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A soil sample with void ratio of 0.45 is having water content of 10% and the specific gravity of soil solid is 2.7. The air content in the soil sample will be
- a)20%
- b)30%
- c)40%
- d)50%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A soil sample with void ratio of 0.45 is having water content of 10% a...
For a given soil sample,
S × e = w × G
where
S = degree of saturation
e = void ratio
w = water content
G = specific gravity of the soil solid
S = 0.6
Air content + Degree of saturation = 1
ac + S = 1
ac = 1 − S = 1 − 0.6 = 0.4
ac = 40%
S × e = w × G
where
S = degree of saturation
e = void ratio
w = water content
G = specific gravity of the soil solid
S = 0.6
Air content + Degree of saturation = 1
ac + S = 1
ac = 1 − S = 1 − 0.6 = 0.4
ac = 40%
Most Upvoted Answer
A soil sample with void ratio of 0.45 is having water content of 10% a...
The given problem requires us to determine the air content in a soil sample based on its void ratio, water content, and specific gravity of soil solid.
Given data:
Void ratio (e) = 0.45
Water content (w) = 10%
Specific gravity of soil solid (Gs) = 2.7
To solve this problem, we need to understand the concept of void ratio and its relation to the water and air content in the soil.
1. Understanding Void Ratio:
Void ratio (e) is defined as the ratio of the volume of voids to the volume of solids in a soil sample. It is a measure of the compactness or density of the soil.
Mathematically, void ratio (e) is given by the equation:
e = Vv / Vs
Where:
Vv = Volume of voids in the soil
Vs = Volume of solids in the soil
2. Relation between Void Ratio and Water Content:
In a soil sample, the voids can be occupied by either air or water. The water content (w) represents the ratio of the volume of water to the volume of solids in the soil.
Mathematically, water content (w) is given by the equation:
w = Vw / Vs
Where:
Vw = Volume of water in the soil
We can rearrange this equation to express the volume of water (Vw) in terms of the water content (w) and the volume of solids (Vs):
Vw = w * Vs
3. Relation between Void Ratio, Water Content, and Air Content:
The total volume of voids in the soil sample can be expressed as the sum of the volumes of air and water present in the soil.
Mathematically, the total volume of voids (Vv) is given by the equation:
Vv = Va + Vw
Where:
Va = Volume of air in the soil
We can rearrange this equation to express the volume of air (Va) in terms of the total volume of voids (Vv) and the volume of water (Vw):
Va = Vv - Vw
4. Determining the Air Content:
Now, let's substitute the given values into the equations and calculate the air content.
Given:
e = 0.45
w = 0.10 (10%)
Gs = 2.7
From equation (1):
e = Vv / Vs
Substituting the values:
0.45 = Vv / Vs
From equation (2):
w = Vw / Vs
Substituting the values:
0.10 = Vw / Vs
Rearranging equation (3):
Va = Vv - Vw
Substituting the values:
Va = Vv - (0.10 * Vs)
We know that the specific gravity (Gs) is defined as the ratio of the density of soil solids to the density of water. Mathematically, it is given by the equation:
Gs = ρs / ρw
Where:
ρs = Density of soil solids
ρw = Density of water
Let's assume the unit weight of water (γw) is 1 kN/m³. Therefore, ρw = γw / g = 1 / 9.81 = 0.1019 kN/m³.
The density of soil solids (ρs) can be calculated using the
Given data:
Void ratio (e) = 0.45
Water content (w) = 10%
Specific gravity of soil solid (Gs) = 2.7
To solve this problem, we need to understand the concept of void ratio and its relation to the water and air content in the soil.
1. Understanding Void Ratio:
Void ratio (e) is defined as the ratio of the volume of voids to the volume of solids in a soil sample. It is a measure of the compactness or density of the soil.
Mathematically, void ratio (e) is given by the equation:
e = Vv / Vs
Where:
Vv = Volume of voids in the soil
Vs = Volume of solids in the soil
2. Relation between Void Ratio and Water Content:
In a soil sample, the voids can be occupied by either air or water. The water content (w) represents the ratio of the volume of water to the volume of solids in the soil.
Mathematically, water content (w) is given by the equation:
w = Vw / Vs
Where:
Vw = Volume of water in the soil
We can rearrange this equation to express the volume of water (Vw) in terms of the water content (w) and the volume of solids (Vs):
Vw = w * Vs
3. Relation between Void Ratio, Water Content, and Air Content:
The total volume of voids in the soil sample can be expressed as the sum of the volumes of air and water present in the soil.
Mathematically, the total volume of voids (Vv) is given by the equation:
Vv = Va + Vw
Where:
Va = Volume of air in the soil
We can rearrange this equation to express the volume of air (Va) in terms of the total volume of voids (Vv) and the volume of water (Vw):
Va = Vv - Vw
4. Determining the Air Content:
Now, let's substitute the given values into the equations and calculate the air content.
Given:
e = 0.45
w = 0.10 (10%)
Gs = 2.7
From equation (1):
e = Vv / Vs
Substituting the values:
0.45 = Vv / Vs
From equation (2):
w = Vw / Vs
Substituting the values:
0.10 = Vw / Vs
Rearranging equation (3):
Va = Vv - Vw
Substituting the values:
Va = Vv - (0.10 * Vs)
We know that the specific gravity (Gs) is defined as the ratio of the density of soil solids to the density of water. Mathematically, it is given by the equation:
Gs = ρs / ρw
Where:
ρs = Density of soil solids
ρw = Density of water
Let's assume the unit weight of water (γw) is 1 kN/m³. Therefore, ρw = γw / g = 1 / 9.81 = 0.1019 kN/m³.
The density of soil solids (ρs) can be calculated using the
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A soil sample with void ratio of 0.45 is having water content of 10% and the specific gravity of soil solid is 2.7. The air content in the soil sample will bea)20%b)30%c)40%d)50%Correct answer is option 'C'. Can you explain this answer?
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A soil sample with void ratio of 0.45 is having water content of 10% and the specific gravity of soil solid is 2.7. The air content in the soil sample will bea)20%b)30%c)40%d)50%Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A soil sample with void ratio of 0.45 is having water content of 10% and the specific gravity of soil solid is 2.7. The air content in the soil sample will bea)20%b)30%c)40%d)50%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A soil sample with void ratio of 0.45 is having water content of 10% and the specific gravity of soil solid is 2.7. The air content in the soil sample will bea)20%b)30%c)40%d)50%Correct answer is option 'C'. Can you explain this answer?.
A soil sample with void ratio of 0.45 is having water content of 10% and the specific gravity of soil solid is 2.7. The air content in the soil sample will bea)20%b)30%c)40%d)50%Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A soil sample with void ratio of 0.45 is having water content of 10% and the specific gravity of soil solid is 2.7. The air content in the soil sample will bea)20%b)30%c)40%d)50%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A soil sample with void ratio of 0.45 is having water content of 10% and the specific gravity of soil solid is 2.7. The air content in the soil sample will bea)20%b)30%c)40%d)50%Correct answer is option 'C'. Can you explain this answer?.
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