Important Relationships

Q. A soil has mass unit weight $\gamma$, water content 'w' (as ratio). The specific gravity of soil solids = G, unit weight of water =${\gamma }_w$. 'S' the degree of saturation of the soil is given by

1. $S=\frac{1+w}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{G}}$

2. $S=\frac{w}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{G}}$
3. $S=\frac{(1+w)}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{G}}$
4. $S=\frac{w}{\frac{\gamma w}{\gamma }(1+w)-\frac{1}{wG}}$
   

Q. The ratio of saturated unit weight to dry unit weight of a soil is 1.25. If the specific gravity of solids $\left(G_s\right)$ is 2.65, the void ratio of the soil is

1. 0.625
2. 0.663
3. 0.944
4. 1.325

Q. A dry soil has mass specific gravity of 1.35. If the specific gravity of solids is 2.7, then the void ratio will be

1. 0.5
2. 1.0
3. 1.5
4. 2.0

Q. The natural void ratio of a sand sample is 0.6 and its density index is 0.6. If its void ratio in the loosest state is 0.9, then the void ratio in the densest state will be

1. 0.2
2. 0.3
3. 0.4
4. 0.5

Q.

A sample of saturated sand has a dry unit weight of $18kN/m^3$ and a specific gravity of 2.7. If density of water is $10kN/m^3$, the void ratio of the soil sample will be

1. 0.5
2. 0.6
3. 0.4
4. 0.9

Q. In a wet soil mass, air occupies one-sixth of its volume and water occupies one-third of its volume. The void ratio of the soil is

1. 0.25
2. 0.5
3. 1.00
4. 1.50

Q. A soil has specific gravity of its solids equal to 2.65. The mass density of water is $1000kg/m^3$. Considering zero air voids and 10% moisture content of the soil sample, the dry density (in kg/$m^3$, round off to 1 decimal place) would be _____ .

1. 2094.862

Q. Proctor's compaction test for the maximum dry density of a certain soil gave the results as: 1.77 gm/cc and OMC 14.44%. The specific gravity of the clay soil grain was 2.66. What was the saturation degree for this soil?

1. 44%
2. 55%
3. 66%
4. 77%

Q. Consider the following statements in relation to the given table:

1. Soil is partially saturated at degree of saturation = 60%
2. Void ratio =40%
3. Water content = 30%
4. Saturated unit weight = 1.5 g/cc
Which of these statements is/are correct?

1. 1, 2 and 3
2. 1, 3, and 4
3. 2, 3 and 4
4. 1, 2 and 4

Q. If the soil sample is having porosity 50% and degrees of saturation at 90% then its percentage air voids is :

1. 5%
2. 50%
3. 45%
4. 4.5%

Q. In its natural condition a soil sample has a mass of 1.980 kg and a volume of $0.001m^3$. After being completely dried in an oven; the mass of the sample is 1.800 kg. Specific gravity is 2.7. Unit weight of water is $10kN/m^3$. The degree of saturation of soil is

1. 0.65
2. 0.70
3. 0.54
4. 0.61

Q. The natural water content of the soil sample was found to be 40% , specific gravity is 2.7 and void ratio 1.2 then the degree of saturation of the soil will be

1. 100%
2. 69%
3. 87%
4. 90%

Q. A soil sample having a void ratio of 1.3, water content of 50% and a specific gravity of 2.60, is in a state of

1. partial saturation
2. full saturation
3. over saturation
4. under saturation

Q. A certain soil has the following properties, $G_s=2.71,n=40$% and $w=20$% .The degree of saturation of the soil rounded off to the nearest percentage is _______ .

1. 81

Q. Which one of the following relation gives the value of degree of saturation S, in terms of unit weight $\gamma$ water content w (as ratio) and specific gravity of soil solids $G_s,{\gamma }_w$ is unit weight of water?

1. $S=\frac{W}{\left(\gamma /{\gamma }_w\right)(1+W)-1/G_s}$

2. $S=\frac{W}{\left(\gamma /{\gamma }_w\right)(1+W)+1/G_s}$

3. $S=\frac{W}{\left({\gamma }_w/\gamma \right)(1+W)+1/G_s}$

4. $S=\frac{W}{\left({\gamma }_w/\gamma \right)(1+W)-1/G_s}$

Q. Two soil sample A and B have porosities$n_A=40$% and $n_B=60$% respectively. What is the ratio of void ratios $e_A$ : $e_B$?

1. 2 : 3
2. 3 : 2
3. 4 : 9
4. 9 : 4

Q. A sample of soil was prepared by mixing a quantity of dry soil with 25% of water by mass. Find mass of the wet mixture required to produce cylindrical specimen of 15 cm depth and 5% air content. If specify gravity of solids is 2.68 and dia cylinder is 20 cm.

1. 7200 gm
2. 9260 gm
3. 9060 gm
4. 9300 gm

Q. Which one of the following correctly represents the dry unit weight of a soil sample which has a bulk unit weight of ${\gamma }_t$ at a moisture content of W%?

1. $\frac{w{\gamma }_t}{100}$

2. ${\gamma }_t(1+\frac{w}{100})$

3. ${\gamma }_t\left(\frac{100}{100+w}\right)$

4. $\frac{{\gamma }_t(100-w)}{100}$

Q. Match List -I (Terms) with List -II (Formulae) and select the correct answer using the codes given below the lists:

List -I Lists -II

A. Void Ratio 1. $\frac{V_V}{V}$

B. Porosity 2. $\frac{W_W}{W_S}$

C. Degree of saturation 3. $\frac{V_W}{V_V}$

D. Water content 4. $\frac{W}{V}$

5. $\frac{V_V}{V_S}$

1. A B C D
   4 3 5 1
   
2. A B C D
   5 4 3 1
3. A B C D
   4 1 5 2
4. A B C D
   5 1 3 2

Q. Consider the following effects as indicative of complete saturation of a soil sample:

1. Pore water pressure is positive
2. Volume of water to volume of voids is equal to 1..
3. Relative density is equal to 1.

Which of the above statements are correct?

1. 1 and 2
2. 1 and 3
3. 2 and 3
4. 1, 2 and 3