Foundation Engineering / module 15
Pile capacity in sand — the β-method
Effective stress all the way down — until the measurements stop agreeing with it.
What you will understand
- Apply the β-method to compute shaft resistance in sand
- Explain what K and δ each represent, and which one installation changes
- Apply a limiting effective vertical stress in the illustrative shaft model and a limiting base pressure, and state the dispute over both
- Compare the shaft-base split in sand with the equivalent in clay
Lessons
The β-method
Shaft friction that grows with depth — in the calculation, at least.
The two limits
Where the calculation and the measurements part company.
Module summary
- β = K·tan δ, and shaft resistance is β·σ′v summed down the pile
- K is an installation effect and δ an interface property — neither is a soil property
- Uncapped, the example pile gave 2834 kN of shaft; a 100 kPa limiting stress cut it to 1814 kN, a 36% reduction
- Base resistance uses a DEEP Nq, several times the shallow-foundation value at the same φ′
- The pile came out 48% shaft, against 85% in clay — sand piles are far more base-dependent
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
Practice
A bored pile has K = 0.5 against sand with an interface friction angle δ = 25°. What is β?
Practice
Uncapped shaft resistance is 2834 kN; with a limiting effective stress it becomes 1814 kN. What percentage did the cap remove?