GATE CE 2017 Set 2 — Question 37
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Geotechnical Engineering → Effective Stress & Compaction → Drained & Undrained Strength
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Question
For the construction of a highway, a cut is to be made as shown in the figure.
The soil exhibits , , and the undrained shear strength . The unit weight of water is . The unit weights of the soil above and below the ground water table are and , respectively. If the shear stress at Point is , the factors of safety against the shear failure at this point, considering the undrained and drained conditions, respectively, would be
Correct answer
(A) 1.6 and 0.9
Solution
The factor of safety () is the ratio of shear strength to shear stress.1. Undrained Condition:
In undrained condition, the shear strength is the undrained shear strength .2. Drained Condition:
In drained condition, the shear strength is .
From the figure, Point is at a depth of from the ground surface. The water table is below the ground surface.
Total vertical stress at , .
Pore water pressure at , .
Effective vertical stress at , .
Shear strength, .Thus, the factors of safety are and .
In undrained condition, the shear strength is the undrained shear strength .2. Drained Condition:
In drained condition, the shear strength is .
From the figure, Point is at a depth of from the ground surface. The water table is below the ground surface.
Total vertical stress at , .
Pore water pressure at , .
Effective vertical stress at , .
Shear strength, .Thus, the factors of safety are and .
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