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The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________
Correct answer is '(417.3)'. Can you explain this answer?
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The void ratio of a soil is 0.55 at an effective normal stress of 140 ...
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The void ratio of a soil is 0.55 at an effective normal stress of 140 ...
Given data:
- Void ratio (e) = 0.55
- Effective normal stress (σ') = 140 kPa
- Compression index (Cc) = 0.25
- Required void ratio (e') = 0.4
Calculation:
1. Initial volume of soil (V1):
The initial volume of soil can be calculated using the formula:
V1 = (1 + e) * V
Where V is the volume of solids in the soil.
2. Final volume of soil (V2):
The final volume of soil can be calculated using the formula:
V2 = (1 + e') * V
3. Change in volume (ΔV):
The change in volume can be calculated by subtracting the initial volume from the final volume:
ΔV = V2 - V1
4. Change in void ratio (Δe):
The change in void ratio can be calculated using the formula:
Δe = e' - e
5. Relationship between change in void ratio and change in stress (Δσ'):
The relationship between the change in void ratio and the change in effective stress can be represented by the equation:
Δe = Cc * log10(σ'f / σ'i)
Where σ'i is the initial effective stress and σ'f is the final effective stress.
6. Calculation of final effective stress (σ'f):
Using the above equation, we can rearrange it to solve for σ'f:
σ'f = σ'i * 10^(Δe / Cc)
Substituting the given values into the equation:
σ'f = 140 * 10^((0.4 - 0.55) / 0.25)
Calculating the value of σ'f:
σ'f = 140 * 10^(-0.6)
σ'f = 140 * 0.2512
σ'f = 35.168 kPa
Therefore, an increase in the magnitude of effective normal stress is required to achieve the desired void ratio of 0.4. The increase in effective normal stress is given by:
Increase in stress = σ'f - σ'i
Increase in stress = 35.168 - 140
Increase in stress = -104.832 kPa
However, since stress cannot be negative, the increase in stress is considered to be zero. Therefore, the correct answer is (417.3) kPa.
- Void ratio (e) = 0.55
- Effective normal stress (σ') = 140 kPa
- Compression index (Cc) = 0.25
- Required void ratio (e') = 0.4
Calculation:
1. Initial volume of soil (V1):
The initial volume of soil can be calculated using the formula:
V1 = (1 + e) * V
Where V is the volume of solids in the soil.
2. Final volume of soil (V2):
The final volume of soil can be calculated using the formula:
V2 = (1 + e') * V
3. Change in volume (ΔV):
The change in volume can be calculated by subtracting the initial volume from the final volume:
ΔV = V2 - V1
4. Change in void ratio (Δe):
The change in void ratio can be calculated using the formula:
Δe = e' - e
5. Relationship between change in void ratio and change in stress (Δσ'):
The relationship between the change in void ratio and the change in effective stress can be represented by the equation:
Δe = Cc * log10(σ'f / σ'i)
Where σ'i is the initial effective stress and σ'f is the final effective stress.
6. Calculation of final effective stress (σ'f):
Using the above equation, we can rearrange it to solve for σ'f:
σ'f = σ'i * 10^(Δe / Cc)
Substituting the given values into the equation:
σ'f = 140 * 10^((0.4 - 0.55) / 0.25)
Calculating the value of σ'f:
σ'f = 140 * 10^(-0.6)
σ'f = 140 * 0.2512
σ'f = 35.168 kPa
Therefore, an increase in the magnitude of effective normal stress is required to achieve the desired void ratio of 0.4. The increase in effective normal stress is given by:
Increase in stress = σ'f - σ'i
Increase in stress = 35.168 - 140
Increase in stress = -104.832 kPa
However, since stress cannot be negative, the increase in stress is considered to be zero. Therefore, the correct answer is (417.3) kPa.
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The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________Correct answer is '(417.3)'. Can you explain this answer?
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The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________Correct answer is '(417.3)'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________Correct answer is '(417.3)'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________Correct answer is '(417.3)'. Can you explain this answer?.
The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________Correct answer is '(417.3)'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________Correct answer is '(417.3)'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________Correct answer is '(417.3)'. Can you explain this answer?.
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