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by Kathleen H. Frizell(1)

Study results verify that a stepped overlay, whether individual blocks or formed, continuously placed concrete steps, provide protection against overtopping for a wide range of dam heights and overtopping flows. Experimental studies undertaken by the Bureau of Reclamation have led to development of design criteria that address the step shape and thickness, training wall heights, and toe treatment required.


Over the years, dam safety inspections have determined that thousands of embankment dams throughout North America have inadequate spillway capacity, and would be overtopped during the Probable Maximum Flood (PMF). It is widely accepted that unprotected compacted earth fill dams will fail at some point, depending upon the duration and magnitude of overtopping flows. The dam failure may result in catastrophic loss of life, but certainly produces an economic loss. Reclamation (Wahl, 1996) has assembled a database of 107 embankment dams that have breached because of overtopping flows.

There are many alternatives available to the designer to protect an embankment dam that is predicted to fail during overtopping. The method of protection chosen depends upon the height of the dam, the location of the dam, the expected flow magnitude and duration, and the susceptibility of the embankment material to erode. Depending upon the many design factors entering into the choice of a protective system, the use of a concrete stepped overlay is cost competitive, whether a system of individual blocks or roller compacted concrete is used. The effectiveness of these types of treatments has been proven beyond the level of most other embankment dam protective measures.

The Bureau of Reclamation (Reclamation), in conjunction with EPRI (Electric Power Research Institute), and CSU (Colorado State University), has completed a four year research study on concrete step overlay protection for embankment dams. The program included laboratory and large-scale hydraulic model studies. The laboratory flume studies investigated various step shapes installed on 2:1 (H:V) to 4:1 slopes. Performance of the best design was verified in a large-scale facility. These test programs showed that a properly designed stepped overlay is inherently stable because of the combined effect of the impact of the flow on the step surfaces and the ability of the stepped overlay to relieve the uplift pressure.


photo of flow in overtopping protection test flume

An outdoor overtopping facility, located at CSU in Fort Collins, Colorado, was sized to be similar in height to a typical embankment dam in need of rehabilitation. The facility consists of a concrete head box or reservoir, chute, tail box, and sump with a pump. The concrete chute is on a 2:1 (H:V) slope and has a height of 50 feet. The maximum width of 10 feet was reduced to a width of 5 feet to increase the unit discharge capacity to 32 ft3/s/ft for the stepped overlay testing.

Based on prior laboratory studies, overlapping, tapered, concrete blocks, (figure 1) were designed and constructed for the large-scale tests. The blocks were 1.23-feet-long and 0.21-feet-high with a maximum thickness of 0.375 feet. The blocks were placed over a 0.5-foot- thick filter layer of free-draining, angular, gravel material (USBR, 1987).

Consideration had to be given to placement of the filter and blocks on the steep concrete floor of the flume. As a result, angle iron (with a gap above the floor to allow free discharge underneath) was placed every 6 feet up the slope to prevent sliding of the gravel. A wooden strip was installed along each wall to easily screen the gravel filter and to prevent unnatural failure along the wall contact during operation.

Drains, which aspirate water from the filter layer, are formed in the overlapped portion of the block. A combination of 2-foot and 1-foot wide blocks were placed on the "embankment" in shingle-fashion from the slope toe, leaving no continuous seams in the flow direction.


At the crest of the structure, a small concrete cap was placed to transition from the flat approach to the first row of blocks. At the toe of the concrete slope is an anchored concrete toe block. Every twenty fifth row, blocks were anchored to prevent gradual migration of filter material which could result in bowing or settling of the block overlay. Where the blocks will be under the tailwater at the toe of the slope, the blocks are pinned together longitudinally through the overlapping area parallel to the slope. These types of slope and toe treatments are recommended for real dam applications.

Flow Description

Any protective layer for an embankment dam must include a filter and drainage system to prevent uplift due to seepage through the dam or the protective system. With the block system, small gaps were present between blocks that allowed water to flow into the underlying filter. During initial startup of the flume, under a very low discharge, the fines and dirt were flushed from the filter material. Flushing lasted a very short time and was observed by the color of the water. After shutting off the water, slight settling of the blocks was apparent; however, there was no sliding or noticeable trend to the settling. Throughout the testing no further noticeable settling of the blocks occurred. The maximum settlement was about 1 inch. The blocks were exposed to two winters of freezing conditions with no discernible movement or damage.

The many discharges tested in the flume produced varied flow conditions over the blocks. Very small flows were almost entirely broken up by the block shape leaving no noticeable thickness of solid water and a tumbling, highly-aerated flow condition, often referred to as nappe flow. As the discharge increased, the thickness of the jet and the velocities increased, producing skimming flow. During this flow regime, the jet separates off the step forming a low pressure zone in the shadow of the step. The vents, located in this area, aspirate water from the filter layer, preventing a buildup of uplift forces. The jet then impacts on the step tread, providing additional downward force for stability. For the largest flow rate, the flow does not become fully aerated until traveling about 50 feet down the slope. The blocks at the toe of the slope were exposed to both skimming flow and the pressure fluctuations from the hydraulic jump.


Tests of the block system were completed in the large-scale, outdoor facility in the fall of 1993. The block system remained stable and performed excellently, even after some blocks were intentionally broken and partially removed.

Model/prototype comparisons, between the laboratory and the outdoor facility, were used to develop general design guidelines that provide the necessary information to design a stepped overlay for embankment dams with downstream slopes of approximately 2:1 slope. These design guidelines are described in the following sections.

Discharge Coefficient

The discharge coefficient for an overtopping embankment dam is a function of the upstream slope of the dam, the top width, and the abutment geometry (for short crest lengths), and varies with the overtopping head. The typical broad-crested weir equation, is used to determine the discharge, Q, over the dam,


where C=discharge coefficient, L=horizontal crest length, and H=upstream head. An average coefficient, C, of about 2.9 may be used for most flood routing applications to determine the depth of overtopping that will pass the desired Probable Maximum Flood (PMF).

Block Shape

The block design is a function of several issues:

The most stable block shape on a 2:1 slope is the 15o tapered or sloping block (Frizell, 1992). The block design criteria is based upon keeping the difference between the top slope and the embankment slope constant for a given embankment dam slope. Therefore, when designing a block to provide effective aspiration, a difference between block and embankment slope of about 11o has been found to work fairly well. Obviously, this criteria is only applicable to embankment slopes greater than this difference of 11o. Inappropriate block slopes may produce instabilities by providing an overly large low pressure zone or normal forces that are too small.

In addition, a general guideline is to keep the ratio of the step length exposed to the flow to the step height between four and six (Baker, 1991). This criteria assures that the step height and tread length proportions are adequate to produce the correct jet impingement on the step tread. If the step height is chosen to match that of our testing, 2.5 inches, then the tread length should be chosen between 10 to 15 inches. This would produce slightly different horizontal tread lengths for dams of different slopes based upon the chosen top slope of the block. This horizontal tread length is then used to determine the length of the block surface along the embankment slope.

Included in this recommendation is that the percent of the vertical step face area occupied by the vents be 2.8% (Baker, 1991). This block shape was successfully tested in the large-scale facility for unit discharges up to 32 ft3/s/ft.

The block thickness is determined from the stability analysis. A minimal thickness 2 inches at the upstream end of the block is required to maintain the integrity of the concrete and allow proper forming of the block.


The question of stability of the protective system is the most critical for an embankment dam. Any failure or instability in the system could cause a catastrophic failure of the entire dam during an overtopping event. The block geometry is used to optimize the hydraulic forces to produce downward impact pressure and aspiration of subgrade pressures.

Laboratory data show that the ability of the blocks to relieve the uplift pressure, combined with the impact of the water on the block surface, make the blocks inherently stable. The 1-foot-wide, 15o sloping block used for the large-scale tests had a dry weight of 38.4 pounds.

Pressure data were gathered to compute the magnitude of the forces acting on the block surfaces and in the underlying filter. For discharges producing skimming flow, impact pressures increase with discharge to a maximum about 44 steps down the slope, then decrease due to reduced water density caused by the air that was entrained into the water at that location. The filter pressures were assumed to vary linearly between the measurement locations. The filter pressures show a gradual increase to about 0.5 of pressure head over about the top 40 steps, indicating a buildup of flow in the filter near the top of the slope for all flow rates. At about 45 steps down the slope the filter pressure head quickly decreases to an average of about 0.1 foot below atmospheric as aspiration increased at the toe of the slope for all flow rates.

The stability of the block system has been analyzed as a function of the total forces acting on individual blocks down the slope. Block weight and pressure yield a net downward or positive force normal to the slope. The uplift pressure in the filter material underneath the block and the low pressure zone created by the block offset act in an upward (negative) direction tending to lift the blocks from the embankment surface (figure 2).

force diagram

Not included in the analysis is the additional stability provided by the block overlap which creates an interlocking affect. To allow additional flexibility in the design, it was decided to not use the block weight in the analysis so that any combination of block dimensions could be easily compared. This would allow the design to be driven by the hydraulic forces and the block thickness determined according to other less critical parameters.

net hydraulic force chart

The hydraulic stability of the block system is quantified in the graph showing the net hydraulic force/foot of block width versus the vertical distance below the crest (figure 3). This graph shows the sum of the hydraulic forces normal to the slope including integration of the pressure profile on the step tread and the measured filter layer pressure (uplift). The sum of the forces are positive for this block shape and filter indicating a stable overlay for a 2:1 slope for the range of critical depth (Dc) to step height (Hs) ratios tested. Skimming flow occurred for all flow rates tested above Dc/Hs=3.36. Critical depth is used to represent discharge and is given by the equation:


where q is discharge per unit width and g is the acceleration of gravity. The submerged block weight of about 13 lbs. has been added to the forces in the curve formed by the dashed line for Dc/Hs = 10.36 to show the additional stability added by a block of minimal thickness. These results indicate an increase in block system stability with unit discharge.

The Construction Industry Research and Information Association (CIRIA) has developed a criteria for determining the optimum percent of port area to vertical surface area of the step face. Ports for providing aspiration of filter pressures should be 2.8% of the surface area of the step. Proper sizing of the port area will limit the uplift pressure developed in the filter layer. The gradation of the filter must be designed to prevent the filter material from being transported through the aspiration ports. The length of blocks used across the width of the dam will also influence the amount of flow entering the filter. Using longer blocks across the dam width will reduce the jointing, thus the infiltration of flow to the filter layer. If excessive seepage is expected, then the block weight could easily be increased accordingly.

Energy Dissipation or Toe Velocity

Of secondary benefit is the amount of energy dissipated by flow over the steps formed by the block surface. In general, a stepped surface reduces the energy of the flow at the dam toe compared to a smooth surface. A figure presented in Frizell (1994) allows the designer to vary the step height (within reason), for a dam of a given height and known unit discharge, to directly determine the desired velocity at the toe of the dam as a function of the energy remaining.

It was found that the larger the step height, for a given dam height, the less the energy remaining in the flow at the toe of the dam. Conversely, as the ratio of the step height to dam height decreases the energy in the flow increases. The energy remaining in the flow is also a function of the critical flow depth to step height ratio. Terminal velocity was attained for the flow range tested indicating that the energy remaining at the toe of a 50 foot or higher dam could be predicted if designs are within the flow range tested.

If the tailwater elevation and velocities indicate that a hydraulic jump will occur over the blocks, then the blocks should be pinned longitudinally to restrict rotation caused by the dynamic pressure fluctuations of the jump. Loosely pinned blocks were successfully tested under a hydraulic jump at the CSU facility.

Roughness and Bulked Depth

Darcy-Weisbach friction factors are computed based upon velocity profiles, corrected for air concentration. The friction factor, f, varied down the slope, as the flow developed, eventually becoming constant at 0.11 (Manning's n=0.03) for uniform flow. Using this value in a standard step method calculation will determine the flow depths down the chute. An average air concentration of 36% is reached for the fully developed flow condition on a 2:1 slope; therefore, the wall heights should be raised by 36% above the calculated flow depths to contain the flow. This measured value of air concentration compared favorably with findings by previous investigators on smooth slopes (Wood, 1983) and existing data may be used to extrapolate to other slopes. An additional safety factor may be added if determined necessary.


This design example will demonstrate the use of the design information by presenting a feasibility level design of a block system on a small embankment dam. The design example will include the crest treatment, block dimensions and stability on the slope, and required toe treatment based upon energy remaining at the toe of the dam.

A small embankment dam owned by the Department of Interior is scheduled for rehabilitation due to its inability to pass the PMF. The embankment dam is about 27-feet-high with a 2.5:1 downstream slope. An outlet works tunnel is located through the dam on the right side and an emergency, grass-lined spillway on the left abutment. The lake formed by the dam is a highly used recreational site with hiking trails crossing the dam and following the left abutment. The top of the existing dam is at elevation 2498 feet. The 40-foot-wide grass-lined spillway with crest elevation 2495.6 feet, is currently designed to pass less than 500 ft3/s before the dam is overtopped. Overtopping is predicted to breach the dam, resulting in a discharge of 23,000 ft3/s for 20 minutes, which is unacceptable. To prevent overtopping of the dam another spillway constructed with the tapered, overlapping blocks has been designed. The design must still allow pedestrian passage across the top of the dam and have minimal impact to the existing aesthetics. As a result, the block system will be covered with topsoil.

The reservoir water surface elevation is restricted to 2502 feet by reservoir rim development. The top of the dam will be raised by 5 feet with a rock and masonry wall tied to the existing impervious core wall to prevent overtopping of the existing dam during the PMF. Pedestrian access will be upstream of the new rock wall, over the top of the covered blocks. After using several spillway crest elevations and widths to route the PMF with maximum water surface elevation of 2502 feet, the spillway configuration on figure 4 was chosen.

Flood Routing and Crest Detail

The block spillway will have a maximum spillway discharge of 4183 ft3/s or 32.2 ft3/s/ft. Using a crest coefficient of 2.9 in the flood routing, it was determined that a 130-foot-long block spillway crest at elevation 2497 feet is needed, 1 foot below the top of the existing dam.

plan view

The grass-lined spillway will pass a maximum of 2,230 ft3/s and will begin discharging when the reservoir is 1.5 feet below the block spillway crest. The top of the dam upstream of the block spillway crest will also be covered with blocks to prevent undermining the slope protection by flows over the top of the dam. To prevent seepage through the dam, a cutoff trench will be placed along the axis of the dam that extends from the top of the existing core wall to the surface where the spillway blocks will be placed.

Block Design

The tapered blocks will be designed for effective aspiration or stability on the 2.5:1 (21.8o) downstream slope of the dam.

Top slope of block: 21.8o-11.6o = 10.2o

This top slope on the block produces the following geometry for the remainder of the block surfaces on the 2.5:1 slope.

Tread length exposed to the flow: 11.7 in (same as 15o step on 2:1 slope)

Horizontal length: 12.5 in

Block length along the embankment slope: 11.5 in/cos(21.8o) = 12.4 in

The step height should be between the ratio of tread length to step height of 4 to 6. Thus, the step height, Hs, could be between 1.9 to 2.9 in. A 2.5 in step height was chosen.


The block thickness is then determined by finding the block weight required for stability based upon the predicted uplift or seepage pressure. Inspection of the dam indicates that excessive seepage will not be a concern. As a result, a free-draining gravel filter underneath the block system will be adequate and stability may be predicted from figure 3. A dam height of 27 feet and Dc/Hs =15.21 gives a total positive force between 15 to 60 pounds/ft along the spillway from the crest to the toe to hold the blocks on the surface. Therefore, a minimal block thickness at the upstream end of the block of 2 in and appropriate aspiration port area will produce a stable block (figure 5).


Figure 6 shows the toe block and placement of the first rows of blocks required for stability at the toe of the slope. The toe block is used as a base for the first row of overlapping blocks and continues completely across the spillway width at the toe of the dam. At least the first row of blocks should be pinned into the toe block. Blocks located beneath the tailwater should be cast with two holes per block to receive loose-fitting pins or dowels. This detail will produce stability of the rows of block exposed to the fluctuating pressures of the hydraulic jump (figure 6).

see caption

Toe Velocity and Energy Dissipator

The velocity at the toe of the dam was determined for an overlay with a 2.5-inch-high step height. Using this velocity in Reclamation's Monograph 25 (Peterka, 1978), and the depth of flow computed by continuity, the stilling basin length was determined to be 50 feet . This result is shown on figure 4, and will most likely be formed with grouted riprap.

Spillway Wall Height

The wall height at the crest must be equal to the overtopping depth, or in this case, simply the reservoir elevation, giving a wall height of 5 feet. The flow depth down the chute is determined by using the friction factor and velocities down the slope in a standard step calculation. This calculation produces a required wall height that varies down the slope to a minimum of 1 foot at the toe. (As expected, this value compares well with the depth computed using continuity.) Adding the bulking due to 36% air concentration gives the necessary freeboard to contain the highly aerated flow over the spillway blocks and a wall height of 1.36 feet at the dam toe, measured from the tip of the steps. This wall could easily be obtained by anchoring highway jersey barriers in the embankment and butting the blocks up to them.


The dam owners have labor available to work on the rehabilitation of the dam. This makes the block design an attractive alternative. A general cost estimate obtained for manufacturing and installing the block system on a typical embankment dam varied between $110 to $195/yd2. These costs included crest and toe treatments, preparation of the embankment slope and placement of the filter, blocks, and precast spillway walls. The predicted cost for initial production of the forms for the blocks varied greatly and was probably substantially overestimated. Reclamation and CSU have both formed blocks with great success and minimal cost. Construction of the block overlay only (not the dam raise, etc), and assuming a coverage of 1050 yd2 for the small embankment dam used as the case study, would cost a total of $115,500 to $204,750.


The tapered block system has been tested well beyond the limits of other concrete revetment systems. The design criteria presented defines their application for a wide range of overtopping. The block system is particularly applicable for dams in remote or environmentally sensitive locations where use of a batch plant or large machinery is limited. The cost of the system is not well known at this time, but will be competitive once the forms have been constructed and the ease of placement discovered. We are so sure of the many cost-effective application of the tapered block system that Reclamation engineers and EPRI have obtained a patent on the block design and shape(2).

In addition, the capability of the stepped overlay to dissipate energy documented during this testing will assist in the design of any stepped overlay, including those constructed with roller-compacted concrete.


1. Frizell, K.H., 1992, "Hydraulics of Stepped Spillways for RCC Dams and Dam Rehabilitations," Proceedings, 1992 ASCE Roller Compacted Concrete III Conference, pp. 423-439, San Diego, CA, February 2-5, 1992.

2. Baker, R., "Performance of Wedge-shaped Blocks in High Velocity Flow," CIRIA Research Project 407, Stage 2, University of Salford, England, August 1991.

3. Peterka, A.J., 1978, "Hydraulic Design of Stilling Basins and Energy Dissipators," Engineering Monograph No. 25, Bureau of Reclamation, Denver, Colorado, 1978.

4. Wahl, Tony L., "Prediction of Embankment Dam Breach Parameters," PAP-735, Bureau of Reclamation, Denver, CO 80225, 1996.

5. ____, "Design Standards No. 13 - Embankment Dams Chapter 5 - Protective Filters" Bureau of Reclamation, Denver, CO 80225, 1987.

6. Frizell, K.H., "Stepped Overlays Proven for Use in Protecting Overtopped Embankment Dams," ASDSO 11th Annual Conference, Boston, MA, Sept. 11-14, 1994.

7. Wood, I.R., "Uniform Region of Self-Aerated Flow," Journal of Hydraulic Engineering, ASCE, 109(3), pp. 447-461, 1983.

1. Ms. Frizell is a Research Hydraulic Engineer with the Bureau of Reclamation, Hydraulic Investigations and Laboratory Services Group, Mail Code 86-68460, PO Box 25007, Denver, CO 80225.

2. U.S. Patent No.5,544,973.