1. Bearing Capacity
ظرفيت باربري

2. Shallow Foundations
Footing

3. Shallow Foundations
Footing

4. Shallow Foundations B
Typical Buried Footing Q D

5. Shallow Foundations Typical Buried Footing Equivalent Surface Footing= g D
Equivalent Surface Footing s

6. Shallow Foundations Typical Buried Footing Equivalent Surface Footing= g D
Equivalent Surface Footing s
Shallow Foundations have D/B < 1

7. Shallow Foundations Methods of analysis Lower bound approach
failure stress state in equilibrium
failure load less than or equal to true collapse
Upper bound approach
failure mechanism assumed
failure load greater than or equal to true collapse

8. Shallow Foundations
Footing q
Surcharge q f s

9. Shallow Foundations Frictionless Discontinuity Footing q Surcharge q H

10. Shallow Foundations Frictionless Discontinuity Footing q Surcharge q H
Soil at state
of Active
Failure with s
> s v h
Frictionless Discontinuity

11. Shallow Foundations Frictionless Discontinuity Footing q Surcharge q H
Soil at state
of Active
Failure with s
> s v h
Frictionless Discontinuity

12. Shallow Foundations Frictionless Discontinuity Footing q Surcharge q H
Soil at state
Soil at state
of Active
of Passive
Failure with
Failure with s
> s s
> s v h h v
Frictionless Discontinuity

13. Shallow Foundations Frictionless Discontinuity Footing q Surcharge q H
Soil at state
Soil at state
of Active
of Passive
Failure with
Failure with s
> s s
> s v h h v
Frictionless Discontinuity

14. Shallow Foundations
sv = s1
sh = s3
sh = s1
sv = s3

15. Shallow Foundations
sv = s1
sh = s3
sh = s1
sv = s3

16. Shallow Foundations
sv = s1
sh = s3
sh = s1
sv = s3

17. Shallow Foundations
sv = s1
sh = s3
sh = s1
sv = s3

18. Shallow Foundations

19. Shallow Foundations

20. Shallow Foundations

21. Shallow Foundations
This solution will give a lower bound to the true solution because of the simplified stress distribution assumed in the soil
Similar terms occur in all bearing capacity expressions. They are functions of the friction angle and
the surcharge applied to the soil surface
the self weight of the soil
cohesion

22. Shallow Foundations
A general bearing capacity equation can be written

23. Shallow Foundations A general bearing capacity equation can be written
The terms Nq, Ng and Nc are known as the bearing capacity factors

24. Shallow Foundations A general bearing capacity equation can be written
The terms Nq, Ng and Nc are known as the bearing capacity factors
Values can be determined from charts

25. Shallow Foundations

26. Mechanism analysed by Terzaghi
Shallow Foundations Q f B q = g D f D f
Mechanism analysed by Terzaghi

27. Effect of Foundation Shape
Continuous strip footing

28. Effect of Foundation Shape
Continuous strip footing
Square footing

29. Effect of Foundation Shape
Continuous strip footing
Square footing
Circular footing

30. Effective Stress Analysis
Effective stress analysis is needed to assess the long term foundation capacity.
Total and effective stresses are identical if the soil is dry. The analysis is identical to that described above except that the parameters used in the equations are c´, f´, gdry rather than cu, fu, gsat.
If the water table is more than a depth of 1.5 B (the footing width) below the base of the footing the water can be assumed to have no effect.

31. Effective Stress Analysis
If the soil below the base of the footing is saturated, the analysis must account for the water pressures.

32. Effective Stress Analysis
If the soil below the base of the footing is saturated, the analysis must account for the water pressures.
Q = q B f q = g D s
u = u o

33. Effective Stress Analysis
If the soil below the base of the footing is saturated, the analysis must account for the water pressures.
Q = q B f q = g D s
u = u o

34. Effective Stress Analysis
If the soil below the base of the footing is saturated, the analysis must account for the water pressures.
Q = q B f q = g D s
u = u o

35. Effective Stress Analysis
If the soil below the base of the footing is saturated, the analysis must account for the water pressures.
Q = q B f q = g D s
u = u o

36. Effective Stress Analysis
These effective quantities are required because Mohr Coulomb failure criterion must be expressed in terms of effective stress

37. Effective Stress Analysis
These effective quantities are required because Mohr Coulomb failure criterion must be expressed in terms of effective stress
The total vertical stress, pore pressure and effective vertical stress at any depth z beneath the footing are

38. Effective Stress Analysis
These effective quantities are required because Mohr Coulomb failure criterion must be expressed in terms of effective stress
The total vertical stress, pore pressure and effective vertical stress at any depth z beneath the footing are

39. Effective Stress Analysis
These effective quantities are required because Mohr Coulomb failure criterion must be expressed in terms of effective stress
The total vertical stress, pore pressure and effective vertical stress at any depth z beneath the footing are

40. Effective Stress Analysis
s’v = s’1
s’h = s’3
s’h = s’1
s’v = s’3

41. Effective Stress Analysis
The simple analysis leads to

42. Effective Stress Analysis
The simple analysis leads to
This is similar to the previous expression except that now all terms involve effective quantities.

43. Effective Stress Analysis
The simple analysis leads to
This is similar to the previous expression except that now all terms involve effective quantities.
As before a general expression can be written with the form

44. Effective Stress Analysis
The simple analysis leads to
This is similar to the previous expression except that now all terms involve effective quantities.
As before a general expression can be written with the form
The Bearing Capacity Factors are identical to those from Total Stress Analysis

45. Effective Stress Analysis
The simple analysis leads to
This is similar to the previous expression except that now all terms involve effective quantities.
As before a general expression can be written with the form
The Bearing Capacity Factors are identical to those from Total Stress Analysis
Note that the Total Bearing Capacity qf = q’f + uo

46. Effective Stress Analysis
Analysis has so far considered
soil strength parameters
rate of loading (drained or undrained)
groundwater conditions (dry or saturated)
foundation shape (strip footing, square or circle)
Other important factors include
soil compressibility
embedment (D/B > 1)
inclined loading
eccentric loading
non-homogeneous soil

47. Effective Stress Analysis
More theoretically accurate bearing capacity factors are given on pages 69 to 71 of the Data Sheets
In practice the Terzaghi factors are still widely used.
The bearing capacity equation assumes that the effects of c', g, and f' can be superimposed.
This is not correct as there is an interaction between the three effects because of the plastic nature of the soil response.

48. Effective Stress Analysis
The formulae give the ultimate bearing capacity
Significant deformations and large settlements may occur before general bearing failure occurs
Local failure (yield) will occur at some depth beneath the footing at a load less than the ultimate collapse load
The zone of plastic (yielding) soil will then spread as the load is increased. Only when the failure zone extends to the surface will a failure mechanism exist.
A minimum load factor of 3 against ultimate failure is usually adopted to keep settlements within acceptable bounds, and to avoid problems with local failure.

49. Example
B = 5m Q
D = 2m

50. Example
B = 5m Q
D = 2m
Determine short term and long term ultimate capacity given

51. Example
Equivalent surface footing
Q=q B f q s

52. Example Q=q B q Equivalent surface footing
Short term - Undrained (total stress) analysis

53. Example Q=q B q Equivalent surface footing
Short term - Undrained (total stress) analysis
Position of water table not important - soil must be saturated

54. Example Q=q B q Equivalent surface footing
Short term - Undrained (total stress) analysis
Position of water table not important - soil must be saturated

55. Example
fu = Nq = 1, Ng = 0 and Nc = 5.14

56. Example
Short term capacity q N B c f s = + g 2

57. Example Short term capacity q N B c = + g 2 q = 30 ´ 1 + 0 + 25 ´f s = + g 2 q
= 30
5.14 = kPa (Bearing capacity) f

58. Example Short term capacity q N B c = + g 2 q = 30 ´ 1 + 0 + 25 ´f s = + g 2 q
= 30
5.14 = kPa (Bearing capacity) f
Q = q
B =
5 = kN/m (Bearing Force) f

59. Example
Long term capacity
Effective stress (fully drained) analysis

60. Example
Long term capacity
Effective stress (fully drained) analysis

61. Example
Long term capacity
Effective stress (fully drained) analysis

62. Example
Long term capacity
Effective stress (fully drained) analysis

63. Example
Long term capacity
Effective stress (fully drained) analysis

64. Example
f’ = Nq = 13, Ng = 10 and Nc = 24.5

65. Example
Long term capacity

66. Example
Long term capacity

67. Example
Long term capacity

68. Total Stress Analysis fu = 0

69. Total Stress Analysis fu = 0

70. Bottom heave into excavationsD
heave

71. Bottom heave into excavationsgD

72. Bottom heave into excavationsgD

73. Bottom heave into excavationsgD

74. Bottom heave into excavationsgD