Plainwater response:

This report presents the findings of a study to develop design guidelines, material specifications and test methods, construction specifications, and construction, inspection, and quality control guidelines for riprap at streams and riverbanks, bridge piers and abutments, and bridge scour countermeasures. Recommendations are provided on a design equation or design approach for each application. Filter requirements, material and testing specifications, construction and installation guidelines, and inspection and quality control procedures are also recommended for each riprap application.

To guide the practitioner in developing appropriate designs for riprap armoring systems for these applications, the findings and recommendations are combined to provide design guideline appendixes for (1) Design and Specification of Rock Riprap Installations and (2) Construction, Inspection, and Maintenance of Rock Riprap Installations. This report will be particularly useful to bridge, hydraulic, and highway engineers, as well as bridge maintenance and inspection personnel responsible for design, construction, inspection, and maintenance of bridges and other highway structures.

Many different techniques are currently used to determine the size and extent of a riprap installation, and existing techniques and procedures for design of riprap protection can be confusing and difficult to apply. Depending on the technique used to size riprap, the required size of stone can vary widely. Most states have specifications for classifying riprap size and gradation, but there is not a consistent classification system or set of specifications that can be used when preparing plans or assembling a specification package for a project.

In addition, various construction practices are employed for installing riprap; many of them are not effective and projects requiring the use of riprap historically have suffered from poor construction practices and poor quality control. The intent of this study was to develop a unified set of guidelines, specifications, and procedures that can be accepted by the state DOTs.

This textbook offers a thorough mechanical analysis of rivers from upland areas to oceans. It scrutinizes state-of-the-art methods, underlining both theory and engineering applications.

Each chapter includes a presentation of fundamental principles, followed with an engineering analysis and instructive problems, examples, and case studies illustrating engineering design. The emphasis is on river equilibrium, river dynamics, bank stabilization, and river engineering. Channel stability and river dynamics are examined in terms of river morphology, lateral migration, aggradation, and degradation.

The text provides a detailed treatment of riverbank stabilization and engineering methods. Separate chapters cover physical and mathematical models of rivers. This textbook also contains essential reading for understanding the mechanics behind the formation and propagation of devastating floods, and offers knowledge crucial to the design of appropriate countermeasures to reduce flood impact, prevent bank erosion, improve navigation, increase water supply, and maintain suitable aquatic habitat.

More than 100 exercises (including computer problems) and nearly 20 case studies enhance graduate-student learning, while researchers and practitioners seeking broad technical expertise will find it a valuable reference. Pierre Y. Julien is Professor of Civil Engineering at Colorado State University.

The Federal Highway Administration document “Highways in the River Environment – Hydraulic and Environmental Design Considerations” was first published in 1975, was revised in 1990, and is now issued as Hydraulic Design Series 6, “River Engineering for Highway Encroachments.” This document has proven to be a singularly authoritative document for the design of highway associated hydraulic structures in moveable boundary waterways. This revised document incorporates many technical advances that have been made in this discipline since 1990. In addition, Hydraulic Engineering Circulars (HEC) 18, 20, and 23, have been published since 1990. This document and the HECs provide detailed guidance on stream instability, scour, and appropriate countermeasures. In HDS-6, hydraulic problems at stream crossings are described in detail and the hydraulic principles of rigid and moveable boundary channels are discussed.

In the United States, the average annual damage related to hydraulic problems at highway facilities on the Federal-aid system is $40 million. Damages by streams can be reduced significantly by considering channel stability. The types of river changes to be carefully considered relate to: ( 1) lateral bank erosion; (2) degradation and aggradation of the streambed that continues over a period of years, and (3) natural short-term fluctuations of streambed elevation that are usually associated with the passage of floods. The major topics are: sediment transport, natural and human induced causes of waterway response, stream stabilization (bed and banks), hydraulic modeling and computer applications, and countermeasures. Case histories of typical human and natural impacts on waterways are analyzed.

This has been superseded by Caltrans New Riprap Classes.

Caltrans Standard Specifications

72-2 ROCK SLOPE PROTECTION

72-2.02A Rock

For method A placement and the class of RSP described, comply with the rock grading shown in the following table:

For method B placement and the class of RSP described, comply with the rock grading shown in the following table:

Rock must have the values for the material properties shown in the following table:

Select rock so that shapes provide a stable structure for the required section. If the slope is steeper than 2:1, do not use rounded boulders and cobbles. Angular shaped rock may be used on any planned slope. Flat or needle shaped rock must not be used unless the individual rock thickness is greater than 0.33 times the length.

72-2.02B Fabric

Fabric must be RSP fabric that complies with the class shown in the following table:

72-4 SMALL-ROCK SLOPE PROTECTION

72-4.02 MATERIALS

Rock must be cobble, gravel, crushed gravel, crushed rock, or any combination of these.

If the rock layer is shown as 7 inches thick, comply with grading shown in the following table:

If the rock layer is shown as 5 inches thick, comply with the grading shown in the following table:

If the rock layer is shown as 4-inches thick, comply with grading shown in the following table:

Granular material must contain at least 90 percent crushed particles when tested under California Test 205.

10.2 RIPRAP APRON

The most commonly used device for outlet protection, primarily for culverts 60 in (1500 mm) or smaller, is a riprap apron. An example schematic of an apron taken from the Central Federal Lands Division of the Federal Highway Administration is shown in Figure 10.4.

Figure 10.4. Placed Riprap at Culverts (per Central Federal Lands Highway Division Detail C251-50). Click images to enlarge.

They are constructed of riprap or grouted riprap at a zero grade for a distance that is often related to the outlet pipe diameter. These aprons do not dissipate significant energy except through increased roughness for a short distance. However, they do serve to spread the flow helping to transition to the natural drainage way or to sheet flow where no natural drainage way exists. However, if they are too short, or otherwise ineffective, they simply move the location of potential erosion downstream. The key design elements of the riprap apron are the riprap size as well as the length, width, and depth of the apron.

Several relationships have been proposed for riprap sizing for culvert aprons and several of these are discussed in greater detail in Appendix D of HEC-14. The independent variables in these relationships include one or more of the following variables: outlet velocity, rock specific gravity, pipe dimension (e.g. diameter), outlet Froude number, and tailwater. The following equation (Fletcher and Grace, 1972) is recommended for circular culverts:

where,

• D₅₀ = riprap size, m (ft)
• Q = design discharge, m³/s (ft³/s)
• D = culvert diameter (circular), m (ft)
• TW = tailwater depth, m (ft)
• g = acceleration due to gravity, 9.81 m/s² (32.2 ft/s²)

Tailwater depth for Equation 10.4 should be limited to between 0.4D and 1.0D. If tailwater is unknown, use 0.4D.

Whenever the flow is supercritical in the culvert, the culvert diameter is adjusted as follows:

where,

• D’ = adjusted culvert rise, m (ft)
• y_n = normal (supercritical) depth in the culvert, m (ft)

Equation 10.4 assumes that the rock specific gravity is 2.65. If the actual specific gravity differs significantly from this value, the D₅₀ should be adjusted inversely to specific gravity.

The designer should calculate D₅₀ using Equation 10.4 and compare with available riprap classes. A project or design standard can be developed such as the example from the Federal Highway Administration Federal Lands Highway Division (FHWA, 2003) shown in Table 10.1 (first two columns). The class of riprap to be specified is that which has a D₅₀ greater than or equal to the required size. For projects with several riprap aprons, it is often cost effective to use fewer riprap classes to simplify acquiring and installing the riprap at multiple locations. In such a case, the designer must evaluate the tradeoffs between over sizing riprap at some locations in order to reduce the number of classes required on a project.

The apron dimensions must also be specified. Table 10.1 provides guidance on the apron length and depth. Apron length is given as a function of the culvert rise and the riprap size. Apron depth ranges from 3.5⋅D₅₀ for the smallest riprap to a limit of 2.0⋅D₅₀ for the larger riprap sizes. The final dimension, width, may be determined using the 1:3 flare shown in Figure 10.4 and should conform to the dimensions of the downstream channel. A filter blanket should also be provided as described in HEC 11 (Brown and Clyde, 1989).

For tailwater conditions above the acceptable range for Equation 10.4 (TW > 1.0⋅D), Figure 10.3 should be used to determine the velocity downstream of the culvert. The guidance in Section 10.3 may be used for sizing the riprap. The apron length is determined based on the allowable velocity and the location at which it occurs based on Figure 10.3.

Over their service life, riprap aprons experience a wide variety of flow and tailwater conditions. In addition, the relations summarized in Table 10.1 do not fully account for the many variables in culvert design. To ensure continued satisfactory operation, maintenance personnel should inspect them after major flood events. If repeated severe damage occurs, the location may be a candidate for extending the apron or another type of energy dissipator.

Design Example: Riprap Apron (CU)

Design a riprap apron for the following CMP installation. Available riprap classes are provided in Table 10.1. Given:

• Q = 85 ft^3/s
• D = 5.0 ft
• TW = 1.6 ft

Solution

Step 1. Calculate D₅₀ from Equation 10.4. First verify that tailwater is within range.

Step 2. Determine riprap class. From Table 10.1, riprap class 2 (D₅₀ = 6 in) is required.

Step 3. Estimate apron dimensions.

From Table 10.1 for riprap class 2,

• Length, L = 4⋅D = 4⋅5 = 20 ft
• Depth = 3.3⋅D₅₀ = 3.3⋅6 = 19.8 in = 1.65 ft
• Width (at apron end) = 3⋅D + (2/3)⋅L = 3⋅5 + (2/3)⋅20 = 28.3 ft

Design Example: Riprap Apron (SI)

Design a riprap apron for the following CMP installation. Available riprap classes are provided in Table 10.1. Given:

• Q = 2.33 m³/s
• D = 1.5 m
• TW = 0.5 m

Solution

Step 1. Calculate D₅₀ from Equation 10.4. First verify that tailwater is within range.

Step 2. Determine riprap class. From Table 10.1, riprap class 2 (D₅₀ = 0.15 m) is required.

Step 3. Estimate apron dimensions.

From Table 10.1 for riprap class 2,

• Length, L = 4⋅D = 4⋅1.5 = 6 m
• Depth = 3.3⋅D₅₀ = 3.3⋅0.15 = 0.50 m
• Width (at apron end) = 3⋅D + (2/3)⋅L = 3⋅1.5 + (2/3)⋅6 = 8.5 m

HEC-15 Section 6.2 – PERMISSIBLE SHEAR STRESS

Values for permissible shear stress for riprap and gravel linings are based on research conducted at laboratory facilities and in the field. The values presented here are judged to be conservative and appropriate for design use. Permissible shear stress is given by the following equation:

where,

• τ_p = permissible shear stress, N/m² (lb/ft²)
• F* = Shield’s parameter, dimensionless
• γ_s = specific weight of the stone, N/m³ (lb/ft³)
• γ = specific weight of the water, 9810 N/m³ (62.4 lb/ft³)
• D₅₀ = mean riprap size, m (ft)

Typically, a specific weight of stone of 25,900 N/m³ (165 lb/ft³) is used, but if the available stone is different from this value, the site-specific value should be used.

Recalling Equation 3.2,

τ_p ≥ SF.τ_d

and Equation 3.1,

τ_d = γ.d.S_o

Equation 6.7 can be written in the form of a sizing equation for D₅₀ as shown below:

where,

• d = maximum channel depth, m (ft)
• SG = specific gravity of rock (γ_s/γ), dimensionless

Changing the inequality sign to an equality gives the minimum stable riprap size for the channel bottom. Additional evaluation for the channel side slope is given in Section 6.3.2.

Equation 6.8 is based on assumptions related to the relative importance of skin friction, form drag, and channel slope. However, skin friction and form drag have been documented to vary resulting in reports of variations in Shield’s parameter by different investigators, for example Gessler (1965), Wang and Shen (1985), and Kilgore and Young (1993). This variation is usually linked to particle Reynolds number as defined below:

where,

• R_e = particle Reynolds number, dimensionless
• V* = shear velocity, m/s (ft/s)
• ν = kinematic viscosity, 1.131×10^-6 m²/s at 15.5 deg C (1.217×10^-5 ft²/s at 60 deg F)

Shear velocity is defined as:

where,

• g = gravitational acceleration, 9.81 m/s² (32.2 ft/s²)
• d = maximum channel depth, m (ft)
• S = channel slope, m/m (ft/ft)

Higher Reynolds number correlates with a higher Shields parameter as is shown in Table 6.1. For many roadside channel applications, Reynolds number is less than 4×104 and a Shields parameter of 0.047 should be used in Equations 6.7 and 6.8. In cases for a Reynolds number greater than 2×105, for example, with channels on steeper slopes, a Shields parameter of 0.15 should be used. Intermediate values of Shields parameter should be interpolated based on the Reynolds number.

Higher Reynolds numbers are associated with more turbulent flow and a greater likelihood of lining failure with variations of installation quality. Because of these conditions, it is recommended that the Safety Factor be also increased with Reynolds number as shown in Table 6.1. Depending on site-specific conditions, safety factor may be further increased by the designer, but should not be decreased to values less than those in Table 6.1.

As channel slope increases, the balance of resisting, sliding, and overturning forces is altered slightly. Simons and Senturk (1977) derived a relationship that may be expressed as follows:

where,

• Δ = function of channel geometry and riprap size.

The parameter Δ can be defined as follows (see HEC-15 Appendix D for the derivation):

where,

• α = angle of the channel bottom slope
• β = angle between the weight vector and the weight/drag resultant vector in the plane of the side slope
• θ = angle of the channel side slope
• Φ = angle of repose of the riprap.

Finally, β is defined by:

where,

• η = stability number.

The stability number is calculated using:

Riprap stability on a steep slope depends on forces acting on an individual stone making up the riprap. The primary forces include the average weight of the stones and the lift and drag forces induced by the flow on the stones. On a steep slope, the weight of a stone has a significant component in the direction of flow. Because of this force, a stone within the riprap will tend to move in the flow direction more easily than the same size stone on a milder gradient. As a result, for a given discharge, steep slope channels require larger stones to compensate for larger forces in the flow direction and higher shear stress.

The size of riprap linings increases quickly as discharge and channel gradient increase. Equation 6.11 (not shown) is recommended when channel slope is greater than 10 percent and provides the riprap size for the channel bottom and sides. Equation 6.8 is recommended for slopes less than 5 percent. For slopes between 5 percent and 10 percent, it is recommended that both methods be applied and the larger size used for design. Values for safety factor and Shields parameter are taken from Table 6.1 for both equations.

HEC-15 Section 6.1 – MANNING’S ROUGHNESS

Manning’s roughness is a key parameter needed for determining the relationships between depth, velocity, and slope in a channel. However, for gravel and riprap linings, roughness has been shown to be a function of a variety of factors including flow depth, D₅₀, D₈₄, and friction slope, S_f. A partial list of roughness relationships includes Blodgett (1986a), Limerinos (1970), Anderson, et al. (1970), USACE (1994), Bathurst (1985), and Jarrett (1984). For the conditions encountered in roadside and other small channels, the relationships of Blodgett and Bathurst are adopted for this manual.

Blodgett (1986a) proposed a relationship for Manning’s roughness coefficient, n, that is a function of the flow depth and the relative flow depth (d_a/D₅₀) as follows (Equation 6.1):

where,

• n = Manning’s roughness coefficient, dimensionless
• d_a = average flow depth in the channel, m (ft)
• D₅₀ = median riprap/gravel size, m (ft)
• α = unit conversion constant, 0.319 (SI) and 0.262 (CU)

Equation 6.1 is applicable for the range of conditions where 1.5 ≤ d_a/D₅₀ ≤ 185. For small channel applications, relative flow depth should not exceed the upper end of this range.

Some channels may experience conditions below the lower end of this range where protrusion of individual riprap elements into the flow field significantly changes the roughness relationship. This condition may be experienced on steep channels, but also occurs on moderate slopes. The relationship described by Bathurst (1991) addresses these conditions and can be written as follows (See Appendix D for the original form of the equation):

where,

• d_a = average flow depth in the channel, m (ft)
• g = acceleration due to gravity, 9.81 m/s² (32.2 ft/s²)
• Fr = Froude number
• REG = roughness element geometry
• CG = channel geometry
• α = unit conversion constant, 1.0 (SI) and 1.49 (CU)

Equation 6.2 is a semi-empirical relationship applicable for the range of conditions where 0.3<d_a/D₅₀<8.0. The three terms in the denominator represent functions of Froude number, roughness element geometry, and channel geometry given by the following equations:

where,

• T = channel top width, m (ft)
• b = parameter describing the effective roughness concentration.

The parameter b describes the relationship between effective roughness concentration and relative submergence of the roughness bed. This relationship is given by:

Equations 6.1 and 6.2 both apply in the overlapping range of 1.5 ≤ d_a/D₅₀ ≤ 8. For consistency and ease of application over the widest range of potential design situations, use of the Blodgett equation (6.1) is recommended when 1.5 ≤ d_a/D₅₀. The Bathurst equation (6.2) is recommended for 0.3<d_a/D₅₀<1.5.

As a practical problem, both Equations 6.1 and 6.2 require depth to estimate n while n is needed to determine depth setting up an iterative process.