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Bridge Scour and Stream Instability Countermeasures: Experience, Selection, and Design Guidance-Third Edition

Design Guideline 17 Riprap Design for Wave Attack

17.1 INTRODUCTION

Environments subject to wave attack frequently require some type of protection to ensure the stability of highway and/or bridge infrastructure. Bank and shoreline protection measures may be classified according to the materials used for construction, the general shape of the device, or their function or application. For example, seawalls, groins, jetties, riprap, and precast concrete armor units have all been used for protecting banks or shorelines against wave-induced erosion. This design guideline provides information on wave characteristics and procedures for designing rock riprap as protection against wave attack.

Rock riprap is commonly used for bank and shoreline protection in rivers, lakes, and estuaries (Figure 17.1). In coastal applications subject to large sea states, very heavy rock slope protection is frequently used. When adequate stone size is not available, precast concrete armor units designed for specific purposes are used. Riprap protection is usually the most economical when stones of sufficient size, quality and quantity are available. The following determinations must be made in the design of rock slope protection for wave attack:

  • Size and specific gravity of stone
  • Foundation depth (below scour depth or to solid rock)
  • Height of riprap placement (at an elevation above wave runup or deep water wave height for protection from splash and spray)
  • Thickness (sufficient to accommodate the largest stones; additional thickness on the slope will not compensate for undersized stones)
  • Filter blanket (uniformly graded stone filter, geotextile filter fabric, or both to prevent embankment material from being washed out through the voids of the stone.
  • Slope of bank or shoreline
  • Uniform gradation is preferred

When used for shore protection, riprap has several advantages compared to other materials. For example, the rough surface of riprap reduces wave runup compared to smoother types of protection. Other types of armor can be used to protect a slope, but stone is frequently the least expensive and more readily available, particularly for projects for which the design wave height is not greater than about 6 feet (1.8 m). Equally important to the success of the protection is the placement of the stone and the underlying filter materials.

A typical section schematic is shown in Figure 17.2 (after AASHTO 2004). The figure shows a toe trench that is typical with all revetments. The toe trench is used to prevent scour from occurring and undermining the revetment. Sometimes a sheetpile wall at the toe of the revetment fulfills this function.

Photograph by S. Douglas of a steep Pacific coast shore line protected by large riprap
Figure 17.1. Riprap revetment in a wave environment, Pacific Coast Highway, California. (from HEC-25, 2nd Edition)

Sketch of riprap shore protection indicating: Geotextile or granular filter substrate under riprapped; maximum shore slope of 1 vertical to 1.5 horizontal; vertical extent of riprap above design still water level which is above normal water level; toe in at base of slope with a large volume of riprap.
Figure 17.2. Riprap shore protection - typical design configuration.

17.2 WAVE CHARACTERISTICS
17.2.1 Wind Waves

In order to properly design riprap to resist wave forces, an understanding of the basic characteristics of waves is necessary. This section provides an introduction to short period waves and is primarily focused on defining the variables and characteristics that are pertinent to predicting wind-induced wave heights in the vicinity of roadways and bridges. The primary variables used in describing waves are wavelength L (the horizontal distance between wave crests), height H (the vertical difference between the wave crest and adjacent trough) and period T (the time between successive crests) (Figure 17.3). The wave speed, or celerity, is the wave length divided by the period (C = L/T). Another factor that affects wave height is the still-water depth D, which is the depth of water if there were no waves.

Sketch of wave characteristics indicating: Wave length L from crest to crest; wave height H - vertical distance from trough to crest; still water depth, D - Vertical distance from ground to midline of wave; celerity direction also indicated.
Figure 17.3. Wave characteristics.

Waves are classified as deep, transitional and shallow water waves. For deep water waves, the wave height is virtually unaffected by the depth and the wave celerity is unaffected by the bottom. For transitional water waves the bottom has some effect on the wave height and celerity. For shallow water waves the celerity is only a function of depth. If the water depth is greater than 0.5 times the wave length, it is considered a deep water wave. If the water depth is less than 0.04 times the wave length, it is a shallow water wave. Transitional water waves are in the range between 0.04 and 0.5 times the water depth.

Waves that are produced by wind are affected by the wind speed, wind duration and fetch. Fetch is the distance that an unobstructed and constant wind, both in terms of speed and direction, acts over a body of water. Land is an absolute limit to fetch but changes in water depth and wind direction can also limit fetch. For very large bodies of water, the change in wind directions due to the circular wind field of a hurricane can limit fetch.

It is possible to predict wave heights for specific wind and waterway conditions. The primary factors are water depth, wind speed and fetch. If the wind duration is not sufficient to produce the computed wave height, then the waves are duration-limited rather than fetch-limited. If the waves are duration-limited, the fetch distance used for computations should be reduced until the required duration equals the actual wind duration.

Wave heights and lengths also have a random nature such that successive waves, even in a constant wind field, do not have the same height or arrive at a consistent interval. Predictive equations have been developed to estimate the significant wave height, Hs, which is defined as the average of the highest one-third of all the waves. Thus the significant wave height Hs can also be denoted H0.333. The heights of larger and less frequent waves can be estimated based on the significant wave height. For example, H0.10, H0.05, H0.01, and H0.001, the average of the ten, five, one, and one-tenth percent highest waves, are approximately 1.27, 1.38, 1.67, and 2.0 times the significant wave height. The frequency of these waves can be estimated by using the wave period (T) divided by the percentage represented as a fraction. Significant wave height can also be defined by a frequency spectrum representation of the water surface elevation that leads to a primary wave height, the notation for the spectral significant wave height is Hs=Hmo.

17.2.2 Determining the Design Wave Characteristics

The recommended methodology for computing wave characteristics is presented in the U.S. Army Corps of Engineers' Coastal Engineering Manual (USACE 2006). The data required to compute wave heights are: wind speed, water depth, and fetch length. Methods for determining the sustained wind speed for estimating the design wave height are provided in the Coastal Engineering Manual.

Because flow depth on a floodplain is typically much smaller than that in the main channel, separate wave height computations should be conducted for the channel and floodplain. The computed wave height is the significant wave height Hs as defined in the previous section. Depending on the riprap sizing equation and the desired safety factor, the significant wave height may be converted to a ten percent, five percent, or one percent wave, by multiplying Hs by 1.27, 1.38, or 1.67, respectively, for use as the design wave height.

For the purposes of computing wave heights at bridges or roadways in rivers, estuaries or lakes during a storm event, such as a hurricane, the definition of fetch requires the greatest judgment. Fetch is the distance of unobstructed wind with fairly uniform speed and direction. Figure 17.4 shows a road embankment and bridge crossing a floodplain and channel. The floodplain is assumed to have some relatively shallow depth of flooding during the storm surge. The wind is assumed to be oriented in the worst-case direction with respect to the channel, but within a range of directions that can be reasonably produced near the peak of the storm surge. The range of directions should be limited to within 45 degrees of the storm track. As noted, land is an absolute limit to the fetch. Because waves tend to break in shallow water, the length of deeper channel could limit the fetch. It is reasonable, however, to extend the fetch somewhat upwind of the deep channel area, perhaps by 1,000 to 2,000 feet. For small waterways with heavily wooded floodplains, it is reasonable to assume that wind waves will be minimal during a storm surge.

Sketch showing wind over water with fetch length indicated as the length over the deeper water that a given wind can act on.
Figure 17.4. Definition sketch for wave calculations at channels and floodplains.

The Coastal Engineering Manual provides a simplified wave prediction method which is suitable for most riprap sizing applications. The method is described as follows:

Step 1: Estimate the wind speed, fetch length, and still water depth (USACE Coastal Engineering Manual).

Step 2: Calculate the drag coefficient (Cd) :

Equation 17.1, Drag coefficient C subscript d equals 0.001 times (1.1 plus Units conversion factor coefficient K subscript u times sustained wind velocity V subscript wind) (17.1)

where:

Cd = Coefficient of drag, dimensionless
Vwind = Sustained design wind velocity measured at 10 m height, ft/s (m/s)
Ku = Coefficient equal to 0.0107 for wind velocity in ft/s, and 0.035 for wind velocity in m/s

Step 3: Calculate the friction velocity (u*):

Equation 17.2. Friction velocity u subscript * equals sustained wind velocity V subscript wind times the square root of (Coefficient of drag C subscript d) (17.2)

where:

u* = Friction velocity, ft/s (m/s)

Step 4: Calculate dimensionless fetch length (X circumflex) :

Equation 17.3. Dimensionless Fetch Length, X circumflex equals (g times X) divided by (u subscript *) squared. (17.3)

where:

H circumflex = Dimensionless fetch length
g = Gravity constant, 32.2 ft/s2 (9.81 m/s2)
X = Actual fetch length, ft (m)

Step 5: Calculate dimensionless wave height (H circumflex) :

Equation 17.4: Dimensionless Wave Height, H circumflex equals 0.0413 times X circumflex to the power 0.5. (17.4)

where:

H circumflex = Dimensionless wave height

X circumflex = Dimensionless fetch length

Step 6: Calculate the significant wave height (Hs) :

Equation 17.5. Significant wave height H subscript s equals H circumflex times (u subscript *) squared all divided by g   (17.5)

where:

Hs = Significant wave height, ft (m)
H circumflex = Dimensionless wave height

Step 7: Calculate the dimensionless wave period (T circumflex, subscript p):

Equation 17.6. Dimensionless wave period, T circumflex, subscript p, equals 0.751 times X circumflex to the power 0.33 (17.6)

where:

T circumflex, subscript p = Dimensionless wave period

H circumflex = Dimensionless fetch length

Step 8: Calculate the wave period (T) :

Equation 17.7. Wave period, T, equals T circumflex, subscript p times (u subscript *) all divided by g  (17.7)

where:

T = Wave period, sec
T circumflex, subscript p = Dimensionless wave period

Step 9: Check the calculated wave height vs. still water depth:

If Hs is greater than 0.8 times the still water depth (d), use Hs = 0.8d.

17.3 DESIGN PROCEDURE FOR RIPRAP BANK REVETMENT IN WAVE ENVIRONMENTS
17.3.1 Riprap Size

Two methods for determining riprap size for stability under wave action are presented in this section: (1) the Hudson method (Douglass and Krolak 2008), and (2) the Pilarczyk method (Pilarczyk 1997). Riprap, when placed in a wave attack environment, should have a uniform gradation. A lot of riprap used in coastal areas have specific gravity values less than 2.65, designers should not assume specific gravity equal to 2.65.

(1) The Hudson method: The Hudson method considers wave height, riprap density, and slope of the bank or shoreline to compute a required weight of a median-size riprap particle:

Equation 17.8: Weight of the median riprap particle size, W subscript 50 equals [gamma subscript r times H cubed times tangent of theta] divided by [K subscript d, times (S subscript r minus S subscript w) cubed] (17.8)

where:

W50 = Weight of the median riprap particle size, lb (kg)
γr = Unit weight of riprap, lb/ft3 (kg/m3)
H = Design wave height, ft (m)
(Note: Minimum recommended value for use with the Hudson equation is the 10 percent wave, H0.10 = 1.27Hs )
Kd = Empirical coefficient equal to 2.2 for riprap
Sr = Specific gravity of riprap
Sw = Specific gravity of water (1.0 for fresh water, 1.03 for seawater)
θ = Angle of slope inclination

The median weight W50 can be converted to an equivalent particle size d50 by the following relationship (Lagasse et al. 2006):

Equation 17.9: Median riprap particle size, d subscript 50 equals the cube root of [Weight of the median riprap particle size, W subscript 50 divided by (0.85 times Unit weight of riprap Gamma subscript r)] (17.9)

(2) The Pilarczyk method: Compared to the Hudson method, the Pilarczyk method considers additional variables associated with particle stability in different wave environments, and therefore should more thoroughly characterize the rock stability threshold. As confirmed by Van der Meer (1990), the hydraulic processes that influence rock revetment stability are directly related to the type of wave that impacts the slope, as characterized by the breaker parameter. The breaker parameter is a dimensionless quantity that relates the bank slope, wave period, wave height, and wave length to distinguish between the types of breaking waves. This parameter is defined as:

Equation 17.10: Dimensionless breaker parameter, ksi, equals tangent of theta divided by the square root of [H subscript s, divided by L subscript zero] equals tangent theta times Units conversion factor coefficient K subscript u times T, divided by the square root of H subscript s (17.10)

where:

ξ = Dimensionless breaker parameter
θ = Angle of slope inclination
Lo = Wave length, ft (m)
Hs = Significant wave height, ft (m)
T = Wave period, sec
Ku = Coefficient equal to 2.25 for wave height in ft, and 1.25 for wave height in m

The wave types corresponding to the breaker parameter are listed in Table 17.1 and illustrated schematically in Figure 17.5.

Table 17.1. Dimensionless Breaker Parameter and Wave Types (Pilarczyk 1997).
Value of the Dimensionless Breaker Parameter ξ Type of Wave
ξ < 0.5 Spilling
0.5 < ξ < 2.5 Plunging
2.5 < ξ < 3.5 Collapsing
ξ < 3.5 Surging

Sketch of four wave types in profile as they interact with the upward sloping shore: spilling - backwards sloping with whitecaps, collapsing - almost vertical with front face of whitewater, plunging - curling over breaking, and surging - backwards sloping with base of wave interacting with retreating water.
Figure 17.5. Schematic illustration of wave types (from HEC-25).

The Pilarczyk method, like the Hudson method, uses a general empirical relationship for particle stability under wave action. The Pilarczyk equation is:

Equation 17.11: H subscript s divided by Delta D equals (Psi subscript u) times (phi) times (cosine theta), divided by (ksi to the power b)   (17.11)

where:

Hs = Significant wave height, ft (m)
Δ = Relative unit weight of riprap, Δ = (γr-γw)/γw
D = Armor size or thickness, ft (m) (for riprap, D = d50)
ψu = Stability upgrade factor ( = 1.0 for riprap)
φ = Stability factor ( = 1.5 for good quality, angular riprap)
θ = Angle of slope inclination
ξ = Dimensionless breaker parameter from Equation 17.10
b = Exponent ( = 0.5 for riprap)

Rearranging Equation 17.11 to solve for the required stone size, and inserting the recommended values for riprap with a specific gravity of 2.65 and a fresh water specific gravity of 1.0 yields the following equation for sizing rock riprap for wave attack:

Equation 17.2: Median riprap particle size, d subscript 50 equals two thirds times [(H subscript s times ksi to the power b) divided by (1.64 times cosine theta)] (17.12)
17.3.2 Layout Details for Riprap Bank Revetment

Elevation of Riprap Protection: The recommended vertical extent of riprap for wave attack includes consideration of high tide elevation, storm surge, wind setup, wave height, and wave runup. Details can be found in Hydraulic Engineering Circular 25 (HEC-25) (Douglass and Krolak 2006). The values for tide, storm surge and wind setup are considered part of the "design still water level" as described in that document (Figure 17.6). Adding the wave runup, which includes wave height, to the still water level, and including the required freeboard (typically 2 to 3 feet, or 0.6 to 1 meter) establishes the design elevation for a riprap installation.

Schematic of a shore in cross section. Parameters used in freeboard calculations are located.  Design Still Water Level - at approximately mid wave height. Significant wave height, H subscript s, vertical distance from trough to crest. Distance from shore break to Design Still Water Level, d subscript s. Angle of inclination of shore, Theta, acute angle measured from horizontal. Vertical height of run-up on slope, R subscript u, measured from Design Still Water Level to point of maximum wave runup.
Figure 17.6. Wave runup schematic for freeboard calculations (from HEC-25).

Wave runup can be calculated using the following equation (Douglass and Krolak 2008):

Equation 17.3: Vertical height of run-up on slope, R subscript u, equals 1.6 times H subscript s times (r times ksi)., with an upper limit of Ru = 3.2(rHs) (17.13)

where:

Ru = Vertical height of runup on slope, ft (m)
Hs = Significant wave height, ft (m)
r = Coefficient for armor roughness ( = 0.55 for riprap)
ξ = Dimensionless breaker parameter from Equation 17.10

Thickness of Riprap Protection: The minimum riprap layer thickness should be the greater of 2 times the d50 stone size (calculated by either the Hudson or Pilarczyk equation), or the d100 (maximum stone size) of the specified gradation.

17.3.3 Filter Requirements

There are two kinds of filters used in conjunction with riprap; granular filters and geotextile filters. Some situations call for a composite filter consisting of both a granular layer and a geotextile. The specific characteristics of the base soil determine the need for, and design considerations of, the filter layer.

The filter must retain the coarser particles of the subgrade while remaining permeable enough to allow infiltration and exfiltration to occur freely. It is not necessary to retain all the particle sizes in the subgrade; in fact, it is beneficial to allow the smaller particles to pass through the filter, leaving a coarser substrate behind. Detailed aspects of filter design are presented in Design Guideline 16 of this document.

17.3.4 Design Example

A bank slope of 2H:1V is to be protected against wave attack in the vicinity of a bridge. The bridge is located in a fresh water reach of river that is tidally influenced. The significant wave height Hs is 4.9 ft (1.5 m), and the still-water depth (including the effects of tide, wave setup and storm surge) is 13 ft (4 m) at the toe of the slope. The wave period is estimated to be 3.0 seconds. Angular riprap with a specific gravity of 2.65 is locally available.

Calculate the required size of riprap using both the Hudson and Pilarczyk equations. Also, provide recommended specifications for the layout of the riprap protection.

A. Hudson Equation:

Step 1. Calculate the design wave H0.10 for use with the Hudson Equation:

H0.10 = 1.27Hs = 1.27(4.9 ft) = 6.2 ft (1.9 m)

Step 2. Calculate the median stone weight W50 :

Weight of the median riprap particle size, W subscript 50 equals [gamma subscript r times H cubed times tangent of theta] divided by [K subscript d, times (S subscript r minus 1) cubed] = [2.65 times 62.4 pounds per cubic foot times [6.2 ft] cubed times tangent of 26 degrees] divided by [2.2 times (2.65 minus 1) cubed] = 2,000 lb (920 kg)

Step 3. Convert W50 to d50:

Median riprap particle size, d subscript 50 equals the cube root of [Weight of the median riprap particle size, W subscript 50 divided by (0.85 times Unit weight of riprap Gamma subscript r)]  = cube root of [2000 lb divided by (0.85 times 2.65 times 62.4 pounds per cubic foot)] = 2.4 ft or 29 inches (0.74 m)

B. Pilarczyk Equation:

Step 1. Calculate the dimensionless breaker parameter ξ:

Dimensionless breaker parameter, ksi, equals tangent of theta divided by the square root of [H subscript s, divided by L subscript zero] equals tangent theta times Units conversion factor coefficient K subscript u times T, divided by the square root of H subscript s 	 equals tangent 26 degrees times 2.26 times 3.0 seconds, divided by (the square root of 4.9 ft) = 1.53

Step 2. Calculate the minimum allowable median stone size d50 :

Median riprap particle size, d subscript 50 equals two thirds times [(H subscript s times ksi to the power b) divided by (1.64 times cosine theta)] = two thirds times [(4.9 ft times 1.53 to the power 0.5) divided by (1.64 times cosine 26 degrees)] = 2.8 ft or 34 inches (0.84 m)

C. Layout Specifications:

Step 1. Determine the wave runup:

Vertical height of run-up on slope, R subscript u, equals 1.6 times H subscript s times (r times ksi). = 1.64(4.9ft)(0.55)(1.53) = 6.6 ft (2.0 m)

Check the upper limit of Ru = 3.2(rHs) = (3.2)(0.55)(4.9 ft) = 8.6 ft (2.6 m)

Therefore use Ru = 6.6 ft (2.0 m)

Step 2. Determine vertical height of riprap above the toe of slope:

Vertical height = (Still water depth) + (Wave height) + (Runup) + (Freeboard)

= (13 ft) + (4.9 ft) + (6.6 ft) + (2 ft) = 26.5 ft (8.1 m)

Step 3. Determine minimum thickness of riprap layer:

Using the recommended standard gradations in NCHRP Report 568 (See Design Guideline 4 of HEC-23, 3rd Edition), Class VIII or Class IX riprap would be appropriate. Select Class VIII riprap for economy, because it has a nominal d50 size of 30 inches, with a minimum allowable d50 of 28.5 inches and a maximum allowable d50 of 34 inches.

Minimum thickness of riprap layer tmin = 2.0(d50) or d100, whichever is greater.

For Class VIII riprap, tmin = max[2.0x28.5 inches, or 60 inches]

Specify minimum riprap thickness tmin = 60 inches (5 ft or 1.5 m)

Step 4: Sketch the recommended layout (Figure 17.5):

Schematic of installation of shoreline riprap detailing the design layout with values as previously determined in the example problem. Inclination of slope is 2 horizontal to 1 vertical. Riprap on slope from key in trench to freeboard elevation is Class VIII Riprap, Nominal d 50 = 30 inches (0.75 m), Minimum layer thickness = 60 inches (1.5 m). A geotextile or granular filter underlies the riprap. Riprap fills Key in trench at bottom of slope to provide toe of slope protection. Key trench bottom width = 1.5 times riprap thickness on slope. Key trench depth = maximum depth of scour (See Design Guideline 4). Vertical extent to top of freeboard from toe of slope = Design Still Water depth - 13 ft, plus, Waves 4.9 ft, plus, Runup 6.6 ft.
Figure 17.5. Recommended layout of riprap slope protection for example problem.

17.4 REFERENCES

Douglass, S.L. and Krolak, J., 2008. "Highways in the Coastal Environment." Federal Highway Administration, Hydraulic Engineering Circular No. 25, 2nd Edition, February.

Lagasse, P.F., Clopper, P.E., Zevenbergen, L.W., and Ruff, J.R., 2006. "Riprap Design Criteria, Recommended Specifications, and Quality Control." National Cooperative Highway Research Program Report No. 568, Transportation Research Board of the National Academies of Science, Washington, D.C.

Pilarczyk, K.W. (editor), 1998. "Dikes and Revetments - Design, Maintenance, and Safety Assessment." A.A. Balkema Publications, Rotterdam, Netherlands.

U.S. Army Corps of Engineers, 2006. "Coastal Engineering Manual." Part 2, Chapter 2, latest revision June 01.

Van der Meer, J.W., 1990. "Static and Dynamic Stability of Loose Materials," in Coastal Protection (Pilarczyk, ed.) , A.A. Balkema Publications, Rotterdam, Netherlands.

Zevenbergen, L.W., Lagasse, P.F., and Edge, B.L., 2004. "Tidal Hydrology, Hydraulics, and Scour at Bridges." Federal Highway Administration, Hydraulic Engineering Circular No. 25, 1st Edition, December.

Updated: 09/22/2011

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