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A soil sample has a porosity of 40 percent, its void ratio is
- a)0.06
- b)0.28
- c)0.40
- d)0.66
Correct answer is option 'D'. Can you explain this answer?
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Porosity and Void Ratio in Soil Mechanics
Definition:
- Porosity: Porosity is defined as the ratio of the volume of voids (empty spaces) to the total volume of the soil sample. It is expressed as a percentage.
- Void Ratio: Void ratio is defined as the ratio of the volume of voids to the volume of solids in a soil sample. It is a dimensionless quantity.
Given:
- Porosity = 40% = 0.40
To Find:
The void ratio of the soil sample.
Solution:
The relationship between porosity (n) and void ratio (e) can be expressed using the following formula:
n = e / (1 + e)
Given that porosity (n) is 0.40, we can substitute this value in the equation:
0.40 = e / (1 + e)
Multiplying both sides by (1 + e):
0.40(1 + e) = e
Expanding the equation:
0.40 + 0.40e = e
Subtracting 0.40e from both sides:
0.40 = e - 0.40e
Combining like terms:
0.40 = 0.60e
Dividing both sides by 0.60:
0.40 / 0.60 = e
0.6667 = e
Therefore, the void ratio (e) of the soil sample is approximately 0.6667, which is equivalent to 0.66 (rounded to two decimal places).
Conclusion:
The correct option for the void ratio of the soil sample is option 'D' (0.66).
Definition:
- Porosity: Porosity is defined as the ratio of the volume of voids (empty spaces) to the total volume of the soil sample. It is expressed as a percentage.
- Void Ratio: Void ratio is defined as the ratio of the volume of voids to the volume of solids in a soil sample. It is a dimensionless quantity.
Given:
- Porosity = 40% = 0.40
To Find:
The void ratio of the soil sample.
Solution:
The relationship between porosity (n) and void ratio (e) can be expressed using the following formula:
n = e / (1 + e)
Given that porosity (n) is 0.40, we can substitute this value in the equation:
0.40 = e / (1 + e)
Multiplying both sides by (1 + e):
0.40(1 + e) = e
Expanding the equation:
0.40 + 0.40e = e
Subtracting 0.40e from both sides:
0.40 = e - 0.40e
Combining like terms:
0.40 = 0.60e
Dividing both sides by 0.60:
0.40 / 0.60 = e
0.6667 = e
Therefore, the void ratio (e) of the soil sample is approximately 0.6667, which is equivalent to 0.66 (rounded to two decimal places).
Conclusion:
The correct option for the void ratio of the soil sample is option 'D' (0.66).
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A soil sample has a porosity of 40 percent, its void ratio isa)0.06b)0.28c)0.40d)0.66Correct answer is option 'D'. Can you explain this answer?
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A soil sample has a porosity of 40 percent, its void ratio isa)0.06b)0.28c)0.40d)0.66Correct answer is option 'D'. 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 has a porosity of 40 percent, its void ratio isa)0.06b)0.28c)0.40d)0.66Correct answer is option 'D'. 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 has a porosity of 40 percent, its void ratio isa)0.06b)0.28c)0.40d)0.66Correct answer is option 'D'. Can you explain this answer?.
A soil sample has a porosity of 40 percent, its void ratio isa)0.06b)0.28c)0.40d)0.66Correct answer is option 'D'. 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 has a porosity of 40 percent, its void ratio isa)0.06b)0.28c)0.40d)0.66Correct answer is option 'D'. 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 has a porosity of 40 percent, its void ratio isa)0.06b)0.28c)0.40d)0.66Correct answer is option 'D'. Can you explain this answer?.
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