Analysis of the Efficiency of Slope Evacuation for Dense Crowds in Urban Street-Type Public Spaces

Abstract

Street-type spaces, characterized by their relative closedness and propensity for human congregation, inherently carry potential safety evacuation risks. In order to study the influence of slopes on the evacuation efficiency of pedestrians in street-type public spaces under the state of passenger flow surge during holidays, this study systematically analyzes the changing rules and behavioral characteristics of pedestrian evacuation in downhill movement through a three-phase analysis of the risk of crowd gathering in urban street-type spaces (before, during, and after) and evacuation simulation experiments combining variables such as slope, street width, obstacle layout, disability type, and group movement. The findings indicate that, in the structural design of street-type spaces, slopes of more than 4° should be minimized to maintain the smooth flow of pedestrians. Areas in streets with widths narrower than 2 m are high-risk zones for crowd gathering and should be better supervised. The number and location of obstacles should be reasonably arranged under the condition of satisfying the safety of pedestrians’ passage. The differences in the ability of evacuees should be taken into account to improve evacuation system deficiencies and ensure that everyone can evacuate safely. Ultimately, we propose a preventive mechanism for the safe evacuation of urban street-type public spaces to reduce the risk of crowd gathering and safeguard pedestrians. This study provides a theoretical framework for understanding the dynamics of pedestrian evacuation in inclined street-type spaces, thereby guiding urban planners and public safety managers to enhance the design and management of such spaces.

1. Introduction

China’s urban development has entered a new stage characterized by the renewal and optimization of existing spaces. Tourism and leisure streets have become some of the most dynamic carriers of urban revitalization, contributing significantly to local economic growth. In the first half of 2024, the 164 national-level tourism and leisure streets received 875 million visitors, up 15.94% year-on-year [1]. The hot tourism economy has injected vitality into the economic development of various regions, but the risk of crowd gathering brought about by such large-scale festivals cannot be ignored. Tourism and leisure streets and other street-type spaces are characterized by frequent, continuous, and dynamic flows of people, and large-scale passenger flows can cause scenic spots to be overloaded, increase the risk of crowd gathering, and even cause sudden stampede accidents [2].

The Itaewon stampede in South Korea is a typical example of this problem: 159 people died and 196 were injured during the Halloween celebrations on 29 October 2022, due to overcrowding [3]. However, such street-type spaces with slope characteristics are not unique to South Korea. For instance, in the historic city of San Francisco in the United States, many streets have significant slopes. The steep slopes of Lombard Street, known as the “crookedest street in the world”, not only pose challenges to traffic flow but also affect pedestrian movement during peak tourist seasons [4]. In Hong Kong, China, the unique geographical layout of the city has created numerous slopes, with a total of 29 downhill sections in the territory, including 12 on Hong Kong Island, 4 in Kowloon, and 13 in the New Territories. The gradient of these sections ranges from about 10% to 17%, and their length varies from about 500 m to 2000 m [5]. These areas face similar challenges with regard to slope stability, pedestrian access, and emergency evacuation.

Scholars worldwide have carried out relevant studies on the mechanism of crowd stampede accidents from the aspects of stampede accident mechanism [6,7], risk assessment method [8,9,10], simulation analysis of stampede accidents [11], and stampede prevention and management [12,13]. Prior studies have focused mostly on crowd movement evacuation risks in large public spaces or building interiors. However, street-type spaces, which are relatively confined and feature unique spatial constraints, have received less attention in the literature. Furthermore, previous studies on pedestrian movement characteristics have focused on the case of evacuation on flat ground, overlooking the impact of sloped terrain. Sloped terrain can affect the walking mechanism of pedestrians and allow them to perform different behaviors [14]. Slope design is often required in urban roads as well as sidewalks to meet the need for accessibility, and a systematic study of the movement characteristics of pedestrians on slopes is an important guide for the design of such facilities.

Unlike previous studies that focused only on crowd gathering or slope evacuation, this study focuses on the complex scenario of slope evacuation under dense crowd conditions, aiming to explore the influence of the coupling effect between complex crowds and special spatial structures on evacuation efficiency. On the basis of analyzing the mechanism of disaster caused by a stampede accident of a dense crowd on a slope in a street-type space, an evacuation model was constructed with a typical street-type space, Itaewon Numerical simulation experiments were carried out in terms of slope, street width, obstacle layout, disability types, and group movement, to analyze the rule of change in people’s evacuation state during the evacuation process, and compare the difference in movement between different groups. The findings of this study are expected to offer a solid theoretical foundation for urban planners and designers to optimize the design and safety of street-type public spaces. Additionally, it aims to contribute to enhancing the emergency management capabilities of urban public safety, filling a crucial gap in the existing research on the combined impact of dense crowds and slope-related evacuation in street-type spaces.

The structure of the rest of this study is as follows: Section 2 introduces the current status of research related to the safe evacuation of street-type public spaces. Section 3 analyzes the risk of crowd gathering on slopes in urban street spaces. Section 4 introduces the evacuation objects studied, evacuation methods used, evacuation models created, and the relevant parameter settings. Section 5 presents the evaluation of the simulation model and the results. Section 6 compares and discusses the results obtained. Section 7 summarizes the research content of this paper.

2. Related Works

2.1. Study on Street-Type Public Space

Hoogendoorn carried out a micro-behavioral test of pedestrians in bottleneck space, discussed the results of narrow and wide bottleneck tests, and subsequently constructed a multi-class continuum model that can capture the key characteristics of pedestrian flow to explore the causes of crowd congestion in more depth [15]. Zuo proposed a method to improve the effectiveness of emergency evacuation for the complex spatial structure of streets and alleys in urban centers, aiming at simulating, evaluating, and optimizing cyclic evacuation by using Analogic software and an ArcGIS v10.2-based facility siting tool, so as to optimize the layouts of shelters and evacuation routes [16]. Liu quantitatively assessed the risk of crowd congregation in street-type public spaces from the perspective of street space and crowd activity characteristics, and organized simulation experiments of crowd movement activities in field scenarios to quantitatively study the safety risk of crowd movement in urban street spaces [17].

Overall, previous research on street-based public spaces has made significant contributions to understanding some aspects of pedestrian behavior and safety. However, these studies have typically focused on isolated factors such as bottleneck geometry, basic evacuation optimization, or risk assessment based on limited scenarios. They fail to comprehensively consider the highly dynamic and complexity of crowds in street spaces. In this paper, we present a detailed study of complex evacuation scenarios for sloped streets under dense crowd conditions.

2.2. Simulation Study of Pedestrian Flow on Slopes

At present, a small number of scholars are concerned with the simulation study of pedestrian flow on slopes. For example, Tang analyzed the personnel evacuation test in different slope scenarios from the perspective of dynamics, and obtained the empirical formulas of the relationship between walking speed, step length, and slope, which provide a basis for the fire evacuation design, evacuation modeling, and the accuracy of the grid division of complex and large-scale buildings [18]. Jian established a potential function field cellular automata model of counter flow in a sloped channel and realized the simulation of the pedestrian flow dynamics and the phenomenon of falling down [19]. Hu improved the social force model to realize the simulation of pedestrian falls, injuries, and impatience in the scenario of opposing pedestrian flows on slopes and conducted a single-file pedestrian flow experiment with varying slope angles to investigate the effects of slope angle on stepping behaviors [20,21].

The studies mentioned above on pedestrian flow on slopes have mainly concentrated on the movement of pedestrians in low-density scenarios. They overlook the complex and realistic situations that occur during high-density events, such as festivals or emergencies. Therefore, there is an urgent need for more comprehensive models to address the various evacuation challenges associated with slopes in the real world, especially in high-density pedestrian street spaces, and our study achieves this by considering multiple factors simultaneously.

2.3. Pedestrian Movement in Groups

The small groups formed by family, friendship, and other social relationships often account for more than 70% of the number of tourists [22], so it is necessary to focus on the effect of group movement of pedestrians on the overall evacuation of the crowd. Zaki developed a method for automated analysis of pedestrian group behavior in urban settings using movement trajectory data from videos [23]. Templeton highlighted the importance of understanding influences on pedestrian movement, particularly in large group relations and counterflow scenarios. They discussed the psychological factors that can influence interactions between large groups in pedestrian dynamics [24]. Hu conducted experiments on the movement characteristics of social groups in unidirectional flow, emphasizing the influence of social groups on pedestrian movement in various situations [25].

From the aforementioned literature, it can be observed that the research on group movement of crowds mainly focuses on large open public places. They have largely ignored the unique characteristics and challenges presented by narrow street-type spaces and slopes, and they have failed to consider the influence of the age composition of the group on the overall evacuation of the crowd. There is a gap in research on group movement in these specific spatial environments that limits our ability to develop effective safety evacuation strategies in street spaces with complex topography, and our study aims to fill this gap by considering group movement during slope evacuation of dense crowds in street spaces.

3. Risk Analysis of Crowd Gathering on Slope in Urban Street Spaces

3.1. Risk Analysis of Slope Evacuation

The force conditions of a single pedestrian moving on a slope among a crowd are shown in Figure 1. Neglecting the effect of air resistance, $G$ is the force of gravity ($G_{\tau }$ for the tangential component of gravity, $G_n$ for the normal component of gravity); $Ff$ are the pedestrians to move forward when the feet stirrup the ground generated by the static friction; $N$ is the support force on the slope for pedestrians; $T$ is the surrounding of other pedestrians to push ($T_{\tau }$ for the tangential component of the force, $T_n$ for the normal component of the force), in a crowded crowd, pushing and shoving are the main reasons for the fall; $\theta$ is the slope of the street, $\theta >0$ for uphill, $\theta =0$ for level ground, and $\theta <0$ for downhill. The forces on pedestrians vary depending on the inclination of the slope. The combined force $Fr$ on pedestrians in the direction of the slope is:

$$F_r=\left\{\begin{array}{ccc}{T}_{\tau }+Ff-G_{\tau }& ,& \theta >0\\ T+Ff& ,& \theta =0\\ T_{\tau }+G_{\tau }-Ff& ,& \theta <0\end{array}\right.$$

(1)

When pedestrians go uphill, the force of the body is upward, the center of gravity of the body is downward, and the two are balanced by each other. Pedestrians’ knees bear three to four times their body weight, pedestrians move with a larger stride. Pedestrians’ downhill stride decreases, and the force of the body and the center of gravity of the body are downward. Pedestrians’ knees bear six to seven times their body weight, as the knee joints are subjected to greater recoil from the ground. In order to maintain balance and stability, pedestrians are required to control the entire sole of the foot against the slope with the ankle to prevent slips or falls. Therefore, this paper only studies the more dangerous downhill movement.

3.2. Mechanism of Slope Stampede Formation in Street-Type Public Space

According to the chain process to categorize the street-type public space slope stampede risk into three stages: pre-accident period, accident evolutionary period, and consequences of the accident, as shown in Figure 2. By focusing on weak links, emergency managers can improve the system of emergency response systems.

(1)

Pre-accident period: During the holidays, the number of tourists to be received at major tourist attractions multiplies, causing a large number of people to spontaneously converge in the street-type field. The narrow spatial characteristics of the street space tend to lead to poor visibility for pedestrians and chaotic conflicts with multi-directional pedestrian flows [17]. Adverse weather conditions, such as rain and fog, can have a significant impact on pedestrian behavior. Pedestrians’ perception of safety is disturbed by weather factors. For example, in low visibility conditions, pedestrians’ cognitive abilities may be affected since the capabilities of visual and auditory cognitions of the environment are reduced [26]. Poor light quality, especially in the evening or in poorly lit areas, further impairs pedestrians’ ability to assess the safety of their surroundings and avoid collisions [27]. Additionally, the presence of obstacles or temporary facilities blocking pedestrian paths exacerbates congestion by creating bottlenecks [28]. The density of the crowd in this stage is relatively low, and the crowd is still able to move freely, but the number and density of the crowd are on the rise.

(2)

Accident evolutionary period: As the density of the crowd increases, the movement of the crowd is progressively restricted, especially under the compounding effects of poor weather or lighting conditions. When the flow of people gradually reaches the capacity limit of the space, the phenomenon of stagnation and congestion occurs. When the flow of people in the field exceeds the critical value, irrational competition for space and time triggers pushing and shoving [29,30]. The presence of obstacles exacerbates the creation of bottleneck areas, while the panic caused by the rapid spread of rumors further accelerates the deterioration of the situation [31].

(3)

Consequences of the accident: Stampede accidents cause serious casualties and damage to public facilities. Poor lighting conditions can make evacuation difficult, impede rescue operations, and increase the psychological stress for trapped people. Excessive psychological stress on the crowd may lead to mass riots or disturbances, with lasting effects on the individuals and communities involved. With the rapid intervention of evacuation, rescue, pacification, investigation, and public opinion response, the incident gradually subsided and the authorities began to identify the cause and restore order, allowing the incident to enter the final phase.

3.3. Analysis of Factors Affecting Pedestrian Movement Speed

3.3.1. Effect of Crowd Density on the Speed of Pedestrian Movement

The Pathfinder Technical Guidance Manual states that the maximum speed at which a pedestrian can move and the density of people in the current environment combine to influence the speed of pedestrian movement $v$ [32].

$$v=v_{\max }\cdot v_{f(\rho )}$$

(2)

In Equation (2), $v_{\max }$ is the maximum pedestrian movement speed, m/s; $\rho$ is the current crowd density in the evacuation environment, pedestrians/m².

$v_{f(\rho )}$ is a speed fraction as a function of density as follows:

$$v_{f(\rho )}=\left\{\begin{array}{cc}1& \begin{array}{cc},& \rho <0.55\end{array}\\ \max \left[0.15v_{\max },{\displaystyle \frac{1}{0.85}}\left(1-0.266\rho \right)\right]& \begin{array}{cc},& \rho \ge 0.55\end{array}\end{array}\right.$$

(3)

3.3.2. Effect of Slope on the Speed of Pedestrian Movement

Sarmady proposed a speed fraction $v_{ft}$ to calculate the speed at which pedestrians move at different slopes [33]. $v_{ft}$ depends on the type of terrain being traversed by the pedestrian. Walking speed on the slope depends on the slope degree and the free-flow speed of the pedestrian (i.e., at 0° slope):

$$v_{ft}={\displaystyle \frac{v_{\theta }}{v_0}}$$

(4)

In Equation (4), $v_{\theta }$ is the value of the pedestrian’s speed when the slope is $\theta$, m/s; $v_0$ is the value of the pedestrian’s speed on the horizontal terrain, m/s.

3.3.3. Effect of Environmental Factors on the Speed of Pedestrian Movement

Factors such as poor lighting conditions and unfavorable weather conditions (e.g., rain, fog) are contributing factors to poor visibility for pedestrians. Pedestrians’ sensory sensitivity, psychological tension response, and alertness are heightened in dimly lit environments [27], which can have a significant impact on their speed of movement. Road conditions indirectly affect pedestrian speed by changing the difficulty of path travel, while obstacles indirectly affect pedestrian speed by changing path length or increasing avoidance frequency. Therefore, Equation (2) was further modified as follows:

$$v^{\prime }=v_{\max }\cdot v_{f(\rho )}\cdot v_{ft}\cdot {\sigma }_s\cdot {\sigma }_p$$

(5)

In Equation (5), ${\sigma }_s$ is the sensory response factor, which combines factors such as weather, light, and psychological tension, usually ranging from 0 to 1, depending on the strength of the effect of the environmental stimulus on the pedestrian’s psychology. ${\sigma }_p$ is the path efficiency factor, which takes into account the effects of obstacles and pavement conditions.

$${\sigma }_p={\displaystyle \frac{d_{ideal}}{d_{actual}}}$$

(6)

$d_{\mathrm{ideal}}$ is the distance of the ideal path, m; $d_{\mathrm{actual}}$ is the actual distance under the influence of road conditions and obstacles, m.

In summary, the actual movement speed of pedestrians changes to different degrees under the influence of different crowd densities, different terrain features, and environmental factors, as shown in

Table 1. Variation in pedestrian speed in different scenarios.

Slope (Degrees)	Density (Pedestrians/m2)	${\mathit{v}}_{\mathbf{max}}$ (m/s)	${\mathit{v}}_{\mathit{f}\mathit{t}}$	${\mathit{\sigma }}_{\mathit{s}}$	${\mathit{\sigma }}_{\mathit{p}}$	Actual Speed: ${\mathit{v}}^{\prime }$ (m/s)
0	0.5	1.4	1	0.9	1	1.26
−4	1.0	1.4	1.18	0.9	0.91	1.17
−4	1.5	1.4	1.28	0.8	0.77	0.78
−10	1.0	1.4	0.75	0.9	0.91	0.74
−10	1.5	1.4	0.85	0.8	0.83	0.56

.

4. Evacuation Scenario Setup

Itaewon is a famous business district in Seoul, South Korea, and it is surrounded by numerous bars, nightclubs, restaurants, and other entertainment venues, making it a popular choice for young Koreans and tourists to relax and have fun. Because Itaewon’s location is close to the subway station, it is a typical place for crowds to gather, as shown in Figure 3.

The Itaewon stampede occurred on a downhill street near the Hamilton Hotel in front of Metro Exit 1 of Itaewon Station, which has a slope of 7°, a street width of 4 m, and a length of 45 m [29,30]. The street was flanked on both sides by merchants and hotel facades, creating a blocked situation, as shown in Figure 4.

Based on on-site video observations of pedestrian orientation, the north side of the street was identified as the entrance and the south side of the street as the exit. At the time of the accident, this narrow street was severely overloaded and was swarming with hundreds of people at one time. This narrow, closed environment was not only an environmental factor in the stampede but also exacerbated the crowd buildup, making rescue more difficult. In order to accurately and thoroughly explore the key issues of slope evacuation, this paper will analyze in detail the specific impacts of slope topography, obstacle layout, and other factors on the evacuation of people in a specific area, centering on the accident site.

4.1. Software Introduction

Pathfinder v2019, developed by Thunderhead Engineering (Manhattan, KS, USA), is a powerful agent-based egress simulator [32]. The software features high-quality 3D visualizations that allow users to clearly observe the dynamics of the evacuation process, such as crowd formation and congestion points. It supports the import of AutoCAD v2022 files in DXF and DWG formats, making it easy to integrate actual architectural drawings into the simulation environment to ensure high simulation accuracy. In addition, it can simulate various evacuation paths like stairs, escalators, and slopes, and allows users to customize population density and quantity, as well as set different attributes for each individual in the simulation, such as age, gender, and mobility, to better reflect the diversity of the crowd. It is widely used in the design of evacuation routes and the evaluation of safety evacuation effects in various buildings [34].

4.2. Physical Model

In this paper, numerical simulations were performed using Pathfinder, a personnel evacuation simulation software. The layout of the evacuation scene is shown in Figure 5. The field is a street-type space for pedestrian safety evacuation through a narrow ramp (width = 4 m, length = 45 m). There are two safety exits, both with an effective width of 4 m.

4.3. Evacuee Parameters

The evacuees were categorized according to age and physical health status, as shown in

Table 2. Normal population simulation parameters.

Categories	Age (Years)	Maximum Speed: v (m/s)	Shoulder Width (m)	Share (%)
Juvenile	6 ≤ age ≤ 18	0.90	0.4000	20
Middle-aged people	18 < age ≤ 60	1.40	0.4558	70
Older people	age > 60	1.00	0.4558	10

and

Table 3. Different groups of people with mobility impairments simulation parameters.

Type of Mobility Impairment	Maximum Speed: v (m/s)	Shoulder Width (m)
People without disabilities	1.40	0.4558
Unassisted walking using a wheelchair	0.69	0.6100
Unassisted walking using a cane	0.94	0.4558
Visually impaired	0.86	0.4558
Hearing impaired	1.25	0.4558

[35,36]. All evacuees were randomly distributed in the simulated environment; the festival participants are mainly middle-aged people, comprising a set percentage of 70%, older people and juveniles at a set percentage of 30%.

4.4. Evacuation Scenarios

4.4.1. Range of Slope

According to the grading requirements for slopes in the “Technical Regulation of the Third Nationwide Land and Resources Survey”(TD/T 1055-2019) [37], this paper selects one to three grade slopes for the simulation study of street-type public space, and sets up a total of 15 slopes, including 1°, 2°, 3°, 4°, 5°, 6°, 7°, 8°, 9°, 10°, 11°, 12°, 13°, 14°, and 15°, to analyze the characteristics of the evacuation behaviors of pedestrians under different slopes.

4.4.2. Range of Street Width

As the width of the street changes, the openness of the pedestrian’s field of vision and the degree of perception of the surrounding environment will be affected. Therefore, in this section, we set the street widths of 1 m, 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, and 9 m to simulate the effect of street width on evacuation under different crowd densities. In order to reduce the error, the simulation was performed three times for each width.

4.4.3. Obstacle Layout Pattern

The obstacle layout of the sloping street is shown in Figure 6, keeping the slope of 7° unchanged, while the width and length of the street are fixed at 4 m and 45 m, respectively, to simulate the influence of obstacle layout on evacuation under different crowd densities. Obstacles are set up in the sloping street, including three types of obstacle layouts: street sides, middle of the street, and mixed layout, with a total of seven layout patterns.

4.4.4. Type and Percentage of Disability

During an evacuation, the health of pedestrians directly affects their response time and ability to evacuate during an emergency. Pedestrians’ evacuation abilities and needs are related to the type of disability. In order to study the extent to which the type and percentage of disabled pedestrians in the evacuating crowd affect evacuation efficiency, this paper sets up 40 working conditions, as shown in

Table 4. The types and percentages of disabled pedestrians in the evacuated crowd.

Type of Mobility Impairment	Percentage with Disabilities (%)
Unassisted walking using a wheelchair	10	20	30	40	50	60	70	80	90	100
Unassisted walking using a cane	10	20	30	40	50	60	70	80	90	100
Visually impaired	10	20	30	40	50	60	70	80	90	100
Hearing impaired	10	20	30	40	50	60	70	80	90	100

.

4.4.5. Group Movement

There are group movements during crowd evacuation due to kinship, friendship, and other social relationships, etc. It is necessary to study the effects of group size, as well as age differences on evacuation times. Comparison of the effect of different numbers of group members and different age compositions on evacuation time by numerical simulation when the total number of people is 3000 and the percentage of groups is 70%. We grouped the three categories in Table 2; 16 group types were obtained by combining, as shown in

Table 5. Types of Different Groups.

Group Size	Working Condition	Group Type	Working Condition	Group Type
Group of 2	1	O-O	2	M-M
	3	O-M	4	O-J
	5	M-J	6	J-J
Group of 3	7	O-O-O	8	M-M-M
	9	O-O-M	10	O-M-M
	11	O-O-J	12	O-M-J
	13	M-M-J	14	O-J-J
	15	M-J-J	16	J-J-J

. In the table, “O”, “M”, and “J” represent the use of old age, middle age, and juvenile, respectively. For example, “O-M-J” means that there is an older person, a middle-aged person, and a juvenile in the group.

5. Results

5.1. Effect of Slope on Evacuation Time

Evacuation simulations were conducted separately with an initial crowd density of 0.50 to 2.00 pedestrians/m² (with a step size of 0.50 pedestrians/m²), without considering road obstacles or any human intervention. Due to the randomness of the simulation results, in order to reduce the error, we performed three simulations for each slope and took the average value to draw a line graph of the change in evacuation time under different slopes, as shown in Figure 7.

The total evacuation time of the crowd at different densities showed a fluctuating upward trend as the slope increased. In Figure 7, the slope time curves at different crowd densities have obvious inflection points at 4° and 8°, which means that the evacuation efficiency of pedestrians increases rather than decreases at this slope. The reasons for this phenomenon include both individual and group factors:

(1)

In terms of personal factors, on nearly horizontal ramps with a slope of less than 4°, pedestrians’ speed of movement increases to some extent due to the effect of gravity during the descent. However, on gently inclined ramps with a slope of more than 4°, pedestrians will reduce their speed to maintain their stability to prevent falling due to the increased perception of the slope by the human body itself;

(2)

In terms of group factors, at a steeper 8° slope, especially in emergencies, evacuating crowds tend to step faster unconsciously and are more motivated to evacuate. Crowds tend to be closer to each other when evacuating, and the phenomenon of pedestrians pushing each other will be strengthened, which requires pedestrians to exert more physical strength and attention to maintain their balance. To a certain extent, this will increase the risk of stampede accidents.

Slope landings place more stress on the knee joint than horizontal landings. As the slope increases, so does the risk of knee injury. Taken together, 4° is the ideal slope for different population densities. At this slope, pedestrians can maintain the continuity of pedestrian flow while avoiding the blockage and stoppage caused by the steep slope, reducing the time lost due to congestion. The 4° slope is also relatively easier to walk on and control for people of different ages and physical conditions, such as the elderly and children.

The time slope curves at each density were obtained by fitting, and the slope of the curves was used to indicate the degree of influence of slope on evacuation time (Figure 7), which is known as the ratio of time to slope. Figure 8 shows the variation in the average evacuation time at different slopes and the ratio of time to slope for different crowd densities, which leads to the following conclusions:

(1)

There is a linear positive correlation between the average evacuation time at different slopes and the crowd density as the crowd density increases.

(2)

As the crowd density increases, the degree of influence of slope on evacuation time grows in parallel. When the crowd density is in the range of 0.50–1.00 pedestrians/m², the curve grows more gently, the degree of influence of the slope on the evacuation time is weak; when the crowd density is greater than 1.00 pedestrians/m², the curve begins to steepen, the degree of influence of the slope on the evacuation time is enhanced.

In summary, evacuation times are affected by both crowd density and slope. When the crowd density is less than 1.00 pedestrians/m², the evacuation process is relatively smooth and the effect of slope on evacuation time is small. This may be due to the fact that at low densities, people have enough space to move freely, and the effect of the slope is masked by other factors (such as individual evacuation intentions and mobility). The effect of slope on evacuation time is significantly enhanced at crowd densities greater than 1.00 pedestrians/m², where crowding among personnel may make movement difficult. At high densities, the slope may make it more difficult for people to move, increasing the overall time required for evacuation.

5.2. Effect of Street Width on Evacuation Times

The extreme points of each curve appear in Figure 7 when the slope is 7°, which proves that the safety of evacuation is weaker at this slope and needs to be further researched and investigated. Therefore, in this section, we simulate and analyze the effect of street width changes on evacuation results when the slope is 7°. The variation in evacuation time for different street widths is shown in Figure 9.

The width–time curves for each different crowd density were obtained by fitting according to the equation $y=A{e}^{R_{0}x}+y_0$, as shown in

Table 6. Fitting result.

Fitted Equation	$\mathit{y}=\mathit{A}{\mathit{e}}^{{\mathit{R}}_0\mathit{x}}+{\mathit{y}}_0$
Density	$\mathit{\rho }=0.50$	$\mathit{\rho }=1.00$	$\mathit{\rho }=1.50$	$\mathit{\rho }=2.00$
y0	305.61306 ± 7.71701	319.06594 ± 13.5872	345.00357 ± 16.78607	373.99962 ± 18.79928
A	2655.19675 ± 168.95449	3127.81417 ± 249.12569	3702.67456 ± 303.17803	4261.36783 ± 328.76825
R0	−1.10557 ± 0.05901	−1.02977 ± 0.07287	−1.02344 ± 0.07483	−1.00995 ± 0.07032
R2	0.99735	0.99518	0.99484	0.99529

. The goodness-of-fit R² of each curve is greater than 0.99, which shows that the evacuation time decreases exponentially as the street width increases.

According to Figure 9, when the street width is less than 2 m, the total evacuation time of the crowd increases exponentially, and the evacuation effect decreases significantly. When the street width is 2 m to 6 m, as the width increases, the evacuation time of the crowd under different densities decreases, while the differences among them gradually narrow. When the street width is greater than 6 m, the curves tend to be flat, and the enhancement effect of the continued increase in the width on the evacuation efficiency is nearly zero. The reasons include physiological and psychological aspects:

(1)

Physiologically, when the width of the slope reaches a certain level, the pedestrian movement speed stabilizes at its limit value, and the flow rate of the evacuation channel reaches saturation. This phenomenon is consistent with the typical flow rate model: $Q=\rho v$, where $Q$ is flow rate, $\rho$ is density, and $v$ is speed. At a certain crowd density, when pedestrian speeds reach their limit values, further increasing the street width does not significantly increase the flow rate, so the change in evacuation time stabilizes.

(2)

Psychologically, in a wider evacuation channel, the overall crowd density and congestion decrease. Pedestrians will feel more relaxed without a sense of urgency. The effect of crowd flow may be influenced by other factors, such as the composition of the crowd, the direction of walking, the interaction between the crowd, and environmental factors.

5.3. Effect of Obstacle Layout on Evacuation Time

The evacuation results of different densities of people under each obstacle layout are shown in

Table 7. Evacuation results for crowds of different densities under each obstacle layout.

Layout Number		Evacuation Time (s)							Number of Stranded People
		1	2	3	4	5	6	7	1	2	3	4	5	6	7
Density (pedestrians/m2)	0.50	359	435	556	543	446	625	703	0	0	19	20	0	10	34
	1.00	407	498	653	631	515	748	764	0	0	21	23	0	12	35
	1.50	454	567	763	701	584	858	874	0	0	22	25	0	14	37
	2.00	503	634	840	788	653	965	1142	0	0	25	29	0	17	40

. The cumulative use of evacuation paths for pedestrians is compared for different obstacle layouts at the same crowd density, as shown in Figure 10. The number of obstacles, as well as their location distribution, jointly affects the evacuation of pedestrians.

As the number of obstacles increases, the available space for normal pedestrian movement diminishes, as vividly shown by the color changes in Figure 10. In Layout 1, with no obstacles, the color mainly leans toward lighter shades, indicating shorter usage times and smoother pedestrian flow. Layouts with more obstacles will have darker colors, such as Layout 7, which implies longer usage times and reflects poor crowd flow, congestion, and reduced mobility.

Particularly in narrow corridors or exits, obstacles can cause crowds to be stranded, thus delaying evacuation. As can be seen in Table 7, the evacuation time of the crowd increased in the order of layouts 1, 2, 5, 4, 3, 6, and 7. With the exception of Layouts 1, 2, and 5, the remaining layouts had varying degrees of stranded persons unable to complete evacuation. The number of stranded people increased in the order of layouts 3, 4, 6, and 7. The irrational layout of obstacles and the excessive number of obstacles will have a negative impact on the evacuation of pedestrians:

(1)

When the number of obstacles is the same, the number of stranded people with obstacles distributed on both sides of the street (e.g., Layout 4) is almost twice that of the centered layout (e.g., Layout 6), which suggests that pedestrians had to change the direction of their movement frequently to avoid these obstacles when the obstacles were located on both sides of the street, leading to an increase in evacuation time. On the contrary, if the obstacles are located in the middle of the street, pedestrians can travel more directly along straighter paths, reducing the frequency of direction changes, thus shortening evacuation time and reducing the risk of being stranded.

(2)

The number of people stranded in Layout 3 is slightly lower than the number of people stranded in Layout 4 when the obstacles are distributed on both sides of the street. This phenomenon indicates that in Layout 3, the symmetrically distributed barriers on both sides provide similar and regular walking routes for pedestrians during evacuation. Pedestrians can plan their routes in a relatively orderly manner, reducing mutual interference and congestion. However, in Layout 4, due to the asymmetrical distribution of obstacles, the evacuation routes for pedestrians become complicated and irregular. Pedestrians may get confused due to sudden changes in the routes when avoiding obstacles, leading to increased local congestion.

(3)

Although the obstacles in both Layout 5 and Layout 6 are centrally arranged, only Layout 6 produces the phenomenon of stranded people. This is because in Layout 5, pedestrians can move forward relatively straight along the vertically aligned obstacles, and the presence of the obstacles instead serves to divert the crowd so that the flow of people can be smooth and continuous. In contrast, in Layout 6, the side-by-side placement of barriers exacerbates the fluctuating changes in evacuation route widths and adversely affects the stability of pedestrian flow, highlighting the importance of carefully considering the location of barriers when designing evacuation routes and public spaces.

(4)

Layout 7 resulted in the highest number of stranded pedestrians due to the highest number of obstacles and the most complex layout, which severely restricted the movement of pedestrians, disrupted the flow of people, and made it difficult for pedestrians to find suitable evacuation routes, and the negative impacts of such a situation should be circumvented as far as possible.

5.4. Effect of Disability Type on Evacuation Time

As can be seen from the data in Figure 11, evacuation times gradually increase as the percentage of people with disabilities increases, regardless of the type of disability. The linear fitting curves for each type of disability are obtained according to the equation $y=ax+b$. The goodness-of-fit R² values close to 1 for all curves indicate a strong linear relationship between the percentage of people with disabilities and evacuation time. From the fitting results, it can be seen that there is a significant difference in the effect of different disability types on pedestrian evacuation time.

(1)

The most significant impact on evacuation efficiency is felt by people with mobility impairments (wheelchair users), the slope of the fitted curve for wheelchair users is 5.07915, which is the largest among the four types. Wheelchair users are dependent on assistive devices, move slower, and require more space or additional help in evacuation, reducing the capacity of the aisles and increasing the complexity of evacuation. In addition, wheelchair users are at greater risk on sloped streets, where loss of control can lead to serious falls and injuries.

(2)

Visually impaired people have the second highest impact on evacuation efficiency, the slope of the fitted curve for visually impaired people is 2.62776. These people are highly dependent on the environment, have difficulty in recognizing directions, cannot see signs or exit directions, are prone to making mistakes or staying in the same place, and need to rely on other people’s guidance or on auxiliary facilities (e.g., blind corridors) to complete evacuation.

(3)

Pedestrians using canes and hearing-impaired pedestrians had a relatively minor impact on evacuation times. The slopes of the fitted curve for these two types of disabled people are 1.09939 and 1.10182, respectively. Although the results of the study showed that the evacuation time of hearing-impaired pedestrians was lower than that of pedestrians using canes, the slope of the fitted curve for hearing-impaired pedestrians was slightly higher. This phenomenon is explained by the fact that hearing-impaired pedestrians have an information reception barrier and cannot hear critical evacuation information, such as sirens or voice announcements. As the percentage of hearing-impaired pedestrians in a crowd increases, the problem of miscommunication will become more pronounced, which will make coordinated evacuation more difficult. Pedestrians using canes, although limited in their mobility, have a greater advantage in accessing information and, therefore, have a relatively lower rate of increase in evacuation time.

According to the degree of influence of different types of disabilities on evacuation efficiency, for high-impact groups (e.g., wheelchair users and visually impaired persons), focus should be placed on the design of assisted evacuation measures, including widening of evacuation corridors, optimization of evacuation path markings, and addition of assistive devices. For low-impact groups (e.g., hearing-impaired persons), multi-modal communication of evacuation information should be strengthened, such as adding visual warning signs and information bulletins to make up for the shortcomings in their information reception.

5.5. Effect of Group Movement on Evacuation Time

Based on the simulation results, when pedestrians move in groups, the evacuation time at different slopes is shown in Figure 12. The figure uses color variations to visualize the change in evacuation time for different group combinations in each row. From the figure we can observe the following:

(1)

The results show that the color gradient in each row is subtle as the slope increases from 1° to 15°. This suggests that the evacuation times for different group combinations change very little as the slope increases. In contrast, the color differences were more pronounced when comparing the colors of different group types. Thus, under congested conditions, the effect of pedestrian group movement on evacuation time is significantly greater than the effect of slope.

(2)

There are substantial color differences across different group types. For group types with a single age composition like “M-M-M” or “J-J-J”, the colors are more homogeneous within the row. This is largely dependent on the relatively consistent pedestrian evacuation ability within the single age group. In multi-age mixed group types, such as “M-J-J” or “O-M-J”, the colors show more variation within the row. This implies that evacuation efficiency varies with crowd size and age composition, the implications of which are highlighted below.

5.5.1. Effect of Group Size on Evacuation Time

The age of group members has a significant effect on evacuation efficiency (Figure 13). The middle-aged group showed higher efficiency in the evacuation process. Although the elderly group is more adaptable in responding to emergencies, their ability to evacuate is limited by their mobility and response capacity. The juvenile group, with slower mobility and prone to fear and panic in emergencies, often needs the accompaniment and guidance of adults in the evacuation process in order to evacuate safely.

With the same age composition, evacuation time increases with group size, especially for groups with weaker evacuation abilities. Two-person groups tend to evacuate faster and more efficiently, with greater overall flexibility. Three-person groups, due to their increased size, the more complex relationships between members, and the need for coordination, have correspondingly more configurations in which the group is in motion, as illustrated in Figure 14, and are more susceptible to blockages during evacuation, thus resulting in slower overall movement.

5.5.2. Effect of Different Age Compositions on Evacuation Times

The effect of age composition on evacuation time, when the group size is the same, is shown in Figure 15. The evacuation results were categorized into two levels based on the evacuation time with t = 1000 s as the dividing line.

There are six types of groups for two-person groups (Figure 15A). When the age of the group members is similar and the average age is large, the evacuation time belongs to the first level and the evacuation efficiency is better. When the group members contain juveniles, the evacuation efficiency is low and belongs to the second level.

As the size of the group increased, there was a corresponding increase in the number of group types, with ten group types in the three-person group (Figure 15B). The percentage of group types belonging to the first level increased from 50% to 70%, indicating that a reasonable age composition can effectively increase the efficiency of group evacuation, even when the group size increases.

In multi-age mixed groups, the improvement of evacuation efficiency needs to comprehensively consider the characteristics of different age groups. Middle-aged people have better physical condition and reaction ability and can provide necessary assistance and guidance to the vulnerable members of the group, which can effectively shorten the overall evacuation time and improve the overall evacuation efficiency.

6. Discussion

This paper investigates the effects of different terrain features (slope, road width, obstacle layout) and group movement (disability type, group size, age composition) on evacuation, carries out evacuation simulation experiments for crowds of different densities, obtains various types of evacuation indexes, and carries out a comprehensive analysis of the pattern of change in the crowd’s evacuation state and behavioral characteristics in the process of going downhill.

Current research suggests that pedestrians move faster downhill than on level ground on slopes less than 4°, and that excessive slopes reduce the speed of pedestrian movement. Previous research [18,20,21] provides strong support for this conclusion. This can be interpreted as when the slope is small, the downward component of gravity acts as an additional driving force for pedestrians, facilitating their walking process. However, when the slope is large, pedestrians have to counteract the excessive acceleration caused by gravity by providing sufficient friction in the opposite direction of advancement. When the slope is the same as the Itaewon stampede site at 7°, the extreme points of the curves are especially obvious when the crowd density is greater than 1.00 pedestrians/m², further indicating that the coupled effect of slope and crowd density is an important cause of the accident. From the application point of view, in urban planning, the maximum slope of public space slopes should be designed within the safety range (less than 4°), and controlling the slope angle can improve the stability of walking during pedestrian evacuation and reduce the risk of accidents. For existing street-type spaces with steep slopes, anti-skid facilities, and additional handrails can be installed to help pedestrians overcome the effects of gravity and improve walking safety.

We study the effect of field of view opening on pedestrian evacuation by changing the width of the road. The simulation data show that when the street width is less than 6 m, the field of vision of pedestrians is restricted to a very limited range, the spatial scale of human activities becomes narrower, and pedestrian evacuation is significantly affected. The narrow field of view not only physically limits the observation range of pedestrians but also psychologically causes stress and hesitation. Pedestrians may become more cautious and make frequent adjustments to their walking direction, which in turn reduces the overall evacuation efficiency. Therefore, the ratio between the street width D and the building height H on both sides should be carefully considered when designing the spatial scale of the street. When D/H < 1, the visual space is limited, and the street space is high and narrow [17]. Measures such as widening the street or appropriately lowering the building height can be taken to improve the visual space for pedestrians. For existing streets with spatial scale D/H < 1, such as Itaewon Street, traffic control and clear guide signs can be used to direct pedestrian flow and improve evacuation safety.

Obstacles can cause pedestrians to fall or be injured. This not only affects the safety of individual pedestrians but may also result in subsequent pedestrians not being able to cross in time due to congestion. In this study, obstacles are set up in the street space according to seven layout patterns. The evacuation effects are in order of accessibility, middle of the street, street sides, and mixed layout. Meanwhile, in the simulation process involving obstacles, the phenomenon of some pedestrians being stranded and unable to evacuate exists; the higher the number of stranded people, the higher the level of collision risk. The simulation results are different from those of the predecessor [17,28]; the reason is that the predecessor’s results were obtained from the field experiment. As the number of experiments increases, the experimenter’s familiarity with the environment is stronger, which impacts the evacuation results. This shortcoming can be effectively circumvented by numerical simulation. In terms of street space management, obstacles should be regularly inspected and cleared to ensure that evacuation routes are clear. For obstacles that must be installed, such as garbage cans and utility poles, the layout should be rationalized, giving priority to layouts that have little impact on evacuation.

Previous studies on group movement behavior have mostly been conducted in two-person groups, with group types categorized by gender [23,24,25]. Considering the variability of the evacuation ability of people of different age groups and disability types and the effect of group movement on the evacuation process, this paper simulated the effect of different disability types and proportional distributions on the evacuation effect, explored the temporal performances of two-person and three-person groups in the evacuation process, and comparatively analyzed the complexity of the group configurations of the two combinations and their differences in performance in emergency situations. In addition, the evacuation times of 16 different types of groups under the same conditions were evaluated. Differences in the evacuation capabilities of different groups, such as the limited mobility of disabled people and the relative slowness of the elderly and children, highlight the importance of considering different groups in evacuation planning. In public places, special evacuation routes and supporting facilities should be provided for different groups.

Based on the above conclusions, in order to avoid the occurrence of similar accidents, we propose a preventive mechanism for the safe evacuation of slopes in urban street-type public spaces, as shown in Figure 16.

7. Conclusions

This study provides a theoretical framework for understanding pedestrian evacuation dynamics in sloped street-type spaces. The findings highlight the importance of slope gradients, street width, obstacle layout, disability type, and group movement in influencing evacuation efficiency. While the study is primarily theoretical, it offers guidance for urban planners and public safety managers to improve the design and management of street-type spaces. Based on these experimental results, the main conclusions can be summarized as follows:

(1)

From the perspective of spatial design, the slope of the street-type space should not be more than 4°, which can maintain the continuity of the flow of people while avoiding the congestion and stagnation caused by excessive slope.

(2)

From the perspective of site management, when the width of the evacuation channel is less than 2 m, it is more likely to cause congestion of dense crowds, which falls into the high-risk zone. Relevant management units should increase the deployment of security forces and enhance police dispatch to deal with emergencies.

(3)

In order to optimize pedestrian evacuation, it is necessary to reasonably plan the setup and layout of obstacles when designing public space, to improve the pedestrian’s access efficiency and comfort, and to ensure the smoothness of the evacuation channel.

(4)

From the perspective of crowd control, the age of evacuees and the variability of their evacuation ability should be taken into account to formulate an emergency evacuation plan to maximize the overall evacuation efficiency through reasonable control and guidance.

8. Limitations and Future Work

The model constructed in this paper applies to tourist and leisure neighborhoods, which often consist of street-type spaces and a dense flow of people, with the risk of crowd congregation. Despite its contributions, the study has several limitations: this research focuses on theoretical insights derived from numerical simulations. Due to the limitations of the simulation software’s functionality, the numerical models used in this study simplify certain conditions in the real world. The simulation does not take into account road surface conditions and terrain features such as steps or sudden elevation changes, which may have an impact on the movement process of pedestrians. While the study includes population groups with different physical abilities, it does not account for cultural, social, or behavioral diversity, which may affect evacuation patterns in heterogeneous populations. This simplification may limit the applicability of the results to diverse populations.

Future research should include a broader range of pedestrian characteristics, such as cultural backgrounds and social groups. Including more diverse populations will help to validate the generalizability of the study results. Additionally, psychological factors such as panic reactions and risk perceptions should be explored to enhance evacuation strategies and emergency management effectiveness.