Flood-related hazard criteria during the human evacuation of underground spaces through stairs: a state-of-the-art review

Vol.:(0123456789) Natural Hazards https://doi.org/10.1007/s11069-024-07002-4 REVIEW ARTICLE Flood‑related hazard criteria duringthehuman evacuation ofunderground spaces throughstairs: astate‑of‑the‑art review CarlosH.AparicioUribe1 · BeniaminoRusso1 · JacksonTéllez‑Álvarez1,2 · EduardoMartínez‑Gomariz1,3 Received: 29 February 2024 / Accepted: 27 October 2024 © The Author(s) 2024 Abstract Due to the increasing urbanisation trend and more recurrent flood events worldwide that are affecting exposed habitable areas like underground spaces. This state-of-the-art review presents a comprehensive analysis of the available literature that focuses on defining instability criteria for hazard assessment during human evacuation of underground flooded stairs. The studies are outlined in three main groups: theoretical, experimental campaigns and numerical approaches. Several methods for defining specific criteria were found, most of these criteria were described as a function of water depth (D) alone or in combination with velocity (V) highlighting the importance of these two water-related parameters for flood-related hazard evaluation. Succinctly, the most relevant findings and limitations of these studies are discussed and summarised in tables. A comparison with other floodrelated hazard criteria in plain and mild-slope areas is presented. Finally, potential future investigation lines are proposed. Thus, this state-of-the-art review could offer a comprehensive overview of the topic and stimulate new exploratory studies in this research field yielding valuable insights that can be easily transmitted to stakeholders or non-experts and foster urban resilience during floods. Keywords Flood-related hazard assessment· Instability criteria· Urban resilience· Underground space· Human evacuation· Flooded stairs * Carlos H. Aparicio Uribe carlos.humberto.apar[email protected] * Beniamino Russo beniamino.r[email protected] 1 Flumen Research Institute, Universitat Politècnica de Catalunya – Centre Internacional de Mètodes Numèrics en Enginyeria, Campus Nord, Carrer de Jordi Girona, 1-3, B0 S1, 08034Barcelona, Spain 2 Consorci Besòs Tordera, Aveneu Sant Julià, 241, Obres i Enginyeria, 08403Granollers, Spain 3 Aigües de Barcelona, Empresa Metropolitana de la Gestió del Cicle de l’Aigua, C/General Batet 1-7, 08028Barcelona, Spain Natural Hazards 1 Introduction Over the last decade, floods have been the most recurrent global natural disaster (CREDUNDRR 2020). An aggravation of extreme weather conditions due to climate change is expected in the upcoming years leading to increasing events such as flash and large-scale river floods (Kvočka etal. 2016; Monjo etal. 2023). Besides, according to the booklet The World’s Cities (UnitedNations 2018) “more than two-thirds of the world’s population will live in urban areas by 2050”. This growing concentration of people is a trend that causes significant environmental disruptions (Aparicio Uribe etal. 2022). Urbanisation modifies soil surface worsening the impact of floods due to impermeabilisation that drastically reduces water infiltration (Ribeiro etal. 2021). Moreover, the densification of habitable areas consequently triggers the development of underground spaces to supply room for human activities such as commercial malls, parking lots, subway, and metro systems. In this rapid urbanisation trend and global climate change context, many cities worldwide experience more frequent and intense floods (Martínez-Gomariz etal. 2019). Their underground spaces could be considered highly exposed flood-prone areas (Lyu etal. 2018; Yu etal. 2019; Forero-Ortiz etal. 2020a, b; Forero-Ortiz and Martínez-Gomariz 2020; and Iagua Magazine 2021). Between 2021 and 2023 several cases could illustrate this; in the Chinese province of Henan, a total of 25 people died after a record-breaking rainfall of 624mm with 208mm falling in just one hour. Moreover, in Zhengzhou, the province capital, the underground railway tunnels were flooded trapping passengers and resulting in 12 deaths (BBC News 2021a). In New York City, USA a record rainfall caused by the tropical storm Ida made authorities declare a state of emergency, the transport system collapsed and most of the city’s subway was flooded (BBC News 2021b). In Seoul, South Korea’s capital, authorities reported the worst precipitation in the last 80years that resulted after 100mm of rain in just one hour. The public transport system collapsed and the authorities confirmed 8 fatalities and 6 missed people (El Mundo News 2022a). In Paris, France’s capital the public transport system collapsed during one single rain on 16 August, with 40mm of rain in just 90min representing almost 70% of the monthly total rain during a normal season between the years 1991 and 2020 (El Mundo News 2022b). In Madrid, Spain’s capital underground metro lines L2 and L7 cancelled operations due to water intrusion after a rainfall of around 50mm per hour (Torres and Olaizola 2023). With this pressing background, an appropriate response of the underground urban-associated infrastructure during extreme weather events is an essential requirement to guarantee urban resilience (Russo etal. 2020a, b). The aim of preserving this infrastructure in such crisis episodes is to maintain the provided services and at the same time users’ safety. Underground spaces can be significantly crowded during peak hours and it creates a potential scenery for incidents that could result in fatalities. In addition, underground infrastructure plays a crucial role in the cargo transport, financial strength, security, and stability of people and cities (Avci and Ozbulut 2018). Thus, a better understanding of their vulnerability and how it affects users will enhance their resilience (Lyu etal. 2018). Considering that human activity in flood-prone areas is inevitable (Cox et al. 2010; Russo etal. 2013), a deep comprehension of people’s capabilities during floods is important to ensure their safety and explore hazard mitigation measures during evacuations (Dias etal. 2021). Many studies about human stability in flat or mild-slope areas have been presented in the literature (e.g., Foster and Cox 1973; Love etal. 1989; Takahashi etal. 1992; Témez 1992; Nanía 1999; Karvonen etal. 2000; Yee 2003; Cox etal. 2004; Goméz 2008; Jonkman and Penning-Rowsell 2008; Russo 2009; Shand etal. 2010; Xia etal. 2014; Natural Hazards Martínez-Gomariz etal. 2016; and Okamoto etal. 2022). However, regarding human stability in flooded stairs, available information is limited. Therefore, it is paramount to analyse flow patterns in such environments accounting for their singularities (Hou etal. 2022). Also, a more accurate understanding of various aspects of flood hazards for pedestrians is necessary (Musolino etal. 2020). Thus, having in mind underground stairs with their sitespecific constraints and how they affect human-flow interactions, further research should be addressed. After the introduction (1), the methodological approaches will be mentioned (2) starting from theoretical approaches (2.1) then, continuing with the experimental campaigns on straight-run stairs (according to BUEDRI 2005; ICC 2011; MOHURD 2013) the most commonly used stairs form in underground space entrances (see Fig.1) and straight-run stairs with rest platform (2.2). Afterwards, research based on numerical models will be presented (2.3). Finally, a discussion comparing the different approaches and suggesting future studies and some conclusions will be given (3). 2 Methodological approaches As mentioned in the introduction the hazardous conditions in flooded urban areas have been of interest for several decades. Nonetheless, there is no extensive revision jet focusing onspecific state of the art about flood-related hazardous conditions during the evacuation of underground spaces and their proposed safety criteria. Therefore, the goal of this review is to conduct a thorough examination of the available literature, providing a consulting resource on the topic. This is highly valuable because of the consolidation of the existing knowledge and the identification of gaps that should be focused on in the coming years. Most of the cited studies have been accessed from existing indexed databases (i.e. Web of Science, Scopus, etc.) or peer-reviewed/refereed articles and their respective citations. These contributions have been divided into three groups following specific research approaches: theoretical, experimental and numerical. The theoretical studies include analyses that used conceptual or mathematical approaches without relying on empirical or experimental data. The experimental approaches refer to all studies that conducted tests to explore the events. Finally, the numerical approaches resort to algorithms to obtain approximate solutions to the studied phenomena. The terms safe evacuation and critical evacuation will be mentioned frequently. The first one refers to a condition Fig. 1 Stairs’ forms: straight-run (a), straight-run with rest platform (b), L-shape (c), U-shape (d), and straight-run with junction in the rest platform (e) Natural Hazards in which the evacuee could evacuate without any help, and the second refers to a condition in which the person trapped would not be able to evacuate, at least without any help or external intervention. 2.1 Theoretical approaches 2.1.1 Mechanics‑based analysis ofhuman instability instairs Considering human interactions in floods there are three potential instability mechanisms: sliding, toppling and floating. This last one can occur when the water depth exceeds the body height, but in practice floating probability is small considering that human density is slightly greater than water density (Xia etal. 2014). Focusing on sliding and toppling mechanisms according to Li etal. (2022), the forces acting on a human body immersed in a flood (Fig.2) are: the drag force of the flow FD, the frictional force between human feet and step surface FR, the gravitational force Fg, the buoyancy force Fb, the human lift force FL, and the normal reaction force from the ground FN. Human height is hp and the flowing water depth over the feet on the step is hf. The angle of force FL in the vertical direction is θ. The geometric parameters of the human body were simplified as a prism of height hp width w’ and length d (Lind etal. 2004). Consequently, the acting forces can be defined as: (1) Fg =𝜌 g ⋅g ( h p ⋅d⋅w �) Fig. 2 Schematics of the human body and acting forces in flooding stairs according to Li etal. (2022) Natural Hazards where μ is the effective viscosity, V is water velocity, D is water depth, ρ is the fluid density, ρg is the human body density, CD is the drag coefficient and CL is the lift coefficient. The critical condition for sliding instability will be given by Eq. (6): And the critical condition for toppling instability will be given by Eq. (7): 2.1.2 Theoretical studies defining safety criteria Human instability and evacuation in underground flood-prone areas through stairs started to be deeply studied two decades ago. Takedomi etal. (2001) presented the first criterion to evaluate this. The authors proposed the Momentum of Flow (MF) with Eq. (8) as the critical value to assess human evacuation in flooded stairs. where V (m/s) is water velocity and D (m) is water depth. Later, in a guideline the Japanese Committee of Countermeasures against Inundation Disasters in Underground Spaces, (CCIDUS 2002) suggested that 0.3m is the critical water level (D) at the top of stairs to safely walk and evacuate. Besides, the committee highlighted that underground evacuation time is composed of five intervals: (a) the danger recognition interval, which is the required time for the flood to reach a water level of 0.1m either in the upper part of the stairs or the underground space, (b) the decision-making interval, that is the required time for the evacuee to decide that evacuation needs to be done, (c) the underground evacuation interval, that is the required time to move from the farthest location in the underground space until reaching the area next to the stairs, (d) the stairs entrance passing interval, which is the required time to pass the crowded (supposing that several people evacuate at the same time) area before reaching the first step, and (e) the evacuation interval on the stairs, that is the required time to pass the stairs. A subsequent study by Shao (2010) pointed out that, although the evacuation process could comprise several stages, the controlling condition is the ability to walk on stairs. (2) Fb =𝜌⋅g ( h f ⋅d⋅w �) (3) F D= 1 2 𝜌VCD(hp⋅w� ) (4) F L= 1 2 𝜌VCL(D⋅w� ) (5) FR=𝜇FN=𝜇(Fg−Fb+FD ⋅ sin 𝜃−FL ⋅ cos 𝜃) (6) FR=FD ⋅ cos 𝜃+FL ⋅ sin 𝜃 (7) ( Fg−Fb+FD⋅sin 𝜃−FL⋅cos 𝜃)⋅d=(FD⋅cos 𝜃+FL⋅sin 𝜃)⋅ 1 2 hf (8) ( M F) =V 2 ⋅D=1.5 m 3 ∕ s Natural Hazards 2.2 Experimental approaches 2.2.1 Campaigns instraight‑run stairs Trying to provide experimental data to complement previous 2D numerical and scaled models on underground flood behaviour (Ishigaki etal. 2003, 2004; Toda etal. 2004), the first real-scale studies on evacuation in underground flooded spaces found in the literature were done by Ishigaki etal. (2005, 2006) at the Disaster Prevention Research Institute (DPRI) in Kyoto University, Japan. The authors evaluated different situations that a person could face evacuating an underground flooded space: flow over stairs, relative time to evacuate flooded stairs, force acting on a leg due to the water dragging effect and the maximum water level at which a person could open a door. The stairs prototype consisted of 20 steps, with 0.3m tread, 0.15m riser, 3.0m height, and 1.0m wide (Fig.3), the discharge was up to 0.8 m3/s. 49 subjects were tested: 16 females and 33 males. Four flow patterns between 0.1 and 0.4m water depth were used. Results showed that water depths between 0.3 and 0.4m made evacuees require the use of a safety lifeline and with 0.4m water depth, the relative time for evacuation increases up to 2.5 times for females and 1.6 times for males compared to no Fig. 3 Schematics of the stairs prototype (Ishigaki etal. 2008b) Fig. 4 Relative evacuation time for females and males using different water depths (Ishigaki etal. 2005), T0 is the required time without water and TD is the required time under different water depths Natural Hazards water in the staircase (Fig.4). Therefore, it was evidenced that a water depth of 0.3m on the top ground of the stairs is critical for evacuation. The acting force on the leg was measured using a prototype using four different shoe types: barefoot, sneakers, trousers, and boots was measured with a load scale that registered approximately a maximum of 4, 6, and 8 kgf when water depth was respectively 0.2, 0.3, and 0.4m. The lowest required force to generate sliding was with barefoot and the highest with trousers. Besides, when the foot position was closer to the side of the stair, the registered force was approximately 30% higher when compared to the foot positioned in the centre of the stair (Fig.5). The critical limit for safe evacuation was evaluated based on the Momentum of Flow as Takedomi etal. (2001) previously proposed (Eq.8). Nevertheless, after the analysis of the experimental campaign’s results (Fig.6). Ishigaki etal. (2005) suggested a more conservative value to match the experimental outcomes, being the critical limit for safe evacuation based on the Momentum of Flow redefined as it is presented in equation (Eq. 9). Continuing with this experimental campaign, Onishi et al. (2007), Ishigaki etal. (2008a), and Ishigaki etal. (2009) increased the number of tested subjects to a total of 304: 47 females and 257 males with an average age of 30 and 25years respectively. Also, a new test condition was implemented considering a pathway with an initial water level at the lower platform before the stairs. It was found that with a water depth of 0.3m, 2% of the males and 34% of the females needed to use handrails and with a water (9) ( M F) =V 2 ⋅D=1.2 m 3 ∕ s Fig. 5 Acting force on a leg for different footwear cases (left) and acting force on a leg for different locations of the foot (right) (Ishigaki etal. 2005) Fig. 6 Velocity distribution (left) and Momentum of Flow distribution along stairs (right) (Ishigaki etal. 2005). The red dashed line is the evacuation criterion of MF = 1.2 Natural Hazards depth of 0.4m, 13% of the males and 78% of the females needed it. Regarding the previously defined criteria Momentum of Flow (MF), under the new test condition, adequacy was limited (Fig.7). Therefore, a new criterion was proposed by Ishigaki etal. (2008b). This criterion was called Specific Force Per Unit Width (SFPUW), Eq. (10). where V is water velocity, D water depth and g is the gravitational acceleration. After the experimental campaign Ishigaki etal. (2008b) recommended a value of M0 = 0.125 m3/m as the safe evacuation limit and a value of M0 = 0.25 m3/m as the critical limit for evacuation (Fig.8). A later study done by Matsuo etal. (2011) stated this as the most conservative criterion compared to the Momentum of Flow. A subsequent study done by Ishigaki et al. (2010) developed an approximative method to try to assess the evacuation of elderly people (70years or more), the most vulnerable population altogether with children (14years or less). Elderly were represented by adding to young adults, devices that limited the freedom of movement in the waist and knees and weights on ankles and wrists. It was found that elder people have roughly 80% of a young adult capacity. Consequently, new values for safe and critical evacuation limits were presented based on age and sex (Table1). In this review, the use of the term “Sex” is based on the definitions presented by the SAGER guidelines developed by Heidari etal. (2016). Original studies may have used another terminology. (10) M 0 =V 2 D∕g+D 2 ∕2; ( m 3 ∕m ) Fig. 7 Distribution of (MF) along the stairs in previous test conditions (left) and new test condition (right) the stagnation water level is from 6 to 14m distance (Ishigaki etal. 2008b). The red line is the MF = 1.2 evacuation criterion Fig. 8 Distribution of (SFPUW) along the evacuation route in the stairs test (left) and the stairs-corridor test (right) The stagnation water level is from 6 to 14m distance (Ishigaki etal. 2008b). The red dashed line is the M0 = 0.125 and the red line is the M0 = 0.25 evacuation criteria Natural Hazards A study conducted by Baba et al. (2017) built on the previous research works expanded the number of tested subjects, 100 more were tested including 11 children aged 8, and 3 children aged 12. The experimental campaign was carried out with different water depths at the top (0, 0.1, 0.2, 0.3, and 0.4m) and consisted of measuring the required time to evacuate. It was observed that in all children, male, and female cases, the duration of evacuation increases as the depth conditions become deeper. Besides, evacuation rates for children are substantially greater than those for adults (Fig. 9). However, the study itself stated that the limited sample implies a constraint for further deductions. Focused on the Korean underground housing trend, a study by Joo and Kim (2015) evaluated the required evacuation time in flooding stairs. This experiment approached water depths (D) based on anthropomorphic characteristics. The selected water levels were related to human body parts immersed in the fluid: one for the ankle (0.17m), another for the shin (0.35m) and one more for the knee (0.45m). The straight-run stairs prototype consisted of 20 steps, with 0.3m tread, 0.15m riser, 3.0m height, 1.0m wide and an upper platform 2.0m wide. Water depth and velocity were measured on the lower step. For D = 0.17m, the average water velocity was 3.59m/s. For D = 0.35m the average water velocity was 5.41m/s, and for D = 0.45m the average water velocity was 6,48m/s. The test measured evacuation time at these three water depths while volunteers wore different shoes, with and without using handrails. The study did not specify how many people were tested, but the authors highlighted that the sample number was insufficient for statistical analysis. Results showed that while using handrails barefoot always registered the fastest evacuation time, and slippers were the latest. When the handrail was not used, evacuation time significantly increased with the increment in water depth (Fig.10). Besides, human feelings exerted additional pressure on tested people and influenced results. For Table 1 Differentiation by sex for the SFPUW criterion (Ishigaki etal. 2010) Limit of safe evacuation Difficult without any help Male 0.125 0.250 Elderly male 0.100 0.200 Female 0.100 0.200 Elderly female 0.080 0.160 Fig. 9 Comparison of required time for stairs evacuation (Baba etal. 2017) Natural Hazards Using the software FLOW-3D, Lee et al. (2016) evaluated slope effects using three stairs’ models (Table3). All of them were 2.88m in height and 1.2m wide, with 0.28m tread, but presented changes in risers that changed the steps’ numbers. Four different discharges of 0.3, 0.5, 0.7, and 1.0 m3/s were applied and human safe evacuation was evaluated based on the SFPUW criteria. The study concluded that the critical water depth for the evacuation of elderly people is around 0.2m and with water depths of 0.36m even young males will face troubles without any help. Also, it was evidenced that slope is not as relevant as water depth for human safe evacuation of stairs. Finally, the most relevant finding of this study was that the values of the studied hydraulic parameters used to determine the SFPUW criteria vary even inside every step (Fig.23). Hou etal. (2022) investigated the slope effects through a 2D numerical model (without considering width) of four stairs and two escalators (Table4). The chosen modelling tool was FLUENT 17.0. The simulation was validated with data corresponding to the stairs (26.6° slope) used in the experimental campaigns carried out at the DPRI of Kyoto University in Japan. Three different discharges (0.14, 0.28, and 0.6 m2/s) were used to compare Fig. 22 Mean air–water mixture velocity (a, b, and c) and (MF) criteria along the stepped chutes of three types of stairs (d, e, f). (Shao etal. 2015). The red line represents (MF) = 1.2; (a) & (d) C1: Straight-run, (b) & (e) C5: L-shape and (c) & (f) C6: U-shape Table 3 Specification of the stairs’ models for every case (Lee etal. 2016) Model Type Step Height (m) Total Length (m) Number of Steps (u) Slope (°) Case A Mild 0.12 6.72 21 23.2 Case B Normal 0.14 5.60 19 27.2 Case C Steep 0.18 4.48 17 32.7 Natural Hazards velocity and water depth along the steps. The analysis was divided into four different parts: (a) slope effects of different stable water depths, (b) slope effects on different stable discharges, (c) the influence of a permanent downstream water depth on evacuation risks and (d) uncertainty analysis to assess the reliability of the selected criterion MF = 1.2 m3/s2. Part (a) showed that the velocity increases gradually from the entrance to the exit, in the upper and middle segments of the stairs and escalators, whereas it was relatively stable in the lower segment. In part (b) As a general inference, the study concluded that under slopes ranging from 26.6° and 28.2° a water level of 0.3m at the entrance or a unit width discharge of 0.28 m2/s a safety evacuation occurs. But with slopes beyond 28.2°, the safety index is higher than the defined critical value. Part (c) considered a water stagnating condition in the corridor next to the stairs. For this, just the stairs with a slope of 26.6° were implemented. The initial downstream water depth was fixed at 0.3m, and the critical unit width discharge was 0.28 m2/s. It was found that sometimes, in these cases, discontinuities like hydraulic jumps occurred and the Momentum of flow (MF) at these locations was triggered becoming higher than the safety evacuation limit. This reinforced previous findings about the inadequacy of this criterion under this condition. Finally, in part (d) the study included different stairs forms (see Fig.1) and it was concluded that the criterion (MF) = 1.2 m3/s2 properly responds in straight-run stairs. However, for straight-run stairs with a rest platform, the value of (MF) = 1.2 m3/s2 in the steps downstream needs to be appropriately reduced while for L-shape and U-shape stairs, the evaluation index value of the steps downstream could be increased. Tellez Alvarez et al. (2022) created a 3D numerical model using the software FLOW-3D (Flow Science 2023) to analyse one of the access stairs in the Paral·lel station of Barcelona’s metro system (Spain). The model setup consisted of the 3D Reynolds-averaged, Navier–Stokes (RANS) equations considering free surface flow with Fig. 23 Evaluation of (M0) criterion along the stairs’ centreline for a discharge of 0.5 m3/s in case B (Lee etal. 2016) Table 4 Stairs and electric escalator typologies with different slopes (Hou etal. 2022) Typology Slope (°) Step Height – Riser (m) Step Length— Tread (m) Type—A1 30° 0.15 0.260 Type—A2 29.1° 0.15 0.270 Type—A3 28.2° 0.15 0.280 Type—A4 26.6° 0.15 0.300 Type—A5 35° 0.24 0.345 Type—A6 30° 0.24 0.416 Natural Hazards the Re-Normalization Group (RNG) turbulence model, air entrainment, drift-flux, density evaluation, and bubble and phase change. The stairs constructed with data from “Transports Metropolitans de Barcelona” consisted of 20 steps with a 0.34m tread and 0.17m riser. A constant flow rate of 0.2 m3/s was used, and measurements were done as an average at the centre line of each step. The study focused on analysing variations in hydraulic parameters (velocity and depth) due to the changes in cell sizes (0.01 and 0.02m). Results showed a maximum variation in velocities of around 25% evidencing the incidence on the mesh in the outputs. Li etal. (2022) validated a series of numerical Large Eddy Simulation (LES) models coupled with the VOF method using experimental results from previous campaigns. The straight-run stairs and the straight-run stairs with rest platform implemented respectively by Ishigaki etal. (2005) and Jiang etal. (2014) were used for calibration and validation. The last one was also employed to analyse how hydraulic behaviour affects the stability of human beings depending on their location over stairs. This selection lies in the evidence stated by Jiang etal. (2014) and Shao etal. (2015) that the rest platform amidst the stairs increases critical conditions for people trying to evacuate. To represent the aeration phenomenon in the stairs, the theoretical solution for air concentration distribution proposed by Chanson (2001) was implemented. A grid sensitivity analysis was undertaken with four different mesh sizes; 0.0050, 0.0075, 0.01, and 0.015m. The marginal error was small in all cases; therefore, in the domain’s places where the human body was not located a mesh size of 0.025m was applied and a 0.01m mesh size was selected for encompassing the human shape. The numerical models were 1:2 scale (same as the experimental campaign). Four numerical models were carried out. Three of an adult human body on representative locations of the stairs: the upper, the lower part, and the rest platform and the last one with a younger human (14years or less) in the lower part of the stairs after the rest platform. The hazard conditions were evaluated based on the (MF) criterion comparing Ishigaki etal. (2005) and Takedomi etal. (2001) recommended values. The authors concluded that the human-fluid interaction evidenced changes in fluid behaviour. The mechanics-based analysis showed that the dominant instability failure cause was sliding and was higher in the dummy representing the younger human. Also, the resulting jet flow after the rest platform was shown to be the most hazardous zone for human evacuation as previous studies pointed out (Fig.24). Liang etal. (2023) investigated the flood dynamics on stairs with a junction in the rest platform (Fig.25). Using three scenarios (Table5), the authors evaluated how shorter or longer steps and risers influence safety evacuation. A 2D model based on Shallow Water Equations (SWE) was used. The experimental campaign results by Ishigaki etal. (2005) were used to validate the model. For the first scenario, the steps were adjusted from 0.3 to 0.5m with risers ranging from 0.15 to 0.25m, maintaining a 1:2 ratio. Afterwards, in the second scenario, the steps maintained a length of 0.3m while the risers ranged from 0.15 to 0.21m, with slopes ranging from 26.56˚ to 34.99˚. Finally, in the third scenario, the straight-run stairs with a junction in the rest platform was modelled. In all cases, water depth at the top of the stairs ranged from 0.1 to 0.9m. In the first scenario, when maintaining the proportion between steps and risers, water depth increases when the step’s length increases too, while water velocity decreases. For the second scenario, greater risers correlated with higher water velocity and low water depths. However, this correlation is almost invisible with water depths below 0.5m. Therefore, for flood-related hazard evaluation during human evacuation, as mentioned before by other authors (Lee etal. 2016) slope effects have little impact. Finally, in the third scenario, results evidenced that the water depth and flow velocity on the branch are lower compared Natural Hazards to those values in the main line of the stairs (Fig.26). Therefore, this could be a good option to avoid hazardous conditions in the lower part of straight-run stairs with a rest platform. Fig. 24 Trend of the (MF) criterion along the stairs with rest platform (Li etal. 2022) Fig. 25 Schematics of the straight-run stairs with junction in the rest platform (Liang etal. 2023) Table 5 Summary of design scenarios (Liang etal. 2023)Stairs shape and scenario Step length (m) Step height (m) Straight stairs (Validation) 0.3 0.15 Straight stairs (1st scenario) 0.3–0.5 0.15–0.25 Straight stairs (2nd scenario) 0.3 0.15–0.21 Stairs with junction in the rest platform (3rd scenario) 0.3 0.15 Natural Hazards 3 Comparison ofmethodological approaches, future perspectives andconclusions 3.1 Discussion The present review showed the different “base studies” and subsequent “complementing studies” proposed to evaluate flood-related hazard during the evacuation of underground stairs. They were classified as experimental, theoretical, or numerical approaches. The five “base studies” (Table6) defined safety criteria either relying on water depth “D” alone or in combination with water velocity “V” underscoring the importance of these two hydraulic parameters for flood-related hazard assessment. Later, these criteria were used as a benchmark by the “complementing studies” (Table7) to modify them based on new findings or add information about other relevant conditioners that influence hazard indicators, like human age and sex, or stairs’ slope and shape. The studies highlighted above provided useful information although some limitations could be discussed. In some cases, these limitations were overcome by posterior studies but others still need to be addressed. The major limitation of the theoretical studies (Takedomi etal. 2001; CCIDUS 2002) is the lack of experimental evidence to support their proposed criteria. For instance, the Takedomi etal. (2001) criterion MF = 1.5 m3/s2 was later reduced to 1.2 m3/s2 due to experimental campaign results obtained by Ishigaki etal. (2005). The CCIDUS (2002) guideline besides proposing a water depth of 0.3m in the upper part of the stairs as the critical limit for evacuation, also suggested a series of intervals that composed the total required time to evacuate. These parameters were rarely implemented or assessed by other studies despite their potential impact on the safety evacuation of people and could be considered that the main reason is its dependence on site-specific constraints. The experimental campaigns could be divided into three groups: the first two consisted of real-scale prototypes, one carried out in Japan (Ishigaki etal. 2005, 2008a, b, 2009, 2010; Onishi etal. 2007; Baba 2017) and the other in South Korea (Joo and Kim 2015; Kim etal. 2018). The third was a 1:2 scaled model developed in China (Jiang etal. 2014). The Japanese campaign started by Ishigaki etal. (2005) has been widely referenced (e.g., Gotoh etal. 2006; Toda 2007; Yoneyama etal. 2009; Shao etal. 2015; Lee etal. 2016; Ishigaki etal. 2016; Baba etal. 2017; Nakasaka etal. 2020; Hou etal. 2022; Nakasaka and Ishigaki 2021; Wu etal. 2021; Lin etal. 2022). It surged to provide real data to verify previous numerical models and as a response to heavy damages caused by urban floods that Fig. 26 Water depth and velocity when D = 0.2m (left) and D = 0.3m (right) at the top of the stairs (Liang etal. 2023) Natural Hazards Table 6 Summary of the base studies/guidelines. The column “exposed elements/subjects” refers to people or objects that have been tested during the experiments or numerical models on the flooded stairs Approach & Involved Parameters Author & Year Input Criteria Observations Exposed Elements / Subjects Risk Management Countermeasures Theoretical Water velocity (V) Water depth (D) Takedomi etal. (2001) Proposed the first criterion, Momentum of Flow (MF) ( MF ) =V 2 ⋅D=1.5 m 3 ∕ s Defined the first critical value for human evacuation in stairs N/A N/A Theoretical Time (t) Water depth (D) Japanese Committee of Countermeasures against Inundation Disasters in Underground Spaces (CCIDUS 2002) Stated that the evacuation of the underground spaces is composed of several intervals (5 in total) Critical water depth (D) = 0.3 m Divided the evacuation process into several intervals Critical depth for evacuation is 0.3 m on the top ground of the stair N/A Water levels at the stairs’ entrances below 0.3 m will guarantee safe evacuation Experimental Water velocity (V) Water depth (D) Ishigaki etal. (2005) First real-scale experiments (i) Evacuation in flooded stairs (ii) Relative time to evacuate (iii) force acting on a leg due to the water-dragging effect Critical water depth (D) = 0.3 m ( MF ) =V 2 ⋅D=1.2 m 3 ∕ s The critical depth for evacuation is 0.3 m on the top ground of stairs. · 16 females and 33 males were tested. · 0.4 m water depth increased evacuation time by 2.5 times for females and 1.6 times for males · The maximum acting force on the leg model of 4, 6, and 8 kgf when water depth was respectively 0.2, 0.3, and 0.4 m Humans Water levels at the stairs’ entrances below 0.3 m will guarantee safe evacuation The definition of evacuation plans and rescue systems for underground spaces is urgent Natural Hazards Table 6 (continued) Approach & Involved Parameters Author & Year Input Criteria Observations Exposed Elements / Subjects Risk Management Countermeasures Experimental Water velocity (V) Water depth (D) Ishigaki etal. (2008b) Proposed the (M0) criterion -Specific Force Per Unit Width (SFPUW) M 0=V 2 D g +D 2 2=0.125m3∕ m M 0=V 2 D g +D 2 2=0.25m3∕ m Found that considering a stagnation water level in the lower corridor before the stairs the adequacy of Momentum of flow is limited · (M0) = 0.125 as the safe evacuation limit · (M0) = 0.25 as the value for the critical evacuation limit Humans By using a hazard criterion coupled with a flood model self-evacuation routes could be chosen and a safe evacuation plan defined Experimental Water depth (D) based on anthropomorphic characteristics Joo and Kim (2015) Assessed evacuation in flooded stairs and the force needed to open a door. Water levels were based on anthropomorphic characteristics (ankle D = 0.17 m, shin D = 0.35 m, and knee D = 0.45 m) Critical water depth (D) in the last step D = 0.35 m High heels are critical footwear for evacuation Humans Legislation should guarantee the presence of handrails in floodprone stairs to improve people’s evacuation response Natural Hazards Table 7 Summary of the subsequent studies following the base studies/guidelines Approach & involved Variables Author & Year Input Criteria Observations Exposed Elements / Subjects Risk Management Countermeasures Experimental Onishi etal. (2007), Ishigaki etal. (2008a, 2009) Continued with Ishigaki etal. (2005) experimental campaign. The authors increased the number of tested people and also added a new condition which considered a water level stagnation in the lower corridor before the stairs’ lower part · 47 females and 257 males were tested for the classical stairs test · 16 females and 83 males were tested considering the initial water level in the lower corridor before the stairs’ lower part. · When D = 0.3 m, 2% of males and 34% of females needed to use handrails and with D = 0.4 m, 13% of males and 78% of females needed it Humans Water levels at the stairs’ entrances below 0.3 m will guarantee safe evacuation Natural Hazards Table 7 (continued) Approach & involved Variables Author & Year Input Criteria Observations Exposed Elements / Subjects Risk Management Countermeasures Experimental Water velocity (V) Water depth (D) & subject differentiation by sex and age Ishigaki etal. (2010) Developed an approximative method (by using young adults and adding weight to their bodies and limiting their mobility) to assess evacuation of aged people (70 years or more) and differentiated the SFPUW criteria by sex and age M 0=0.25 m 3 m ,M0=0.2 m 3 m, M 0=0.16 m 3 m ,M0=0.125 m 3 m, M 0=0.1 m 3 m ,M0=0.08 m 3 m · For males M0 = 0.125 is the safe evacuation limit and M0 = 0.25 is the critical evacuation limit. · For females and elderly males M0 = 0.1 is the safe evacuation limit and M0 = 0.2 is the critical evacuation limit · For elderly females M0 = 0.08 is the safe evacuation limit & M0 = 0.16 is the critical evacuation limit Humans Risk management countermeasures should be focused on the most vulnerable population: aged adults, children and people with handicaps Numerical Stairs slope (°) Water depth (D) Lee etal. (2016) Evaluated slope effects using three different stairs models with slopes of 23.3°, 27.2°, and 32.7° · The authors concluded that stairs slope is not as relevant as water depth for flood-related hazard assessment during human evacuation of underground stairs. · With a water depth D = 0.36 m even young males will face troubles without any help N/A Water depth over underground stairs should be kept below 0.2 m for people’s safe evacuation Natural Hazards Table 7 (continued) Approach & involved Variables Author & Year Input Criteria Observations Exposed Elements / Subjects Risk Management Countermeasures Experimental Water depth (D) Baba etal. (2017) Expanded the number of tested subjects continuing with Ishigaki etal. (2005) experimental campaign and included a new experiment: evacuation from cars · 100 subjects were tested including 11 children aged 8, and 3 children aged 12. · 44 males and 12 females were tested trying to open a room’s door. · Concluded that the critical flood depth for females and males to evacuate stairs are 0.3 m and 0.4 m respectively Humans Risk management countermeasures should be focused on the most vulnerable population: aged adults, children and people with handicaps Natural Hazards is safe. This differs from other urban areas in which these values could represent a hazardous zone depending on the authors’ limit. More than 0.25m of water depth with velocities higher than 2.0m/s in plain and mild slope areas represent hazardous conditions for all limits and this critical condition could be obtained with less than 0.15m water depth and velocities of 4.5m/s. In contrast, the hazard level of these water depths and velocities in stairs depends on the selected criteria. In the case of flooded stairs, the hazardous conditions appeared with water depths from 0.36m onwards and velocities greater than 4.5m/s. Therefore, the limits for safe evacuation considering all the studied criteria in stairs will be 0.36m for water depth and 4.5m/s for velocity. The uncertainty zone allows higher water depths to be considered as possibly safe compared to the plain/mild slope areas in urban environments but limits velocities to a maximum of 4.5m/s. To determine which of these criteria matches the best flood situations in stairs is necessary to identify instability zones along the stairs under specific discharges. These zones will provide hydraulic parameters (water depth and velocity) to allocate hazard points in Fig.27 (right) and contrast the hazard limits presented by the authors and evaluate their accuracy. 3.2 Future research lines according tothis review Although all these studies have been useful and successfully applied to analyse different situations, the comprehension of some challenges and details still needs to be addressed for ensuing research. According to the critical review of this article, the following points could be studied in the future: (1) All the experimental campaigns have been developed undergoing the idealisation that evacuation happens with just one single person climbing the stairs at a time, but as concluded by several authors, during emergency events, underground spaces could be crowded and several people will try to evacuate simultaneously (Jiang etal. 2014; Avci and Ozbulut 2018; Okamoto etal. 2022). A deep understanding of how this humanfluid interaction can alter safety conditions established in the aforementioned criteria is of relevance. This part could be handled with experimental and numerical campaigns that include two or more people on the stairs at the same time. Fig. 27 Representation of hazard limits in plane/mild-slope areas (left) and stairs (right) Natural Hazards (2) Characterisation of instability zones is crucial to verify hazardous conditions implementing hazard points and contrasting them against the recommended safety criteria. To do so, future experimental campaigns must provide this information. (3) Evaluate flood-related hazard when humans transit stairs not only in underground spaces. Cities with hilly areas usually have stairs that can also face flood events. For instance, this is the case of the stepped street stairs in Istanbul, Turkey studied by Halat etal. (2021). Hazard assessment based on previously mentioned criteria could be implemented in such stairs. Maybe some criterion could be generalized for stairs not just located in underground spaces but also in open areas and the entire urban cluster. (4) The study carried out by Kim etal. (2018) mentioned that under flooding conditions in which the flow is affected only by atmospheric pressure, flood-related hazard during the evacuation of stairs could be defined using just water depth because each one has a limited velocity in the stairs, step by step. Further analysis is required to determine how it is related to the stair’s characteristics like shape and slope. This is worth studying in further research either by experimental studies, by numerical models or even by combined campaigns. (5) The possibility that evacuees have to face objects transported by the flux while climbing the stairs and how this could affect their safety or stability have not been studied. The only available information is the experimental campaign performed by Ribeiro etal. (2021) which presented a methodology to analyse 5 prismatic solids in a flow over scaled stairs assessing instability through semi-empirical dimensionless formulas. As a particularity, to capture part of the flow a draining grid was added to represent the “draining staircases”, this allows the simultaneous use of the stairs as water drainage and human locomotion (Mangieri 2014). Two related possible research lines could surge: one to evaluate the possibilities offered with the implementation of draining stairs in underground spaces to reduce the flux in stairs and the evaluation of the feasible interaction between human beings and floating objects during the evacuation of underground spaces. (6) Although the importance of effective communication has been mentioned because it highly contributes to reducing social vulnerability (Maranzoni etal. 2022), the development of some guidance for raising public awareness and consequently improving the adaptive capacity of subjects to face critical events such as underground flooding is still needed. The creation of clearly understandable hazard maps and evacuation procedures including signalization that could be easily interpreted by end-users (most of them non-experts) should be promoted and be as simple as possible because it could be a powerful tool that positively influences urban resilience and general awareness. (7) It has been seen that the calculation of the required time to evacuate underground flooded spaces could be complex. An estimation of the average speed of people during the evacuation of flooded stairs under different water depths could be a useful tool to help simplify the complexity of this calculation. The assumption that the required time can be seen as a sum of different intervals could be summarized as (i) recognition and decision-making interval, (ii) evacuation of plane areas, and (iii) evacuation of stairs. Having defined the first interval, the distance of the farthest plane area, and the total distance of unavoidable stairs to be evacuated. In the case of the second and third intervals, multiplying them by the human average speed (related to a specific water depth) in each scenario could help to give an overall evacuation time that simplifies calculations. This could give policymakers, stakeholders, and rescue services cuttingedge knowledge about evacuation time for an appropriate response. Natural Hazards 3.3 Conclusion Due to the growing interest in researching this field mainly because of the appearance of more recurrent catastrophic events that affect underground areas. This review could be of great interest to fill some knowledge gaps that need to be addressed to improve resilience in urban areas and consequently human safety. Specifically, in Europe, no related studies were found focusing on the safety evacuation of underground flooded stairs. With the occurrence of urban floods that are recurrently affecting metro stations in European cities, this knowledge and its dissemination are of great relevance for the present and future. It will help to guarantee a proper adaptation of the underground infrastructure that in turn will help to face flood scenarios amidst climate change context in a more resilient manner. The goal of this review is to provide a consulting reference to anyone interested. The main studies aiming to evaluate flood-related hazard during the human evacuation of stairs and define safety criteria are presented based on their approaches. Also, the subsequent studies that complement or help to detail the previous main research on this phenomenon and how it affects people have been considered. The discussion session offers an overview of the limitations of these studies, comparisons with hazard limits in other urban areas and future research lines to be considered. This aims to continue spreading the available information and research. Thus, it is expected that new contributions in the study of flood-related hazard during underground evacuation through stairs might be encouraged, providing valuable information that could be simply transmitted to stakeholders and non-experts. As it was detailed, although underground stairs are encompassed in the urban cluster their hazard limits based on water depth and velocity differ from those presented for plane and mild slope areas, this differentiation needs to be researched in detail. Besides, among the future research lines, some require urgent attention. For instance, it is paramount to develop research based on the assumption that during emergency events, several people will try to evacuate underground stairs simultaneously and identify the incidence of the human-fluid interaction on safe evacuation. Also, it is urgent to identify the instability zones along the stairs to know where are the major complications during an evacuation emergency. This could help to detail future emergency evacuation plans. Author’s contribution Conceptualization: CHAU, BR, JTÁ, and EM-G; Literature search: CHAU; data Analysis: CHAU; Investigation: CHAU; Methodology: CHAU, BR, JTA, and EM-G; Supervision: BR, JTÁ, and EM-G Visualization: CHAU; Writing—original draft: CHAU; Writing—review & editing: CHAU, BR, JTÁ, and EM-G. Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was supported by the Spanish national research project PID2019-110965RB-I00 “Analysis of flood hazard considering vehicles and other floating elements”. Declarations Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this review. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article Natural Hazards are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. References Aparicio Uribe CH, Bonilla Brenes R, Hack J (2022) Potential of retrofitted urban green infrastructure to reduce runoff - a model implementation with site-specific constraints at neighborhood scale. Urban for Urban Green. https:// doi. org/ 10. 1016/j. ufug. 2022. 127499 Avci O, Ozbulut O (2018) Threat and vulnerability risk assessment for existing subway stations: a simplified approach. Case Stud Transp Policy 6(4):663–673. https:// doi. org/ 10. 1016/j. cstp. 2018. 08. 005 Baba Y, Ishigaki T, Toda K (2017) Experimental studies on safety evacuation from underground spaces under inundated situations. J Jpn Soc Civil Eng 5(1):269–278. https:// doi. org/ 10. 2208/ journ alofj sce.5. 1_ 269 BBC News (2021a) China floods: 12 dead in Zhengzhou train and thousands evacuated in Henan. https:// www. bbc. com/ news/ worldasiachina57861 067 BBC News (2021b) Storm Ida: Floodwater pours into New York City subway station. https:// www. bbc. com/ news/ av/ worlduscanada58418 627 Bernardini G, Quagliarini E, D’Orazio M, Brocchini M (2020) Towards the simulation of flood evacuation in urban scenarios: experiments to estimate human motion speed in floodwaters. Safety Sci. https:// doi. org/ 10. 1016/j. ssci. 2019. 104563 BUEDRI (Beijing Urban Engineering Design & Research Institute Co., Ltd.) (2005) Code for design of metro (In Chinese) CCIDUS (Committee of Countermeasures against Inundation Disasters in Underground Spaces). (2002). Guideline for Measures against Inundation of Underground Spaces. Ministry of Land, Infrastructure, Transport and Tourism (MLIT), Japan (in Japanese) Chanson H (1993) Stepped spillway flows and air entrainment. J Civ Eng 20(3):422–435 Chanson H (2001) Characteristics of skimming flow over stepped spillways. J Hydraul Eng-Asce 126(11):860–873. https:// doi. org/ 10. 1061/ (ASCE) 07339429(2000) 126: 11(860) Cox RJ, Shand TD, Blacka MJ (2010) Australian Rainfall and Runoff Revision Project 10: Appropriate Safety Criteria for People, Stage 1 report P10/S1/006, prepared by the Water Research Laboratory, University of New South Wales, Sydney Cox RJ, Yee M, Ball J (2004) Safety of People in Flooded Streets and Floodways. In: 8th National Conference on Hydraulics in Water Engineering, Gold Coast. The Institution of Engineers, Australia CRED-UNDRR (2020) The human cost of disasters: An overview of the last 20 years (2000–2019). Centre for Research on the Epidemiology of Disasters - UN Office for Disaster Risk Reduction. https:// www. undrr. org/ media/ 48008/ downl oad? start Downl oad= true Dias C, Rahman NA, Zaiter A (2021) Evacuation under flooded conditions: experimental investigation of the influence of water depth on walking behaviors. Int J Disaster Risk Reduct. https:// doi. org/ 10. 1016/j. ijdrr. 2021. 102192 El Mundo (2022a) Las peores lluvias en 80 años en Corea del Sur dejan al menos 8 muertos. https:// www. elmun do. es/ inter nacio nal/ 2022/ 08/ 09/ 62f22 ca2fd ddffb 92d8b 45ba. html El Mundo (2022b) París, colapsada por las fuertes lluvias y el viento. https:// www. elmun do. es/ inter nacio nal/ 2022/ 08/ 17/ 62fc9 08fe4 d4d84 8498b 45a3. html Flow Science, Inc., Santa Fe, NM, USA.FLOW-3D®Version 2023R1 (2023) Forero Ortiz E, Martínez Gomariz E (2020) Hazards threatening underground transport systems. Nat Hazards. https:// doi. org/ 10. 1007/ s1106902003860-w Forero-Ortiz E, Martínez-Gomariz E, Cañas Porcuna M (2020a) A review of flood impact assessment approaches for underground infrastructures in urban areas: a focus on transport systems. Hydrol Sci J 65(11):1943–1955. https:// doi. org/ 10. 1080/ 02626 667. 2020. 17844 24 Forero Ortiz E, Martínez Gomariz E, Porcuna MC, Locatelli L, Russo B (2020b) Flood risk assessment in an underground railway system under the impact of climate change-A case study of the Barcelona Metro. Sustainability (Switzerland). https:// doi. org/ 10. 3390/ su121 35291 Foster DN, Cox RJ (1973) Stability of Children on Roads Used as Floodways. Technical Report No.73/13, Water Research Laboratory of the University of New South Wales, Manly Vale, Australia Natural Hazards Goméz M (2008) Curso de hidrología Urbana (7ª Edición). Univeritat Politècnica de Catalunya, Barcelona, Flumen Research Institute Gotoh H, Ikari H, Sakai T, Tanioka H (2006) Computation mechanics of a force on a human leg in flow over an underground staircase in urban flood. Proc Hydraul Eng 50:865–870. https:// doi. org/ 10. 2208/ prohe. 50. 865 Goyal T, Kahali D, Rastogi R (2020) Analysis of pedestrian movements on stairs at metro stations. Transp Res Proc 48:3786–3801. https:// doi. org/ 10. 1016/j. trpro. 2020. 08. 040 Halat OM, Ciritci İ, Yucel G (2021) Modelling of urban flooding and waterfall effect on stepped streets in Istanbul, Turkey. Eskişehir Techn Univ J Sci Technol A Appl Sci Eng 22(2):148–159. https:// doi. org/ 10. 18038/ estub tda. 811503 Heidari S, Babor T, De Castro P, Tort S, Curno M (2016) Sex and gender equity in research: rationale for the SAGER guidelines and recommended use. Res Integrity Peer Rev. https:// doi. org/ 10. 1186/ s410730160007-6 Hou J, Chen G, Zhang Y, Li B, Yang S, Tong Y, Zhang D, Fu D (2022) A simulation study on risks of pedestrian evacuation from flooded staircases of different slopes in the underground space. Nat Hazards 110(1):519–543. https:// doi. org/ 10. 1007/ s1106902104956-7 Iagua Magazine (2021) Metro e inundaciones, una peligrosa combinación. https:// www. iagua. es/ notic ias/ locken/ metro-einund acion espelig rosacombi nacion ICC (International Code Council) (2011) International Building Code (IBC). (distributed by Cengage Learning) Ishigaki T, Toda K, Inoue K (2003) Hydraulic model tests of inundation in urban area with underground space. Proceedings of the IAHR world Congress, Thessaloniki, Greece, 30:487–493 Ishigaki T, Nakagawa H, Baba Y (2004) Hydraulic model tests and calculation of flood in urban area with underground space. In: 4th Congress of APD-IAHR, Hong Kong, 2:1411–1416 Ishigaki T, Baba Y, Toda K, Inoue K (2005) Experimental study on evacuation from underground space in urban flood. 31st IAHR Congress, pp 1116–1123 Ishigaki T, Toda K, Baba Y, Inoue K, Nakagawa H (2006) Experimental study on evacuation from underground space by using real size models. Proc Hydraul Eng 50:583–588. https:// doi. org/ 10. 2208/ prohe. 50. 583 Ishigaki T, Onishi Y, Asai Y, Toda K, Shimada H (2008a) Evacuation criteria during urban flooding in underground space. In: Proceedings of the 11th International Conference on Urban Drainage Modelling, 7. Scotland, UK Ishigaki T, Onishi Y, Baba Y, Toda K (2008b) Criterion and its application for safety evacuation during underground flooding. Proc Hydraul Eng 52:841–846. https:// doi. org/ 10. 2208/ prohe. 52. 841 Ishigaki T, Kawanaka R, Onishi Y, Shimada H, Toda K, Baba Y (2009) Assessment of safety on evacuating route during underground flooding. advances in water resources and hydraulic engineering. In: Proceedings of 16th IAHR-APD Congress and 3rd Symposium of IAHR-ISHS, pp 141–146. https:// doi. org/ 10. 1007/ 978-354089465-0_ 27 Ishigaki T, Asai Y, Nakahata Y, Shimada H, Baba Y, Toda K (2010) Evacuation of aged persons from inundated underground space. Water Sci Technol. https:// doi. org/ 10. 2166/ wst. 2010. 455 Ishigaki T, Kawanaka R, Ozaki T, Toda K (2016) Vulnerability to underground inundation and evacuation in densely urbanized area. J Disaster Res 11(2):298–305. https:// doi. org/ 10. 20965/ jdr. 2016. p0298 Jiang LJ, Shao WY, Zhu DZ, Sun ZL (2014) Forces on surface-piercing vertical circular cylinder groups on flooding staircase. J Fluids Struct 46:17–28. https:// doi. org/ 10. 1016/j. jflui dstru cts. 2013. 12. 011 Jonkman SN, Penning-Rowsell E (2008) Human instability in flood flows. J Am Water Resour Assoc 44(5):1208–1218. https:// doi. org/ 10. 1111/j. 17521688. 2008. 00217.x Joo J, Kim T-H (2015) An experimental study on evacuation ability during underground space inundation. J Korean Soc Hazard Mitig 15(2):189–196. https:// doi. org/ 10. 9798/ kosham. 2015. 15.2. 189 Karvonen T, Hepojoki A, Kotola J, Hunta H-K (2000) The use of physical models in dam-break flood analysis: rescue actions based on dam-break flood analysis; Final Report of Helsinki University of Technology; Helsinki University of Technology: Helsinki, Finland Kim M, Lee DH, Kim JS, Eom JH (2018) A study on evacuation safety at inundated stairs by using realscale hydraulic model experiment. E3S Web of Conferences. https:// doi. org/ 10. 1051/ e3sco nf/ 20184 006016 Kramer M, Chanson H (2018) Transition flow regime on stepped spillways: air-water flow characteristics and step-cavity fluctuations. Environ J Fluid Mech 18(4):947–965 Kvočka D, Falconer RA, Bray M (2016) Flood hazard assessment for extreme flood events. Nat Hazards 84(3):1569–1599. https:// doi. org/ 10. 1007/ s110690162501-z Natural Hazards Leandro J, Bung DB, Carvalho R (2014) Measuring void fraction and velocity fields of a stepped spillway for skimming flow using non-intrusive methods. Exp Fluids 55(5):1732. https:// doi. org/ 10. 1007/ s003480141732-6 Lee DH, Kim M, Rhee DS (2016) Evacuation safety evaluation of inundated stairs using 3D numerical simulation. Int J Smart Home 10(3):149–158. https:// doi. org/ 10. 14257/ ijsh. 2016. 10.3. 15 Lee HK, Hong WH, Lee YH (2019) Experimental study on the influence of water depth on the evacuation speed of elderly people in flood conditions. Int J Disaster Risk Reduct. https:// doi. org/ 10. 1016/j. ijdrr. 2019. 101198 Li Q, Xia J, Xie Z, Zhou M, Deng S (2022) Hazard and vulnerability in urban inundated underground space: Hydrodynamic analysis of human instability for stairway evacuation. Int J Disaster Risk Reduct. https:// doi. org/ 10. 1016/j. ijdrr. 2021. 102754 Liang C, Guo K, Guan M (2023) Influence of staircase design on flood characteristics in underground spaces. Tunnell Undergr Space Technol. https:// doi. org/ 10. 1016/j. tust. 2023. 105511 Lin Z, Hu S, Zhou T, Zhong Y, Zhu Y, Shi L, Lin H (2022) Numerical simulation of flood intrusion process under malfunction of flood retaining facilities in complex subway stations. Buildings 12(6):853. https:// doi. org/ 10. 3390/ build ings1 20608 53 Lind N, Hartford D, Assaf H (2004) hydrodynamic models of human stability in a flood. J Am Water Resour Assoc 40(1):89–96. https:// doi. org/ 10. 1111/j. 17521688. 2004. tb010 12.x Love RJ, Abt SR, Wittler RJ, Taylor A (1989) Human stability in a high flood hazard zone. AWRA Water Resour Bull 25(4):881–890. https:// doi. org/ 10. 1111/j. 17521688. 1989. tb054 04.x Lyu HM, Sun WJ, Shen SL, Arulrajah A (2018) Flood risk assessment in metro systems of mega-cities using a GIS-based modeling approach. Sci Total Environ 626:1012–1025. https:// doi. org/ 10. 1016/j. scito tenv. 2018. 01. 138 Mangieri LSG (2014) Avaliação dos sistemas de escadarias e rampas drenantes implantadas em assentamentos espontâneos na cidade do Salvador - Bahia. Revista Eletrônica De Gestão E Tecnologias Ambientais. https:// doi. org/ 10. 9771/ gesta. v2i1. 11977 Maranzoni A, D’Oria M, Rizzo C (2022) Quantitative flood hazard assessment methods: a review. J Flood Risk Manag. https:// doi. org/ 10. 1111/ jfr3. 12855 Martínez-Gomariz E, Gómez M, Russo B (2016) Experimental study of the stability of pedestrians exposed to urban pluvial flooding. Nat Hazards 82(2):1259–1278. https:// doi. org/ 10. 1007/ s110690162242-z Martínez-Gomariz E, Locatelli L, Guerrero M, Russo B, Martínez M (2019) Socio-economic potential impacts due to urban pluvial floods in Badalona (Spain) in a context of climate change. Water (Switzerland) 11(12):2658. https:// doi. org/ 10. 3390/ W1112 2658 Matsuo K, Natainia L, Yamada F (2011) Flood and evacuation simulations for urban flooding related papers flood and evacuation simulations for urban flooding, pp 391–398 MOHURD (Ministry of Housing and Urban-rural Development of the People’s republic of China) (2013) Code for design of civil buildings. Chinese Architecture and Building Press (in Chinese) Monjo R, Locatelli L, Milligan J, Torres L, Velasco M, Gaitán E, Pórtoles J, Redolat D, Russo B, Ribalaygua J (2023) Estimation of future extreme rainfall in Barcelona (Spain) under monofractal hypothesis. Int J Climatol 43(9):4047–4068. https:// doi. org/ 10. 1002/ joc. 8072 Musolino G, Ahmadian R, Falconer RA (2020) Comparison of flood hazard assessment criteria for pedestrians with a refined mechanics-based method. J Hydrol X. https:// doi. org/ 10. 1016/j. hydroa. 2020. 100067 Nakasaka Y, Ishigaki T (2021) Vulnerability to mega underground inundation and evacuation assuming devastating urban flood. J Disaster Res 16(3):321–328. https:// doi. org/ 10. 20965/ jdr. 2021. p0321 Nakasaka Y, Ishigaki T, Kawanaka R (2020) A study on safe evacuation from inundated underground mall by a multi-agent model. 22nd Congress of the International Association for Hydro-Environment Engineering and Research-Asia Pacific Division, IAHR-APD 2020: Creating Resilience to Water-Related Challenges. Sapporo, Japan https:// www. iahr. org/ libra ry/ infor? pid= 7627 Nanía LS (1999) Metodología numérico experimental para el análisis del riesgo asociado a la escorrentía pluvial en una red de calles. Technical University of Catalonia, Barcelona, Spain, PhD tesis Okamoto T, Watanabe C, Oka S (2022) Experiment study on falling down risk during evacuation in underground flood. J Jpn Soc Civ Eng Ser. F2 (Underground Space Research), 78(1):1–8. https:// doi. org/ 10. 2208/ jscej usr. 78.1_1 Onishi Y, Ishigaki T, Baba Y, Toda K (2007) Difficulty of evacuation during underground inundation and opinions of users on urban flood. Proc Hydraul Eng 51:559–564. https:// doi. org/ 10. 2208/ prohe. 51. 559 Qu Y, Gao Z, Xiao Y, Li X (2014) Modeling the pedestrian’s movement and simulating evacuation dynamics on stairs. Saf Sci 70:189–201. https:// doi. org/ 10. 1016/j. ssci. 2014. 05. 016 Ribeiro HDB, Simões ALA, Kelly LDD, Mangieri LSG, Schulz HE, Schulz HE (2021) Stability of solids in stepped flume nappe flows: subsidies for human stability in flows. J Appl Fluid Mech 14(3):681–690. https:// doi. org/ 10. 47176/ jafm. 14. 03. 31815 Natural Hazards Russo B (2009) Design of surface drainage systems according to hazard criteria related to flooding of urban areas. [Doctoral thesis, Technical University of Catalunya]. https:// dialn et. uniri oja. es/ servl et/ tesis? codigo= 258828 Russo B, Gómez M, Macchione F (2013) Pedestrian hazard criteria for flooded urban areas. Nat Hazards 69(1):251–265. https:// doi. org/ 10. 1007/ s110690130702-2 Russo B, Velasco M, Locatelli L, Sunyer D, Yubero D, Monjo R, Martínez-Gomariz E, Forero-Ortiz E, Sánchez-Muñoz D, Evans B, Gómez AG (2020a) Assessment of urban flood resilience in Barcelona for current and future scenarios. The RESCCUE Project. Sustainability (Switzerland) 12(14):5638. https:// doi. org/ 10. 3390/ su121 45638 Russo B, Velasco M, Monjo R, Martínez-Gomariz E, Sánchez D, Domínguez JL, Gabàs A, Gonzalez A (2020b) Evaluación de la resiliencia de los servicios urbanos frente a episodios de inundación en Barcelona. El Proyecto RESCCUE. Ingeniería Del Agua 24(2):101. https:// doi. org/ 10. 4995/ ia. 2020. 12179 Shao WY (2010) Critical rainfall intensity for safe evacuation from underground spaces with flood prevention measures. J Zhejiang Univ, Sci, A 11(9):668–676. https:// doi. org/ 10. 1631/ jzus. A1000 137 Shand TD, Cox RJ, Smith G, Blacka M (2010) Appropriate criteria for the safety and stability of people in stormwater design. Proceedings Stormwater 2010. National Conference of the Stormwater Industry Association, pp 1–12 Shao WY, Jiang LJ, Zhang YP, Zhu DZ, Sun ZL (2014) Hydraulic features of air-water mixture flow on staircase with rest platforms. J Hydraul Eng 140(6):04014016. https:// doi. org/ 10. 1061/ (ASCE) HY. 19437900. 00008 72 Shao WY, Jiang LJ, Fang L, Zhu DZ, Sun ZL (2015) Assessment of the safe evacuation of people walking through flooding staircases based on numerical simulation. J Zhejiang Univ, Sci, A 16(2):117–130. https:// doi. org/ 10. 1631/ jzus. A1400 154 Shirvani M, Kesserwani G, Richmond P (2020) Agent-based modelling of pedestrian responses during flood emergency: mobility behavioural rules and implications for flood risk analysis. J Hydroinf 22(5):1078– 1092. https:// doi. org/ 10. 2166/ hydro. 2020. 031 Takahashi S, Endoh K, Muro ZI (1992) Experimental study on people’s safety against overtopping waves on breakwaters Takedomi K, Tachi K, Mizukusa K, Yoshitani J (2001) An experimental study on the danger to walkers caused by inundation flow over stairs into underground space. Proceedings 56th Annual Conference on JSCE (in Japanese), Part 2, 244–245 Tellez Alvarez J, Gomez M, Russo B (2022) Numerical simulation of the hydraulic behavior of stepped stairs in a metro station. Advance in Hydroinformatics. Springer Water. Singapore, pp 1001–1009. https:// doi. org/ 10. 1007/ 978981191600-7_ 62 Témez JR (1992) Control del desarrollo urbano en las zonas inundables. Monogr. de Col. Ing. Caminos, Canales y Puertos Nº 10. Madrid, Spain, pp 105–115 Toda K (2007) Urban flooding and measures. J Disaster Res 2(3):143–152. https:// doi. org/ 10. 20965/ jdr. 2007. p0143 Toda K, Inoue K, Oyagi R, Nakai T, Takemura N (2004) Hydraulic model test of inundation water intrusion into complicated underground space (Japanese). Proceedings 4th Congress of APD-IAHR, pp 1403–1409 Torres V, Olaizola B (2023) La lluvia provoca cortes en el Metro de Madrid, la M-30 y la M-40 y 337 salidas de los bomberos: “No podemos vivir ahí.” El Mundo. https:// elpais. com/ espana/ madrid/ 20230915/ cortesendoslineasdemetro-yenla-m30-acausadelalluvia. html# UnitedNations D. of E. and S. A. P. D (2018) The World’s Cities in 2018. Data booklet (ST/ESA/ SER.A/417). https:// www. un. org/ en/ devel opment/ desa/ popul ation/ publi catio ns/ pdf/ urban izati on/ the_ worlds_ cities_ in_ 2018_ data_ bookl et. pdf ISBN / ISSN 9789211483062 Wu Q, Yao Y, Zhao Y, Zhang X, Xu H, Du Y, Du Z (2021) Numerical assessment of the water-flow hazard to workers in the water disaster of underground mine. J Hydroinf 23(6):1325–1342. https:// doi. org/ 10. 2166/ HYDRO. 2021. 044 Xia J, Falconer RA, Xiao X, Wang Y (2014) New criterion for the stability of a human body in floodwaters. J Hydraul Res 52(1):93–104. https:// doi. org/ 10. 1080/ 00221 686. 2013. 875073 Yee M (2003) Human stability in floodways. Undergraduate honours thesis, University of New South Wales, Australia Yoneyama N, Toda K, Aihata S, Yamamoto D (2009) Numerical analysis for evacuation possibility from small underground space in urban flood. In: Advances in Water Resources and Hydraulic Engineering - Proceedings of 16th IAHR-APD Congress and 3rd Symposium of IAHR-ISHS, pp 107–112. https:// doi. org/ 10. 1007/ 978-354089465-0_ 21 Yu H, Liang C, Li P, Niu K, Du F, Shao J, Liu Y (2019) Evaluation of waterlogging risk in an urban subway station. Adv Civ Eng. https:// doi. org/ 10. 1155/ 2019/ 53931 71 Natural Hazards Zheng Y, Li XG, Jia B, Jiang R (2019) Simulation of pedestrians’ evacuation dynamics with underground flood spreading based on cellular automaton. Simul Model Pract Theory 94:149–161. https:// doi. org/ 10. 1016/j. simpat. 2019. 03. 001 Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.