Probabilistic Methods in Geotechnical Engineering (1995) / Chapter Skim
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2. Use of Probabilistic Methods
2. Use of Probabilistic Methods
Pages 8-35
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From page 8... ...
Included are uncertainties due to the variable nature of soil and rock properties and other in situ conditions, uncertainties about the reliability of design and construction methods, and uncertainties about the costs and benefits of proposed design strategies. Probability theory is a mathematical tool that can be used to formally include such uncertainties in an engineering design and to assess their implications on performance.
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From page 9... ...
Where alternative courses of action are cast in terms of likely ranges of cost and benefit, probability theory can provide an avenue for better communication between the geotechnical engineer and the layman (e.g., owners, regulators, and the public)
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From page 10... ...
Probabilistic methods and deterministic methods complement each other in solving geotechnical problems. Probability is not a substitute for traditional design approaches such as comprehensive site investigations, laboratory test programs, mechanistic analyses, or engineering judgment; rather, it should be used to complement these more traditional geotechnical engineering tools.
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From page 11... ...
Where regulations require it, for example, in many types of geo-environmental problems, probability theory has been adopted and used effectively. Probability theory has also been used in connection with economic analysis of alternative courses of action, where it provides a useful basis for decision making, and in geotechnical engineering for offshore structures, where a significant effort has been made to assess the uncertainties and biases in offshore pile design methods and to use the information to improve these practices.
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From page 12... ...
There appears to be no single reason why probabilistic methods have not been more readily adopted and more widely used. Where regulations require it, or where the benefits are clear, probability theory has been adopted readily in geotechnical engineering.
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From page 13... ...
Example 7 shows how the probabilistic method can be used to establish quality-control guidelines. Example ~ shows how the probabilistic method can be used to predict the skirt penetration resistances of an offshore gravity platform during installation.
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From page 14... ...
To work effectively with the public and these regulatory agencies, geotechnical engineers must have some knowledge of probability theory and reliability methodologies, as well as traditional geotechnical expertise. Probabilistic methods can be used to evaluate risks on the basis of available data, current technology, and engineering judgment.
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From page 15... ...
More urgently, if such improvements were needed, they wanted to know if any interim safety actions were necessary until the remedial actions were completed. To address these concerns, it was necessary to obtain a measure of the risk to the existing dam by estimating the average time until the next earthquake that is large enough to induce liquefaction (also known as the return period of the triggering earthquake)
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From page 16... ...
The return period of (i.e., average time until) the triggering earthquake is simply the reciprocal of 0.0009, or 1,100 years.
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From page 17... ...
Moreover, sensitivity analyses were also performed to examine the effect of different input assumptions on the estimated return period. Despite the simple seismic risk study performed for this dam, the information obtained with respect to the annual risk of a triggering earthquake and to the average time to the next triggering earthquake was useful to the Bureau of Reclamation in addressing their earlier concerns.
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From page 18... ...
This allowed the owner to become involved in an important part of the design process; and by being willing to accept project risks, the owner has avoided the cost of risk-reducing contingencies that might otherwise have been adopted. Example 4: Selecting Pumping Rates for an Extraction Well This example illustrates the use of the decision-analysis approach to select a pumping rate for an extraction well that is intended to capture a small plume of contaminated groundwater (Massmann et al., 19911.
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From page 19... ...
Higher pumping rates would also result in increased pumping costs and, more importantly, the additional cost of treating more extracted water. In view of the uncertainties, one option for the owner was to adopt a high pumping rate by means of a conservative (but excessively costly)
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From page 20... ...
The relative likelihoods of the actual direction and magnitude over these respective ranges are subjectively estimated from topographic and hydrogeologic characteristics of the site. A flow-simulation program with inputs that reflect the site characteristics was used to determine if failure occurred for each combination of groundwater-flow direction and magnitude as a function of the pumping rate.
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From page 21... ...
In both cases, the preferred alternative based on minimum overall cost was to pump at the higher rate of 40 m3/hr. Hence the preferred higher pumping rate is robust with respect to failure costs since these costs did not affect the owner's decision.
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From page 22... ...
Uncertainties about the properties of sand were estimated by analyzing the various models used to correlate penetration resistance with angle of internal friction. During this initial phase of site exploration, the strength of the clay was estimated from cone penetration resistance and results of biaxial compression tests.
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From page 23... ...
method to estimate the undrained shear strength of the clays, and (3) perform load tests to infer the internal friction angle of the sand in addition to the use of ADP method for clay.
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From page 24... ...
The high dikes involved larger slip surfaces than the Tow dikes. When the random spatial variations of soil properties were averaged over the slip surface, the variance of that average decreased with the size of the slip
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From page 25... ...
Hence the uncertainty due to random spatial variation was smaller for the higher dikes. Uncertainty in the mean soil properties for the high dike was smaller than that for the low dike because of sophisticated strength testing and field monitoring for the high dike as compared with the low dike, which was designed using field vanes.
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From page 26... ...
described how probability theory can be used to obtain a consistent CQA program. To evaluate the integrity of the seam, samples for destructive testing are commonly required at a minimum frequency of ~ per ~ 50 m of seam; if a given sample fails to meet the specified strength, the extent of the incompetent seam is determined by additional testing on either side of the initial sample location.
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From page 27... ...
A plot of the probability that the final fraction exceeds 10 percent versus the destructive testing interval is shown in Figure 2-4 for several measured fractions of failing destructive tests. Prior to installation, this plot can be used to specify a testing interval to meet a selected design criterion.
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From page 28... ...
Example 8: Penetration Resistance of an Offshore Gravity Platform Concrete gravity platforms have been used extensively for offshore of! exploration and production in the North Sea.
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From page 29... ...
The figures show that there is good agreement between the predicted and observed values. The width of the probability bands depends on the accuracy of the correlation of skirt penetration resistance with cone penetration resistance values, the degree of spatial variation of the resistances, and the number of CPTs performed, and it would thus vary from site to site.
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From page 30... ...
The problem that confronted the engineer in this case was how to select the undrained shear strength of the soil for the design of the slope, in view of the large variation in the measured strengths. This slope actually failed after construction, and the average shear strength at failure was about 970 psf (pounds per square foot)
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From page 31... ...
If slickensides are present in sufficient numbers, the mobilized shear strength may be close to the residual strength. One may infer from a study by Skempton (1964)
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From page 32... ...
If a deterministic design is made with Hypothesis (~) and a conventional safety factor of I.5 on the mean undrained shear strength of 1,620 psf, the design strength is 1,080 psf and failure would also result.
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From page 33... ...
The engineer may adopt any of the last three hypotheses and produce a successful design using either a deterministic or a probabilistic analysis. This shows that probabilistic analysis can reflect the judgment and reasoning behind each hypothesis, but it cannot replace the important role of judgment in choosing the correct hypothesis.
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From page 34... ...
Journal of Geotechnical Engineering, American Society of Civil Engineers 109~24: 260-268. Gilbert, R.B., and W
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From page 35... ...
Journal of Geotechnical Engineering, American Society of Civil Engineers lOl(GT9~: 913-932.
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