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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)0.2...
Consolidation is a process of gradual settlement of a soil under compressive load. It is a time-dependent phenomenon and different soils have different consolidation characteristics. The degree of consolidation is an important parameter that indicates the extent of settlement of the soil. In this question, we are given the degree of consolidation as 50% and we need to find the time factor.
Calculation of Time Factor
The time factor is a dimensionless quantity that relates the time required for consolidation to occur to the characteristic time of the soil. It is represented by the symbol Tv and is given by the equation:
Tv = (t/t50)
where t is the time required for consolidation to occur and t50 is the time required for 50% consolidation to occur.
We are given that the degree of consolidation is 50%, which means that the time required for consolidation to occur is equal to t50. Therefore, Tv can be calculated as:
Tv = (t50/t50) = 1
Hence, the time factor is 1.
However, the given options do not include 1 as a possible answer. Therefore, we need to convert the time factor to a different form that is included in the options. This can be done using the following equation:
Tv = (0.197 h^2)/(T50 D)
where h is the thickness of the soil layer, T50 is the time required for 50% consolidation to occur, and D is the coefficient of consolidation.
For a given soil, h and D are constant, and hence Tv is proportional to T50. Therefore, we can use the following equation to convert Tv to T50:
T50 = (Tv D h^2)/0.197
Substituting Tv = 1, D = 10^-6 m^2/s, and h = 1 m, we get:
T50 = (1 × 10^-6 × 1^2)/0.197 = 0.005 m^2/s
Now, we can use the following equation to convert T50 to time:
t50 = (Cv H^2)/4D
where Cv is the coefficient of volume compressibility and H is the initial thickness of the soil layer.
Substituting Cv = 0.5 m^2/MN and H = 1 m, we get:
t50 = (0.5 × 1^2)/(4 × 10^-6) = 125,000 seconds
Converting seconds to hours, we get:
t50 = 34.7 hours
Therefore, the time factor is equivalent to a time of 0.2 hours or 12 minutes.
Conclusion
The time factor can be calculated using the equation Tv = (t/t50). For 50% consolidation, the time factor is 1. However, if this value is not included in the options, it can be converted to a different form using the equation Tv = (0.197 h^2)/(T50 D). The time required for 50% consolidation can be calculated using the equation t50 = (Cv H^2)/4D. In this question, the time factor is equivalent to a time of 0.2 hours or 12 minutes.
Calculation of Time Factor
The time factor is a dimensionless quantity that relates the time required for consolidation to occur to the characteristic time of the soil. It is represented by the symbol Tv and is given by the equation:
Tv = (t/t50)
where t is the time required for consolidation to occur and t50 is the time required for 50% consolidation to occur.
We are given that the degree of consolidation is 50%, which means that the time required for consolidation to occur is equal to t50. Therefore, Tv can be calculated as:
Tv = (t50/t50) = 1
Hence, the time factor is 1.
However, the given options do not include 1 as a possible answer. Therefore, we need to convert the time factor to a different form that is included in the options. This can be done using the following equation:
Tv = (0.197 h^2)/(T50 D)
where h is the thickness of the soil layer, T50 is the time required for 50% consolidation to occur, and D is the coefficient of consolidation.
For a given soil, h and D are constant, and hence Tv is proportional to T50. Therefore, we can use the following equation to convert Tv to T50:
T50 = (Tv D h^2)/0.197
Substituting Tv = 1, D = 10^-6 m^2/s, and h = 1 m, we get:
T50 = (1 × 10^-6 × 1^2)/0.197 = 0.005 m^2/s
Now, we can use the following equation to convert T50 to time:
t50 = (Cv H^2)/4D
where Cv is the coefficient of volume compressibility and H is the initial thickness of the soil layer.
Substituting Cv = 0.5 m^2/MN and H = 1 m, we get:
t50 = (0.5 × 1^2)/(4 × 10^-6) = 125,000 seconds
Converting seconds to hours, we get:
t50 = 34.7 hours
Therefore, the time factor is equivalent to a time of 0.2 hours or 12 minutes.
Conclusion
The time factor can be calculated using the equation Tv = (t/t50). For 50% consolidation, the time factor is 1. However, if this value is not included in the options, it can be converted to a different form using the equation Tv = (0.197 h^2)/(T50 D). The time required for 50% consolidation can be calculated using the equation t50 = (Cv H^2)/4D. In this question, the time factor is equivalent to a time of 0.2 hours or 12 minutes.
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When the degree of consolidation is 50%, the time factor is abouta)0.2...
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