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

Design Guideline 5 Riprap Design for Embankment Overtopping

5.1 INTRODUCTION

When flow overtops an embankment, spur, or guide bank, locally high velocities and shear stresses will create strong erosion forces, typically at the downstream shoulder and on the embankment slope, that are too great for the soil of the embankment to withstand. Two primary processes of erosion occur during an overtopping event.

When the overtopping flow is submerged, erosion of the embankment typically begins with the downstream shoulder. This condition is often experienced by roadways and bridge approach embankments. Figure 5.1 (Chen and Anderson 1987) shows the progression of this type of failure at times t1, t2, and t3. As the flow accelerates over the embankment, a surging hydraulic jump is formed that causes a nick point between the shoulder and the downstream slope. This nick point will begin to migrate upstream because of the high velocities, and erosion will begin to move downstream. The downstream migration of the erosion is caused by the turbulence associated with the hydraulic jump. This condition would also apply to most river training countermeasures, such as spur and guide banks, under overtopping conditions.

The second general erosion pattern results from the case of free flow. With low tail water, the flow will accelerate down the slope with high velocity and shear stress associated with supercritical flow. Erosion typically initiates near the toe of the embankment, whether or not a hydraulic jump is present. Erosion progresses in the upslope and upstream direction through the embankment. Figure 5.2 (Chen and Anderson 1987) illustrates this progression. This condition would typically apply to earth dams, spillways, or levees protected by revetment riprap.

Sketch of an overtopping submerged trapezoidal embankment in cross section. Erosion of downstream top corner edger is shown initiating at shoulder and increasing in severity from t1 through t2 to t3. Erosion shown is almost equal from the top and rear face of the embankment.
Figure 5.1. Typical embankment erosion pattern with submerged flow.

Sketch of a trapezoidal embankment in cross section experiencing free flow overtopping. Erosion of downstream face is shown initiating at the base at t1. Erosion increases in severity from t1 through t2 to t3 and progressively removes material in a steep scarp from the rear face of the embankment.
Figure 5.2. Typical embankment erosion pattern with free flow.

Traditionally, riprap has been placed on the downstream slope of embankment dams for erosion protection during heavy rainfall and has commonly been assumed inadequate for protection from overtopping flows. Although prototype verification is limited, several investigators have studied riprap stability on steep embankment slopes when subject to flow. Flow hydraulics on steep embankment slopes cannot be analyzed with standard flow and sediment transport equations. Uniform flow and tractive shear equations do not apply to shallow flow over large roughness elements or highly aerated flow, both of which can occur during overtopping. Riprap design criteria for overtopping protection of embankment dams should prevent stone movement and ensure the riprap layer does not fail. Empirically derived design criteria currently offer the best approach for design (Frizell et al. 1990).

Riprap design to resist overtopping flow is dependent upon the material properties (median size, shape, gradation, porosity, and unit weight), the hydraulic gradient or embankment slope, and the unit discharge. Flume studies were performed to investigate flow through and over rock fill dams, using crushed granite, pebbles, gravel, and cobbles on a range of slopes (Abt et al. 1987, 1988, 1991). Threshold flows where incipient stone movement occurs were defined. The maximum unit discharge that resists stone movement on steep slopes is a function of the mean water depth, the critical velocity at which the stone begins to move, and an aeration factor defined as the ratio of the specific weight of the air-water mixture to the specific weight of the water. A comparison of the various expressions for overtopping flow conditions shows them to be valid for crushed stone with angular shape (Abt and Johnson 1991). Knauss developed a rock stability function based on unit discharge, slope, rock packing, and air concentration for sizing riprap, and determined that aeration of flow increases the critical velocity for which riprap on a steep slope remains stable (Oswalt et al. 1994).

Studies were performed in a near-prototype-size embankment overtopping facility to establish new criteria relating the design of the riprap layer to the interstitial velocity of water flowing through the riprap layer (Mishra 1998). An equation was developed to predict the interstitial velocity of water through the rock layer. A universal formula for designing riprap was derived. This equation was tested for the data obtained in the 1998 study and previous research studies. The universal riprap design equation was found to satisfactorily predict the size of the riprap to be used for a specific unit discharge and a given embankment slope.

5.2 BACKGROUND

Near-prototype flume tests were conducted by CSU (Oswalt et al. 1994) with riprap placed on embankment slopes of 1,2, 8, 10, and 20% and subjected to overtopping flows until failure. Failure was defined by exposure of the underlying sand and gravel bedding. Based on the results of five tests, rounded-shape riprap was found to fail at a unit discharge about 40% less that that of angular stones of the same median size, demonstrating the importance of stone shape on riprap layer stability. Angular stones tend to wedge or interlock and require fewer fines to fill voids, compared to similarly graded round stones. Rounded stones are much more likely to slide or roll, especially on the steeper slopes. Riprap specifications normally require angular shaped stone.

Channelization was observed to occur between the threshold and collapsing stages of the overtopping flow. Channels form in the riprap layer as the smaller stones are washed out, producing flow concentrations and increasing the localized unit discharge. Studies at Colorado State University (CSU) suggest flow concentrations of three times the normal unit discharge are possible. The average point of incipient channel formation was identified at about 88% of the unit discharge at failure.

Wittler and Abt (1990) investigated the influence of material gradation and the stability of the riprap layer with overtopping flow. In general, uniformly graded riprap displays a greater stability for overtopping flows but fails suddenly, while well-graded riprap resists sudden failure as voids are filled with smaller material from upstream; this process is referred to as "healing." Additional studies at CSU from 1994-1997 provided more details on the failure mechanism (Mishra 1998). Again, failure of the riprap slope was defined as removal or dislodgment of enough material to expose the bedding material. Failure of the riprap layer occurred with the measured water depth still within the thickness of the rock layer. A layer of highly aerated water was flowing over the surface of the riprap, but this surface flow was only a small portion of the total flow (see Figure 5.10).

5.3 LABORATORY STUDIES

Through the cooperative agreement signed in 1991, the U.S. Bureau of Reclamation (USBR) and Colorado State University (CSU) built a near-prototype size embankment overtopping research facility with a 50% slope (1V:2H). Riprap (angular) tests were conducted in the summers of 1994, 1995, and 1997 on this facility (Mishra 1998).

The first two riprap test sections covered the full width of the chute and extended 60 ft (18.29 m) down the slope from the crest. The first test (1994) consisted of a 0.67-foot (203-mm) thick gravel bedding material with a 2-foot (0.61-m) overlay of large riprap with a d50 of 1.27 ft (386 mm) (Figure 5.3). The second test (1995) utilized the first test bed with a second layer of approximately 2 ft (0.61 m) thick riprap with d50 of 2.15 ft (655 mm). The schematic diagram for this set up is presented in Figure 5.5.

The third test (1997) covered the full width of the chute and extended 100 ft (30.48 m) from the crest down the slope to the toe of the facility. A 0.67-foot (203-mm) thick gravel bedding material with a d50 of 0.16 ft (48 mm) was overlaid with a main riprap layer of thickness 1.75 ft (533 mm) with a d50 of 0.89 ft (271 mm). A berm was built at the bottom of the flume to simulate toe treatment at the base of the embankment. The configuration of the test setup in 1997 is given in Figure 5.4. The schematic diagram for the 1997 setup is illustrated in Figure 5.6.

For all the tests, a gabion composed of the same rocks used on the slope, was placed at the crest of the embankment. This was done to provide a smooth transition of water from the head box to the embankment and to prevent premature failure of the riprap at the transition between the concrete approach at the crest of the embankment and the concrete chute. The gabion covered the entire width of the flume and extended about 2.46 ft (0.75 m) down the flume from the crest. The top surface of the gabion was horizontal.

The test series provided the opportunity to gather important data regarding flow through large size riprap. The visual observations provided information on aeration, interstitial flow, stone movement, and the failure mechanism on the slope. Data was collected on discharge flowing down the chute through the riprap, the head box depth for overtopping heads, manometer readings for depth of flow down the chute and the pressure heads, and electronic recording of electrical conductivity versus time to determine interstitial velocities.

1994 photograph looking up a steep rectangular test flume. In the no-flow conditions riprap can be seen in the flume.
Figure 5.3. Test set up for 1994,
d50 = 1.27 ft (386 mm).
                              1997 photograph looking up a steep rectangular test flume. In the no-flow conditions bands of colored riprap can be seen progressing up the flume
Figure 5.4. Test set up for 1997,
d50 = 0.89 ft (271 mm).

Sketch in cross section along the centerline of the flume showing the slope, general layout and two layers of riprap, - filter and cover riprap
Figure 5.5. Riprap configuration in 1994 and 1995.

Sketch in cross section along the centerline of the flume showing the slope, the general layout and two layers of riprap. Flume detail sketch shows mounding of riprap material at toe of slope.
Figure 5.6. Riprap Configuration in 1997.

5.4 RIPRAP FAILURE ON EMBANKMENT SLOPES

Prior to failure of the riprap slope, many individual stones moved or readjusted locations throughout the test period. Movement of these stones is referred to as incipient motion. This occurs when the displacing and overturning moments exceed the resisting moments. The force in the resisting moment is given by the component of the weight perpendicular to the embankment and interlocking between stones in the matrix. The overturning forces are the drag (or the jet impact on a stone), the lift, buoyancy, and to a lesser degree, the component of the weight parallel to the embankment depending on the point(s) of contact with other stones. Even though buoyancy plays an important role in the removal of rocks, the hydrodynamic forces have the major role in producing failure of the protective layer. This observation is supported by the depth measurements, which revealed that the stones on the surface were not entirely submerged. It was also concluded that on steep embankments, riprap failure on the slope is more critical than the failure at the toe.

Failure of the riprap slope was defined as removal or dislodgement of enough material to expose the bedding material. Failure of the riprap layer occurred with the measured water depth still within the thickness of the rock layer. A layer of highly aerated water was flowing over the surface of the riprap, but this surface flow was only a small portion of the total flow and was not measurable by piezometers. Riprap failures are illustrated in Figures 5.7, 5.8, and 5.9 and failure characteristics are given in Table 5.1.

Table 5.1. Riprap Failure Characteristics.
Year d50 ft (mm) Coefficient of Uniformity, Cu

(d60/d10)
Failure Discharge

ft3/s/ft

(m3/s/m)
1994 1.27 (386) 1.90 2.4 (0.223)
1995 2.15 (655) 1.55 10 (0.929)
1997 0.89 (271) 1.81 2.2 (0.204)

Photograph looking up the flume after the 1994 test. Riprap point of failure is indicated.
Figure 5.7. Riprap failure in 1994 tests (d50 = 1.27 ft (386 mm))

Post test photograph of riprap caught by the porous mesh barrier below the test section after riprap failure. The individual riprap stones are numbered.
Figure 5.8. Failure of riprap in 1995 tests (d50 = 2.15 ft (655 mm))

1997 Photograph of failure point in the riprap slope post test. The smaller sized stones in the under layer are exposed.
Figure 5.9. Riprap failure in 1997 tests (d50 = 0.89 ft (271 mm)).

5.5 DESIGN OF RIPRAP FOR OVERTOPPING FLOW
5.5.1 Sizing the Riprap

When flow overtops an embankment, spur, or guide bank, locally high velocities occur at the downstream shoulder of the structure. When tailwater is low relative to the crest of the structure, the flow will continue to accelerate along the downstream slope. Guidance for riprap stability under these conditions was developed from the laboratory testing described in Section 5.3 (Mishra 1998). For slopes steeper than 1V:4H, the method requires that all the flow is contained within the thickness of the riprap layer (interstitial flow). For milder slopes, a portion of the total discharge can be carried over the top of the riprap layer. The three equations necessary to assess the stability of rock riprap in overtopping flow are given below. The design procedure is illustrated by examples in Sections 5.5.2 and 5.5.3.

Equation 5.1 the Interstitial velocity V subscript I equals 2.48 times the square root of (acceleration due to gravity, g times the particle D subscript 50) times [(S to the power 0.58) divided by (C subscript u to the power 2.22)], with terms explained in the text.   (5.1)

where:

Vi = Interstitial velocity, ft/s (m/s)
g = Acceleration due to gravity, 32.2 ft/s2 (9.81 m/s2)
d50 = Particle size for which 50% is finer by weight, ft (m)
Cu = Coefficient of uniformity of the riprap, d60/d10
S = Slope of the embankment, ft/ft (m/m)
Equation 5.2: Particle size for which 50% is finer by weight, d subscript 50 equals [K subscript u times q subscript f to the power 0.52] divided by [C subscript u to the power 0.25 times S to the power 0.75] times [sine alpha divided by [(S subscript g times cosine alpha minus 1) times (cosine alpha times tangent phi minus sine alpha)] ] to the power 1.11. terms explained text below.  (5.2)

where:

d50 = Particle size for which 50% is finer by weight, ft (m)
Ku = 0.525 for English units

0.55 for SI units
qf = Unit discharge at failure, ft3/s/ft (m3/s/m)
Cu = Coefficient of uniformity of the riprap, d60/d10
S = Slope of the embankment, ft/ft (m/m)
Sg = Specific gravity of the riprap
α = Slope of the embankment, degrees
φ = Angle of repose of the riprap, degrees

When the embankment slope is less than 1V:4H (25%), the allowable depth of flow (h) over the riprap is given by:

Equation 5.3: allowable depth of flow over the riprap. h, equals [0.6 times (S subscript g minus 1) times tangent phi] divided by [ 0.97 times S] (5.3)
5.5.2 Example Application for Slopes Milder Than 1V:4H (25%)

Riprap is to be designed to protect a 1V:5H slope from overtopping flow. The riprap has a specific gravity (Sg) of 2.65, uniformity coefficient (Cu) of 2.1, porosity η of 0.45 and an angle of repose φ of 42°. The following data are provided for the design.

Variable English Units SI Units
Value Units Value Units
Total discharge (Q) cfs 2000 m3/s 56.63
Embankment overtopping length (L) ft 1000 m 304.8
Unit discharge (qf) cfs/ft 2.0 m2/s 0.186
Weir flow coefficient (C) ft0.5/s 2.84 m0.5/s 1.57
Riprap sizing equation coefficient (Ku) s0.52/ft0.04 0.525 s0.52/m0.04 0.55
Manning-Strickler coefficient 0.034 0.0414
Slope (S) ft/ft 0.2 m/m 0.2
Slope angle (α) degrees 11.3 degrees 11.3

Step 1: Determine the overtopping depth using the broad-crested weir equation:

Q = CLH1.5
H = (Q/CL)2/3 = [2000/(2.84x1000)]2/3 = 0.79 ft (0.24 m)

Step 2: Compute the smallest possible median rock size (d50) using Equation 5.2:

Substituting Values from the text above into Equation 5.2 the median rock size (d50) value is 0.31 feet equals 3.7 inches or 0.094 meters

Note: Use next larger size class (see Volume 1, Chapter 5).

Step 3: Select Class I riprap from Table 4.1 of Design Guideline 4: d50 = 6 inches (0.15 m)

Step 4: Compute the interstitial velocity and the average velocity using Equation 5.1:

Substituting Values from the text above into Equation 5.1 the interstitial velocity value is 0.75 feet per second or 0.228 meters per second

From Vi, find the average velocity Vavg

Vave = ηVi = 0.45(0.75) = 0.34 ft/s (0.103 m/s)

where: η the porosity of the rock.

Step 5: Compute the average flow depth (y) as if all the flow is contained within the thickness (t) of the riprap layer (i.e., t = y):

y = qf/Vavg = 2.0/0.34 = 5.9 ft (1.81 m)

NOTE: If the average depth is less than 2d50 then the design is complete with a riprap thickness of 2d50. If the depth is greater than 2d50 and the slope is greater than 0.25, go to Step 11. Otherwise, go to Step 6.

5.9 ft > 2d50 (1.0 ft) and S (0.2) < 0.25, so go to step 6.

Step 6: Find the allowable flow depth over the riprap using Equation 5.3:

Substituting Values from the text above into Equation 5.3 the allowable flow depth value is 0.23 or 0.069 meters

Step 7: Calculate the Manning roughness coefficient, n

Manning's roughness, n, equals 0.034 times (median rock size, d subscript 50) to the power one sixth equals 0.030.

Step 8: Calculate the unit discharge, q1, which can flow over the riprap using Manning's equation:

Unit discharge, q1 equals (1.486 divided by n) times y to the power 5 thirds times S to the power one half equals 1.486 divided by 0.03) times 0.23 to the power 5 thirds times 0.02 to the power one half equals 1.91 foot cubed per second per foot equals 0.173 meters cubed per second per meter.

Step 9: Calculate the required interstitial flow, q2, through the riprap and the flow provided by a riprap thicknesses of 2d50.

q2 = qf - q1 = 2.0 - 1.91 = 0.09 ft3/s/ft (0.013 m3/s/m)
q = 2d50(Vavg ) = 2(0.5)(0.34) = 0.34 ft3/s/ft (0.031 m3/s/m)

NOTE: If the flow (q) provided by a 2d50 thickness is greater than or equal to the required flow (q2), the design is complete with a thickness of 2d50. If the flow provided by 2d50 is less than the required flow, proceed to Step 10.

q (0.34 ft3/s/ft) > q2 (0.09 ft3/s/ft)

Therefore, the design is complete using a thickness of 2d50 and a riprap d50 of 6 inches.

Step 10: (not needed for this example). Calculate the flow provided by a 4d50 thickness of riprap. If the flow provided is greater than the required flow, the design is complete with a thickness of 4d50 (or an appropriate intermediate thickness). If the flow provided by a 4d50 thickness is less than the required flow, proceed to Step 11.

Step 11: (not needed for this example). Increase the riprap size to the next gradation class and return to Step 4.

5.5.3 Example Application for Slopes Steeper Than 1V:4H (25%)

Using the same data as the previous example, design riprap for a 1V:2H slope (50%). Because the slope is steeper than 1V:4H, the riprap is designed such that all the flow is through the riprap (interstitial flow).

Variable English Units SI Units
Value Units Value Units
Total discharge (Q) cfs 2000 m3/s 56.63
Embankment overtopping length (L) ft 1000 m 304.8
Unit discharge (qf) cfs/ft 2.0 m2/s 0.186
Weir flow coefficient (C) ft0.5/s 2.84 m0.5/s 1.57
Riprap sizing equation coefficient (Ku) s0.52/ft0.04 0.525 s0.52/m0.04 0.55
Manning-Strickler coefficient 0.034 0.0414
Slope (S) ft/ft 0.5 m/m 0.5
Slope angle (α) degrees 26.6 degrees 26.6

Step 1: Determine the overtopping depth using the broad-created weir equation:

Q = CLH1.5
H = (Q/CL)2/3 = [2000/(2.84x1000)]2/3 = 0.79 ft (0.24 m)

Step 2: Compute the smallest possible median rock size (d50):

Substituting Values from the text above into Equation 5.2 the median rock size (d50) value is 0.96 feet equals 11.5 inches or 0.29 meters

Step 3: Select Class III riprap from Table 4.1 of Design Guideline 4: d50 = 12 inches (0.15 m).

Step 4: Compute the interstitial velocity and the average velocity:

Substituting Values from the text above into Equation 5.1 the interstitial velocity value is 1.81 feet per second or 0.548 meters per second

Vave = ηVi = 0.45(1.81) = 0.81 ft/s (0.247 m/s)

Step 5: Compute the average flow depth (y) as if all the flow is contained within the thickness (t) of the riprap layer (i.e., t = y):

y = qf/Vavg = 2.0/0.81 = 2.5 ft (0.75 m)

NOTE: If the average depth is less than 2d50 then the design is complete with a riprap thickness of 2d50. If the depth is greater than 2d50 and the slope is greater than 0.25, go to step 11. Otherwise, go to Step 6.

2.5 ft > 2d50 (2.0 ft) and S (0.5) > 0.25, so go to Step 11.

Step 11: Increase the riprap size to the next gradation class and return to Step 4.

Step 12: Select Class IV riprap with d50 of 15 inches from Table 4.1 (Design Guideline 4) and return to Step 4.

Step 4 (trial 2): Compute the interstitial velocity and the average velocity:

Substituting Values from the text above, increasing the D 50 to 1.25 feet, into Equation 5.1 the interstitial velocity value is 2.03 feet per second or 0.617 meters per second

Vave = ηVi = 0.45(2.03) = 0.91 ft/s (0.278 m/s)

Step 5 (trial 2): Compute the average flow depth (y) as if all the flow is contained within the thickness (t) of the riprap layer (i.e., t = y):

y = qf/Vavg = 2.0/0.91 = 2.2 ft (0.67 m)

NOTE: If the average depth is less than 2d50 then the design is complete with a riprap thickness of 2d50. If the depth is greater than 2d50 and the slope is greater than 0.25, go to Step 11. Otherwise, go to Step 6.

2.2 ft < 2d50 (2.5 ft), so design is complete with d50 = 15 inches and a riprap thickness of 2.5 feet. This check ensures that all the flow is contained within the thickness of the riprap layer (interstitial flow).

5.6 FILTER REQUIREMENTS

The importance of the filter component of any embankment riprap installation should not be underestimated. Geotextile filters and granular filters may be used in conjunction with riprap embankment protection. When using a granular stone filter, the layer should have a minimum thickness of 4 times the d50 of the filter stone or 6 inches, whichever is greater.

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.

5.8 REFERENCES

Abt, S.R. and Johnson, T.L., 1991, "Riprap Design for Overtopping Flow," ASCE Journal of Hydraulic Engineering, Vol. 117, No. 8, pp. 959-972.

Abt, S.R., Khattak, M.S., Nelson, J.D., Ruff, J.F., Shaikh, A., Wittler, R.J., Lee, D.W., and Hinkle, N.E., 1987, "Development of Riprap Design Criteria by Riprap Testing in Flumes: Phase I," NUREG/CR-4651, U.S. Nuclear Regulatory Commission, Vol. 1, 48-53.

Abt, S.R., Wittler, R.J., Ruff, J.F., Lagrone, D.L., Nelson, J.D., Hinkle, N.E., Lee, D.W., and 1988, "Development of Riprap Design Criteria by Riprap Testing in Flumes: Phase II," NUREG/CR-4651, U.S. Nuclear Regulatory Commission, Vol. 2, 57-65.

Abt. S.R., Ruff, J.F., and Wittler, R.J., 1991, "Estimating Flow Through Riprap," ASCE Journal of Hydraulics, Vol. 5, 670-675.

Chen, Y.H. and Anderson, B.A., 1987, "Development of a Methodology for Estimating Embankment Damage Due to Flood Overtopping," FHWA Report No. FHWA-RD-86/126.

Frizell, K.H., Mefford, B.W., Dodge, R.A., and Vermeyen, T.B., 1990, "Protecting Embankment Dams Subject to Overtopping During Major Flood Events," Proceedings American State Dam Safety Officials Conference, New Orleans, LA.

Oswalt, N.R., Buck, L.E., Hepler, T.E., and Jackson, H.E., 1994, "Alternatives for Overtopping Protection of Dams," ASCE, Task Committee on Overtopping Protection of the Hydraulics Division, New York, NY, pp 136.

Mishra, S.K., 1998, "Riprap Design for Overtopped Embankments," Ph.D. Dissertation, Department of Civil Engineering, Colorado State University, Fort Collins, CO, 140 pp.

Robinson, K.M., Rice, C.E., and Kadavy, K.C., 1995, "Stability of Rock Chutes," Proceedings, Water Resources Engineering, ASCE, San Antonio, TX, Vol. 2, 1476-1480.

Whittler, R.J. and Abt, S.R., 1990, "The Influence of Uniformity on Riprap Stability," Proceedings, Hydraulic Engineering Vol. 1, of the 1990 ASCE National Conference, San Diego, CA, July 30-August 3, pp. 251-265.

Updated: 09/22/2011

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