Impulse wave in the Brazilian Lake of Capitólio

Maciel, Geraldo de Freitas; Pereira, João Batista; Sáo, Yuri Taglieri; Ferreira, Fabiana de Oliveira; Ferreira, Laine Garcia

doi:10.1590/2318-0331.282320230036

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Scientific/Technical Article • RBRH 28 • 2023 • https://doi.org/10.1590/2318-0331.282320230036 copy

Impulse wave in the Brazilian Lake of Capitólio

Onda de impulso no Lago Brasileiro de Capitólio

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This note proposes a technical approach towards the disaster occurred on January 8, 2022, in the tourism region of Capitólio (Minas Gerais state, Brazil), where a massive quartzite rock broke from a cliff and toppled on to pleasure boaters drifting on a lake, leaving 10 people dead and 30 others injured. Even though the rockfall was decisive in the tragedy, it is reasonable to affirm that the submersion-wave impact certainly potentialized the accident. Along these lines, this work not only aims to videographically explore the geometric / kinematic characteristics of the solid block, but also to discuss the specificities pertaining the event. Lastly, with basis on the Noda Method (1970), this manuscript also estimates the resulting wave amplitude (near the impact) and the energy-transfer coefficient between the block and the body of water.

Keywords:
Impulse wave; Capitólio rockfall; Noda method; Maximum amplitude wave

Base dimensions of the block $λ$ (m)	Width of the parameterized box $\hat{λ}$ (m)	Local mean depth $d$ (m)	Relative width of the box $\hat{λ} / d$	Impact velocity* $V$ (m/s)	Impact Froude number $F r_{i m p}$	Wave pattern	Relative maximum amplitude $\frac{η {(0, t)}_{m a x}}{\hat{λ}}$	Maximum amplitude $η_{m a x}$ (m)
8 $\pm 0.8$	4 $\pm 0.4$	4 $\pm 0.4$	1 $\pm 0.14$	$7.85 \pm 0.76$ ^* * Two velocity situations were taken into account: 1Vmin for a free-fall time of 6 s and 2Vmax for a free-fall time of 5 s. ¹	1.25 $\pm 0.14$	- non-linear wave	0.91	3.62 $\pm 0.12$
						- solitary wave
						- bore wave
				$9.42 \pm 0.94$ ^*2	1.50 $\pm 0.17$	- non-linear wave	0.94	3.75 $\pm 0.06$
						- solitary wave
						- bore wave

Reference	Equation	$η_{m a x}$ (m)	$Δ η$ (%)	Energy variation (%)
Noda (1970)Noda, E. K. (1970). Water waves generated by landslides. Journal of Waterways, Harbors and Coastal Engineering Division, 96(4), 835-855. http://dx.doi.org/10.1061/AWHCAR.0000045. http://dx.doi.org/10.1061/AWHCAR.0000045...	$η (x, t) / λ = f (V / \sqrt{g d}, x / d)$	3.75 $\pm 0.06$	Basis	14.9
(2D block model)	$η (x, t) / λ = f (V / \sqrt{g d}, x / d)$	3.75 $\pm 0.06$	Basis	14.9
Noda (1970)Noda, E. K. (1970). Water waves generated by landslides. Journal of Waterways, Harbors and Coastal Engineering Division, 96(4), 835-855. http://dx.doi.org/10.1061/AWHCAR.0000045. http://dx.doi.org/10.1061/AWHCAR.0000045...	$η_{m a x} = 1.32 d (V / \sqrt{g d}$ )	7.94 $\pm 1.19$	+110	45.9
(2D piston-type model)	$η_{m a x} = 1.32 d (V / \sqrt{g d}$ )	7.94 $\pm 1.19$	+110	45.9
Heller (2007)Heller, V. (2007). Landslide generated impulse waves - Prediction of near field characteristics (Ph.D. thesis), ETH Zurich, Zürich, Switzerland.	$A_{m} = (4 / 9) P^{4 / 5}$ ^* * Parameter Am=ηmax/d is the relative maximum wave amplitude.	1.62 $\pm 0.42$	-57	4.2
(2D granular slide model)		1.62 $\pm 0.42$	-57	4.2

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[1] E-mails: geraldo.f.maciel@unesp.br (GFM), jbpereira.eng@gmail.com (JBP), yuri.taglieri27@gmail.com (YTS), fabiana.oliveira@fsa.br (FOF), laine.g.ferreira@gmail.com (LGF)