Index Properties - Free MCQ Practice Test with solutions, GATE Civil Soil

Concept:
Degree of saturation (Sr): 
Degree of saturation is defined as the ratio of the volume of water (V_w) to the volume of voids (V_v).

Calculation:
Given data:
Weight of soil solid in sample (W_s) =1.0 g
Weight of water in sample (W_w) = 0.15 g
Volume of soil solid in sample (V_s) = 0.3704 cm³
Volume of water in sample (V_w) = 0.15 cc or 0.15 cm³
Volume of voids in sample (V_v) = 0.2349 cm³
Volume of air  in sample (V_a) = 0.2349 - 0.15 = 0.0849 cc
Volume of air  in sample (V_a) = 0.0849 cc

Degree of saturation in a given sample (S_r) = 0.6385

Concept:
Pycnometer method is used to determine specific gravity and water content both. This method is suitable for cohesionless soils.
Pycnometer is a glass jar of 1-liter capacity that is fitted at its top by a conical cap made of brass. It has a screw type cover and there is a small hole at its apex of 6 mm diameter.

W₁ = Mass of empty volume of pycnometer
W₂ = Mass of pycnometer + Mass of moist sample
W₃ = Mass of pycnometer + soil + water
W₄ = Mass of pycnometer full of water
G, = Specific gravity of soil solids
Water content of the soil sample is given by:

Specific gravity is usually reported at 27°C and it is given by:

Fuller's Maximum Density Criteria:

• This method is economical to design for a minimum amount of cement-water paste in a concrete mix.
• Fuller assumes that the greater the amount of solid particles that can be packed in a given volume of concrete, the higher will be its strength.
• According to Fuller's maximum density criteria, Percentage of total material smaller than size d is given as:

Where P = % passing sieve size d , D = Maximum size of particle
Given, maximum size of particle = 4 mm 
∴ Percentage particles between 4 mm and 2 mm, by weight can be calculated by: P_4mm - P_2mm  

Concept:
Core cutter test:

• This method is used to find in-situ unit weight in the case of fine-grained cohesive soils without stones.
• This method cannot be used in the case of hard and gravelly soils.

Equipment used:

1. Cylindrical core cutter, 100 mm internal diameter and 130 mm long.
2. Steel rammer of mass 9 kg and overall length 900 mm
3. Steel Dolley, 25 mm high and 100 mm diameter
4. Weighing balance of accuracy up to 1 gm
   

Concept:
From a fundamental relationship, the density of soil is given by:

Where
γ = Density of soil, 
γ_w = Density of water, G = Specific gravity of soil, S = Degree of saturation, w = Water content, and e = void ratio
For the dry density of soil: Degree of saturation (S) = 0
The dry density of soil(γ_d) is given by

Given data
The specific gravity of solids = 3
The mass-specific gravity = 2
The dry density of soil(γ_d) is given by

Where G_m = Mass specific gravity

e = 0.5
The void ratio is 0.5.

Concept:
Relative density: 

• Relative density is the measure of the compactness of cohesion-less soil.
• Relative density represents whether the soil is closest to its densest state or loosest state.
• It is defined as the ratio of the difference between the voids ratio of the soil in its loosest state and its natural state to the difference between the voids ratio in the loosest and densest state.

The relationship between the Relative Density and Void ratio of the soil sample is depicted in the graph below:

∴ Relative density varies inversely to the void ratio.
Classification of soil as per relative density as follows:

Calculation:
e_max = 0.6, e_min = 0.2, and natural void ratio (e) = 0.4

Expressing it in percentage = 0.5 × 100 = 50%

Concept:
The fundamental relation between dry density (γ_d), bulk density (γ) and water content (ω), is

Calculation:
Given, 
γ = 22 kN/m³,  w = 10 %

Concept:
The formula for finding the dry unit weight of soil is given by:

where, 
γ_d = Dry unit weight of soil
γ = Total Unit weight of soil
w = Water content
Calculations:
Given Data:
γ = 5 kN/m³
w = 17 % = 0.17
So, 

Concept:
The liquidity index is defined as a ratio of the difference between the natural water content of a soil and plastic limit to the plasticity index.
The liquidity index is also known as the water plasticity ratio.
Liquidity Index of a soil is given by:


Hence, when the liquidity index is greater than 1, it indicates the soil is in a liquid state.

The shrinkage limit is the water content of the soil when the water is just sufficient to fill all the pores of the soil and the soil is just saturated.
The volume of the soil does not decrease when the water content is reduced below the shrinkage limit.

Where,
w_L = liquid limit
wp = plastic limit
ws = shrinkage limit
V_L = Volume of soil mass corresponding to liquid limit
V_p = Volume of soil mass corresponding to plastic limit
V_d = Volume of soil mass corresponding to shrinkage limit
V_s = Volume of solids