Question

Derive an expression for bulk density of a partially saturated soil in terms of specific gravity of particles (Gs), the void ratio (e), the degree of saturation (Sr), and the density of water.

Answer 1

$\gamma = \frac{Total \space weight}{Total \space volume}= \frac{W}{V}=\frac{W_s+W_w}{V_s+V_w}\\ S=\frac{V_w}{V_v}\\ \gamma=\frac{e_1V_s \rho _w +V_v \rho _w S}{V_s+V_v}\\ \frac{V_v}{V_s}=e\\ \gamma=\frac{e_1+Se}{1+e} \rho_w$