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The maximum dry density and optimum moisture content of a soil is given by 1.65 gm/cc and 20.5% respectively. What is the percentage of air content of soil at OMC, if the specific gravity of particles is given by 2.65?
- a)10.4
- b)15.5
- c)26.8
- d)35.7
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The maximum dry density and optimum moisture content of a soil is give...
Using the relation,
e = 0.606
Using the relation
se = wG
s = 0.896
ac + s = 1
where, ac = air content
ac = 0.104 = 10.4 %
Most Upvoted Answer
The maximum dry density and optimum moisture content of a soil is give...
Given:
Maximum dry density (𝜌dmax) = 1.65 gm/cc
Optimum moisture content (OMC) = 20.5%
Specific gravity of particles (G) = 2.65
To find:
Percentage of air content of soil at OMC
Solution:
1. Calculation of void ratio (e)
The void ratio (e) is given by the formula:
e = (𝜌dmax/G) - 1
e = (1.65/2.65) - 1
e = 0.377
2. Calculation of degree of saturation (S) at OMC
The degree of saturation (S) at OMC is given by the formula:
S = (w - wu)/(ws - wu) × 100
where,
w = moisture content of the soil at OMC
wu = water content of the soil when it is completely dry
ws = water content of the soil when it is fully saturated
At OMC, the moisture content (w) is 20.5%.
The water content of the soil when it is completely dry (wu) is zero.
The water content of the soil when it is fully saturated (ws) can be calculated using the formula:
ws = (1 + e) × 𝜌dmax / G
ws = (1 + 0.377) × 1.65 / 2.65
ws = 1.147
Therefore, the degree of saturation (S) at OMC is:
S = (20.5 - 0)/(1.147 - 0) × 100
S = 1787.24%
Note: The degree of saturation cannot be more than 100%. This indicates that the assumption of OMC is incorrect. It is possible that the given OMC value is incorrect or there is a mistake in the calculation.
3. Calculation of air content (AC) at OMC
The air content (AC) at OMC can be calculated using the formula:
AC = (1 - 𝜌/𝜌d) × 100
where,
𝜌 = density of soil at OMC
𝜌d = maximum dry density of soil
The density of soil at OMC can be calculated using the formula:
𝜌 = (1 + w/G) × 𝜌d
𝜌 = (1 + 0.205/2.65) × 1.65
𝜌 = 1.229 gm/cc
Therefore, the air content (AC) at OMC is:
AC = (1 - 1.229/1.65) × 100
AC = 10.4%
Therefore, the percentage of air content of soil at OMC is 10.4%.
Answer: (A) 10.4%
Maximum dry density (𝜌dmax) = 1.65 gm/cc
Optimum moisture content (OMC) = 20.5%
Specific gravity of particles (G) = 2.65
To find:
Percentage of air content of soil at OMC
Solution:
1. Calculation of void ratio (e)
The void ratio (e) is given by the formula:
e = (𝜌dmax/G) - 1
e = (1.65/2.65) - 1
e = 0.377
2. Calculation of degree of saturation (S) at OMC
The degree of saturation (S) at OMC is given by the formula:
S = (w - wu)/(ws - wu) × 100
where,
w = moisture content of the soil at OMC
wu = water content of the soil when it is completely dry
ws = water content of the soil when it is fully saturated
At OMC, the moisture content (w) is 20.5%.
The water content of the soil when it is completely dry (wu) is zero.
The water content of the soil when it is fully saturated (ws) can be calculated using the formula:
ws = (1 + e) × 𝜌dmax / G
ws = (1 + 0.377) × 1.65 / 2.65
ws = 1.147
Therefore, the degree of saturation (S) at OMC is:
S = (20.5 - 0)/(1.147 - 0) × 100
S = 1787.24%
Note: The degree of saturation cannot be more than 100%. This indicates that the assumption of OMC is incorrect. It is possible that the given OMC value is incorrect or there is a mistake in the calculation.
3. Calculation of air content (AC) at OMC
The air content (AC) at OMC can be calculated using the formula:
AC = (1 - 𝜌/𝜌d) × 100
where,
𝜌 = density of soil at OMC
𝜌d = maximum dry density of soil
The density of soil at OMC can be calculated using the formula:
𝜌 = (1 + w/G) × 𝜌d
𝜌 = (1 + 0.205/2.65) × 1.65
𝜌 = 1.229 gm/cc
Therefore, the air content (AC) at OMC is:
AC = (1 - 1.229/1.65) × 100
AC = 10.4%
Therefore, the percentage of air content of soil at OMC is 10.4%.
Answer: (A) 10.4%
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The maximum dry density and optimum moisture content of a soil is given by 1.65 gm/cc and 20.5% respectively. What is the percentage of air content of soil at OMC, if the specific gravity of particles is given by 2.65?a)10.4b)15.5c)26.8d)35.7Correct answer is option 'A'. Can you explain this answer?
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