Bearing Capacity of Soils: Terzaghi's Theory, IS 6403 & Safe Bearing Capacity

Bearing capacity is the maximum load per unit area that a soil can support without shear failure. It is the fundamental output of any foundation design process. Every building, bridge, dam, and retaining wall begins with the question: what is the safe bearing capacity of this soil? This guide covers the theoretical framework, IS 6403:1981 provisions, and practical application.

Types of Bearing Capacity

Types of Shear Failure

• General shear failure: Dense sand, stiff clay; well-defined failure surface reaching ground level; sudden, brittle failure — Terzaghi's theory applies directly
• Local shear failure: Loose sand, soft clay (relative density 20–65%); failure surface doesn't reach ground level; gradual settlement without dramatic failure
• Punching shear failure: Very loose sand, very soft clay; soil compresses under footing; no distinct failure surface; only vertical movement

Terzaghi's Bearing Capacity Equation (1943)

For a strip footing (L/B → ∞) on general shear failure:

qult = c × Nc + q × Nq + 0.5 × γ × B × Nγ
Where:
c = cohesion of soil (kN/m²)
q = overburden pressure at foundation level = γ × Df
γ = unit weight of soil below foundation (kN/m³)
B = foundation width (m)
Nc, Nq, Nγ = dimensionless bearing capacity factors (function of φ)

Terzaghi's Bearing Capacity Factors:

Shape Factors for Rectangular and Circular Footings:

IS 6403:1981 — Code of Practice for Determination of Bearing Capacity

IS 6403:1981 adopts Meyerhof's general bearing capacity equation with correction factors for shape, depth, inclination, and ground slope:

qult = c·Nc·sc·dc·ic + q·Nq·sq·dq·iq + 0.5·γ·B·Nγ·sγ·dγ·iγ

Where s = shape factor, d = depth factor, i = inclination factor.

IS 6403 Depth Factors (Meyerhof):

dc = 1 + 0.2·(Df/B)·Kφ
dq = dγ = 1 + 0.1·(Df/B)·Kφ  for φ ≥ 10°
dq = dγ = 1 for φ = 0°
Kφ = tan(45 + φ/2)

Effect of Water Table on Bearing Capacity

IS 6403 Clause 5.5 — Groundwater table position critically affects bearing capacity through effective stress:

Rule of thumb: Submerged bearing capacity ≈ 50–60% of dry bearing capacity for the same soil.

Safe Bearing Capacity from Field Tests

From SPT (sandy soils):

qnet,s = Cw × (3.6·N²·B + 5.4·(100 + N²))  kPa   [B ≤ 1.2 m, FOS = 3]

From Plate Load Test (IS 1888):

For clay: qf(foundation) = qf(plate) (independent of plate size)
For sand: qf(foundation) = qf(plate) × (Bf/Bp)

Presumptive Bearing Values (IS 1904:1986 Table 1)

For preliminary design only, IS 1904 gives presumptive values:

Worked Example

Problem: Square footing, B = 1.5 m, D_f = 1.2 m, on sand with φ = 30°, c = 0, γ = 18 kN/m³. Find net SBC.

Step 1: N_c = 37.2, N_q = 22.5, N_γ = 19.7 (from Terzaghi's table, φ = 30°)

Step 2: Square footing: q_ult = 0 + 1.0×(18×1.2)×22.5 + 0.4×18×1.5×19.7
= 21.6×22.5 + 0.4×18×1.5×19.7 = 486 + 212.8 = 698.8 kN/m²

Step 3: q_net,ult = 698.8 – 18×1.2 = 698.8 – 21.6 = 677.2 kN/m²

Step 4: q_net,s = 677.2/3 = 225.7 kN/m²

Step 5: Also check settlement — if settlement criterion gives a lower value, that governs.

Frequently Asked Questions