Page 253 - Civil Engineering Formulas

SOIL AND EARTHWORK FORMULAS 187

sat (G e) 0 (1 w)G 0 S 100% (8.6)
1 e 1 e

G 0
dry S 0% (8.7)
(1 e)

(G 1) 0
b S 100% (8.8)
1 e
Unit weights are generally expressed in pound per cubic foot or gram per cubic
centimeter. Representative values of unit weights for a soil with a specific grav-
ity of 2.73 and a void ratio of 0.80 are
3
sat 122 lb/ft 1.96 g/cm 3 (8.9)
dry 95 lb/ft 3 1.52 g/cm 3 (8.10)

b 60 lb/ft 3 0.96 g/cm 3 (8.11)
The symbols used in the three preceding equations and in Fig. 8.1 are

G specific gravity of soil solids (specific gravity of quartz is 2.67; for
majority of soils specific gravity ranges between 2.65 and 2.85; organic
soils would have lower specific gravities)
3
3
unit weight of water, 62.4 lb/ft (1.0 g/cm )
0
e voids ratio, volume of voids in mass of soil divided by volume of solids
in same mass; also equal to n/(1 n), where n is porosity—volume of
voids in mass of soil divided by total volume of same mass
S degree of saturation, volume of water in mass of soil divided by volume
of voids in same mass
w water content, weight of water in mass of soil divided by weight of
solids in same mass; also equal to Se/G

Gas
V(voids) e = 1 + e V(water) Se = 1 + e Water W(water) Se γ 0 = 1 + e V) = γ f γ 0

V = 1 Gγ 0 Se + G 1 + e 1 + w Gγ 0 1 + e

V(solids) 1 = 1 + e Solids W(solids) 1 = 1 + e W(total) (for unit = =

Total volume (solids + water + gas) = 1
FIGURE 8.1 Relationship of weights and volumes in soil.