The factor of safety, Fs, of a rock slope is commonly thought of as the ratio of the maximum load or stress that a slope can sustain to the actual maximum load or stress that is applied during a design lifetime. Suppose that an extensive statistical study has determined that the actual Fs for rock slopes in the Cape Breton Highlands against sliding has a Weibull distribution with median 2.947 and β = 0.3. a) What is λ for this distribution? b) What is the probability that the Fs is less than 1 for a randomly selected rock slope? c) Supposethatdesignstandardsaresuchthatslopeshavingfactorsofsafetyinexcessof2.0 are considered to be “safe”. What fraction of rock slopes in the Cape Breton Highlands would then be considered “unsafe” and so thus in need of remediation?
The factor of safety, Fs, of a rock slope is commonly thought of as the ratio of the maximum load or stress that a slope can sustain to the actual maximum load or stress that is applied during a design lifetime. Suppose that an extensive statistical study has determined that the actual Fs for rock slopes in the Cape Breton Highlands against sliding has a Weibull distribution with
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a) What is λ for this distribution?
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b) What is the
probability that the Fs is less than 1 for a randomly selected rock slope? -
c) Supposethatdesignstandardsaresuchthatslopeshavingfactorsofsafetyinexcessof2.0 are considered to be “safe”. What fraction of rock slopes in the Cape Breton Highlands would then be considered “unsafe” and so thus in need of remediation?
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