1. Bearing Capacity of Shallow Foundations
Ch. 6.

2. B.C. Failures General shear Local shear Punching Dense soils,
Rock, NC clays
Defined failure surf.
Fast failure
Local shear
Intermediate case
+/- gradual failure
Punching
Loose sands,
weak clays (dr.)
F. surf. not defined
Gradual failure

3. B.C. Failures Sand Circular foundations (Vesic, 1963 and 1973)
Deep foundations
(Vesic, 1963 and 1973)

4. We design for the general shear case (for shallow foundations)

5. Bearing Capacity Theory
LIMIT EQUILIBRIUM
Define the shape of a failure surface
Evaluate stresses vs. strengths along this surface

6. Bearing Capacity Theory
LIMIT EQUILIBRIUM
Ultimate bearing capacity = qult = ?
(Bearing press. required to cause a BC failure)
Moments about point A
BC Factor

7. Terzaghi’s Bearing Capacity Theory
Assumptions D < or = B Homogenous and isotropic s = c’ + s’tan(f’) level ground rigid foundation full adhesion between soil and base of footing general shear failure develops

8. Terzaghi’s Bearing Capacity Theory

9. Terzaghi’s Bearing Capacity Theory
Terzaghi developed the theory for continuous foundations (simplest, 2D problem).
From model tests, he expanded the theory to:

10. Terzaghi’s Bearing Capacity Theory
Nc = cohesion factor
Nq = surcharge factor
Nγ = self wt factor
= fn (f’) See table 6.1 for values

11. Groundwater level effects
Shear strength
affects by
Reduction in apparent cohesion - cap (sat. soil for lab tests)
Decrease in s’

12. Groundwater level effects

13. Groundwater level effects
Case I

14. Groundwater level effects
Case II

15. Groundwater level effects
Case III

16. Groundwater level effects
For total stress analysis:
regardless of the case
(gw effects are implicit in cT and fT)

17. Allowable BC = qa FS = function of FS for BC soil type structure type
soil variability
uncertainty
extent of site characterization

18. BC of shallow foundations in practice (per Mayne ‘97)
Undrained
Nc* = 5.14 for strip footing
= 6.14 for square or circular footing
The value of su is taken as the ave. within a depth = to 1B to 1.5B beneath the foundation base
(Mayne, 1980)

19. BC of shallow foundations in practice (per Mayne ‘97)
Drained
Ng* = fn (foundation shape and f’)
Consider gw cases
(I, II, or III to determine g’)

20. BC of shallow foundations in practice (per Mayne ‘97)
Sands
Perform drained analysis
Clays
Perform both

21. Problem formulation – BC design
1. Find B so that FS = 3
Get q
Get q ult (by BC analysis)
Set FS ratio and solve for B
Consider (drained vs. undrained) and methods for obtaining OCR and f’ CPT?

22. Problem formulation– BC design
2. Find B and D so that FS = 3
Get q
Get q ult (by BC analysis)
Set FS ratio and solve for B
Determine this for various D values…
Important too:
Foundation shape (cost and labor)
Moment loads and eccentricity
Weight of the foundations