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Effect of apron length on local scour at the downstream of grade control structures with labyrinth planform

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Abstract

Grade control structures are commonly used for river restoration projects by changing the upstream river bed slope and the approaching flow conditions. Thus, a safe design of grade control structures needs to consider several aspects especially scour process. In the current study, effects of the apron length at the downstream of grade control structures with trapezoidal labyrinth planforms on the main scour parameters like maximum scour depth and length have been experimentally investigated. Experiments are conducted in clear water conditions, over a wide range of upstream flow discharges and two downstream tailwater depths. The trapezoidal labyrinth planform weirs had two and three cycles with different sidewall angles, width and length of cycles in the flow direction. The comparison of results showed that by installing the apron with a length of B (length of the cycle in the direction of flow), the maximum scour depth decreased 34% on average. By increasing the apron’s length to B/HF + 1/2 and B/HF + 1 (HF = height of flow downstream sedimentary bed), the maximum scour depth reduced 62% and 79%, respectively. In addition, to estimate the effect of an apron on the reduction of scour depth downstream of trapezoidal-labyrinth grade control structures, a regression relationship was derived to estimate the desired parameter with acceptable accuracy.

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Abbreviations

\(A\) (L):

Apex width of cycles

\(B\) (L):

Length of cycles

\(C_{0}\) :

Velocity coefficient and is equal to 0.672

\(d\) (L):

Sediment diameter

\(d_{s}\) (L):

Equilibrium scour depth

\(d_{st}\) (L):

Temporal scour depth

F 0 :

Densmetric Froude numbers, defined as \(F_{0} = U_{0} /(\Delta gd)^{0.5}\)

\(h_{0}\) (L):

Height of weirs above tailwater level

\(h_{t}\) (L):

Tailwater depth

\(H_{F}\) (L):

Height of falling

\(g\) (LT−2):

Gravitational acceleration

\({\text{G}}_{{\text{s}}} { = }{{\rho_{s} } \mathord{\left/ {\vphantom {{\rho_{s} } \rho }} \right. \kern-\nulldelimiterspace} \rho }\) :

Relative density of sediments

\(I_{Exp}\) and \(\overline{I}_{Exp}\) (L):

The experimental and average of experimental data, respectively

\(I_{c}\) (L):

Computed data

\(L_{e}\) (L):

Effective weir length

\(L_{A}\) (L):

Apron length

\(P\) (L):

Weir height

\(t\) (T):

Time

\(t_{e}\) (T):

Equilibrium scour time

\(U_{0}\) (LT−1):

Velocity of jet when it enters tailwater

\(U_{c}\) (LT−1):

Critical flow velocity

\(W\) (L):

Width of cycles

\(y_{0}\) (L):

Thickness of jet entering tailwater

\(y_{0}\) (L):

Critical flow depth

\(y_{e}\) (L):

End depth

\(\rho\) :

(ML−3) Mass density of water

\(\rho_{s}\) :

(ML−3) Mass density of sediments

\(\vartheta\) :

(L2T−1) Kinematic viscosity of water

\(\alpha\) :

Downstream cycle sidewall angle

∆ :

Gs-1

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Authors and Affiliations

  1. Department of Water Engineering, Faculty of Agriculture Science, University of Guilan, Rasht, Iran

    Mahdi Esmaeili Varaki, Mohammad Sedaghati & Behnam Shafei Sabet

  2. Department of Water and Environmental Engineering, CSBRC Research Center, University of Guilan, Rasht, Iran

    Mahdi Esmaeili Varaki

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  1. Mahdi Esmaeili Varaki
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  2. Mohammad Sedaghati
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  3. Behnam Shafei Sabet
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Correspondence to Mahdi Esmaeili Varaki.

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Responsible Editor: Amjad Kallel

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Varaki, M.E., Sedaghati, M. & Sabet, B.S. Effect of apron length on local scour at the downstream of grade control structures with labyrinth planform. Arab J Geosci 15, 1240 (2022). https://doi.org/10.1007/s12517-022-10522-7

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  • DOI: https://doi.org/10.1007/s12517-022-10522-7

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