Sediment transport and tractive force approach

Sediment transport in canals

Sediment moves as bed load (rolling, sliding, saltating along the bed) and suspended load (carried up by turbulence). If flow is too slow, sediment settles (silting, loss of capacity); if too fast, it scours the bed and banks. A canal is stable when neither occurs. The movement starts when the tractive force (shear stress) on the bed exceeds the critical value for the particles.

Tractive force approach

Tractive force is the drag of flowing water on the wetted perimeter per unit area:

$$\tau_0 = \gamma R S$$

For a wide channel $R \approx D$:

• Maximum on the bed: $\tau_b = \gamma D S$ (about $0.97\gamma DS$).
• Maximum on the sides: $\tau_s = 0.75\gamma D S$.

Critical (permissible) shear for non-cohesive soil comes from Shields' criterion:

$$\tau_c = \theta_c(\gamma_s - \gamma)d,\qquad \theta_c \approx 0.047$$

or from tables/charts (Lane) for the soil type.

Side slope stability

A particle on a slope $\theta$ (angle with horizontal) with angle of repose $\phi$ resists a smaller shear than on the bed:

$$K = \frac{\tau_{c,\text{side}}}{\tau_{c,\text{bed}}} = \cos\theta\sqrt{1 - \frac{\tan^2\theta}{\tan^2\phi}} = \sqrt{1 - \frac{\sin^2\theta}{\sin^2\phi}}$$

Design steps

1. Obtain $Q$, $S$, soil data ($d$, $\phi$), $n$ and side slope $z$.
2. Compute permissible $\tau_c$ for bed and $K\tau_c$ for side.
3. Bed condition: $\gamma D S \le \tau_c \Rightarrow D \le \dfrac{\tau_c}{\gamma S}$. Side condition: $0.75\gamma DS \le K\tau_c \Rightarrow D \le \dfrac{K\tau_c}{0.75\gamma S}$. The smaller $D$ governs.
4. Using that $D$, find $B$ from Manning's equation so that the section carries $Q$.
5. Check the actual stresses on bed and side against the permissible values and adjust if necessary.

Merits and limits

The approach is rational for canals in coarse, non-cohesive material (stable channels) where there is little sediment inflow, whereas regime theories (Kennedy/Lacey) suit alluvial canals that carry silt. It needs reliable soil data and does not consider the sediment inflow.