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.
γ=Total weightTotal volume=WV=Ws+WwVs+VwS=VwVvγ=e1Vsρw+VvρwSVs+VvVvVs=eγ=e1+Se1+eρw\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_wγ=Total volumeTotal weight=VW=Vs+VwWs+WwS=VvVwγ=Vs+Vve1Vsρw+VvρwSVsVv=eγ=1+ee1+Seρw
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