Foundation Engineering / module 3
How a footing fails
The mechanism under the equation — and why it is exponential in friction.
What you will understand
- Describe the three modes of bearing failure and say which soils produce each
- Explain the failure mechanism beneath a footing in terms of the wedge, the fan and the passive zone
- Explain why bearing capacity is so sensitive to the friction angle
- Recognise when a general shear failure will not develop, and what happens instead
Lessons
Three ways to fail
Only one of them looks like failure.
The mechanism beneath the footing
A wedge, a fan and a passive zone — and where the exponential comes from.
Module summary
- General shear failure gives a clear peak and a visible heave; it belongs to dense, strong soils
- Local and punching failures give no clear peak — the footing simply keeps settling
- The mechanism is a rigid wedge driving a shear fan into a passive zone that must be pushed up and out
- Capacity is exponential in tan φ′ because the fan's radius grows exponentially along it
- In loose or compressible ground the design is governed by settlement long before any of this happens
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Check yourself
Which zone beneath a footing produces the surface heave seen in a general shear failure?
Practice
Using Nq = e^(π tan φ′) · tan²(45° + φ′/2), calculate Nq for φ′ = 35°. Give the answer to one decimal place.