The void ratio of a given soil A is twice that of another soil B, while the effective size of Particles of soil A is one-third of that of soil B. The ratio of height of capillary rise of water in soil A to that B will be 

Concept:

The capillarity rise in soil is calculated using empirical equation proposed by Terzaghi:

\({\rm{h}} = \frac{{\rm{C}}}{{{\rm{e}}{{\rm{D}}_{10}}}}\)

Where

 C is constant with value ranges from 0.1 to 0.5 Sq cm.

e is the void ratio.

D₁₀ is the effective grain size in cm.

Calculation:

Given

e_A = 2 e_B

(D₁₀)_A = 1/3 (D₁₀)_B

Now

\(\frac{{{h_A}}}{{{h_B}\;}} = \frac{{{{\left( {e{D_{10}}} \right)}_B}}}{{{{\left( {e{D_{10}}} \right)}_A}}}\)

Or

\(\frac{{{h_A}}}{{{h_B}}} = \frac{1}{2}\; \times \frac{3}{1}\)

\(\frac{{{h_A}}}{{{h_B}\;}} = 1.5\)