Parâmetros de brecha em rupturas de barragens em cascata utilizando modelagens física, empírica e numérica

Authors contributions Rubens Gomes Dias Campos: Defined objectives and methodology, planned and conducted models tests, and wrote and formatted text. Aloysio Portugal Maia Saliba: Defined objectives, made technical notes, and revised the text. Márcio Benedito Baptista: Made technical notes and revised the text. Victor Hugo Brum Biscaro: Participated on model tests. Júlia Muniz de Miranda Sá: Participated on model tests. Daniel Tuler Passos: Participated on model tests. Stênio Augusto de Souza Coelho: Participated on model tests. José Antonio Mamani Gómez: Participated on model tests.

Range of hydrological flow (m³/s)	Flow on the physical model - Qr (m³/s)
2,500	0.025
1,500	0.015

Variable	Upstream dam	Downstream dam
Crest elevation (m) ¹ 1 Estimated based on Google Earth (2019);	688.00	660.70
Invert elevation (m) ¹	657.00	637.20
Dam height (m) ² 2 Brazilian Mining Dam’s Ranking from the Brazilian Mining Agency (ANM) - January/2019 (Agência Nacional de Mineração, 2019).	31.00	23.50
Dam width (m) ¹	201.0	134.0
Dam length (m) ¹	135.0	81.0
Reservoir volume (m³) ²	800,200	400,000

Variable	Upstream dam	Downstream dam
Breach Formation Factor (1000 m³.m)	24,806	9,400
Storage Intensity (m³/m)	25,813	17,021
Breach formation time ¹ 1 Calculated according to Froehlich (2008). (min.)	9.7	9.1
Crest breach width ¹ 1 Calculated according to Froehlich (2008). (m)	62.2	48.2
Average breach width ¹ 1 Calculated according to Froehlich (2008). (m)	31.2	24.7
Invert breach width ¹ 1 Calculated according to Froehlich (2008). (m)	0.2	1.2
Breach height ¹ 1 Calculated according to Froehlich (2008). (m)	31.00	23.50
ko coefficient ¹ 1 Calculated according to Froehlich (2008).	1.3	1.3
Breach lateral slope ¹ 1 Calculated according to Froehlich (2008). (V/H):	1.0	1.0

Scenario	Distance between dams (cm)	h2’ (cm)	h2” (cm)	h1’ (cm)	h1” (cm)
IP	203.8	2.0	5.0	12.0	17.0

Scenario	Test	Upstream dam		Scenario	Test	Upstream dam
		Right bank	Left bank			Right bank	Left bank
		(h/v)	(h/v)			(h/v)	(h/v)
I	1	-0.02	-0.07	I	1	0.44	0.41
	2	0.02	0.12		2	0.00	1.06
	3	0.00	0.12		3	0.00	0.00
Average		0.00	0.05	Average		0.15	0.49
Scenario	Test	(h/v)	(h/v)	Scenario	Test	(h/v)	(h/v)
II	1	0.08	0.15	II	1	0.00	0.00
	2	1.76	1.45		2	0.00	0.00
	3	-0.05	0.43		3	0.00	0.00
Average		0.60	0.68	Average		0.00	0.00
General average		0.30	0.37	General average		0.07	0.25
Upstream general average			0.33	Downstream general average			0.16

Scenario	Test	Upstream breach width (mm)	Downstream breach width (mm)	Upstream time formation (s)	Downstream time formation (s)	Upstream reservoir volume (m³)	Downstream reservoir volume (m³)
I	1	601.3	803.8	49	16	2.653	0.352
	2	627.3	857.1	31	19
	3	794.8	1000.0	26	20
Average		674.5	887.0	35	18	-	-
II	1	630.4	1000.0	16	13	2.106	0.813
	2	768.2	1000.0	7	6
	3	640.0	1000.0	20	16
Average		679.5	1000.0	14	12	-	-
General average		677.0	943.5	24.8	15.0	-	-

Scenario	BFF Upstream (m³.m)	BFF Downstream (m³.m)	BFF correlation	Width correlation	Time formation correlation
I	0.504	0.067	0.133	1.34	0.33
				1.37	0.61
				1.26	0.77
Average	-	-	-	1.32	0.57
II	0.400	0.154	0.386	1.59	0.81
				1.30	0.86
				1.56	0.80
Average	-	-	-	1.48	0.82
General average	-	-	-	1.40	0.70

Brasil