Soil Bearing Capacity Calculations
The soil bearing capacity is the maximum load per unit area that the soil can safely support without failure or excessive settlement. Accurate calculation is critical for safe foundation design and structural stability.
1. Types of Bearing Capacity
- Ultimate Bearing Capacity (qu): Maximum load soil can bear before shear failure.
- Allowable Bearing Capacity (qa): Ultimate capacity divided by factor of safety.
- Net Bearing Capacity: Ultimate bearing capacity minus soil’s self-weight pressure.
2. Factors Influencing Bearing Capacity
- Soil type and properties (cohesion, friction angle)
- Depth and width of foundation
- Water table location
- Shape and inclination of footing and load
- Load eccentricity and soil stratification
3. Terzaghi’s Bearing Capacity Equation
One of the most widely used for shallow foundations:
qu = c Nc + q Nq + 0.5 γ B Nγ
- c = soil cohesion
- q = effective overburden pressure at foundation depth
- γ = soil unit weight
- B = foundation width
- Nc, Nq, Nγ = bearing capacity factors depending on soil friction angle (φ)
4. Meyerhof’s Bearing Capacity Equation
Extends Terzaghi’s by including shape, depth, and load inclination factors:
qu = c Nc sc dc ic + q Nq sq dq iq + 0.5 γ B Nγ sγ dγ iγ
- sc, sq, sγ = shape factors
- dc, dq, dγ = depth factors
- ic, iq, iγ = load inclination factors
5. Hansen’s Bearing Capacity Equation
Further refines Meyerhof’s by incorporating base inclination and soil weight influence.
6. Sample Calculation (Terzaghi’s Method)
Given:
- Cohesion, c = 25 kPa
- Unit weight, γ = 18 kN/m³
- Foundation width, B = 2 m
- Depth of foundation, Df = 1.5 m
- Soil friction angle, φ = 30°
Calculate factors:
- Nc = 30.14, Nq = 18.4, Nγ = 22.4 (values from tables)
- q = γ × Df = 18 × 1.5 = 27 kPa
Calculate ultimate bearing capacity:
qu = (25 × 30.14) + (27 × 18.4) + 0.5 × 18 × 2 × 22.4 = 753.5 + 496.8 + 403.2 = 1653.5 kPa
Allowable bearing capacity with factor of safety 3:
qa = qu / 3 = 551.2 kPa
7. Design Considerations
- Check settlement limits and differential settlement
- Consider effects of groundwater and soil consolidation
- Account for eccentricity and load distribution
- Use conservative values and verify with in-situ tests
8. Summary of Methods
| Method | Description | Advantages | Limitations |
|---|---|---|---|
| Terzaghi | Simplest, widely used for shallow foundations | Easy application, suitable for cohesive and cohesionless soils | Does not consider shape or load inclination |
| Meyerhof | Includes shape, depth, and load factors for refined results | More accurate for real conditions | Requires more parameters, empirical in nature |
| Hansen | Extends Meyerhof with base inclination and soil weight factors | Better for inclined footings and layered soils | Complex calculations |
Conclusion
Soil bearing capacity calculations are fundamental for safe foundation design. Selecting appropriate methods based on site conditions and foundation type ensures structures remain stable and perform satisfactorily throughout their design life.
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