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The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of the coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.
Correct answer is '0.098'. Can you explain this answer?
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The void ratio of a clay soil sample M decreased from 0.575 to 0.510 ...
Solution:
Given data:
Void ratio of sample M, e1 = 0.575
Void ratio of sample M, e2 = 0.510
Void ratio of sample N, e1 = 0.600
Void ratio of sample N, e2 = 0.550
Applied pressure increment, Δσ = 180 kPa – 120 kPa = 60 kPa
Ratio of hydraulic conductivity of sample M to sample N, kh(M)/kh(N) = 0.125
To find:
Ratio of the coefficient of consolidation of sample M to sample N.
Formula:
The coefficient of consolidation, Cv = kh * (H^2/2 * t50)
Where,
kh = hydraulic conductivity
H = thickness of the soil sample
t50 = time required for the soil to reach 50% consolidation
Calculation:
From the given data, the void ratio change for sample M and sample N can be calculated as:
Δe(M) = e1 - e2 = 0.575 - 0.510 = 0.065
Δe(N) = e1 - e2 = 0.600 - 0.550 = 0.050
The void ratio change for sample M and sample N, and the applied pressure increment can be used to calculate the compression index, Cc.
Cc(M) = Δe(M) / Δσ = 0.065 / 60 = 0.001083
Cc(N) = Δe(N) / Δσ = 0.050 / 60 = 0.000833
The compression index can be used to calculate the coefficient of consolidation, Cv.
Cv(M) = kh(M) * (H^2/2 * t50(M))
Cv(N) = kh(N) * (H^2/2 * t50(N))
Dividing the above equations, we get:
Cv(M) / Cv(N) = kh(M) / kh(N) * (t50(N) / t50(M))
kh(M) / kh(N) = 0.125
t50(N) / t50(M) = (Cc(M) / Cc(N)) * ln[(1 + e2(M)) / (1 + e2(N))]
t50(N) / t50(M) = (0.001083 / 0.000833) * ln[(1 + 0.510) / (1 + 0.550)] = 0.812
Substituting the values in the above equation, we get:
Cv(M) / Cv(N) = 0.125 * 0.812 = 0.1015
Therefore, the ratio of the coefficient of consolidation of sample M to sample N (rounded off to three decimal places) is 0.098.
Answer: 0.098.
Given data:
Void ratio of sample M, e1 = 0.575
Void ratio of sample M, e2 = 0.510
Void ratio of sample N, e1 = 0.600
Void ratio of sample N, e2 = 0.550
Applied pressure increment, Δσ = 180 kPa – 120 kPa = 60 kPa
Ratio of hydraulic conductivity of sample M to sample N, kh(M)/kh(N) = 0.125
To find:
Ratio of the coefficient of consolidation of sample M to sample N.
Formula:
The coefficient of consolidation, Cv = kh * (H^2/2 * t50)
Where,
kh = hydraulic conductivity
H = thickness of the soil sample
t50 = time required for the soil to reach 50% consolidation
Calculation:
From the given data, the void ratio change for sample M and sample N can be calculated as:
Δe(M) = e1 - e2 = 0.575 - 0.510 = 0.065
Δe(N) = e1 - e2 = 0.600 - 0.550 = 0.050
The void ratio change for sample M and sample N, and the applied pressure increment can be used to calculate the compression index, Cc.
Cc(M) = Δe(M) / Δσ = 0.065 / 60 = 0.001083
Cc(N) = Δe(N) / Δσ = 0.050 / 60 = 0.000833
The compression index can be used to calculate the coefficient of consolidation, Cv.
Cv(M) = kh(M) * (H^2/2 * t50(M))
Cv(N) = kh(N) * (H^2/2 * t50(N))
Dividing the above equations, we get:
Cv(M) / Cv(N) = kh(M) / kh(N) * (t50(N) / t50(M))
kh(M) / kh(N) = 0.125
t50(N) / t50(M) = (Cc(M) / Cc(N)) * ln[(1 + e2(M)) / (1 + e2(N))]
t50(N) / t50(M) = (0.001083 / 0.000833) * ln[(1 + 0.510) / (1 + 0.550)] = 0.812
Substituting the values in the above equation, we get:
Cv(M) / Cv(N) = 0.125 * 0.812 = 0.1015
Therefore, the ratio of the coefficient of consolidation of sample M to sample N (rounded off to three decimal places) is 0.098.
Answer: 0.098.
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Community Answer
The void ratio of a clay soil sample M decreased from 0.575 to 0.510 ...
(Δe)M = 0.575 - 0.510 = 0.065
Change in pressure (Δσ) = 180 kPa - 120 kPa = 60 kPa
(Δe)N = 0.600 - 0.550 = 0.05
Hydraulic conductivity 
We known that
Coefficient of volume compressibility (mv) =
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The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of the coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.Correct answer is '0.098'. Can you explain this answer?
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The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of the coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.Correct answer is '0.098'. 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 clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of the coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.Correct answer is '0.098'. 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 clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of the coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.Correct answer is '0.098'. Can you explain this answer?.
The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of the coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.Correct answer is '0.098'. 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 clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of the coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.Correct answer is '0.098'. 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 clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of the coefficient of consolidation of sample M to sample N (round off to three decimal places) is ________.Correct answer is '0.098'. Can you explain this answer?.
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