Formula & Calculator
Bearing Capacity of Soil
Ultimate bearing capacity of shallow foundations.
Interpretation
Bearing capacity of soil: q_u = cN_c + qN_q + 0.5γBN_γ, where c is cohesion, q is surcharge, γ is unit weight, B is footing width, and N factors. Example: clay c=20 kPa, N_c=5.7 → q_u = 114 kPa.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| q_u | Ultimate bearing capacity | Pa |
| c | Cohesion | Pa |
| N_c | Bearing capacity factor (cohesion) | |
| q | Overburden pressure | Pa |
| N_q | Bearing capacity factor (surcharge) | |
| γ | Soil unit weight | N/m³ |
| B | Foundation width | m |
| N_γ | Bearing capacity factor (weight) |
What it means
The bearing capacity of soil is the maximum average contact pressure between a foundation and the soil that will not cause shear failure in the soil. Terzaghi’s bearing capacity equation is widely used: q_u = c N_c + q N_q + 0.5 γ B N_γ, where c is the soil cohesion, q is the effective surcharge at the footing base (γ·D_f), γ is the unit weight of soil, B is the footing width, and N_c, N_q, N_γ are dimensionless bearing capacity factors that depend on the soil’s angle of internal friction (φ). For purely cohesive soils (φ=0), N_c = 5.7, N_q = 1, N_γ = 0, giving q_u = c N_c. This equation is fundamental for designing shallow foundations (footings, raft foundations) to ensure they have a factor of safety against bearing failure. Variations exist for different footing shapes (strip, square, circular) and for inclined loads. The ultimate bearing capacity is reduced by a factor of safety (typically 3) to obtain the allowable bearing pressure. This concept is critical in geotechnical engineering for building foundations, retaining walls, and embankments.
Worked example
Bearing Capacity of Soil – Two Examples
Real‑World| Parameter | Value |
|---|---|
| c | 20 kPa |
| Nc | 5.14 |
| q = γ·Df | 18×1 = 18 kPa |
| Nq | 1.0 |
| γ | 18 kN/m³ |
| B | 2 m |
| Nγ | 0 |
| Parameter | Value |
|---|---|
| c | 0 |
| Nc | 18 |
| q = γ·Df | 17×1.5 = 25.5 kPa |
| Nq | 12 |
| γ | 17 kN/m³ |
| B | 1.5 m |
| Nγ | 8 |
Common mistakes
- Bearing capacity factors: N_c, N_q, N_γ depend on the soil friction angle (φ) – they are not constants. Use proper tables or equations (e.g., Terzaghi, Meyerhof).
- Effective surcharge q: This is the overburden pressure at the base level, often γ×D_f. Do not ignore it.
- Unit weight γ: Use the effective unit weight (submerged if water table is present).
- Footing width B: For rectangular footings, use the smaller dimension; for strip footings, use B=1 m per metre length.
- Shape and depth factors: The basic formula assumes a strip footing; for square/rectangular footings, apply shape factors.
Applications
The bearing capacity of soil is the maximum pressure that the ground can support without shear failure. The Terzaghi bearing capacity equation, q_u = cN_c + qN_q + 0.5γBN_γ, accounts for cohesion (c), surcharge (q), and soil weight (γ), with bearing capacity factors N_c, N_q, N_γ depending on the soil friction angle. This formula is fundamental in geotechnical engineering for designing shallow foundations, spread footings, and raft foundations. Engineers use it to determine the safe bearing pressure, to size footings, and to assess the risk of settlement and instability. The equation is applied in building construction, bridge piers, and even in temporary works like shoring and cofferdams. By understanding bearing capacity, engineers can ensure that foundations are safe, economical, and capable of supporting the applied loads without excessive deformation or failure.
- Design of shallow foundations (footings, mats)
- Analysis of soil bearing capacity for building and bridge foundations
- Assessment of settlement and tilt risks
- Design of temporary structures (shoring, cofferdams)
- Geotechnical investigation and site evaluation
Frequently Asked Questions
The ultimate bearing capacity is the maximum pressure the soil can support before failure. Terzaghi's formula for a strip footing is q_u = cN_c + qN_q + 0.5γBN_γ, where c is cohesion, q is surcharge at foundation level, γ is soil unit weight, B is footing width, and N_c, N_q, N_γ are bearing capacity factors.
- cN_c – contribution from soil cohesion.
- qN_q – contribution from surcharge (overburden) at foundation level.
- 0.5γBN_γ – contribution from the weight of the soil within the failure zone.
The factors are functions of φ (soil friction angle). For example, N_q = tan²(45°+φ/2)·e^(π·tanφ), N_c = (N_q – 1)·cotφ (for φ>0), and N_γ is often from empirical correlations (e.g., N_γ = 2(N_q+1)·tanφ). These are tabulated in soil mechanics textbooks.
- Using the wrong unit weight – use effective unit weight if the water table is above the footing base.
- Not adjusting for footing shape – Terzaghi's formula is for strip footings; for square or circular footings, use shape factors.
- Ignoring depth factors – if the footing is embedded, depth factors increase capacity.
- Using the ultimate capacity without a factor of safety – design uses allowable = q_u / FoS (typically 2.5–3.0).
Water reduces the effective unit weight (γ' = γ_sat – γ_w) and can reduce shear strength if the soil is submerged. If water is above the foundation, use γ' in the third term and reduce q if the surcharge is partly from water. The effect can significantly lower capacity.
- General shear – well‑defined failure surface; occurs in dense/stiff soils.
- Local shear – less defined, occurs in loose/soft soils; use reduced shear parameters (c', φ') in the formula.
- Punching shear – vertical failure; occurs in very loose soils or deep foundations.
For eccentric loads, use effective width B' = B – 2e (and effective length L' = L – 2e_L) in the formula. For inclined loads, reduce the bearing capacity factors using correction factors (e.g., from Meyerhof or Hansen). These adjustments are crucial for realistic foundation design.
The allowable bearing pressure is q_allow = q_u / FoS. Typical FoS ranges from 2.5 to 4.0, depending on the type of structure, soil variability, and consequences of failure. A lower FoS is used when load and soil parameters are well known.
- Assumes a strip footing (infinite length).
- Assumes homogeneous soil.
- Does not account for footing shape, depth, or load inclination (but modified versions do).
- Assumes general shear failure; for local shear, the parameters must be reduced.
These are obtained from site investigation:
- c, φ from triaxial or direct shear tests.
- γ from density measurements (field or lab).
- For cohesionless soils, φ is often correlated with SPT N‑values.
- Use conservative (lower) values for design.