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

Fagundes, Marina Refatti; Fan, Fernando Mainardi; Michel, Gean Paulo; Kobiyama, Masato; Vanelli, Franciele Maria; Monteiro, Leonardo Romero; Campagnolo, Karla; Loss, Jefferson Fagundes; Abatti, Bruno Henrique

doi:10.1590/2318-0331.292420240094

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Scientific/Technical Article • RBRH 29 • 2024 • https://doi.org/10.1590/2318-0331.292420240094 linkcopiar

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

Autoria SCIMAGO INSTITUTIONS RANKINGS

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

Author	Year	Country	Type of study	Experiment location	Considered variables	Hydrodynamic mecanism	Nº of tested individuals	Characteristics of individuals			Flow characteristics		Thresholds considered safe
Author	Year	Country	Type of study	Experiment location	Considered variables	Hydrodynamic mecanism	Nº of tested individuals	Age (years)	Weight (kg)	Height (m)	Depth (m)	Velocity (m/s)	Thresholds considered safe
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	$v_{m a x} = 1.5 m / s$ for
Foster & Cox (1973)	1973	Australia	Experimental	Flume		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	$h < 0.3 m$
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	$v * h < \frac{0.5 m^{2}}{s}$ (for the monolith)
Abt et al. (1989)	1989	United States	Experimental	Flume		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	$P N = e^{0.222 (\frac{p e s o * a l t u r a}{1000}) + 1.088}$ (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	$D V = 0.12 t o 0.55 m^{2} / s$ (children)
Keller e Mitsch (1993)	1993	Australia	Theoretical	NA		Sliding and toppling	2	5 years and adult of unspecified age			NA	NA	$D V = 0.35 t o 1.4 m^{2} / s$ (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	$v * h \leq 0,006 M + 0,3$ For good conditions
													$v * h \leq 0,004 M + 0,2$ For normal conditions
													$v * h \leq 0,002 M + 0,1$ 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	$h v_{c r} = K g$
Lind et al. (2004)	2004	Canada	Theoretical	NA	Depth, velocity, weight and height	Toppling	NA	NA	NA	NA	NA	NA	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	$H a z a r d r a t i n g = d (v + 1,5) + D F$
Ramsbottom et al. (2004, 2006)	2004 e 2006	United Kingdom	Theoretical	NA		Toppling	NA	NA	NA	NA	NA	NA	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	$M_{0} = \frac{v^{2} D}{g} + \frac{D^{2}}{2}$
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	$M_{0} < 0.1$ 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	$h * v < 0.8 m^{2} / s$
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
													$U_{c} = α {(\frac{h_{f}}{h_{p}})}^{β} \sqrt{\frac{m_{p}}{ρ_{f} h_{p} h_{f}} - (\frac{a_{1} h_{f}}{h_{p}} + b_{1}) \frac{(a_{2} m_{p +} b_{2})}{h_{p}^{2}}}$
													*Toppling
													$U_{c} = α {(\frac{h_{f}}{h_{p}})}^{β} \sqrt{\frac{m_{p}}{ρ_{f} h_{f}^{2}} - (\frac{a_{1}}{h_{p}^{2}} + \frac{b_{1}}{h_{f} h_{p}}) (a_{2} m_{p +} b_{2})}$
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
													$h_{h i g h} (U, τ) = \{\begin{matrix} \begin{array}{l} \frac{h (U, T_{m a x}) - h (U, T_{m i n})}{\frac{T_{m a x} - T_{m i n}}{2}} (τ - T_{m i n}) + \\ h (U, T_{m i n}) i f τ \leq T \end{array} \\ h (U, T_{m a x}) i f τ > T \end{matrix}$
													**For low probability events
													$h_{l o w} (U, τ) = \{\begin{matrix} h (U, T_{m i n}) i f τ \leq T \\ \begin{array}{l} \frac{h (U, T_{m a x}) - h (U, T_{m i n})}{\frac{T_{m a x} - T_{m i n}}{2}} (τ - T) + \\ h (U, T_{m i n}) i f τ > T \end{array} \end{matrix}$
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	$v * h < 0.22 m^{2} / s$
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
Chen et al. (2018)	2018	China	Theoretical	NA		Toppling	NA	NA	NA	NA	NA	NA	$U_{c} = α {(\frac{h_{f}}{h_{p}})}^{β} \sqrt{\frac{m_{p}}{ρ_{f} h_{f}^{2}} - (\frac{a_{1}}{h_{p}^{2}} + \frac{b_{1}}{h_{f} h_{p}}) (a_{2} m_{p +} b_{2})}$
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
													$B T I s t a b i l i t y i f \{\begin{matrix} h \leq 1.2 m f o r v < 0.37 m / s \\ \begin{array}{l} h \leq (1.63 e^{- 1.37 v} + 0.22) m f o r v = \\ (0.37 + 3.00) m / s \end{array} \end{matrix}$
													****For forward toppling stability
													$F T I s t a b i l i t y i f \{\begin{matrix} h \leq 1.2 m f o r v < 0.45 m / s \\ \begin{array}{l} h \leq (1.43 e^{- 0.88 v} + 0.24) m f o r v = \\ (0.45 \div 3.00) m / s \end{array} \end{matrix}$
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, $h > (13 Y / 16)$
													For sliding,
													$\sqrt{{(W_{η} + F_{h, η} + F_{a, x, η})}^{2} + {(F_{a, y})}^{2}} > μ (W_{ξ} - B - F_{h, ξ} - F_{a, x, ξ})$
													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	$R D (W) = \frac{1}{1 + {(a / W)}^{b}}$
Lazzarin et al. (2022)	2022	Italy	Theoretical	NA		Sliding	NA	NA	NA	NA	NA	NA	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	$M = 64.1 k g$ up to $h v^{2} < 4.13 m^{3} / s^{2}$ and $M = 101.0 k g$ up to $h v^{2} < 5.49 m^{3} / s^{2}$
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	$\begin{array}{l} \bar{U} = (- 0.22 * l n k + 0.2391) * \\ [α {(\frac{H}{H_{h}})}^{β} \sqrt{\begin{array}{l} \frac{m_{h}}{ρ H^{2}} - \\ (\frac{a_{1}}{H_{h}^{2}} + \frac{b_{1}}{H * H_{h}}) * (a_{2} m_{h} + b_{2}) \end{array}}] \end{array}$

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[TFN1] ^*
Information on the values of each of the parameters used in these calculations can be found at: Xia et al. (2014).

[TFN2] ^**
More information can be found in Equations 23 and 24 and in the Figure 3d (Milanesi et al., 2015).

[TFN3] ^***
For more information on the variables: Chen et al. (2018).

[TFN4] ^****
For more information on the variables: Postacchini et al. (2021).

[5] NA = Not applicable.