A sample of wet silty clay soil has a mass of 126 kg. The following data were obtained from laboratory tests on the sample: Wet density, \rho_{t}=2.1 g / cm ^{3}, G=2.7, water content, w = 15%.
Determine (i) dry density, \rho_{d}, (ii) porosity, (iii) void ratio, and (iv) degree of saturation.
Mass of sample M = 126 kg.
Volume V=\frac{126}{2.1 \times 10^{3}}=0.06 m ^{3}
Now, M_{s}+M_{w}=M, \quad \text { or } M_{s}+w M_{s}=M_{s}(1+w)=M
Therefore, M_{s}=\frac{M}{1+w}=\frac{126}{1.15}=109.57 kg ; \quad M_{w}=M-M_{s}=16.43 kg
Now, V_{w}=\frac{M_{w}}{\rho_{w}}=\frac{16.43}{1000}=0.01643 m ^{3};
V_{s}=\frac{M_{s}}{G_{s} \rho_{w}}=\frac{109.57}{2.7 \times 1000}=0.04058 m ^{3};
V_{v}=V-V_{s}=0.06000-0.04058=0.01942 m ^{3}.
(i) Dry density, \rho_{d}=\frac{M_{s}}{V}=\frac{109.57}{0.06}=1826.2 kg / m ^{3}
(ii) Porosity, n=\frac{V_{v}}{V} \times 100=\frac{0.01942 \times 100}{0.06}=32.37 \%
(iii) Void ratio, e=\frac{V_{v}}{V_{s}}=\frac{0.01942}{0.04058}=0.4786
(i v) Degree of saturation, S=\frac{V_{w}}{V_{v}} \times 100=\frac{0.01643}{0.01942} \times 100=84.6 \%
