---
title: "Sediment transport and tractive force approach"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:sediment-transport-tractive-force"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/sediment-transport-tractive-force
site: BCT Engineering
---

# Sediment transport and tractive force approach

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2069 Bhadra, 10 marks
- Video: [Unit:4 | Design of Canals | Tractive force approach of canal design | Irrigation Engineering | TU,PU](https://www.youtube.com/watch?v=YCJu1hWKmeI) — Prashant YT
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/sediment-transport-tractive-force
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

Explain sediment transport and tractive force approach in canal design.

## Short answer

Sediment transport occurs as bed and suspended load; stability requires tractive force τ = γRS to stay below critical shear from Shields criterion. Design computes permissible depth from bed (τb = γDS) and side (τs = 0.75γDS) conditions, then finds width via Manning's equation. Suitable for coarse non-cohesive material with little sediment inflow.

## Answer

#### 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. When does sediment begin to move?
   A. When velocity is zero
   B. When depth exceeds 1 m
   C. When side slope is 1:1
   D. When tractive force on the bed exceeds the critical value for the particles
   Answer: D. Movement starts at critical shear. (Key point: Sediment movement)

2. What is the average tractive force?
   A. tau0 = gamma R S
   B. gamma D / S
   C. gamma S / R
   D. gamma R^2 S
   Answer: A. Drag of flow per unit wetted area. (Key point: Tractive force)

3. Maximum tractive force on bed and sides is about
   A. bed 0.75, sides 0.97 gamma D S
   B. bed about 0.97 gamma D S, sides 0.75 gamma D S
   C. both gamma D S
   D. bed 0.5, sides 0.5 gamma D S
   Answer: B. The sides carry less stress than the bed. (Key point: Maximum stresses)

4. K = sqrt(1 - sin^2(theta)/sin^2(phi)) represents
   A. Ratio of depth to width
   B. Roughness
   C. Ratio of permissible side shear to permissible bed shear
   D. Silt factor
   Answer: C. Particles on a slope resist less shear. (Key point: Side slope factor)

5. In design, which depth governs?
   A. The larger
   B. The average
   C. Depth from Lacey's formula
   D. The smaller of the bed-limited and side-limited depths
   Answer: D. Both bed and side stresses must be within permissible values. (Key point: Governing depth)

## Related in Irrigation and Drainage Engineering

- [Tractive force design: Q 30](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atractive-q30-slope-13700) — Irrigation and Drainage Engineering, chapter 4, asked 3×
- [Tractive force design: Q 45](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atractive-q45-slope-14500) — Irrigation and Drainage Engineering, chapter 4, asked 3×
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- [Silt excluder, silt ejector, sediment control](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Asilt-excluder-ejector-sediment-control) — Irrigation and Drainage Engineering, chapter 5, asked 10×
- [Design capacity of a canal](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acanal-design-capacity-method) — Irrigation and Drainage Engineering, chapter 4

## Related in other subjects

- [Tractive force design in coarse alluvium, 20 m³/s](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atractive-force-trapezoid-20m3s-d75-2cm) — Hydraulics, chapter 10
- [Tractive force method of channel design](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Atractive-force-method-explain) — Hydraulics, chapter 10, asked 3×
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