1. The density index of natural deposit in its densest state is ______
a) 0
b) 0.5
c) 1
d) 1.5
Discussion
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.
2. 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
Discussion
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.
3. 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) \(\frac{(γ_d-γ_{d,min}) γ_{d,max}}{(γ_{d,max}-γ_{d}) γ_d}\)
Discussion
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=\(\frac{(γ_d-γ_{d,min}) γ_{d,max}}{(γ_{d,max}-γ_{d,min}) γ_d}.\)
4. 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
Discussion
Explanation: 15-35
5. 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
Discussion
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.
6. The relative compaction Rc is given by _______
a) γd,max/γd
b) γd/γd,min
c) γd/γd,max
d) γd,min/γd
Discussion
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 = γd/γd,max.
7. 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%
Discussion
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%.
8. 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) \(\frac{(1+e_{max})}{(1+e_{min})}\)
Discussion
Explanation: The relative compaction is given by,
\(R_c = \frac{γ_d}{γ_{d,max}}\)
Since γd=γs(1+emin)
γd,max=γs(1+e)
\(R_c= \frac{γ_d}{γ_{d,max}}= \frac{γ_s(1+e_{min})}{γ_s(1+e)} \)
\(R_c= \frac{(1+e_{min})}{(1+e)}. \)
9. A soil has a dry unit weight of 17 kN/m3 and water content of 20%, then what will be its bulk unit weight?
a) 19.3 kN/m3
b) 20.4 kN/m3
c) 22.6 kN/m3
d) 24.4 kN/m3
Discussion
Explanation: Given,
Dry unit weight γd = 17 kN/m3
Water content w = 20% = 0.2
Bulk unit weight γ = γd *(1+w)
γ = 17*(1+0.2)
γ = 20.4 kN/m3.
10. The relationship between e, G, w and S is ______
a) \(e=\frac{wG}{S}\)
b) e = wGS
c) \(e=\frac{wS}{G}\)
d) \(e=\frac{GS}{w}\)
Discussion
Explanation: The degree of saturation is given by
S=\(\frac{V_w}{V_V}=\frac{e_w}{e}\) where ew = water void ratio=eS ——-(1)
Water content w=\(\frac{W_w}{W_d}\)
w = \(\frac{e_wγ_w}{γ_s*1}\)
But γs = Gγw
∴ w = \(\frac{e_wγ_w}{Gγ_w}= \frac{e_w}{G}\)
ew = wG ———–(2)
from equation (1) and (2)
\(e=\frac{wG}{S}\).