Análise experimental dos estágios iniciais da onda de ruptura de uma barragem

Espartel, Lélis; Manica, Rafael

Lélis Espartel

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil

https://orcid.org/0000-0002-6931-6666

Rafael Manica

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil

https://orcid.org/0000-0002-0527-1374

E-mails: lelisespartel@gmail.com (LE), manica@iph.ufrgs.br (RM)

Lélis Espartel: Responsible for conducting the experiments, preparing the manuscript and data analyzing, discussion and writing. Rafael Manica: Master's dissertation supervisor, guided the work, elaborated parts of the text, assisted in the data interpretation and revised the manuscript.

Editor-in-Chief: Adilson PinheiroAssociated Editor: Iran Eduardo Lima Neto

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Figure 1
Schematic sketch of the experimental setup (dam-break wave propagates from right to left).

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Figure 2
Example of Plot Digitizer software application on the dam break images. The user manually picks the edge points (black dotted line) of the wave and the software converts into X and Y values. The dashed line shows the maximum wave height of the dam break wave.

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Figure 2
Example of Plot Digitizer software application on the dam break images. The user manually picks the edge points (black dotted line) of the wave and the software converts into X and Y values. The dashed line shows the maximum wave height of the dam break wave.

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Figure 3
Sequence of images from the initial stages of the dam-break wave, for different r values. Note that the last photo of Camera 1 and the first photo of Camera 2 portray the same instant, so they have the same timing and the same distance x.

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Figure 4
Maximum wave height along the first 0.60 m of the flume.

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Figure 5
Non-dimensional maximum wave heights (H_MAX / [M – J]), as function of r for all experimental runs.

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Figure 6
Effective height (H_EF) related to ratio r.

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Figure 7
Initial stages of the dam-break wave velocity for all experiments: i) abrupt velocity ; ii) flow deceleration.

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Figure 8
Effective velocity V_EF developed by the dam-break waves for each reservoir level (M10, M20 and M40) related to r.

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Figure 9
Jet types of dam-break waves and break shape classification as a function of r.

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Figure 10
Relationship between H_EF and V_EF.

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Figure 11
Relationship between maximum and mean dam-break wave velocity and upstream reservoir water depth (M).

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Figure 12
Non-dimensional velocity u as a function of r. Adapted from Hsu et al. (2014)Hsu, H.-C., Torres-Freyermuth, A., Hsu, T.-J., Hwung, H.-H., & Kuo, P.-C. (2014). On dam-break wave propagation and its implication to sediment erosion. Journal of Hydraulic Research, 52(2), 205-218..

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Table 1
Experimental planning with conditions tested. Labelling of runs: e.g. M40 indicates 0.40 m of upstream water depth (reservoir); J8 represents 0.08 m of downstream water depth (flume); # 3 indicates repetition run for a given setting.

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Table 2
Geometry and kinematic parameters measured for all runs.

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Table 3
Jet type and wave-break shape classification as a function of r.

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Table 4
Logarithmic fit lines for various scenarios of simulation.

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N#	M	J	r	Code	N#	M	J	r	Code
N#	(cm)	(cm)	(-)	Code	N#	(cm)	(cm)	(-)	Code
1	10	0	0.00	M10-J0-1	19	20	4	0.20	M20-J4-1
2				M10-J0-2	20				M20-J4-2
3				M10-J0-3	21				M20-J4-3
4		2	0.20	M10-J2-1	22		8	0.40	M20-J8-1
5				M10-J2-2	23				M20-J8-2
6				M10-J2-3	24				M20-J8-3
7		4	0.40	M10-J4-1	25	40	0	0.00	M40-J0-1
8				M10-J4-2	26				M40-J0-2
9				M10-J4-3	27				M40-J0-3
10		8	0.80	M10-J8-1	28		2	0.05	M40-J2-1
11				M10-J8-2	29				M40-J2-2
12				M10-J8-3	30				M40-J2-3
13	20	0	0.00	M20-J0-1	31		4	0.10	M40-J4-1
14				M20-J0-2	32				M40-J4-2
15				M20-J0-3	33				M40-J4-3
16		2	0.10	M20-J2-1	34		8	0.20	M40-J8-1
17				M20-J2-2	35				M40-J8-2
18				M20-J2-3	36				M40-J8-3

M	J	Run	r	H_MAX	H_EF	V_MED	V_MAX	V_EF	Peak Location X
M	J	Run	r	H_MAX	H_EF	V_MED	V_MAX	V_EF	H_MAX	V_MAX
(m)	(m)		(-)	(m)	(m)	(m s^-1)	(m s^-1)	(m s^-1)	(m)	(m)
0.10	0.00	M10-J0	0.00	0.039	∞	1.06	1.30	0.22	0.10	0.40
0.10	0.02	M10-J2	0.20	0.064	2.22	1.01	1.18	0.17	0.20	0.40
0.10	0.04	M10-J4	0.40	0.080	1.00	0.88	1.08	0.23	0.20	0.40
0.20	0.00	M20-J0	0.00	0.077	∞	1.73	2.11	0.22	0.40	0.60
0.20	0.02	M20-J2	0.10	0.102	4.08	1.68	2.15	0.28	0.40	0.60
0.20	0.04	M20-J4	0.20	0.137	2.42	1.46	1.93	0.32	0.30	0.80
0.20	0.08	M20-J8	0.40	0.166	1.07	1.36	1.74	0.28	0.50	1.20
0.40	0.00	M40-J0	0.00	0.119	∞	2.24	2.83	0.27	0.60	1.20
0.40	0.02	M40-J2	0.05	0.167	7.33	2.41	3.17	0.32	0.60	0.80
0.40	0.04	M40-J4	0.10	0.220	4.49	2.24	3.52	0.57	0.60	1.20
0.40	0.08	M40-J8	0.20	0.272	2.40	1.95	2.62	0.35	0.60	1.20

r	Code	M	J	Jet Type	Break Shape
(-)	Code	(cm)	(cm)	Jet Type	Break Shape
0.80	M10-J8	10	8	Undulation movement	No Break
0.40	M20-J8	20	8	Transition Jet	Spilling Break
0.40	M10-J4	10	4	Transition Jet	Spilling Break
0.20	M40-J8	40	8	Mushroom Jet	Plunging Break
	M20-J4	20	4
	M10-J2	10	2
0.10	M40-J4	40	4
0.10	M20-J2	20	2
0.05	M40-J2	40	2
0.00	M40-J0	40	0	Horizontal Jet	No Break
	M20-J0	20	0
	M10-J0	10	0

Condition J	Velocity	Equations	R²
J = 0	V_MED	V_MED = 0.603∙ln(M) + 2.688 (7)	0.804
J = 0	V_MAX	V_MAX = 1.156∙ln(M) + 3.974 (8)	0.989
J > 0	V_MAX	V_MAX = 1.601∙ln(M) + 4.901 (9)	0.982

[1] E-mails: lelisespartel@gmail.com (LE), manica@iph.ufrgs.br (RM)

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Análise experimental dos estágios iniciais da onda de ruptura de uma barragem

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