Dam-Break analysis: proposal of a simplified approach

Rossi, Carlo Lucca Coutinho Ungaretti; Marques, Marcelo Giulian; Teixeira, Eder Daniel; Melo, José Falcão de; Ferla, Rute; Prá, Maurício Dai

doi:10.1590/2318-0331.262120200066

Carlo Lucca Coutinho Ungaretti Rossi

Instituto de Pesquisas Hidráulicas (IPH), Universidade Federal do Rio Grande do Sul (UFRGS) Porto Alegre, Rio Grande do Sul, Brasil

http://orcid.org/0000-0003-3147-886X

Marcelo Giulian Marques

Instituto de Pesquisas Hidráulicas (IPH), Universidade Federal do Rio Grande do Sul (UFRGS) Porto Alegre, Rio Grande do Sul, Brasil

http://orcid.org/0000-0002-9948-3094

Eder Daniel Teixeira

Instituto de Pesquisas Hidráulicas (IPH), Universidade Federal do Rio Grande do Sul (UFRGS) Porto Alegre, Rio Grande do Sul, Brasil

http://orcid.org/0000-0001-7595-486X

José Falcão de Melo

Laboratório Nacional de Engenharia Civil Lisboa, Portugal

http://orcid.org/0000-0002-7056-3306

Rute Ferla

Instituto de Pesquisas Hidráulicas (IPH), Universidade Federal do Rio Grande do Sul (UFRGS) Porto Alegre, Rio Grande do Sul, Brasil

Maurício Dai Prá

Instituto de Pesquisas Hidráulicas (IPH), Universidade Federal do Rio Grande do Sul (UFRGS) Porto Alegre, Rio Grande do Sul, Brasil

http://orcid.org/0000-0002-1858-1531

E-mails: rossi.carlolucca@gmail.com (CLCUR), mmarques@iph.ufrgs.br (MGM), eder.teixeira@ufrgs.br (EDT), jfmelo@lnec.pt (JFM), ruteferla@hotmail.com (RF), mauricio.daipra@ufrgs.br (MDP)

Carlo Lucca Coutinho Ungaretti Rossi: Performed the methodology, obtained the results, analyzed the obtained data, wrote and revised the text.Marcelo Giulian Marques: Oriented the research, analyzed the results and contributed with technical notes.Eder Daniel Teixeira: Co-oriented the research, analyzed the results and contributed with technical notes.José Falcão de Melo: Contributed with technical notes and revised the text.Rute Ferla: Contributed with technical notes and revised the text.Maurício Dai Prá: Contributed with technical notes and revised the text.

Editor Chefe: Adilson Pinheiro

Editor Associado: Iran Eduardo Lima Neto

Author	Equation	Eq. n^o
Froehlich (1995)Froehlich, D. C. (1995). Peak outflow from breached embankment dam. Journal of Water Resources Planning and Management, 121(1), 90-97. http://dx.doi.org/10.1061/(ASCE)0733-9496(1995)121:1(90). http://dx.doi.org/10.1061/(ASCE)0733-949...	$Q_{p} = 0.607 V_{r}^{0.295} H_{w}^{1.24}$	(1)
Webby (1996)Webby, M. G. (1996). Discussion of ‘Peak outflow from breached embankment dam’ by D. C. Froehlich. J. Water Resources Planning and Management, 4(316), 316-317. http://dx.doi.org/10.1061/(ASCE)0733-9496(1996)122:4(316).	$Q_{p} = 0.0443 \sqrt{g} V_{r}^{0.365} H_{w}^{1.405}$	(2)
Azimi et al. (2015)Azimi, R., Vatankhah, A. R., & Kouchakzadeh, S. (2015). Predicting peak discharge from breached embankment dams. 36th IAHR World Congress, Hague, Netherlands.	$Q_{p} = 0.0166. \sqrt{{g V}_{r}} . H_{w}$	(3)
Ferla (2018)Ferla, R. (2018). Análise de aspectos hidráulicos de métodos simplificados envolvendo rompimento de barragens. Porto Alegre: UFRGS.	$\frac{Q_{p} = (V_{r}^{0.56} H_{w}^{0.45})}{3}$	(4)

Author	Equation	Eq. n^o
Bureau of Reclamation (1988)Bureau of Reclamation (1988). Downstream hazard classification guidelines. ACER Tech. Memorandum No. 11, U.S. Department of the Interior, Bureau of Reclamation, Denver, 57.	$t_{p} = 0.033 H_{w}$	(5)
Von Thun & Gillette (1990)Von Thun, J. L., & Gillette, D. R. (1990). Guidance on breach parameters. Internal Memorandum, U.S. Dept. of the Interior, Bureau of Reclamation, Denver, 17.: erodible materials	$t_{p} = 0.015 H_{w}$	(6)
Von Thun & Gillette (1990)Von Thun, J. L., & Gillette, D. R. (1990). Guidance on breach parameters. Internal Memorandum, U.S. Dept. of the Interior, Bureau of Reclamation, Denver, 17.: resistant to erosion	$t_{p} = 0.02 H_{w} + 0.25$	(7)

Dams’ size	Limits for the classification
Small	$\begin{matrix} X \leq 400 \end{matrix}$
Medium	$400 < X \leq 1000$
Large	$X > 1000$

Dam	$\begin{matrix} H_{d} (m) \end{matrix}$	$\begin{matrix} V_{r} (1 0^{6} m^{3}) \end{matrix}$	$X$	Classification
BI	5	5	56	Small
BII	10	5	224	Small
BIII	15	5	503	Medium
BIV	5	10	79	Small
BV	10	10	316	Small
BVI	15	10	712	Medium
BVII	30	10	2,846	Large
BVIII	5	20	112	Small
BIX	10	20	447	Medium
BX	15	20	1,006	Large
BXI	30	20	4,024	Large
BXII	30	50	6,364	Large

Section	Average width ( $m$ )	Thalweg slope ( $m . m^{- 1}$ )	Distance from the dam (m)
A	850	0.001	10,889
B	600	0.0004	16,444
C	800	0.0009	20,667
D	480	0.0011	27,111
E	400	0.001	33,778
F	540	0.001	36,667
G	600	0.0002	38,889
H	760	0.0003	43,556

Dam	$H_{d} (m)$	Peak outflow ( $m^{3} s^{- 1}$ )	Methodology
BI	$5$	863	Ferla (2018)Ferla, R. (2018). Análise de aspectos hidráulicos de métodos simplificados envolvendo rompimento de barragens. Porto Alegre: UFRGS.
BIV		1,179
BVIII		1,611
BII	$10$	1,262	Ferla (2018)Ferla, R. (2018). Análise de aspectos hidráulicos de métodos simplificados envolvendo rompimento de barragens. Porto Alegre: UFRGS.
BV		1,724	Ferla (2018)Ferla, R. (2018). Análise de aspectos hidráulicos de métodos simplificados envolvendo rompimento de barragens. Porto Alegre: UFRGS.
BIX		2,360	Azimi et al. (2015)Azimi, R., Vatankhah, A. R., & Kouchakzadeh, S. (2015). Predicting peak discharge from breached embankment dams. 36th IAHR World Congress, Hague, Netherlands.
BIII	$15$	1,761	Webby (1996)Webby, M. G. (1996). Discussion of ‘Peak outflow from breached embankment dam’ by D. C. Froehlich. J. Water Resources Planning and Management, 4(316), 316-317. http://dx.doi.org/10.1061/(ASCE)0733-9496(1996)122:4(316). & Azimi et al. (2015)Azimi, R., Vatankhah, A. R., & Kouchakzadeh, S. (2015). Predicting peak discharge from breached embankment dams. 36th IAHR World Congress, Hague, Netherlands.
BVI		2,491	Azimi et al. (2015)Azimi, R., Vatankhah, A. R., & Kouchakzadeh, S. (2015). Predicting peak discharge from breached embankment dams. 36th IAHR World Congress, Hague, Netherlands.
BX		3,523	Azimi et al. (2015)Azimi, R., Vatankhah, A. R., & Kouchakzadeh, S. (2015). Predicting peak discharge from breached embankment dams. 36th IAHR World Congress, Hague, Netherlands.
BVII	$30$	5,965	Webby (1996)Webby, M. G. (1996). Discussion of ‘Peak outflow from breached embankment dam’ by D. C. Froehlich. J. Water Resources Planning and Management, 4(316), 316-317. http://dx.doi.org/10.1061/(ASCE)0733-9496(1996)122:4(316).
BXI		7,683	Webby (1996)Webby, M. G. (1996). Discussion of ‘Peak outflow from breached embankment dam’ by D. C. Froehlich. J. Water Resources Planning and Management, 4(316), 316-317. http://dx.doi.org/10.1061/(ASCE)0733-9496(1996)122:4(316).
BXII		11,085	Azimi et al. (2015)Azimi, R., Vatankhah, A. R., & Kouchakzadeh, S. (2015). Predicting peak discharge from breached embankment dams. 36th IAHR World Congress, Hague, Netherlands.

Dam	$\begin{matrix} H_{d} (m) \end{matrix}$	Peak time ( $h$ )	Base time ( $h$ )
BI	$5$	0.08	3.72
BIV			5.22
BVIII			7.40
BII	$10$	0.15	2.70
BV			3.72
BIX			5.20
BIII	$15$	0.23	2.08
BVI			2.73
BX			3.65
BVII	$30$	0.45	1.43
BXI			1.72
BXII			2.78

$H_{d} (m)$	Equations for $a$	Eq. n^o	$R^{2}$
$5$	$a = 2302 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 4.207}$	(10)	0.98
$10$	$a = 4432.2 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 4.957}$	(11)	0.99
$15$	$a = 11203.0 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 5.792}$	(12)	0.97
$30$	$a = 276.6 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 4.772}$	(13)	0.99

$H_{d} (m)$	Equation for $b$	Eq. n^o	$R^{2}$
$5$	$b = 59.789 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 0.879}$	(14)	0.98
$10$	$b = 43.706 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 0.996}$	(15)	0.99
$15$	$b = 22.342 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 0.911}$	(16)	0.97
$30$	$b = 7.926 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 0,725}$	(17)	0.99

$H_{d} (m)$	Equations for $α$	Eq. n^o	$R^{2}$
5	$α = (6.000 10^{- 7}) {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{2.3277}$	(19)	0.99
$10$	$α = (1.212 10^{- 6}) {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{2.7989}$	(20)	1.00
$15$	$α = (1.529 10^{- 5}) {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{2.3921}$	(21)	0.99
$30$	$α = (2.048 10^{- 4}) {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{2.0415}$	(22)	0.93

$H_{d} (m)$	Equations for $β$	Eq. n^o	$R^{2}$
$5$	$β = 5.1713 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 0.55}$	(23)	0.99
$10$	$β = 5.0066 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 0.67}$	(24)	0.99
$15$	$β = 3.5859 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 0.65}$	(25)	1.00
$30$	$β = 2.5466 {(\frac{V_{r}^{\frac{1}{3}}}{H_{d}})}^{- 0.68}$	(26)	0.98

Froehlich (1995) Froehlich, D. C. (1995). Peak outflow from breached embankment dam. Journal of Water Resources Planning and Management, 121(1), 90-97. http://dx.doi.org/10.1061/(ASCE)0733-9496(1995)121:1(90). http://dx.doi.org/10.1061/(ASCE)0733-949...	Webby (1996) Webby, M. G. (1996). Discussion of ‘Peak outflow from breached embankment dam’ by D. C. Froehlich. J. Water Resources Planning and Management, 4(316), 316-317. http://dx.doi.org/10.1061/(ASCE)0733-9496(1996)122:4(316).	Azimi et al. (2015) Azimi, R., Vatankhah, A. R., & Kouchakzadeh, S. (2015). Predicting peak discharge from breached embankment dams. 36th IAHR World Congress, Hague, Netherlands.	Ferla (2018) Ferla, R. (2018). Análise de aspectos hidráulicos de métodos simplificados envolvendo rompimento de barragens. Porto Alegre: UFRGS.
2,398	2,753	3,248	2,739

Bureau of Reclamation (1988) Bureau of Reclamation (1988). Downstream hazard classification guidelines. ACER Tech. Memorandum No. 11, U.S. Department of the Interior, Bureau of Reclamation, Denver, 57.	Von Thun & Gillette (1990) Von Thun, J. L., & Gillette, D. R. (1990). Guidance on breach parameters. Internal Memorandum, U.S. Dept. of the Interior, Bureau of Reclamation, Denver, 17.
	Resistant to erosion	Erodible materials
0.50	0.55	0.23

[1] E-mails: rossi.carlolucca@gmail.com (CLCUR), mmarques@iph.ufrgs.br (MGM), eder.teixeira@ufrgs.br (EDT), jfmelo@lnec.pt (JFM), ruteferla@hotmail.com (RF), mauricio.daipra@ufrgs.br (MDP)

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Dam-Break analysis: proposal of a simplified approach

Análise de ruptura de barragens: proposta de uma abordagem simplificada

ABSTRACT