Overtopping flow occurs when a water detention structure's capacity is surpassed and flow passes over the structure. Potential sites of overtopping flows are embankments such as dams, levees, detention basins, et cetera.
To properly evaluate the level of erosion protection needed, a design discharge must first be ascertained. This may be accomplished using historical record, isohyetal maps, probable maximum flood (PMF) or any number of generally accepted methods.
Good engineering practice dictates that more than one method is used and judgment be used in the final determination of design discharge. Once discharge is established, Equation 1 is the generally accepted method for calculating discharge over an embankment:
Equation 1:
where:
Q = discharge;
C = experimentally determined weir coefficient (C is approximately 3.0 (English units) for levelcrested embankments);
L = embankment length;
H = total head above the embankment crest prior to overflow drop down.
In the case of submerged flow,
Equation 2:
where:
(C_{S}/C) is the submergence coefficient that may be calculated using Figure 1.
Figure 1: Submerged weir coefficient, C
_{S}/C
The terminology used here will be that of a reservoir scenario, though similar conditions exist in the other cases. Without proper protection, these types of embankments may fail as a result of the erosion caused by the overtopping. When discussing the processes of overtopping, it is convenient to divide the flow into three zones as illustrated in Figure 2. Zone 1 is characterized by a change from static energy head to a combination of static and dynamic head as flow accelerates from the nearzero velocity of the reservoir to subcritical velocity in the upstream portion of the dam crest. Zone 2 begins as flow passes through critical velocity and into supercritical flow across the remainder of the crest to the slope change at the opposite side of the embankment. Zone 3 encompasses the rapidly accelerating and turbulent supercritical flow on the downstream slope. As a result of the rapidly accelerating flow off the dam crest, Zone 3 contains a possible separation zone where flow may lose contact with the embankment surface. If this should occur, subhydrostatic pressure will result that must be considered during design. Zone 3 also contains a change in energy state from supercritical flow back to that of subcritical flow and is distinguished by a hydraulic jump. This will occur at the point where slope changes at the toe of the slope or when the flow encounters tailwater having subcritical velocity.
Figure 2: Hydraulic characteristics of overtopping flow (Powledge et al., 1989b)
Zone 1 with its subcritical flow is the least susceptible to erosion. Zone 2 experiences supercritical flow over a short distance. Erosion here will likely occur first at the downstream transition from dam crest to embankment slope. A major concern in this region is the increase in soil pore pressure. As the water level rises in the reservoir, the phreatic surface within the dam will also rise. Any paving surface on the embankment with insufficient drainage capacity may fail from the uplift pressure. This is also a concern in Zone 3. The accelerating supercritical flow in Zone 3 and the associated increasing tractive stress increases the chance of erosion on the downslope. Locations of discontinuity such as slope changes are most likely to experience initial erosion. Typical erosion patterns for submerged overtopping flow are presented in Figure 3 and typical erosion patterns for free flow are presented in Figure 4. Overtopping flows may last for great lengths of time. As a result, protective measures should be used in all zones to prevent dam failure The amount of erosion that may be expected is directly correlated to the velocity and shear stress experienced by the embankment. Assuming uniform flow (Sf = So, friction slope equals bed slope), Manning's equation may be used to calculate flow velocity:
Figure 3: Typical submerged flow erosion pattern (Chen and Anderson, 1987
Figure 4: Typical freeflow erosion pattern(Chen and Anderson, 1987).
Equation 3:
where:
V = flow velocity;
n = Manning's roughness coefficient;
R = hydraulic radius;
S_{o} = bed slope;
Equation 4:
where:
A = flow cross sectional area
P = wetted perimeter.
Average shear stress may be calculated using Equation 5:
Equation 5:
where:
t_{0} = shear stress;
? = unit weight of water;
d = flow depth.
Note that the assumption of uniform flow typically yields conservatively high values for shear stress. To calculate shear stress using nonuniform flow, refer to Clopper and Chen (1988).
The local shear stress may be calculated using Equation 6:
Equation 6:
where:
? = density of water;
f = DarcyWeisbach roughness coefficient, calculated using Equation 7:
Equation 7:
Design for erosion protection during overtopping flow is typically based on a permissible velocity approach or permissible shear stress approach. The permissible velocity method is more commonly used for bare soil or vegetated conditions and is detailed in Hewlett et al. (1987). Permissible shear stress methods result from a forcebalance or a momentum balance representation of stability. The force balance approach is detailed in Lagasse et al. (2001) and the momentum balance approach is detailed in Dunlap (2001).
Overtopping protection options
The following options for overtopping protection are described in detail by the ASCE Task Committee on Overtopping Protection:
 Reinforced vegetation — highperformance turf reinforcement mat (HPTRM);
 Rollercompacted concrete (RCC);
 Soil cement;
 Castinplace concrete;
 Articulating concrete block (ACB);
 Geotextile;
 Riprap; and
 Gabions.
River Engineering for Highway Encroachments (Ayres Associations, 2001) states, "Each of these protection systems has its own unique mode of failure and threshold capability for erosion resistance. When using these systems, careful attention should be placed on the design of termination details at the crest, sides, and toe of the embankment. Powledge, et al. (1989a, 1989b) note that many of these systems were originally designed for uses other than the protection of embankments during overtopping flow, and have been adapted to this application as a result of a recognized need."
The two most potentially environmentally congruous countermeasures are HPTRMs and ACBs. HPTRMs are typically synthetic woven mats designed to be a permanent erosion control feature incorporating the benefits of vegetative cover. Once vegetation is fully established, properly selected and installed HPTRMs may resist shear stresses up to 15 pounds per square foot (lb/ft^{2}) for short periods of time. During erosion prevention testing, failure of HPTRMs is defined as soil loss of greater than 1 inch per hour. During the vegetation establishment phase, maximum allowable stresses are significantly less. Installed costs range from $5 to $20 per square yard.
ACBs are wet or drycast concrete blocks having a wide variety of configurations. Many ACBs have an open configuration for the establishment of vegetation, which gives additional strength, aids in water infiltration/exfiltration, and provides a more natural vegetated look. Select ACBs are also manufactured with openings allowing them to be cabled together laterally, vertically, or both. Precabled ACB mattresses may be shipped from the manufacturer and installed en masse, affording contractors a cost savings. Shape characteristics and interlocking methods are proprietary. Rigorous testing has shown unvegetated ACBs to be capable of withstanding overtopping shear stresses exceeding 34 lb/ ft2 for extended periods of time. Failure of an ACB is defined as "loss of intimate contact" with the soil surface. Installed costs for ACBs range from $35 to $90 per square yard.
Figure 5: Rollercompacted concrete cost per cubic yard
RCC is also an overtopping countermeasure for dams and uses the same ingredients as traditional concrete but is worked in a much drier mixture. RCC uses much of the same heavy equipment as well. The principal difference is in the placement process. Traditional concrete requires forms while RCC is dry enough that it may be dumped, spread by bulldozer, and compacted using vibratory rollers. RCC is typically more economical for large dam projects. Because concrete costs are typically in cubic yards, comparing the cost of a RCC installation versus ACB or HPTRM requires some knowledge of the final project design. Figure 5 presents a cost curve for cost per cubic yard of completed RCC projects. RCC typically has a greater erosion resistance threshold and has been documented withstanding overtopping flows in excess of 16 feet.
ACBs provide an excellent design alternative when considering the level of protection afforded for the installed cost. With any overtopping design, geotechnical concerns are of great importance. The minimum site soil properties that should be obtained for use in the design process are: general soil classification according to ASTM D 2487, Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System), particle size distribution, plasticity, and permeability. Prior to installation of any overtopping measure, slope stability must be ascertained as they are not intended for use in slope stabilization.
Table 1. Base factor of safety, SF_{B}
Example application

SF_{B}

Channel bed or bank

1.2 – 1.4

Bridge pier or abutment

1.5 – 1.7

Overtopping spillway

1.8 – 2.0

An important component of the ACB overtopping countermeasure is a filter sublayer. The filter may be a geotextile or granular filter composed of graded material. The filter is installed between the ACB and the base soil. Its primary function is to allow infiltration/exfiltration while retaining soil particles. A granular filter may also serve the dual purpose of providing a smooth, even surface assisting in the maintenance of intimate contact of the ACB with the soil surface. Careful design and installation of the appropriate filter material is crucial in the longterm performance of an ACB system. The choice of synthetic or gravel filter will dictate the filter design method. Gravel filter design is detailed in United States Army Corps of Engineers EM 111021913, Engineering and Design — Design and Construction of Levees, Appendix D. A method of determining synthetic filter criteria is available in the Harris County Flood Control District Design Manual for Articulating Concrete Block Systems.
Table 2. Consequence of failure
multiplier, X_{C}
Consequence of failure

X_{C}

Low

1.0 – 1.2

Medium

1.3 – 1.5

High

1.6 – 1.8

Extreme or loss of life

1.9 – 2.0

When using ACBs for overtopping protection, a drainage layer may also be incorporated into the design. A drainage layer lies between the countermeasure and any geotextile or filter being used. The drainage layer allows minimal flow beneath the system while maintaining contact with the subsoil under the force of the block weight. Fullscale ACB testing has shown that this appears to increase the hydraulic stability of the ACB system.
Table 3. Multiplier base
on hydraulic model, X_{M}
Hydraulic model

X_{M}

Deterministic

1.0 – 1.3

Empirical or stochastic

1.4 – 1.7

Estimates

1.8 – 2.0

The recommended design procedure for ACBs is the "factor of safety" method. The minimum acceptable target factor of safety is determined from sitespecific details using Tables 1 through 3 and the relationship in Equation 8:
Equation 8:
where:
SF_{T} = the target factor of safety;
SF_{B} = the base factor of safety;
X_{C} = the consequence of failure multiplier;
X_{M} = the multiplier based on the hydraulic model.
The proposed design is then evaluated using a moment balance approach detailed in the National Concrete Masonry Association's TEK 1112. The factor of safety is iteratively evaluated against the minimum acceptable value until an acceptable design is determined.
Although some ACBs have a similar look and shape, subtle differences can produce unique hydraulic performance capabilities. Obtaining fullscale flumetested values, provided by each manufacturer, is critical when determining the appropriate unit for specific project conditions.
Bryan N. Scholl, is a research assistant for Colorado State University.
Christopher I. Thornton, Ph.D., P.E., is director of the Hydraulics Laboratory and Engineering Research Center at Colorado State University.
Barrie King, E.T.I., is the supervisor of engineering for CONTECH Construction Product's Armortec product line.
REFERENCES
 Ayres Associates, 2001, Highways in the River Environment, River Engineering for Highway Encroachments, Hydraulic Design Series Number 6, National Highway Institute, Federal Highway Administration, Washington, D.C.
 Chen, Y.H. and Anderson, B.A., 1987, Development of a Methodology for Estimating Embankment Damage due to Flood Overtopping, FHWA Report No. FHWARD86/126.
 Clopper, P.E. and Chen, Y.H., 1988, Minimizing Embankment Damage During Overtopping Flow, FHWA Report No. FHWARD88/181.
 Dunlap, S., 2001, Design Manual for Articulating Concrete Block Systems, Harris County Flood Control District, Houston.
 Hewlett, H.W.M., Boorman, L.A., and Bramley, M.E., 1987, Design of Reinforced Grass Waterways, Construction Industry Research and Information Association, Report 116, London.
 Lagasse, P.F., Zevenbergen, L.W., Schall, J.D., and Clopper, P.E., 2001, Bridge Scour and Stream Instability Countermeasures, Second Edition, Hydraulic Engineering Circular No. 23 FHWA NHI 01003, Washington, D.C. (www.fhwa. dot.gov/bridge/hydpub.htm)
 Oswalt, N.R., Buck, L.E., Hepler, T.E., and Jackson, H.E., 1994, Alternatives for Overtopping Protection of Dams, Report of the ASCE Task Committee on Overtopping Protection, American Society of Civil Engineers, New York.
 Portland Cement Association, Roller Compacted Concrete, www.cement.org/water/dams_rcc.asp.
 Powledge, G.R., Ralston, D.C., Miller, P., Chen, Y.H., Clopper, P.E., and Temple, D.M., 1989b, Mechanics of Overflow Erosion on Embankments, II: Hydraulic and Design Considerations, Report of the ASCE Task Committee on the Mechanics of Overflow Erosion on Embankments, Journal of Hydraulic Engineering, ASCE, Vol. 115, No. 8.
 Tetra Tech MPS, 2006, Drainage Manual, Michigan Department of Transportation, Lansing, Mich.