## Consistency Atterberg Limits

- Liquid Limit (WL)
- Plastic Limit (Wp)
- Shrinkage Limit (Ws)

** Shrinkage Limits(Ws) **

- It is defined as the maximum water content at which reduction in the water content of soil does not lead to a reduction in the volume of soil, as below (Ws) replacement of water by air in equal volume takes place while reducing the water content.
- It may also be defined as the minimum water content at which soil is completely saturated.
- At shrinkage limit, soil passes semi-solid state of consistency to soil state of consistency & visa-versa.

which soil has more shrinkage limits, and Volume change (Compressibility) is less.

**Note: Ws limit governs the compressibility of soil, the higher the shrinkage limit lower is compressibility (volume change).**

** Determination of Shrinkage Limit **

- Consider a sample of soil having water content more than shrinkage limit, let its mass & volume be M1,V1.
- The soil is subjected to drying as a result of which its volume decreases. At a particular stage of drying, when its water content is equal its shrinkage limit, it mass & volume be M2,V2 on complete drying let its mass of volume be Md &Vd.

we don’t know about stage.2 that water content is equal to shrinkage limit or not . But we know the volume of soil at shrinkage limit is equal to the volume of soil at dry state. so stage 2 is only calculation purpose.

V2=Vd

V2≠Vs

Vd≠Vs

Md=Ms

Mass of water in stage 1= M1-Md.

Loss of water from stage 1 to 2= (V1-V2)\(ρ_w\)=(V1-Vd)\(ρ_w\).

Mass of water in stage 2= Mass of water in stage 1 – Loss of water from stage 1 to 2.

Mass of water in stage 2=(M1-Md) – (V1-Vd)\(ρ_w\).

Shrinkage limit Ws\(=\frac{\text { Mass of water in stage 2 }}{\text { Mass of solids}}\).

\(W_s=\frac{(M_1-Md)-(V1-Vd)ρ_w}{Md}\).

\(W_s=\frac{(M_1-Md)}{Md}-\frac{(V1-Vd)}{Md}\).

\(W_s=w_1-\frac{(V1-Vd)}{Md}\).