Practical risk assessment for embankments, dams, and slopes - Risk and Reliability in Geotechnical Engineering - page 435

620
610
600
590
580
570
560
550
540
530

Existing conditions

After remedial measures

520
510
500
490
480
470
460

1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01

Annual probability of failure (increasing -->)

Figure 11.5 Annual probability of failure versus earth dam peak pool elevation (internal erosion only).

11.2.2.2 Estimation of peak pool elevation annual exceedance probabilities
Table 11.2 shows the AEP that the peak pool elevation equals or exceeds a given level during
a year. These probability estimates were based on historical reservoir pool data for 60 years
of operation and reservoir operation simulation for a target pool level of +498 ft.
The annual probabilities that the pool will exceed a given elevation (PP) in Table 11.2 repre-
sent AEPs, not stage-duration or percent time exceeding. The incremental annual probability
that the pool will exceed a given elevation reflects our approximate procedure for centering the
pool elevation interval probabilities, that is, to put the water levels for the probabilities of fail-
ure and life loss estimates in the center of the interval rather than at the low end, for numeri-
cal integration reasons. For any given peak pool elevation (PPEi), i ), the “centered” incremental
annual probability that the pool exceeds PPEi i (IPP i ) is computed as

( PP − PP )

i − 1 i + 1

(11.2)

IPP =

i

2

The low-end approach, which does not center the pool elevations in the interval, biases
downward the probabilities and annualized life loss (ALL) discussed in Section 11.2.2.4.

11.2.2.3 Estimation of potential loss of life versus peak
pool elevation at time of failure
In our practice, we always separate potential economic consequences from potential loss of
life. Potential loss of life estimates shown in Table 11.3 in terms of lives lost were derived
using inundation maps and corresponding demographic data for eight pool elevations.