### Example Problem: Calculation of Consolidation Settlement**Problem Statement:**A 3m x 3m square footing is constructed at a depth of 2m in a 26m deep clay layer with the following soil properties:- Unit weight (γ) = 16.5 kN/m³- Soil Type: Normally Consolidated Clay- Initial void ratio (e₀) = 0.65- Compression index (Cc) = 0.25- Settlement factor (βs) = 0.5- Modulus of elasticity (Es) = 6.0 MN/m²If there is a 1000 kN structural load on the footing, calculate the consolidation settlement of the footing.**Solution Guide:**1. **Determine the Stage of Settlement:** - Since the clay is normally consolidated, we focus on the primary consolidation settlement.2. **Identify Parameters and Conversion Factors:** - Load on footing (P) = 1000 kN - Area of footing (A) = $3 m \times 3 m = 9 m²$ - Depth of the clay layer (H) = 26m3. **Calculate the Increase in Stress:** \[ \Delta \sigma = \frac{P}{A} = \frac{1000 \, kN}{9 \, m²} = 111.1 \, kN/m² (\text{additional stress on the soil layer due to the load}) \]4. **Compute the Initial Effective Stress ($\sigma'_0$):** \[ \sigma'_0 = \gamma \times (depth - depth of footing) = 16.5 \, kN/m³ \times (26 \, m - 2 \, m) = 16.5 \, kN/m³ \times 24 \, m = 396 \, kN/m² \]5. **Determine the Final Effective Stress ($\sigma'_f$):** \[ \sigma'_f = \sigma'_0 + \Delta \sigma = 396 \, kN/m² + 111.1 \, kN/m² = 507.1 \, kN/m² \]6. **Calculate the Settlement (S):** - Using the formula for consolidation settlement:

1. A 3m x 3m square footing is constructed at a depth of 2m in a 26m deep clay layer with following soil properties: I =16.5kN/m', Normally Consolidated Clay, e,= 0.65, Cc = 0.25,s=0.5 and Es= 6.0 MN/m2. If there is a 1000KN structural load on the footing, calculate the consolidation

1. A 3m x 3m square footing is constructed at a depth of 2m in a 26m deep clay layer with following soil properties: I =16.5kN/m', Normally Consolidated Clay, e,= 0.65, Cc = 0.25,s=0.5 and Es= 6.0 MN/m2. If there is a 1000KN structural load on the footing, calculate the consolidation

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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