A soil sample with specific gravity of solids 3 has a mass specific gravity of 2. Assuming the soil to be perfectly dry, determine the void ratio.a)1.0b)1.5c)0.5d)0.8Correct answer is option 'C'. Can you explain this answer?

Question

Answer

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.

Answer

To determine the void ratio of a soil sample, we need to understand the concept of specific gravity and mass specific gravity.

1. Specific Gravity of Solids:
The specific gravity of solids is defined as the ratio of the density of solids to the density of water at a specified temperature. In other words, it is a measure of how much denser the solids are compared to water.

2. Mass Specific Gravity:
Mass specific gravity is the ratio of the mass of solids to the mass of an equal volume of water at a specified temperature. It is also a measure of how much denser the solids are compared to water.

Given data:
Specific gravity of solids (G_s) = 3
Mass specific gravity (G) = 2

We can use the following relationship to determine the void ratio (e) of the soil sample:

G = (1 - e) / (1 + e)

Let's substitute the given values into the equation and solve for e:

2 = (1 - e) / (1 + e)

Cross-multiplying, we get:

2(1 + e) = 1 - e

Expanding, we have:

2 + 2e = 1 - e

Rearranging the terms, we get:

3e = -1

Dividing by 3, we have:

e = -1/3

Since the void ratio cannot be negative, we discard the negative sign and take the absolute value. Therefore, the void ratio of the soil sample is:

e = 1/3

Now, let's compare this answer with the given options:

a) 1.0
b) 1.5
c) 0.5
d) 0.8

The correct answer is option 'c' (0.5), which matches our calculated void ratio of 1/3.

Therefore, the void ratio of the soil sample is 0.5.

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