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The aim of this study is to address the following issues: 1) revealing the typical behaviors and properties of pedestrian movement when going upstairs and downstairs; 2) constructing a pedestrian evacuation model to formulate the walking process of pedestrians in stair area; 3) verifying that the cell transmission model widely used in the two-dimensional walking space can also be applied to the three-dimensional staircase area. Firstly, an observation experiment is carried out to gain the pedestrian movement data in the process of going upstairs and downstairs. By collating the data, the relation between density and flow in the unidirectional process of going upstairs or going downstairs, and in the bi-directional process of going upstairs and downstairs, are drawn respectively. Then, by analyzing the fundamental diagrams, several characteristics of pedestrian movement in stair area are revealed. Based on these characteristics, an extended cell transmission model is proposed. In this model, a potential correction coefficient is introduced to change the route choice of pedestrians by using the influence of different directional pedestrians on the potential; a flow modification coefficient is introduced to describe the effect of physical parameters on the maximum flow at the boundary between two neighboring cells; and an offset coefficient is introduced to correct movement rules and strengthen the influence of preferential direction on pedestrian route choice. Further, simulations relied on the proposed model are conducted. By comparing the simulation results with the experimental data, the model is calibrated. Then the calibrated model is employed to formulate the pedestrian movement in stair area, and the sensitivity of the potential correction parameter is also discussed. The simulation results indicate that the proposed model can successfully reproduce the movement of pedestrians on stair. Moreover, the route-choice behaviors of pedestrians can be directed by varying the values of the potential correction coefficient, which can present important information about optimizing the evacuation process of pedestrians on stair, thereby reducing the risk of an accident, such as congesting and treading.
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Keywords:
- cellular transmission model /
- pedestrian flow on stairs /
- flow-density relationship /
- sensitivity analysis
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Google Scholar
[2] Yeo S K, He Y P 2009 Fire Saf. J. 44 183
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Yue H, Zhang X, Chen G, Shao C F 2012 Acta Phys. Sin. 61 130509
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Google Scholar
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Yue H, Shao C F, Guan H Z, Duan L M 2010 Acta Phys. Sin. 59 4499
Google Scholar
[8] 陈亮, 郭仁拥, 塔娜 2013 物理学报 62 050506
Chen L, Guo R Y, Ta N 2013 Acta Phys. Sin. 62 050506
[9] 永贵, 黄海军, 许岩 2013 物理学报 62 010506
Yong G, Huang H J, Xu Y 2013 Acta Phys. Sin. 62 010506 (in Chinese)
[10] Sano T, Ronchi E, Minegishi Y, Nilsson D 2017 Fire Saf. J. 89 77
Google Scholar
[11] 任刚, 陆丽丽, 王炜 2012 物理学报 61 144501
Google Scholar
Ren G, Lu L L, Wang W 2012 Acta Phys. Sin. 61 144501
Google Scholar
[12] Hughes R L 2002 Trans. Res. B 32 507
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Google Scholar
Dong L Y, Chen L, Duan X Y 2015 Acta Phys. Sin. 64 220505
Google Scholar
[14] Huang H J, Guo R Y 2008 Phys. Rev. E 78 021131
Google Scholar
[15] Helbing D, Molnar P 1995 Phys. Rev. E 51 4282
Google Scholar
[16] Helbing D, Farkas I, Vicsek T 2000 Nature 407 487
Google Scholar
[17] 杨凌霄, 赵小梅, 高自友, 郑建风 2011 物理学报 60 100501
Google Scholar
Yang L X, Zhao X M, Gao Z Y, Zheng J F 2011 Acta Phys. Sin. 60 100501
Google Scholar
[18] Qu Y C, Gao Z Y, Xiao Y, Li X G 2014 Saf. Sci. 70 189
Google Scholar
[19] Burstedde C, Klauck K, Schadschneider A, Zittart J 2001 Physica A 295 507
Google Scholar
[20] Guo R Y, Guo X 2012 Chin. Phys. B 21 018901
Google Scholar
[21] Guo R Y, Huang H J, Wong S C 2011 Trans. Res. B 45 490
Google Scholar
[22] 霍非舟 2015 博士学位论文 (合肥:中国科学技术大学)
Huo F Z 2015 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[23] Fujiyama T, Tyler N 2010 Transport. Plan. Techn. 33 177202
Google Scholar
[24] Xu X, Song W G 2009 Build. Environ. 44 1039
Google Scholar
[25] Ma J, Song W G, Tian W, Lo S M, Liao G X 2012 Saf. Sci. 50 1665
Google Scholar
[26] 张培红, 鲁韬, 陈宝智, 卢兆明 2005 人类工效学 11 8
Google Scholar
Zhang P H, Lu T, Chen B Z, Lu Z M 2005 Chin. J. Ergon. 11 8
Google Scholar
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Google Scholar
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Google Scholar
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图 1 实验楼梯区域
Figure 1. The experimental staircase area.
图 2 单层楼梯三视图
Figure 2. Single-story staircase three views.
图 3 (a) 上楼过程中楼梯区域平均流量-密度散点图及关系曲线; (b) 下楼过程中楼梯区域平均流量-密度散点图及关系曲线; (c) 上下楼过程中楼梯区域平均流量-密度散点图及关系曲线
Figure 3. (a) The relation of the density against the average flow when going upstairs; (b) the relation of the density against the average flow when going downstairs; (c) the relation of the density against the average flow when going upstairs and downstairs.
图 4 二维斜坡平面行走空间
Figure 4. Walking space on the two-dimensional slope section.
图 5 空间划分: 正六边形元胞
Figure 5. Discretization of space: a regular hexagonal cell.
图 6 上楼过程第10, 30, 60, 90及110时间步模拟结果伪彩图 (颜色深浅表示每个元胞内行人数量与元胞容量之比)
Figure 6. Pseudo-color plots delineating the ratio of the number of pedestrians in each cell to the capacity of the cell at time steps 10, 30, 60, 90 and 110 in the process of going upstairs.
图 7 下楼过程第10, 30, 60, 90及110时间步模拟结果伪彩图 (颜色深浅表示每个元胞内行人数量与元胞容量之比)
Figure 7. Pseudo-color plots delineating the ratio of the number of pedestrians in each cell to the capacity of the cell at time steps 10, 30, 60, 90 and 110 in the process of going downstairs.
图 8 观测 (方形)与实验(圆形)流量-密度关系对比图 (a) 上楼过程， (b) 下楼过程
Figure 8. Comparison of the fundamental density-flow diagram from the observation data (square marks) and the experiment (circle marks) (a) in the process of going upstairs, and (b) in the process of going downstairs.
图 9 双向运动过程的流量-密度关系对比图
Figure 9. Comparison of the fundamental density-flow diagram from the observation (square marks) and the experiment (circle marks) in the process of bi-directional movment .
图 10 (a) 稳定状态之前楼梯区域双向运动的流量-密度关系图; (b) 稳定状态之后楼梯区域双向运动的流量-密度关系图
Figure 10. (a) Fundamental density-flow diagram of the bi-directional pedestrian flow on the stairs before the stabilization process; (b) fundamental density-flow diagram of the bi-directional pedestrian flow on the stairs after the stabilization process.
图 11 楼梯区域双向运动的流量-密度关系散点图 (a) δ = 1.0, θ = 0.8; (b) δ = 0.6, θ = 0.8; (c) δ = 0.3, θ = 0.8; (d) δ = 1.4, θ = 0.8
Figure 11. Fundamental density-flow diagram of the bi-directional pedestrian flow on the stairs when (a) δ = 1.0 and θ = 0.8; (b) δ = 0.6 and θ = 0.8; (c) δ = 0.3 and θ = 0.8; (d) δ = 1.4 and θ = 0.8.
图 12 楼梯区域双向运动中上行行人（左）、下行行人（中）及双向行人（右）模拟结果伪彩图(颜色深浅表示每个元胞内行人数量与元胞容量之比) (a) δ = 1.0, θ = 0.8; (b) δ = 0.6, θ = 0.8; (c) δ = 0.3, θ = 0.8; (d) δ = 1.4, θ = 0.8
Figure 12. Pseudo-color plots delineating the ratio of the number of pedestrians in each cell to the capacity of the cell during the walking process of bi-directional pedestrian flows on the stairs (upward flow in the left, downward flow in the middle, and bi-directional flows in the right) when δ = 1.0 and θ = 0.8 in (a), δ = 0.6 and θ = 0.8 in (b), δ = 0.3 and θ = 0.8 in (c), δ = 1.4 and θ = 0.8 in (d).
表 1 实验楼梯的基本参数
Table 1. The basic parameters of the staircases.
有效宽度/m 有效长度/m 台阶数/级 台阶高度/m 台阶宽度/m 楼梯坡度 tanθ 有效面积/m2 3.16 8.95 38 0.15 0.37 0.40 28.28 
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表 2 楼梯区域上的部分观测数据
Table 2. Some observation data on staircase area.
数据
编号行人数量
N/人流入量
IF/人·$\Delta t$−1流出量
OF/人·$\Delta t$−1T T+10 s U D U D 1 11 13 0 8 0 6 2 25 26 0 12 0 11 3 29 24 0 12 0 17 4 32 31 0 21 0 22 5 33 28 0 19 0 14 6 18 20 12 0 10 0 7 39 36 14 0 17 0 8 29 33 21 0 17 0 9 54 54 12 0 12 0 10 14 12 8 0 10 0 11 18 19 3 3 2 3 12 26 28 6 9 5 8 13 50 46 9 13 10 16 14 48 44 8 8 8 12 15 38 35 8 11 10 12 注: U, 上行; D, 下行.
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表 3 稳定过程中的部分流量数据
Table 3. Some flow data in the stabilization process.
时间步 60 61 62 63 64 65 66 67 68 上楼流量/人·s−1 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 下楼流量/人·s−1 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 时间步 80 81 82 83 84 85 86 87 88 上楼流量/人·s−1 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 下楼流量/人·s−1 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0
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表 4 稳定过程结束后的部分流量数据
Table 4. Some flow data after the stabilization process.
时间步 106 107 108 109 110 111 112 113 114 上楼流量/人·s−1 6.0 5.9 5.7 5.2 4.6 3.9 3.1 2.4 1.8 下楼流量/人·s−1 5.9 5.5 4.7 3.7 2.7 1.8 1.1 0.7 0.4
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表 5 稳定过程结束后的部分行人数据
Table 5. Some pedestrian data after the stabilization process.
时间步 106 107 108 109 110 111 112 113 114 上楼人数/人 96.6 90.6 84.6 78.6 72.6 66.6 60.6 54.6 48.6 下楼人数/人 76.7 70.1 64.8 58.8 52.8 46.8 40.8 34.9 29.0
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[1] Galea E R, Sharp G, Lawrence P J 2008 J. Fire Prot. Eng. 18 291
Google Scholar
[2] Yeo S K, He Y P 2009 Fire Saf. J. 44 183
Google Scholar
[3] Yang L Z, Rao P, Zhu K J, Liu S B, Zhan X 2012 Saf. Sci. 50 1173
Google Scholar
[4] Hoskins B L, Milke J A 2012 Fire Saf. J. 48 49
Google Scholar
[5] 岳昊, 张旭, 陈刚, 邵春福 2012 物理学报 61 130509
Google Scholar
Yue H, Zhang X, Chen G, Shao C F 2012 Acta Phys. Sin. 61 130509
Google Scholar
[6] Shields T J, Boyce K E 2009 Fire Saf. J. 44 881
Google Scholar
[7] 岳昊, 邵春福, 关宏志, 段龙梅 2010 物理学报 59 4499
Google Scholar
Yue H, Shao C F, Guan H Z, Duan L M 2010 Acta Phys. Sin. 59 4499
Google Scholar
[8] 陈亮, 郭仁拥, 塔娜 2013 物理学报 62 050506
Chen L, Guo R Y, Ta N 2013 Acta Phys. Sin. 62 050506
[9] 永贵, 黄海军, 许岩 2013 物理学报 62 010506
Yong G, Huang H J, Xu Y 2013 Acta Phys. Sin. 62 010506 (in Chinese)
[10] Sano T, Ronchi E, Minegishi Y, Nilsson D 2017 Fire Saf. J. 89 77
Google Scholar
[11] 任刚, 陆丽丽, 王炜 2012 物理学报 61 144501
Google Scholar
Ren G, Lu L L, Wang W 2012 Acta Phys. Sin. 61 144501
Google Scholar
[12] Hughes R L 2002 Trans. Res. B 32 507
[13] 董立耘, 陈立, 段晓茵 2015 物理学报 64 220505
Google Scholar
Dong L Y, Chen L, Duan X Y 2015 Acta Phys. Sin. 64 220505
Google Scholar
[14] Huang H J, Guo R Y 2008 Phys. Rev. E 78 021131
Google Scholar
[15] Helbing D, Molnar P 1995 Phys. Rev. E 51 4282
Google Scholar
[16] Helbing D, Farkas I, Vicsek T 2000 Nature 407 487
Google Scholar
[17] 杨凌霄, 赵小梅, 高自友, 郑建风 2011 物理学报 60 100501
Google Scholar
Yang L X, Zhao X M, Gao Z Y, Zheng J F 2011 Acta Phys. Sin. 60 100501
Google Scholar
[18] Qu Y C, Gao Z Y, Xiao Y, Li X G 2014 Saf. Sci. 70 189
Google Scholar
[19] Burstedde C, Klauck K, Schadschneider A, Zittart J 2001 Physica A 295 507
Google Scholar
[20] Guo R Y, Guo X 2012 Chin. Phys. B 21 018901
Google Scholar
[21] Guo R Y, Huang H J, Wong S C 2011 Trans. Res. B 45 490
Google Scholar
[22] 霍非舟 2015 博士学位论文 (合肥:中国科学技术大学)
Huo F Z 2015 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[23] Fujiyama T, Tyler N 2010 Transport. Plan. Techn. 33 177202
Google Scholar
[24] Xu X, Song W G 2009 Build. Environ. 44 1039
Google Scholar
[25] Ma J, Song W G, Tian W, Lo S M, Liao G X 2012 Saf. Sci. 50 1665
Google Scholar
[26] 张培红, 鲁韬, 陈宝智, 卢兆明 2005 人类工效学 11 8
Google Scholar
Zhang P H, Lu T, Chen B Z, Lu Z M 2005 Chin. J. Ergon. 11 8
Google Scholar
[27] Kretz T, Grunebohm A, Kessel A, Klupfel H, Meyer Konig H, Schreckenberg M 2008 Saf. Sci. 46 72
Google Scholar
[28] Peacock R D, Hoskins B L, Kuligowski E D 2012 Saf. Sci. 50 1655
Google Scholar
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