π Reading time: 1 minute

The important parameters related to shrinkage limit in soil engineering are shrinkage index, shrinkage limit, volumetric shrinkage, and linear shrinkage. Each parameter is briefly explained in this article.

Contents:

## 1. Shrinkage Index ( *I*_{s} )

_{s}

The numerical difference between the liquid limit ( *w _{l}* ) and the shrinkage limit (

*w*) is called as shrinkage Index. It is given by:

_{s}**I**_{s}** = w**_{l}** -w**_{s}

Also Read: Determination of Shrinkage Limit

Also Read: Determination of Liquid Limit

## 2. Shrinkage Ratio (SR)

The shrinkage ratio can be defined as the ratio of given volume change to the corresponding change in water content of the soil sample. The given volume change is expressed in terms of percentage of the dry volume.

The shrinkage ratio can be given by the formula:

Where, V_{1} is the volume of the soil mass at a water
content βw1β, βV_{2}β is the volume of the soil mass at a water content
of βw2β. βV_{d}β is the volume of the dry soil mass.

If w2 is the water content corresponding to the shrinkage limit,
then V_{2} becomes V_{d}, then shrinkage ratio is given by:

The shrinkage limit, shrinkage ratio and the mass gravity of the soil at the dry state (Gm) can be related as:

## 3. Volumetric Shrinkage (VS)

Volumetric shrinkage is the representation of the change in volume that is expressed in percentage of the dry volume when the water content of the given soil mass is reduced from an initial value to a shrinkage limit. Hence,

**VS = [(V**_{1}** -V**_{d}**)/V**_{d}**] x 100**

From the relation of shrinkage ratio,

[(V_{1} β V_{d})/V_{d}] x 100 =
SR(w1-w2)

Therefore,

**VS = SR (w1-w2)**

## 4. Linear Shrinkage (LS)

When the water content in the soil is reduced to shrinkage limit, there is variation in the length. Linear shrinkage is defined as the change in length divided by the initial length. LS is represented in percentage. It is reported as a whole number.

The test conducted to determine linear shrinkage of soil is expensive and it is employed mostly on dispersive soil types.