# Soil Mechanics Questions and Answers – Stress Distribution – Equivalent Point Load Method

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This set of Soil Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Stress Distribution – Equivalent Point Load Method”.

1. In Terzaghi’s Theory of one dimensional consolidation, load is applied in _____________
a) one direction only
b) two directions only
c) three directions only
d) none of the direction

Explanation: In Terzaghi’s Theory of one dimensional consolidation, load is applied in one direction only. This direction is usually the vertical direction and the load is applied from the top of the sample.

2. In Terzaghi’s Theory of one dimensional consolidation, the deformation occurs in __________
a) one direction only
b) two directions only
c) three directions only
d) none of the direction

Explanation: In Terzaghi’s Theory of one dimensional consolidation, load is applied in one direction only. Therefore, the deformation also occurs in one direction only. This direction is usually the vertical direction as the load is applied from the top of the sample.

3. In Terzaghi’s Theory of one dimensional consolidation, soil is restrained against lateral deformation.
a) True
b) False

Explanation: In Terzaghi’s Theory of one dimensional consolidation, load is applied in one direction only and so the deformation occurs in one direction only. Therefore, as an assumption, the soil is restrained against lateral deformation.
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4. In Terzaghi’s Theory of one dimensional consolidation, excess pore water drains out in __________
a) horizontal direction only
b) tangential direction only
c) vertical direction only
d) both horizontal and vertical direction

Explanation: In Terzaghi’s Theory of one dimensional consolidation, as the load is applied in one direction only, excess pore water drains out in in one direction and that is the vertical direction.

5. In Terzaghi’s Theory of one dimensional consolidation, the boundary is considered to be __________
a) free surface offering resistance to flow of water
b) free surface offering no resistance to flow of water
c) fixed surface offering resistance to flow of water
d) curved surface offering resistance to water flow

Explanation: In Terzaghi’s Theory of one dimensional consolidation, the boundary is considered to be free surface offering no resistance to flow of water. This is because, when the surface offers resistance to the water flow, it will cause addition pressure to build up. This addition pressure makes the problems complicated to solve.

6. In Terzaghi’s Theory of one dimensional consolidation, the change in thickness of a layer during consolidation is ___________
a) significant
b) insignificant
c) large
d) very large

Explanation: In Terzaghi’s Theory of one dimensional consolidation, the change in thickness of a layer during consolidation is insignificant. This assumption is because change in thickness is too small to measure.

7. In Terzaghi’s Theory of one dimensional consolidation, the time lag in consolidation is ___________
a) due to permeability of soil and viscosity of water or fluid
b) due entirely to seepage pressure of water
c) due entirely to permeability of soil
d) due entirely to viscosity of water or fluid

Explanation: The time lag is the delay in consolidation due to slow drainage of water. This entirely depends upon the permeability of the saturated soil and not on the seepage pressure of the water between the soil particles.

8. In one-dimensional consolidation, secondary consolidation is __________
a) considered at the start of test
b) considered at the middle of test
c) considered at the end of test
d) disregarded

Explanation: Since in Terzaghi’s Theory of one dimensional consolidation, the time lag in consolidation is due entirely to permeability of soil, there is very slow drainage of water that leads to neglecting of the secondary consolidation.

9. The hydraulic gradient in terms of pore water pressure is given by _________
a) $$i=\frac{γ_w \overline{u}∂h}{∂z}$$
b) $$i=\frac{\overline{u}∂h}{γ_w ∂z}$$
c) $$i=\frac{\overline{u}∂h}{∂z}$$
d) $$i=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z}$$

Explanation: The hydraulic gradient i is given by,
$$i=\frac{∂h}{∂z} \,where\, h=\frac{\overline{u}}{γ_w}$$
∴ from the two equations, we get,
$$i=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z}.$$

10. The rate of change of pore water pressure along the depth of layer represents ____________
a) seepage pressure
b) seepage stress
d) permeability of the soil

Explanation: The hydraulic gradient is the change in total head divided by the distance over which the change occurs. Therefore, the rate of change of pore water pressure along the depth of layer represents the hydraulic gradient.

11. The velocity with which the excess pore water flows is _________
a) $$v=\frac{k}{2}\frac{∂\overline{u}}{∂z}$$
b) $$v=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z}$$
c) $$v=\frac{k}{γ_w}\frac{∂\overline{u}}{∂z}$$
d) $$v=\frac{∂\overline{u}}{∂z}$$

Explanation: The velocity with which the excess pore water flows is given by Darcy’s law,
$$v=ki, \,where\, i=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z}$$
Therefore, $$v=\frac{k}{γ_w}\frac{∂\overline{u}}{∂z}.$$

12. The rate of change of velocity along the depth of layer is ___________
a) $$\frac{∂v}{∂z}=\frac{1}{γ_w}\frac{∂^2 \overline{u}}{∂z^2}$$
b) $$\frac{∂v}{∂z}=\frac{k}{γ_w}\frac{\overline{u}}{∂z^2}$$
c) $$\frac{∂v}{∂z}=\frac{∂^2\overline{u}}{∂z^2}$$
d) $$\frac{∂v}{∂z}=\frac{k}{γ_w}\frac{∂^2 \overline{u}}{∂z^2}$$

Explanation: The velocity with which the excess pore water flows is given by Darcy’s law,
$$v=ki=\frac{k}{γ_w}\frac{∂\overline{u}}{∂z} ——————————-(1)$$
Differentiating the equation (1) with respect to depth z, we get,
∴$$\frac{∂v}{∂z}=\frac{k}{γ_w}\frac{∂^2\overline{u}}{∂z^2}.$$

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