Investigation of riprap stability at downstream of spillway flip bucket without and with energy dissipators

Figures & data

Figure 1. Scour profile downstream of a flip bucket.

Figure 2. A view of solid bucket.

Figure 3. A sketch of a dentated bucket.

Figure 4. Schematic view of flume and installation position of the dentated flip bucket.

Figure 5. Sketch of dentated triangular spillway.

Figure 6. Properties on the spillway and riprap on the downstream.

Table 1. Results of the experiment at movement threshold of riprap.

simple flip bucket					simple triangular sill
d 50 mm	Q (I/S)	Fr t	D50/Yt	SN t	d 50 mm	Q (I/S)	Fr t	D50/Yt	SN t
23.1	0.007	0.28	0.36	0.38	23.1	0.007	0.26	0.34	0.4
12.7	0.007	0.26	0.19	0.5	12.7	0.007	0.25	0.18	0.52
11.23	0.007	0.24	0.16	0.52	11.23	0.007	0.24	0.16	0.54
9.52	0.007	0.22	0.13	0.53	9.52	0.007	0.22	0.13	0.56
23.1	0.008	0.27	0.33	0.39	23.1	0.008	0.25	0.31	0.41
12.7	0.008	0.24	0.17	0.51	12.7	0.008	0.24	0.16	0.53
11.23	0.008	0.23	0.14	0.53	11.23	0.008	0.23	0.14	0.55
9.52	0.008	0.21	0.11	0.54	9.52	0.008	0.21	0.11	0.57
23.1	0.01	0.26	0.28	0.41	23.1	0.01	0.24	0.26	0.43
12.7	0.01	0.23	0.14	0.53	12.7	0.01	0.23	0.14	0.56
11.23	0.01	0.22	0.12	0.55	11.23	0.01	0.21	0.12	0.57
9.52	0.01	0.2	0.1	0.56	9.52	0.01	0.2	0.09	0.59
23.1	0.012	0.25	0.24	0.43	23.1	0.012	0.23	0.22	0.44
12.7	0.012	0.22	0.12	0.56	12.7	0.012	0.22	0.12	0.58
11.23	0.012	0.21	0.1	0.57	11.23	0.012	0.2	0.1	0.59
9.52	0.012	0.19	0.08	0.58	9.52	0.012	0.19	0.08	0.6
23.1	0.015	0.24	0.2	0.45	23.1	0.015	0.22	0.19	0.46
12.7	0.015	0.21	0.1	0.57	12.7	0.015	0.21	0.1	0.6
11.23	0.015	0.2	0.09	0.59	11.23	0.015	0.19	0.08	0.61
9.52	0.015	0.18	0.07	0.61	9.52	0.015	0.18	0.07	0.62
dentated flip bucket					dentated triangular sill
d 50 mm	Q (I/S)	Fr t	D50/Yt	SN t	D 50 mm	Q (I/S)	Fr t	D50/Yt	SN t
23.1	0.007	0.24	0.33	0.42	23.1	0.007	0.23	0.32	0.44
12.7	0.007	0.23	0.17	0.55	12.7	0.007	0.22	0.17	0.56
11.23	0.007	0.22	0.15	0.57	11.23	0.007	0.21	0.14	0.57
9.52	0.007	0.21	0.12	0.58	9.52	0.007	0.19	0.11	0.59
23.1	0.008	0.23	0.3	0.43	23.1	0.008	0.22	0.28	0.45
12.7	0.008	0.22	0.16	0.56	12.7	0.008	0.21	0.15	0.57
11.23	0.008	0.21	0.14	0.58	11.23	0.008	0.2	0.13	0.59
9.52	0.008	0.2	0.11	0.59	9.52	0.008	0.18	0.1	0.6
23.1	0.01	0.22	0.25	0.46	23.1	0.01	0.21	0.24	0.48
12.7	0.01	0.21	0.13	0.58	12.7	0.01	0.2	0.13	0.59
11.23	0.01	0.2	0.11	0.59	11.23	0.01	0.19	0.11	0.6
9.52	0.01	0.19	0.09	0.61	9.52	0.01	0.17	0.09	0.63
23.1	0.012	0.21	0.21	0.47	23.1	0.012	0.2	0.2	0.5
12.7	0.012	0.2	0.11	0.6	12.7	0.012	0.19	0.11	0.61
11.23	0.012	0.19	0.1	0.62	11.23	0.012	0.18	0.09	0.63
9.52	0.012	0.17	0.08	0.63	9.52	0.012	0.16	0.07	0.65
23.1	0.015	0.2	0.18	0.49	23.1	0.015	0.19	0.17	0.52
12.7	0.015	0.19	0.09	0.63	12.7	0.015	0.18	0.09	0.64
11.23	0.015	0.18	0.08	0.64	11.23	0.015	0.17	0.08	0.66
9.52	0.015	0.16	0.06	0.65	9.52	0.015	0.16	0.06	0.67

Figure 7. Investigation of the riprap stability based on the froude number at instability downstream of the spillways.

Figure 8. Relative energy loss in all of the spillways.

Figure 9. Comparison of the results of this study with those obtained by Steiner, Heler, Hager, and Minor (2008).

Figure 10. Investigation of the riprap stability based on the relative diameter.

Figure 11. Comparison of the results of this study with the results obtained by some other researchers.

Figure 12. The effect of relative particle diameter based on the froude number.

Table 2. Estimating the parameters of eq. (4), for the four spillways categories studied.

Parameter	Estimation	Std. error	Min	Max
Spillway with simple flip bucket
A	1.671	1.47E + 07	−3.11E + 07	3.11E + 07
B	−41.029	5.84E + 07	−1.23E + 08	1.23E + 08
C	4.292	0.293	−4.911	−3.673
Spillway with dentated flip bucket
A	1.446	3.45E + 07	−7.28E + 07	7.28E + 07
B	−56.518	9.36E + 07	−1.98E + 08	1.98E + 08
C	4.878	0.773	3.248	6.508
Spillway with simple triangular sill
A	1.61	7.445E5	−1.571E6	1.57079
B	−47.992	8.687E7	−1.833E8	1.833E8
C	4.636	0.140	−0.334	0.258
Spillway with dentated triangular sill
A	1.870	3.847E7	−8.116E7	8.116E7
B	−49.370	1.137E8	−2.398E8	2.398E8
C	4.477	0.616	3.178	5.777

Table 3. The statistical analysis of the suggested equations for estimation of the relative particle diameter.

	Relation	RMSE	R^2	% Error
Simple flip bucket	1	0.0316	0.872	0.214
Simple triangular sill	1	0.0774	0.590	0.160
Dentated flip bucket	1	0.0447	0.564	0.173
Dentated triangular sill	1	0.0316	0.616	0.159

Figure 13. Correlation between the measured relative particle diameters and the values calculated.

Table 4. Comparison of the results of the present study with those of the other researchers.

The conducted research	RMSE atmovement threshold
Present study, flip bucket Present study, triangular sill	0.032 0.077
Present study, dentated flip bucket Present study, dentated triangular sill	0.045 0.032
New Zealand and Australia Transport Agency (1994)	0.017
Simons, D.B. and G. L. Lewis. (1971)	0.033
Pagan-Ortiz, J. E.) 1991(, support with round-tipped wall	0.046
Pagan-Ortiz, J. E.) 1991(, support with vertical wall	0.07

Steiner, R., Heler, V., Hager, W. H., & Minor, H. E. (2008). Deflector ski jump hydraulics. Journal of Hydraulic Engineering, 134(5), 571–562. doi:10.1061/(ASCE)0733-9429(2008)134:5(562)

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