250+ TOP MCQs on Density Index and Relative Compaction and Answers

Soil Mechanics Multiple Choice Questions on “Density Index and Relative Compaction”.

1. The density index I_D does not express the relative compactness of a natural cohesion-less soil.
a) True
b) False
Answer: b
Clarification: 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 I_D is used for cohesion-less soil only.
a) True
b) False
Answer: a
Clarification: The term density index I_D is not applicable to cohesive soil because of uncertainties in the laboratory determination of the voids ratio in the loosest state of the soil (e_max).

3. The formula for density index I_D is ______
a) (e_max – 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})})
Answer: d
Clarification: The density index is defined as the difference between the voids ratio of the soil in its loosest state e_max and its natural void ratio e to the difference between the voids ratio in the loosest and densest state.
I_D=(frac{(e_{max} – e)}{(e_{max}-e_{min})}).

4. When the natural state of cohesion-less soil is in its loosest form, its density index I_D is equal to ____
a) 0
b) 0.5
c) 1
d) 1.5
Answer: a
Clarification: Cohesion-less soil is in its loosest form will have its void ratio e=e_max.
Since I_D=(frac{(e_{max} – e)}{(e_{max}-e_{min})})
I_D=(frac{(e_{max} – e_{max})}{(e_{max}-e_{min})})
I_D=0.

5. The density index of natural deposit in its densest state is ______
a) 0
b) 0.5
c) 1
d) 1.5
Answer: c
Clarification: Cohesion-less soil is in its loosest form will have its void ratio e=e_min.
Since I_D=(frac{(e_{max} – e)}{(e_{max}-e_{min})})
I_D=(frac{(e_{max} – e_{min})}{(e_{max}-e_{min})})
I_D=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
Answer: c
Clarification: Given,
Porosity of 30%=0.3
voids ratio in the loosest state e_min= 0.35
voids ratio in the densest state e_max=0.92
e=(frac{n}{(1-n)})
e=(frac{0.3}{(1-0.3)})
e=0.429
I_D=(frac{(e_{max} – e)}{(e_{max}-e_{min})})
I_D=(frac{(0.92 –0.429)}{(0.92-0.35)})
I_D= 0.861.

7. The density index I_D 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})
Answer: b
Clarification: The density index is given by,
I_D=(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
I_D=(frac{((frac{Gγ_w}{γ_{d,min}}) – (frac{Gγ_w}{γ_d}))}{((frac{Gγ_w}{γ_{d,min}})- (frac{Gγ_w}{γ_{d,max}}))})
I_D=(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
Answer: b
Clarification: 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