# Soil Mechanics Questions and Answers – Calculation of Voids Ratio and Coefficient of Volume Change

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This set of Soil Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Calculation of Voids Ratio and Coefficient of Volume Change”.

1. From the consolidation test, the final voids ratio at end of pressure increment can be calculated by ________________
a) height of solids method only
b) change in voids ratio method only
c) both height of solids method and change in voids ratio method
d) no method are available

Explanation: The equilibrium voids ratio or the final voids ratio can be calculated by the following methods:

• height of solids method
• change in voids ratio method.

2. The change in voids ratio method is applicable for _________________
a) only dry specimens
b) only fully saturated specimens
c) only partially saturated specimens
d) for all types of specimens

Explanation: For the change in voids ratio method the final voids ratio is calculated by the relation of ef=wf G. Where the wf represents the final water content and the degree of saturation is one percent.

3. The height of solids method is applicable for ________
a) only dry specimens
b) only fully saturated specimens
c) both saturated and unsaturated samples
d) only partially saturated specimens

Explanation: The height of solids method is applicable for both saturated and unsaturated samples but the change in voids ratio method is applicable only for fully saturated soil specimens.
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4. The height HS of the solids of the specimen is calculated from _______________
a) $$H_s=\frac{M_d}{GA}$$
b) $$H_s=\frac{M_d}{Gρ_w}$$
c) $$H_s=\frac{M_d}{Aρ_w}$$
d) $$H_s=\frac{M_d}{GAρ_w}$$

Explanation: The height HS of the solids of the specimen is calculated from the expression,
$$H_s=\frac{M_d}{GAρ_w},$$
where, Hs=height of solids
Md=mass of dried soil sample
G=specific gravity of solid particles
A=cross-sectional area of specimen
ρw=mass density of water.

5. The height Hs of the solids of the specimen with respect to weight of dried specimen is _____________
a) $$H_s=\frac{W_d}{Gρ_w}$$
b) $$H_s=\frac{W_d}{GAρ_w}$$
c) $$H_s=\frac{W_d}{GA}$$
d) $$H_s=\frac{W_d}{Aρ_w}$$

Explanation: Since the height HS of the solids of the specimen is calculated from the expression,
$$H_s=\frac{W_d}{GAρ_w}$$ and the dry weight in relation to dry mass is given by,
$$W_d=\frac{M_d}{ρ_w}.$$ Therefore, the The height Hs of the solids of the specimen with respect to weight of dried specimen is,
$$H_s=\frac{W_d}{GA}.$$

6. The voids ratio with respect to height of solids is given by equation______________
a) $$e=\frac{H}{H_s}$$
b) $$e=\frac{H_s}{H}$$
c) $$e=\frac{H+H_s}{H_s}$$
d) $$e=\frac{H-H_s}{H_s}$$

Explanation: The voids ratio is calculated from the equation of,
$$e=\frac{H-H_s}{H_s},$$ where e=voids ratio
H=height of specimen at equilibrium
Hs= height of solids.

7. The height of the specimen at various applied pressures is given by _____________
a) H=H0*∑∆H
b) H=H0-∑∆H
c) $$H=\frac{H_0}{∑∆H}$$
d) H=H0+∑∆H

Explanation: The height of specimen at equilibrium under various applied pressures is,
H=H0+∑∆H,
where, H0=initial height of the specimen
∆H= change in specimen thickness under any pressure increment. The sum of each pressure increment is ∑∆H.

8. From the consolidation test, by the change in voids ratio method, the final void is given by _______
a) ef=wf G
b) ef=wf AG
c) $$e_f=\frac{w_f}{G}$$
d) $$e_f=\frac{G}{w_f}$$

Explanation: In the change in voids ratio method of consolidation test, the final voids ratio is given by, ef=wfG.
Where, wf=final water content
G=specific gravity of solid particles
The degree of saturation is one (S=1).

9. The change in voids ratio of the consolidation test is calculated from the relation of________
a) $$∆e=\frac{1+e_f}{2} ∆H$$
b) $$∆e=\frac{1+e_f}{H_f} ∆H_f$$
c) $$∆e=\frac{1+e_f}{H}$$
d) $$∆e=\frac{e_f}{H_f} ∆H$$

Explanation: The change in voids ratio with the pressure increment is given by the relation,
$$\frac{∆e}{1+e_f}=\frac{∆H}{H_f},$$ therefore on rearranging the equation, we get,
$$∆e=\frac{1+e_f}{2} ∆H.$$

10. From the consolidation test data using the ‘change in void ratio’ method, the coefficient of volume change can be calculated by _____________
a) $$m_v=-\frac{∆e}{1+e_o} \frac{1}{σ’}$$
b) $$m_v=-\frac{∆e}{1+e_o}$$
c) $$m_v=-\frac{∆e}{1+e_o} \frac{10}{∆σ’}$$
d) $$m_v=-\frac{∆e}{1+e_o} \frac{1}{∆σ’}$$

Explanation: Using the change in void ratio method, the coefficient of volume change can be defined as the change in volume of a soil per unit of initial volume due to a given increase in unit pressure.
∴ $$m_v=-\frac{∆e}{1+e_o} \frac{1}{∆σ’}.$$

11. From the consolidation test data using the ‘Height of solids’ method, the coefficient of volume change can be calculated by _____________
a) $$m_v=-\frac{∆H_o}{H_o}\frac{1}{∆σ’}$$
b) $$m_v=\frac{∆H}{H_o} \frac{1}{∆σ’}$$
c) $$m_v=-\frac{∆H}{H_o} \frac{1}{∆σ’}$$
d) $$m_v=-\frac{∆H}{H}\frac{1}{∆σ’}$$

Explanation: Since we know the relation of change in voids ratio with the pressure increment is given by the relation,
$$\frac{∆e}{1+e_0}=\frac{∆H}{H_0},$$ and coefficient of volume change is given by $$m_v=-\frac{∆e}{1+e_o}\frac{1}{∆σ’}.$$
Therefore, from the two equations, we get,
$$m_v=-\frac{∆H}{H_o} \frac{1}{∆σ’}.$$

12. The coefficient of volume change is ______________
a) reciprocal of compressibility modulus
b) equal to compressibility modulus
c) double compressibility modulus
d) equal to three times the compressibility modulus

Explanation: The compressibility modulus is a measure of the relative volume change of a fluid or solid as a response to a pressure change. The coefficient of volume change is the reciprocal of compressibility modulus and has units in the form of m2/kN.

13. The unit of coefficient of volume change is
a) m2/kN
b) m3/kN
c) m2/N
d) m3/N

Explanation: The coefficient of volume change can be defined as the change in volume of a soil per unit of initial volume due to a given increase in unit pressure.
$$m_v=-\frac{∆H}{H_o}\frac{1}{∆σ’},$$ Hence it has the units in the form of m2/kN (reciprocal of pressure).

14. From the calculations consideration of a consolidation test data, the change in thickness can be both positive and negative.
a) True
b) False

Explanation: From the calculations consideration of a consolidation test data, the change in thickness can be both positive and negative. The negative sign denotes the decrease height due to loading and the positive sign denotes the increase in height due to unloading of the specimen.

15. The Rowe cell apparatus also measures the pore pressure.
a) False
b) True

Explanation: The Rowe cell apparatus allows the consolidation test based on the theory of consolidation and measure pore water pressure and the rate of dissipation. The change in sample height can also be measured during the test.

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