### 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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Concept explainers

Load and resistance factor design

Load and resistance factors design (LRFD), also known as Limit state design (LSD), refers to the design method used in building engineering. A boundary condition is a condition of a structure where it can no longer meet the relevant design requirements. The condition may refer to the load level or other actions on the structure, while the terms refer to the integrity of the structure, suitability for use, durability, or other design requirements. A structure designed for LRFD is limited to keeping track of all possible actions during its design time and is always ready for use, with the appropriate level of reliability in each boundary condition. LRFD-based construction codes clearly define the appropriate levels of reliability in their instructions.

Question

### 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/m²

If 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) = 26m

3. **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:

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