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The uncertainties associated with the three design cases differ from one another because each re ects a different mixture of spatial variability and systematic uncertainty. This has an important implication. A 1% probability of failure deriving from spatial variability alone implies that, on average, one per cent of the length of a long dike would fail. Conversely, a one per cent probability of failure due to systematic uncertainty alone would imply that, on average, one out of one hundred of a large number of similar dikes would fail along its entire length. In any speci c case, such as this one, the probability of failure derives from both spatial variability and systematic uncertainty. Figure 14.5 shows the contributions of the two components for the three cases. In the single stage case with H = 6 m the distribution of F for different sections along the dike is broad, but the uncertainty on the location of the mean is small. In the multi-stage case the distribution of F along the dike is narrow, but there is proportionally more uncertainty on the location of the mean. In other words, the uncertainty in the case of a single stage dike with H = 6 m deals principally with the fraction of the dike that will fail, but the uncertainty in the case of a multi-stage dike deals principally with the failure of all or a large portion of the dike.

IL_0009

IL_0019: ret } // end of method LinkedList::Dump .method public hidebysig specialname rtspecialname instance void .ctor() cil managed { .maxstack 1 IL_0000: ldarg.0 IL_0001: call instance void [mscorlib]System.Object::.ctor() IL_0006: ret } // end of method LinkedList::.ctor } // end of class LinkedList

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Baecher et al. (1980) determined that the historical rate of failure of modern, wellengineered dams is about 10 4 per dam-year. The details of failures are often imprecise in the catalogues from which this result was computed, but it appears that about one third of the failures were due to overtopping and another one third to internal erosion, piping, or seepage. These numbers are close to what would be expected from professional judgment and experience. The remaining one third are due to slides and other mechanisms, which include the subject of the present analysis. The relative contribution of different modes of failure should be kept in mind when a target probability of failure is being selected. It makes little sense to reduce the computed probability of failure due to slope stability problems if other causes of failure are not addressed at the same time. The historical data would suggest that, for a dam with a life of 100 years, the overall probability of failure is 0.01, in the absence of speci c attention during design and construction to mitigate the hazards. Since well less than one third of the failures are due to slope instability per se, a target probability of failure of slope stability failure of about 0.001 seems reasonable for design purposes and consistent with past experience. Figure 14.7 indicates that to achieve this target probability the stability analysis should give factors of safety of 1.84, 1.53, and 1.36 for the 6 m, 12 m, and 23 m cases, respectively. If the effects of model uncertainty were included, the values of

Listing 12.4 (continued)

If there is a wind bend, it may be caused by a landmass, which will dictate the favoured side. Here, you need to be very careful not to tack too early and miss the centre of the wind bend, but remember you may need to tack under the expected lay line, as you will be lifted out on the other tack.

0.01 23 m 0.001

The LinkedList object contains a ListHead member of type ListItem (from Listing 123), and two methods (not counting the constructor): AddItem and Dump Let s begin with AddItem This method starts with an interesting sequence where the NewItem parameter is pushed into the stack, followed by the first parameter, which is the this reference for the LinkedList object The next line uses the ldfld instruction to read from a field in the LinkedList data structure (the specific instance being read is the one whose reference is currently at the top of the stack the this object) The field being accessed is ListHead; its contents are placed at the top of the stack (as usual, the LinkedList object reference is popped out once the instruction is done with it).

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