2. Before the design of a tunnel through a rocky region, geological exploration was conducted to investigate the joints and potential slip surfaces that exist in the rock strata. For economic reasons, only portions of the strata are explored. In addition, the measurements recorded by the instruments are not perfectly reliable. Thus, the geologist can only conclude that the condition of the rock may be either highly fissured (H), medium fissured (M), or slightly fissured (L) with relative likelihoods of 1:2:7. Based on this information, the engineer designs the tunnel and estimates that; - If the rock condition is L, the probability of failure is 0.002, - If the rock condition is M, the probability of failure will be 3 times of the one for the condition L, - If the rock condition is H, the probability of failure is 8 times of the failure for condition L. a) What is the probability of failure of the proposed tunnel design? b) A more reliable device is subsequently used to improve the prediction of rock condition. Its results indicate that a highly fissured condition for the rock around the tunnel is practically impossible, but it cannot give better information on the relative likelihood between rock conditions M and L. In the light of this information, what would be the revised failure probability of the proposed tunnel design?
2. Before the design of a tunnel through a rocky region, geological exploration was conducted to investigate the joints and potential slip surfaces that exist in the rock strata. For economic reasons, only portions of the strata are explored. In addition, the measurements recorded by the instruments are not perfectly reliable. Thus, the geologist can only conclude that the condition of the rock may be either highly fissured (H), medium fissured (M), or slightly fissured (L) with relative likelihoods of 1:2:7. Based on this information, the engineer designs the tunnel and estimates that; - If the rock condition is L, the probability of failure is 0.002, - If the rock condition is M, the probability of failure will be 3 times of the one for the condition L, - If the rock condition is H, the probability of failure is 8 times of the failure for condition L. a) What is the probability of failure of the proposed tunnel design? b) A more reliable device is subsequently used to improve the prediction of rock condition. Its results indicate that a highly fissured condition for the rock around the tunnel is practically impossible, but it cannot give better information on the relative likelihood between rock conditions M and L. In the light of this information, what would be the revised failure probability of the proposed tunnel design?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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Transcribed Image Text:2. Before the design of a tunnel through a rocky region, geological exploration was conducted to investigate the joints
and potential slip surfaces that exist in the rock strata. For economic reasons, only portions of the strata are explored.
In addition, the measurements recorded by the instruments are not perfectly reliable. Thus, the geologist can only
conclude that the condition of the rock may be either highly fissured (H), medium fissured (M), or slightly fissured
(L) with relative likelihoods of 1:2:7. Based on this information, the engineer designs the tunnel and estimates that;
- If the rock condition is L, the probability of failure is 0.002,
- If the rock condition is M, the probability of failure will be 3 times of the one for the condition L,
- If the rock condition is H, the probability of failure is 8 times of the failure for condition L.
a) What is the probability of failure of the proposed tunnel design?
b) A more reliable device is subsequently used to improve the prediction of rock condition. Its results indicate
that a highly fissured condition for the rock around the tunnel is practically impossible, but it cannot give
better information on the relative likelihood between rock conditions M and L. In the light of this information,
what would be the revised failure probability of the proposed tunnel design?
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