Local Scour at Downstream Sloped Submerged Weirs

This paper presents an experimental study of local scour at submerged weirs with different downstream slopes. Thirty-three tests of coarse sand ($d_{50}=0.85\mathrm{mm}$) and 24 tests of fine sand ($d_{50}=0.26\mathrm{mm}$) were carried out in a sand-recirculating flume. The tests for each sand type used four weirs with different downstream weir slopes ($\pi /6$, $\pi /4$, $\pi /3$, and $\pi /2$ to horizontal for the fine sand; $\pi /12$, $\pi /6$, $\pi /4$, and $\pi /2$ to horizontal for the coarse sand). The results show that the upstream scour depth is independent of the downstream weir slope $\beta$. For both sand types, the downstream weir slope has no effect on the downstream scour depth when it is greater than the upstream slope of the downstream scour hole $\theta$. For $\beta <\theta$, the downstream weir surface is partly exposed to flow, resulting in a downstream scour depth at the weir surface $d_w$, which can be increased by the increase in either downstream scour depth or $\theta$. In this situation, the upstream water level rises because of the reduced flow cross-section area, and the overflow jet is deflected to be approximately aligned with the downstream weir surface. For the coarse sand tests, when $\beta =\pi /6$, the effect of the rising upstream water level is predominant because $\beta$ is close to ${\theta }_a$ (time-averaged value of $\theta$). This results in larger downstream scour depths. When $\beta$ is considerably smaller than ${\theta }_a$, the effect of jet deflection starts to be predominant in the coarse sand tests, generating lower downstream scour depths when $U_0/U_c<2.6$. Those two effects balance each other when $2.6<U_0/U_c<3.1$ for $\beta =\pi /12$, resulting in the same downstream scour depths as those for a rectangular weir. For the fine sand tests, the jet deflection effect is predominant because the downstream weir slope has limited effect on the upstream water level. A conservative design method accounting for both effects is proposed for the local scour at downstream sloped submerged weirs.