# The ratio of a given volume change, expressed as a percentage of dry volume to the corresponding change in water content, is known as:

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The ratio of a given volume change, expressed as a percentage of dry volume to the corresponding change in water content, is known as:
1. index ratio
2. volumetric ratio
3. linear ratio
4. shrinkage ratio

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Correct Answer - Option 4 : shrinkage ratio

Shrinkage ratio  (S.R.):

• It is defined as the ratio of volume change expressed as the percentage of dry volume to the corresponding change in water content above the shrinkage limit.

$S.R. = \frac{\frac{(V_o-V_d)}{V_d}×100}{w_o -w_s} =\frac{S_r}{w_o-w_s}= \frac{M_d}{\rho_wV_d}=\frac{γ_d}{γ_w} = G_m$         ...(1)

Here,

Vo - Initial volume of saturated sample at water content wo

Vd - Final volume of the soil sample at water content ws

Md - Mass of dry volume 'Vd' of the sample

γd, γw - Unit weight of dry volume of soil and water respectively.

Gm - Mass specific gravity of soil in its dry state.

Sr - Degree of shrinkage = $\frac{(V_o-V_d)}{V_d}×100$

Soil may be classified into four groups as follows based on the degree of shrinkage -

 Type of soil Degree of shrinkage, Sr (%) Good < 5 Medium Good 5 - 10 Poor 10 - 15 Very Poor > 15