Understanding Tsunami Evacuation via a Social Force Model While Considering Stress Levels Using Agent-Based Modelling

Abstract

Given massive events, such as demonstrations in coastal cities exposed to tsunamigenic earthquakes, it is essential to explore pedestrian motion methods to help at-risk coastal communities and stakeholders understand the current issues they face to enhance disaster preparedness. This research targets SDG 11 Sustainable Cities and Communities. It strengthens resilience in coastal areas by implementing a social force model using a microscopic agent-based model to assess the impact of human behaviour on evacuation performance by introducing evacuation stress levels due to a tsunami triggered in central Chile. Two scenarios with two environments and three crowd sizes are implemented in NetLogo. In Scenario 1, pedestrians walk at a relaxed velocity. In Scenario 2, tsunami evacuation stress is incorporated, resulting in pedestrians walking at a running velocity, taking, on average, four times less time to evacuate. We explored more realistic settings by considering the internal susceptibility of each agent to spread tsunami evacuation stress among other evacuees. Results from Scenario 2 show that internal susceptibility effects almost double the mean evacuation time for 200 agents. Findings suggest a trade-off between realism and the minimization of evacuation time. This research is considered a first step toward including stress in tsunami evacuations for sustainable evacuation planning.

1. Introduction

Events such as celebrations, sports competitions, pilgrimages, and demonstrations are examples of massive gatherings where thousands of people unite simultaneously in a specific location. For instance, on 27 October 2019, an extensive march gathered 100,000 people in the streets of Valparaiso City, central Chile [1]. A similar number of people—approximately 80,000—gathered in the Itaewon district of Seoul, South Korea, on 29 October 2022 during Halloween celebrations, but with fatal consequences [2]. Evacuations caused by false bomb alarms [3], car attacks [3], fires [4], or disasters such as earthquakes [5,6] or tsunamis [7] can rapidly raise people’s stress levels, triggering a variety of behavioural responses. In emergencies, for instance, stressed individuals walk faster during evacuations than they do under non-evacuation scenarios [3,8,9].

To prevent crowd disasters, such as the one that occurred in the Itaewon district [2], where more than 150 casualties were reported because of crowd surges due to extremely high densities in narrow streets, it is essential to understand the dynamics and emergent phenomena behind heterogeneous crowds. There is significant uncertainty about human behaviour in life-threatening situations, especially under stress.

Agent-based models (ABMs) are powerful and flexible tools used in diverse disciplines, from natural and social sciences to engineering [10]. The tsunami evacuation field is not an exception; ABMs are suitable for studying pedestrian evacuation modelling due to their ability to simulate the emergent phenomena resulting from agent–agent and agent–environment interactions [7,11,12,13]. For instance, the comprehensive multimodal ABM work of [7] addresses the controversial topic of vehicle usage in tsunami evacuations in Kamakura, Japan. In their simulations, the consideration of the behaviours and the degree of interactions of residents and visitors with the urban settings is of great importance for disaster preparedness in touristic cities. After the Great East Japan Earthquake (GEJE) in 2011, the authors of [11] modelled a village-wide multimodal evacuation using the ABM NetLogo. With a geographically explicit model that includes building layouts, road networks, tsunami safe zones, and shelters, they examined several behaviours related to the GEJE tsunami. The simulations considered shelter capacity, casualty estimation, traffic jam location, and a collision avoidance algorithm for pedestrian motion and subsequent interaction.

The social force model (SFM) is a continuous microscopic approach utilized to represent pedestrian motion under the concepts of driving, interacting, and physical forces. These forces enable evacuees to move toward a destination, help them avoid collisions with other evacuees while maintaining their private space, and prevent them from colliding with environmental features, such as walls or obstacles [14]. The SFM can realistically reproduce pedestrian movement in normal and emergency contexts [14,15,16]. The implementation of a pedestrian motion approach capable of realistically representing individual evacuees’ movement (SFM) in a platform (ABM) where interactions between evacuees and the environment can be analyzed at the individual level is a reasonable method for the numerical modelling of human behaviour in the context of a tsunami evacuation event. According to the extensive pedestrian evacuation ABM review of [17] that covered eighty-one research papers over a period of ten years, in building and outdoor evacuations—regardless of the type of hazard (e.g., floods or tsunamis)—human behaviour is the main topic of study, meaning that this technique is a reliable and extensively used tool for emergency evacuation simulations.

2. Literature Review

Socio-psychological aspects in evacuations have been studied for various emergency situations [3,4,5,6]. However, few are dedicated to the tsunami hazard and its consequent evacuation process. A multiagent-based model employing a microsimulation based on the SFM was used on French Riviera beaches to study tsunami evacuation behaviour [18]. Another study combined an agent-based simulation (ABS) with a Susceptible-Exposed-Infectious-Recovered (SEIR) model to analyze the COVID-19 spread in a tsunami evacuation in Iquique, Chile [19]. Susceptible, exposed, infectious, and recovered agents with different contagion rules based on probability functions were modelled in this study. An ABS for a city-wide tsunami evacuation, including a simplified SFM, was utilized in the two Chilean cities of Iquique and Viña del Mar, as well as in Kesennuma, Japan [20]. Similarly, in Viña del Mar [21,22] and Valparaiso [22], city-wide and drill-wide tsunami evacuation simulations incorporated a collision avoidance algorithm into an ABM. León and March [23] analyzed the impact of urban features on evacuation times in the tsunami-exposed city of Talcahuano in Chile, via an ABM. In the authors’ preliminary work [24], to represent pedestrian motion in tsunami settings, initial values for the parameters of the SFM are tested. Using the ABM NetLogo, pedestrian evacuees walking both at a relaxed velocity and evacuating at high velocities are simulated. Additionally, a preliminary proposal to estimate stress levels is introduced.

Indoor and semi-open investigations covering quantitative methods to estimate emotion contagion and stress variations in evacuation settings have highlighted the need to include such variables in computer models, seeking to simulate more realistic situations. For instance, Cornes et al. [3] developed a method for spreading fear in crowds, which was inspired by real-life dangerous situations captured on video. They combined the SFM and a Susceptible-Infected-Recovered-Susceptible (SIRS) model to simulate emotional contagion from nearby pedestrians, considering contagion efficiency and internal stress fluctuations. In the context of fire evacuations, Cao et al. [4] studied stress variation in a building evacuation through the SFM. They utilized a sigmoid function to estimate evacuees’ stress level based on the distance from the fire source. The earthquake evacuation research of [6] developed a group emotion contagion model based on the OCEAN (Openness, Conscientiousness, Extraversion, Agreeableness, Neuroticism) personality model, considering leadership effect, agent–environment interaction, and pedestrian motion planning. Also being in the earthquake-related field of research, the ABM work of [5] carried out by means of a modified version of the BDI (Belief, Desired, Intentions) approach, proposed a procedure to model anxiety based on perceptions. Agents make decisions based on the perception of the estimated evacuation time, crowd density, and visibility of exits via exponential functions. The evacuation process considered structural and non-structural damage to buildings.

Except for [24], none of these studies have incorporated stress levels in tsunami evacuations utilising a microscopic pedestrian motion approach, for instance, the social force model in a platform capable of simulating interactions at an individual level, such as agent-based modelling. This research aims to fill this gap by investigating human behaviour in a hypothetical near-field tsunami evacuation in Valparaiso City, central Chile, while incorporating stress levels using the NetLogo 6.3.0 software (Figure 1b). The present research is regarded as an initial step in integrating stress variables into numerical modelling within the context of tsunami evacuations. From a risk reduction point of view, the more we understand the complexities of human behaviour in tsunami evacuations, the better we can prepare for future scenarios. Despite the lack of real-world data, hypothesizing behavioural features such as stress in computer simulations can help decision-makers more quickly understand the challenges ahead and the measures required to improve the effectiveness of the current evacuation plans, paving the way to sustainable evacuation strategies.

The remaining sections are organized as follows. In Section 3, the materials and methods used, including the Social Force Model, experimental scenarios, tsunami evacuation stress estimation and spread, parameter setting, and NetLogo interface, are explained in detail. In Section 4, the results for the different scenarios are presented. Section 5 outlines the discussion, and conclusions are drawn in Section 6.

3. Materials and Methods

3.1. Study Area

Chile is one of the most tectonically active areas in the world due to the convergence zone between the Nazca and South American plates which lies underneath it [25]. Earthquakes with magnitudes greater than Mw 8 occur once every 10 years [26]. Over the recent 14 years, the country has witnessed three major earthquakes that triggered tsunamis (Figure 1a): the Maule earthquake on 27 February 2010 of magnitude Mw 8.8, the Iquique earthquake on 1 April 2014 of magnitude Mw 8.2, and the Coquimbo earthquake on 16 September in 2015 (Mw 8.4) [27]. According to Carvajal et al. [28], in 1730, an earthquake of Mw 9.1–9.3 struck Metropolitan Chile (see Figure 1c). Since that time, neither of the latest earthquakes of 1822, 1906, and 1985 have liberated most of the shallow slip accumulated in the area. Future tsunamis have great potential to be destructive, posing a significant risk for the coastal communities in Metropolitan Chile, where Valparaiso City is located (Figure 1b).

The study area, shown in yellow in Figure 1c, is a section of Argentina Avenue in Valparaiso City. This is the main perpendicular street with respect to the shoreline where people gathered and walked toward the march destination (white star in Figure 1c) on 27 October 2019. The crowd, with a length of approximately 7 km, was composed mainly of families and friends. The concept of a crowd is still challenging to define because of its diversity in terms of sizes and types, i.e., physical or psychological crowds, to name a few [29]. According to [30], a proper definition of a crowd would be a group of “20 people standing in close proximity at a specific location to observe a specific event over a one-hour period, who feel united by a common identity and, despite being strangers, are able to act in a socially coherent way”.

3.2. Social Force Model

The social force model (SFM) is a microscopic continuous physics-based approach proposed by Helbing and Molnár in 1995 [14]. In this pioneering work, they introduced the study of pedestrian movement via social interactive and driven forces. The driving force (goal force) directs pedestrians to their destination or goal. To ensure a degree of comfort, interactive forces between pedestrians and their surroundings (e.g., walls or obstacles) are repulsive in nature, permitting individuals to maintain their private space while moving to their intended destination. Additionally, attractive forces are incorporated into the model to account for the effect of approaching friends or objects of interest. To consider situations occurring beyond the agents’ field of view, for instance, backwards, weights with mild effects are introduced, depending on the deviations from the desired direction. Lastly, this version of the SFM considers fluctuations because of random or unpredictable behaviours.

In Helbing et al.’s [8] following work in 2000, which aimed to quantitatively study high-density panicking situations, a crowd scenario was introduced. Values were presented for the key parameters for the repulsive interactive forces, named strength (A_i, A_iw) and reach (B_i, B_iw). Physical forces that are relevant in high-density scenarios, both normal and tangential, were also described, along with their respective parameters. These physical interactive forces help evaluate potential injuries in emergencies or unsafe situations, which is out of the scope of the present study.

$$\frac{d{v}_i}{\mathit{dt}}=f_{\mathit{des}}+{\displaystyle {\sum }_{j=1}^N}{f}_{\mathit{ij}}+{\displaystyle {\sum }_{j=1}^N}{f}_g$$

(1)

In the context of escape panics, according to Helbing et al. [8], Newton’s motion equations are utilized to represent velocity variations of N pedestrians over time (dv_i/dt) by taking into account one driving and two interactive repulsive forces—the desired force (f_des), the social force (f_ij), and the granular force (f_g)—as shown in Equation (1). The latter force represents physical contact at high densities where body force and sliding friction emerge either because of the interactions between pedestrians or a pedestrian and walls/objects.

$$f_{\mathit{des}}=\frac{v_{\mathit{des}}^i\left(t\right)e_{\mathit{des}}^i\left(t\right)-v^i\left(t\right)}{\tau }$$

(2)

In Equation (2), the driving force (f_des) accounts for any pedestrian i navigating toward a goal (e.g., safe zone or evacuation shelter) in a desired direction ($e_{d\mathit{es}}^i\left(t\right)$) at a desired velocity ($v_{d\mathit{es}}^i\left(t\right)$). Deceleration due to interactions with the environment and other individuals triggers deviations from the desired velocity, causing agents to instead move at a current velocity ($v^i\left(t\right)$). As pedestrians strive at every time step to attain their desired velocity, the concept of relaxation time (τ) is incorporated to represent agents’ behaviour. Small values for τ result in individuals walking more aggressively [14].

$$f_{ij}=f_{sij}+f_{bij}=A_i e^{(rij-dij)/Bi} n_{ij}+k_n g\left(r_{ij}-d_{ij}\right) n_{ij}$$

(3)

Interactions between pedestrians and interactions of pedestrians with walls or objects are taken into consideration by the socio-psychological force or social force (f_ij) in Equation (3). The social force equation for interactions between pedestrians considers socio-psychological (f_sij) and physical or contact forces (f_bij). Once in motion, individuals desire to preserve a minimum distance from others, walls, or objects. Figure 2 shows a schematic representation of two interacting agents, in which the pedestrian radius (r_i, r_j) symbolises the personal or private space. Interactions, which are repulsive in nature, are ruled by an exponential function decay with two constant values, A_i strength of social interaction and B_i reach of social interaction. If the length of the distance separating pedestrian i and pedestrian j’s centre of mass is greater than the sum of the pedestrian’s radius ($d_{\mathit{ij}}$ > $r_{\mathit{ij}}$), agents are not in contact; hence, they do not collide (Figure 1). Conversely, if the sum of the pedestrian’s radius exceeds the length of the distance between the pedestrian’s centre of mass, $r_{\mathit{ij}}$ > $d_{\mathit{ij}}$ agents collide with each other. The collision triggers a physical force f_bij with a body force coefficient k_n and a Heaviside function $g\left(r_{\mathit{ij}}-d_{\mathit{ij}}\right)$ set to zero when there is no contact between agents, or it is set to the argument if collisions occur. Lastly, the unit vector n_ij points from pedestrian j to pedestrian i.

$$f_g={f_{siw}+f_{biw}=A}_{iw} e^{(ri-diw)/Biw} n_{iw}+k_n g\left(r_i-d_{iw}\right) n_{iw}$$

(4)

The social force for interactions between pedestrians and walls or objects is shown in Equation (4). These interactions are also repulsive in nature, and they are ruled by the exponential function decay with constant parameters A_iw (strength of the social interaction between pedestrians and walls or objects) and B_iw (reach of the social interaction between agents and walls or objects). The term r_i represents the radius of any pedestrian i, d_iw is the normal distance from the current agents’ position to the wall, and n_iw is the unit vector heading its direction from the wall into any given pedestrian i. Similar to Equation (3), if agents make contact with walls, physical forces with a body force coefficient k_n and the corresponding Heaviside function appear. Finally, to account for the interactions between agents and obstacles (${\mathrm{f}}_{\mathrm{si}\_\mathrm{obs}},{\mathrm{f}}_{\mathrm{bi}\_\mathrm{obs}}$), the same Equation (4) is used.

SFM Parameters

Given the absence of empirical data and the use of a hypothetical case, this study adopts a theoretical approach to investigate pedestrian dynamics in a tsunami evacuation event in central Chile, with two experimental scenarios implemented in NetLogo. To represent pedestrian movement more realistically, we applied the SFM and set up the parameters for the interactive and driven forces based on values from the literature, both in the context of emergencies and during normal situations (

Table 1. Suggested parameters for the SFM in the literature.

Reference	Ai [m/s2]	Bi [m]	Aiw [m/s2]	Biw [m]	τ [s]	vi [m/s]
Helbing et al. [8]	27	0.08	27	0.08	0.5	0.8
Helbing et al. [16]	3	0.2	5	0.1	1	Normal distribution. Mean = 1.3 SD 0.3

).

In a preliminary work [24], the authors tested the SFM in NetLogo in a unidirectional corridor using the following values from [1]: A_i = 10 N, A_iw = 2000 N, B_i = 0.13 m, and B_iw = 0.08 m. However, the constant oscillations of agents led to the conclusion that further calibration is necessary to adequately represent pedestrian motion.

In the present research, several experiments were carried out to determine the most suitable set of parameters for the two scenarios (Scenario 1 and Scenario 2). While testing the values in Table 1, oscillations and undesired behaviours (such as pushy behaviour and unrealistic large jumps) emerged from the simulations. To address this issue, sensitivity and trajectory analyses were performed. Research on parameter calibration of the social force model with empirical data indicates that a different parameter combination might produce equivalent outcomes [31,32,33]. The parameter setting criterion applied in this study was to identify the combination that eliminates oscillations, overlapping, and unrealistic behaviour with a minimum variation from the values in Table 1. We minimised the oscillations as much as possible while avoiding overlapping, which is a well-known dual issue in the SFM [34,35,36]. The chosen values for the strength and reach of the interactive repulsive force f_sij were 3 m/s² and 0.2 m, respectively, while for the repulsive forces for walls and obstacles, they were 40 m/s² and 0.2 m, respectively (refer to

Table 2. Experimental parameters for the SFM.

Parameter		Scenario 1	Scenario 2
Symbol	Unit
Ai	m/s2	3
Bi	m	0.2
Aiw, Aiobs	m/s2	40
Biw, Biobs	m	0.2
τ	s	1		0.6
${\mathrm{v}}^i$	m/s	0.6 + 0.1		1
vdes	m/s	0.66		Sigmoid
ri	m	Normal distribution. Mean = 0.466, SD 0.031
mass	kg	78.45
${\mathrm{k}}_{\mathrm{n}}$	kg/s2	1.2 × 105
FOV_radius	m	3		1
rj_radius	m	3		1
FOV_obs	m	3		1
FOV_walls	m	3		1
k		-		2
spread_radius	m	-		>1

).

3.3. Experimental Scenarios

The agent-based model (ABM) NetLogo [37] is used to implement the SFM. NetLogo is a robust and flexible open-source ABM widely utilized to model complex systems with a broad range of applications, including the pedestrian evacuation field and tsunami evacuations [10,37]. Several studies have used NetLogo for modelling tsunami evacuations in Japan [11,38], Indonesia [13,38], Peru [39], and Chile [12,24]. NetLogo employs a bottom-up approach to simulate complex systems. Agent-based models are useful for modelling systems or natural phenomena using agents (autonomous adaptive heterogeneous entities), an environment (a computational world where agents move), and agent–agent/agent–environment interactions. One of the key properties of complex systems is emergent phenomena (macro-level aggregated behaviours), which result from the reciprocal interaction between agents and the environment, even when straightforward rules are followed [10].

Figure 3 shows a summary of the model’s implementation. After setting up the model by assigning attributes to the agents and producing the environments, two scenarios were executed. Scenario 1 depicts the protest with agents walking on Valparaiso’s city street at an easy pace. Scenario 2 is a hypothetical tsunami evacuation event that includes tsunami evacuation stress. In the simulations, crowd sizes of 50, 100, and 200 agents were examined. Evacuation time varies depending on the number of agents and environment settings, but the maximum mean evacuation time considering all agents evacuated for the largest crowd is ~130 s (check

Table 3. Mean evacuation times for 50, 100, and 200 agents in two different environments in Scenario 1.

Agents	No Obstacles	Obstacles	Difference
50	92.70	98.53	6.29%
100	103.67	108.67	4.82%
200	123.33	129.23	4.78%

). The effect of obstacles on the mean evacuation time is also investigated, and both scenarios are compared. Results are shown in Section 4, including the outcomes of the tsunami evacuation stress spread for low, intermediate, and high susceptibility levels.

3.4. Tsunami Evacuation Stress and Spread

Recent studies investigating quantitative approaches to estimate stress fluctuations in indoor and semi-open emergency evacuations have utilized sigmoid [4] and exponential decay functions [3,5]. Behavioural changes in evacuees’ moving velocities due to stress variations are discussed in the context of the SFM in references [3,4]. In the authors’ previous work [24], a similar method was proposed to calculate tsunami evacuation stress, in which velocity alterations because of escalating stress were accounted for by the desired force (Equation (2)). It is well established that people move faster in emergencies or life-threatening circumstances than in ordinary situations. Therefore, their desired velocities exceed those in non-emergency situations (e.g., Scenario 2 vs. Scenario 1). Then, according to [24], a sigmoid function fluctuating in the range [0, 1], in which 1 symbolizes the maximum tsunami stress level and 0 the minimum tsunami stress level, was proposed (Equation (5)). Stress varies based on the distance ($d_i^{\mathit{exit}}\left(t\right))$ to the safe zone, where the farther the distance from the agents’ actual position to the safe zone, the higher the stress. The closer they are to the safe zone, the lower the stress. Lastly, k is the slope of the sigmoid function (see Table 2).

$$S_i^t=\frac{1}{1+e^{(-k \times d_i^{\mathit{exit}}\left(t\right))}}$$

(5)

In our preliminary work [24], the piecewise function was modified from Cao et al. [4], with velocity values as follows to account for the variations in the desired velocity because of tsunami evacuation stress. For the high stress level, the value of 5 m/s came from [8]. We referred to [4] for intermediate stress, while the low stress level value of 0.66 m/s was obtained from secondary data. The desired velocity is modified and adapted to a tsunami context in the present research, as shown in Equation (6). Agents in the high stress level have a maximum speed of 2.77 m/s, which is the mean of the low, moderate, and fast running speeds from Wood et al. [40]. The results of Fraser et al. [41], after studying the probability of pedestrians running at slow, moderate, and fast speeds in a least-cost tsunami evacuation model, emphasize the positive effect in the evacuation time of integrating evacuees moving at running speeds in computer simulations. In the present study, the decision to select running speed values is to minimise the evacuation time in a tsunami scenario and to simulate a high-stress situation caused by a near-field tsunami with less than 15 min before the arrival of the first wave. Mild-stress velocity is determined from secondary data from [24] (further details in Section 3.5 and Table 2), including a randomness of 0.34 m/s to resemble agents walking faster than in relaxing settings. The intermediate stress value for the desired velocity corresponds to the linear equation between the mild and high stress levels.

$$v_d^i\left(t\right)=\left\{\begin{array}{c}2.77 high stress if S_i^t\ge 0.9\\ 2.2125\times { S}_i^t+0.77875 intermediate stress if 0.9>S_i^t\ge 0.1 \\ 1 mild stress if S_i^t<0.1\end{array}\right.$$

(6)

One of the limitations of this approach is that stress drops in the vicinity of the exit. For most of the simulation time, agents navigate the environment at a high stress level, resembling a running crowd. Evacuees with similar distances to the safe zone have the same stress level. Hence, stress variations among the crowd are low. A valid question is how realistic this approach is, especially considering that stress levels could vary between individuals in a real tsunami event. To explore more real-life settings, further experiments are executed to clarify the impact of the spread of stress on the total mean evacuation time. Each agent’s tsunami evacuation stress spread is linked to its internal susceptibility level. At the beginning of the simulation, every agent is randomly assigned one of the three proposed susceptibility levels: high, intermediate, and low. The resulting number of agents in each of the levels is approximately proportional to 70, 63, and 67 for 200 agents, representing the worst condition in terms of crowdedness.

Drawing from the fear propagation method of [3], in which a contagion efficiency-based formulation is introduced to spread emotions among individuals in crowding contexts, the efficiency of spreading is a function of the effective contagion stress and the proportion of individuals in fear state within a certain radius. In this research, a new stress variation method is proposed using a simpler approach adapted to a tsunami context. Based on the contagion rate C, individuals shift their stress level from intermediate to high, defined as the ratio of neighbours in high stress over the total number of neighbours in a given spread radius, as shown in Equation (7) and Figure 4. Since the settings of this scenario comprise a near-field tsunami evacuation event with a short evacuation time, mild stress is not taken into consideration.

$$C=\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{a}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h} \mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}}{number of neighbors}$$

(7)

Various researchers have investigated the tendency of individuals to imitate other people’s actions during evacuations. Often, individuals follow their neighbours’ lead rather than making decisions themselves, which is a form of social influence [42]. In this research, agents with a high level of susceptibility mimic others easily, leading to the transition from an intermediate stress level to a high level. This transition happens if C > 0, signifying that the presence of even a single neighbour (within the spread radius) under high stress can trigger a change in their current stress level. In the simulations, agents compute their contagion rate at every time step. Those with medium susceptibility shift their stress level if C > 0.5. Lastly, agents with low susceptibility are less likely to mimic others; to alter their current level of stress they require all neighbours to be under high stress (C = 1).

3.5. Model Parameter Setting

In this section, the parameters selected for each of the experimental scenarios are explained and listed in Table 2. As mentioned in Section 3.2, the relaxation time represents the reactiveness with which pedestrians correct variations from their instantaneous velocity in relation to the desired one. The lower this value is, the more aggressive the agent is when reacting to deviations [8,14]. For Scenario 1 (no tsunami), the decision to choose τ = 1 s is to resemble pedestrians walking at a relaxed velocity; hence, choosing a higher relaxation time will make pedestrians react in a more relaxed fashion. In contrast, for Scenario 2 (tsunami), a lower value is considered appropriate for an evacuation context including stress. τ = 0.6 s in Table 2 slightly varies from that of Helbing et al. [8] due to better performance in sensitivity analysis. The variation from the suggested value is 20%, as oscillations increase significantly when τ = 0.5 s.

The value for the actual/instantaneous velocity for Scenario 1 is obtained from [24], with a randomness of 0.1 m/s being added to it. According to [24], drone footage that was recorded for 4 min and 1 s captured the demonstration moving between the cities of Viña del Mar and Valparaiso [43]. The recording angle and the continuous drone motion are the footage’s limitations for data extraction, posing difficulties to extract densities and velocities manually. It was found that there are only a few records available in a static position. Two video sections that are six seconds in length, starting at 00:49 (mm:ss) and 02:49 (mm:ss) were used to estimate local density and instantaneous velocity. After manually counting people inside the yellow square junction (see [43] at 00:52 (mm:ss)) and following representative pedestrians located at the centre of the square, a density of 1.3 ped/m² and a velocity of 0.66 m/s were obtained. Although the data are discrete, and the drone record does not cover Argentina Avenue (yellow area in Figure 1c), the values are regarded as indicative of the entire crowd, which extends to a length of approximately 7 km. To provide a distinct instantaneous velocity value to each agent in the simulation and account for the discontinuous nature of the metrics, a randomness of 0.1 m/s was introduced into the model (Table 2). The desired velocity (v_des) for Scenario 1 is equal to the actual velocity (0.66 m/s); for Scenario 2, it is set according to the value of the sigmoid function, as explained in Section 3.4.

To increase heterogeneity in the model, the radius (biacromial breadth/2) of the circular specification used in this study follows a normal distribution with a mean of 0.466 m and a standard deviation of 0.031 m [44]. The mass, fixed at 78.45 kg for all agents in the simulation, is the mean of both female and male Chilean adult workers aged 18–65+ years [44]. The body force coefficient is from Helbing et al. [8]. The field of view (FOV, Figure 2) specifies how in advance agents can inspect features of the environment, such as obstacles (FOV_obs), walls (FOV_walls), or other individuals (FOV_radius, rj_radius) at each time step. Previous studies have used a radius of view of 5 m in their models [11,15,20,45]. Other experiments were performed using a maximum length of view of 10 m [46]. However, some papers considered 5 m to be a sufficiently large distance for interactions in terms of numerical efficiency [47]. For Scenario 1 (no tsunami), the field of view is 3 m because of the computational efficiency. Sensitivity analysis revealed that differences in the field of view did not affect the evacuation time. Tunnel vision may occur during stressful and unsafe situations [48]. To consider this effect in the modelling carried out in this study, the field of view in Scenario 2 (tsunami) equals 1 m. The slope of the sigmoid function is 2 [4]. Finally, as the sensitivity analysis showed, the evacuation time is not sensitive to spread radii between 0.5 m and 3 m, and the spread radius is greater than 1 m.

3.6. NetLogo Model Setup

Figure 5 illustrates the unidirectional corridor with dimensions of 51 × 13 cells and a spatial resolution of 1 m, replicating a section of Argentina Avenue (Figure 1c). Agents are created on the left side (purple vertical line) and navigate the world from left to right until reaching the narrow rectangular exit, which is coloured brown. The walls are lime-coloured (1 m width). Pedestrians in white are circular in shape and denote Chilean adults between 18 and 65+ years old [44]. After postprocessing the SRTM 30 m resolution DEM, it was determined that the slope in the study area is mild (less than 3.5%); therefore, the slope effect is neglected in the simulations.

Figure 6 shows the interface and the settings for environments with obstacles. We placed three lines comprising five obstacles each, which are represented by green squares. The upper and lower lines are two cells away from the walls, and the distance between obstacles is seven cells. The central line is in the middle of the street. The criteria used for the settings is to leave enough space to create agents and to let them exit the street. To allow for sufficient interaction between agents and obstacles, we set the obstacles as equidistant as possible within the NetLogo environment. The simulation time step is 0.033 s. The code was modified from Mas et al. [11].

4. Simulation Results

4.1. Mean Evacuation Time: Scenario 1 and Scenario 2

The evacuation time corresponds to the time it takes for all agents to successfully evacuate the environment (exit in brown, see Figure 5). To investigate the effect of diverse environment settings and crowd sizes on the evacuation time, multiple experiments were carried out for Scenario 1 and Scenario 2. Results outline the mean evacuation time for ten runs.

The evacuation curve for crowd sizes of 50, 100, and 200 evacuees for Scenario 1 (no tsunami) is presented in Figure 7. At every time step of 0.033 s, each cell has a 50% probability of creating an agent of size 2r_i. To avoid overlapping once creating the agents, a separation of 1 m is defined. At the beginning of the simulation, between 0 and 40 s, the positive slope corresponds to the increasing number of agents according to the given probability, every 0.033 s, for each crowd size. Regardless of the presence of obstacles, each curve enters the stationary phase when the threshold—either 50, 100, or 200 agents—is reached. The larger the crowd size, the sharper the evacuation curve. Additionally, a great number of agents reduces the length of the stationary phase, for instance, 60 s for 50 agents, 50 s for 100 agents, and 30 s for 200 agents. This is because 50 agents occupy less area than 200 agents, meaning that the crowd remains in the simulation for a longer duration before the first agent is successfully evacuated, indicating the end of the stationary phase. The curves keep descending until no agents are left in the simulation.

The longest simulation time, over 120 s, for environments with and without obstacles is for 200 agents, as shown in Table 3. This result is reasonable; the larger the crowd size, the longer the mean evacuation time. The impact on the evacuation time because of the presence of obstacles is mild. When evaluating the mean of the three-group sizes of agents, environments with obstacles take 5.30% longer to evacuate; this difference explains why the coloured lines are parallel to the black lines in Figure 7. Check Table 3 for the details for each crowd size.

Figure 8 presents the mean evacuation time for both scenarios considering environments with and without obstacles. Because of the higher desired velocities in the tsunami scenario, agents take approximately four times less to evacuate, regardless of the existence of obstacles. This scenario follows a similar trend as Scenario 1, in which the larger the crowd, the longer the evacuation time for all of the evacuees. For instance, for settings without obstacles, 200 agents take 30.77 s, 100 agents take 24.40 s, and 50 agents take 21.53 s; refer to Table 3 and

Table 4. Mean evacuation time for each crowd size and environments in Scenario 2.

Agents	No Obstacles	Obstacles	Difference
50	21.53	23.63	9.75%
100	24.40	31.43	28.83%
200	30.77	31.40	2.06%

for more details. Cases with obstacles also take longer to evacuate—on average, they take 13.55% longer to evacuate, considering the three crowd sizes. The impact on the mean evacuation time because of obstacles is greater for 100 agents, taking 28.83% more time to evacuate (see Table 4). In contrast, for 200 agents, this impact is only 2%, indicating that obstacles practically do not affect the mean evacuation time. A similar situation occurs for 50 agents, in which the difference in the mean evacuation time due to obstacles is less than 10%.

4.2. Impact of the Tsunami Evacuation Stress

In the formulation of tsunami evacuation stress, which is described in Section 3.4, the sigmoid function’s value depends solely on the distance from the current agents’ position to the exit. Agents with equivalent distance values exhibit the same stress level, which is in accordance with Equations (5) and (6). This distance-dependent formulation yields most agents moving at desired velocities near to 2.77 m/s, evoking a running crowd in a high stress level, which is a very low-probability scenario. Despite the positive impact of tsunami stress on the mean evacuation time—agents take on average four times less time to evacuate—we may argue that in an actual evacuation, the stress level in a crowd certainly can vary among evacuees, with some individuals being in high stress and others in intermediate stress. To better understand the effect of mixed stress levels and subsequent spread, considering the internal susceptibility of agents in the crowd, the outcomes that were obtained are discussed below.

The mean evacuation time for the different crowd sizes for settings without and with obstacles plus a spread radius equals 2 m, is presented in (Figure 9). Compared to the results of Scenario 1 and Scenario 2, a similar trend is observed in terms of the number of agents in the simulation; the larger the crowd is, the longer the time it takes to evacuate 100% of pedestrians, with 49.73 s, 53.77 s, and 60.33 s for 50, 100, and 200 agents, respectively; for more details, see

Table 5. Mean evacuation time for each crowd size and environments for the tsunami spread scenario.

Agents	No Obstacles	Obstacles	Difference
50	49.73	50.60	1.74%
100	53.77	53.37	−0.74%
200	60.33	63.70	5.58%

. With the inclusion of the tsunami stress propagation, the mean evacuation time almost doubled compared to the values in the tsunami scenario (see Table 4 and Table 5). This increment is reasonable, considering it as a trade-off between simulations with more realistic settings and simulations targeting the minimization of evacuation time.

Furthermore, the same tendency is observed in terms of longer evacuation times and reduced impact due to the presence of obstacles; differences are less than 2% and 6% for 50 and 200 agents, respectively (see Table 5). For 100 agents, it takes slightly less time to evacuate settings with obstacles, with the difference being less than 1%.

Finally, in Figure 10, the mean crowdedness (agents’ local density over time) is calculated based on the largest crowd. The crowdedness is not sensitive to spread radii between 0.5 m and 3 m. Overall, both environments show comparable patterns. When the simulation starts and agents are created, both curves increase steeply up to 5 s and continue growing up until 200 agents are reached. Because of obstacle avoidance and consequent manoeuvres, the instantaneous crowdedness remains below 0.45 ped/m² for environments with obstacles (black line). For cases without obstacles, the crowdedness is greater—approximately 0.56 ped/m², due to a higher concentration of agents. As a consequence of stress propagation, agents moving at comparable instantaneous velocities lead to the formation of groups, as depicted by cyan- and magenta-coloured lines in Figure 6. This clustering behaviour causes a sharp decrease at 30 s, when around 70% of agents have already evacuated. This drop continues until all agents in the simulation are evacuated and the crowdedness equals zero.

5. Discussion

To better understand the dynamics and verify whether the model can reproduce the macroscopic speed/density relationship in the cells adjacent to the exit, time windows for each scenario and crowd sizes are analysed. R-squared values are obtained to assess the capability of the model to replicate the linear relationship between the speed and density of agents. In this instance, the higher the density, the lower the mean speed, and vice versa. The emergent dynamics of our model are validated via the trend shown in Figure 11. The rest of the R-squared values are outlined in

Table A1. Speed/density R-squared values for both scenarios and environments.

Scenario	Agents	Time Frame (s)	No Obstacles	Obstacles
Scenario 1	50	66.50–78.13	89.59%
	50	65.93–77.53		57.16%
	100	66.66–87.83	76.24%
	100	65.37–82.30		79.24%
	200	66.20–99.80	63.80%
	200	65.83–92.87		83.60%
Scenario 2	50	16.83–19.10	84.53%
	50	16.76–19.63		81.19%
	100	16.90–20.43	77.36%
	100	16.83–21.43		69.99%
	200	16.70–19.20	90.84%
	200	16.80–21.77		58.86%

.

Even when the model can reproduce the speed/density relationship near the exit, to validate the simulation results, it is necessary to compare Scenario 1 against empirical data via a fundamental diagram. Yet, validation is more challenging for the hypothetical tsunami case (Scenario 2) due to data scarcity. Records from real tsunami evacuations are generally complicated to obtain. Because of ethical and safety reasons, these real-life emergencies are difficult to replicate under laboratory conditions. Even so, available CCTV records from governmental agencies or third parties are useful resources to obtain metrics. Through video processing techniques, pedestrian metrics (such as global and local density, instantaneous velocities, and trajectories) can help elucidate the complexities of human behaviour and the decision-making process in relation to tsunami evacuations.

6. Conclusions

In this study, a quantitative approach is proposed to estimate tsunami evacuation stress due to the occurrence of a near-field tsunami in central Chile. To represent pedestrian motion in ordinary situations but also in an evacuation context, the authors applied the social force model. Experimental scenarios are run in NetLogo for cases with and without a tsunami, utilising different desired velocity values. For the case of a tsunami, using a distance-dependent sigmoid function, the authors calculate tsunami stress for each agent. Three stress levels are defined: mild, intermediate, and high. Later, running values in the desired velocity, which are used to resemble individuals walking at a fast pace, are introduced. Simulation results show the positive impact on the mean evacuation time of implementing tsunami evacuation stress (Scenario 2). Agents take, on average, four times less time to evacuate compared to the case without a tsunami (Scenario 1). Nonetheless, one of the limitations of the approach is the limited stress variation among the crowd. In further simulations, to produce more realistic settings, a method to spread tsunami stress based on the internal susceptibility level of agents and the contagion rate should be presented. Due to the capability of agents to shift their stress levels from intermediate to high, and vice versa, the mean evacuation time nearly doubled when compared to the case with a tsunami. Still, the effect of spreading tsunami evacuation stress between evacuees is reasonable; the mean evacuation time is an intermediate value between Scenario 1 and Scenario 2. This result is considered a trade-off between simulations with more realism and simulations aiming at minimising the total evacuation time. Nevertheless, the outcomes of this research are valuable to advance the understanding of human behaviour in tsunami evacuations.

During a real tsunami scenario, it is not possible to predict a crowd’s behaviour. However, the outcomes of this research are helpful for deepening our understanding of the benefits of including socio-psychological variables such as tsunami evacuation stress in computer models. Incorporating such variables in tsunami evacuation simulations is useful for improving current evacuation plans and preparedness in tsunami-prone cities. A better understanding of the complexities of human behaviour is necessary for sustainable evacuation. Therefore, this research contributes to SDG 11 Sustainable cities and communities by increasing disaster resilience.

For future works, to consider the effect of inundated cells in the simulations, a repulsive tsunami interactive force accounting for the willingness of pedestrians to move away from flooded areas would be helpful for representing the evacuation process more accurately. This enhancement of the social force model in a tsunami context would improve the realism of evacuations, contributing to sustainable evacuations and increasing disaster preparedness in coastal areas at risk to tsunamis. Moreover, city-wide evacuations can be investigated by enlarging the environment. The capability of agents to avoid obstacles successfully while maintaining their private space makes it possible to explore post-earthquake settings by analysing the debris on roads or sidewalks. Finally, in the context of global climate change, the need for multi-hazard and interdisciplinary approaches is becoming evident. This research has great potential to contribute to multi-hazard disaster preparedness.