In cohesive soil, if the active earth pressure is zero, then the depth (z) is given by-
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A.
(2C/ã) taná
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B.
(C/ã) cotá
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C.
(2C/ã) cotá
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D.
(C/ã) taná
Correct Answer:
A. (2C/ã) taná
Explanation:
According to Rankine's theory for cohesive soils, the active earth pressure (Pa) at a depth z is calculated using the formula Pa = Kaγz - 2c√Ka. The pressure is zero at a specific depth known as the depth of the tensile crack (Zc). By setting Pa to zero, the equation becomes Kaγz = 2c√Ka. Solving for z gives z = 2c / (γ√Ka). Since √Ka is equal to tan(45° - φ/2) or cot(45° + φ/2), the depth where the active earth pressure is zero is expressed as (2c/γ) tanα, where α is the angle of the failure plane with the vertical.
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