Environmental Engineering Reference
In-Depth Information
described in this chapter require only modest extra effort as compared to that required to
evaluate factors of safety, but they will add considerable value to the results of the analyses.
3.2 ProbabIlItY oF FaIlure anD rISk
This chapter focuses on methods of evaluating the probability of failure for geotechnical
structures such as retaining walls, slopes, levees, and dams. Probabilities of failure are asso-
ciated with particular modes of failure, such as retaining wall sliding, overturning, or bear-
ing capacity failure.
Risk is related to the probability of failure, and also includes the consequences of fail-
ure—what will be the consequences if failure occurs? For example, would the consequences
of retaining wall sliding be simply an unattractive but still stable wall, or would sliding
require expensive remediation, or, in the extreme, could it pose a threat to life? Evaluating
risk involves evaluating both the probability of failure and the consequences should fail-
ure occur. Where loadings recur over time, for example, river stage variation as shown in
Figure 3.1,
risk can be stated on an annual basis. A study of the probability of levee failure
due to overtopping and underseepage could be stated as “the annualized risk of flood dam-
age is X dollars per year for this section of levee,” or “the annualized risk to human life is Y
lives lost per year for this section of levee.”
3.3 language oF StatIStICS anD ProbabIlItY
3.3.1 Variables
When tests are performed to measure values of a physical property, for example, the und-
rained shear strength of saturated clay, it is commonly found that a different value is mea-
sured in each test. In this context physical properties of soil or rock are appropriately called
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0.1%
1.0%
Probability of exceedance (%)
10.0%
100.0%
Figure 3.1
Flood frequency curve for a reservoir.
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