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When the degree of consolidation is 50% , the time factor is about
- a)0.2
- b)0.5
- c)1.0
- d)2.0
Correct answer is option 'A'. Can you explain this answer?
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When the degree of consolidation is 50% , the time factor is abouta)0....
The degree of consolidation (U) is a measure of how much consolidation has occurred in a soil layer. It is defined as the ratio of the excess pore water pressure dissipated to the initial excess pore water pressure. The degree of consolidation ranges from 0 to 100%, with 0% indicating no consolidation and 100% indicating complete consolidation.
The time factor (Tv) is a dimensionless quantity that represents the time required for a given degree of consolidation to occur. It is defined as the ratio of the time elapsed to the time required for complete consolidation. The time factor is used to estimate the time required for consolidation to occur in a soil layer.
The relationship between the degree of consolidation and the time factor is given by the following equation:
U = 1 - (1 - Tv)^2
where U is the degree of consolidation and Tv is the time factor.
Given that the degree of consolidation is 50% (U = 0.5), we can rearrange the equation to solve for the time factor:
0.5 = 1 - (1 - Tv)^2
Simplifying the equation, we get:
(1 - Tv)^2 = 0.5
Taking the square root of both sides, we have:
1 - Tv = √0.5
Solving for Tv, we get:
Tv = 1 - √0.5
Calculating the value, we find:
Tv ≈ 0.2929
Since the time factor is approximately 0.2929, the closest option is 0.2 (option A).
The time factor (Tv) is a dimensionless quantity that represents the time required for a given degree of consolidation to occur. It is defined as the ratio of the time elapsed to the time required for complete consolidation. The time factor is used to estimate the time required for consolidation to occur in a soil layer.
The relationship between the degree of consolidation and the time factor is given by the following equation:
U = 1 - (1 - Tv)^2
where U is the degree of consolidation and Tv is the time factor.
Given that the degree of consolidation is 50% (U = 0.5), we can rearrange the equation to solve for the time factor:
0.5 = 1 - (1 - Tv)^2
Simplifying the equation, we get:
(1 - Tv)^2 = 0.5
Taking the square root of both sides, we have:
1 - Tv = √0.5
Solving for Tv, we get:
Tv = 1 - √0.5
Calculating the value, we find:
Tv ≈ 0.2929
Since the time factor is approximately 0.2929, the closest option is 0.2 (option A).
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When the degree of consolidation is 50% , the time factor is abouta)0.2b)0.5c)1.0d)2.0Correct answer is option 'A'. Can you explain this answer?
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