Thresholds of human body stability in water flows: advances, challenges, and guidelines for flood risk management

Limiares de estabilidade do corpo humano em fluxos de água: avanços, desafios e diretrizes para o gerenciamento de risco de inundação

ABSTRACT

The occurrence of floods causes hundreds of drowning deaths annually. Therefore, it is necessary to develop measures and risk management policies related to flood disasters. One approach is the definition of stability thresholds for individuals in water flows, as safety is compromised when people are exposed to flows that surpass their ability to stand or cross. Based on these considerations, the objective of the study was to conduct a literature review of experimental, empirical, and theoretical studies on this topic, evaluating stability thresholds for individuals exposed to water flow. In total, 34 studies conducted until the year 2023 were identified. Key factors influencing stability include water flow characteristics and the physical attributes of individuals. In addition to these factors, adverse conditions such as uneven terrain, poor lighting, and psychological factors were also considered important. However, it was noted that few studies have assessed such adverse conditions, and there is a gap in the experimental analysis of these variables. Therefore, this study emphasizes the importance of conducting more physical experiments to address these gaps, obtain a more comprehensive database, and improve precision in numerical and experimental models, ultimately supporting tools for flood risk management.

Keywords:  Hazard index; Floods; Stability thresholds; Adverse conditions

RESUMO

A ocorrência de inundações causa centenas de mortes por afogamento anualmente, o que destaca a necessidade de desenvolver políticas de gestão de riscos relacionadas a esses eventos. Uma possível abordagem é por meio da definição dos limiares de estabilidade de pessoas quando expostas fluxos de água, visto que sua segurança é comprometida quando a força do fluxo excede sua capacidade de se manter de pé. Sendo assim, o objetivo desse estudo foi realizar uma revisão bibliográfica dos estudos experimentais, empíricos e teóricos realizados sobre o tema. No total, foram identificados 34 estudos realizados até o ano de 2023. Foi identificado que os principais fatores que influenciam a estabilidade das pessoas incluem as características do fluxo de água e os atributos físicos dos indivíduos. Condições adversas, como irregularidades no terreno, baixa iluminação e fatores psicológicos, também foram apontadas como relevantes. Entretanto, poucos estudos analisaram essas condições adversas, revelando uma lacuna na análise experimental dessas variáveis. Portanto, este estudo enfatiza a importância de realizar mais experimentos físicos para preencher essas lacunas, obter uma base de dados mais abrangente e melhorar a precisão em modelos numéricos e experimentais, a fim de aprimorar as ferramentas disponíveis para a gestão de riscos de inundações.

Palavras-chave:  Índice de perigo; Inundações; Limiares de estabilidade; Condições adversas

INTRODUCTION

Floods and flash floods are violent water flows and are the natural hazards that most affect the global population, more than any other natural and technological hazards (Chanson et al., 2014; Xia et al., 2016; Arrighi et al., 2017). The occurrence of these events has the potential to cause significant damage, especially when houses, vehicles, and/or people are directly exposed to water flow. These obstacles and individuals then become susceptible to being damaged (or injured), pushed, and/or carried away by the force of the flow, potentially causing human death (Smith, 2015).

Specifically, regarding the exposure of individuals to water flows, it can be stated that the occurrence of floods causes hundreds of drowning deaths annually in the world (Parkinson et al., 2010). According to CNN (2023), the year 2023 witnessed significant flood events, with at least 10 countries experiencing severe floods in just one month (September), affecting thousands of people in America, Africa, Europe and Asia. Among all these events, the most severe occurred in Libya, where floods caused at least 11,000 deaths and left thousands of people missing. Greece, Turkey and Bulgaria were also affected by storms that caused severe flooding, impacting many people (CNN, 2023). In Brazil, it is not different. The Public Security Department of Rio Grande do Sul (Secretaria da Segurança Pública do Rio Grande do Sul, 2023) mentions that the occurrence of intense rains in the southern part of the country caused floods in several cities, resulting in at least 48 drowning deaths, 10 missing people, and affecting approximately 360,000 people.

Kreibich et al. (2022) analyzed a global dataset of 45 flood and drought events on different continents and concluded that although risk management reduces the vulnerability, the impacts of these events continue to increase due to the high-magnitude and unprecedented events strongly, making it challenge to carry out effective management. In this scenario, it is important to develop people preparedness behaviour, which are also related to a person self-save abilities, and for this reason, people must to be aware of the phenomenon characteristics and how to to be prepared and act in the disaster situation (Hamilton et al., 2020). Specifically concerning Brazil, CNM (2023) shows that deaths due to intense rainfall and, consequently, floods have been increasing in recent years.

Thus, to reduce flood disaster impacts and to support the government and other institutions in decision-making and flood risk management, there is a need to develop methods to estimate the hazard to which people are exposed in such situations (Wade et al., 2005). In terms of flood risk management, a quantitative method can be used to assess the stability of structures (Stephenson, 2002; Smith, 2015), vehicles (Bonham & Hattersley, 1967; Gordon & Stone, 1973; Keller & Mitsch, 1993; Shand et al., 2011), and the human body when exposed to water flow (Stephenson, 2002). This information could serve as a basis for the creation of risk maps (Xia et al., 2016), adoption of structural reinforcements, and other measures.

It can be stated that people's safety is compromised when exposed to water flows that exceed their ability to remain standing or traverse flow paths (Russo et al., 2013). In other words, dangerous situations can occur when a person loses stability. Several studies confirm that human stability in water flows is primarily influenced by the depth and velocity of the flow (Foster and Cox, 1973; Abt et al., 1989; Takahashi et al., 1992; Stephenson, 2002; Cox et al., 2010; Martínez-Gomariz et al., 2016).

In basic terms, human balance is associated with two main factors: the vertical projection of the body's center of mass (CoM) (Winter, 1995a) and the horizontal velocity of the CoM (Pai and Patton, 1997). However, other factors can also influence person's stability, such as the presence of debris and irregularities on the bed surface (Ramsbottom et al., 2006; Russo et al., 2013; Martínez-Gomariz et al., 2016), the turbidity of flowing water (Russo et al., 2013; Martínez-Gomariz et al., 2016; Zhu et al., 2023), the person's clothing, especially their footwear (Takahashi et al., 1992; Martínez-Gomariz et al., 2016), as well as psychological factors that cause each individual to react differently in an extreme event situation (Foster & Cox, 1973; Simões et al., 2016).

Consequently, in order to develop measures and risk management policies for floods, it is necessary to define stability thresholds for individuals exposed to water flows, so that the most appropriate decision can be made in managing the site for each situation. For this purpose, two types of analysis are generally developed: i) conducting physical experiments with real human bodies or mannequins and, consequently, establishing regression relationships; and ii) using empirical or theoretical formulas derived from an analysis based on classical mechanics (Defra and Environment Agency, 2006; Cox et al., 2010; Xia et al., 2014). Additionally, currently, various computational models (for example, the numerical model developed by Arrighi et al., (2017)) have also been used for this purpose.

Many of the empirical and theoretical studies conducted were based on the results of experimental studies, which aimed to determine stability thresholds or used the results of these studies for model calibration (e.g., Lind et al., (2004)). However, each of the experimental studies considered specific conditions regarding the hydraulic characteristics of the experiment and also in relation to the physical characteristics and abilities of the participants. The variations in experimental conditions led to significant differences in the perceived safety of stability thresholds among the experiments, which require an overview of several studies to establish a global understanding of people stability threshold in water flows. Therefore, the objective of this study was to present an overview of people stability loss mechanisms in water flows by analysis of several experimental and theoretical studies that evaluated stability thresholds of individuals when exposed to water flow in flood situations, by checking the conditions considered by each of them and compare their results.

METHODOLOGY

First, we present an overview of people stability loss mechanisms in water flows, showing stability threshold and its relationship with flood hazard index to explore and expand discussions on the subject. Then, we conducted a descriptive research based on literature review aiming to understanding the methods applied studies on human body stability in water flows. We performed searches on the Scopus, Google Scholar and Capes Journals databases. The keywords used for this research were “people stability in floodwaters”, “people stability in waterflows”, “threshold of stability for people in floods” and “studies of human stability in floods”. In the encountered studies, their references were also checked in order to look for more information about the theme of this research.

A total of 34 studies were retrieved, screened and categorized according to the following criteria: (a) country of the study; (b) type of study; (c) experiment location; (d) considered variables; (e) hydrodynamic mechanism; (f) number of tested individuals; (g) characteristics of individuals in relation to age, weight and height; (h) flow characteristics: depth and velocity; and (i) thresholds considered safe. Thus, we provide an overview of the physical experimental studies, highlighting how they were carried out, the thresholds used, their main differences and contributions. Additionally, we identified theoretical studies conducted on the topic to assess the methods employed in determining safety thresholds.

Mechanisms of stability loss and hazard index

When exposed to a water flow, a person may lose stability and be carried away by the force of the flow. This situation is common during urban floods (Russo et al., 2013) meanwhile it can also occur during recreational and leisure activities conducted near or in watercourses (Fagundes et al., 2020).

Among the main hydrodynamic mechanisms that can cause a person to lose stability against a water flow, sliding (or frictional instability) and toppling (or moment instability) can be mentioned (Jonkmann & Penning-Rowsell, 2008; Shand et al., 2011; Xia et al., 2014; Martínez-Gomariz et al., 2016). Sliding occurs when the drag force induced by the horizontal flow of fluid impacting the legs and torso of the individual is greater than the friction resistance between the foot and the ground surface (Shand et al., 2011; Martínez-Gomariz et al., 2016). Toppling occurs when the moment caused by the water flow in the individual exceeds the moment due to the resultant weight of the body (Jonkmann & Penning-Rowsell, 2008). Figure 1 illustrates the mechanisms of stability loss for individuals when exposed to water flow, while also depicting the forces acting upon them.

Figure 1
Representation of the mechanisms of person’s stability loss when exposed to water flows. Forces F, Fa, and Fb can be decomposed into their x and y components. H is the person’s height (m); Fm is the person’s weight (N); d is the water depth (m); v is the water velocity (m/s); θ is the terrain slope (m/m).

In addition to these two main hydrodynamic mechanisms of stability loss, some authors also consider the third mechanism: flotation. Since the density of the human body is similar to the water’s one, flotation can occur if the water depth exceeds a person's height. In this case, to assess whether a person will be carried away by the water flow, the same equations used to determine stability loss due to sliding or toppling are not applied (Jonkmann & Penning-Rowsell, 2008). Thus, this mechanism was not considered by most studies, which focused solely on stability loss due to sliding and toppling. Among all the studies encountered, only two theoretical studies developed by Milanesi et al. (2015) and Wang & Marsooli (2021) considered flotation in their analyses. In the study by Wang & Marsooli (2021), flotation was referred to drowning.

The analysis of the forces acting on an individual exposed to a water flow makes it possible to determine when a certain mechanism is predominant over another and what the critical condition is in terms of depth and velocity of the flow. In this sense, Xia et al. (2014) mentioned that the critical condition for sliding is when the drag force of the water flow equals the frictional force between the individual's foot and the ground surface, which occurs mainly at low depths and high velocities. In other words, sliding is more influenced by velocity than by the flow depth (Nanía, 1999), and the stability threshold is related to the product of depth versus velocity squared (Jonkmann & Penning-Rowsell, 2008):

$\text{SST}=\text{d}.\text{v}²$ (1)

where SST is the Sliding Stability Threshold (m³/s²); d is the water flow depth (m); and v is the average flow velocity (m/s).

On the other hand, toppling instability occurs when the moment generated by the drag force is equals or is greater than the moment resulting from the effective weight of the body (weight force minus buoyancy force or hydrostatic weight), which occurs mainly at larger depths and lower velocities (Xia et al., 2014). In other words, toppling is more influenced by the depth of the flow, and the stability threshold can be determined by the product of d versus v (Jonkmann & Penning-Rowsell, 2008):

$\text{TST}=\text{d}.\text{v}$ (2)

where TST is the Toppling Stability Threshold (m²/s).

Thus, this relationship of stability loss with d and v can be considered a way to quantify the hazard for a person to face when exposed to water flow. Stephenson (2002) named this relationship the Hazard Index (HI), which represents the hazards associated with water flows resulting from a flood event. According to this author, HI is expressed by Equation 2, where the larger the value of these variables, the greater the damage caused.

Although the term “Hazard Index” was proposed by Stephenson (2002), the quantification of hazard in terms of d and v had been previously considered by other studies such as Foster & Cox (1973), Abt et al. (1989), Takahashi et al. (1992), Keller & Mitsch (1993), and Karvonen et al. (2000). These authors quantified the hazard that water flows pose to people considering d and v, even though they did not give this term to this relationship between hazard and hydraulic flow characteristics. Furthermore, these studies considered other variables that influenced the people’s stability when attempting to quantify the hazard of water flow.

However, despite the HI being representable in a simplified form by Equation 2, there are some variations of this formula depending on what one wishes to analyze, whether it is structures, vehicles, and/or people. As mentioned above, when considering HI applied to people, other variables can be taken into account to assess their stability.

Bibliographic review of studies on human stability

Several studies were conducted until the year 2023 attempting to define a range of values in which the flow poses hazard or not to a person with certain physical characteristics. The experimental studies sought to establish limit conditions, in terms of d and v, in which an individual exposed to water flow loses stability. Each of these studies focused on a specific scenario, and therefore, in addition to d and v, the authors considered other variables that can influence the stability of individuals. Images depicting how the experiments were conducted can be found in the original manuscripts, for example: Abt et al. (1989), Takahashi et al. (1992), Jonkmann & Penning-Rowsell (2008), and Martínez-Gomariz et al. (2016).

Parallel to the development of experimental studies, empirical and theoretical studies were also carried out to define the stability limits of individuals exposed to water flows. In empirical and theoretical studies, stability thresholds were determined by evaluating the forces acting on a person when exposed to a water flow, resulting in an equation to define these thresholds. Most studies calibrated the coefficients of the equations using data obtained from previously conducted experimental studies. Therefore, the importance of conducting experimental studies is emphasized, because this allows equations to be calibrated and evaluated more faithfully.

Among the 34 studies, 25 main author were identified. Thus, a total of twenty three physical experimental studies and eleven empirical and theoretical studies were identified. It is noted that some of the experimental studies conducted a theoretical analysis concurrently. Table 1 demonstrates a chronological summary of the experimental and theoretical studies, highlighting the methodology used, the variables considered, and briefly outlining the safety thresholds obtained.

Table 1
Summary of the experimental and theoretical studies conducted so far.

Author	Year	Country	Type of study	Experiment location	Considered variables	Hydrodynamic mecanism	Nº of tested individuals	Characteristics of individuals			Flow characteristics		Thresholds considered safe
								Age (years)	Weight (kg)	Height (m)	Depth (m)	Velocity (m/s)
Foster & Cox (1973)	1973	Australia	Experimental	Flume	Age, height, weight, psychological factors, depth, velocity, type of clothing and friction factor between the child's feet and the road	Sliding	6	9 to 13	24.9 to 36.7	1.27 to 1.44	0.09 to 0.41	0.76 to 3.12	$v_{max}=1.5m/s$for
													$h<0.3m$
Abt et al. (1989)	1989	United States	Experimental	Flume	Age, height, weight, velocity, depth, type of footwear, type of surface, slope (0.8 and 2.6%)	Toppling	20 plus a monolith	19 to 54	40.9 to 91.4	1.52 to 1.83	0.49 to 1.2	0.36 to 3.05	$v*h<\frac{0.5m^2}{s}$ (for the monolith)
													$PN=e^{0.222\left(\frac{peso*altura}{1000}\right)+1.088}$ (for people)
Takahashi et al. (1992)	1992	Japan	Experimental and theoretical	Experimental basin	Depth, velocity, height, weight, different types of surface, clothing and footwear used	Sliding and toppling	3	NA	63 to 73	1.64 to 1.83	0.44 to 0.93	0.58 to 2.00	For a concrete surface covered in algae: i) 0.4 to 0.6 m2/s, in situations where people are facing or facing away from the flow; ii) 0.7 to 0.8 m2/s when people are standing sideways; and iii) 0.3 to 0.5 m2/s when people are sitting.
Keller e Mitsch (1993)	1993	Australia	Theoretical	NA	Depth, velocity, height, mass, drag and friction coefficients	Sliding and toppling	2	5 years and adult of unspecified age	HM ratio = 21 for the child and for the adult was not specified		NA	NA	$DV=0.12to0.55m^2/s$ (children)
													$DV=0.35to1.4m^2/s$ (adults)
Karvonen et al. (2000)	2000	Finland	Experimental	Basin	Depth, velocity, weight and height	Sliding and toppling	7	17 to 60	48 to 100	1.60 to 1.95	0.3 to 1.1	0.6 to 2.75	$v*h\le \mathrm{0,006}M+\mathrm{0,3}$ For good conditions
													$v*h\le \mathrm{0,004}M+\mathrm{0,2}$ For normal conditions
													$v*h\le \mathrm{0,002}M+\mathrm{0,1}$ For bad conditions
Yee (2003)	2003	Australia	Experimental and theoretical	Flume	Depth, velocity, height, weight and age	Sliding and toppling	4	6 to 8	19 to 25	1.09 to 1.25	0.18 to 0.53	0.89 to 2.12	HV thresholds between 0.51 and 0.55 m2/s
Lind et al. (2004)	2004	Canada	Theoretical	NA	Depth, velocity, weight and height	Toppling	NA	NA	NA	NA	NA	NA	$h{v}_{cr}=Kg$
													Where Kg is a calibrated constant based on experimental studies
Ramsbottom et al. (2004, 2006)	2004 e 2006	United Kingdom	Theoretical	NA	Depth, velocity, presence of debris and turbidity conditions	Toppling	NA	NA	NA	NA	NA	NA	$Hazardrating=d\left(v+\mathrm{1,5}\right)+DF$
													Safe level when Hazard rating < 0,75 m2/s
Ishigaki et al. (2005, 2008a, 2008b, 2010)	2005, 2008a, 2008b and 2009	South Korea	Experimental and theoretical	Flume	Depth, velocity and age	Toppling	49	Average of 25.8	NA	NA	0.1 to 0.4	0.5 to 1.125	$M_0=\frac{v^{2}D}{g}+\frac{D^2}{2}$
													$M_0<0.1$ safe evacuation for seniors, $M_0<0.125$ safe evacuation for men, $M_0<0.2$ threshold for the elderly, $M_0<0.25$ threshold for men
Jonkmann, S. N., & Penning-Rowsell (2008)	2008	United Kingdom	Experimental	In natura (modified river, with natural banks)	Depth, velocity and position in relation to the flow	Sliding and toppling	1	NA	68.25	1.70	0.5 to 1.2	0.5 to 3.0	$h*v<0.8m^2/s$
Russo (2009); Russo et al. (2010, 2013)	2009, 2010 and 2013	Spain	Experimental	Urban artificial channel	Height, weight, depth, velocity, slope (0, 2, 4, 6, 8 and 10%) and visibility conditions	Sliding	23	14 to 49	48 to 100	1.48 to 1.82	0.11 to 0.16	1.17 to 3.17	For depths between 0.09 and 0.16 m:
													Low hazard: $v<1.51$
													Moderate hazard: $1.51<v<1.88$
													High hazard: $v>1.88$
Xia et al. (2011, 2014, 2016)	2011, 2014 and 2016	China	Experimental and theoretical	Flume	Depth, velocity, position in relation to the flow and slope	Sliding and toppling	1 model human body	NA	0.334 kg (60 kg)	0.3 m (1.70 m)	Approximately 0.025 to 0.125 on scale (1:5.54)	Approximately 0.25 to 1.75	*Sliding
													$U_c=\alpha {\left(\frac{h_f}{h_p}\right)}^{\beta }\sqrt{\frac{m_p}{{\rho }_f{h}_p{h}_f}-\left(\frac{a_1{h}_f}{h_p}+b_1\right)\frac{\left(a_2{m}_{p+}{b}_2\right)}{h_p^2}}$
													*Toppling
													$U_c=\alpha {\left(\frac{h_f}{h_p}\right)}^{\beta }\sqrt{\frac{m_p}{{\rho }_f{h}_f^2}-\left(\frac{a_1}{h_p^2}+\frac{b_1}{h_f{h}_p}\right)\left(a_2{m}_{p+}{b}_2\right)}$
Milanesi et al. (2015, 2016)	2015 and 2016	Italy	Theoretical	NA	Depth, velocity, weight, height, slope, fluid density and coefficient of friction	Sliding, toppling and flotation	2	Children aged 7 and adults of unspecified age	Child weighing 22.4 kg and adult weighing 71 kg	Child 1.21 m and adult 1.71 m	0 a 1.40	0 a 4.0	**For high probability events
													$h_{high}\left(U,\tau \right)=\left\{\begin{array}{c}\begin{array}{l}\frac{h\left(U,T_{max}\right)-h\left(U,T_{min}\right)}{\frac{T_{max}-T_{min}}{2}}\left(\tau -T_{min}\right)+\\ h\left(U,T_{min}\right)if\tau \le T\end{array}\\ h\left(U,T_{max}\right)if\tau >T\end{array}\right.$
													**For low probability events
													$h_{low}\left(U,\tau \right)=\left\{\begin{array}{c}h\left(U,T_{min}\right)if\tau \le T\\ \begin{array}{l}\frac{h\left(U,T_{max}\right)-h\left(U,T_{min}\right)}{\frac{T_{max}-T_{min}}{2}}\left(\tau -T\right)+\\ h\left(U,T_{min}\right)if\tau >T\end{array}\end{array}\right.$
Martínez-Gomariz et al. (2016)	2016	Spain	Experimental	Urban artificial channel	Weight, height, velocity, depth, type of footwear, different visibility conditions, use of hands, inclination of the channel and position in relation to the flow	Sliding	26	6 to 55	37 to 71	1.32 to 1.73	NA	NA	$v*h<0.22m^2/s$
Simões et al. (2016)	2016	Brazil	Theoretical	NA	Factors related to the health and psychological characteristics of individuals, fluid density, dynamic viscosity, gravity, flow depth and velocity, surface roughness, slope, height and weight	Sliding	NA	NA	NA	NA	NA	NA	For information on the dimensionless parameters that affect human stability go to: https://www.scielo.br/j/rbrh/a/hzyHD5JyMwGbTTDsCDTvxJD/?format=html
Arrighi et al. (2017)	2017	Italy	Theoretical	NA	Depth, velocity, relative submersion, foot size	Sliding and toppling	NA	NA	NA	NA	NA	NA	For information on stability thresholds go to: https://hess.copernicus.org/articles/21/515/2017/
Chen et al. (2018)	2018	China	Theoretical	NA	Postural adjustment, different physical characteristics of people from different locations, depth, velocity, height and weight of the individual, drag and friction coefficient.	Toppling	NA	NA	NA	NA	NA	NA	***For tilting angles of 90º
													$U_c=\alpha {\left(\frac{h_f}{h_p}\right)}^{\beta }\sqrt{\frac{m_p}{{\rho }_f{h}_f^2}-\left(\frac{a_1}{h_p^2}+\frac{b_1}{h_f{h}_p}\right)\left(a_2{m}_{p+}{b}_2\right)}$
Lee et al. (2019)	2019	South Korea	Experimental	Swimming pool	Depth, age, cross walking or running	NA	32	27.2 and 23.92 average age for men and women	71.6 and 59.27 average weight of men and women	1.75 and 1.66 average height for men and women	0.1 to 0.5	0	Presence or absence of flooding
Bernardini et al. (2020)	2020	Italy	Experimental	Flume	Depth, weight, height, age, gender, cross walking or running	NA	203	5 to 68	21 to 120	1.15 to 1.98	0.2 to 0.7	0	-
Postacchini et al. (2021)	2021	Italy	Experimental	Flume	Depth, velocity and position in relation to the flow	Toppling	1 physical model	NA	19.57 (scale 80)	1.125 (scale 1.80)	0.16 to 1.20	0.4 to 3.0	****For backward toppling stability
													$BTIstabilityif\left\{\begin{array}{c}h\le 1.2mforv<0.37m/s\\ \begin{array}{l}h\le \left(1.63e^{-1.37v}+0.22\right)mforv=\\ \left(0.37+3.00\right)m/s\end{array}\end{array}\right.$
													****For forward toppling stability
													$FTIstabilityif\left\{\begin{array}{c}h\le 1.2mforv<0.45m/s\\ \begin{array}{l}h\le \left(1.43e^{-0.88v}+0.24\right)mforv=\\ \left(0.45÷3.00\right)m/s\end{array}\end{array}\right.$
Wang et al. (2021)	2021	United States	Theoretical	NA	Wind, slope, weight, height, depth, velocity, age	Sliding, toppling and flotation (drowning)	2	A child aged 7 and adults aged between 20 and 60	22.4 to 81.6	1.21 to 1.69	Not specified	Not specified	For drowing, $h>\left(13Y/16\right)$
													For sliding,
													$\sqrt{{\left(W_{\eta }+F_{h,\eta }+F_{a,x,\eta }\right)}^2+{\left(F_{a,y}\right)}^2}>\mu \left(W_{\xi }-B-F_{h,\xi }-F_{a,x,\xi }\right)$
													For toppling
													$F_{a,y}{z}_{F_{a,y}}+B_z{y}_{B_z}>W_{y_W}$
Ribeiro et al. (2021)	2021	Brazil	Experimental and theoretical	Rectangular stepped chute	Discharge, slope, weight, and height.	Sliding and toppling	5 (obstacles representing the human body)	-	0.1539 to 0.5491 (on scale)	0.09 to 0.17 (on scale)	Not specified	Not specified	For information on stability thresholds go to Equations 21 and 22 of the manuscript: https://www.jafmonline.net/article_1113.html
Lazzarin et al. (2022)	2022	Italy	Theoretical	NA	Depth, velocity, height, weight, density of body and water, drag, friction and lift coefficient, front width of body and average length of body in the direction of flow	Sliding	NA	NA	NA	NA	NA	NA	$RD\left(W\right)=\frac{1}{1+{\left(a/W\right)}^b}$
													Where: RD is the relative damage; W is a parameter that combines the depth and speed of the flow; a is a calibration parameter; b is the average length of the body in the direction of the flow
Wüthrich et al. (2023)	2023	Netherlands	Experimental	Wave overtopping simulator	Height, weight, gender, depth, velocity and slope	Sliding	8	25 to 33	62.6 to 101.0	1.61 to 1.83	Up to 0.30	3.1 to 7.2	$M=64.1kg$ up to $h{v}^2<4.13m^3/s^2$ and $M=101.0kg$ up to $h{v}^2<5.49m^3/s^2$
Zhu et al. (2023)	2023	China	Experimental	Flume	Depth, velocity, turbulence of floodwater, height, weight, sex, age, type of shoes, orientation of the human body, postural adjustment of the body, friction coefficient, existence of surrounding neighbours and architectures	Toppling	5 dummies	Not specified	26.3 to 70.3 kg (385 to 579g in scale)	1.19 to 1.69 m (23.8 to 34 cm in scale)	10.19 to 23.68 cm in scale	0.12 to 0.86	$\begin{array}{l}\overline{U}=\left(-0.22*lnk+0.2391\right)*\\ \left[\alpha {\left(\frac{H}{H_h}\right)}^{\beta }\sqrt{\begin{array}{l}\frac{m_h}{\rho H^2}-\\ \left(\frac{a_1}{H_h^2}+\frac{b_1}{H*H_h}\right)*\left(a_2{m}_h+b_2\right)\end{array}}\right]\end{array}$

• ^*
  Information on the values of each of the parameters used in these calculations can be found at: Xia et al. (2014).
• ^**
  More information can be found in Equations 23 and 24 and in the Figure 3d (Milanesi et al., 2015).
• ^***
  For more information on the variables: Chen et al. (2018).
• ^****
  For more information on the variables: Postacchini et al. (2021).
• NA = Not applicable.

DISCUSSIONS

Study locations

An analysis was conducted regarding the locations where the studies were carried out (Figure 2). It is noted that a few countries conducted studies of this kind, with a concentration in three countries (Italy, China, and Australia), representing approximately 41.17% of the total publications. Despite Australia is not the country with the most experimental and theoretical studies, it has many guidelines, research, and manuals developed based on the results of previously conducted studies, such as Agriculture and Resource Management Council of Australia and New Zealand (2000), Cox et al. (2010), Shand et al. (2011), Smith (2015), and so forth. Furthermore, Australia has conducted studies since the 1970s. On the other hand, though Italy has the highest number of publications, research related to human stability began just in 2015.

Figure 2
Number of experimental and theoretical studies conducted in each country.

Although there have been severe floods in African countries in recent years that have resulted in human loss, such as the floods that occurred in South Africa in early 2022 that left more than 400 dead and 40,000 affected (South Africa Government, 2022), and the floods in Nigeria in mid-2022 that left approximately 600 dead and more than 1.3 million homeless (Nigeria's National Emergency Management Agency, 2022), no experimental or theoretical study related to human stability in water flows in Africa has been identified.

It is worth noting that only studies attempting to define thresholds for human stability through experimental or theoretical analysis were considered. Those studies that used these thresholds for flood risk management, such as Loat & Petrascheck (1997), which provides recommendations for territorial zoning in France, were not included in this study.

Chronology

When evaluating the evolution of publications on studies related to human stability in water flows, it is observed that until the end of the 1990s, few studies had been published. From the 2000s onwards, more research and studies were conducted (Figure 3). The increase in the number of studies might result from the fact that recent increasing in the world population and in extreme hydrological events have been causing more frequently flood disasters. Since many people live in high-risk areas, it is necessary to quantify the hazard to which these individuals are exposed in order to carry out flood risk management.

Figure 3
Evolution of the publication of studies over the years.

Variables that influence human stability

In Table 1, there are many variables that can influence human stability during a flood event. It can be noted that most of all studies considered the influence of hydraulic conditions on the stability loss of individuals in terms of d and v (Figure 4). The only study that did not consider either the depth or the flow velocity was Ribeiro et al. (2021). In this case, the authors considered only the total flow circulated by the rectangular stepped chute utilized during the experimental protocol. In addition, Lee et al. (2019) and Bernardini et al. (2020) considered d but not v, because the authors sought to analyze the evacuation time of enclosed spaces during a flood. In total, the depth was considered in 33, and the v influence was assessed for 31 among 34 studies.

Figure 4
Number of studies that analyzed each of the variables.

Following d and v, other variables considered by most studies are the physical characteristics of exposed individuals in terms of mass and height. In this regard, the safety thresholds established by laboratory studies are highly dependent on the physical characteristics of the mannequin or individual, as well as the cognitive characteristics of the tested individuals. In all the experiments, it was observed that individuals of shorter stature and smaller mass tend to be moved more easily by the flow force. This is because less force is required to carry an object with lower mass. Additionally, the shorter stature of the person causes a larger proportion of their body to be submerged compared to a taller person, favoring buoyancy and, consequently, stability loss.

The person's age is also an important aspect to consider, because the older persons are more susceptible to injury due to the high prevalence of clinical diseases (Rubenstein, 2006). Lee et al. (2019) used geriatric simulators to assess the difference in mobility between young and old individuals in a flooding situation. They observed that, with increasing age, the mobility of each individual significantly decreases. They emphasized that the presence of flooding itself, even in cases where the flow has zero velocity, already hinders the evacuation of older individuals from flooded areas.

Among the variables considered as “Other” in Figure 4 there are: i) the relative submersion of the human body in the water, which influences buoyancy; ii) the size of the person's foot, which affects stability; iii) gravity; and iv) the relation of the person's origin (China, Europe, or America) with their physical characteristics such as height and mass. In addition to these variables, some studies also considered the density of the human body, the frontal width of the body exposed to the flow, the average length of the body in the direction of the flow, the turbulence of the water, the influence of the wind, and the presence of people and structures around each individual.

A crucial point is the fact that vulnerability classes to flood hazard are typically given in terms of d and v (Shand et al., 2011). Despite this, some of these expressions also take into account people's physical characteristics, but this dependency makes the expression difficult to apply to the population for planning or design purposes. Cox et al. (2010) stated that the use of human size characteristics (mass x height) as an independent variable in defining general flood flow safety guidelines is not considered practical, given the wide range of such characteristics within the population. Furthermore, it can be stated that few people know their own mass x height relation to compare with the safety thresholds that are used to manage flood events (Wright et al., 2010).

For educational purposes, Arrighi et al. (2017) suggests that recognizing a level of submersion of the human body (water level reaching the ankles, knees, or waist) may be more useful in maintaining people's safety than referring to absolute water depths or mass x height relationships. This type of understanding can be addressed for local population awareness. According to Kruel (1994), depth of submersion reduces the effect of body weight by 2.4% with water at ankle height, 12.1% at knee height, 46.6% at hip height, and 54.9% if the water reaches the level of the navel scar.

Stability thresholds

Regarding the stability thresholds, the values considered as safe varied significantly among the reviewed studies. Among the factors that influence this variation are the specific conditions considered by each experiment, as well as the different profiles of the tested individuals, mainly in terms of height, mass, age and specific abilities.

Additionally, Cox et al. (2010) stated that the definition of a stability or instability situation varied among the studies, which may influence the different threshold values for human stability obtained in various experiments. Some of them considered that individuals lost stability when they felt insecure and/or grabbed the sides of the experimental channel flume (e.g., Foster & Cox, 1973, and Yee, 2003), when individuals lost stability or maneuvering capability (Karvonen et al., 2000), or when individuals were literally carried away by the flow force (Abt et al., 1989).

Although the experimental studies in Table 1 focused mainly on similar parameters, including height, and mass of individuals, depth and velocity of the flow, the locations where the experiments were conducted and the flow regimes considered differed between the studies (Shand et al., 2011). For example, the results of Abt et al. (1989) showed substantially higher stability conditions than all other data for adults. One possible explanation is that the aim of the experiments was to determine the absolute limit of the subjects' stability until failure (until they fell) where the subjects failed rather than to determine whether their safety was compromised or whether the limits for a safe rescue action were extrapolated. The aim of Karvonen et al. (2000) was similar.

Wüthrich et al. (2023) commented that when individuals fall during experiments, it is not usually a sudden event. In general, the people being tested first use their hands and body to try to balance themselves. After this initial phase of imbalance, individuals end up losing the stability of one of their legs and end up shifting all their weight onto the other leg. Thus, they increase the normal force, being capable to withstand slightly greater flows before falling.

The variation in tolerable flow during the experiments is attributed to the “training (experience)” of the individuals being tested, because during the experiments individuals learn to position their bodies to resist the flow in the best possible way. This was observed in several studies, for example, Wüthrich et al. (2023) observed that, after the initial fall, most of individuals were able to withstand a second test conducted under the same flow conditions as the first one.

In this regard, Chen et al. (2018) mentioned that most studies did not take into account the actual ability of the human being to adjust its position in relation to water flow. In real conditions, humans can adjust their position to brace against the flow force, enabling them to withstand stronger currents than those considered in idealized situations presented in theoretical studies. Thus, the authors reiterated that, although postural adjustment has not been considered by most theoretical studies, it cannot be neglected, because it can influence the degree of the human body stability.

Human stability and adverse conditions

Despite the differences in the safety thresholds among different studies, many authors state that loss of stability can occur at lower flows when adverse conditions are encountered, such as: i) uneven or slippery bottom conditions and the presence of floating debris; ii) when the lighting is weak; iii) due to human factors, such as physical attributes or psychological factors; and iv) the type of clothing, footwear and objects that the individual may be carrying (Cox et al., 2010; Wright et al., 2010; Shand et al., 2011). In fact, supercritical flows are more energetic when shallower, for the same flow rate, and have greater force. In this sense, after building a database and analyzing the results of experimental and theoretical studies carried out on the subject up to 2010, Cox et al. (2010) suggested that more studies should be carried out considering these other variables that can influence people's loss of stability when exposed to water flows.

At this point, it was noted that the evaluation of different surfaces in the loss of human stability in water flows was only analyzed by Abt et al. (1989), where four different surfaces (grass, smooth concrete, steel and a mixture of sand and gravel with a maximum grain diameter of 0.95 cm) were analyzed. The results showed no significant differences in the safety thresholds and it was concluded that the type of surface has no significant influence on the loss of stability. However, the surfaces used during the experiments can be considered homogeneous and similar to each other, with no significant irregularities, i.e. no holes or depressions. Thus, there is a lack of testing in cases of bedrock, for example, to identify people's stability thresholds in cases where the surfaces are uneven.

The presence of surface irregularities is a type of situation encountered in natural areas, such as those encountered by hikers when crossing a watercourse during a trail. In these environments, the terrain is heterogeneous, and the hydrodynamic conditions of the water flow (d and v) change significantly with each step taken while crossing the riverbed, due to the presence of large pebbles and woody debris. Such conditions are very different from those evaluated by laboratory experiments as well as from the conditions found in urban areas. Therefore, there is a gap in experimental studies related to natural environments.

Figure 5A and B show a flood in an urban location where the surface is even, and a river crossing in a natural area, which has extremely uneven terrain, respectively. The images presented in the figure clearly show that the two environments are completely different and, consequently, the stability of an individual walking in these places can be influenced by the irregularities. Different hydraulic phenomena occur in the uneven bed, where in certain locations the flow is supercritical while in others it is subcritical and in still others there can be hydraulic rebounds. The variation in the flow itself can be an instability factor when crossing the river.

Figure 5
Difference between surfaces: A) urban area; B) natural environment. Images taken by the first author.

Apart from Abt et al. (1989), the other experiment conducted on grass was only Wüthrich et al. (2023). Compared to previous studies, their results showed that individuals tend to have greater stability when exposed to water flows on this type of surface due to the increased friction provided by the grass on the foot.

For urban environments, experiments have already been conducted with focus on this type of situation, for example, Russo et al. (2010), Martínez-Gomariz et al. (2016) and Zhu et al. (2023). For natural areas, no studies were found. Among all studies, the one that most resembled the conditions that people would encounter when exposed to water flow in a natural river is the study by Jonkmann & Penning-Rowsell (2008). However, although the tests were carried out on a river and not in a laboratory, the stretch considered during the test was modified and had a regular concrete surface as the background, not representing a natural river. Furthermore, the flow conditions in the river section used during the tests were regulated by a sluice. At this point, it should be noted that most studies were carried out considering permanent water flows, which is generally not the case in a real flood situation (Wüthrich et al., 2023).

With regard to the existence of slippery surfaces, only Takahashi et al. (1992) analyzed differences in people's stability, considering situations where the concrete is covered or not covered by algae. The presence of floating debris in the runoff was considered in the stability thresholds only by Ramsbottom et al. (2006), whose formula includes a term relating to this variable. However, the value used to determine the presence or absence of floating debris presented by the formula is generic and indicates only whether there is a lot of debris in the flow, a few debris or no debris, and the used values were not based on any more specific analysis.

With regard to lighting and visibility, only Russo et al. (2013) and Martínez-Gomariz et al. (2016) carried out experiments to compare the differences in stability in situations of good visibility and poor visibility. In this regard, it should be noted that Chanson & Brown (2018) analyzed the limiting conditions of d and v of water flow through the analysis of other studies previously carried out, focusing on the case of the flood that occurred in 2011 in an urban area in Australia. These authors confirmed that collecting data during the twilight and early evening hours was extremely difficult. Despite the presence of artificial lighting, individuals in the water easily became disoriented.

The results of laboratory experiments considered steady and uniform flow regimes and environments with good lighting, which is a situation very different from those encountered in a real flood scenario. Thus, some authors affirmed that some of the existing guidelines in human stability studies may not be representative of flooding situations in urban environments, characterized by high levels of turbulence and inadequate visibility (Chanson & Brown, 2018; Zhu et al., 2023). As urban areas have intense lighting, especially at night, the influence of this variable should be investigated more in studies of human stability.

No experimental study has conducted an in-depth analysis of the psychological factors of individuals. Martínez-Gomariz et al. (2016) interviewed the participants with the aim of assessing the emotional state and perception of people during the test scenarios, but this study did not explicitly present the results of the conducted interviews. Yee (2003) evaluated the case of children and found that more active and aggressive children tend to resist more than children who have calmer behavior.

In relation to theoretical studies, Simões et al. (2016) considered in their formulations, a factor related to the momentary psychological characteristics of each person as well as a factor related to individual's health. The authors showed that these factors have a strong correlation with a person's age, physical abilities, and knowledge level. According to Ramsbottom et al. (2006), the behavior of individuals is an important point regarding the life loss of people exposed to water flows. Although it is an extremely difficult factor to predict and quantify, it undoubtedly plays a significant role in life-threatening disaster occurrences.

In natural environments, the psychological factor can have an even stronger impact on person's loss of stability. For example, during a hike, people's fear of an accident can increase their likelihood of losing balance and falling, especially toward the end of the trip when people tend to show signs of fatigue. Therefore, the influence of the psychological factor on the loss of stability is an issue that should be further investigated in future research.

Finally, one variable that can be highlighted due to its significant influence on people's stability, and which has not been the main focus of any studies conducted so far, is the drag coefficient. This coefficient represents the resistance that fluids exert on bodies when there is a relative velocity between them. It is mainly related to the density of the fluid, and it is expressed by a pressure and a shear stress effects in the body surface. Of the 34 studies identified in this literature review, only 7 considered directly the influence of this parameter on people's stability when exposed to a water flow.

Currently, Computational Fluid Dynamics (CFD) has been extensively used to study and predict the drag forces acting on various submerged objects, ranging from human swimmers (Takagi et al. (2023) and Audot (2024)) to underwater vehicles (Javanmard et al. (2020)) and structures (Du et al. (2021)). Therefore, researches as the one developed by Arrighi et al. (2017), which involves CFD application designed specifically to analyze the stability of people when exposed to water flows can be indeeped to analyse people exposed to water flows during many floods situations.. This allows for practical and efficient testing of the influence of the drag coefficient and other variables on the loss of stability.

The use of these CFD simulations also makes it possible to compare the average physical capacity of an individual (for example, muscle strength and body weight) with the drag coefficient, allowing for detailed information on the risk of falling. Additionally, this type of simulation can be used to identify hazardous zones in urban and rural areas to support evacuation planning and improve people's safety.

In the general overview, it is clearly observed that several authors comment on the need for more experiments to construct a more comprehensive database regarding the conditions that can cause the loss of stability in individuals and the threshold values of the tested variables (Simões et al. 2016). Although the tests cannot fully represent the real conditions of a flood (Milanesi et al., 2016), they provide important data to identify the thresholds above which people cannot be exposed to a flood with their balance due to the velocity of the water and/or without buoyancy in deep water (Wade et al., 2005; Lazzarin et al., 2022).

CONCLUSIONS

From the literature review, it was found that the study of the stability of individuals in water flows is a globally addressed topic and holds significance for preventing adverse situations and even human deaths. In this regard, determining the hazard thresholds to which an individual is exposed when subjected to water flow is a key factor for developing flood risk management policies.

The review showed that a small number of studies tested individuals and mannequins, being that only 15 scientific articles were published in this regard over a period of 50 years. Considering the entirety of the studies, a significant portion assessed the influence of hydraulic conditions (depth and velocity) on the loss of stability in individuals, but the thresholds considered as safe varied considerably among the studies. Standardizing the concept of stability loss may be a challenge to achieve more comparable results among the tests in future studies.

In addition to the influence of hydraulic conditions and physical characteristics of individuals, other factors can cause stability loss, for example, the presence of irregularities on the surface and water turbidity. Most of the studies highlighted the need for a greater number of experimental analyses, especially regarding tests that evaluate different surfaces, including debris and floating objects. This type of situation is common during flooding events and can lead to complications and even loss of lives. However, these analyses have not been conducted yet.

Therefore, it is recommended to conduct more tests that consider adverse conditions that may be present during a flooding event in order to create a robust database. These data can serve as a basis for public flood management policies. This technique is very useful in the context of Disaster Risk Reduction. For example, Monteiro et al. (2021) and Vasconcellos et al. (2021) used the defined hazard thresholds to elaborate more detailed flood hazard maps in Brazilian municipalities.

As the main challenges to assess the instability of individuals in water flow, there is the fact that many factors influence the loss of stability and each individual reacts differently in dangerous situations. Hence, more comprehensive assessments allow for a more appropriate determination of extreme dangerous situations. It is also important for the population to be aware of the proposed hazard classifications so that they know how to act during these events.

Parkinson, J. N., Goldenfum, J. A., & Tucci, C. E. M. (2010). Integrated urban water management: humid tropics In: UNESCO Urban Water Series (chap. 6, pp. 109-127). Paris: UNESCO

ACKNOWLEDGEMENTS

This work was supported by Coordination of Superior Level Staff Improvement (CAPES); and National Council for Scientific and Technological Development (CNPq).

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Edited by

• Editor-in-Chief:
  Adilson Pinheiro

• Associated Editor:
  Iran Eduardo Lima Neto

Publication Dates

• Publication in this collection
  13 Dec 2024
• Date of issue
  2024

History

• Received
  14 Sept 2024
• Reviewed
  14 Oct 2024
• Accepted
  16 Oct 2024