Channel Lining Design

Open Channel Lining Design

Select and size erosion protection for open channels using the FHWA HEC-15 tractive-force method. This guide covers applied and permissible shear stress, the four major flexible-lining families (rock, vegetative, RECP, gabion), bend-induced shear amplification, and the full design procedure — including a comparison of lining types and integration with Channel Analysis.

Introduction

Channel lining design is the process of selecting and sizing erosion protection materials for open channels. Whenever water flows in a channel, it exerts shear forces on the channel bed and sides. If these forces exceed the resistance of the channel boundary material, erosion occurs — leading to channel widening, deepening, migration, and potential structural failure of adjacent infrastructure.

Erosion protection is critical for constructed channels (roadside ditches, stormwater conveyances, spillway chutes) and for natural channels downstream of hydraulic structures where flow conditions have been altered. The consequences of inadequate protection range from routine maintenance headaches to catastrophic failures that endanger life and property.

The FHWA HEC-15 tractive-force method is the industry-standard approach for flexible channel-lining design. It provides a rational, physics-based framework for comparing the shear stress that flowing water applies to the channel boundary against the permissible shear stress that a given lining material can withstand.

What this guide covers

This guide explains the engineering principles behind the Channel Lining Design calculator. It covers the tractive-force design philosophy, applied and permissible shear-stress calculations for four flexible-lining types (rock, vegetation, RECP, and gabion), bend effects, and step-by-step design procedures. Rigid linings (concrete, asphalt, grouted stone) are treated as permissible-velocity structures and fall outside the HEC-15 scope — refer to SANRAL Drainage Manual Chapter 8 for rigid-lining design.

Design Philosophy

The tractive-force approach is conceptually simple: the lining is adequate when its resistance exceeds the force applied to it. Formally, this is expressed as a comparison of two shear stresses:

$$\tau_{p} \;\ge\; \mathrm{SF} \times \tau_{d}$$

Tractive-force design criterion

Where:

• $\tau_d$ = applied (design) shear stress from the flowing water (Pa or N/m²)
• $\tau_p$ = permissible shear stress of the lining material (Pa or N/m²)
• $\mathrm{SF}$ = safety factor (typically 1.0 to 1.5, depending on consequences of failure)

If the permissible shear stress exceeds the factored applied shear stress, the lining is adequate. If not, the designer must choose a more resistant lining, reduce the channel slope, or modify the channel geometry to reduce the applied shear.

When to use channel lining design

• Constructed channels conveying stormwater, irrigation water, or spillway flows.
• Roadside ditches and median channels along highways.
• Channels downstream of culvert outlets, energy dissipators, or dam spillways.
• Stream-bank stabilisation at bridge abutments and other structures.
• Any channel where the native material cannot resist the design-flow shear stress.

Safety factor selection

Consequence of Failure	Recommended SF
Low (minor maintenance)	1.0
Moderate (property damage)	1.2 – 1.3
High (structural damage, public safety)	1.3 – 1.5

Practical safety factors

For most roadside drainage channels, a safety factor of 1.0 is acceptable because the consequences of lining failure are limited to additional maintenance. For channels protecting critical infrastructure (bridge approaches, dam spillways), use 1.3 to 1.5 to account for uncertainty in flow estimates and material properties.

Applied Shear Stress

When water flows in a channel under uniform-flow conditions, the gravitational component of the water weight acting along the channel bed creates a shear force on the channel boundary. This boundary shear stress varies across the cross-section: it is highest on the channel bed and lower on the side slopes.

Bed Shear

The maximum shear stress occurs at the channel bed. For uniform flow, the bed shear stress is given by HEC-15 Equation 3.1:

$$\tau_{d} \;=\; \gamma \cdot d \cdot S_{0}$$

HEC-15 bed shear stress (Eq. 3.1)

Where:

• $\gamma$ = unit weight of water = 9 810 N/m³ (at standard conditions)
• $d$ = maximum flow depth in the channel (m)
• $S_0$ = longitudinal bed slope of the channel (m/m)

This equation follows directly from the balance of forces on a control volume of water: the weight component along the channel (proportional to $\gamma$, $d$, and $S_0$) is balanced by the shear force on the boundary. It is the foundation of all lining design calculations.

Depth vs hydraulic radius

HEC-15 uses flow depth ($d$) rather than hydraulic radius ($R$) in the shear-stress equation. For wide channels where the width-to-depth ratio exceeds about 10, $R \approx d$ and the results are nearly identical. For narrower channels, using depth provides a conservative (higher) estimate of shear stress.

Side Slope Shear

The shear stress on the channel side slopes is lower than the bed shear stress. HEC-15 applies a reduction factor $K_1$ that depends on the side-slope geometry:

$$\tau_{\mathrm{side}} \;=\; K_1 \cdot \gamma \cdot d \cdot S_{0}$$

Side-slope shear stress

The factor $K_1$ is typically in the range 0.7 to 0.8 for trapezoidal channels. For a channel with a bottom-width-to-depth ratio ($B/d$) of 4, $K_1 \approx 0.75$ — meaning the side-slope shear is about 75% of the maximum bed shear. $K_1$ increases toward 1.0 for very narrow channels and decreases for very wide channels.

B/d Ratio	$K_1$ (Side Shear Factor)
1	0.77
2	0.74
4	0.75
6	0.76
≥ 8	0.76 – 0.78

Side-slope stability

For rock and gabion linings on steep side slopes, the permissible shear stress on the side slope must also be reduced to account for the gravitational component acting down the slope. This is handled through the angle-of-repose correction (see the Rock Lining section below).

Lining Types

The HEC-15 methodology covers four major categories of flexible channel lining. Each has distinct performance characteristics, cost profiles, and application niches. The following subsections describe each lining type, its permissible-shear calculation, and practical design guidance.

Rock Lining (Riprap / Cobble / Gravel)

Rock lining is the most widely used flexible erosion-protection method for channels with moderate to high shear stresses. It consists of a layer of graded stone (riprap) placed on the channel bed and sides, often over a geotextile filter fabric to prevent fine material from piping through the rock voids.

When to use:

• Channels with applied shear stresses exceeding 50 Pa.
• Steep channels (slopes > 2%) where vegetative linings fail.
• Permanent protection with a design life of 50+ years.
• Channels requiring immediate protection (no establishment period).
• Spillway chutes, dam toes, and culvert outlet protection.

Permissible shear stress

The permissible shear stress for rock lining is based on the Shields stability criterion, relating the critical shear to the stone size and submerged weight:

$$\tau_{p} \;=\; F^{*} \cdot (\gamma_{s} - \gamma_{w}) \cdot D_{50}$$

Shields permissible shear for rock lining

Where:

• $F^{*}$ = Shields parameter (dimensionless stability coefficient)
• $\gamma_s$ = unit weight of rock (typically 25 500 – 26 500 N/m³)
• $\gamma_w$ = unit weight of water (9 810 N/m³)
• $D_{50}$ = median stone diameter (m) — the size for which 50% of the rock by weight is smaller

Shields parameter ($F^*$)

Rock Type	F* Range	Typical F*
Crushed angular	0.047 – 0.10	0.082
Angular to sub-angular	0.06 – 0.12	0.094
Rounded (river cobble)	0.03 – 0.06	0.047

Angular vs round rock

Angular and crushed rock interlock better than rounded river cobble, giving significantly higher permissible-shear values. Always specify angular or sub-angular rock for high-shear applications. Round stones are only suitable where shear stresses are low and aesthetics are a priority.

Rock shape and angle of repose

Rock shape affects the angle of repose ($\phi$), which is the steepest angle at which loose rock remains stable. This angle determines the side-slope shear-reduction factor.

Rock Shape	Angle of Repose ($\phi$)
Very angular, crushed	40° – 42°
Angular	38° – 40°
Sub-angular to sub-rounded	34° – 38°
Rounded	30° – 34°

The side-slope stability factor ($K_2$) reduces the permissible shear on side slopes to account for the gravitational component acting down the slope:

$$K_{2} \;=\; \sqrt{ 1 - \frac{\sin^{2}\theta}{\sin^{2}\phi} }$$

Side-slope stability factor

where $\theta$ is the channel side-slope angle (from horizontal) and $\phi$ is the angle of repose. The side-slope permissible shear becomes $\tau_{p,\mathrm{side}} = K_{2} \cdot \tau_{p}$.

Side-slope limits

The channel side-slope angle ($\theta$) must always be less than the angle of repose ($\phi$). If $\theta \to \phi$, $K_2 \to 0$ and the rock is unstable regardless of shear stress. As a practical rule, the side slope should not be steeper than about 2H:1V (26.6°) for most rock linings.

Manning’s n for rock lining

The roughness of rock lining varies with the ratio of flow depth to stone size. HEC-15 provides the following relationship:

$$n \;=\; \alpha \cdot D_{50}^{1/6}$$

Manning's n for rock lining

where $\alpha \approx 0.0395$ (SI units with $D_{50}$ in metres). The roughness coefficient typically ranges from 0.025 for small gravel ($D_{50} = 25$ mm) to 0.060 for large riprap ($D_{50} = 500$ mm). Larger rock creates more flow resistance, so the same channel carries less water per unit area.

South African rock gradation classes

In South African practice, rock for erosion protection is classified by nominal stone diameter following SANRAL specifications. Common classes include:

Class	$D_{50}$ (mm)	Typical Application
Gravel	25 – 75	Low-shear channels, filter layers
Light riprap	100 – 200	Roadside ditches, minor channels
Medium riprap	200 – 350	Stormwater channels, culvert outlets
Heavy riprap	350 – 500	Spillway chutes, high-velocity channels
Very heavy riprap	500 – 750	Dam toes, extreme shear applications

Rock-layer thickness and gradation

The minimum riprap layer thickness should be at least $1.5 \cdot D_{50}$ (or $1.0 \cdot D_{100}$, whichever is greater). This ensures adequate coverage, interlocking, and filter separation. Always specify a well-graded rock with $D_{85}/D_{15}$ between 2.0 and 6.0. Place over a geotextile or graded granular filter to prevent piping of fines.

Vegetative Lining

Vegetative linings use established grass or other ground cover to protect the channel boundary. The root system binds the soil, and plant stems increase roughness to slow the flow and reduce shear on the underlying soil. Vegetation is the most common lining for low-gradient channels in residential and agricultural settings.

When to use:

• Channels with applied shear stresses below approximately 100 Pa (well-established grass).
• Low to moderate channel slopes (typically < 5%).
• Applications where aesthetics and environmental integration are important.
• Situations where long-term maintenance (mowing) is feasible.
• Temporary erosion protection during construction phases.

Permissible shear stress

The permissible shear for vegetative linings depends on both the soil type and the vegetation coverage factor. HEC-15 uses a combined approach:

$$\tau_{p} \;=\; \tau_{p,\mathrm{soil}} \cdot C_{f}$$

Vegetative lining permissible shear

Where:

• $\tau_{p,\mathrm{soil}}$ = base permissible shear of the underlying soil
• $C_f$ = vegetation coverage factor (enhancement multiplier, typically 1.5 to 5.0)

Vegetation retardance classes

HEC-15 classifies vegetation into five retardance classes (A through E) based on stem height and density. These classes determine the Manning’s $n$ value, which varies with flow depth:

Class	Description	Stem Height	n Range
A	Very tall, dense grass (e.g. weeping lovegrass)	> 750 mm	0.10 – 0.40
B	Tall grass (e.g. bermuda, tall fescue)	300 – 600 mm	0.06 – 0.20
C	Medium grass (e.g. mowed bermuda)	150 – 300 mm	0.04 – 0.12
D	Short grass (e.g. closely mowed lawn)	50 – 150 mm	0.03 – 0.08
E	Very short, sparse vegetation	< 50 mm	0.02 – 0.05

Soil type considerations

The underlying soil type is critical because vegetation does not fully protect the soil during extreme events when stems are flattened. Base permissible shear stresses for bare soil:

Soil Type	$\tau_{p,\mathrm{soil}}$ (Pa)
Non-cohesive fine sand ($D_{75} < 1.3$ mm)	1 – 3
Non-cohesive coarse sand / gravel	3 – 10
Cohesive lean clay (PI = 10 – 20)	5 – 10
Cohesive stiff clay (PI > 20)	10 – 20

Establishment period

Vegetative linings provide no protection until the vegetation is fully established (typically 6 to 12 months). During construction and establishment, the channel must either be protected with temporary measures (RECP, erosion blankets) or only exposed to low flows. Design for the worst-case bare-soil condition if temporary protection is not provided.

Maintenance requirements

Vegetative linings require ongoing maintenance to remain effective:

• Regular mowing to maintain the design retardance class.
• Re-seeding of bare or damaged areas before the wet season.
• Weed and invasive-species control.
• Fertilisation and irrigation during droughts (especially during establishment).
• Sediment removal where significant deposition occurs.

RECP Lining — Rolled Erosion Control Products

RECPs are manufactured products that are rolled out on the channel surface to provide immediate erosion protection. They range from temporary biodegradable blankets to permanent turf reinforcement mats (TRMs) that work in combination with established vegetation.

When to use:

• Temporary protection during vegetation establishment (construction phase).
• Channels with moderate shear stresses (20 – 300 Pa, depending on product type).
• Steep slopes where grass seed alone would wash away before germination.
• Environmentally sensitive areas where vegetation is the long-term goal.
• Applications requiring immediate protection without heavy equipment access.

Types of RECPs

Type	Description	$\tau_p$ (Pa)	Lifespan
Open-weave textile (OWT)	Jute, coir, or straw netting	20 – 55	6 – 24 months
Erosion control blanket (ECB)	Straw, coconut, or excelsior fibre in a degradable net	45 – 100	1 – 3 years
Turf reinforcement mat (TRM)	Permanent UV-stable polymer matrix	100 – 300+	Permanent
TRM-W (vegetated TRM)	TRM with fully established grass	300 – 500+	Permanent

Permissible shear calculation

RECP permissible shear depends on the product type and underlying soil. For unvegetated RECPs, the permissible shear is the product’s rated threshold. For vegetated RECPs (TRMs with established grass), the combined permissible shear is:

$$\tau_{p} \;=\; \tau_{p,\mathrm{product}} + \tau_{p,\mathrm{veg}}$$

Combined permissible shear for vegetated RECPs

Where $\tau_{p,\mathrm{product}}$ is the manufacturer’s tested permissible shear for the bare product, and $\tau_{p,\mathrm{veg}}$ is the additional shear resistance provided by the established vegetation. TRMs with fully established grass can achieve combined permissible shear values exceeding 300 Pa.

Product selection

Always request independent test data (per ASTM D6460 or equivalent) for RECP permissible-shear values. Manufacturer claims can vary significantly. For critical applications, use products tested at accredited laboratories with documented performance data.

Gabion Lining

Gabion mattresses are flat, rectangular wire-mesh baskets filled with rock, placed as a continuous lining on the channel bed and sides. The wire mesh provides structural confinement that significantly increases the erosion resistance compared to loose riprap of the same stone size. Gabions also allow vegetation to grow through them, improving long-term aesthetics and ecological value.

When to use:

• Steep channels with high velocity where loose riprap may be displaced.
• Applications requiring thinner lining than equivalent loose riprap.
• Sites where smaller, locally available stone is available (gabion confinement allows use of smaller rock).
• Channels where ecological integration and habitat creation are priorities.
• Curved channels where gabion mattresses can conform to the bank shape.

Permissible shear stress

The permissible shear for gabion-mattress lining is based on both the mattress thickness and the stone-fill size. The HEC-15 formula is:

$$\tau_{p} \;=\; 0.0091 \cdot (\gamma_{s} - \gamma_{w}) \cdot (t + D_{50})$$

Gabion mattress permissible shear

Where:

• $t$ = gabion mattress thickness (m)
• $D_{50}$ = median stone-fill diameter (m)
• $\gamma_s$ = unit weight of rock fill (N/m³)
• $\gamma_w$ = unit weight of water (9 810 N/m³)
• 0.0091 = empirical coefficient from gabion stability testing

Mattress thickness selection

Thickness (mm)	Typical $D_{50}$ (mm)	Approx. $\tau_p$ (Pa)	Application
150	75 – 100	35 – 40	Low shear, channel banks
230	100 – 150	55 – 65	Moderate channels
300	100 – 200	70 – 85	Major stormwater channels
500	150 – 250	100 – 120	High-velocity channels, spillways

Rock-fill requirements

• Stone must be hard, durable, and weather-resistant (not susceptible to slaking or freeze-thaw degradation).
• $D_{50}$ should be between 1.0 and 2.0 times the mesh opening size.
• $D_{85}/D_{15}$ ratio should be between 1.5 and 3.5 for dense packing.
• Minimum stone specific gravity of 2.5 (preferably > 2.6).
• Wire mesh should be galvanised and PVC-coated for corrosive or marine environments.

Gabion vs loose riprap

For the same stone size, gabion mattresses provide significantly higher permissible shear than loose riprap because the wire mesh prevents individual stone displacement. This means gabions can use smaller, more readily available stone to achieve the same erosion resistance. However, gabions have higher installation costs due to basket assembly and stone hand-packing.

Bend Effects

Channel bends create secondary currents that redirect flow toward the outer bank, significantly increasing the local shear stress. This is one of the most common causes of channel-lining failure in practice. HEC-15 addresses this through a bend shear multiplier.

Bend shear multiplier ($K_b$)

The bend multiplier increases the applied shear stress on the outer bank of a bend:

$$\tau_{d,\mathrm{bend}} \;=\; K_{b} \cdot \tau_{d}$$

Bend-adjusted applied shear

The multiplier $K_b$ depends on the ratio of the channel centreline bend radius ($R_c$) to the top width of flow ($T$):

$R_c / T$	$K_b$	Bend Classification
< 2	2.0	Very tight bend
2 – 3	1.8 – 2.0	Tight bend
3 – 5	1.5 – 1.8	Moderate bend
5 – 10	1.2 – 1.5	Gentle bend
> 10	1.0	Effectively straight

Protection length downstream of bends

The increased shear from a bend persists for a significant distance downstream. HEC-15 recommends extending the bend protection for a length $L_p$ downstream of the bend exit:

$$L_{p} \;=\; K_{b} \cdot \frac{R_{c}}{T}$$

Downstream bend-protection length

For tight bends ($R_c/T < 3$), the elevated shear may persist for 5 to 10 channel widths downstream. It is common practice to extend the heavier lining for at least this distance before transitioning to the standard lining.

Super-elevation at bends

Flow around a bend creates a water surface that is higher on the outside and lower on the inside. The super-elevation ($\Delta y$) must be considered for freeboard calculations:

$$\Delta y \;=\; \frac{V^{2} \cdot T}{g \cdot R_{c}}$$

Super-elevation at bends

Where:

• $V$ = average flow velocity (m/s)
• $T$ = top width of flow (m)
• $g$ = gravitational acceleration (9.81 m/s²)
• $R_c$ = centreline bend radius (m)

Tight bends are dangerous

Bends with $R_c/T < 2$ can double the applied shear stress on the outer bank. This is where most lining failures occur. Wherever possible, design channel alignments with gentle curves ($R_c/T > 5$). If tight bends are unavoidable, specify a heavier lining for the bend section and extend it well downstream.

Design Procedure

The following step-by-step procedure outlines the complete channel-lining design process using the HEC-15 tractive-force method. The Channel Lining Design calculator automates these steps, but understanding the procedure is essential for interpreting and validating results.

1. Define channel geometry and flow conditions. Establish the channel cross-section (shape, dimensions, side slopes), longitudinal bed slope, and design flow rate. The design flow is typically derived from a hydrological analysis for a specified return period (e.g. 1:50 year for major stormwater channels). Use Channel Analysis to solve for flow depth and velocity.

2. Calculate applied shear stress. Compute the maximum bed shear ($\tau_d = \gamma \cdot d \cdot S_0$) and the side-slope shear ($\tau_{\mathrm{side}} = K_1 \cdot \tau_d$). If the channel has bends, apply the bend multiplier $K_b$ to the outer-bank shear.

3. Select lining type. Based on the magnitude of applied shear stress, project constraints (cost, aesthetics, maintenance), and material availability, select a candidate lining type: rock, vegetation, RECP, or gabion. Use the comparison table below as a starting point.

4. Calculate permissible shear stress. Using the appropriate formula for the selected lining type, compute the permissible shear stress. For rock: use the Shields equation with the chosen $D_{50}$. For vegetation: combine the soil base shear with the coverage factor. For RECP: use the manufacturer’s tested value. For gabion: use the mattress-thickness formula.

5. Apply safety factor. Multiply the applied shear stress by the safety factor appropriate for the consequences of failure (see the Safety Factor Selection table above). The factored applied shear is the demand that the lining must resist.

6. Check adequacy. Verify that $\tau_p \ge \mathrm{SF} \cdot \tau_d$ for both the bed and side slopes. Check both the bed lining and side-slope lining independently, as the controlling condition may differ. The design ratio ($\tau_p / (\mathrm{SF} \cdot \tau_d)$) should be at least 1.0; values between 1.0 and 1.3 are considered efficient.

7. Iterate if needed. If the lining is inadequate, increase the stone size (rock), use a thicker mattress (gabion), select a higher-rated product (RECP), or change the lining type entirely. If the lining is excessively over-designed (design ratio > 2.0), consider downsizing for cost savings. Repeat the check.

8. Consider bend effects. If the channel has bends, check the outer-bank shear with the bend multiplier $K_b$. A heavier lining may be required for bend sections. Determine the protection length downstream of each bend and check freeboard for super-elevation.

9. Determine freeboard. Add freeboard above the design water surface to account for wave action, flow surges, debris, and super-elevation at bends. Typical freeboard is 0.15 to 0.60 m depending on channel size and the consequences of overtopping. Extend the lining to above the freeboard level.

Quick design check

As a rapid preliminary check: if the applied bed shear is < 30 Pa, vegetative lining is likely sufficient. Between 30 and 100 Pa, consider TRMs, gabions, or light riprap. Above 100 Pa, rock riprap or heavy gabions are typically required. This rule of thumb helps narrow the options before detailed analysis.

Comparison of Lining Types

The table below provides a side-by-side comparison of the four flexible-lining types across key design criteria. Use this as a starting point for lining selection, then refine based on project-specific constraints.

Criterion	Rock Riprap	Vegetative	RECP	Gabion
$\tau_p$ range (Pa)	50 – 500+	5 – 100	20 – 300	35 – 120
Manning’s n range	0.025 – 0.060	0.020 – 0.400	0.020 – 0.045	0.025 – 0.040
Relative cost	Medium – High	Low	Low – Medium	Medium – High
Durability	50+ years	Indefinite (with maintenance)	6 months – permanent	25 – 50 years
Aesthetics	Natural stone appearance	Excellent (green channel)	Good (once vegetated)	Good (vegetation through mesh)
Ecological value	Moderate (habitat in voids)	High	Moderate – High	High (diverse habitat)
Installation	Heavy equipment needed	Seeding / sodding	Manual roll-out + anchoring	Manual assembly + fill
Maintenance	Low (periodic inspection)	High (mowing, reseeding)	Low – Medium	Low (wire inspection)
Immediate protection	Yes	No (6 – 12 month establishment)	Yes	Yes

Importing from Channel Analysis

The Channel Lining Design calculator integrates with the Channel Analysis tool. This allows you to define your channel hydraulics first, then import the results directly into the lining-design workflow.

Workflow

1. Channel Analysis: Define your channel geometry, Manning’s $n$, and slope. Solve for normal depth at your design flow rate. Save the calculation.
2. Import: In the Channel Lining Design calculator, use the import feature to pull in the channel geometry, flow depth, velocity, and slope from your saved Channel Analysis calculation.
3. Lining design: With the hydraulic parameters pre-filled, select your lining type, specify lining parameters (stone size, vegetation class, etc.), and run the shear-stress comparison.
4. Iterate: If the lining is inadequate, adjust parameters and re-check without returning to the Channel Analysis tool. The imported hydraulic data remains available for reference.

Manual entry also supported

You do not have to use the import feature. All hydraulic parameters can be entered manually if you have results from another analysis tool, hand calculations, or HEC-RAS output. The import simply saves time and reduces transcription errors.

Related Tools

• Channel Analysis — compute the uniform-flow depth, velocity, and bed shear that feed directly into the lining design.
• GVF Profiles — for non-uniform reaches where the shear stress varies along the channel.
• Weir Analysis — for backwater-producing structures that increase upstream lining demand.
• Culvert Designer — for inlet and outlet protection where roadway channels transition into culverts.

References

• FHWA HEC-15: Kilgore, R.T. and Cotton, G.K. (2005). Design of Roadside Channels with Flexible Linings. Hydraulic Engineering Circular No. 15, Third Edition. Federal Highway Administration, Publication No. FHWA-NHI-05-114.
• FHWA HDS-4: Schall, J.D., Richardson, E.V., and Morris, J.L. (2008). Introduction to Highway Hydraulics. Hydraulic Design Series No. 4, Fourth Edition. Federal Highway Administration.
• USACE. (1994). Hydraulic Design of Flood Control Channels. Engineer Manual EM 1110-2-1601. US Army Corps of Engineers, Washington DC. Complementary guidance on rigid and flexible channel design.
• Chow, V.T. (1959). Open-Channel Hydraulics. McGraw-Hill, New York. Classical derivation of the tractive-force concept (Chapter 7).
• SANRAL Drainage Manual: South African National Roads Agency Limited (2013). Drainage Manual, Sixth Edition. Chapter 8 — Erosion Protection of Open Channels.
• Shields, A. (1936). Application of Similarity Principles and Turbulence Research to Bed-Load Movement. California Institute of Technology, Pasadena (translated from German). Original derivation of the incipient-motion stability parameter used for rock lining.
• CIRIA C683: CIRIA, CUR, CETMEF (2007). The Rock Manual: The Use of Rock in Hydraulic Engineering. Second edition. CIRIA Publication C683. London.
• ASTM D6460: Standard Test Method for Determination of Erosion Control Blanket (ECB) Performance in Protecting Earthen Channels from Stormwater-Induced Erosion. ASTM International, West Conshohocken, PA.

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Open Channel Lining Design