Table of Contents
1. Introduction to Bearing Capacity
Bearing capacity is the maximum pressure that soil can support from a foundation without shear failure or excessive settlement. Two fundamental concepts govern foundation design: ultimate bearing capacity (qu), the pressure causing shear failure in the soil, and allowable bearing capacity (qa), the maximum safe pressure considering a factor of safety against failure and settlement limits.
The choice of bearing capacity theory depends on soil type, foundation geometry, and loading conditions. Terzaghi's 1943 theory forms the foundation, with subsequent refinements by Meyerhof (1963), Hansen (1970), and Vesic (1973) adding depth, shape, inclination, and base factors for more general applications.
Bearing capacity depends on soil shear strength (c, phi), unit weight (gamma), foundation depth (Df), width (B), and water table position. The Soil Bearing Capacity Calculator implements all major theories for rapid comparison.
2. Terzaghi's Bearing Capacity Theory
Karl Terzaghi's 1943 bearing capacity equation is the most widely used method for shallow foundation design. The general form for a strip footing is:
Where Nc, Nq, and N gamma are bearing capacity factors that depend on the soil friction angle phi. For strip footings, Terzaghi assumed a general shear failure mechanism with three zones: an elastic wedge directly under the footing, a radial shear zone, and a mixed shear zone. For square footings: qu = 1.3cNc + gamma Df Nq + 0.4 gamma B N gamma. For circular footings: qu = 1.3cNc + gamma Df Nq + 0.3 gamma B N gamma.
Terzaghi's bearing capacity factors: Nq = a^2 / (2 cos^2(45 + phi/2)) where a = e^(0.75pi - phi/2)tan(phi). Nc = (Nq - 1)cot(phi). N gamma = (tan(phi)/2) * ((Kp gamma / cos^2(phi)) - 1). For phi = 30 deg: Nc = 37.2, Nq = 22.5, N gamma = 19.7. For phi = 35 deg: Nc = 57.8, Nq = 41.4, N gamma = 42.4.
Terzaghi's theory assumes homogeneous soil, horizontal ground, and vertical centric loading. It does not include depth or inclination factors, limiting applicability for embedded or inclined-loaded foundations.
3. Meyerhof's General Solution
Meyerhof (1963) extended Terzaghi's work by including depth, shape, and inclination factors. The general equation is:
Meyerhof's failure surface uses a logarithmic spiral extending above the footing base, accounting for shearing resistance above foundation level. Depth factors (dc, dq, d gamma) increase capacity with depth, shape factors (sc, sq, s gamma) handle rectangular/square geometries, and inclination factors (ic, iq, i gamma) reduce capacity for inclined loads.
Meyerhof N gamma factors: N gamma = (Nq - 1)tan(1.4phi). At phi = 30 deg: Nc = 30.1, Nq = 18.4, N gamma = 15.7. These differ from Terzaghi due to the different failure mechanism assumption.
4. Hansen and Vesic Modifications
Hansen (1970) added base factors (for inclined base) and ground factors (for sloping ground). The Hansen equation is the most comprehensive and is recommended for general foundation design. Key additions: base tilt factors bc, bq, b gamma and ground slope factors gc, gq, g gamma, all equal to 1.0 for footings on horizontal ground with horizontal base.
Vesic (1973) modified N gamma and shape factors based on extensive model tests. Vesic's N gamma is widely accepted: N gamma = 2(Nq + 1)tan(phi). For phi = 30 deg: N gamma = 2(18.4 + 1)tan(30) = 22.4. Vesic's shape factors are used in Eurocode 7 and many national codes.
For practice, Hansen's method with Vesic's N gamma is recommended. The Soil Bearing Capacity Calculator allows selecting among all four methods for comparison.
5. Field Testing — SPT, CPT, PLT
The Standard Penetration Test (SPT) is the most common in-situ test for bearing capacity. SPT N-value (blows per 300 mm) correlates with phi and bearing capacity. For granular soils, Meyerhof: phi = 27.1 + 0.3N - 0.00054N^2 (for phi between 28 and 45 deg). For cohesive soils, qu = N/16 (kPa) for N less than 8.
| SPT N-value | Relative Density | Phi (deg) | SBC (kPa) |
|---|---|---|---|
| 0 to 4 | Very Loose | less than 29 | less than 50 |
| 4 to 10 | Loose | 29 to 30 | 50 to 150 |
| 10 to 30 | Medium Dense | 30 to 36 | 150 to 300 |
| 30 to 50 | Dense | 36 to 41 | 300 to 500 |
| greater than 50 | Very Dense | greater than 41 | greater than 500 |
The Cone Penetration Test (CPT) provides continuous soil resistance profiles. Cone resistance qc correlates with bearing capacity using qc/N ratios (4 to 6 for sands). The Plate Load Test (PLT) directly measures bearing capacity and settlement by loading a steel plate (300-750 mm diameter) and recording load-settlement behavior. PLT is the most reliable but most expensive method.
Field test results require correction for overburden pressure, water table, and procedure variations. The Bearing Capacity Calculator incorporates standard correction factors from ASTM and IS codes.
6. Design Values and Settlement Criteria
Allowable bearing capacity is the smaller of: (a) ultimate bearing capacity divided by factor of safety (typically 2.5 to 3.0), and (b) bearing pressure corresponding to allowable settlement (typically 25 mm for isolated footings, 50 mm for rafts). Settlement governs for most large foundations on sand.
Net bearing capacity = qu - gamma Df (pressure in excess of overburden). Net allowable bearing capacity is used for footing sizing: A = P / qnet,allowable. This accounts for the soil already being stressed by overburden at foundation level.
Presumptive bearing capacity values from building codes (IS 1904, IBC) provide conservative starting values: soft clay 50-100 kPa, stiff clay 150-300 kPa, loose sand 100-200 kPa, dense sand 300-500 kPa, hard rock greater than 2000 kPa. Always verify with field testing for final design. The Footing Size Calculator uses bearing capacity to compute required dimensions.
7. Worked Example
Compute Bearing Capacity for a Square Footing
Given: Square footing 2.0 m x 2.0 m. Depth Df = 1.5 m. Soil: silty sand with c = 5 kPa, phi = 32 deg, gamma = 18 kN/m3. Water table at 3.0 m depth. Factor of safety = 3.0.
Terzaghi method: For phi = 32 deg: Nc = 44.0, Nq = 28.5, N gamma = 26.0. Shape: square (sc = 1.3, s gamma = 0.4). qu = 1.3(5)(44.0) + 18(1.5)(28.5) + 0.4(18)(2.0)(26.0) = 286 + 770 + 374 = 1430 kPa. qa = 1430 / 3.0 = 477 kPa.
Meyerhof method: For phi = 32 deg: Nc = 35.5, Nq = 23.2, N gamma = 22.0. sc = 1.20, sq = 1.10, dc = 1.27, dq = 1.14. qu = 5(35.5)(1.20)(1.27) + 18(1.5)(23.2)(1.10)(1.14) + 0.5(18)(2.0)(22.0)(1.10)(1.14) = 271 + 785 + 496 = 1552 kPa. qa = 1552 / 3.0 = 517 kPa.
SPT check: If SPT N = 18 at foundation level, typical bearing capacity for medium dense sand = 150-300 kPa. The Terzaghi value of 477 kPa may be unconservative if settlement governs. Check settlement for 477 kPa loading. Use the Soil Bearing Capacity Calculator for detailed comparison.
Common Mistakes in Bearing Capacity Analysis
Ignoring water table effects: When the water table rises above the failure zone, effective unit weight reduces by approximately 50%, substantially reducing bearing capacity. Always check the highest anticipated water table level.
Confusing net and gross bearing capacity: Gross bearing capacity includes overburden stress, while net bearing capacity subtracts gamma Df. Footing sizing should be based on net allowable bearing capacity.
Using uncorrected SPT N-values: Raw N-values must be corrected for overburden (CN), hammer efficiency (CE), rod length (CR), and sampler type (CS). Use corrected N60 for correlations.
Best Practices
- Compute bearing capacity using at least two independent methods (e.g., Terzaghi and Meyerhof) for cross-verification.
- Check both shear failure and settlement criteria—settlement usually governs for large footings on sand.
- Use a minimum factor of safety of 2.5 for shear failure; use 3.0 when soil parameters are estimated.
- Consider the effect of adjacent footings—bearing capacity superposition can reduce individual capacity.
- Always engage a geotechnical engineer for bearing capacity determination on major projects.
8. Frequently Asked Questions
What is the difference between safe and ultimate bearing capacity?
Ultimate bearing capacity (qu) is the pressure causing shear failure. Safe (allowable) bearing capacity (qa) is qu / FOS or the pressure at allowable settlement, whichever is smaller.
What factor of safety should be used?
Minimum FOS of 2.5 for shear failure. Use 3.0 when soil parameters come from correlations or for critical structures. Eurocode 7 uses partial safety factors on loads and soil parameters instead.
How do I convert SPT N-value to bearing capacity?
For sands: qa = 12N (kPa) for B up to 1.2 m, qa = 8N (kPa) for B over 2.0 m. For clays: qu = N/16 (kPa) or perform unconfined compression tests.
How is plate load test corrected for footing size?
For sands: qf = qp (Bf / Bp). For clays: qf = qp (no size correction). Bf is footing width, Bp is plate width, qp is PLT bearing pressure at design settlement.
What is the effect of water table on bearing capacity?
If water table is within the failure zone (depth B below footing base), reduce gamma in the third term to effective unit weight. If above foundation level, also reduce the surcharge term. Reduction can be 30-50%.
How is eccentric loading handled?
Use effective area method: B' = B - 2e, L' = L - 2e. Compute bearing capacity using effective B' and L'. Also check overturning stability.
How to handle layered soils?
For soft over stiff, use weighted average properties within the failure zone (depth about 1.5B). For stiff over soft clay, check punching shear into the underlying layer using Hanna and Meyerhof method.
Which governs: bearing capacity or settlement?
For sands, settlement typically governs. For clays, bearing capacity often governs. Always check both and use the more conservative.
What is the difference between net and gross bearing capacity?
Gross ultimate is total pressure at foundation base causing failure. Net ultimate = gross - gamma Df. Footing sizing uses net values because overburden exists before construction.
What are presumptive bearing capacity values?
Conservative values from codes: soft clay 50 kPa, stiff clay 200 kPa, loose sand 100 kPa, dense sand 300 kPa, hard rock 2000+ kPa. Preliminary design only—verify with testing.
Related Calculators
References & Standards
- Terzaghi, K. Theoretical Soil Mechanics. Wiley, 1943.
- Meyerhof, G.G. "Some Recent Research on the Bearing Capacity of Foundations." Canadian Geotechnical Journal, 1963.
- Hansen, J.B. "A Revised and Extended Formula for Bearing Capacity." Danish Geotechnical Institute, 1970.
- Vesic, A.S. "Analysis of Ultimate Loads of Shallow Foundations." ASCE, 1973.
- IS 6403:1981. Bearing Capacity of Shallow Foundations. BIS, 1981.
- EN 1997-1:2004. Eurocode 7: Geotechnical Design. CEN, 2004.
- Civil Engineering Handbook — Geotechnical chapter.
- Engineering Formula Library — Bearing capacity formulas.
- Engineering Standards Reference — ACI 318, Eurocode 7, IS 6403.
- Engineering Glossary — Geotechnical and foundation terms.