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Risk Assessment for CERP Impoundments

Introduction Since the 1800’s, the Corps of Engineers has planned, designed, constructed, and operated dams in order to protect people and property from the damaging effects of floods. As expected, the Corps’ policy has always been to do so safely and the agency has had an extraordinary record of success. However, despite policies and criteria, all dams put the very people and property they are designed to protect at risk of catastrophic flooding. This risk, while small, is always present and may be the result of (1) a large operational release from the dam, or (2) a large accidental release due to dam failure.

Large Operational Release Generally speaking, the basis for design of reservoirs is a record of historical flooding in or near the watershed of interest, coupled with an evaluation of floods that could occur in the watershed. Historical flooding is considered when making decisions regarding the size and configuration of the reservoir storage and operational outlet works. Potential flooding is considered when making decisions regarding emergency release facilities, including the reservoir’s emergency spillway.

This process is documented in ER 1110-8-2(FR) which “sets forth hydrologic engineering requirements for selecting and accommodating the inflow design floods (IDF) for dams and reservoirs.” That document also stipulates that “the possible loss of life is obviously unacceptable … and, therefore, failure cannot be tolerated.” Accordingly, the ER requires that if a dam’s location places human life at risk, that dam should be designed “with appropriate freeboard, spillways, regulating outlets, and structural designs … such that the dam will safely pass an IDF computed from the probable maximum precipitation (PMP) occurring over the watershed”, where the PMP is defined as “the greatest depth of precipitation for a given duration that is [theoretically] physically possible over a given size storm area at a particular geographic location at a certain time of year.” The probable maximum flood (PMF) is the corresponding runoff, assuming the most severe hydrologic conditions, associated with the PMP. By definition, this event is extremely rare. Should the PMF occur, dams designed in accordance with the ER will maintain their structural integrity. However, because the PMF inflow from a gravity-based system typically exceeds the economical flood control capacity of a reservoir, large operational releases may be required to ensure the structural integrity of the dam. These operational releases, which may be anticipated but which are nevertheless very large, may exceed downstream channel capacity and, while this is not a dam failure, it does create a flood hazard for people and property downstream.

Large Accidental Release This type of release is typically associated with dam failure where the dam structure breaches and the reservoir ceases to store water. This results in an uncontrolled release of

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water into the downstream channel or surrounding areas. Such a failure may be a consequence of: • Geological and Geotechnical Problems. In this case, the soils and geological

formations upon which the dam is built or in which the reservoir’s water is impounded behave in an unanticipated manner, leading to failure of the dam. Examples of these problems include (1) geotechnical failure of the reservoir rim, abutment, or foundation, as illustrated in Figure 1; (2) seepage through cracks or faults at the dam site or in the reservoir; (3) landslide, in which soils along the reservoir rim slip into the reservoir; (4) failure of embankment and foundation due to piping; (5) deformation of dam under load (due to the force of the impounded water, ice formation, failure of an upstream reservoir, or some other catastrophic event); or (6) liquefaction, in which saturated soils behave as a liquid, often as a consequence of an earthquake.

Figure 1. Illustration of geotechnical problem that could lead to large accidental release

• Maintenance or Operation Problems. In this case, a component that is critical to control the impounded water fails due to improper operation or as a consequence of improper maintenance. The result is an uncontrolled release. For example, on July 17, 1995, a spillway gate on the Folsom Dam, near Sacramento, CA, failed as it was being raised. One contributing factor to the failure was trunnion pin friction on the tainter gate. As the gate was raised, uneven forces caused the gate to bend and flex, and eventually it failed, as shown in Figure 2. This caused an uncontrolled release of approximately 40,000 cfs, with nearly 40 percent of the impounded water eventually draining from the reservoir before the broken gate could be repaired. The reservoir

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Figure 2. Illustration of failure due to operation problem

• Sabotage. This is intentional destruction of the dam or a vital component of the water control structure. Figure 3 illustrates an extreme case of this: a dam in Germany’s Ruhr Valley that was bombed by the 617 Squadron of the British Royal Air Force during World War II. This sudden large breach in the dam, caused by specially designed bombs, resulted in widespread flooding downstream. It also disrupted industry, communications, and utility service.

Figure 3. Illustration of sabotage of dam

• Seismotectonic (Earthquake) Events. Although an earthquake itself may not cause a dam failure, it may lead to geological and geotechnical problems, as described above.

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• Structural Failure. As noted earlier, it is the policy of the Corps of Engineers to design dams that will not fail. Nevertheless, structure failure is a reality, as demonstrated by Malpasset Dam in southern France. This thin concrete arch dam failed due to cracking on the downstream side near the base of the dam. Approximately 500 people were killed as a result of the dam break.

A more comprehensive listing of potential engineering assessment factors for dam failure mechanisms is provided in Table 1.

Table 1. Potential Engineering Assessment Factors For Dams FLOOD INITIATING EVENTS

Embankment Liquefaction Stability (includes excessive deformation) Foundation Liquefaction Stability Fault movement Instrumentation NORMAL OPERATING INITIATING EVENTS

Embankment Geotechnical Piping Stability Toe erosion Surface Erosion Wave action Abutments Foundation Piping Reservoir Rim Stability Loss Of Capacity Erodibility Mines Instrumentation

EARTHQUAKE INITIATING EVENTS

Concrete Gravity Section External stability Internal stability Foundation Piping Abutment Foundation Stability (Dam Structure) Overall flood capacity PMF Overtopping Spillway and stilling basin system Structural Stability Hydraulic capacity Walls - overtopping Gates - structural capacity Gate piers - structural capacity Erodibility Mechanical Systems Electrical Systems Obstructions Drift and Debris Failed Slopes Sill Outlet Works Piping Electrical Systems Mechanical Systems Stability Intake Tunnel/Conduit Obstructions

Concrete Gravity Section External stability Internal stability Reservoir Stability Loss Of Capacity Mining Spillway and stilling basin system Structural Stability Gates - structural capacity Gate piers - structural capacity Appurtenances Outlet works

Concrete Gravity Section Foundation sliding Foundation piping Stresses within dam body Reservoir Reservoir rim stability Appurtenances Outlet works piping Outlet works gates Embankment Piping Slope stability Foundation Piping Stability Instrumentation Deterioration of Materials

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Risk Associated with Large Dam Releases Risk is defined as the exposure to a chance of injury or loss. The likelihood of this injury or loss is commonly expressed in terms of probability. The severity of the injury or loss may be expressed with any understandable metric. Severity of dam emergencies can be classified as follows, based on the guidance of ER 1110-2-1155 and FEMA 333 (April 2004): • Loss of Life or Injury. The direct loss of human life or bodily injury is a clear index

(tangible) of severity of a dam emergency. Related intangible impacts of dam emergencies include additional stress to floodplain occupants, stress to families and friends outside the floodplain who are unable to contact floodplain occupants, and so on.

• Property Loss. This is tangible, economic loss. It may be a direct loss—an economic cost in the floodplain downstream of or adjacent to the dam and reservoir. That cost includes, for example, damage to property due to inundation, cost of lost business, emergency cost, and clean up and recovery cost. In addition, the property loss may be an indirect loss—an economic cost to those outside the area directly affected by the dam emergency. That includes, for example, the cost of lost production in the flooded area, the loss of water supply due to release, and the cost of lost power revenue.

• Lifeline Loss. This is the tangible or intangible cost of loss of transportation links, utility lines, or other critical facilities.

• Environmental Loss. This is intangible damage to the environment caused by dam failure or large release. Examples include disturbance to downstream fisheries, elimination of riparian habitat, or dispersion of toxic material captured in the reservoir (such as hazardous mine waste).

Procedures for Preparing for and Dealing with Dam Emergencies Although the goal of USACE is to design, build, and operate dams that do not fail, there are limits in our ability to analyze and evaluate all engineering processes which could result in the failure of every structure. As a result, USACE developed the documents shown in Table 2. to provide procedures for preparing for and dealing with dam emergencies. The focal point of these documents is to protect life and property in the unlikely event of a large operational or accidental release.

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Table 2. USACE Dam Emergency Documents

Document title (1)

Summary of contents (2)

EM 1110-2-1420 Hydrologic engineering requirements for reservoirs (1997a)

Provides guidance for hydrologic engineering investigations for planning and designing reservoir projects. Presents typical study methods. Describes causes of dam failures and techniques for evaluating hydrologic and hydraulic impacts.

EP 1110-2-13 Dam safety preparedness (1996b)

Provides general guidance and information concerning dam safety preparedness. Includes planning and design guidelines, operation and maintenance guidelines. Provides a detailed description of contents of emergency action plans (EAPs).

ER 1110-2-1155 Dam safety assurance program (1997b)

Provides guidance and procedures for investigation and justification of modifications to completed dams when necessary for safety, as defined by new hydrologic or seismic data or changes in state-of-the-art design or construction criteria.

ER 1110-2-1156 Dam safety—organization, responsibilities, and activities (1992)

Prescribes policy, organization, responsibilities, and procedures for implementing dam safety activities. Calls for coordination with local officials for each dam’s emergency action plan.

ER 1110-8-2(FR) Inflow design floods for dams and reservoirs (1991)

Sets forth hydrologic engineering requirements for selecting and accommodating inflow design floods for dams and reservoirs. Calls for design, construction, and operation of dams such that they do not create a threat of loss of life or inordinate property damage. Stipulates use of PMP for design of dams capable of placing human life at risk or causing a catastrophe, should they fail.

ER 1130-2-530 Flood control operations and maintenance policies (1996c)

Establishes policy for operation and maintenance of Corps’ flood control structures. Identifies components of emergency plan. Provides guidance for developing evacuation plans for areas downstream of Corps’ dams.

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Risk Application for Impoundments Since there are limitations in our ability to predict and protect structures against every possible event (or combination of events), risk and the management of risk are key elements in the design and construction of all structures, particularly impoundments. Consequently, a risk assessment for these impoundments is an essential step in the design process to prevent these structures from being over or under designed. To perform a risk assessment, sufficient analyses must be conducted to provide a clear understanding of the exposure to the array of risks associated with the proposed facility, the need for risk reduction measures, the potential level of risk reduction for each measure, and the need for additional investigations to validate the key assumptions.

In order to adequately evaluate risk, we must first identify and understand the various failure modes for the structure with the recognition that this identification/understanding process is the foundation upon which the risk assessment is built. This assessment must be performed using considerable care and skill to avoid significant distortions in risk estimates. Another risk factor that must be considered is the evaluation and comparison of failure probabilities from an initiating event or events, and the case of the multiple or combined probabilities. For example, the probability of various, specific, events which may lead to failure must be considered along with the combined probability of two or more events occurring simultaneously. For a specific project configuration, the geotechnical or structural characteristics of the embankment materials may govern the overall design as opposed to the hydrologic/hydraulic conditions of the facility. By considering an array of that clearly defines the specific initiating modes of failure as well as the combination of events that may occur, the evaluation of risk based methodologies will be more easily understood, evaluated, and appropriately mitigated. For impoundments, one of the key components leading to a safe design which is completely based on an accurate assessment of risk is the determination of the embankment height. Since dams are capable of placing human life at risk or causing catastrophic damage, should they fail, they must be designed with appropriate superiority, appurtenance works, and regulation schedules so that the dam will safely pass the IDF. However, the requirements of ER 1110-8-2 (FR) only require that the dam “safely pass”, not fully contain, the IDF. Therefore, a dam may sustain damage during this rare event as long as it retains its structural integrity.

USACE has utilized the term superiority as an alternative terminology to freeboard as a means to address uncertainty and methodology in the analytical approach for establishing the top of protection for a dam or levee system. The control location for a levee as described does provide a means to reduce stresses along other segments of the system as is the case with spillway segments within a dam. When determining superiority, two major elements to consider are overtopping and over-wash, which are defined as follows:

• Overtopping. A static and/or dynamic event which occurs when the height of the

pool and/or associated waves exceed the maximum height of the embankment.

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• Over-wash. A dynamic event where the maximum height of the wave does not exceed the embankment height, but the wave run-up and/or wind borne spray associated with the energy dissipation of the breaking waves exceed the embankment height.

The differentiation between these two events is of extreme importance, particularly for impoundments with a relatively large spatial extent and exposure to severe wind events, which can create significant dynamic pool conditions. To completely prevent all over-wash during an IDF event, embankment superiorities must be extremely high which adds significant cost to projects. However, ER 1110-8-2 states that “zero over-wash is not always required under infrequent high pool conditions, but it is required that over-wash will not be of such a magnitude and duration as to threaten the safety of the dam.” In other words, infrequent over-wash events may not warrant absolute prevention since these pulsed loads may not lead to dam failure. Therefore, if the design over-wash event occurs, then the embankment height may be optimized to minimize costs while ensuring the structural integrity of the impoundment under the extreme event. For example, a large earthen embankment constructed of highly erosive materials may require zero over-wash in order to maintain structural integrity. However, if the embankment is constructed of non-erodible materials, such as monolithic or roller compacted concrete, the dam may be able to tolerate not only over-wash but also overtopping. Similarly, the evaluation and comparison of failure probabilities from an initiating event or events, in the case of the multiple or combined probabilities, must also be performed. For example, the probability of various, specific meteorological events which lead to failure must be considered along with the combined probability of two or more of these events occurring simultaneously. However, these probabilities must be compared to the probability of failure for other events such as the geotechnical or structural characteristics of the embankment which may govern the overall design. In other words, designers must consider the fact that a structure may be more likely to fail due to uncertainties in the geotechnical or structural analyses than due to a series of potential hydrologic events. By considering and evaluating a full array of failure probabilities that clearly define the specific initiating modes of failure, as more realistic and prudent evaluation of risk can be made. Application to CERP Design flood conditions for the CERP impoundments include an IDF based on the hazard classification of the impoundment and potential impacts due to flooding. Unlike typical reservoirs, CERP impoundments are formed by a fully encircling embankment that will be filled by pumping and direct precipitation. For these impoundments, there are no gravity (tributary) inflows. In addition to precipitation and pumped inflows, considerations are also given to wind setup and wave run-up for determining the final embankment heights due to annual tropical storm and hurricane events. Furthermore, many of these dams will likely be constructed out of sandy and crushed rock materials mined and processed locally. Interior slopes will be fully protected to prevent damage due to wave action and exterior slopes will be grassed, to the maximum possible extent.

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As with any probabilistic analysis, a standard set of stochastic and deterministic analyses are followed in order to accurately assess the risk of failure causing accidental releases of water. To illustrate the concepts discussed above, the following example is based on work done for the Everglades Agricultural Area Reservoir to determine the appropriate level of superiority.

Corps of Engineers Dam Safety criteria requires that any dam “safely pass” the probable maximum flood event. In South Florida, this is typically associated with either a large tropical storm or a series of smaller tropical storms which produce large amounts of rain. For the EAA project, several scenarios were evaluated and a probability matrix for the South Florida region was developed to identify the IDF based on numerical modeling of the hydrologic conditions for CERP impoundments which has been clearly defined in the CERP Design Criteria Memorandum (DCM-2), titled, “Wind and Precipitation Criteria for Freeboard.” The methodology described in DCM-2 is the accepted industry standard for IDF development of the PMF and subsequent calculation of wind set-up and wave run-up values. A study was conducted through the Hydrologic Engineering Center (HEC) to determine the risk of overtopping given the proposed embankment height and the increased residual risk for other, lower embankment heights. While specifically utilizing data for study of the EAA project, similar generalizations can be drawn that are applicable to other facets of the CERP program. Once the appropriate design events are established, the overall superiority can be developed through statistical and probabilistic evaluations of precipitation and wind events in conjunction with wave height/run-up estimates generated from accepted numerical models. Assessing the probability of the maximum precipitation/wind blown reservoir stage was conducted by computing the joint probability of these 2 events occurring simultaneously. Data available for building probability distributions of wind speed and precipitation were:

1) Hurricanes hitting Florida, 1894 to present (with data gaps) 2) Daily precipitation and maximum wind speed at West Palm Beach (1965-2004)

and Ft. Lauderdale (1973 – 2004) from the NCDC 3) TP-49 reported 100-year, 3-day precipitation of 16 inches and ASCE reported

100-year wind speed of 125 mph (3-second gust) From the data available, frequency curves were developed to estimate the probabilities for the worst case scenarios. Initially, the wind and precipitation were assumed to be independent, which is the simplest analysis to conduct. Based on this assumed independence, the probability of seeing any combination of rainfall and wind speed is simply the product of their separate probabilities: P (rain>r and wind>w) = P (rain>r) * P (wind>w) Following this logic, the computations for the hydrologic matrix are summarized in Table 3, below. Based on this data, it is obvious that Case 1 is by far the least probable

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(maximum rainfall paired with a rare wind event) and that Case 3 is most common (rare wind event paired with normal reservoir pool). However, regulations govern that a high hazard dam such as the EAA reservoir must be able to safely pass the IDF. Therefore, for this project, Case 1 governs the design. Table 3. Probability of Wind/Rain Combinations

The probabilities in Table 3 depict the likelihood that both the specified wind and rainfall of each case are exceeded. However, the variable of interest for the EAA is the maximum reservoir stage, and there are multiple combinations of wind and rain that could all produce the same maximum reservoir stage. The probabilities of all of those combinations must be summed to accurately capture the probability of exceeding that reservoir stage. A maximum reservoir stage vs. frequency curve provides a more useful answer. Considering independent correlation yields a more conservative approach. Final consideration should be give to effects of meteorological factors on reservoir stage.

To develop a stage versus frequency curve, the USACE Coincident Frequency method (EM 1110-2-1415) was used. The inputs to the coincident frequency method are:

1. Frequency curve of maximum wind speed 2. Duration curve of 3-day precipitation 3. Response surface for maximum reservoir stage

The “response surface” is meant to provide the reservoir stage resulting from any pair of precipitation and wind speed. Many event pairs were modeled to determine the resulting wind-blown reservoir stage. For this particular analysis, model runs were performed with a specified starting reservoir stage of 12 feet, embankment configuration of rough 3:1 slope, and no spillway. The result of the coincident frequency analysis was a stage vs. frequency curve for each reservoir cell (the project is divided into two, independent cells). Figures 4 and 5 contain the curves for each of the reservoir cells and Table 4 contains the resulting exceedance probabilities for several reservoir embankment heights

Case 3-day rainfall Probability Max. Wind Speed Probability Joint Probability

Case 1: PMP, 57.5in

.0024% or 1 in 42000

100-year, 125 mph (3-sec gust), 102 mph (1-hour dur)

1% or 1 in 100

1 in 4,200,000

Case 2: 100-year, 16in

1% or 1 in 100

Category 5 hurricane, 156 mph (3-sec gust), 124 mph (1-hour dur)

.21% or 1 in 490

1 in 49,000

Case 3: normal pool, 0in

99.9% or ~1 in 1

PMW, 200 mph (3-sec gust), 161 mph (1-hour dur)

.0024% or 1 in 42000

1 in 42,000

Case 4: Hurricane Easy, 39in

.043% or 1 in 2200

Hurricane Easy, 125 mph (3-sec gust), 102 mph (1-hour dur)

1% or 1 in 100

1 in 310,000

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– assuming independence of wind speed and rainfall. The exceedance probabilities listed in Table 4 can be considered the residual risk of each height of embankment. In other words, these are the probabilities that the embankment will be overtopped, even if the embankment is built to that height. Another factor to consider is the probability that the dam is at full pool. An argument could be made that the storage pool may not be at full pool at initiation of the IDF, therefore additional risk may be taken. However, although it is anticipated the facility will not constantly reside at full pool, the final design must consider the maximum operational pool unless specific, operational restrictions are placed on the reservoir in the authorizing documents. This understanding of the normal operating stage being potentially lower than maximum may only be considered qualitatively rather than quantitatively for risk. In a like manner, operational consideration may only tend to bolster the flexibility for regulating pools; however, dam safety regulations govern that operations must not be considered as a means to reduce superiority, thereby subjecting the facility to failure.

.2.1 .01 .001.55 12102550759095990

5

10

15

20

25

30

35

Frequency of Exceedance (%)

Cel

l 1 M

axim

um O

ver-

was

hing

Sta

ge (f

eet)

Figure 4. Maximum Reservoir Overtopping Stage versus Frequency for Cell 1 (Assuming Independent Correlation)

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.2.1 .01 .001.55 12102550759095990

5

10

15

20

25

30

35

Frequency of Exceedance (%)

Cel

l 2 M

axim

um O

ver-

was

hing

Sta

ge (f

eet)

Figure 5. Maximum Reservoir Overtopping Stage versus Frequency for Cell 2 (Assuming Independent Correlation) Table 4. Exceedance Probability assuming Independent Correlation

Probability of Exceedance (%) Reservoir Rim Height (ft) EAA Cell 1 EAA Cell 2 12 100 96 13 88 67 14 10 18 15 4.7 8.4 16 2.5 4.7 17 1.4 2.8 18 0.81 1.83 19 0.42 1.19 20 0.20 0.76 21 0.09 0.45 22 0.04 0.25 23 0.016 0.135 24 0.006 0.069 25 0.002 0.034 26 0.0009 0.0166 27 0.0003 0.0078 28 0.0001 0.0036

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Based on the results from these analyses, the Figure 6 shows the relationship between embankment superiority and flow rate at the inner rim of the embankment.

0.0

0.5

1.0

1.5

2.0

2.5

7 8 9 10 11 12 13 14

Superiority (ft)

Ove

rwas

h (c

fs/lf

)

Figure 6. Superiority versus Flow Rate at embankment inner rim. A cursory review of Figure 6 would indicate that the embankment superiority for the EAA reservoir would need to be 13 feet in order to ensure zero overflow (or over-wash) over the dam. However, other considerations need to be considered such as the probability of failure due to geotechnical or structural conditions. For the EAA reservoir, there has been particular concern and debate as to whether the embankment materials can resist the over-wash forces during severe events. The probability of dam failure has been studied by several researchers including Cullen (1990), International Committee on Large Dams (ICOLD, 1997), Foster et al. (1998), and Foster et al. (2000). In general, the probability of failure was determined through a statistical examination of over 45,000 existing dams worldwide. ICOLD determined that the probability of failure for all embankment dams ranged from 1.0x10-3 to 4.0x10-3 and that the probability of failure from internal erosion or piping was twice as likely as through overtopping – based on the assumption that an extreme hydrologic event led to active overtopping resulting in erosive failure. Foster et al. (1998) developed similar findings with a cumulative probability range from 6.3 x 10-4 to 3.5 x 10-3. Foster et al. (1998) suggested that the probability of failure from internal erosion or piping was similar to that of overtopping. For failures caused by internal erosion or piping, Foster et al. (2000) developed more specific probability estimates of various dam types through a detailed review of available design/construction information. Table 5 lists the average annual probability of dam failure for the most common types of embankment dams studied.

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Table 5. Probability of Failure for Embankment Dams

Dam Type Probability Homogeneous Earthfill – Average Annual Probability 2.09x10-3 Earthfill with filter – Average Annual Probability 1.9x10-4 Zoned Earthfill – Average Annual Probability 1.9x10-4 Zoned Earth and Rockfill – Average Annual Probability 1.5x10-4 Concrete or other Face on Earthfill – Average Annual Probability 6.9x10-4 Concrete Core with Earthfill – Average Annual Probability <1.3x10-3 Similar relationships for failure can also be drawn for other construction material types such as monolithic concrete or RCC. Structural design guidance moved to a reliability approach in the early 1980s and design methodology used by USACE and nationally recognized specifications and standards specify appropriate nominal load values and combination of loads to be used in design along with load factors to be applied to different categories of loads and resistance factors applied to material strengths. These loading requirements have evolved gradually and have been studied using probabilistic methodology. Utilizing guidance presented in ITL-95-2, titled, “Event Combination Analysis for Design and Rehabilitation of U.S. Army Corps of Engineers Navigation Structures”, the relative probability of failure of a RCC structure (as may be designed for the EAA) has been determined to be on the order of 1x10-4. Therefore, the relative probabilities of failure for a zoned earth embankment or a RCC embankment are on the order of 1.9x10-4 or 1.0x10-4, respectively. As indicated in Table 3, the relative probability of the design hydrologic event has been determined to be on the order of 1 in 4,200,000 or 2.4x10-7, under the premise that Case 1 hydrology of DCM-2 is considered as the IDF (noting that this event in itself may not result in failure but merely represents the probability of occurrence). If Case 1 is used alone, however, the probability associated with it should be the total probability of the reservoir stage it causes. Utilizing the stage frequency relationship for EAA, Cell 1 the probability would be 2x10-5; similarly for Cell 2 the probability would be 7.8x10-5. As noted earlier, with an embankment and superiority established at a level for full containment of the IDF, the relative probabilities of a geotechnical or structural circumstance causing uncontrolled release is more likely than the probabilities of over-wash with the combined extreme events as is with Case 1 (resulting in failure). From this comparison it appears that the probabilistic criteria for determining the crest height should not be more restrictive than that commonly accepted for geotechnical or structural reliability. Recognizing that failure of the facility is more likely to occur due to a latent geotechnical or structural defect than to a rare hydrologic event, 11 feet of superiority represents a much more acceptable level of over-wash for the EAA reservoir than the initial estimate of 13 feet. Superiority was determined through a deterministic assessment of the numerical approach with support rationale being presented from a probabilistic approach.

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Conclusion Considerable time has been expended to research, define, evaluate, and discuss acceptable levels of over-wash relative to superiority determination of CERP impoundments. The use of stochastic analyses and data to determine superiority and “acceptable” over-wash can be a very effective tool. When probabilities and joint probabilities of failure are not fully considered, the interpretation of dam safety criteria will always lead to a more conservative and less cost-effective design than necessary. On the other hand, undo emphasis can be placed on numerical modeling results when computer models produce results that appear much more accurate than the data used to generate them. In doing so, overemphasis has been placed on the numerical results for defining “zero over-wash” when a more balanced evaluation of the data should be relied upon. Figure 6 depicts the asymptotic relationship of the superiority to over-wash rates for the EAA project. As shown, the steep downward slope of the curve is indicative of the reduced risk of increased over-wash rates with increased embankment elevations. The question that must be answered is how far along the curve is enough when determining practical risk for over-wash. Considering the probability of the design hydrologic event (i.e., IDF being the PMP plus wind) and the asymptotic relationship of the superiority over-wash rates, defining “zero over-wash” and the final embankment superiority must be based on a holistic evaluation of the available data and grounded with sound engineering judgment. Based on the principles and concepts presented in this paper, the overall risk associated with any CERP reservoir should consider both the probability of different failure mechanisms (e.g., overtopping, shear, internal erosion) and the consequences of the failure as measured by potential loss of life and property. In addition, consideration of each of these failure mechanisms must be balanced, uniform, and based on sound data. Furthermore, evaluation of tolerable or acceptable risk should be considered for each CERP impoundment on an individual basis by considering the probability of failure and the subsequent consequences of failure.

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