Coulomb Wedge Theory

Q. An unsupported excavation is made to the maximum possible depth in a clay soil having ${\gamma }_t$ = $18kN/m^3$, $C=100kN/m^2$, $\varphi ={30}^{\circ }$. The active earth pressure, according to Rankine's theory, at the base level of the excavation is

1. $115.47kN/m^2$
2. $54.36kN/m^2$
3. $27.18kN/m^2$
4. $13.0kN/m^2$

Q. In cohesive soils the depth of tension crack $\left(Z_{cr}\right)$ is likely to be

1. $Z_{cr}\ge \frac{2C}{\gamma }tan({45}^{\circ }-\frac{\varphi }{2})$
2. $Z_{cr}\ge \frac{2C}{\gamma }tan({45}^{\circ }+\frac{\varphi }{2})$
3. $Z_{cr}\ge \frac{4C}{\gamma }tan({45}^{\circ }-\frac{\varphi }{2})$
4. $Z_{cr}\ge \frac{4C}{\gamma }tan({45}^{\circ }+\frac{\varphi }{2})$

Q. Coulomb's theory of earth pressure is based on

1. the theory of elasticity
2. the theory of plasticity
3. empirical rules
4. wedge theory

Q. For the determination of earth pressure, Coulomb's wedge theory assumes that

1. the back of wall is smooth and vertical
2. the soil is non homogeneous and anisotropic
3. the slip surface is circular
4. the wall surface is rough

Q. A 5m high vertical wall has a saturated clay backfill. The saturated unit weight and cohesion of clay are $18kN/m^3$ and 20 kPa, respectively. The angle of internal friction of clay is zero. In order to prevent development of tension zone, the height of the wall is required to be increased. Dry sand is used as backfill above the clay for the increased portion of the wall. The unit weight and angle of internal friction of sand are $16kN/m^3$ and ${30}^{\circ }$, respectively. Assume that the back of the wall is smooth and top of the backfill is horizontal. To prevent the development of tension zone, the minimum height (in m, round off to one decimal place) by which the wall has to be raised, is .

1. 2.5

Q. The depth of tension crack in a soft clay $({\varphi }_u=0)$ is

1. $\frac{4C_u}{\gamma }$
2. $\frac{2C_u}{\gamma }$
3. $\frac{C_u}{\gamma }$
   
4. $\frac{C_u}{2\gamma }$

Q. A vertical cut is to be made in a soil mass having cohesion c, angle of internal friction $\varphi$, and unit weight $\gamma$. Considering $K_{a}and{K}_p$ as the coefficient of active and passive earth pressures, respectively, the maximum depth of unsupported excavation is

1. $\frac{4c}{\gamma \sqrt{K_p}}$
2. $\frac{2c\sqrt{K_p}}{\gamma }$
3. $\frac{4C\sqrt{K_a}}{\gamma }$
4. $\frac{4c}{\gamma \sqrt{K_a}}$

Q. Surcharge loading required to be placed on the horizontal backfill of a smooth retaining vertical wall so as to completely eleminate tensile crack is

1. 2c
2. $2c{K}_a$
3. $2c\sqrt{K_a}$
4. $2c/\sqrt{K_a}$

Q. Using ${\varphi }_u=0$ analysis and assuming plane failure as shown, the minimum factor of safety against shear failure of a vertical cut of height 4 m in a pure clay having $C_u=120kN/m^{2}and{\gamma }_{sat}=20kN/m^3$ is

1. 1
2. 6
3. 10
4. 20

Q. Assertion (A): Rankine's earth pressure theory should not be used for concrete retaining walls and Coulomb's theory should not be used for estimating passive earth pressures
Reason (R): Rankine assumed that the retaining wall has a vertical back and Coulomb assumed that the resultant reaction due to earth pressure acts at one-third the height of the wall.

1. both A and R are true and R is the correct explanation of A
2. both A and R are true but R is not a correct explanation of A
3. A is true but R is false
4. A is false but R is true

Q. Consider the following statements:

1. Uniform surcharge increases active earth pressure even as it decreases passive resistance.
2. For analyzing the conditions at a masonry gravity wall, application of Coulomb's theory of earth pressure is preferred.
3. Culmann's method is applicable to a stratified backfill; whereas Poncelet's method is not.

Which of the above statements are correct?

1. 1 and 2
2. 1 and 3
3. 2 and 3
4. 1, 2 and 3

Q. Consider the following statements:

1. Coulomb's earth pressure theory does not take the roughness of wall into consideration.
2. In case of non-cohesive soils, the coefficients of active earth pressure and earth pressure at rest are equal.
3. Any movement of retaining wall away from the fill corresponds to active earth pressure condition.

Which of these statements is/are correct?

1. 1 alone
2. 1 and 2
3. 2 alone
4. 3 alone