1. Shallow Foundations Bearing Capacity
The problems of soil mechanics can be divided into two principal groups - stability problems and elasticity problems
- Karl Terzaghi, 1943

2. Karl Terzaghi (1883-1963) Father of modern soil mechanics
Born in Prague, Czechoslovakia
Wrote “Erdbaumechanick” in 1925
Taught at MIT ( )
Taught at Harvard (1938 and after)

3. Karl Terzaghi at Harvard, 1940

4. Bearing Capacity Failure

5. Transcosna Grain Elevator Canada (Oct. 18, 1913)
West side of foundation sank 24-ft

6. Stability Problem Bearing Capacity Failure
Chapter 6. Bearing Capacity Analysis
How do we estimate the maximum bearing pressure that the soil can withstand before failure occurs?

7. Bearing Capacity Failures
Types/Modes of Failure
general shear failure
local shear failure
punching shear failure

8. General Shear Failure

9. Punching Shear Failure

10. Model Tests by Vesic (1973)

11. General Guidelines Footings in clays - general shear
Footings in Dense sands ( > 67%)
-general shear
Footings in Loose to Medium dense
(30%< < 67%) - Local Shear
Footings in Very Loose Sand ( < 30%) punching shear

12. Bearing Capacity Formulas

13. Terzaghi Bearing Capacity Formulas

14. Terzaghi Bearing Capacity Formulas
For Continuous foundations:
For Square foundations:
For Circular foundations:

15. Terzaghi Bearing Capacity Factors

16. Bearing Capacity Factors

17. Terzaghi Bearing Capacity Formulas
D  B
No sliding between footing and soil
soil: a homogeneous semi-infinite mass
general shear failure
footing is very rigid compared to soil

18. Further Developments Skempton (1951) Meyerhof (1953)
Brinch Hanson (1961)
De Beer and Ladanyi (1961)
Meyerhof (1963)
Brinch Hanson (1970)
Vesic (1973, 1975)
See Extra Handout

19. Vesic (1973, 1975) Formulas Shape factors….… Eq. 6.14, 6.15 and 6.16
Depth Factors ……. Eq. 6.17, 6.18 and 6.19
Load Inclination Factors …. Eq. 6.20, 6.21 and 6.22
Base Inclinations factors .. Eq and 6.26
Ground Inclination Factors…. Eq and 6.28
Bearing Capacity Factors …. Eq. 6.29, 6.30 and 6.31

20. Vesic Formula Shape Factors

21. Vesic Formula Depth Factors

22. Bearing Capacity of Shallow Foundations
6.3 Groundwater Effects
6.4 Allowable Bearing Capacity
6.5 Selection of Soil Strength Parameters
6.6 Local & Punching Shear Cases
6.7 Bearing Capacity on Layered Soils
6.8 Accuracy of Bearing Capacity Analyses
6.9 Bearing Capacity Spreadsheet

23. Groundwater Table Effect

24. Groundwater Table Effect; Case I
Modify ′zD
Calculate ′ as follows:

25. Groundwater Table Effect; Case II
No change in ′zD
Calculate ′ as follows:

26. Groundwater Table Effect; Case III
No change in ′zD
No change in ′

27. Allowable Bearing Capacity
F …. Factor of safety

28. Factor of Safety Depends on: Type of soil
Level of Uncertainty in Soil Strength
Importance of structure and consequences of failure
Likelihood of design load occurrence

29. Minimum Factor of Safety

30. Selection of Soil Strength Parameters
Use Saturated Strength Parameters
Use Undrained Strength in clays (Su)
Use Drained Strength in sands,
Intermediate soils that where partially drained conditions exist, engineers have varying opinions; Undrained Strength can be used but it will be conservative!

31. Accuracy of Bearing Capacity Analysis
In Clays …..Within 10% of true value (Bishop and Bjerrum, 1960)
Smaller footings in Sands…. Bearing capacity calculated were too conservative – but conservatism did not affect construction cost much
Large footings in Sands … Bearing capacity estimates were reasonable but design was controlled by settlement

32. Accuracy; Bearing Capacity Analysis

33. Bearing Capacity Spreadsheet
Can be downloaded from
See Appendix B (page 848) for further instructions