plastic model, while its constitutive curve ground, and pedestrians simultaneously get through follows the uniaxial stress-strain relationship speci- the damaged area. The size of the suspended ceilings fied in the code for the design of concrete struc- is considered as 600 mm × 600 mm (Qiqi, Zhe, and Xie tures (Industry Standard of the People’s Republic et al. 2019). Figure 14 and figure 15 illustrates the of China 2010). The reinforcement in the floor slab suspended ceiling with a failling rate of 5% and 30% is determined as a bilinear steel model with a post respectively. 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 4. Case study model uses the Timoshenko beam element B31 to simulate beam and column members. The floor 4.1. Nonlinear time history of target building simulation for floor slab uses the S4R quadrilateral 4.1.1. Overview of target building shell element, which considers arbitrary large The target building is a seven-story office building deformation and effective membrane strain. In of a Power Gas Company located in Dujiangyan, the analysis steps, the Rayleigh damping and gen- Sichuan Province, China. The structural type is eral contact algorithm are used in the finite ele- a reinforced concrete frame structure (cf. ment model. The ground is simulated by an Figure 16). Although the structure is originally analytical rigid body. Finally, the ground and col- designed based on a seismic intensity of 7 in umn are consolidated. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 13 Figure 15. Structural plan layout. Figure 16. Architectural plan layout. Figure 17. Finite element model in ABAQUS. Figure 18. Displacement under a moderate earthquake of intensity 8. 14 G. ZHONG ET AL. Figure 19. Time history of Wolong earthquake record. Figure 20. Response spectrum of Wolong earthquake record. Figure 21. Inter-story drift ratios for different earthquake intensities. (a) Minor earthquake (b) Moderate earthquake (c) Major earthquake JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 15 Figure 22. Crowd evacuation process under a minor earthquake of intensity 8. (a) Distribution of pedestrians at 1.92 s (b) Distribution of pedestrians at 23 s (c) Distribution of pedestrians at 142 s (d) Distribution of pedestrians at 420 s. Figure 23. Relationship between the time and the number of people completing evacuation. 4.1.3. Nonlinear time history analysis down to 0.07 g, 0.2 g and 0.4 g in order to commensu- This study considers the 2008 Wenchuan earthquake rate with the PGA under minor, moderate, and major ground motion record (Wolong Station N-S), in order earthquakes of intensity 8. The duration of the Wolong to perform the nonlinear time history analysis. The ground motion is 60 s. The inputted direction is along time histories and response spectra of Wolong ground the weak axis of the structure. The inter-story drift motion, are illustrated in Figures 19 and 20, respec- ratios of the case structure under different earthquake tively. The peak ground accelerations (PGA) are scaled intensities, are illustrated in Figure 22Figure 21. 16 G. ZHONG ET AL. Table 1. Damage indexes and strength parameters for suspended ceilings. Literature Damage state Strength parameter Gilani, Takhirov and Tedesco . (2013) Falling rate: 0, <5%, 5%~20%, 20%~50%, >50% – – Qiqi, Zhe, and Xie et al. (2019) Falling rate: 0, <5%, 5%~30%, >30% PFA Zaghi, Soroushian, and Echevarria Heiser et al. Damage rate of keel or falling rate: 0, <5%, 5%~30%, 30% PFA (2016) ~70%, >70% Soroushian, Rahmanishamsi, and Ryu et al. Falling rate: 0, <5%, 5%~20%, >20% PFA/ Inertial forces in horizontal (2016) direction Badillo, Whittaker, and Reinhorn (2007) Falling rate: 1%, 1%~10%, 10%~33%, keel grid damaged PFA/ Floor response spectrum Table 2. Fragility functions of nonstructural components used for damage assessment (Data extracted from ATC 2012) Applied ). Technology Council 2012 Nonstructural component x Damage state x Partition walls Peak interstory drift ratio (rad) D1 0.0021 D2 0.0071 D3 0.0012 Suspended ceiling with area < 23 m Peak floor acceleration (g) D1 1.00 D2 1.80 D3 2.40 2 2 Suspended ceiling with 23 m < area < 93 m Peak floor acceleration (g) D1 0.70 D2 1.15 D3 1.80 2 2 Suspended ceiling with 93 m < area < 232 m Peak floor acceleration (g) D1 0.45 D2 0.7 D3 1.00 Suspended ceiling with area > 232 m Peak floor acceleration (g) D1 0.35 D2 0.55 The damage states of partition walls are D (screws fall out, minor cracking of wallboard occurs, and tape warps or cracks); D (moderate cracking or 1 2 crushing of wallboard occurs, typically in corners and at corners of openings), and D (significant cracking or crushing of wallboard occurs, studs buckle, and tracks tear). The damage states of suspended ceilings are D (5% of tiles dislodge and fall), D (30% of tiles dislodge and fall, t-bar grid is damaged), 1 2 and D (ceiling tiles and t-bar grid entirely collapse).(Data extracted from ATC 2012) Figure 24. Crowd evacuation process under a moderate earthquake of intensity 8. (a) Distribution of pedestrians at 0.92s (b) Distribution of pedestrians at 2.88 s (c) Distribution of pedestrians at 17.28 s (d) Distribution of pedestrians at 389 s. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 17 Figure 25. Crowd evacuation process under a major earthquake of intensity 8. (a) Distribution of pedestrians at 0.92s (b) Distribution of pedestrians at 2.4s (c) Distribution of pedestrians at 23.52 s (d) Distribution of pedestrians at 289 s. Table 3. Damage information of suspended ceilings. Earthquake intensity Floor Falling time Falling rate Major earthquake of intensity 8 1 2.44 s 5% Major earthquake of intensity 8 2 2.44 s 30% Major earthquake of intensity 8 3 2.48 s 30% Major earthquake of intensity 8 4 2.5 s 30% Major earthquake of intensity 8 5 3.62 s 30% Major earthquake of intensity 8 6 3.52 s 100% Moderate earthquake of intensity 8 1 – – 0% Moderate earthquake of intensity 8 2 2.44 s 5% Moderate earthquake of intensity 8 3 – – 0% Moderate earthquake of intensity 8 4 2.5 s 5% Moderate earthquake of intensity 8 5 3.62 s 5% Moderate earthquake of intensity 8 6 3.52 s 5% Table 4. Damage information of partition walls. Earthquake intensity Floor Collapse time Scope of damaged partition walls Major earthquake of intensity 8 1 3 s 0.41 m Major earthquake of intensity 8 2 2.42 s 0.92 m Major earthquake of intensity 8 3 2.42 s 0.72 m Major earthquake of intensity 8 4 2.44 s 0.68 m Major earthquake of intensity 8 5 1.98 s 0.96 m Major earthquake of intensity 8 6 2.92 s 1.0 m Moderate earthquake of intensity 8 1 – – 0 m Moderate earthquake of intensity 8 2 3.1 s 0.46 m Moderate earthquake of intensity 8 3 3.08 s 0.68 m Moderate earthquake of intensity 8 4 – – 0 m Moderate earthquake of intensity 8 5 – – 0 m Moderate earthquake of intensity 8 6 – – 0 m 18 G. ZHONG ET AL. not damaged, the casualties induced by the damage of 4.2. Evacuation model under earthquake and non-structural components account for 4.58% of the prediction for casualties total population. The emergent new obstacles obstruct The number of pedestrians stranded on each floor under the evacuation routes and exits, which results in the different earthquake intensities, distribution of pedes- phenomenon that the pedestrians will re-select trians at different moments, casualties on different parts a reasonable evacuation route in the evacuation pro- of the building and number of people completing eva- cess. Therefore, it is necessary to consider the influence cuation at the end of the earthquake, are studied based of damage on the non-structural components, in seis- on the results of evacuation simulation and nonlinear mic evacuation simulation. time history analysis. According to previous analysis, the Figure 25 illustrates that under a major earthquake of parameters of the improved CA model are determined as intensity 8, the floors of the whole structure that are follows: the influence coefficient of static attraction (k ), nd above the 2 floor collapse, the suspended ceilings and influence coefficient of dynamic attraction (k ), influence partition walls of non-structural components are ser- coefficient of exit choice function (k ), influence coeffi - iously damaged. At the end of the earthquake, 617 cient of “risk value” (k ) and friction coefficient (μ) are pedestrians are stranded in the damaged structure, determined as 2.5, 1.0, 1.2, 4 and 0.5, respectively. 406 pedestrians are injured and killed, while 177 pedes- The improved CA model proposed in section 2, is trians complete the evacuation. Most of the pedestrians used to develop the seismic evacuation model. The who successfully escaped are originally located in the number of casualties is determined based on the cou- first floor. By analyzing the evacuation process, it can be pling rules proposed in section 3. Tables 3 and 4 present deduced that the areas with high incidence of casualties the damage degree and failure time of the suspended are concentrated in corridors and staircases. If the ceilings and partition walls on each floor, for different pedestrians are anxious to evacuate, they will be earthquake intensities. It can be seen that, under crowded in corridors or staircases. Once high population a minor earthquake of intensity 8, the overall structure density areas are damaged, the consequences will be does not collapse, the suspended ceilings do not fall, very serious. If there is no sufficient evacuation time and the partition walls do not collapse. Under under strong earthquakes, the pedestrians choose to a moderate earthquake of intensity 8, the overall struc- enter a relatively safe area for emergency shelter, ture does not collapse. However, the suspended ceilings which is an efficient way of self-protection. nd th th th on the 2 , 4 , 5 and 6 floors drop out, with a falling nd rate of 5%. In addition, the partition walls on the 2 and 5. Conclusion and discussion rd 3 floors collapse. Under a major earthquake of inten- sity 8, the inter-story drift ratios of floors 2, 3 and 4 Due to the randomness of the pedestrian evacuation exceed the limit for collapse (1/20), and therefore the process, a damage of building structure and ground whole structure collapses. The partition walls collapse motion occurs, and therefore the evacuation time, eva- and the suspended ceilings are damaged on each floor. cuation route and casualties under earthquake have The falling rate of the suspended ceilings on the first indeterminacy. This paper proposes a high-precision floor is 5%. The falling rates of the suspended ceilings model to simulate crowd evacuation under earthquake, nd th from the 2 floor to the 6 floor is 30%. and an approach for casualties assessment based on The initial number of pedestrians inside the building evacuation simulation. In order to perform the assess- is 1200. Under a minor earthquake of intensity 8, the ment of casualties, this paper develops the finite ele- structural and non-structural components in the target ment method to simulate the seismic damage of building are not damaged, and no obstacles are newly building structure. In addition, it proposes the improved generated during the evacuation process. All the CA model in order to accurately simulate the evacuation pedestrians can complete the evacuation. The evacua- process. Moreover, the criterion for determining casual- tion process is illustrated in Figure 23. The total eva- ties, which considers the damage of structural and non- cuation time reaches 528 s. The relationship between structural components, is proposed. Based on this cri- the time and the number of people completing eva- terion, the prediction of casualties is performed by cuation is presented in Figure 24. The congestion spatial and temporal combination of the finite element mainly occurs in corridors and stairs. model and evacuation simulation model. The crowd Under a moderate earthquake of intensity 8, the evacuation simulation model is an improved CA overall structure is not damaged. However, the sus- model, which accurately demonstrates the geometric pended ceilings and partition walls are damaged. The dimensioning of the evacuation environment and evacuation process under the moderate earthquake of obstacles. The influence of the evacuation distance intensity 8 is illustrated in Figure 25. It can be seen that and crowd density at the exits are considered, when 55 pedestrians do not complete the evacuation and the pedestrians select target exits. The improved CA casualties occur. The overall evacuation time is model also considers the herd behavior, conflict phe- reached after 570 s. Although the whole structure is nomenon and falling non-structural components on JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 19 evacuation process. Compared with the current empiri- high-vulnerability areas in buildings, which is condu- cal and statistical casualty prediction methods, the pro- cive to the formulation of a post-earthquake rescue posed approach is more accurate, and can give more plan. quantitative results. The proposed approach has the following advantages: Disclosure statement (1) The improved CA model based on meticulous No potential conflict of interest was reported by the author(s). and discrete cellular space, can more accurately describe the geometric dimensions of the evacuation environments and obstacles. It can also improve the Funding accuracy of the simulation results. The improved CA This work was supported by the National Natural Science model uses eight neighborhood types. It arranges Foundation of China (Grant No. 52108053); Natural Science pedestrians to move in eight directions, and can con- Foundation of Jiangsu Province (Grant No. BK20200762); sider different evacuation speeds. The assignment Social Science Foundation of Jiangsu Province (Grant method is used to determine the static attraction, No. 20ZZC001). which is applicable to the evacuation environment with or without obstacles. Therefore, the quantized location information of cells is more reasonable. Notes on contributors (2) The rules for movement on the improved CA Guangchun Zhong, PhD Candidate, Research Interest: model perform the coupling of several evacuation Structural Optimization, Evacuation Simulation, Finite behaviors under earthquake. The crowd’s herd behavior Element Modelling. is simulated based on dynamic attraction, the crowd’s Guofang Zhai, Professor, Research Interest: Disaster choice behavior in multi-exit environment is simulated Prevention and Mitigation, Evuacuation Simulation. based on exit-choice function, and the crowd’s avoid- Wei Chen, Associate Professor, Research Interest: Disaster ance behavior of obstacles is simulated based on “risk Prevention and Mitigation, Evacuation Simulation. value”. The improved rules for movement more accu- rately reflect the evacuation behavior of pedestrians under earthquake, and improve the authenticity and References accuracy of the evacuation simulation. 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Evacuation simulation of multi-story buildings during earthquakes based on improved cellular automata model

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© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China.
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10.1080/13467581.2022.2070491
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JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING https://doi.org/10.1080/13467581.2022.2070491 Evacuation simulation of multi-story buildings during earthquakes based on improved cellular automata model a a b Guangchun Zhong , Guofang Zhai and Wei Chen a b School of Architecture and Planning, Nanjing University, Nanjing, PR China; School of Geographic and Biologic Information, Nanjing University of Posts and Telecommunications, Nanjing, PR China ABSTRACT ARTICLE HISTORY Received 28 January 2022 The simulation of the authentic evacuation process is conducive to accurately evaluate the Accepted 22 April 2022 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 KEYWORDS model simulates the attraction of exits to crowds, herd behavior of crowds, avoidance behavior Earthquake; evacuation for obstacles, decision-making behavior for paths/exits selection, and conflict between pedes- simulation; modified cellular trians in the evacuation process. Based on the video, which records authentic evacuation under automata model; non- earthquake, the influence coefficients of each factors are determined. In addition, the modified structural components; casualty prediction 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. 1. Introduction 2005; Shapira, Aharonson-Daniel, and Shohet et al. 2015; Shaohong and Jin 2015; Gul and Guneri 2016). The existing casualty assessment methods are mainly These studies can perform the assessment of casualties based on empirical formula or probability statistical on regional scales from macro perspective, and they methodology (Badal, Vázquez-Prada, and González CONTACT Wei Chen chen_wei@njupt.edu.cn School of Geographic and Biologic Information, Nanjing University of Posts and Telecommunications, Nanjing, PR China © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 G. ZHONG ET AL. have an acceptable accuracy. However, they are not evacuation. Currently, most of the researchers use the suitable for predicting the number of casualties in cellular automata model to simulate the crowd evacua- building scale. In order to satisfy the requirements of tion under fire (Cao, Song, and Liu et al. 2014), flood accurate rescue plan after earthquake and accurately (Simonovic and Ahmad 2005; Liu, Okada, and Shen determine the number of refugees, it is necessary to 2009), toxic gas leakage (Cao, Fan, and Shuxia 2016), efficiently assess the number and location distribution hurricane (Koshute 2013), terrorist attack (Liu 2018), or of casualties in small-scale. The observations after the without considering the disaster environment (Tan, earthquakes illustrate that the evacuation process Mingyuan, and Lin 2015; Ma, Lo, and Song 2012; affects the casualties during the earthquake (Shuang, Zhao, Yang, and Jian 2006). Some researchers intro- Xiaohui, and Zhang et al. 2018). Considering the influ - duced the field intensity of fire (Jin, Ruan, and Yue ence of the evacuation process is a more accurate 2018), repulsive force of fire (Meng, Zhou, and Rao approach for the evaluation of casualties in building 2009) and fire risk, in order to improve the traditional dimensions under earthquake. CA model. The calculation formula of movement prob- In the emergency evacuation field, several research- ability is modified to simulate the pedestrians’ avoid- ers simulate the process of crowd evacuation using ance behavior and panic psychology under fire source. computer simulations (Gwynne, Galea, and Lawrence However, the evacuation simulation under earthquake et al. 1999; Lindell 2008). The crowd emergency eva- based on cellular automata model is rare. cuation models are divided into macro and micro In addition, the cells size in the CA model is too models. The macro model (Henderson 1971) considers coarse (0.5 m × 0.5 m (Zhao, Yang, and Jian 2008) or the movement of pedestrians as flow. It uses the partial 0.4 m × 0.4 m (Chen, Wang, and Heng et al. 2020)), differential equation in fluid dynamics in order to which cannot accurately simulate the authentic size of describe the variation trend of pedestrians’ speed obstacles. The CA model with more precise cellular and density function of time. It has a high computa- space should be further studied. The human behavior tional efficiency. However, it cannot reflect the inter- and the interaction between human and environment, action and heterogeneity between individuals. The are critical factors having a crucial influence on the micro model considers the pedestrians as individual evacuation process and evacuation time. Defining particles. It can simulate a specific evacuation beha- and simulating the human behavior and movement vior, interaction and heterogeneity between indivi- law of pedestrians, are important for evacuation simu- duals. The micro model has the advantage of leading lation under earthquake. However, the current studies to accurate simulation results. Moreover, the descrip- on evacuation behavior mostly concentrate on one or tions of the pedestrians’ movement are accurate and two behavioral characteristics. The studies on coupling natural. The most common micro models include the multiple behaviors are rare. With the development of social force model (Helbing and Molnar 1995), cellular the evacuation simulation model and accuracy, studies automata (Burstedde et al. 2001), multi-agent model on multiple evacuation behaviors are crucial. (Pan, Han, and Dauber et al. 2007), lattice gas model Combining the crowd emergency evacuation pro- (Muramatsu, Irie, and Nagatani 1999) and RVO model cess with the structural damage process, is also crucial (Wei, Chen, and Jiheng et al. 2010). for the evacuation model under earthquake. Xiao et al. The social force model (Helbing, Farkas, and Vicsek (2017) perform the evacuation simulation of residential 2000) is integrated into the underlying algorithm of buildings (Xiao, Chen, and Yan et al. 2016) and primary Anylogic platform (8.5.0). It has high accuracy and schools during the Ludian earthquake. The required characteristics of continuous micro simulation. safe evacuation time (REST) is estimated by the non- However, the simulation efficiency is not ideal. The linear time history analysis of building structure. The cellular automata (CA) model is suitable to describe reduction of speed under earthquake is also consid- the dynamic process of evacuation, and considers the ered. However, the damage process of building struc- complex human behavior (Burstedde, Klauck, and ture is not coupled with the evacuation process. Liu, Schadschneider et al. 2001). It is a grid dynamics Jacques, and Szyniszewski et al. (2016) and Cimellaro, model based on the continuous evolution of the states Ozzello, and Vallero et al. (2017) assume that the eva- of adjacent cells in the time dimension and spatial cuation starts when the vibration induced by the earth- dimension. It can simulate the spatial-temporal evolu- quake stops. This assumption does not consider the tion of complex systems. It can also simulate the spe- evacuation behavior in the evacuation simulation cific evacuation behavior and psychology, including model when the building is vibrating. Shuang, the avoidance (Song, Zhang, and Huo et al. 2020), Xiaohui, and Zhang et al. (2018), Shuang, Zhai, and panic (Varas, Cornejo, and Mainemer et al. 2007), fol- Xie (2015) propose a novel evacuation simulation lowing (Can, Qun, and Chen 2019), herd (Yuan and Tan model in order to perform casualty assessment of 2007), helping (Gao and Guan 2018) and inertial (Zhai, a teaching building. It is assumed that, when the rela- Jie, and Hou et al. 2020) behaviors. Therefore, it is tive displacement of adjacent floors is less than the widely used to simulate the process of crowd critical value, the casualties will occur in this position. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 3 The model combines the collapse process of building evacuation process and complex evacuation behavior structure with the evacuation process. However, it can be simulated by establishing the rules for pedes- does not consider the influence of the failure of non- trians in order to move to the surrounding cellular structural components on the evacuation process. units, the interaction rules between pedestrians, and This study aims at improving the traditional CA the interaction rules between the pedestrians and dis- model, and proposes an approach for casualty assess- aster environment. This section proposes an evacua- ment in building scale. It solves three existing critical tion simulation model based on the improved CA issues: simulation of crowd evacuation behavior under model. The refined cellular space is then developed. earthquake, establishment of highly refined cellular The crowd’s decision-making behavior for exits and units, and combining the structural damage process avoidance behavior for obstacles under a multi-exit with the evacuation process. The improved CA model evacuation scenario, are simulated. under earthquake is proposed to simulate panic psy- chology, herd behavior and decision-making behavior 2.1.1. Improving the size of the cellular unit under multi-exit environment. The model combines Typical sizes of the cellular unit are 0.4 m × 0.4 m (Chen, the damage process of structural and non-structural Wang, and Heng et al. 2020) and 0.5 m × 0.5 m (Dewei components with the crowd evacuation process. It also and Han 2015). The refined cellular unit can more accu- proposes a refined cellular unit to more accurately rately simulate the geometrical dimensions of the eva- simulate the spatial size of obstacles, and improve cuation environments and obstacles. In addition, the the simulation accuracy. The model can provide struc- influence of multiple velocities on the evacuation pro- tural designers, architects and rescuers with important cess can be considered. The evacuation speed under pffiffiffi information such as the evacuation route, total evacua- diagonal direction is determined as 2 m/s. When peo- tion time and casualties under earthquake, for exam- ple move through the horizontal or vertical direction, ple. Based on the provided information, the optimal the evacuation speed is determined as 1 m/s. Compared evacuation paths can be determined on the architec- with the cellular unit of 0.1 m × 0.1 m dimension, the cell tural design stage, or the locations where casualties having a dimension of 0.2 m × 0.2 m is able to accurately occurred on existing buildings can be predicted. represent the geometric size of obstacles and decrease The remainder of this paper is organized as follows. the computational load. Therefore, the size of the In section 2, a seismic evacuation model based on an refined cellular unit is determined as 0.2 m × 0 2 m. In improved CA model is proposed. According to the order to ensure the space pedestrians need and swing coefficient of variation and a video of the evacuation amplitudes of four limbs during evacuation, this study process in authentic earthquake scenarios, the para- stipulates that one pedestrian should occupy four cel- meters of the evacuation model are calibrated. lular units. The cellular space occupied by pedestrians is Section 3 puts forward the coupling rules between presented in Figure 1, where the blue circle represents the damage process of the structural and non- one pedestrian, and the grey shaded area denotes the structural components with the process of crowd eva- space occupied by the pedestrian, which cannot be cuation under earthquake. The judgment criteria of occupied by other people. casualties are also developed. In section 4, a 7-story reinforced concrete frame structure in Wenchuan 2.1.2. Simulation of evacuation behavior earthquake is considered as an empirical case, in In each time step, the pedestrians determine the order to verify the efficiency and rationality of the movement direction and target cell for the next time proposed approach. Finally, section 5 summarizes the step, according to the local rules. The influence of the advantages of the proposed method and concludes static attraction, dynamic attraction, exit-choice func- the paper. tion and falling components (obstacles) during the evacuation process is considered. The static attraction simulates the self-driving behavior that pedestrians 2. Development of the evacuation model move towards the exit. The dynamic attraction simu- under earthquake lates the interaction between the pedestrians and herd behavior. The function for exit choice simulates the 2.1. Evacuation simulation model: improved selective behavior in the multi exit/multi-route evacua- cellular automata model tion environment. The “risk value” simulates the avoid- The spatial dimensions, time dimensions and state of ance behavior for falling components (obstacles). units in the CA model are discrete. The CA model (1) Static attraction discretizes the evacuation space into cellular units, The static attraction represents the attraction from where the pedestrians and obstacles occupy one or exits to pedestrians. The value of the static attraction more cellular units. The state of each cellular unit is does not change with time nor with the pedestrians’ determined by the state of its adjacent cellular unit in movement. It is quantified by the distance from the the last time step and a series of local rules. The cellular units to the exits: 4 G. ZHONG ET AL. Figure 1. Cellular space occupied by pedestrians. � � qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of dynamic attraction (α∈[0,1], β∈[0,1]), respectively. 2 2 S ¼ max ði i Þ þðj j Þ i;j e s e n In each time step, the dynamic attraction will spread ði ;j Þ s s qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi with probability value α and attenuate with probability 2 2 ði iÞ þðj jÞ (1) value β, which affects the adjacent cellular units. The diffusion phenomenon is considered as: where (i , j ) represents the position coordinates of exit e e e, (i , j ) denotes the position coordinates of all the s s tþΔt t D ¼ ð1 αÞD cellular units, and (i, j) are the location coordinates of i;j i;j t t t t t a cellular unit. D D D D D iþ1;j i 1;j i;jþ1 i;j 1 i 1;j 1 þ αð þ þ þ þ Under multiple-exits environment, the S of each i,j 8 8 8 8 8 t t t D D D exit should be first calculated separately, and then i 1;jþ1 iþ1;j 1 iþ1;jþ1 þ þ þ Þ determined as the maximum value. 8 8 8 (3) Kirchner uses the Euclidean distance to calculate the static attraction (Kirchner and Schadschneider Simultaneously, the attraction of cell (i, j) will decay 2002), which is only applicable to simple scenarios with time after the pass of occupant. The decay phe- with convex boundaries and without obstacles. For nomenon is considered as: the evacuation scenario with obstacles, the following methods are used to determine the static attraction: (1) tþΔt tþΔt D ¼ ð1 βÞD (4) The static attraction of the cellular unit at the exit is i;j i;j assigned as 0; (2) The static attraction of each cellular According to the order that dynamic attraction first unit is calculated from the exits to the inside. The value diffuses and then attenuates, this section combines of the adjacent cellular unit in vertical and horizontal equation (3) and (4) to determine the dynamic attrac- directions increases by 1, while the value in the diag- tion of cell (i, j) at moment t + 1: onal direction increases by 1.5; (3) The static attractions of walls and obstacles are determined as the maximum tþΔt t D ¼ ð1 αÞð1 βÞD values; (4) When all the cellular units are assigned, the i;j i;j t t t t D D D D static attraction of each cellular unit is determined by iþ1;j i 1;j i;jþ1 i;j 1 þ αð1 βÞð þ þ þ subtracting the value of the current cellular unit from 8 8 8 8 t t t t D D D D i 1;j 1 i 1;jþ1 iþ1;j 1 iþ1;jþ1 the maximum value. þ þ þ þ Þ (5) 8 8 8 8 (2) Dynamic attraction The dynamic attraction determined the interaction (3) Function for exit choice and route choice between pedestrians and herd behavior. In contrast to In a multi-exits evacuation environment, the eva- the static attraction, the dynamic attraction changes cuation route choice is affected by the evacuation with time and evacuation process. Its initial value D is ij distance and population density at the exit (Jia et al. set to zero, and increases with the occupied frequency. 2018). In the process of choosing exits, the pedestrians When people occupy the cellular unit (i, j) at moment t, estimate the waiting time according to congestions at and leave at moment t+ Δt, the dynamic attraction different exits and evacuation distances, thus con- increases by 1: stantly adjusting the target exit and evacuation route. D ¼ D þ 1 (2) ij;tþΔ t ij;t This study develops the exit-choice function E in order to simulate the pedestrians’ choice of exit during eva- The dynamic attraction is related to the evacuation cuation. For the evacuation environment with two time, and has dynamic characteristics of diffusion and exits, the exit-choice function of each cell at moment attenuation. This study uses α and β to describe the diffusion characteristics and attenuation characteristics t is expressed as: JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 5 Figure 2. Extended Moorish domain. density Aþdensity B S � ðd r Þ=d r � d > ij ij ij E ðAÞ ¼ < i;j density A R ¼ (9) ij distance to Aþ distance to B þ (6) : distance to A 0 r > d ij where R is the risk value of cell (i, j), S denotes the ij i,j density Aþdensity B static attraction when cell (i, j) is occupied by the initial E ðBÞ ¼ i;j density B obstacles, and r represents the distance from the ij distance to Aþ distance to B “hazard source” to cell (i, j). þ (7) distance to B 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 E ¼ max½E ðAÞ; E ðBÞ� (8) i;j i;j i;j traditional Von Neumann neighborhood and Moore neighborhood, an extended Moore neighborhood is where density A and density B, respectively, represent proposed. Since all the rules in the CA model are the population density at exit A and exit B, distance developed for cells rather than lattice points, the A and distance B represent the distance from cell (i, j) improved CA model uses cells to represent pedes- to exit A and exit B, respectively. trians, and ensures that cell (i, j), cell (i + 1, j), cell (4) Avoidance behavior for obstacles (i + 1, j-1) and cell (i, j-1) will not be occupied by The avoidance and panic psychology for other pedestrians. damaged structural or non-structural components, The people determine the movement probability of are typical behaviors and psychology in seismic eight directions based on the attraction of neighbor- evacuation. The cell where damaged components hood cells, as shown in Figure 2. The target cell in the are located in is referred to as “hazard source”. next time step is determined on the movement prob- Similar to the original obstacles, the “hazard source” ability. The attraction level and movement probability will not be occupied or crossed by pedestrians. The are determined by the static attraction, dynamic attrac- difference between the “hazard source” and the tion, exit choice function, “hazard source” and state of original obstacles is that the “hazard source” will cells (whether cells are occupied or not). The move- radiate into the surrounding area. Based on the video analysis of evacuation in the classroom ment probability of eight neighborhood cells is com- (Xiaolin, Zhongliang, and Yingchun 2010), when an puted as: earthquake occurs, the distance for pedestrians to P ¼ N exp ½k S þ k D þ k E k R �ð1 n Þð1 m Þ avoid obstacles does not exceed three meters. ij s ij d ij e ij r ij ij ij Therefore, the radiation radius of the “hazard (10) source” is determined as 3 m. The radiation inten- where S , D , E and R , respectively, represent the sity of cell (i, j) decreases when the distance from ij ij ij ij static attraction, dynamic attraction, exit-choice func- cell (i, j) to the “hazard source” increases. The risk tion and risk value, k , k , k and k respectively, denote value of the “hazard source” is similar to that of the s d e r the influence coefficient of the static attraction, static attraction of the cell when it is occupied by dynamic attraction, exit-choice function and risk value, original obstacle. The risk value of cell (i, j) is n = 1 indicates that the neighborhood cell is occupied given by: i,j 6 G. ZHONG ET AL. Figure 3. Diagram of conflict during evacuation. by pedestrians (otherwise, n = 0), and m = 1 indi- greater than µ , the pedestrian having the highest i,j i,j cates that the neighborhood cell is occupied by obsta- movement probability will enter the target cell. cles (otherwise, m = 0). Otherwise, all the pedestrians remain in the original i,j N is then introduced as a normalized coefficient: position in the next time step. (4) The evacuation process uses the synchronous update rule to update the position status of all the N ¼ (11) ð1 n Þ exp½k S þ k D i;j s ij d ij pedestrians within the same time step. ði;jÞ (5) While updating the pedestrians’ location, the þk E k R �ð1 n Þð1 m Þ e ij r ij ij ij static attraction, dynamic attraction, exit choice func- tion and risk value of each cell are updated. Finally, the If the target cell is not occupied and multiple pedes- model enters the next cycle simulation. trians simultaneously compete for one target cell, a collision will occur. In the authentic evacuation pro- cess, due to the influence of psychological, physiologi- 2.2. Parameter analysis cal and environmental factors, the pedestrians will In the parameter analysis, a video, which records an hesitate or avoid each other when they compete for authentic evacuation under earthquake (https://m.v. one target cell. In order to solve the competition and qq.com/z/msite/play-short/index.html?cid=&vid= collision during the evacuation process, the friction o08073ef0ll&qqVersion=0) is considered as an empirical coefficient µ is introduced. Firstly, a number ranging case. The size of the double-exit room is 10.0 m × 8.0 m. between 0 and 1, is randomly generated. When the The number of people is 51 and the width of the exit is random number is greater than µ , the pedestrians will 1.2 m, as shown in Figure 6. Due to the model random- compare their movement probability with each other. ness, the evacuation process of each simulation is uncer- The pedestrian having the highest movement prob- tain and different. Therefore, under the same evacuation ability can enter the target cell in the next time step. environment, the evacuation routes and evacuation When the random number is less than µ , the pedes- time of people are not the same in each simulation. It trians will not compare the movement probability and is deduced that the evacuation time tends to be stable remain in their original position in the next step. after 30 calculations. When the computation time con- Therefore, no pedestrians will enter into the target tinues to increase, the average value of the evacuation cell. Figure 4 demonstrates the confilict process during time is not influenced. Therefore, the average value of evacuation. the evacuation times after 30 computations is consid- In general, figure 5 illustrates the updating rules for ered as the final evacuation time. cells of the proposed seismic evacuation model The influence coefficients in equation (11) are include the following steps: determined using three different methods: (1) exist- (1) Calculate the movement probability to the sur- ing methods of the literature; (2) calibration based rounding eight neighborhood directions; on the video, which records the authentic evacua- (2) The pedestrians select the target cell in the next tion scenario; (3) evacuation time and its coefficient time step, based on the movement probability of eight of variation. The influence coefficients of exit-choice neighborhood directions; function and risk value are calibrated based on the (3) In the local area where collision occurs, when video of authentic evacuation. In this section, the multiple pedestrians choose the same target cell in influence coefficient of static attraction (k ) and next time step, if the generated random number is s JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 7 Figure 4. Procedures of the evacuation simulation. Figure 5. Evacuation process in a real earthquake scenario. Figure 6. Evacuation model based on aacuation model based on a real evacuation scenario. 8 G. ZHONG ET AL. Figure 7. Influence of k on the evacuation time and coefficient of variation. (a) Influence of k on the evacuation time (b) Influence s s of k on the coefficient of variation. Figure 8. Influence of k on the evacuation time and coefficient of variation. (a) Influence of k on the evacuation time (b) Influence d d of k on the coefficient of variation. influence coefficient of dynamic attraction (k ), are weakened, which results in a gradual decrease of the evaluated by parameter analysis. In the latter, evacuation time. When the value of k is larger than 2.5, α = 0.1, β = 0.3, k = 1.2, k = 4 and µ = 0.5 are the proportion of static attraction increases, and the e r used as standard parameter sets. evacuation time tends to be gradually stable. Figure 7) illustrates the influence of k on the eva- In order to reflect the fluctuation of the evacuation cuation time for values of k equal to 0, 1, 2, 5 and 10. time, Figure 8) illustrates the influence of k on the D s For k = 0, the evacuation Fig 8b process is not related variable coefficient of evacuation time for values of k d d to the dynamic attraction, and it is only affected by equal to 0, 1, 2, 5 and 10. For k = 0, because the static attraction. The evacuation time is not affected by evacuation process is not related to the dynamic the change of k . In this situation, the pedestrians do attraction, and the evacuation time is not affected by not blindly follow the crowd. Therefore, the evacuation the change of k , the coefficient of variation is small time is stable. For values of k equal to 1, 2, 5 and 10, and stable. For values of k equal to 1, 2, 5 and 10, with D D the influence of the static attraction and dynamic a small value of k (such as k = 0.05), the variation s s attraction should be simultaneously taken into coefficient of evacuation time reaches the highest account. For a small value of k (such as k = 0.05), level. With the increase of k , the coefficient of variation s s s people are familiar with the exits. The influence coeffi - gradually decreases and tends to be stable. When the cient of dynamic attraction is relatively large, and the value of k increases to 2.5, the static attraction plays blind conformity is clear, which results in a longer a leading role, and the pedestrians can quickly and evacuation time. When k increases, the static attrac- orderly find the exits. tion has a greater influence on the evacuation process, Figure 9) presents the influence of k on the eva- people are more familiar with the location of exits, and cuation time for values of k equal to 0.4, 1.0, 2.5 and the phenomenon of blind conformity is gradually 5.0. For k = 5.0 and 2.5, the static attraction plays s JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 9 a dominant role in the evacuation process. People are for k = 1.2, the curve showing the relationship familiar with the position of exits. The evacuation time between the time and the number of people complet- is stable, since is not affected by the change of k . For ing evacuation fits well with the curve of authentic k = 0.4 and 1.0, the pedestrians’ familiarity with exits evacuation. reaches a low level. For a small value of k , the static Based on the surveillance video of classroom during Wenchuan earthquake (http://v.youku.com/v_show/ attraction still dominates, and the pedestrians are not id-XMjk3 NjE40Dg = .html), Xiaolin, Zhongliang, and significantly affected by the surrounding people. With Yingchun (2010) performed a statistical analysis on the the increase of k , the influence of the dynamic attrac- relationship between the evacuation time and the tion gradually increases, and the phenomenon of blind number of pedestrians completing evacuation. For dif- conformity becomes clearer, which results in the gra- ferent values of the influence coefficient of risk k , the dual increase of the evacuation time. When the influ - curves showing the relationship between the time and ence coefficient of dynamic attraction is large (such as the number of people on simulation model are com- k = 5), the dynamic attraction gradually occupies pared with the curve of authentic evacuation. Some a dominant position and the evacuation time becomes curves that are similar to the authentic situation and their corresponding risk values, are shown in Figure 12. stable. When the values of k and k are, respectively, s d It can be seen from Figure 12 that the value of k 1.0 and 5, the evacuation time tends to decrease, mainly affects the amplitude of avoidance to the which indicates that a certain extent of conformity is “hazard sources”. The larger the value of k , the greater conducive to improving the evacuation speed. the amplitude of avoidance, which results in a longer In order to reflect the fluctuation of the evacuation evacuation time. In addition, for k = 4, the evacuation time, Figure 9) illustrates the influence of k on the time required by pedestrians is similar to the actual variable coefficient of evacuation time, for values of k situation. The two reasons for the difference between equal to 0.4, 1.0, 2.5 and 4.0. For k = 5.0 and 2.5, the the simulation model and authentic evacuation sce- variation coefficient of evacuation time is very small. nario are summarized as follows: (1) the behavior pat- For k = 0.4 and 1.0, the variation coefficient gradually tern of pedestrians is a very complex process. The increases when k increases. As the value of k con- d d simulation algorithm cannot consider all the types of tinues to increase, the evacuation time tends to be behaviors and coupling between different behaviors; stable, and the coefficient of variation decreases. (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 2.3. Verification of the evacuation model the average value under repeated numerical experi- Based on the video, which records the authentic evacua- ments, which is more stable. tion under earthquake, it is deduced that the pedes- Considering that the probability of whether colli- trians are familiar with the location of exits during the sion during evacuation is 50%, the value of the friction evacuation process. Therefore, the influence coefficient coefficient µ is determined as 0.5. of static attraction k should not be too small. It can be observed from Figure 8 that, when the value of k is less 3. Criteria for determining casualties than 2.5, the evacuation time rapidly decreases with the increase of k . When the value of k is greater than 2.5, s s The casualties during evacuation under earthquake are the evacuation time becomes stable. Therefore, the induced by the overall collapse of the building structure, influence coefficient of static attraction is determined floor collapse and damage of non-structural compo- as 2.5, according to the parameter analysis. Since the nents. The evacuation simulation based on the teachers and students in the video record are familiar improved CA model is combined with the seismic non- with the exit environments, the blind conformity phe- linear time history analysis of building structures in time nomenon will not occur. Therefore, the influence coeffi - dimensions and spatial dimensions, in order to deter- mine the casualties. The evacuation space has two cient of dynamic attraction k should not be too large, superimposed grid systems: cellular automata grid and and it is determined as 1.0 in this study (Shuang, Zhai, finite element grid. The spatial coordinates of damaged and Xie 2015). components are tracked by a finite element mesh. The Based on the video, which records the authentic cellular automata mesh in the lower floor, overlapped evacuation process under earthquake (https://m.v.qq. with the vertical projection of damaged components, is com/z/msite/play-short/index.html?cid=&vid= then identified. If people are located in the cellular o08073ef0ll&qqVersion=0), the evacuation simulation automata grid, which overlaps with the projection of model for a double-exit room (cf. Figure 10) is devel- damaged components during evacuation, then casual- oped to calibrate the influence coefficient of exit- choice function k . It can be seen from Figure 11 that, ties will occur, as shown in Figure 13. e 10 G. ZHONG ET AL. Figure 9. Evacuation simulation model for a double-exit room. Figure 10. Relationship between the time and the number of people completing evacuation. Besides acquiring information on casualties, The criteria of casualties induced by damaged struc- another function of the developed coupling model is tural components are determined as follows: (1) to simulate the dynamically changing obstacles. In the according to the average height of Chinese people, process of authentic evacuation, the structural and this study assumes that, when the relative vertical non-structural components fall down as the time displacement between adjacent floors is less than change, which results in casualties and newly gener- 1.65 m, the casualties will occur at the corresponding ated obstacles during subsequent evacuation. The position (Shuang, Zhai, and Xie 2015); (2) when the coupling model simulates the phenomenon that peo- interstory drift ratio of floor j exceeds the limit value ple re-select a reasonable evacuation route after new of collapsed state at moment t, pedestrians in floor j, obstacles exist. If casualties occur, they will stay in j + 1, j + 2 . . . will stop the evacuation after this place and then become new obstacles for other pedes- moment. Pedestrians who have not completed the trians during evacuation. evacuation will suffer from casualties. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 11 Figure 11. The relationship between the time and the number of people completing evacuation, for different k values. Figure 12. Schematic diagram of the spatio-temporal coupling of crowd evacuation model, and nonlinear time history analysis under earthquake. Figure 13. Suspended ceiling falling scenario, with a falling rate of 5% by random number generation. Figure 14. Suspended ceiling falling scenario, with a falling rate of 30% by random number generation. 12 G. ZHONG ET AL. The evacuation simulation model considers the 1997, it was damaged during the Wenchuan earth- damage of infilled walls and suspended ceilings. quake. The structure has a plan dimension of According to the experimental results in (Guoqiang, 50.4 m × 17.4 m (cf. Figure 17). The height of stories Zhao, and Sun et al. 2003; Guoqiang, Fang, and Liu 1 to 7 is 4.6 m, 4.2 m, 3 × 3.6 m, 4.2 m and 3.6 m, et al. 2005; Cheng, Liu, and Liu 2010), when the peak respectively. The cross sections of frame beams are acceleration at the center of the infilled wall reaches 350 mm × 600 mm, and those of the columns 1.0 g, the infilled wall will collapse out of plane. When change along the structural height from 800 mm the infilled wall collapses, it is assumed that the col- × 800 mm to 500 mm × 500 mm. The thickness of lapse probability on both sides is the same. The range the slab is 100 mm. All the concrete design grades of a collapsed wall is determined using equation (12) are C30. The infilled wall is made by air brick with (Xinzheng, Yang, and Paolo Cimellaro et al. 2019). The a thickness of 200 mm. An analytical structural evacuation process based on the CA model is com- model is developed by ABAQUS (cf. Figure 18). bined with the collapse process of infilled wall in time and spatial dimensions. If an infilled wall collapses at 4.1.2. Development of finite element model moment t, casualties will occur while the pedestrians This study uses the ABAQUS (Systèmes 2013) soft- simultaneously get through the collapsed area. ware to simulate the building damage under the pffiffiffiffiffiffiffiffiffiffiffiffi earthquake excitation. The ABAQUS software d¼v 2h =g (12) i i i includes two algorithms: ABAQUS/implicit and where d represents the collapsed area, v denotes the ABAQUS/explicit. Due to the refined division of velocity at floor i + 1, h is the height of floor i, and elements in the finite element model, complexity g represents the gravitational acceleration. of material model and contact type, the implicit Several researchers proposed different damage algorithm leads to a large number of iterative pro- indexes and strength parameters to analyze the vul- cesses. Each iterative process requires to solve nerability of suspended ceilings (cf. Table 1). Based on a large number of nonlinear equations, which not ATC specification (cf. Table 2), the damage of sus- only decreases the calculation efficiency but also pended ceilings is divided into three states depend- results in a difficult convergence. Therefore, the ing on the falling rate: 5% (D1, slight damage), 30% implicit algorithm for finite element analysis has (D2, moderate damage) and 100% (D3, severe a high cost. The explicit algorithm uses the central damage). This study considers the peak floor accel- difference method for calculation, which does not eration as the strength parameter, and then gener- require to iterate and solve a large number of ates falling suspended ceilings using the stochastic equations. In terms of the definition of element method. For instance, if a room has 100 suspended mass, the explicit algorithm uses the centralized ceilings, when the falling rate reaches 30%, 30 sus- mass matrix, which reduces the inversion process pended ceilings are generated by the stochastic of mass matrix when calculating the inertial force. method. Based on the approach which combines the Therefore, it has a high calculation efficiency. evacuation process with the collapse process in time Therefore, the explicit algorithm is used for calcu- and spatial dimensions, casualties will occur when lation. The concrete material uses the concrete suspended ceilings are damaged and fall on the damage plastic model, while its constitutive curve ground, and pedestrians simultaneously get through follows the uniaxial stress-strain relationship speci- the damaged area. The size of the suspended ceilings fied in the code for the design of concrete struc- is considered as 600 mm × 600 mm (Qiqi, Zhe, and Xie tures (Industry Standard of the People’s Republic et al. 2019). Figure 14 and figure 15 illustrates the of China 2010). The reinforcement in the floor slab suspended ceiling with a failling rate of 5% and 30% is determined as a bilinear steel model with a post respectively. 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 4. Case study model uses the Timoshenko beam element B31 to simulate beam and column members. The floor 4.1. Nonlinear time history of target building simulation for floor slab uses the S4R quadrilateral 4.1.1. Overview of target building shell element, which considers arbitrary large The target building is a seven-story office building deformation and effective membrane strain. In of a Power Gas Company located in Dujiangyan, the analysis steps, the Rayleigh damping and gen- Sichuan Province, China. The structural type is eral contact algorithm are used in the finite ele- a reinforced concrete frame structure (cf. ment model. The ground is simulated by an Figure 16). Although the structure is originally analytical rigid body. Finally, the ground and col- designed based on a seismic intensity of 7 in umn are consolidated. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 13 Figure 15. Structural plan layout. Figure 16. Architectural plan layout. Figure 17. Finite element model in ABAQUS. Figure 18. Displacement under a moderate earthquake of intensity 8. 14 G. ZHONG ET AL. Figure 19. Time history of Wolong earthquake record. Figure 20. Response spectrum of Wolong earthquake record. Figure 21. Inter-story drift ratios for different earthquake intensities. (a) Minor earthquake (b) Moderate earthquake (c) Major earthquake JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 15 Figure 22. Crowd evacuation process under a minor earthquake of intensity 8. (a) Distribution of pedestrians at 1.92 s (b) Distribution of pedestrians at 23 s (c) Distribution of pedestrians at 142 s (d) Distribution of pedestrians at 420 s. Figure 23. Relationship between the time and the number of people completing evacuation. 4.1.3. Nonlinear time history analysis down to 0.07 g, 0.2 g and 0.4 g in order to commensu- This study considers the 2008 Wenchuan earthquake rate with the PGA under minor, moderate, and major ground motion record (Wolong Station N-S), in order earthquakes of intensity 8. The duration of the Wolong to perform the nonlinear time history analysis. The ground motion is 60 s. The inputted direction is along time histories and response spectra of Wolong ground the weak axis of the structure. The inter-story drift motion, are illustrated in Figures 19 and 20, respec- ratios of the case structure under different earthquake tively. The peak ground accelerations (PGA) are scaled intensities, are illustrated in Figure 22Figure 21. 16 G. ZHONG ET AL. Table 1. Damage indexes and strength parameters for suspended ceilings. Literature Damage state Strength parameter Gilani, Takhirov and Tedesco . (2013) Falling rate: 0, <5%, 5%~20%, 20%~50%, >50% – – Qiqi, Zhe, and Xie et al. (2019) Falling rate: 0, <5%, 5%~30%, >30% PFA Zaghi, Soroushian, and Echevarria Heiser et al. Damage rate of keel or falling rate: 0, <5%, 5%~30%, 30% PFA (2016) ~70%, >70% Soroushian, Rahmanishamsi, and Ryu et al. Falling rate: 0, <5%, 5%~20%, >20% PFA/ Inertial forces in horizontal (2016) direction Badillo, Whittaker, and Reinhorn (2007) Falling rate: 1%, 1%~10%, 10%~33%, keel grid damaged PFA/ Floor response spectrum Table 2. Fragility functions of nonstructural components used for damage assessment (Data extracted from ATC 2012) Applied ). Technology Council 2012 Nonstructural component x Damage state x Partition walls Peak interstory drift ratio (rad) D1 0.0021 D2 0.0071 D3 0.0012 Suspended ceiling with area < 23 m Peak floor acceleration (g) D1 1.00 D2 1.80 D3 2.40 2 2 Suspended ceiling with 23 m < area < 93 m Peak floor acceleration (g) D1 0.70 D2 1.15 D3 1.80 2 2 Suspended ceiling with 93 m < area < 232 m Peak floor acceleration (g) D1 0.45 D2 0.7 D3 1.00 Suspended ceiling with area > 232 m Peak floor acceleration (g) D1 0.35 D2 0.55 The damage states of partition walls are D (screws fall out, minor cracking of wallboard occurs, and tape warps or cracks); D (moderate cracking or 1 2 crushing of wallboard occurs, typically in corners and at corners of openings), and D (significant cracking or crushing of wallboard occurs, studs buckle, and tracks tear). The damage states of suspended ceilings are D (5% of tiles dislodge and fall), D (30% of tiles dislodge and fall, t-bar grid is damaged), 1 2 and D (ceiling tiles and t-bar grid entirely collapse).(Data extracted from ATC 2012) Figure 24. Crowd evacuation process under a moderate earthquake of intensity 8. (a) Distribution of pedestrians at 0.92s (b) Distribution of pedestrians at 2.88 s (c) Distribution of pedestrians at 17.28 s (d) Distribution of pedestrians at 389 s. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 17 Figure 25. Crowd evacuation process under a major earthquake of intensity 8. (a) Distribution of pedestrians at 0.92s (b) Distribution of pedestrians at 2.4s (c) Distribution of pedestrians at 23.52 s (d) Distribution of pedestrians at 289 s. Table 3. Damage information of suspended ceilings. Earthquake intensity Floor Falling time Falling rate Major earthquake of intensity 8 1 2.44 s 5% Major earthquake of intensity 8 2 2.44 s 30% Major earthquake of intensity 8 3 2.48 s 30% Major earthquake of intensity 8 4 2.5 s 30% Major earthquake of intensity 8 5 3.62 s 30% Major earthquake of intensity 8 6 3.52 s 100% Moderate earthquake of intensity 8 1 – – 0% Moderate earthquake of intensity 8 2 2.44 s 5% Moderate earthquake of intensity 8 3 – – 0% Moderate earthquake of intensity 8 4 2.5 s 5% Moderate earthquake of intensity 8 5 3.62 s 5% Moderate earthquake of intensity 8 6 3.52 s 5% Table 4. Damage information of partition walls. Earthquake intensity Floor Collapse time Scope of damaged partition walls Major earthquake of intensity 8 1 3 s 0.41 m Major earthquake of intensity 8 2 2.42 s 0.92 m Major earthquake of intensity 8 3 2.42 s 0.72 m Major earthquake of intensity 8 4 2.44 s 0.68 m Major earthquake of intensity 8 5 1.98 s 0.96 m Major earthquake of intensity 8 6 2.92 s 1.0 m Moderate earthquake of intensity 8 1 – – 0 m Moderate earthquake of intensity 8 2 3.1 s 0.46 m Moderate earthquake of intensity 8 3 3.08 s 0.68 m Moderate earthquake of intensity 8 4 – – 0 m Moderate earthquake of intensity 8 5 – – 0 m Moderate earthquake of intensity 8 6 – – 0 m 18 G. ZHONG ET AL. not damaged, the casualties induced by the damage of 4.2. Evacuation model under earthquake and non-structural components account for 4.58% of the prediction for casualties total population. The emergent new obstacles obstruct The number of pedestrians stranded on each floor under the evacuation routes and exits, which results in the different earthquake intensities, distribution of pedes- phenomenon that the pedestrians will re-select trians at different moments, casualties on different parts a reasonable evacuation route in the evacuation pro- of the building and number of people completing eva- cess. Therefore, it is necessary to consider the influence cuation at the end of the earthquake, are studied based of damage on the non-structural components, in seis- on the results of evacuation simulation and nonlinear mic evacuation simulation. time history analysis. According to previous analysis, the Figure 25 illustrates that under a major earthquake of parameters of the improved CA model are determined as intensity 8, the floors of the whole structure that are follows: the influence coefficient of static attraction (k ), nd above the 2 floor collapse, the suspended ceilings and influence coefficient of dynamic attraction (k ), influence partition walls of non-structural components are ser- coefficient of exit choice function (k ), influence coeffi - iously damaged. At the end of the earthquake, 617 cient of “risk value” (k ) and friction coefficient (μ) are pedestrians are stranded in the damaged structure, determined as 2.5, 1.0, 1.2, 4 and 0.5, respectively. 406 pedestrians are injured and killed, while 177 pedes- The improved CA model proposed in section 2, is trians complete the evacuation. Most of the pedestrians used to develop the seismic evacuation model. The who successfully escaped are originally located in the number of casualties is determined based on the cou- first floor. By analyzing the evacuation process, it can be pling rules proposed in section 3. Tables 3 and 4 present deduced that the areas with high incidence of casualties the damage degree and failure time of the suspended are concentrated in corridors and staircases. If the ceilings and partition walls on each floor, for different pedestrians are anxious to evacuate, they will be earthquake intensities. It can be seen that, under crowded in corridors or staircases. Once high population a minor earthquake of intensity 8, the overall structure density areas are damaged, the consequences will be does not collapse, the suspended ceilings do not fall, very serious. If there is no sufficient evacuation time and the partition walls do not collapse. Under under strong earthquakes, the pedestrians choose to a moderate earthquake of intensity 8, the overall struc- enter a relatively safe area for emergency shelter, ture does not collapse. However, the suspended ceilings which is an efficient way of self-protection. nd th th th on the 2 , 4 , 5 and 6 floors drop out, with a falling nd rate of 5%. In addition, the partition walls on the 2 and 5. Conclusion and discussion rd 3 floors collapse. Under a major earthquake of inten- sity 8, the inter-story drift ratios of floors 2, 3 and 4 Due to the randomness of the pedestrian evacuation exceed the limit for collapse (1/20), and therefore the process, a damage of building structure and ground whole structure collapses. The partition walls collapse motion occurs, and therefore the evacuation time, eva- and the suspended ceilings are damaged on each floor. cuation route and casualties under earthquake have The falling rate of the suspended ceilings on the first indeterminacy. This paper proposes a high-precision floor is 5%. The falling rates of the suspended ceilings model to simulate crowd evacuation under earthquake, nd th from the 2 floor to the 6 floor is 30%. and an approach for casualties assessment based on The initial number of pedestrians inside the building evacuation simulation. In order to perform the assess- is 1200. Under a minor earthquake of intensity 8, the ment of casualties, this paper develops the finite ele- structural and non-structural components in the target ment method to simulate the seismic damage of building are not damaged, and no obstacles are newly building structure. In addition, it proposes the improved generated during the evacuation process. All the CA model in order to accurately simulate the evacuation pedestrians can complete the evacuation. The evacua- process. Moreover, the criterion for determining casual- tion process is illustrated in Figure 23. The total eva- ties, which considers the damage of structural and non- cuation time reaches 528 s. The relationship between structural components, is proposed. Based on this cri- the time and the number of people completing eva- terion, the prediction of casualties is performed by cuation is presented in Figure 24. The congestion spatial and temporal combination of the finite element mainly occurs in corridors and stairs. model and evacuation simulation model. The crowd Under a moderate earthquake of intensity 8, the evacuation simulation model is an improved CA overall structure is not damaged. However, the sus- model, which accurately demonstrates the geometric pended ceilings and partition walls are damaged. The dimensioning of the evacuation environment and evacuation process under the moderate earthquake of obstacles. The influence of the evacuation distance intensity 8 is illustrated in Figure 25. It can be seen that and crowd density at the exits are considered, when 55 pedestrians do not complete the evacuation and the pedestrians select target exits. The improved CA casualties occur. The overall evacuation time is model also considers the herd behavior, conflict phe- reached after 570 s. Although the whole structure is nomenon and falling non-structural components on JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 19 evacuation process. Compared with the current empiri- high-vulnerability areas in buildings, which is condu- cal and statistical casualty prediction methods, the pro- cive to the formulation of a post-earthquake rescue posed approach is more accurate, and can give more plan. quantitative results. The proposed approach has the following advantages: Disclosure statement (1) The improved CA model based on meticulous No potential conflict of interest was reported by the author(s). and discrete cellular space, can more accurately describe the geometric dimensions of the evacuation environments and obstacles. It can also improve the Funding accuracy of the simulation results. The improved CA This work was supported by the National Natural Science model uses eight neighborhood types. It arranges Foundation of China (Grant No. 52108053); Natural Science pedestrians to move in eight directions, and can con- Foundation of Jiangsu Province (Grant No. BK20200762); sider different evacuation speeds. The assignment Social Science Foundation of Jiangsu Province (Grant method is used to determine the static attraction, No. 20ZZC001). which is applicable to the evacuation environment with or without obstacles. Therefore, the quantized location information of cells is more reasonable. Notes on contributors (2) The rules for movement on the improved CA Guangchun Zhong, PhD Candidate, Research Interest: model perform the coupling of several evacuation Structural Optimization, Evacuation Simulation, Finite behaviors under earthquake. The crowd’s herd behavior Element Modelling. is simulated based on dynamic attraction, the crowd’s Guofang Zhai, Professor, Research Interest: Disaster choice behavior in multi-exit environment is simulated Prevention and Mitigation, Evuacuation Simulation. based on exit-choice function, and the crowd’s avoid- Wei Chen, Associate Professor, Research Interest: Disaster ance behavior of obstacles is simulated based on “risk Prevention and Mitigation, Evacuation Simulation. value”. The improved rules for movement more accu- rately reflect the evacuation behavior of pedestrians under earthquake, and improve the authenticity and References accuracy of the evacuation simulation. 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Journal

Journal of Asian Architecture and Building EngineeringTaylor & Francis

Published: Mar 4, 2023

Keywords: Earthquake; evacuation simulation; modified cellular automata model; non-structural components; casualty prediction

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