Calculation of Consolidation Settlement

Given:

Effective stress increment (Δσ') = 1 kg/cm²

Initial void ratio (e₀) = 0.4

Thickness of soil stratum (H) = 7m

Change in void ratio due to effective stress increment (Δe) = 0.1

Solution:

Step 1: Calculation of coefficient of volume compressibility (C_v)

C_v = Δe / Δσ' = 0.1 / 1 = 0.1 cm²/kg

Step 2: Calculation of coefficient of consolidation (C_c)

Assuming the soil to be normally consolidated, we can use Terzaghi's one-dimensional consolidation theory to calculate C_c.

C_c = (t₅₀) (C_v)² / H²

Where t₅₀ is the time required for 50% consolidation.

Assuming t₅₀ = 1 year, we get

C_c = (1 year) (0.1 cm²/kg)² / (7m)² = 0.000163 cm²/s

Step 3: Calculation of consolidation settlement (s)

s = (Δσ') (H²) / (C_v) (t₅₀)

s = (1 kg/cm²) (7m)² / (0.1 cm²/kg) (1 year)

s = 490 cm = 4.9 m

Explanation:

Consolidation settlement is the settlement that occurs in a soil layer due to the expulsion of water from its pores as a result of the application of load. The settlement occurs due to the compression and rearrangement of soil particles as the water is expelled from the voids. The coefficient of volume compressibility (C_v) is a measure of the soil's ability to compress under load. The coefficient of consolidation (C_c) is a measure of the rate at which the soil consolidates under load. The consolidation settlement is calculated using the change in effective stress, soil thickness, and the coefficients of volume compressibility and consolidation. The time required for consolidation to occur is also a factor in the calculation of C_c.