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Modelling Energy Dissipation Over Stepped-gabion Weirs by Artificial Intelligence

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The hydraulics of energy dissipation over stepped-gabion weirs is investigated by carrying out a series of laboratory experiments, building models to explain the experimental data, and testing their robustness by using the data reported by other researchers. The experiments comprise: six different stepped-gabion weirs tested in a horizontal laboratory flume, a wide range of discharge values, two weir slopes (V:H): 1:1 and 1:2, and gabion filling material gravel size (porosity equal to 38 %, 40 % and 42 %). These experimental setups were selected to ensure the development of both the nappe and skimming flow regimes within the measured dataset. The models developed for computing energy dissipation over stepped-gabion weirs comprise: multiple regression equations based on dimensional analysis theory, Artificial Neural Network (ANN) and Gene Expression Programming (GEP). The analysis shows that the measured data capture both flow regimes and the transition in between them and above all, and by using all of the data, it may be possible to identify the range of each regime. Energy dissipation modelled by the ANN formulation is successful and may be recommended for reliable estimates but those by GEP and regression analysis can still serve for rough-and-ready estimates in engineering applications.

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Plate 1


b :

Weir/Spillway width

E 1 :

Energy at the downstream of spillway before hydraulic jump

E 0 :

Total energy at the upstream of Weir/spillway

ΔE = E 0 − E 1 :

Energy difference between upstream and downstream of Weir/spillway

F r :

Froude number = \( {V}_1/\sqrt{g{y}_1} \)

g :

Acceleration due to gravity

h :

Each step height

H w :

The height of the crest of Weir/spillway from flume bed

l :

Each step length

K :

Relative energy dissipation defined as K = (E 0 − E 1)/H w

n :

Stone porosity filled in gabion

q :

Discharge per unit width

Q :


R e :

Reynolds number = V 1 y i /v

S :

Weir/spillway slope (V: H)

V α :

Approach velocity = q/y

V 1 :

Velocity at the toe of the spillway

y 0 :

Depth of flow about 0.60 m upstream of the spillway above its crest

y 1 :

Depth before hydraulic jump at the Weir/spillway toe

y 2 :

Depth after hydraulic jump, and

α :

Weir/spillway angle (degree) with horizontal line.


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Correspondence to Rahman Khatibi.

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Khatibi, R., Salmasi, F., Ghorbani, M.A. et al. Modelling Energy Dissipation Over Stepped-gabion Weirs by Artificial Intelligence. Water Resour Manage 28, 1807–1821 (2014).

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  • Stepped-gabion weir
  • Energy dissipation
  • Artificial intelligence
  • Nappe
  • Skimming and transition regimes