Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 241
APPENDIX E
Risk Analysis Approach to Dam
Safely Evaluations
This Appendix considers the issues involved in decision analysis proce-
dures addressing the consequences of dam operation and dam failure during
extraordinary flood events. Issues addressed are extrapolation of the fre-
quency curve to the probable maximum flood (PMF), calculation of the
consequences of large floods and the matrix decision approach, calculation
and use of expected costs, and finally the justification of doing a careful risk
analysis of project operations. An example of the application of risk analysis
to design alternatives for a hypothetical reservoir problem is outlined.
EXTRAPOLATION OF FREQUENCY CURVES
A complete risk-based analysis sometimes requires an extension of flood-
frequency curves beyond the 50-, 100-, or 500-year return periods, which is
usually considered as defining the outer limits of the ability to make credible
frequency estimates. As discussed in Appendix D, this is generally unjustified
from available systematic flood flow records and records of historical floods.
This poses a difficult problem if a frequency curve out to the PMF is to be
employed unless some means is adopted to assign return periods to events
such as the calculated PMF. Procedures for estimating the return period of
PMF events are also discussed in Appendix D. Such direct methods are very
involved. Lacking a simple alternative, a reasonable result can be obtained
by considering the PMF to be the one in a million (106) year event, or the one
in 10,000 (104) year event. Since use of the latter value would lead to higher
estimates of risk-costs, it may be considered the more conservative assump-
241
OCR for page 242
242
do
8-
~VH38lO
]~,NDSID
CQ
'Q
'Q
_
3
V
OCR for page 243
Appendix E 243
tion. Buehler (1984) recommended use of the 106 value. With such an as-
sumption, one can extend the standard (Bulletin 17) frequency curve (on
lognormal probability paper) to pass through the PMF with the specified
exceedance probability. Figure E-1 provides an example of lognormal paper
that can be used for this purpose. Here 104 and 106 represent a very conserva-
tive and a more reasonable value of the return period of PMF estimates, even
though higher return period values have been suggested and in some cases
are more likely (Newton, 1983~. Ideally, these target values would be a
function of the region of the country in which one was working, and the size
of the river basin of concern for both of these factors should explain varia-
tions in the return periods of PMF estimates.
There are several reasonable pathways of extending the empirical fre-
quency curve from the 100-year flood to the PMF. A simple linear extension
of the empirical frequency curve from the 100-year flood to the PMF on
lognormal paper is one reasonable procedure. The Bureau of Reclamation
(1981a) uses a log-flow versus log-exceedance probability graph to extend
the frequency curve; their guidelines also specify that the frequency curve
should pass through a box bouncied vertically by 40 and 60 percent of the
PMF and horizontally by vertical lines drawn at the 200- and 500-year
return periods. In practice, curves often are drawn to just pass through the
lower right-hand corner of that box. Thus, the general effect of their proce-
dure is to make the 0.4 PMF flood the 500-year event, irrespective of the size
of the 100-year flood or the return period assigned to the PMF.
The Bureau s box constraint adds little to the analysis. While they may
describe hydrologic experience in parts of southern California, these bounds
should not be arbitrarily imposed upon flood-frequency curves for river
basins in that region or elsewhere. Research should address the impact and
advisability of using different axis scales to extend frequency curves to the
PMF. However, because one is interpolating between the PMF with a speci-
fied exceedance probability and a specified 100-year flood, the differences
should not be too great and should generally result in smaller variations in
damage estimates than do use of either 1O-4 or 10-6 as alternative values for
the exceedance probability of the PMF.
Other problems arise when one attempts to make the flood-frequency
curve approach the PMF flood asymptotically, as the Bureau suggests. Such
efforts seem to reflect the mistaken belief that the PMF estimate is in fact the
maximum possible flood that can occur. This is certainly not true (see discus-
sion in Chapter 2 and Newton (1983~) . Furthermore, the practice of treating
the PMF estimates as the maximum possible flood can yield physically im-
plausible bimodal flood distributions whose use can distort risk-cost analy-
ses. This procedure implicitly assigns the values of 1O-4 or 10-6 to the event
that the PMF estimate occurs rather than to the event that the PMF is
OCR for page 244
244
Appendix E
exceeded. Finally, this practice tempts one to think that if a dam were just
designed for the PMF estimate, then there would be no risk of the dam
overtopping. This is not the case. The PMF estimate is indeed a very large
flood, but it can be exceecled.
Clearly, care should be exerciser! when extending flood-frequency rela-
tionships to PMF values. Additional research is clearly needed in this area.
At present, reasonable and realistic risk investigations can be conducted by a
linear extension (on lognormal paper or some reasonable alternative) of the
frequency curve out through the PMF estimate, which is assigned a return
period of 106 years, or the smaller and more conservative value of 104 years.
By using alternative flood-frequency relationships that jointly span the rea-
sonable range one can capture the sensitivity of the expected damage costs
and, in particular, the ranking of the alternative projects, to our uncertainty
as to the true flood-frequency relationship.
One should also remember that available flood records yield 100-year
flood estimates with considerable uncertainty (Kite, 1977~; thus it can be
appropriate to include the sensitivity analysis, both alternative values of the
exceedance probability of the PMF and also the 100-year flood. Procedures
for calculating confidence intervals for the 100-year flood are available
(Stedinger, 1983c).
EVALUATING RISKS
A risk-based analysis needs to consider the consequences and costs of
reservoir operation (including damages from high lake levels and discharge,
and also damage to the dam and from interruption of services) and the
relative likelihood of such events. In general, four metrics are used to de-
scribe the consequences for each alternative considered:
1. likely loss of life;
2. economic damages from lake levels, releases, and damage to the dam;
3. the cost of actions associated with each modification of the dam, reser-
voir, and associated channels and any flood warning system; and
4. the cost of discontinued or interruptions in service due to damage to or
the failure of the dam because of an extraordinary hydrologic event.
An American Society of Civil Engineers (ASCE) task-force (ASCE, 1973)
has recommended that an economic value be assigned to loss of life so that all
quantities can be added on an annual basis to obtain a total-cost function.
While such a step is attractive and can be done as an extra computation, in
general, initially displaying expected loss of life in a separate category is
advisable.
The Bureau of Reclamation (1981a, 1984) provides a discussion of how
OCR for page 245
Appendix E
risk-cost analysis can be performed. The key step is to provide a numerical
approximation to the expected loss of life and the expected damage costs.
Comparison of project benefits in terms of only expected damages and loss
of life is a problem in that it averages or integrates over many possible events.
In addition and before calculating expected costs, engineers should compute
and examine matrices such as that in Figure E-2, which can show expected
loss of life and economic damages associated with each alternative project
over a range of inflow floods. As noted by Interagency Committee on Dam
Safety (ICODS) (1983, pp. 30-31), such calculations are necessary for risk-
cost analyses.
One big unknown in any analysis of damages anticipated from dam over-
topping and failure is the rate of breach development ant] the size of breach
that will develop. Fortunately, we do not have many case histories of breach
of large dams on which to base such estimates. A sensitivity analysis assum-
ing a range of rate of development and size of breaches could show if these
assumptions are critical for a specific case.
Intentionally breaching or destroying a clam, or widening or lowering a
spillway, can result in increased discharges for modest 50- to 200-year return
period floods, thereby increasing downstream damage cost associated with
relatively likely events even though such structural modifications allow pas-
sage of the relatively improbable PMF without structural failure. On the
other hancl, given the size of near-PMF floods even without structural failure
of the dam, sudden or progressive dam breach during a flood may have a
245
Flow Rate 10,000
(100-yr
flood)
Proposal
20,000 30,000 50,000 70,000
.
Dl2 D13 D14 Dls
(L12) (L13) (L14) , (L15)
D52 Ds3 Ds4 D5s
(L52) (L53) (Ls4) (L55)
90,000
cfs
(PM F)
Do nothing Dll
(Lll)
Dl6
(~16)
Modify spillway—1
Modify spillway—2
Change operating policy
plus modification—1
Breach Ds1
dam (Lsl)
Ds6
(L56)
FIGURE E-2 Sample decision matrix for risk analysis (expected damages Djj associated with
proposal i and inflow flood level j and also the corresponding expected loss of life).
OCR for page 246
246
Appendix E
very modest incremental impact on potential loss of life and economic dam-
ages. All these issues should be considered when selecting an appropriate
modification of a structure and can be considered even before probabilities
are employed to calculate expected loss of life and damage costs.
AN EXAMPLE
To illustrate the use of risk analyses and the balancing of the increment of
property and lives at risk due to spillway inadequacies against retrofitting
costs, we consider an example that is a generalization of several studies
conducted by the Bureau of Reclamation. In this example, a reservoir con-
structed in the 1920s has a storage capacity 20,000 acre-feet. It has been
found to have an inadequate spillway due to defects in the design of the
spillway as well as a design discharge, which is substantially smaller than
current PMF estimate. The PMF for the dam is currently estimated to be
120,000 cubic feet per second (cfs), while the 100-year flood is 20,000 cfs.
The current spillway, given the design defects, is estimated to be capable of
carrying 50,000 cfs. The minimum damage flood is 10,000 cfs, which is
about the 50-year flood.
Alternative designs have been considered. One can (1) do nothing, (2)
modify the existing spillway to pass 75,000 cfs, (3) rebuild the spillway and
raise the dam so that it can pass the PMF, or (4) lower the spillway crest and
lengthen it so that the full PMF can be passed without raising the dam. Table
E-1 summarizes these options and their amortized annual costs.
The question is whether to stay with the current spillway with capacity of
50,000 cfs, to increase the capacity to 75,000 cfs for an annual cost of
TABLE E-1 Design Options and Costs for Illustrative
Example
Design Flow Annual Cost
Option (cfs) ($/yr)
1. Do nothing 50,000 0
2. Modify exist- 75,000 80,000
ing spillway
3. Rebuild spill- 120,000 200,000
way and raise
dam
Rebuild spill- 120,000 120,000
way and lower
or lengthen
crest
OCR for page 247
Appendix E
$80,000, or to increase the capacity to the full PMF of 120,000 cfs at an
annual cost of either $120,000 or $200,000.
A key ingredient in any decision may be the expected downstream (and
sometimes upstream) property damages that result from large flood flows
and reservoir operations. In this example, damages in the valley below the
dam (designated by M) are assumed to rise monotonically toward an upper
bound or maximum M if the dam does not fail. Any actual failure of this
large dam is assumed to result in a flood wave that causes the maximum
damages. The mathematical form of the damage function and other details
of this analysis are provided at the end of Appendix D.
Clearly some trade-off is necessary between lives at risk, the possible cost
of the project's destruction and the resulting loss of benefits, and the incre-
mental flood damages that would result should the dam fail.
In this example, the incremental risk of loss of life due to clam failure
during an extraordinary flood event is assumed to be negligible. Down-
stream residents would have been evacuated already or could be evacuated
before the flood wave from a dam failure would reach them.
One must also consider the possible cost of replacing the dam should it fail
and the cost of loss of services until the dam is again operational if that is the
chosen course of action. The cost of reconstructing the dam and the present
value of loss of services until the dam could be replaced are denoted by the
letter L. Thus, if a flood overtops the reservoir, causing a breach, the total
losses M + L are those due to downstream property damage and loss of the
reservoir and the services not supplied until the reservoir can be rebuilt.
The matrices of costs that result from five different but reasonable combi-
nations of M, L, and a third (damage-shape) parameter are shown in Table
E-2. Each matrix represents the damage costs that occur from the flood flows
or M + L if the dam is overtopped and by assumption fails. One must be
careful when interpreting the cost functions because they are discontinuous
at the spillway design flood. For example in case 1, if option 2 were pursued
and a 75,000 cfs flood occurred, then downstream damages would be $9.6
million. However, a 76,000-cfs flood is assumed to overtop the reservoir
causing total damages of $40 million.
In the first three cases in Table E-2 the committee has considered a range of
L values representing a relatively low-cost dam with small loss of service
costs to either a high-cost dam and/or high loss of service costs. Cases 4 and 5
correspond to low loss of service costs with two high downstream damage
cost cases. Two things stand out in matrices: (1) the higher the spillway
design discharge, the larger the range over which dam failure is avoided and
damages stay below the maximum, and (2) the fourth inexpensive option of
lowering, or lengthening, the spillway results in larger damage costs. What
is not simple is the trade-off of annual modification costs in the $80,000-
247
OCR for page 248
248
Appendix E
TABLE E-2 Matrices of Damages (in millions) for Different Flows and
Design Options
Design Peak Flood Flow
Option 20K 50K
100K
120K
Case 1: M = $20 million, L = $20 million
1 1.9 6.6
2 1.9 6.6
3 1.9 6.6
4 3.6 11
Case 2: M = $20 million, L = $100 million
1 1.9 6.6
2 1.9 6.6
3 1.9 6.6
4 3.6 11
2
3
2
3
4
Case 3: M = $20 million, L = $400 million
1.9 6.6
1.9 6.6
1.9 6.6
3.6 11
Case 4: M = $100 million, L = $20 million
9.5 33
9.5 33
9.5 33
18 55
2
3
40
9.6
9.6
15
120
9.6
9.6
15
420
9.6
9.6
15
120
48
48
73
Case 5: M = $200 million, L = $20 million
5.9 23
5.9 23
5.9 23
9.8 36
220
35
35
55
40
40
12
17
120
120
12
17
420
420
12
17
120
120
59
83
220
220
47
72
40
40
13
18
120
120
13
18
420
420
13
18
120
120
67
89
220
220
56
85
NOTE: In the first four cases, the damage function shape parameter s (see Appendix D)
equaled 1 x 10-5 for design options 1-3 and 2 x 10-5 for design option 4 (lower spillway
crest); for case 5 the values were 3 x 10-6 and 5 x 10-6, respectively.
$200,000 range with possible but very unlikely damages in the $10,000,000-
$420,000,000 range.
To trade off dam failure prevention costs with possible flood damage and
dam failure costs, an extended flood-frequency curve was constructed. A
shifted exponential distribution was used to describe the flood-frequency
distribution. Its two parameters were chosen so that 20,000 cfs was the 100-
year flood (or 1 percent chance event) and the PMF of 120,000 cfs was the T-
OCR for page 249
Appendix E
249
year event for T = 104 or 106. The expected damages due to flood events
between the minimum damage flood of 10,000 cfs and the PMF were then
calculated analytically (see Appendix D). The results are given in Table E-3
along with the sum of the expected damages plus the annualized construc-
tion costs from Table E-1.
Examination of Table E-3 illustrates a range of situations that might be
encountered. In case 1, on an economic basis, no construction seems justi-
fied; even when the PMF is only the 10,000-year event, the least total cost
option is to do nothing. This is consistent with the Table E-2 matrix for this
case, which shows that damages in the event of a dam failure are of the same
order of magnitude as damages without a failure.
Going to case 2, L increases from $20 million to $100 million. As a result,
on an economic basis, option 2 with a 75,000-cfs spillway gives lowest indi-
cated average annual cost if the PMF is only the 10,000-year flood, whereas
to do nothing is indicated if the PMF is the million-year event.
Finally, in case 3 the cost of loss of the dam is very large, $400 million, and
the inexpensive 120,000-cfs spillway design (option 4 involving lowering the
crest) gives indicted lowest cost for T = 104, while the 75,000-cfs spillway
design (option 2) shows lowest cost if T = 106. Unfortunately, the least cost
solution in both cases 2 and 3 is sensitive to T.
Cases 4 and 5 consider situations where downstream damages are the
important factor rather than the loss of the dam and the services it provides.
In case 4, building the 75,000-cfs spillway (option 2) only shows lowest
indicated cost if T is as small as 104. In case 5, with M = $200 million,
construction seems to give lowest indicated cost options, though different T
values again lead to different decisions. However, in both cases 4 and 5, the
lower crest 120,000-cfs spillway (option 4) is very unattractive because of the
larger downstream damages it causes at all inflow levels up to and including
the PMF. This stands in contrast to case 3, which had relatively small down-
stream damage potential, making the low-cost, lower crest spillway more
attractive on an indicated cost basis. One should also remember that this
analysis is based solely on the dollar values of property damage and excludes
loss of life, which is assumed not to be a concern in this case.
USE OF EXPECTED COSTS
Actually calculating the expected costs and benefits associated with differ-
ent designs provides some guidance or confirmation as to which design
alternatives on balance are most attractive. However, an expected cost anal-
ysis does have some practical and philosophical problems.
On the practical side, at the extreme, one is multiplying estimates of large
costs times rather poor estimates of small probabilities. The resultant prod-
OCR for page 250
250 Appendix E
TABLE E-3 Expected Damages for Different Design Options, Cases, and
Return Periods
T Assigned to PMF
Expected Annual Damages
($1,000/yr)
Option T= 104 T= 106
Expected Annual Damages
Plus Construction Costs
($1,000/yr)
-
T= 106
Case 1: M = $20 million, L = $20 million
1 130 70 130 70
2 75 50 155 130
3 55 50 255 250
4 94 90 214 210
Case 2: M = $20 million, L = $100 million
1 320 120 320 120
2 130 55 210 135
3 55 50 255 250
4 95 90 215 210
Case 3: M = $20 million, L = $400 million
1 1050 310 1050 310
2 340 75 420 155
3 55 50 255 250
4 95 90 215 210
Case 4: M = $100 million, L = $20 million
1 460 300 460 300
2 320 250 400 330
3 275 245 475 445
4 470 450 590 570
Case 5: M = $200 million, L = $20 million
1 640 280 640 280
2 310 170 390 250
3 185 160 385 360
4 300 260 420 380
NOTE: Minimum cost value is underlined for each case and value of T.
OCR for page 251
Appendix E
251
uct may be a very imprecise estimate of the desired expected cost associated
with extreme events. Thus, these calculations only provide a credible guide
for decision making if sensitivity analyses considering alternative but credi-
ble costs and flood-frequency relationships yield a similar ranking of the
alternatives.
An even more philosophical question is whether expected loss of life and
expected damages are appropriate metrics to describe possible catastrophic
events that are unlikely to occur in contrast to construction costs, which
definitely will be experienced. Few argue against the use of probabilities in
the analysis of recurring events without catastrophic consequences; exam-
ples are the analysis of the cost and benefits associated with frequent floods,
year-to-year hydropower operations, or recurring navigational issues on
waterways. However, the failure of a major dam in an extraordinary flood
should not be a recurring event for which one can weigh the average annual
costs that will be experienced from failures with the costs paid to reduce the
likely severity and frequency of those failures. The issue is how much mem-
bers of society are willing to pay to avoid such unlikely events. It is highly
plausible that they are willing to pay more than the expected cost.
The cost society should bear to avoid the consequences of dam failure
(both immediate and those due to the inability of the facility to continue to
provide the anticipated services) is difficult to determine. When loss of life is
a major issue, most people agree that little risk is acceptable and PMF
standards for safety are appropriate. But why not a little more or a little less?
LOSS OF LIFE CALCULATIONS
The balancing of reservoir construction and retrofitting costs against the
expected incremental property damage costs from improbable but possible
dam failure is a balancing of monies expended for protection versus proper-
ties damaged for which monetary compensation can be provided. This com-
parison can be performed on an annual cost basis (amortized reservoir
construction costs versus the expected incremental damages avoided per
year) given an interest rate and a planning period. Alternatively, given the
interest rate and a planning period, one can make the equivalent comparison
between the present value of the two time streams. Loss of life considerations
pose fundamentally different considerations, particularly in a time value
context. First, one must be willing to specify the amount of federal monies
that society is willing to expend to avoid an accidental death or on average
one accidental death that could occur during the next fiscal year. While no
one is anxious to specify a particular dollar value for such a death, reasonable
ranges can be surmised.
The question dam safety raises is, how much is society willing to pay today
OCR for page 252
252
Appendix E
to avoid an accidental death that could occur in 25, 50, or 100 years? If the
interest is 10 percent per year (or 5 percent per year) and society would be
willing to pay as much as $1 million per expected accidental death avoided in
the immediate future, would society be willing to pay only the present value
of $1 million in 50 years at 10 percent per year, which is $8,519 (or $87,200
for i = 5 percent), to avoid an expected death at that time? Certainly the first
value is too small and probably also the second.
Discounting the value of life with the discount rate for federal expendi-
tures does not seem appropriate. An alternative is not to discount the value
assigned to loss of life or to discount it very little. If this is done, one must be
careful not to compare amortized capital and construction costs with annual
expected loss of life values; that would be equivalent to discounting the value
of life at the discount rate for construction costs.
What are the consequences of not discounting loss of life? If loss of life is
not discounted, then it is easiest to compare the cost of construction and
spillway modification costs with the present value of incremental damages
avoided (calculated with the interest rate for property) and the incremental
expected number of accidental deaths avoided per year times the number of
years in the planning period. Thus, if a dam modification in expectation
saves 0.02 lives per year, this is equivalent to saving 1 life in 50 years, 2 lives in
100 years, and 4 lives in 200 years. Because the number of expected lives the
dam modification is credited with saving increases linearly with time, and
the dam may be around for a long time, the value of life can loom large in the
analysis. Of course, if the expected lives lost per year is only 1O-4, then after
200 years the expected loss of life is still only 0. 02.
With these considerations before us and given the long service lives of
many dams, there is no rigorous method to decide how to properly balance
construction and spillway modification costs with loss of life values. Clearly,
absolute safety cannot in general be provided. However, our society seems
willing to spend large sums of money so that federal dams and other large
projects do not put people's lives at risk without their explicit consent, re-
gardless of what people choose to do voluntarily. Clearly the federal govern-
rnent wants to continue to protect the lives of its citizens.
ADVANTAGES AND LIMITATIONS OF RISK ANALYSIS APPROACH
In Chapter 5 some of the limitations and advantages of the risk analysis
approach are outlined. For example, a key feature of the matrix decision
approach and expected cost analyses is that the selected design is not con-
fined to a specified SEF. The analysis probably would include the PMF as
one of the safety evaluation floods, but no single flood is specified as the
unique inflow hydrograph against which a design should be tested. This is as
OCR for page 253
Appendix E
253
it should be, because no single event can capture the character of all of the
small and large floods to which a dam may be subjected. Strict reliance on
PMF as inflow design floods or some other unique safety evaluation flood in a
real sense can distract designer and public attention from the real flood risk,
which is probably due to less extreme but much more likely hydrologic
events as well as from structural and foundation problems with the dam.
which can also cause dam failure. Kirby (1978) suggests that just"the
concept of probable maximum flood diverts our attention toward the illu-
sion of absolute safety and away from the hard necessity to accept risk and
minimize it by balancing opposing risk." The matrix decision table may
make these trade offs more apparent.
Dams are major social investments, and their failures due to the occur-
rence of large floods is of much concern both because of the loss of the
investment embodied by the dam and the likely loss of life and property such
a dam failure might cause. In the design against extreme hydrologic events,
dam designers have had to assess the hydrologic risk present at a particular
dam site. There are basically two approaches that can or have been applied
to assess that risk. One is to consider the probable maximum flood event that
would occur following a probable maximum precipitation event in conjunc-
tion with other unfavorable factors. The second approach would entail the
probabilistic analysis of a wide range of scenarios so as to construct a flood-
frequency relationship. The Harriman Dam analysis (see Appendix A, Yan-
kee Atomic Electric Company) illustrates such an effort.
While there are substantial difficulties in estimating the return period of
the PMF or in estimating the 10,000-year flood using probabilistic tech-
niques, all of the difficulties are also associated with characterizing worst
case analyses such as the probable maximum flood calculation. Both ap-
proaches require judgment. Neither are automatic. To be done satisfactorily,
both approaches require understanding of the underlying processes generat-
ing extreme events.
Traditionally, the appropriate level of safety was often determined by
professionals involved in the construction and regulatory agencies of the
federal government. Based on their collective and joint consideration, reser-
voir designs were adopted that reflected reasonable standards of safety.
However, decision making patterns in our society are changing, so that a
large audience, including more of the general public, is becoming involved
in important social decisions. There are two dangers. The first is that the
decision making and safety standard setting process will come to include so
many participants and interests that acceptable and appropriate decisions
cannot be made. On the other hand, the decision making process will lose its
social legitimacy if too few groups or only a select group can become in-
volved. This can occur if professionals treat important social decisions as
OCR for page 254
254
Appendix E
simply technical issues that they feel authorized to resolve. While society
once may have delegated such authority to design engineers, social decision
patterns have and are continuing to change. Thus, federal dam-building
agencies need to remain open to and should encourage public discussion of
their design practices to assure that their practices enjoy general public and
professional support. One advantage of the matrix decision approach is that,
in the context on a particular decision, it displays the range of alternatives
that were considered and illustrates the performance of the dam over a wide
range of floods.
Historically, (lam designers have appropriately been concerned that their
profession not be discredited nor public confidence lost by the failure of
dams during large floods or earthquakes. However, in view of the greater
technical expertise available today and society's current outlook on the allo-
cation of resources, safety factors and overdesign practices that once may
have been appropriate may no longer be reasonable. Thus, government
agencies should carefully determine if the marginal increments in damages
that result from changes in operating rules, structural modifications, and
dam failures on balance indicate that structural modification and operating
rule changes for existing dams are both justified and well advised. The
procedures discussed in this Appendix can facilitate such determinations.
Representative terms from entire chapter:
expected loss
