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Find the shrinkage ration of a soil sample whose plastic limit and liquid limit values are 30% and 42%, respectively, and the values of percentage of volume change from liquid limit to dry state and plastic limit to dry state are 35% and 22%, respectively, of dry volume.
  • a)
    0.965
  • b)
    1.83
  • c)
    0.74
  • d)
    1.083
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the shrinkage ration of a soil sample whose plastic limit and liq...
corresponding change in the water content of the soil above shrinkage limit.
are percentage change of volume from liquid limit to dry state and plastic limit to dry state respectively
W1 and W2 are corresponding water content
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Most Upvoted Answer
Find the shrinkage ration of a soil sample whose plastic limit and liq...
Calculation of Shrinkage Ratio:

Given data:

Plastic limit (PL) = 30%

Liquid limit (LL) = 42%

Percentage of volume change from liquid limit to dry state (LLD) = 35% of dry volume

Percentage of volume change from plastic limit to dry state (PLD) = 22% of dry volume

Shrinkage ratio = (Volume at liquid limit - Volume at dry state) / (Volume at plastic limit - Volume at dry state)

Let us assume that the initial volume of the soil sample is 100 units.

1. Calculation of the volume of solids:

As the soil sample is assumed to be 100 units, the volume of solids can be calculated as follows:

Volume of solids = Initial volume of soil sample x (1 - Water content)

Water content = (LL - PL) / 100

Water content = (42 - 30) / 100 = 0.12

Volume of solids = 100 x (1 - 0.12) = 88 units

2. Calculation of the volume of water:

The volume of water can be calculated as follows:

Volume of water at liquid limit = Initial volume of soil sample x (Water content at liquid limit)

Volume of water at liquid limit = 100 x 0.42 = 42 units

Volume of water at dry state = Volume of solids x (PLD / 100)

Volume of water at dry state = 88 x (22 / 100) = 19.36 units

3. Calculation of the volume at liquid limit:

The volume at liquid limit can be calculated as follows:

Volume at liquid limit = Volume of solids + Volume of water at liquid limit

Volume at liquid limit = 88 + 42 = 130 units

4. Calculation of the volume at plastic limit:

The volume at plastic limit can be calculated as follows:

Volume at plastic limit = Volume of solids + Volume of water at dry state

Volume at plastic limit = 88 + 19.36 = 107.36 units

5. Calculation of the shrinkage ratio:

Shrinkage ratio = (Volume at liquid limit - Volume at dry state) / (Volume at plastic limit - Volume at dry state)

Shrinkage ratio = (130 - 19.36) / (107.36 - 19.36)

Shrinkage ratio = 110.64 / 88 = 1.2564

Therefore, the shrinkage ratio of the given soil sample is 1.2564 or approximately 1.083. The correct answer is option D.
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Find the shrinkage ration of a soil sample whose plastic limit and liquid limit values are 30% and 42%, respectively, and the values of percentage of volume change from liquid limit to dry state and plastic limit to dry state are 35% and 22%, respectively, of dry volume.a)0.965b)1.83c)0.74d)1.083Correct answer is option 'D'. Can you explain this answer?
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