RISK INDEXING TOOL TO ASSIST IN PRIORITIZING IMPROVEMENTS TO

EMBANKMENT DAM INVENTORIES

By Glen R. Andersen,1 Luc E. Chouinard,2 William H. Hover,3 and Chad W. Cox4

ABSTRACT: A risk indexing tool is proposed to assist in the prioritization of maintenance, repair, and evaluationtasks on embankment dams that are generally less than 33 m (100 ft) high and for which there is little or noinstrumentation, limited or no information concerning as-built conditions, and little or no information on theperformance history. Under such circumstances, there may not be enough information available to performanything other than an ‘‘indexing’’ type of analysis to assist in prioritization. The risk indexing tool is basedupon identifying potential deficiencies in the physical condition of the dam and rating the overall importanceof these deficiencies to the safety of the structure. It is meant as an index of risk (indication) and not as a directmeasure of risk. Checklists are presented for onsite inspections to determine current physical condition. Conditionis defined in terms of a condition function that is based upon a condition indexing scale. Four potential failuremodes are considered: (1) overtopping; (2) external erosion; (3) piping; and (4) mass movement (slope insta-bility). Absolute probabilities are specifically not factored into the analysis. Conditional probabilities are esti-mated for each failure mode using a Bayesian updating procedure based on dam attributes. A simple failurecriticality analysis is performed wherein specific changes in physical condition of the dam are considered tocontribute to the probability of failure for each mode. From this failure criticality analysis and the conditionalprobabilities of failure, the relative importance of the various changes in physical condition is determined. Thephysical condition and the relative importance are then combined for each observable deficiency to form a riskindex. These risk indices are used to prioritize expenditures for improvements on the premise that actions toaddress the most significant physical deficiencies are preferred.

INTRODUCTION

Decision analysis for the management of an inventory ofaging embankment dams should include a consideration of theoverall risk or probability of a failure within the inventory.Engineering risk can be defined as the probability of failuremultiplied by the cost of failure and hence is the expected costof failure. The price of a failure can include but is not limitedto: replacement cost; loss of service cost; loss of life; damageto the environment; or other societal costs.

The price of a classical risk analysis and the time requiredfor its implementation may not be justified for dams on whichthere has been no modern engineering analysis and for whichthere is little or no information available concerning as-builtconditions and performance history and for which there is littleor no instrumentation. For such dams, current budgets avail-able to state regulators may only enable a rapid walk-throughinspection once every several years. Information necessary toperform a risk analysis may not be obtainable under currentbudgeting constraints and in order to help prioritize mainte-nance, repair, and evaluation tasks on such dams, a simplifiedprocedure that can be conducted in real time during a walk-through inspection at nominal additional cost may be justified.The indexing system proposed herein is intended for this pur-pose.

In an effort to develop decision analysis tools that can bemore readily applied to large inventories of civil engineering

1Sr. Engr., Burns Cooley Dennis Inc., Ridgeland, MS 39157; formerly,Asst. Prof. of Civ. Engrg., Michigan State Univ., East Lansing, MI 48823.

2Assoc. Prof. of Civ. Engrg., McGill Univ., Montreal, Quebec, CanadaH3A 2K6.

3Prin. and Sr. Vice Pres., GZA GeoEnvironmental Technologies, Inc.,Norwood, MA 02062.

4Asst. Proj. Mgr., GZA GeoEnvironmental Technologies, Inc., Nor-wood, MA 02062.

Note. Discussion open until September 1, 2001. Separate discussionsshould be submitted for the individual papers in this symposium. Toextend the closing date one month, a written request must be filed withthe ASCE Manager of Journals. The manuscript for this paper was sub-mitted for review and possible publication on September 27, 1999; re-vised December 8, 2000. This paper is part of the Journal of Geotech-nical and Geoenvironmental Engineering, Vol. 127, No. 4, April, 2001.qASCE, ISSN 1090-0241/01/0004-0325–0334/$8.00 1 $.50 per page.Paper No. 21939.

JOURNAL OF GEOTEC

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subj

facilities in a cost effective manner, the U.S. Army Corps ofEngineers, under the Repair, Evaluation, Maintenance, and Re-habilitation (REMR) program, has focused on condition orphysical state as determined through on-site inspections ratherthan focusing directly on risk. The approach to decision anal-ysis based solely upon physical condition is known as ‘‘con-dition indexing.’’ A joint research project by Hydro-Quebecand the Corps of Engineers developed a decision analysis ap-proach that bridges the gap between decision-making basedsolely on condition and decision-making based upon classicalrisk analysis while incorporating the most desirable aspects ofeach (Andersen et al. 1998). This new approach considers thecurrent physical state and the impact that such a state mayhave upon a potential failure. The theoretical underpinningsfor this new approach, termed ‘‘function-based condition as-sessment,’’ were presented by Andersen and Torrey (1995).This new approach is based upon conditional probabilities offailure rather than absolute probabilities of failure thus avoid-ing one of the most controversial aspects of risk analysis ap-plied to embankment dams (i.e., that it might not be possibleto reliably predict an actual probability of failure for an em-bankment dam).

The purpose of this paper is to present a simplified ‘‘index-ing-type’’ tool that can be used to help prioritize maintenanceand repair tasks for large inventories of dams for safety offi-cials, practicing engineers, and owners/operators of inventoriesof dams for which no or limited modern engineering analysishas been performed, for which there is little or no instrumen-tation, and for which there is little or no information availableon as-built conditions or performance history. This tool is asimplified version of the one developed for the Corps of En-gineers and Hydro-Quebec. The term indexing is used hereinas providing an indication of a potential problem in much thesame way that Atterberg Limits are routinely used in geotech-nical engineering practice to provide an indication of potentialsensitivity problems, expansive soil problems, compressibilityproblems, etc.

Risk-indexing is based upon identifying deficiencies in thephysical condition of the dam and rating their overall impor-tance to the safety of the structure in terms of a postulatedfailure. On-site inspections are employed to determine currentphysical condition, where condition is defined in terms of a

HNICAL AND GEOENVIRONMENTAL ENGINEERING / APRIL 2001 / 325

ect to ASCE license or copyright; see http://pubs.asce.org/copyright

FIG. 1. Summary of Risk Indexing Methodology

condition function that is based upon a standardized conditionindexing scale. The relative importance of these potentialphysical conditions is determined by considering the condi-tional probability of failure modes and the conditional proba-bility that each physical condition would be associated with aparticular failure mode. Four potential failure modes are con-sidered: (1) overtopping; (2) external erosion; (3) piping; and(4) mass movement (slope instability). These modes are eval-uated in terms of the failure-initiating event (or proximatecause) or the first event in a sequence of events that could leadto an uncontrolled release of the reservoir. Conditional prob-abilities are estimated for each failure mode. A simplified fail-ure criticality analysis is performed wherein specific changesin physical condition of the dam are considered to contributeto the probability of failure for each mode. From this failurecriticality analysis, the relative importance of the variouschanges in physical condition is determined. Then, an on-siteinspection is performed in order to determine the physical stateor condition of the dam. The physical condition and the rela-tive importance are then combined for each observable defi-ciency to form a risk index.

SUMMARY OF RISK INDEXING TOOL

The tool presented herein is called a risk index because itprovides an indication of potential levels of risk that might beassociated with an embankment dam failure. This tool is nota measure of risk but provides an indication of potential levelsof risk. These risks are quantified as deficiencies in the currentphysical state or condition of the dam and are weighted bytheir overall importance to the safety of the dam and by thevulnerability and hazard potential of the dam. Herein, an em-bankment dam failure is defined as an uncontrolled release ofthe reservoir.

Fig. 1 presents a flowchart for the proposed methodology.The first step is to determine the overall importance of thedam through a consideration of the vulnerability of the damand the downstream environment and its hazard potential in amanner similar to that developed by Hydro-Quebec for theirdams, Dascal (1991), but modified according to the general

326 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENG

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subje

guidelines presented by FEMA (1998). The relative impor-tance of various observable physical conditions that could leadto a failure is then determined through a Bayesian updatingprocedure and a simplified failure criticality analysis basedupon conditional probabilities of failure determined by expertelicitation. An onsite inspection is then performed to determinethe current physical state. Inspection forms that describe var-ious indicators of physical state are provided herein. The rel-ative importance of the physical conditions is combined withthe importance of the dam in the inventory to obtain the over-all importance with respect to the entire inventory. The resultsof the importance determination are then combined with thecurrent physical condition (in a simple multiplication) to com-pute a risk index for each observed deficiency. For a particulardam, these risk indices are summed to estimate an overall riskindex. Prioritization can be accomplished based on particularphysical deficiencies or upon the overall risk index.

IMPORTANCE OF EMBANKMENT DAMIN INVENTORY

The importance of an embankment dam within an inventorycan be determined through a rough indication of the potentialrisk that it poses. The guidelines presented herein for damimportance have been adapted from those developed by theDam Safety Directorate of Hydro-Quebec (Dascal 1991) andthose presented by FEMA (1998). These guidelines and pro-posed vulnerability and hazard potential measures are pre-sented for illustrative purposes only. Should any organizationwishing to use this risk indexing procedure find other measuresof dam importance rather than the vulnerability and hazardpotential proposed herein that are more relevant to their in-ventory, or should they wish to adopt a more direct measureof risk for determining dam importance, they are encouragedto do so. For example, Hydro-Quebec is currently developinga direct risk-based measure for dam importance to be used inconjunction with their condition measurement tool.

An indication of the potential risk that a dam break posescan be expressed in terms of a vulnerability function (V ) anda hazard potential function (H). The vulnerability of the damand downstream environment can be defined as the capabilityof or susceptibility to being damaged or harmed. In this sense,a vulnerability measure would involve the susceptibility of thedam and the susceptibility of the downstream environment todamage. Conversely, the hazard potential can be defined as ameasure of the specific types of damage such as property lossor loss of life that may result in the event of a dam breach.From these two definitions it is possible to imagine a dam andthe associated downstream environment that might be verysusceptible to damage (if it had a high likelihood of failureand there was a large storage capacity so that a large areadownstream would be susceptible) but with a low hazard po-tential (if there were very few inhabited structures in the po-tential flood zone).

According to the dam safety directorate in Hydro-Quebec,a vulnerability measure for the dam and the downstream en-vironment can depend upon intrinsic and time-invariant char-acteristics (I ) of the dam (I1 = height; I2 = dam type; I3 =foundation type; and I4 = storage capacity) and upon externaltime-variant factors (E) associated with the dam (E1 = age;and E2 = seismicity). Additionally, it can depend upon designcharacteristics (D’s) associated with the dam (D1 = spillwayadequacy; and D2 = mass movement factor of safety). Notethat seepage and internal erosion are not included in this mea-sure of design characteristics because for the types of damstargeted by this methodology there is generally no design in-formation to indicate that internal erosion defense measures orseepage control measures have been incorporated into the

INEERING / APRIL 2001

ct to ASCE license or copyright; see http://pubs.asce.org/copyright

TABLE 2. Intrinsic Characteristics (I2 = Type of Dam)

Type ofdam(1)

Description(2)

Score(3)

Rockfill Composed primarily of cobble or larger sized par-ticles

4

Earthfill Composed primarily of gravel, sand, and/or silt andclay sized particles

10

TABLE 1. Intrinsic Characteristics (I1 = Height of Dam)

Height of dam[m (ft)]

(1)Score

(2)

<2.7 (<9) 12.7–12.2 (9–40) 312.2–30.5 (40–100) 6>30.5 (>100) 10

Note: Ranges and scores can be modified for specific owner require-ments.

foundation or the embankment and these are generally hiddenfrom visual observation.

A discussion for the use of each of these surrogate factorsas a measure of vulnerability is as follows: (1) the dam heightis the determinant factor of the hydraulic load magnitude onthe dam and one of the main factors influencing the magnitudeof the area affected downstream in the event of a break (extentof the break wave); (2) statistical studies have shown variousfailure probabilities for different dam types; (3) the resistanceto internal piping of the foundation and the stability of thefoundation to resist a mass movement varies according to thematerial of which it is made and hence is related to the prob-ability of a dam breach; (4) the storage capacity is a secondfactor that is related to the magnitude of the flooded areadownstream following a dam break; (5) there is a correlationbetween the likelihood of failure of an embankment dam andits age in the sense that a larger percentage of embankmentdams have failed during initial filling or early on in their lives(deterioration of components with age is considered in the con-dition assessment portion of this proposed methodology andas a result is not considered specifically in this vulnerabilitymeasure); (6) seismicity has a strong effect on the likelihoodof a failure; (7) an inadequate spillway capacity will result inan overtopping; and (8) inadequate factors of safety againstmass movement will result in a failure of the dam. Several ofthese justifications can be found in Dascal (1991).

Each of the factors in the vulnerability function are treatedon a scale from 1 to 10 with the overall vulnerability beingexpressed as the product of the mean value of the intrinsictime-invariant characteristics, the mean value of the externaltime-variant factors, and the mean value of the design char-acteristics according to the following equation:

(I 1 I 1 I 1 I ) (E 1 E ) (D 1 D )1 2 3 4 1 2 1 2V = ? ? (1)

4 2 2

where all terms have been previously defined. Note that themaximum vulnerability score is 1,000 in accordance with (1).Thus, a three-order-of-magnitude range is available for clas-sifying dams within the same inventory according to vulner-ability. This three-order-of-magnitude range might be similarto that from a probability of failure analysis to dams in similarinventories. Tables 1–8 present each of the vulnerability fac-tors, the suggested criteria, and the suggested scores that areused in the calculation. Note that the relationship between thecriteria and the ‘‘scores’’ proposed is approximately ‘‘linear.’’These criteria are in general conformance with similar criteria

JOURNAL OF GEOTEC

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subj

TABLE 7. Spillway Adequacy (D1)

Conditions(1)

Score(2)

(a) Known conditions

Spillway capacity is less than half the required capacity 10Spillway capacity is greater than half the required capacity 5Spillway capacity is greater than required 1

(b) Suspected conditions

Spillway capacity is less than required 5Spillway capacity is greater than required 2

Note: Only select known conditions if a hydrologic and hydraulic anal-ysis has been performed.

TABLE 6. External Factors (E2 = Seismicity)

Modified Mercalli intensity(1)

Score(2)

V or lower 1VI 2VII 6VIII 8IX 10

Note: Uniform Building Code seismic zones or other relevant seismiccriteria could be used in place of modified Mercalli Intensity scale.

TABLE 5. External Factors (E1 = Age of Dam)

Age of dam(years)

(1)Score

(2)

0–9 1010–29 830–59 560–99 2>100 1

TABLE 4. Intrinsic Characteristics (I4 = Storage Capacity)

Storage capacity[ha ?m (acre-ft)]

(1)Score

(2)

<6.17 (<50) 16.17–123 (50–999) 3123–6,170 (1,000–50,000) 6>6,170 (>50,000) 10

Note: Ranges are in accordance with summarized ranges published byFEMA (1998). Actual ranges could be modified to reflect particular in-ventory within state or jurisdiction.

TABLE 3. Intrinsic Characteristics (I3 = Type of Foundation)

Type of foundation(1)

Score(2)

Rock 1Moraine 5Alluvium 10

developed by several states as summarized by FEMA (1998).For any particular state or jurisdiction, these criteria, the cor-responding scores, and the relationship between them (linearversus nonlinear) can be modified to be representative of theapplicable regulations or in accordance with the users’ per-sonal preferences, experience, or judgment. Additionally, othervulnerability factors can be employed that might be more rep-resentative of the particular dams in that jurisdiction.

The hazard potential of the dam is determined in accordancewith specific types of damage that could occur downstream as

HNICAL AND GEOENVIRONMENTAL ENGINEERING / APRIL 2001 / 327

ect to ASCE license or copyright; see http://pubs.asce.org/copyright

TABLE 8. Mass Movement Factor of Safety (D2)

Conditions(1)

Score(2)

(a) Known conditions

Factor of safety against mass movement is less than required 10Factor of safety against mass movement is greater than required 1

(b) Suspected conditions

Factor of safety against mass movement is less than required 7Factor of safety against mass movement is greater than required 2

Note: Select known conditions only if slope stability analyses havebeen conducted. Select factor of safety suspected to be less than requiredonly if there is visible evidence of potential slope instabilities.

a result of a dam breach following the recommendations byFEMA (1998) and is quantified in terms of a number (H) ona scale from 1 to 10. Three hazard potential ranges, high, me-dium, and low, are proposed. High hazard dams (score of 10)are classified uniquely in terms of the potential for loss of life(i.e., if there is the potential for loss of life then it is a highhazard dam). Medium hazard dams (score of 5) are those forwhich there is no potential for loss of life but for which thereare significant possible economic losses, environmental dam-age, and/or disruption of life-line facilities. These dams areoften located in rural or agricultural areas with population andsignificant infrastructure. Low hazard dams (score of 1) arethose for which there is no potential loss of life and for whichthere are minor economic and/or environmental losses. Oftenthese losses would be limited to the owner’s property. Thesehazard potential ranges are suggested. For any particular stateor jurisdiction, they may be modified to reflect applicable reg-ulations or varying conditions.

The importance of a dam (IDam) in an inventory is deter-mined as its overall dam vulnerability score multiplied by itshazard potential score in accordance with the following equa-tion:

I = V 3 H (2)Dam

where all terms have been previously defined.The maximum importance of a dam is 10,000 in accordance

with (2). Thus, the hazard potential consideration permits anadditional order-of-magnitude variation in the importance ofdams within an inventory. A dam possessing the highest scoresin each category and having a high hazard potential will havean importance score of 10,000, while a dam with the lowestscores in each category will have an importance of 1 thusproviding a four-order-of-magnitude range.

RELATIVE IMPORTANCE OF PHYSICAL CONDITIONS

There are various physical conditions (physical states) thatcan lead to failure of an embankment dam. These include: (1)loss of the spillway capacity; (2) erosion of the spillway: (3)loss of function of the low-level outlet works; (4) loss of crestelevation; (5) loss of the embankment surface protection ma-terial; (6) piping in the embankment or along the low-leveloutlet; (7) piping in the foundation; (8) a slide in the embank-ment; and (9) a slide in the foundation and embankment. Fora particular dam, the relative importance of these physical con-ditions will vary. This relative importance is defined as therelative likelihood that each would be associated with a failureevent. For the purposes of this analysis, the association be-tween changes in physical state and failure is defined in termsof the ‘‘Failure Initiating Event.’’ In other words, the relativeimportance of physical conditions is assessed in terms of theirlikelihood of being the initiating event in a sequence of eventsthat could lead to a failure. The analysis depicted in Fig. 2presents a simplified failure criticality analysis that is used to

328 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGIN

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subject

FIG. 2. Simplified Failure Criticality Analysis for Determina-tion of Relative

estimate the relative importance of each physical condition interms of conditional probabilities of the four potential failuremodes (overtopping, external erosion, piping, and mass move-ment).

The relative importance is defined as the probability thateach physical condition (or physical state) would be the ini-tiating event in a sequence of events that could lead to a failureof the dam. These conditional probabilities are determined ina two-step process. First, the evaluator must consider all ofthe construction, performance, and behavioral information thatis available for the dam (generally after an on-site inspection)and then determine the relative (conditional) probabilities ofthe four potential failure modes, P[Mi uF ], interpreted as theprobability of mode i given a failure. Remember that the fail-ure modes are considered to be the failure-initiating events. Inassigning these conditional probabilities, the evaluator can usethe following question:

Considering a failure of the dam, what is the relative like-lihood that each of the four failure modes will be the ini-tiating event?

and assign these probabilities directly using subjective judg-ment. In this case, it is suggested that a precision no greaterthan 10% be used and that any failure mode with a conditionalprobability of less than 10% be given zero conditional prob-ability. If actual probabilities of failure have been determinedfor each of the failure modes in a risk or reliability analysis,these can be used in place of the direct elicitation. Note thatthe consequence of assigning a zero conditional probability toa failure mode at this stage is to cause all physical deficienciesassociated with it to have a zero risk index in the final analysis.

General guidance can be provided for the selection of theseconditional probabilities from the reported dam incidents sum-marized by the United States Committee on Large Dams Sub-committee of Dam Incidents and Accidents (USCOLD 1988).For those incidents involving a failure of the dam (failure type1 or failure type 2 as outlined in the report), 81 were associated

EERING / APRIL 2001

to ASCE license or copyright; see http://pubs.asce.org/copyright

TABLE 9. Prior Conditional Probabilities for Failure Modes(USCOLD)

Failure mode(1)

Prior conditional probability(2)

Overtopping 0.49Piping 0.32Mass movement 0.09Surface erosion 0.10

with embankment dams. A type 1 failure is defined as ‘‘Amajor failure of an operating dam, which has involved com-plete abandonment of the dam.’’ A type 2 failure is defined as‘‘A failure of an operating dam, which at the time may havebeen severe, but was of a nature, and extent which permittedthe damage to be successfully repaired and the dam againplaced in operation.’’ Of the reported failures, 49% were at-tributed to overtopping, 32% were attributed to piping, 10%were attributed to erosion, and 9% were attributed to massmovement. In the absence of additional information, the en-gineer may consider using these percentages as a startingpoint. Clearly, the actual conditional probabilities for a partic-ular dam are a function of site specific and dam specific factorsand can vary dramatically from the national averages reportedby USCOLD (Table 9). Note that the probabilities in Table 9assume that the dam has failed but do not say anything aboutthe likelihood of failure, just the mode of failure.

An objective procedure has been developed to assist in es-timating the conditional probabilities of failure for the fourmajor failure modes should the evaluator not wish to relywholly upon subjective opinion. The probabilities of failureobtained from the 1998 USCOLD data base can be used asprior probabilities and represent the best estimates of the rel-ative probabilities of failure in the absence of information rel-ative to a given dam, P[Mi uF]. These prior conditional prob-abilities can be updated using Bayes Theorem (Benjamin andCornell, 1970) with information available on dam attributes inaccordance with the following equation:

JOURNAL OF GEOTECH

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subject

P[X uM ù F] ?P[M uF ]i i iP 0[M uX ù F] = (3)i i 4

P[X uM ù F] ?P[M uF ]i i iOi=1

where Xi = an observation of the presence of an attribute rel-ative to failure mode i, and P0[Mi uXi ù F] is the updatedconditional probability of failure mode i in the presence ofattribute Xi and failure. In the above equation, the denominatoris a summation over the four possible failure modes. The equa-tion is applied recursively for all the attributes Xi that are pres-ent at the dam using the latest posterior probabilities as thenew prior probabilities. Eq. (3) assumes that each attribute hasa first-order effect and that there is no synergy between attri-butes (in order to simplify the analysis). The conditional prob-abilities relating the attributes to the failure modes, P[Xi uMi ùF] in (3), must be determined and placed in Fig. 3. The writerspropose the use of expert elicitation for this purpose relyingupon engineering judgment and where appropriate upon ananalysis of existing data bases on dam performance. Note thatthe probabilities of the complementary events can be obtainedby subtraction.

A conditional probability of 0.5 indicates that an attributehas no effect on the updated conditional probability of thefailure mode while a conditional probability larger/smallerthan 0.5 indicate that the presence of the attribute increases/decreases the likelihood of the failure mode, respectively. Inother words, if the likelihood of an attribute being presentgiven a failure mode and failure is 0.5, then its converse (like-lihood that the attribute is absent) is (1–0.5) or 0.5 and theattribute is a neutral indicator for that particular failure modegiven failure. These updating conditional probabilities are de-fined for four cases: (1) when the attributes are known to bepresent (A in Fig. 3); (2) when they are suspected to be present(B in Fig. 3); (3) when they are suspected to be absent (C inFig. 3); and (4) when they are known to be absent (D in Fig.3). In other words, for each attribute that is applicable to aparticular dam, the evaluator answers whether or not the at-

FIG. 3. Conditional Probabilities of Attributes Given at Failure Mode and Failure

NICAL AND GEOENVIRONMENTAL ENGINEERING / APRIL 2001 / 329

to ASCE license or copyright; see http://pubs.asce.org/copyright

TABLE 10. Hypothetical Calculation for Relative Importance of Physical Conditions (from Direct Elicitation)

Conditional probabilitiesfor failure modes

(1)

Conditional probabilities forphysical conditions

(2)

Relative importanceof observable physical

conditions to dam(3)

Relative importanceof observable physicalconditions to inventory

IDam = 1,000(4)

Overtopping (60%) Loss of or inadequacy in spillway capacity 30% 30% 3 60% = 18% 0.18 3 1,000 = 180Overtopping (60%) Loss of crest elevation 10% 10% 3 60% = 6% 0.06 3 1,000 = 60Overtopping (60%) Loss of function of outlet works 60% 60% 3 60% = 36% 0.36 3 1,000 = 360External Erosion (0%) —a —a —a

Piping (30%) Piping in embankment 70% 70% 3 30% = 21% 0.21 3 1,000 = 210Piping (30%) Piping in foundation 30% 30% 3 30% = 9% 0.09 3 1,000 = 90Mass movement (10%) Slide in embankment 50% 50% 3 10% = 5% 0.05 3 1,000 = 50Mass movement (10%) Slide in foundation and embankment 50% 50% 3 10% = 5% 0.05 3 1,000 = 50

aNo further calculations are necessary because the initial conditional probability was assessed to be less than 10%.

tribute is present and whether or not she/he suspects or knowsthat it is.

Next, the evaluator considers each failure mode and assignsconditional probabilities to each of the physical conditions thatare associated with it P[Cj uMi], interpreted as the probabilityof physical condition j being associated with failure mode i.In assigning these probabilities, the evaluator can use the fol-lowing question:

Considering the particular failure mode, what is the relativelikelihood that each of the associated physical conditionswould have precipitated it?

Again, the evaluator should not use a conditional probabilityless than 10% and any physical condition that is assessed tohave a conditional probability of less than 10% should begiven a zero. If the actual probabilities of failure have beendetermined for each of these physical conditions, as may bethe case in a risk or reliability analysis, these can be used todetermine the conditional probabilities in place of expert elic-itation.

After assigning the second level of conditional probabilities,the relative importance of each physical condition (RIj) is com-puted by simply forming the product of the conditional prob-abilities from the two analysis levels depicted in Fig. 2, withthe importance of the dam in accordance with the followingequation:

RI = P[C uM ] ?P[M uF ] ? I (4)j j i i Dam

where all terms have been previously defined. Under this def-inition, the relative importance of the jth physical conditionon a dam is the conditional probability that it would lead to afailure of the dam multiplied by the importance of the dam inthe inventory. Table 10 presents a hypothetical relative impor-tance determination for the physical conditions on a fictitiousembankment dam. In this example the importance of the em-bankment dam in the inventory is assumed to be 1,000. Ac-cording to the hypothetical calculation presented in Table 10,the most significant changes in physical conditions at this par-ticular dam would be the loss of function in the outflow works,piping in the embankment, and the loss of the spillway ca-pacity.

Note that this analysis for relative importance of physicalconditions is generally conducted after an onsite inspection orafter an analysis of existing dam safety inspection reports,when the engineer would have more information about thecurrent physical condition of the dam and the most likelymodes of failure. In other words, the current physical state canand should have an impact on the perceived importance of thephysical conditions.

330 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGI

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subjec

TABLE 11. Objective Based Condition Function Scale

Conditionfunction

(C)(1)

General condition description(2)

10 Excellent: Fully functional. Some aging or wear may be vis-ible.

9–8 Good: Only slight loss of function or slight deterioration.7–6 Fair: Some loss of function or some deterioration, but per-

formancce is not significantly affected.5–4 Marginal: Moderate loss of function or moderate deteriora-

tion but performance is still adequate.3–2 Poor: Serious loss of function or serious deterioration and

performance is inadequate.1 Very Poor: Extensive loss of function or extensive deterio-

ration. Barely barely able to perform.0 Failed: No longer functions. Cannot perform role.

ON-SITE INSPECTION AND CHECKLISTS

An on-site visual inspection is performed to determine thecurrent physical state of the dam in terms of the nine physicalconditions listed in Fig. 2. Each of the nine physical conditionsis quantified in terms of a condition function (CFj). The con-dition function (CFj) is a number ranging from 0 (failed) to10 (ideal). The task of the inspector is to observe indicatorsof each of the nine physical conditions and to quantify themin terms of the appropriate condition function (CFj). The pro-posed condition function scale is a modification of the U.S.Army Corps of Engineers REMR condition index scale. Table11 presents this modified scale consisting of general conditiondefinitions and the corresponding numerical scores. The con-dition categories range form ‘‘excellent’’ with a numericalscore of 10 to ‘‘failed’’ with a numerical score of 0. Eachcondition category is provided with a brief description. Thetask of the inspector is to match her/his observations of thenine physical conditions to the brief descriptions and then toassign an appropriate condition score.

The inspector may not be able to directly determine thephysical condition for some of the inspection items but mustinfer it through various indicators or clues. For example, ‘‘pip-ing in the embankment’’ can be inferred from sinkholes ordepressions on the dam, seepage containing soil fines or evi-dence of the buildup of pore pressures. Nine inspection check-lists are presented in Tables 12–20 containing the suggestedindicators to assist the inspector in quantifying each of thephysical conditions. Each of the indicators is given with sug-gested ranges in condition. For a physical condition that hasmultiple indicators, the one resulting in the lowest conditionfunction is used in the subsequent risk index computation.Note that in the absence of any indicator, the inspector shouldassign a condition function of 10.

NEERING / APRIL 2001

t to ASCE license or copyright; see http://pubs.asce.org/copyright

TABLE 12. Condition Inspection Checklist for Spillway Ca-pacity

Indicator(1)

Suggestedcondition

range(2)

Part of the spillway cross section if obstructed0–10% obstructed 7–1010–25% obstructed 4–7>25% obstructed 0–4

Note: In the absence of any obstruction assign a condition of 10.

TABLE 13. Condition Inspection Checklist for Crest Elevation

Indicator(1)

Suggestedcondition

range(2)

Deviations from original crest elevation in terms ofloss of designed or estimated freeboard

0–10% loss 7–1010–25% loss 4–7>25% loss 0–4

Trees on or near crest 0–5

Note: In the absence of either indicator assign a condition of 10.

TABLE 14. Condition Inspection Checklist for Loss of Func-tion of Low-Level Outlet Works

Indicator(1)

Suggestedcondition

range(2)

Obstructions in cross section of outlet pipes0–10% obstructed 7–1010–25% obstructed 4–7>25% obstructed 0–4Suspected but unverified obstruction 7–10

Valves and gates for outlet worksFunctioning properly or recently repaired 6–10Not operated recently 0–5Owner not willing to exercise valves and gates 0–1Valves and gates cannot be opened 0

Note: In absence of any indicator assign a condition of 10. If there isno low-level outlet then do not consider.

TABLE 15. Condition Inspection Checklist for Spillway Ero-sion

Indicator(1)

Suggestedcondition

range(2)

Observed erosion/deterioration of spillway channelNone to minor 7–10Some to moderate 4–7Serious to extensive 1–4Critical with sill lost 0

Note: In absence of any erosion or deterioration assign a condition of10.

COMBINATION OF RELATIVE IMPORTANCE WITHACTUAL CONDITION

The final step in the methodology is to combine the resultsof the on-site inspection with the results of the relative im-portance determination to generate a set of risk indices, or‘‘weighted’’ deficiencies in the current physical condition. Foreach condition that has been observed on the dam and that hasbeen assigned a nonzero relative importance, the risk index for

JOURNAL OF GEOTECH

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subjec

TABLE 16. Condition Inspection Checklist for Loss of Em-bankment Surface Protection Material

Indicator(1)

Suggestedcondition

range(2)

Loss of upstream slope protectionNone to isolated and moderate loss or degradation 4–10Serious to extensive loss or degradation 1–4Critical loss or degradation (esposure of bedding

material) 0Loss of embankment surface material

Slight [0–0.3 m (0–1 ft)] 7–10Moderate [0.3–0.6 m (1–2 ft)] 5–7Extreme >0.6 m (>2 ft) 0–5

Note: In event of no loss of surface protection material assign a con-dition of 10.

TABLE 17. Condition Inspection Checklist for Piping in Em-bankment

Indicator(1)

Suggestedcondition

range(2)

Turbid flowsEvidence of prior occurrence that has gone uncor-

rected 2–7Actively occurring 0–2

Sinkholes or depressions on the surface of dam 0–5Build-up of pore water pressure in embankment as in-

ferred by uncontrolled seepage areasChanges in surface vegetation 5–10Soft/wet areas on the surface 4–8Constant surface flow 2–7Increasing surface flow 0–4

Stumps and root systems left in place on embankmentor small animal burrows present 0–5

Note: In absence of any indicator, assign a condition of 10.

TABLE 18. Condition Inspection Checklist for Piping in Foun-dation

Indicator(1)

Suggestedcondition

range(2)

Turbid flowsEvidence of prior occurrence 2–7Actively occurring 0–2

Sinkholes or depressions on dam, toe, or abutments 0–5Buildup of pore water pressure in foundation as in-

ferred by uncontrolled seepage areas in toe andabutment areas

Changes in surface vegetation 5–10Soft/wet areas on surface 4–8Constant surface flow 2–7Increasing surface flow 0–4

Note: In the absence of any indicator assign a condition of 10.

the jth condition can be computed according to the followingequation:

(10 2 CF )jRisk Index for jth Condition = RI ? (5)j 10

where all terms have been previously defined. Note that aphysical condition with a relative importance of 0 and/or acondition function of 10 will have a zero risk index. A zerorisk index does not imply that a deficiency is insignificant butthat compared with other deficiencies it is of lessor impor-

NICAL AND GEOENVIRONMENTAL ENGINEERING / APRIL 2001 / 331

t to ASCE license or copyright; see http://pubs.asce.org/copyright

TABLE 19. Condition Inspection Checklist for Slide in Em-bankment

Indicator(1)

Suggestedcondition

range(2)

Buildup of pore water pressure in embankment as in-ferred by uncontrolled seepage areas

Changes in surface vegetation 5–10Soft/wet areas on the surface 4–8Constant surface flow 2–7Increasing surface flow 0–4

Surface evidence of impending mass movement suchas cracking, shallow slides, and differentialmovement in the embankment or between theembankment and foundation

Minor and localized 2–8Major and extensive 0–2

Note: In the absence of any indicator assign a condition of 10.

TABLE 20. Condition Inspection Checklist for Slide in Em-bankment and Foundation

Indicator(1)

Suggestedcondition

range(2)

Buildup of pore water pressure in embankment andfoundation as inferred by uncontrolled seepageareas

Changes in surface vegetation 5–10Soft/wet areas on the surface 4–8Constant surface flow 2–7Increasing surface flow 0–4

Surface evidence of impending mass movement suchas cracking, shallow slides, and bulging

Minor and localized 2–8Major and extensive 0–2

Note: In the absence of any indicator assign a condition of 10.

tance. The overall risk index of the dam is obtained by sum-ming risk index over all potential failure modes.

DISCUSSION

Relationship of Current Approach to ClassicalRisk Analysis

The proposed methodology to calculate risk indices is com-patible with a classical risk analysis in that: (1) the importanceof the dam (IDam) is estimated through a consideration of sur-rogate factors that are related to the likelihood of failure andconsequences of failure; and (2) the relative importance ofpotential changes in physical state are determined in a failurecriticality analysis based upon their relative likelihood of caus-ing a failure. It is possible to directly incorporate the resultsof a classical risk or reliability analysis into this methodologyby using estimated probabilities of failure to determine theconditional probabilities of failure for each failure mode. Ad-ditionally, the dam importance determination can be taken di-rectly from a risk analysis by using the estimated risk insteadof the vulnerability and hazard considerations proposed herein.The dam with the highest risk would be deemed the mostimportant. Thus, information determined during a detailed riskor reliability analysis could supplant the information devel-oped herein.

The proposed methodology provides no measure of the ac-tual probability of failure. This is by design. In the writers’opinion, the determination of probability of failure for a smallembankment dam carries a considerable amount of uncertainty

332 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENG

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subj

and is currently the subject of much controversy. There is dis-agreement within the dam safety profession as to whether ornot it is possible to reliably determine the probability of failureof a dam and whether or not the probability of failure is ofvalue for the prioritization of maintenance, repair, and evalu-ation tasks in an inventory of dams. At the onset of this de-velopment, the writers decided to table this controversial issueuntil the profession could agree on the ability and usefulnessof determining absolute probabilities of failure. They decidedinstead to base the analysis on the use of conditional proba-bilities. The expert panel members during the development ofthe initial condition assessment methodology (senior damsafety engineers from the Corp of Engineers and Hydro-Que-bec) were much more comfortable answering questions deal-ing with conditional probabilities than with absolute probabil-ities.

The prioritizations accomplished by this methodology relysolely on observational factors coupled with engineering judg-ment. This can be potentially misleading when dealing withactual dam failures. However, in the absence of engineeringanalysis, with the lack of knowledge of a performance history,with the lack of knowledge of as-built conditions, and withseverely restricted budgets, the writers feel that expert elici-tation based on observational factors (as developed herein) isan appropriate manner in which to develop a tool that can beused to help prioritize improvements to such inventories ofembankment dams.

A fully developed methodology for condition indexing ofembankment dams (from which this approach has been ex-tracted) has been field tested in one of the management regionsof Hydro-Quebec using approximately 30 dams. The resultswere so encouraging that their upper management gave theirauthorization to implement the condition indexing methodol-ogy across their entire inventory of 300 plus embankmentdams and to use the results for the prioritization of mainte-nance and repair tasks. Additionally, Hydro-Quebec, the Corpsof Engineers, and the Bureau of Reclamation are currentlyworking together in a joint research project to develop a con-dition indexing methodology for spillways and flood water dis-charge facilities based upon the same principles used in themethodology for embankment dams. Hence, the ‘‘indexing’’approach is being accepted by owners of large inventories ofdams as a viable alternative to risk analysis for the manage-ment of maintenance and repair tasks. The use of this tooldoes not rule out the use of good judgment.

Broad Context for Decision-Making on Improvementto Dams

In a broader context, having the ability to accurately assessthe current condition of an embankment dam and to prioritizethe observed deficiencies in terms of safety-related concernsif of little value unless such information can be used to gen-erate scope-of-work statements for proposed further investi-gations and improvements and to generate cost estimates. Im-proved decision-making must also consider the followingissues that are not directly addressed by the methodology:

1. Does the current physical state represent an emergencysituation that must be immediately remedied?

2. Is it necessary to completely remedy the observed defi-ciencies to achieve optimal performance or is there somelevel of performance that is acceptable but less expen-sive?

3. What is the cost variance between various improvementoptions, and how confident can we be in the cost esti-mates?

4. Is the physical condition changing at such a rate that ifthe repairs are not effected today, there may be unac-

INEERING / APRIL 2001

ect to ASCE license or copyright; see http://pubs.asce.org/copyright

ceptable condition levels prior to the next budgetary cy-cle?

5. What is the rate of deterioration across the entire inven-tory of dams?

6. How will deferment of improvements affect the cost inthe short term? Long term?

7. How does the cost of the improvements change overtime?

8. Does deferment limit the number of improvement op-tions in the future?

9. How can expenditures be optimized in terms of perfor-mance?

Answering questions such as these requires that the risk in-dexing methodology described herein be linked to a structuredmethodology for scope-of-work definition and cost estimation.These tools can be used at the network level to prioritize lim-ited funds. A well-conceived management system for improve-ments to embankment dams must be capable of evaluatingalternatives ranging from an initial ‘‘do nothing and defer’’scenario through all available repair options. The ultimatechoice between improvement alternatives must be a balancedevaluation of impacts to both embankment dam performanceand cost. A quantitatively derived risk indexing tool (such asthe one presented herein) can be used to more accurately de-fine performance levels (benefits) as well as scope ofwork(cost) thus enabling an improved benefit/cost analysisover the entire service life of an inventory of embankmentdams.

Precision of Risk Indices

In order to interpret the results of this risk indexing proce-dure, it is necessary to consider the precision with which theserisk indices can be determined. The precision of any derivedquantity can be approximated by using a propagation of errorstechnique known as first-order second moment method, Ben-jamin and Cornell (1970). The risk index defined by (4) is theproduct of four terms: (1) the importance of the dam; (2) theconditional probability of failure for a failure mode; (3) theconditional probability that each of the nine physical condi-tions leading to a particular failure mode; and (4) a conditionfunction. Assume that: (1) the importance of the dam is de-terministic; (2) the conditional probabilities of failure for thefour failure modes from expert elicitation will be normallydistributed with a standard deviation (scp) of 10%; (3) the con-ditional probabilities of the nine physical conditions will benormally distributed with a standard deviation (scp) of 10%;and (4) the condition functions would be normally distributedwith a standard deviation (scf) of 10%. The standard deviationfor each risk index (sRI) will depend upon the importance ofthe dam (IDam), upon the conditional probabilities for the phys-ical conditions (P[Mi uF ], P[Cj uMi]), and upon the conditionfunction (CFj). Under the assumption that the conditionalprobabilities for the failure modes and physical conditions andthe condition functions are independent, the standard deviationof the risk index (sRI) for any condition j can be expressed bythe following equation:

2 2 2(10 2 CF ) (10 2 CF ) P[M uF ] ?P[C uM ]j j i j i2 2 2s = I (6)P[M uF ] s 1 P[C uM ] s 1 sRI DamÎ i cp j i cp cfH J H J H J10 10 10

where all terms have been previously defined. For dams in-dexed according to this methodology, the writers have foundthat the standard deviation of a risk index [from (6)] has acoefficient of variation that is approximately 25% under theuncertainty assumptions given previously. Thus, the interpre-tation of the risk index for prioritization of improvements

JOURNAL OF GEOTECH

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subject

should reflect this uncertainty and dams whose risk indicesthat fall within 6 25% of each other should be given identicalpriority. Note that the terms in (6) are not independent as as-sumed in this analysis and hence the actual standard deviationof a risk index may be distinct from that presented herein andthe actual variation in overall risk indices between inspectorswill need to be established by multiple results of inspectionswith different inspectors. The reader is encouraged to look atthe companion paper (Andersen et al. 2001) where two engi-neers worked independently on the same inventory of 10 damsand their overall risk indices (sum of individual risk indicesfor a particular dam) fell within a range of variation of 625%for most of the dams rated. Clearly, more specific statementsabout uncertainty must be based on consideration of depen-dency between the variables in (5) and must be calibrated withmore exhaustive field experience.

CONCLUSIONS

Ratings of embankment dams that are developed accordingto the risk indexing methodology reflect the opinion of theengineer/inspector in terms of the most likely modes of failureand the observable physical deficiencies of the dams in theinventory. Vulnerability and hazard potential estimates are di-rectly incorporated to permit comparisons across an inventory.This simplified methodology captures the most significant as-pects of a classical risk analysis and hence can be consideredas an index of risk.

The methodology leads the dam safety engineer/inspectorthrough a consideration of the physical deficiencies on a damin terms of the likelihood that these would be associated witha failure.

This methodology stands as a bridge between classical riskanalysis and condition indexing and is a cost-effective alter-native to enable the prioritization of improvements over largeinventories of dams. Engineers and managers attempting to tierisk analysis to periodic inspections can use this tool to pro-vide a valuable support for such an effort.

APPENDIX I. GLOSSARY

Condition: Current physical state of embankment dam as de-termined from observational data during walk-through in-spection.

Condition function: Numerical score ranging from 0 (poor) to10 (excellent) that rates current physical state of portion ofembankment dam in terms of its function in preventing oneor more failure modes, CF for jth condition.

Condition indexing: Process of quantifying current physicalstate of facility in terms of set of predetermined rules.

Conditional probability: Probability of particular event underpremise that another event has occurred.

Failure criticality analysis: Systematic assessment of eventsthat can lead to failure and determination of their corre-sponding importance.

Hazard potential: Measure of specific types of damage suchas property loss or loss of life that may result in event ofdam breach.

Risk: Probability of failure of dam multiplied by cost of suchfailure, in other words, expected cost for failure.Risk index: Measure of importance of embankment dam (vul-nerability of dam and environment and hazard potential of dambreak) and current physical condition that provides indicationof potential levels of risk.

NICAL AND GEOENVIRONMENTAL ENGINEERING / APRIL 2001 / 333

to ASCE license or copyright; see http://pubs.asce.org/copyright

Vulnerability: Referring to dam and downstream environmentit is capability of or susceptibility to be damaged or harmed.Vulnerability function: Function defined by (1) to developmeasure of vulnerability in terms of surrogate factors.Vulnerability score: Numerical score given to each surrogatefactor as defined in Tables 1–8 and subsequently usedin (1).

ACKNOWLEDGMENTS

The ideas for this simplified risk indexing tool were developed by thewriters while working on an embankment dam prioritization pilot projectfunded by the Commonwealth of Massachusetts Department of Environ-mental Management, under the general supervision of R. David Clark,Chief of Dam Safety. The writers greatly acknowledge their support. Theauthors also acknowledge the support of professor W. Edward Back ofClemson University who has helped to place this contribution in thebroader context of decision-making strategies for civil engineering facil-ities.

APPENDIX II. REFERENCES

Andersen, G. R., Chouinard, L. E., Bouvier, C. Y., and Abdo, F. (1998).‘‘Condition Assessment Methodology for Embankment Dams.’’ FinalRep. prepared for U.S. Army Corps of Engineers and Hydro-Quebec,Texas A&M University, College Station, Tex.

Andersen, G. R., Chouinard, L. E., Bouvier, C., and Back, W. E. (1999).‘‘Ranking procedure on maintenance tasks for monitoring of embank-ment dams.’’ J. Geotech. and Geoenvir. Engrg., ASCE, 125(4), 247–259.

Andersen, G. R., Cox, C. W., Chouinard, L. E., and Hover, W. H. (2001).‘‘Prioritization of ten embankment dams according to physical defi-ciencies.’’ J. Geotech. and Geoenvir. Engrg., ASCE, 127(4), 335–345.

Andersen, G. R., and Torrey, V. H., III. (1995). ‘‘Function-based condition

334 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENG

Downloaded 20 May 2009 to 140.194.193.5. Redistribution subje

indexing for embankment dams. J. Geotech. Engrg., ASCE, 121(8),579–588.

Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics, anddecision for civil engineers, McGraw-Hill, New York.

Chouinard, L. E., Robichaud, J. G., Blanchette, G., and Gervais, R.(1998). ‘‘Priority ranking for maintenance activities on embankmentdams.’’ Conf. Can. Dam Safety Assn., Canadian Dam Safety Associa-tion, Halifax, Canada, 252–265.

Dascal, O. (1991). ‘‘Risk of failure and hazard potential classification ofHydro-Quebec dams.’’ Dam Safety ’91, Canadian Dam Safety Asso-ciation, Edmonton, Alberta, Canada, 287–299.

Federal Emergency Management Agency. (1998). Federal Guidelines forDam Safety: Hazard Potential Classification Systems for Dams, Na-tional Dam Safety Program, Interagency Committee Dam Safety, Wash-ington, D.C.

USCOLD Subcommittee of Dam Incidents and Accidents. (1988). Les-sons from dam incidents. USA-II, ASCE, New York.

APPENDIX III. NOTATION

The following symbols are used in this paper:

IDam = Importance of dam as defined by (2) or othersuitable measure proposed by regulatingagency;

P[Mi uF ] = conditional probability of failure mode i giventhat failure has occurred;

P[Xi uMi ù F ] = conditional probability of attribute Xi in pres-ence of failure mode i and failure;

P[Mi uXi ù F ] = conditional probability of failure mode i inpresence of attribute Xi and failure;

P[Cj uMi] = conditional probability of physical condition jbeing associated with failure mode i; and

RIj = relative importance of physical condition j asdefined by (4).

INEERING / APRIL 2001

ct to ASCE license or copyright; see http://pubs.asce.org/copyright