1. A soil sample has a porosity of 40%. The specific gravity of solids is 2.70. Calculate (a) void ratio (b) dry density (c) unit weight if the soil is 50% saturated, and (d) unit weight if the soil is completely saturated
(a) Void ratio (e) can be calculated as:
e = Porosity / (1 - Porosity)
e = 0.40 / (1 - 0.40)
e = 0.40 / 0.60
e = 0.67
(b) Dry density can be calculated using the formula:
γd = (1 + e) * Gs * ρw / (1 + e * Gs)
Where:
γd = Dry density
Gs = Specific gravity of solids = 2.70
ρw = Density of water = 1000 kg/m^3
γd = (1 + 0.67) * 2.70 * 1000 / (1 + 0.67 * 2.70)
γd = 4.148 kg/m^3
(c) Unit weight if the soil is 50% saturated can be calculated as:
γ = γd + (1 - S) * ρw
Where:
S = Degree of saturation = 50% = 0.50
γ = 4.148 + (1 - 0.50) * 1000
γ = 4.148 + 500
γ = 4.648 kg/m^3
(d) Unit weight if the soil is completely saturated can be calculated as:
γs = Gs * ρw
γt = γd + γs
γt = 4.148 + 2.70 * 1000
γt = 4.148 + 2700
γt = 7.848 kg/m^3
Therefore, the calculated values are:
(a) Void ratio = 0.67
(b) Dry density = 4.148 kg/m^3
(c) Unit weight if 50% saturated = 4.648 kg/m^3
(d) Unit weight if completely saturated = 7.848 kg/m^3