Introduction
In this question, we are given the shrinkage limit and specific gravity of soil solids and we need to find out the porosity of soil at the shrinkage limit.

Formula
Porosity is the ratio of volume of voids to the total volume of soil. Mathematically, it can be expressed as:

Porosity = Volume of Voids / Total Volume

Solution
Given, shrinkage limit = 10% and specific gravity of soil solids = 2.7

Shrinkage limit means the maximum amount of water that can be removed from the soil without causing any further volume change. At the shrinkage limit, the volume of voids is minimum.

We know that,

Specific Gravity of Soil Solids = Mass of Soil Solids / Volume of Soil Solids

Therefore, Volume of Soil Solids = Mass of Soil Solids / Specific Gravity of Soil Solids

At the shrinkage limit, the volume of voids is minimum. Hence, the total volume of soil at the shrinkage limit can be calculated as:

Total Volume = Volume of Soil Solids / (1 - Shrinkage Limit)

Substituting the given values, we get:

Total Volume = (Mass of Soil Solids / Specific Gravity of Soil Solids) / (1 - 0.1)

Total Volume = (Mass of Soil Solids / Specific Gravity of Soil Solids) / 0.9

Total Volume = (10 / 2.7) / 0.9

Total Volume = 3.7037 m3

Now, we need to find the volume of voids at the shrinkage limit. At the shrinkage limit, the volume of voids is equal to the volume of water that has been removed from the soil. Therefore, we can calculate the volume of voids as:

Volume of Voids = Volume of Water / (1 + Water Content)

At the shrinkage limit, the water content is 10% and the initial water content (i.e. when the soil is fully saturated) is 100%. Therefore, the volume of water that needs to be removed to reach the shrinkage limit is:

Volume of Water = Total Volume x (Initial Water Content - Shrinkage Limit)

Substituting the given values, we get:

Volume of Water = 3.7037 x (1 - 0.1)

Volume of Water = 3.3333 m3

Therefore, the volume of voids at the shrinkage limit is:

Volume of Voids = 3.3333 / (1 + 0.1)

Volume of Voids = 3.0303 m3

Now, we can calculate the porosity at the shrinkage limit as:

Porosity = Volume of Voids / Total Volume

Porosity = 3.0303 / 3.7037

Porosity = 0.8182 or 81.82%

Conclusion
The porosity of soil at the shrinkage limit is 81.82%.