Answer :
Final answer:
The answers to dry unit weight, void ratio, porosity, degree of saturation, volume occupied by water are respectively;
γ_d = 108.93 lb/ft³; e = 0.56; n = 0.36; S = 0.58; V_w = 0.021 ft³
Explanation:
Calculation of Volume and Weight of soil
We are given;
Moist weight; W = 12.2 lb
Volume of moist soil; V = 0.1 ft³
moisture content; w = 12% = 0.12
Specific gravity of soil solids; G_s = 2.72
A) Formula for dry unit weight is;
γ_d = γ/(1 + w)
where γ_w is moist unit weight as;
γ_w = W/V
γ_w = 122/0.1 = 122 lb/ft³
Thus;
γ_d = 122/(1 + 0.12)
γ_d = 108.93 lb/ft³
B) Formula for void ratio is;
e = [(G_s * γ_w)/γ_d] - 1
e = [(2.72 * 122)/108.93] - 1
e = 0.56
C) Formula for porosity is;
n = e/(1 + e)
n = 0.56/(1 + 0.56)
n = 0.36
D) Formula for degree of saturation is;
S = (w * G_s)/e
S = (0.12 * 2.72)/0.56
S = 0.58
E) Volume occupied by water is gotten from;
V_w = S*V_v
where;
V_v is volume of voids = nV
V_v = 0.36*0.1
V_v = 0.036 ft³
Thus;
V_w = 0.58 * 0.036
V_w = 0.021 ft³
complete question:
2. The moist weight of 0.1 ft3 of soil is 12.2 lb. If the moisture content is 12% and the specific gravity of soil solids is 2.72, determine the following: a) dry unit weight, b) void ratio, c) porosity, d) degree of saturation, and e) volume occupied by water.
