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Title: Converging stepped spillways: Simplified momentum analysis approach

Author
item Hunt, Sherry
item TEMPLE, DARREL - Retired ARS Employee
item ABT, STEVEN - Colorado State University
item Kadavy, Kem
item Hanson, Gregory

Submitted to: Journal of Hydraulic Engineering
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/23/2012
Publication Date: 9/12/2012
Citation: Hunt, S.L., Temple, D.M., Abt, S.R., Kadavy, K.C., Hanson, G.J. 2012. Converging stepped spillways: Simplified momentum analysis approach. Journal of Hydraulic Engineering. 138(9):796-802.

Interpretive Summary: Roller compacted concrete (RCC) stepped spillways are growing in popularity for providing overtopping protection for aging dams with inadequate spillway capacity and for the construction of new dams. Site conditions including topography, the presence of residential and industrial development, and rock formations often dictate that these spillways converge. Convergence is defined as a narrowing of the spillway from the crest section to the spillway chute outlet. This narrowing increases the flow depth along the spillway walls and alters the stilling basin design for dissipation of flow energy to prevent erosion downstream. An equation was developed for predicting the minimum vertical wall height necessary to prevent spillway wall overtopping in converging stepped spillways. This expression is a function of flow depth, centerline velocity, chute slope, and convergence angle. A three-dimensional stepped spillway model with an ogee crest and convergence ranging from 0 to 70 degrees was constructed. The data obtained from this model was used to test and refine the equation developed. This resulting relationship provides design engineers with a method for determining minimum wall height necessary to contain the flow in converging stepped spillways within the range of conditions tested.

Technical Abstract: Roller compacted concrete (RCC) stepped spillways are growing in popularity for providing overtopping protection for aging watershed dams with inadequate auxiliary spillway capacity and for the construction of new dams. Site conditions, such as limited right-of-way, topography, and geological formations, often dictate that these spillways converge. Convergence increases the flow depth near the training walls and alters the stilling basin design requirements as compared to traditional straight spillways. A simplified control volume momentum analysis is presented for predicting the minimum vertical training wall height necessary to prevent wall overtopping in converging stepped spillways. An expression is developed to predict vertical training wall height as a function of flow depth, centerline velocity, chute slope, and convergence angle. A three-dimensional 3(H):1(V) sloping stepped spillway model with an ogee crest and convergence ranging from 0 to 70 degrees was constructed to verify this relationship. The evaluation showed approximately 1% error for convergences less than or equal to 30 degrees and slightly larger errors for greater convergence angles. A correction factor was developed as a function of the convergence angle to provide a more universal relationship applicable for all convergences for this particular data set (i.e. convergence from 0 to 70 degrees, chute slope = 3(H):1(V), step height = 0.3 m, and no air entrainment). This relationship provides design engineers with a method for determining minimum training wall height requirements under non-air entrained flow conditions.