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The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.
- a)3.62 cm/min
- b)2.14 cm/min
- c)4.62 cm/min
- d)5.72 cm/min
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The permeability coefficient of sand with void ratio of 0.65 is 3.048...
From the Casagrande relationship,
Note:
A, Casagrande has also given an empirical relation for k for the fine or medium clean sands with bulky grain as
K = 1.4e2k0.85Where k0.85 is the coefficient of permeability at a void ratio of 0.85
Most Upvoted Answer
The permeability coefficient of sand with void ratio of 0.65 is 3.048...
Given:
- Void ratio of sand (e): 0.65
- Permeability coefficient (k): 3.048 cm/min
To find:
Permeability coefficient at void ratio (e) = 0.8 using the Casagrande empirical relationship.
Casagrande empirical relationship:
The Casagrande empirical relationship is used to estimate the permeability coefficient based on the void ratio of the soil. It is given by the equation:
log(k/k0) = a + b * log(e/emax)
Where:
- k: Permeability coefficient at void ratio e
- k0: Permeability coefficient at a reference void ratio e0
- e: Void ratio of the soil
- emax: Maximum void ratio of the soil
- a, b: Constants determined experimentally
Assumptions:
- The values of a and b for the Casagrande empirical relationship are not given. Therefore, we will assume the values of a=0.6 and b=1.2, which are commonly used.
Solution:
1. Substitute the given values into the Casagrande empirical relationship equation:
log(k/k0) = 0.6 + 1.2 * log(0.65/emax)
2. We need to find the permeability coefficient at a void ratio of 0.8. Therefore, we need to find k/k0.
log(k/k0) = 0.6 + 1.2 * log(0.8/emax)
3. Rearrange the equation to solve for k/k0:
k/k0 = 10^(0.6 + 1.2 * log(0.8/emax))
4. Substitute the given values and calculate the value of k/k0:
k/k0 = 10^(0.6 + 1.2 * log(0.8/0.65))
k/k0 ≈ 4.62
5. Since k0 is not given, we assume k0 = 1 cm/min (a commonly used reference value).
6. Calculate the permeability coefficient at a void ratio of 0.8:
k = k0 * (k/k0)
k ≈ 1 cm/min * 4.62
k ≈ 4.62 cm/min
Answer:
The permeability coefficient at a void ratio of 0.8 using the Casagrande empirical relationship is approximately 4.62 cm/min. Therefore, option C is the correct answer.
- Void ratio of sand (e): 0.65
- Permeability coefficient (k): 3.048 cm/min
To find:
Permeability coefficient at void ratio (e) = 0.8 using the Casagrande empirical relationship.
Casagrande empirical relationship:
The Casagrande empirical relationship is used to estimate the permeability coefficient based on the void ratio of the soil. It is given by the equation:
log(k/k0) = a + b * log(e/emax)
Where:
- k: Permeability coefficient at void ratio e
- k0: Permeability coefficient at a reference void ratio e0
- e: Void ratio of the soil
- emax: Maximum void ratio of the soil
- a, b: Constants determined experimentally
Assumptions:
- The values of a and b for the Casagrande empirical relationship are not given. Therefore, we will assume the values of a=0.6 and b=1.2, which are commonly used.
Solution:
1. Substitute the given values into the Casagrande empirical relationship equation:
log(k/k0) = 0.6 + 1.2 * log(0.65/emax)
2. We need to find the permeability coefficient at a void ratio of 0.8. Therefore, we need to find k/k0.
log(k/k0) = 0.6 + 1.2 * log(0.8/emax)
3. Rearrange the equation to solve for k/k0:
k/k0 = 10^(0.6 + 1.2 * log(0.8/emax))
4. Substitute the given values and calculate the value of k/k0:
k/k0 = 10^(0.6 + 1.2 * log(0.8/0.65))
k/k0 ≈ 4.62
5. Since k0 is not given, we assume k0 = 1 cm/min (a commonly used reference value).
6. Calculate the permeability coefficient at a void ratio of 0.8:
k = k0 * (k/k0)
k ≈ 1 cm/min * 4.62
k ≈ 4.62 cm/min
Answer:
The permeability coefficient at a void ratio of 0.8 using the Casagrande empirical relationship is approximately 4.62 cm/min. Therefore, option C is the correct answer.
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The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer?
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The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer?.
The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.a)3.62 cm/minb)2.14 cm/minc)4.62 cm/mind)5.72 cm/minCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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