# Soil Mechanics Questions and Answers – Density Index and Relative Compaction

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This set of Soil Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Density Index and Relative Compaction”.

1. The density index ID does not express the relative compactness of a natural cohesion-less soil.
a) True
b) False

Explanation: The density index is used to express the relative compactness or degree of compaction of a natural cohesion-less soil deposit. It is also known as relative density or degree of density.

2. The term density index ID is used for cohesion-less soil only.
a) True
b) False

Explanation: The term density index ID is not applicable to cohesive soil because of uncertainties in the laboratory determination of the voids ratio in the loosest state of the soil (emax).

3. The formula for density index ID is ______
a) (emax – e)
b) $$\frac{(e_{max} – e)}{(e_{min}-e)}$$
c) $$\frac{(e_{max} – e_{min})}{(e_{max}-e)}$$
d) $$\frac{(e_{max} – e)}{(e_{max}-e_{min})}$$

Explanation: The density index is defined as the difference between the voids ratio of the soil in its loosest state emax and its natural void ratio e to the difference between the voids ratio in the loosest and densest state.
ID=$$\frac{(e_{max} – e)}{(e_{max}-e_{min})}$$.
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4. When the natural state of cohesion-less soil is in its loosest form, its density index ID is equal to ____
a) 0
b) 0.5
c) 1
d) 1.5

Explanation: Cohesion-less soil is in its loosest form will have its void ratio e=emax.
Since ID=$$\frac{(e_{max} – e)}{(e_{max}-e_{min})}$$
ID=$$\frac{(e_{max} – e_{max})}{(e_{max}-e_{min})}$$
ID=0.

5. The density index of natural deposit in its densest state is ______
a) 0
b) 0.5
c) 1
d) 1.5

Explanation: Cohesion-less soil is in its loosest form will have its void ratio e=emin.
Since ID=$$\frac{(e_{max} – e)}{(e_{max}-e_{min})}$$
ID=$$\frac{(e_{max} – e_{min})}{(e_{max}-e_{min})}$$
ID=1.

6. A soil has porosity of 30%. Its voids ratio in the loosest and densest state is 0.35 and 0.92 respectively. What will be its density index?
a) 0.865
b) 0.872
c) 0.861
d) 0.881

Explanation: Given,
Porosity of 30%=0.3
voids ratio in the loosest state emin= 0.35
voids ratio in the densest state emax=0.92
e=$$\frac{n}{(1-n)}$$
e=$$\frac{0.3}{(1-0.3)}$$
e=0.429
ID=$$\frac{(e_{max} – e)}{(e_{max}-e_{min})}$$
ID=$$\frac{(0.92 –0.429)}{(0.92-0.35)}$$
ID= 0.861.

7. The density index ID in terms of densities is given by ______
a) $$\frac{(γ_{d,max}-γ_{d,min}) γ_{d,max}}{(γ_{d,max}-γ_{d}) γ_d}$$
b) $$\frac{(γ_d-γ_{d,min}) γ_{d,max}}{(γ_{d,max}-γ_{d,min}) γ_d}$$
c) $$\frac{(γ_d-γ_{d,min}) γ_{d,max}}{(γ_d-γ_{d,max}) γ_d}$$
d) $$\frac{(γ_d-γ_{d,min}) γ_{d,max}}{(γ_{d,max}-γ_{d}) γ_d}$$

Explanation: The density index is given by,
ID=$$\frac{(e_{max} – e)}{(e_{max}-e_{min})}$$
$$e=(\frac{Gγ_w}{γ_d})-1$$
$$e_{max}=(\frac{Gγ_w}{γ_{d,min}})-1$$
$$e_{min}=(\frac{Gγ_w}{γ_{d,max}})-1$$
substituting the values of voids ratio
ID=$$\frac{((\frac{Gγ_w}{γ_{d,min}}) – (\frac{Gγ_w}{γ_d}))}{((\frac{Gγ_w}{γ_{d,min}})- (\frac{Gγ_w}{γ_{d,max}}))}$$
ID=$$\frac{(γ_d-γ_{d,min}) γ_{d,max}}{(γ_{d,max}-γ_{d,min}) γ_d}.$$

8. The relative density of loose granular soil is given by the range ______ in percentage.
a) 0-15
b) 15-35
c) 35-65
d) 85-100

Explanation: The following table gives the characteristics of density of granular soil on the basis of relative density.

Relative Density (%) Density Description
0-15 Very loose
15-35 Loose
35-65 Medium
65-85 Dense
85-100 Very Dense

9. A soil has a dry density of 17.5kN/m3. It has densities corresponding to most compact and loosest state as 18.5 kN/m3 and 13 kN/m3 respectively. The relative density of the soil is ______
a) 0.871
b) 0.865
c) 0.869
d) 0.860

Explanation: Given,
Dry density γd=17.5 kN/m3
Maximum dry density γd,max=18.5kN/m3
Minimum dry density γd,mim=13kN/m3
Relative density ID= $$\frac{(γ_d-γ_{d,min})γ_{d,max}}{((γ_{d,max}-γ_{d,min}) γ_d )}$$
ID = $$\frac{((17.5-13)*18.5)}{((18.5-13)*17.5)}$$
ID=0.865.

10. The relative compaction Rc is given by _______
a) γd,maxd
b) γdd,min
c) γdd,max
d) γd,mind

Explanation: The relative compaction Rc is defined as the ratio of dry density γd of soil to its dry density corresponding to most compact state γd,max.
Rc = γdd,max.

11. When the soil is in loosest form, density index is zero and its relative compaction Rc is ______
a) 40%
b) 60%
c) 80%
d) 100%

Explanation: The relationship between the relative compaction Rc and density index ID is given by,
Rc=80+0.2ID
When ID=0,
Rc=80+0.2*0
Rc=80%.

12. The relative compaction Rc is related to the void ratio of soil by _______
a) $$\frac{(1+e)}{(1+e_{max})}$$
b) $$\frac{(1+e)}{(1+e_{min})}$$
c) $$\frac{(1+e_{min})}{(1+e)}$$
d) $$\frac{(1+e_{max})}{(1+e_{min})}$$

Explanation: The relative compaction is given by,
$$R_c = \frac{γ_d}{γ_{d,max}}$$
Since γds(1+emin)
γd,maxs(1+e)
∴ $$R_c= \frac{γ_d}{γ_{d,max}}= \frac{γ_s(1+e_{min})}{γ_s(1+e)}$$
$$R_c= \frac{(1+e_{min})}{(1+e)}.$$

Sanfoundry Global Education & Learning Series – Soil Mechanics.

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