Geotechnical Engineering

Shear Strength & Bearing Capacity

Mohr–Coulomb strength, Rankine earth pressure and Terzaghi bearing capacity — the design heart of foundations.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Soil shear strength follows Mohr–Coulomb:

τ_{f} = c + σ^{'} tan ϕ

. A footing fails when the applied pressure reaches the ultimate bearing capacity; Terzaghi superposes cohesion, surcharge and self-weight terms. Lateral earth pressure on retaining walls uses Rankine's coefficients.

The Core Formula Matrix

Mohr–Coulomb:

τ_{f} = c + σ^{'} tan ϕ

Rankine active / passive:

K_{a} = \frac{1 - sin ϕ}{1 + sin ϕ}, K_{p} = \frac{1}{K _{a}}

Terzaghi (strip):

q_{u} = c N_{c} + γ D_{f} N_{q} + 0.5 γ B N_{γ}

**Clay,

ϕ = 0

**:

N_{c} = 5.7, N_{q} = 1, N_{γ} = 0

.

Net safe bearing capacity:

q_{s a f e} = \frac{q _{u}}{FoS}

(FoS usually

3

The ‘IIT Traps’

⚠
Effective stress controls strength. Use $σ^{'}$ (not total $σ$ ) in Mohr–Coulomb.
⚠
** $K_{p} = 1/ K_{a}$ ** only for a smooth vertical wall with horizontal backfill.
⚠
Net vs gross capacity. Subtract the surcharge $γ D_{f}$ for net values.

📚 Standard references

Basic and Applied Soil Mechanics — Gopal Ranjan & A.S.R. Rao · Shear Strength & Bearing Capacity

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

For a cohesionless backfill with

ϕ = 3 0^{\circ}

, the Rankine active earth pressure coefficient

K_{a}

is _____.

Q2MEDIUM2 Marks · NAT

A strip footing at

1 m

depth rests on clay (

c = 30 kPa

ϕ = 0

γ = 18 kN/m^{3}

). Using Terzaghi (

N_{c} = 5.7, N_{q} = 1, N_{γ} = 0

q_{u}

is _____ kPa.

Q3HARD1 Mark · NAT

The ultimate bearing capacity is

450 kPa

. With a factor of safety of

3

, the safe bearing capacity is _____ kPa.