Bearing Capacity (soil)
The bearing capacity of soil is the maximum load per unit area that a soil can support without undergoing shear failure, excessive settlement, or instability below a foundation. The ultimate bearing capacity (q_u) is the stress at which the soil fails in shear, while the safe bearing capacity (q_s) is q_u divided by a factor of safety, and the allowable bearing capacity also accounts for permissible settlement. Terzaghi's bearing capacity equation, later extended by Meyerhof, Hansen, and Vesic, expresses q_u as a function of soil cohesion, surcharge, foundation width, and soil friction angle, forming the basis of IS 6403 in India.
Key Formula
Ultimate bearing capacity = c·Nc + q·Nq + 0.5·γ·B·Nγ (Terzaghi's general shear failure equation)
LaTeX: q_u = cN_c + qN_q + \tfrac{1}{2}\gamma B N_\gamma
| Symbol | Meaning | Unit |
|---|---|---|
| q_u | Ultimate bearing capacity | kPa |
| c | Cohesion of soil | kPa |
| N_c, N_q, N_\gamma | Terzaghi's dimensionless bearing capacity factors | — |
| q | Surcharge at foundation level (= γ·D_f) | kPa |
| \gamma | Unit weight of soil | kN/m³ |
| B | Width of the foundation | m |
Worked Example
Problem
A strip footing of width B = 1.5 m is placed at a depth D_f = 1 m in a sandy soil with c = 0 kPa, φ = 30°, γ = 18 kN/m³. Terzaghi's factors for φ = 30°: Nc = 37.2, Nq = 22.5, Nγ = 19.7. Calculate the ultimate and safe bearing capacity (FOS = 3).
Solution
Step 1: Surcharge q = γ × D_f = 18 × 1 = 18 kPa. Step 2: Apply Terzaghi for strip (no shape factors): q_u = cNc + qNq + 0.5γBNγ. Step 3: q_u = 0×37.2 + 18×22.5 + 0.5×18×1.5×19.7 = 0 + 405 + 266.0 = 671 kPa. Step 4: Safe bearing capacity q_s = q_u / FOS = 671 / 3 ≈ 224 kPa.
Answer
Ultimate bearing capacity q_u ≈ 671 kPa; Safe bearing capacity q_s ≈ 224 kPa
Indicative Safe Bearing Capacities for Common Soil/Rock Types (IS 1904)
| Soil / Rock Type | Safe Bearing Capacity (kPa) | Condition | Foundation Type |
|---|---|---|---|
| Hard rock (granite, basalt) | 3240–6480 | Unweathered | Any shallow foundation |
| Laminated rock | 880–1760 | Not fissured | Spread footing |
| Gravel, sand + gravel | 245–490 | Dense, compact | Spread footing, raft |
| Coarse/medium sand | 245–490 | Dense (SPT N > 30) | Spread footing |
| Fine/silty sand | 100–245 | Compact (SPT N 10–30) | Raft or pile foundation |
| Soft clay / black cotton soil | 50–100 | Low plasticity | Raft or pile foundation |
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Related Terms
Soil Mechanics
Soil mechanics is the branch of geotechnical engineering that applies the principles of mechanics and hydraulics to the engineering behaviour of soils, studying their strength, deformation, permeability, and consolidation under various loading conditions. Founded by Karl Terzaghi in the early 20th century, it provides the theoretical and experimental framework for analysing slope stability, bearing capacity, settlement, earth pressure on retaining walls, and seepage through embankments. In India, soil mechanics principles underpin all foundation design codes including IS 1904, IS 6403, and IS 8009.
Foundation (civil engineering)
A foundation is the lowest part of a structure that transfers all superstructure loads safely to the underlying soil or rock, ensuring stability against settlement, sliding, and overturning. Foundations are broadly classified as shallow foundations (spread footings, combined footings, raft/mat foundations) when the depth of embedment is small relative to width, and deep foundations (piles, caissons, well foundations) when loads must be transferred to deeper, stronger strata. The design of foundations requires knowledge of both the structural loads imposed from above and the geotechnical properties of the soil below, making it an interdisciplinary activity bridging structural and geotechnical engineering.
Factor of Safety
The factor of safety (FOS) is a dimensionless ratio of the ultimate capacity (strength) of a structural element to the actual load (or stress) it is designed to carry, providing a quantitative measure of the margin between safe performance and failure. A factor of safety greater than 1 indicates that the structure can withstand more than the design load, accounting for uncertainties in material properties, load estimation, construction quality, and analytical model assumptions. In structural and geotechnical engineering, typical FOS values range from 1.5 to 3.0 depending on the consequence of failure and the degree of uncertainty involved.
The word "bearing" derives from Old English "beran" (to carry, support), meaning the capacity of the soil to carry or support loads. "Capacity" comes from Latin "capacitas" (ability to hold), from "capax" (able to hold), from "capere" (to take, hold). The compound term was standardised in geotechnical literature through Terzaghi's foundational work in the 1940s and 1950s.