7.2 Design of Canals

7.2 Design of Canals

Introduction to Canal Design

Canals are artificial channels constructed to convey water from a source (river, reservoir) to agricultural fields, industries, or municipalities. Their design is a critical task in irrigation engineering, balancing hydraulic efficiency, construction economy, and long-term stability. The primary challenge is to create a channel that maintains its cross-section, carries the design discharge without excessive silting or scouring, and minimizes water losses. This involves selecting an appropriate alignment, determining the stable cross-sectional dimensions (width, depth, slope), and choosing between lined and unlined construction based on soil conditions and water conservation needs.

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1. Canal Types, Network, and Alignment

1.1 Classification of Canals

1. Based on Function:

   • Main/Feeder Canal: Takes off directly from the source (weir, barrage, reservoir). Carries the total design discharge.

   • Branch Canal: Offtakes from the main canal, serving a large block of the command area.

   • Distributary Canal: Takes off from a branch canal, serving a specific distribution area.

   • Minor/Watercourse: Offtakes from a distributary, delivering water directly to field channels.

   • Field Channel: Final outlet delivering water to individual farm plots.

2. Based on Financial Role:

   • Productive Canals: Revenue generated > Maintenance cost.

   • Protective Canals: Revenue < Maintenance cost (built for famine protection).

3. Based on Lining:

   • Lined Canals: Concrete, brick, plastic. Reduce seepage, prevent erosion, allow steeper slopes.

   • Unlined/Alluvial Canals: Excavated in natural soil (alluvium). Subject to silting and scouring.

1.2 Canal Network Layout

1. Gridiron Pattern: Main canal runs along the ridge (watershed), with branches and distributaries taking off on both sides at nearly right angles. Most common as it ensures gravity flow to fields.

2. Herringbone Pattern: Subsidiaries join the main canal obliquely from one side only. Used where ground slopes predominantly to one side.

3. Natural Pattern: Follows natural drainage lines. Rare for irrigation canals as it requires cross-drainage works.

1.3 Canal Alignment Principles

1. Ridge (Watershed) Alignment:

   • Canal is aligned along the ridge/topographic divide.

   • Advantage: Commands maximum area by gravity on both sides; no drainage crossings.

   • Disadvantage: May involve longer routes and heavy earthwork in cutting.

2. Contour Alignment:

   • Canal follows a specific contour line.

   • Advantage: Economical earthwork (balanced cutting and filling).

   • Disadvantage: Does not command full area, requires numerous cross-drainage structures.

3. Side Slope Alignment:

   • Canal aligns perpendicular to contours, along side slope of a valley.

   • Disadvantage: Commands very little area; mainly used for hydropower canals.

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2. Tractive Force Approach of Canal Design

This is a fundamental, scientific approach to designing stable channels, particularly for non-cohesive sediments.

2.1 Concept of Tractive Force ($τ_o$)

1. Definition: The shear stress or drag force per unit area exerted by flowing water on the channel bed and sides.

2. Formula: $τ_o = γ w R S$ Where:

   • $γ_w$ = Unit weight of water (≈ 9810 N/m³).

   • $R$ = Hydraulic Radius (Area/Wetted Perimeter, m).

   • $S$ = Longitudinal bed slope (friction slope).

2.2 Critical Tractive Force ($τ_c$)

1. Definition: The maximum permissible tractive force that will not cause erosion (scour) of the channel boundary material.

2. Factors Affecting $τ_c$:

   • Particle Size & Shape: Larger, angular particles have higher $τ_c$.

   • Particle Density.

   • Cohesion: Cohesive soils (clays) have much higher $τ_c$ than non-cohesive (sands, silts).

2.3 Design Principle for Stability

1. No-Scour Condition: The actual tractive force ($τ_o$) must be less than or equal to the critical tractive force ($τ_c$) of the bed/side material. $τ_o ≤ τ_c$

2. No-Siltation Condition: For canals carrying sediment, the tractive force must also be high enough to prevent deposition by keeping sediment in suspension. This defines a lower limit.

3. Application: This approach is used to determine a stable longitudinal slope (S) and cross-section for a given material. It is the basis for modern USBR design procedures.

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3. Design of Stable Canals (General Procedure)

The goal is to determine the cross-sectional dimensions (Bed Width B, Depth y, Side Slopes z) and longitudinal slope (S) that satisfy:

1. Conveys the design discharge (Q).

2. Remains hydraulically efficient (minimum wetted perimeter for a given area).

3. Maintains stability (no erosion, no excessive silting).

3.1 Key Design Steps

1. Select Side Slope (z:1): Based on soil type.

   • Rock/Cemented: Near vertical (0:1 to 0.25:1).

   • Stiff Clay: 0.5:1 to 1:1.

   • Loose Sandy Soil: 1.5:1 to 3:1.

2. Assume a Trial Depth (y).

3. Determine Area (A) and Hydraulic Radius (R):

   • For trapezoidal section: $A = (B + zy)y$, $P = B + 2y\sqrt{1+z^2}$, $R = A/P$.

4. Apply Uniform Flow Equation (Manning's/Chezy): $Q = \frac{1}{n} A R^{2/3} S^{1/2} \quad \text{(Manning's)}$ Solve for the unknown B or S.

5. Check Stability: Ensure tractive force ($τ_o = γ_w R S$) is within permissible limits for the soil. For cohesive soils, also check permissible velocity.

6. Check for Hydraulic Efficiency: The best hydraulic section (most efficient) is one that conveys maximum discharge for a given area (i.e., has minimum wetted perimeter). For a trapezoid, this occurs when:

   • Top width = 2 × Sloping side length.

   • Hydraulic radius, $R = y/2$.

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4. Design of Alluvial Canals: Kennedy’s and Lacey’s Theory

Alluvial canals carry water laden with silt (fine sediment) and are excavated in erodible alluvial soils. Their design must ensure regime conditions—a state of dynamic equilibrium where over a period, the canal neither silts nor scours.

4.1 Kennedy’s Theory (1895)

1. Core Hypothesis: Silt is kept in suspension primarily by the vertical component of eddies generated from the bed. Side eddies have no role.

2. Key Equation - Critical Velocity ($V_o$): $V_o = 0.55 m D^{0.64}$ Where:

   • $V_o$ = Critical/Non-silting non-scouring velocity (m/sec).

   • $D$ = Depth of flow (m).

   • $m$ = Critical Velocity Ratio (CVR), depends on silt type. Ranges from 0.7 (light silt) to 1.3 (coarse sand).

3. Design Procedure:

   • Assume a trial depth D.

   • Calculate $V_o$ from Kennedy's equation.

   • For a chosen width-depth ratio (B/D), calculate area $A = (B + zD)D$.

   • Calculate actual mean velocity $V = Q/A$.

   • Adjust D iteratively until $V ≈ V_o$.

   • Use Kutter's or Manning's formula to determine the required bed slope S.

4. Limitations:

   • Considers only depth, not silt grade or channel perimeter.

   • No explicit equation for slope.

   • The design procedure is indirect (iterative).

4.2 Lacey’s Theory (1930)

1. Core Hypothesis: A channel is in regime if it carries a constant discharge under uniform flow in an unlimited, incoherent alluvium of the same grade as the transported silt. Silt is kept in suspension by the total force of friction (generating eddies from the entire wetted perimeter).

2. Lacey's Basic Equations: (All in FPS units originally; here converted to metric rationalized forms).

   • Silt Factor ($f$): $f = 1.76 \sqrt{d_{mm}}$, where $d_{mm}$ is mean particle size in mm.

   • Velocity (V): $V = \left( \frac{Q f^2}{140} \right)^{1/6}$

   • Hydraulic Radius (R): $R = \frac{5}{2} \frac{V^2}{f}$

   • Wetted Perimeter (P): $P = 4.75 \sqrt{Q}$

   • Bed Slope (S): $S = \frac{f^{5/3}}{3340 Q^{1/6}}$

3. Design Procedure (Simplified):

   1. Determine silt factor $f$ from particle size.

   2. For design discharge Q, compute velocity V, wetted perimeter P, and slope S using Lacey's equations.

   3. For a trapezoidal section with side slope z:1, solve:

      • $P = B + 2D\sqrt{1+z^2}$

      • $A = (B + zD)D$

      • $R = A/P$ (Where A = Q/V). Solve for B and D.

4. Key Features:

   • Provides direct equations for all parameters: V, P, R, S.

   • Introduces the concept of regime slope.

   • Accounts for silt grade via silt factor $f$.

5. Comparison with Kennedy:

   Aspect	Kennedy's Theory	Lacey's Theory
   Basic Parameter	Depth (D)	Silt Grade (f) & Discharge (Q)
   Velocity Formula	$V_o = 0.55 m D^{0.64}$	$V = (Qf^2/140)^{1/6}$
   Slope	Determined from Kutter/Manning separately	Directly given: $S = f^{5/3}/(3340 Q^{1/6})$
   Design Approach	Indirect, iterative	Direct, systematic

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5. Design of Lined Canals

Lining a canal with an impervious layer (concrete, shotcrete, geomembrane, bricks) is done to:

• Reduce Seepage Losses (Primary benefit, saves 60-80% water).

• Increase Velocity: Smoother surface (lower Manning's n) allows steeper slopes, smaller cross-sections.

• Prevent Erosion & Weed Growth.

• Reduce Maintenance.

5.1 Types of Linings

1. Hard Surface Linings:

   • Cement Concrete (PCC): Most common, durable, high cost.

   • Reinforced Cement Concrete (RCC): For high-pressure or large canals.

   • Shotcrete (Gunite): Sprayed concrete, good for irregular surfaces.

   • Brick/Stone Masonry: Used where materials are locally available.

2. Membrane Linings:

   • Compact Clay: Cheap but less effective.

   • Buried Plastic/Geomembranes (HDPE, PVC): Excellent seepage control, requires protective cover.

5.2 Hydraulic Design of Lined Canals

1. Higher Allowable Velocity: Due to erosion resistance. Typically 1.5 - 2.5 m/s for concrete.

2. Steeper Slopes: Possible due to higher velocity, reducing earthwork.

3. Smaller Cross-section: For same Q, higher V means smaller A.

4. Lower Manning's Roughness (n):

   • Concrete: n ≈ 0.013 - 0.017.

   • Brick: n ≈ 0.015 - 0.017. (Compare to unlined earth: n ≈ 0.020 - 0.025).

5.3 Design Procedure for Lined Canals

1. Select Lining Type → Determine Manning's n.

2. Choose Side Slope (z): Often steeper (e.g., 1:1 to vertical) due to stability of lining.

3. Select Design Velocity (V):

   • Must be less than the maximum permissible for the lining.

   • Must be greater than the minimum to avoid sedimentation (≈0.6-0.9 m/s).

4. Calculate Area: $A = Q/V$.

5. Determine Dimensions: For trapezoidal section, select a suitable width-depth ratio (B/D) (often based on construction ease or best hydraulic section). Solve $A=(B+zD)D$ and $P=B+2D\sqrt{1+z^2}$ for B and D.

6. Calculate Required Slope (S) using Manning's equation: $S = \left( \frac{n Q}{A R^{2/3}} \right)^2$ Check if the slope is practically achievable with topography.

7. Freeboard: Add freeboard (typically 0.3-0.75m) above design water depth for safety against waves, surges.

5.4 Economic Considerations

• Trade-off: Cost of lining vs. value of water saved and reduced maintenance.

• Section Shape: Trapezoidal is most common. Circular or horseshoe for tunnels or pressurized sections.

Conclusion: Canal design evolves from the fundamental tractive force principle to the empirical regime theories for alluvial canals, culminating in the efficient design of lined channels. The choice of theory and lining depends on sediment load, soil characteristics, and economic factors. A well-designed canal achieves the delicate balance between hydraulic capacity, sediment transport equilibrium, and long-term infrastructural stability, forming the backbone of any irrigation system.