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A stratum of sand and a stratum of clay have the same thickness of 3 m. The coefficient of compressibility of sand is 1/5th of coefficient of compressibility of clay and the permeability -of sand is 1 0,000 times that of the clay. As suming the same void ratio, the ratio of the consolidation time for the clay to that of the sand is
  • a)
    20,000
  • b)
    30,000
  • c)
    40,000
  • d)
    50,000
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A stratum of sand and a stratum of clay have the same thickness of 3 m...
coefficient of consolidation = 
using 1 for sand and 2 forclay
As the thickness of both layer is same, so for same degree of consolidation:
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Most Upvoted Answer
A stratum of sand and a stratum of clay have the same thickness of 3 m...
Given information:
- Thickness of sand and clay layers = 3m
- Coefficient of compressibility of sand = 1/5th of coefficient of compressibility of clay
- Permeability of sand = 1/10,000 times that of clay
- Same void ratio for both layers

To find:
Ratio of consolidation time for clay to sand

Solution:
1. Consolidation time formula:
t = CvH²/4k

Where,
t = consolidation time (in sec)
Cv = coefficient of volume compressibility (in m²/kg)
H = thickness of soil layer (in m)
k = coefficient of permeability (in m/sec)

2. Given that both sand and clay layers have the same thickness (H = 3m) and void ratio, we can assume that their initial volume is also the same. Therefore, we can consider their coefficient of volume compressibility as the only differentiating factor for consolidation time.

3. Let's assume the coefficient of compressibility of clay as Cv1 and that of sand as Cv2.
Cv1 = coefficient of compressibility of clay
Cv2 = 1/5th of Cv1 (given)

4. Let's calculate the consolidation time for the clay layer:
t1 = Cv1H²/4k

5. Now, let's calculate the consolidation time for the sand layer:
t2 = Cv2H²/4k
= (1/5 Cv1)H²/4k
= (1/5) (Cv1H²/4k)
= (1/5) t1

6. Therefore, the ratio of consolidation time for the clay layer to sand layer is:
t1/t2 = t1/(1/5 t1) = 5

Answer:
Therefore, the ratio of consolidation time for the clay layer to sand layer is 5, which is option D.
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A stratum of sand and a stratum of clay have the same thickness of 3 m. The coefficient of compressibility of sand is 1/5th of coefficient of compressibility of clay and the permeability -of sand is 1 0,000 times that of the clay. As suming the samevoid ratio, the ratio of the consolidation time for the clay to thatof the sand isa)20,000b)30,000c)40,000d)50,000Correct answer is option 'D'. Can you explain this answer?
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A stratum of sand and a stratum of clay have the same thickness of 3 m. The coefficient of compressibility of sand is 1/5th of coefficient of compressibility of clay and the permeability -of sand is 1 0,000 times that of the clay. As suming the samevoid ratio, the ratio of the consolidation time for the clay to thatof the sand isa)20,000b)30,000c)40,000d)50,000Correct answer is option 'D'. 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 A stratum of sand and a stratum of clay have the same thickness of 3 m. The coefficient of compressibility of sand is 1/5th of coefficient of compressibility of clay and the permeability -of sand is 1 0,000 times that of the clay. As suming the samevoid ratio, the ratio of the consolidation time for the clay to thatof the sand isa)20,000b)30,000c)40,000d)50,000Correct answer is option 'D'. 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 A stratum of sand and a stratum of clay have the same thickness of 3 m. The coefficient of compressibility of sand is 1/5th of coefficient of compressibility of clay and the permeability -of sand is 1 0,000 times that of the clay. As suming the samevoid ratio, the ratio of the consolidation time for the clay to thatof the sand isa)20,000b)30,000c)40,000d)50,000Correct answer is option 'D'. Can you explain this answer?.
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