Experimental investigation of erosion processes downstream of block ramps in mild curved channels

Abstract

Eco-friendly low-head river restoration structures such as block ramps are of paramount importance with regard to the control of sediment grade in rivers, particularly in the mountains. They also help in the stabilization of river bed and prevent damages due to excessive downstream erosion by dissipating flow energy. Although the hydraulic characteristics of block ramps in straight channels have been thoroughly studied, there are very less studies dealing with the analysis of scour mechanism downstream of block ramps in curved channels. In fact, to the authors’ best knowledge, there are no studies till date investigating the scour process downstream of block ramps in river bends, involving the effect of tailwater and ramp bed slope. Therefore, this study aims to analyze the hydraulic behaviour of block ramps placed at various positions on a curved channel incorporating the effects of the mentioned parameters. Furthermore, the equilibrium morphology of the resulting downstream scour has been analyzed and classified. A dedicated hydraulic model was constructed, and a large range of in situ hydraulic conditions were simulated. Tests were carried out varying ramp slope and locating the structure at different positions along the channel bend. Data analysis revealed that the scour morphology is essentially three-dimensional and depends on flow characteristics, tailwater level and slightly on its location. Finally, a useful design relationship was also developed to evaluate the maximum scour depth taking into consideration the effect of channel curvature and the tailwater level.

Appendix: dimensional analysis

According to Hoffmans [8] and Bombardelli et al. [2], the theoretical diffusion length (z_max + h₀), i.e., the sum of the maximum scour depth, z_max, and the water depth over the original sediment bed level, h₀, depends on the following variables:

$$z_{max} + h_{0} = f\left( {Q, h_{1} ,B, g,\Delta \rho ,\rho ,d_{90} ,\alpha ,R,S_{0} } \right)$$

(10)

By assuming Q, h₁ and ρ as repeating variables, we obtain the following non-dimensional groups:

$$\varPi_{1} = \frac{{z_{max} + h_{0} }}{{h_{1} }}$$

(11)

$$\varPi_{2} = \frac{B}{{h_{1} }}$$

(12)

$$\varPi_{3} = \frac{{h_{1}^{5} g}}{{Q^{2} }}$$

(13)

$$\varPi_{4} = \frac{\Delta \rho }{\rho }$$

(14)

$$\varPi_{5} = \frac{{d_{90} }}{{h_{1} }}$$

(15)

$$\varPi_{6} = \alpha$$

(16)

$$\varPi_{7} = \frac{R}{{h_{1} }}$$

(17)

$$\varPi_{8} = S_{0}$$

(18)

Let’s now re-arrange some of the non-dimensional groups Π_i as follows:

$$\varPsi_{3} = \sqrt {\frac{1}{{\varPi_{3} }}\frac{1}{{\varPi_{2}^{ 2} }}\frac{1}{{\varPi_{5} }}\frac{1}{{\varPi_{4} }}} = \sqrt {\frac{{Q^{2} }}{{h_{1}^{2} B^{2} gd_{90} \frac{\Delta \rho }{\rho }}}} = \frac{V}{{\sqrt {gd_{90} \frac{\Delta \rho }{\rho }} }} = F_{d90}$$

(19)

$$\varPsi_{5} = \frac{{\varPi_{5} }}{{\varPi_{2} }} = \frac{{d_{90} }}{B}$$

(20)

$$\varPsi_{7} = \frac{{\varPi_{2} }}{{\varPi_{7} }} = \frac{B}{R}$$

(21)

Therefore, the non-dimensional functional relationship can be expressed as follows:

$$\varPi_{1} = f\left( {\varPi_{2} , \varPsi_{3} ,\varPi_{4} ,\varPsi_{5} ,\varPi_{6} ,\varPsi_{7} ,\varPi_{8} } \right)$$

(22)

Considering that B, d₉₀, Δρ and ρ are constant, and that the effect of the non-dimensional group Π₂ (= B/h₁) is negligible, Eq. (22) can be re-written as:

$$\varPi_{1} = f\left( {\varPsi_{3} ,\varPi_{6} ,\varPsi_{7} ,\varPi_{8} } \right)$$

(23)

Or, equivalently:

$$\frac{{z_{max} + h_{0} }}{{h_{1} }} = f\left( {F_{d90} ,\alpha ,\frac{B}{R},S_{0} } \right)$$

(24)

As α has negligible effect on the variable (z_max + h₀)/h₁, the governing functional relationship becomes:

$$\frac{{z_{max} + h_{0} }}{{h_{1} }} = f\left( {F_{d90} ,\frac{B}{R},S_{0} } \right)$$

(25)