1. AIN NIHLA KAMARUDZAMAN ainnihla@unimap.edu.my Ext: 8968
School of Environmental Engineering
UNIVERSITI MALAYSIA PERLIS
EAT 314/4 Geotechnical Engineering
Soil Bearing Capacity of Shallow Foundations
AIN NIHLA KAMARUDZAMAN
Ext: 8968

2. COURSE OUTCOME (CO) EAT 314/4
NO.
COURSE OUTCOME (CO) EAT 314/4 1
Ability to analyze soil bearing capacity and design for shallows foundations based on types of soil. 2
Ability to describe type of deep foundation and its installation. 3
Ability to describe and design various concrete retaining walls based on lateral earth pressure. 4
Ability to conduct slope stability analysis and landslide investigations. 5
Ability to discuss common sampling methods for subsoil exploration and report.

3. Outline Introduction Ultimate Bearing Capacity for Shallow Foundation
Terzaghi’s Ultimate Bearing Capacity Equations
Factor of Safety
Effect of Ground Water Table (GWT)
General Bearing Capacity Equation.
Allowable Bearing Pressure in Sand Settlement Consideration.

4. Introduction
Foundations are the building component which transfers building loads to the soil.
There are two basic types of foundations:
SHALLOW - Shallow foundations transfer the load to soil at the base of the substructure.
DEEP - Deep foundations transfer loads far below the substructure.

5. Types of Foundation
SHALLOW vs DEEP
Building
Building
Rock

6. Shallow Foundation Shallow Foundation System
i) Spread Foundation (footing)
ii) Mat or Raft Foundation
Characteristics of shallow foundations are;
Cost (affordable)
Construction Procedure (simple)
Material (mostly concrete)
Labour (doesn’t need expertise)

7. Spread Foundation (footing)
Also known as a footer or footing.
It’s an enlargement at the bottom of a column or bearing wall that spreads the applied structural loads over a sufficiently large soil area.
Each column & each bearing wall has its own spread footing, so each structure may include dozens of individual footings.

8. Spread Foundation (footing) …Cont.
Spread Footing

9. Spread Foundation (footing) …Cont.

10. Mat or Raft Foundation A foundation system in which essentially the
entire building is placed on a large continuous footing.
It is a flat concrete slab, heavily reinforced
with steel, which carries the downward loads of the individual columns or walls.
Raft foundations are used to spread the load from a structure over a large area, normally the entire area of the structure.

11. Mat or Raft Foundation (Cont.)

12. Mat or Raft Foundation (Cont.)

13. Design Criteria:
To perform satisfactory, shallow foundation must have two main criteria:
They have to be safe against overall shear failure in the soil that supports them.
(Safety factor usually between 2.5 to 3.0)
They cannot undergo excessive displacement or settlement.
(Settlement of individual footing on sand 50 mm or 75 mm for footing on clay)

14. Ultimate Bearing Capacity for Shallow Foundation
Definition:
Bearing capacity is ability of a soil to bear the loads transmitted by a footing.
Ultimate bearing capacity is reach when the impose foundation pressure is in equilibrium with resisting soil pressure.
When the pressure exceed the ultimate soil bearing capacity value, the foundation pronounced fail in shear.

15. Ultimate Bearing Capacity for Shallow Foundation
Ultimate Bearing Capacity (qult) is the maximum pressure which can be carried by the soil immediately below foundation.
The theory is developed based on three modes of failure;
General shear failures – for soils (dense or hard state)
Local shear failures – for soils (medium density or firm state)
Punching shear failure – for soils (loose or soft state)

16. Failure modes of Shallow Foundation
bulge
General Shear Failure
bulge
Local Shear Failure
Punching Shear Failure

17. Terzaghi’s Ultimate Bearing Capacity Equations
Terzaghi (1943) – formulated for strip foundation – modified from Prandlt (early 1920)
According to Terzaghi:
Shallow foundation – ratio between the depth of embedment (Df) and the width of foundation (B) is less than 1.
The weight of the soil above the base of foundation is;

18. Terzaghi’s Ultimate Bearing Capacity Equations....Cont.
III I
III II II
Figure: Derivation of Terzaghi’s Bearing Capacity Equation

19. Terzaghi’s Ultimate Bearing Capacity Equations....Cont.
The failure mechanisms of the soil due to foundation load is defined in three failure zone:
Zone 1: The triangular active zone ADC immediately under the foundation.
Zone 2: The Radial shear zones of ADF and CDE.
Zone 3: Two Triangular Rankine Passive zones AFH and CEG
Note: The weight of the foundation and the soil in zone 1 will pushed zone 2 to the sides AND zone 3 to the surface of the soil resulting in the bulge of the soil surface.

20. Terzaghi’s Ultimate Bearing Capacity Equations....Cont.
Terzaghi’s assumption:
The angles CAD and ACD is equal to the soil friction angle, Φ. (that is, α = Φ)
By replacing the weight of the soil above the foundation base by an equivalent surcharge, q, the shear resistance of the soil along the failure surface GI and HJ was neglected.
Remember:

21. Terzaghi’s Ultimate Bearing Capacity Equations....Cont.
Q (vertical load causing a general shear failure of the soil)
Ground surface
G.W.T Df
qult B
The ultimate bearing capacity equation, qult (kPa)

22. Terzaghi’s Ultimate Bearing Capacity Equations....Cont.
For a uniform vertical loading of a strip footing, Terzaghi (1943) assumed a general shear failure in order to develop the ultimate bearing capacity equation:
Where;
c = cohesion of the soil underlying the footing (kPa or kN/m2)
, = unit weight of the soil (kN/m3)
= Distance from the ground surface to the bottom of the footing (m)
B = width of the footing (m)
L = Length of the footing (m)
…..Eq. 1

23. Terzaghi’s Bearing Capacity Factors

24. Terzaghi’s Ultimate Bearing Capacity Equations....Cont.
If the shape factors were considered, the equation was modified to;
For square foundation (B x B in size):
….Eq. 2
For circular foundation (Diameter = B):
….Eq. 3

25. Terzaghi’s Ultimate Bearing Capacity Equations....Cont.
For foundation that exhibit local shear failure mode in soils, Terzaghi suggested modification to Eq. 1 by replacing;
The cohesion c  c’
Where;
The angle of internal friction Φ  Φ’

26. Example #1:
A square footing (2.25 m x 2.25 m) is placed at depth of 1.5 m in a sand with the shear strength parameters c’ = 0 and Φ’ = 38˚. Determine the ultimate bearing capacity of the foundation. The unit weight of the sand is 18 kN/m3.
Given: Df = 1.5 m
B = 2.25 m

27. Solution: Example #1 For a square footing on sand; using Eq. 2.
But, the cohesion of sand, c = 0, then
For Φ = 38˚, by using Table 1 (Terzaghi Bearing Capacity Factors), we get
Nq = 61.5 and Nγ = 82.3

28. Solution: Example #1
Then, the ultimate bearing capacity is

29. Factor of Safety, Fs
Factor of safety, Fs of about 3 or more is applied to the ultimate soil bearing capacity to arrive at the value of the allowable bearing capacity.
There are two basic definition of the allowable bearing capacity of shallow foundation:
Gross allowable bearing capacity, qall
Net allowable bearing capacity, qult(net)

30. Gross allowable bearing capacity, qall
The gross allowable bearing capacity can be calculated as
qall is the allowable load (Qall) per unit area to which the soil under the foundation should be subjected to avoid any chance of bearing capacity failure.

31. Net allowable bearing capacity, qu(net)
The net allowable bearing capacity, qult(net) is the allowable load per unit area of the foundation in excess of the existing vertical effective stress at the level of the foundation.
The vertical effective stress at the foundation level is equal to
So, the net ultimate load is
Hence,

32. Net allowable bearing capacity, qu(net)
In the case of shallow footing – there is no significant difference in the factor of safety obtained in terms of net or gross pressure.
The consideration of net pressure is very important for the case of design of mat or raft foundation.

33. Example #2:
A strip of wall footing 1 m wide is supported by a stiff clay layer with undrained shear strength of 140 kPa. Unit weight of soil is 20 kN/m3. Depth of footing is 0.6 m. Ground water was not encountered during subsurface exploration. Determine the allowable wall load for a factor of safety 3.
Given: B = 1 m, Df = 0.6 m
= 20 kN/m3

34. Solution: Example #2 For strip footing, using Eq. 1
Shear strength parameters: for undrained condition (fully saturated), Φ = 0˚ and c = 140 kN/m2
By using Table 1 (Terzaghi Bearing Capacity Factors), for Φ = 0˚, we get
Nc = 5.7, Nq = 1.0 and Nγ = 0.0

35. Solution: Example #2 Thus, the ultimate bearing capacity is
Note: 1 kPa = 1 kN/m2

36. Solution: Example #2 With safety factor, FS = 3
The gross allowable bearing capacity is
The allowable wall load,

37. Example #3:
A square footing 1.5 x 1.5 m in plan is placed at depth of 1 m in a soil with friction angle, Φ = 20˚ and c = 15.2 kPa. The unit weight of the soil is 17.8 kN/m3. Determine the allowable gross load for a factor of safety 3. Assume general shear failure occurs in the soil.
Given: size: B x L = 1.5 m x 1.5 m,
Df = 1 m
= 17.8 kN/m3

38. Solution: Example #3 For square footing, using Eq. 2
Shear strength parameters: Φ = 20˚ and c = 15.2 kN/m2
By using Table 1 (Terzaghi Bearing Capacity Factors), for Φ = 20˚, we get
Nc = 17.7, Nq = 7.4 and Nγ = 4.4

39. Solution: Example #3
Thus, the ultimate bearing capacity

40. Solution: Example #3 With safety factor, FS = 3
The gross allowable load is

41. Example #4:
From Example #3, calculate total gross load if local shear failure occurs in the soil.
Solution:
Find shear strength parameters;

42. Solution: Example #4 For square footing, using Eq. 2
By using Table 1 (Terzaghi Bearing Capacity Factors), for Φ’ = 14˚, we get
Nc = 12.1, Nq = 4.0 and Nγ = 1.9

43. Solution: Example #4 Thus, the ultimate bearing capacity
Note: 1 kPa = 1 kN/m2

44. Solution: Example #4 With safety factor, FS = 3
The gross allowable load is

45. Effect of Ground Water Table (GWT)
The presence of ground water table will influence the bearing capacity of footing.
Groundwater reduces the density of soil due to buoyancy.
When groundwater is present, the density of the soil needs to be modified.
Depending on the position of water table, the second and third terms in the bearing capacity equation (Eq. 1  Eq. 3) may require modification.

46. Effect of Ground Water Table (GWT)
The effect of groundwater table can be categorized into four conditions;
Case 1:
GWT at the ground surface (Fully submerged)
Case 2:
GWT above foundation base
Case 3:
GWT at the foundation base
Case 4:
GWT at a depth D below the foundation base.

47. Case 1: GWT at the ground surface
If the groundwater table is located at the soil surface, then,
The magnitude of q in the second term of the bearing capacity equation should be calculated as;
Where,
The unit weight of soil, in the second and third term of the bearing capacity equations should be replaced by . GL
GWT
Df = D
= effective unit weight of soil
Note:
= saturated unit weight of soil
= unit weight of water

48. Case 2: GWT above foundation base
If groundwater table is located at a distance D above the bottom of the foundation,
The magnitude of q in the second term of the bearing capacity equation should be calculated as;
Where, GL
GWT
= effective unit weight of soil
The unit weight of soil, in the third term of the bearing capacity equations should be replaced by .

49. Case 3: GWT at the foundation base
If the groundwater table is at the bottom of the foundation,
The magnitude of q in the second term of the bearing capacity equation is equal
to;
However, the unit weight of soil, in the third term of the bearing capacity equations should be replaced by . GL
GWT

50. Case 4: GWT at a depth D below the foundation base.
When the groundwater table is at a depth D below the bottom of the foundation,
The magnitude of q in the second term of the bearing capacity equation is equal to;
The magnitude of in the third term of the bearing capacity equations should be replaced by GL
GWT

51. Example #5:
A square footing (2.25 m x 2.25 m) is placed at depth of 1.5 m in a sand with the shear strength parameters c’ = 0 and Φ’ = 38˚. Determine the ultimate bearing capacity of the foundation if water table exists at the ground surface. The unit weight of the sand is 18 kN/m3 and the saturated unit weight of the sand is 20 kN/m3.
Given: Df = 1.5 m
B = 2.25 m

52. Solution: Example #5 GL
GWT
Df = D = 1.5 m
B = 2.25 m

53. Solution: Example #5 For a square footing on sand; using Eq. 2.
But, the cohesion of sand, c = 0, and the groundwater table exist at the ground surface, then Eq. 2 was modified to,
Where, assumed , then

54. Solution: Example #5 Then, the ultimate bearing capacity is
For Φ = 38˚, by using Table 1 (Terzaghi Bearing Capacity Factors), we get
Nq = 61.5 and Nγ = 82.3
Then, the ultimate bearing capacity is

55. General Bearing Capacity Equation
After the development of Terzaghi’s bearing capacity equation, several investigators worked in this area and refined the solution.
For examples; Meyerhoff (1951, 1963), Hansen (1961) and etc.
Meyerhoff argued that bearing capacity of foundation is not only affected by the shape of foundation but by others factors as well.

56. General Bearing Capacity Equation
The soil-bearing capacity equation for a strip footing given in (Eq. 1) can be modified for general use by incorporating the following factors:
Shape factor: to determine the bearing capacity of rectangular and circular footings.
Depth factor: to account for the shearing resistance developed along the failure surface in soil above the bottom of the footing.
Inclination factor: To determine the bearing capacity of a footing on which the direction of load application is inclined at a certain angle to the vertical.

57. General Bearing Capacity Equation
Meyerhoff (1951,1963) was modified the general bearing capacity formula to account all the factors as follows;
Where;
s = the shape factor,
d = the depth factor,
i = the load inclination factor, and
B and L = the dimension of footing
Nc, Nq and Nγ = Bearing capacity factors Table 2 (Meyerhoff and Brinch & Hansen)

58. Shape factors (De Beer, 1970)
Shape factors for rectangular footing:
(B = width of footing, L = length of footing)

59. Shape factors (De Beer, 1970)
Shape factors for square and circular footing:

60. Example #6 A foundation is designed on a soil with and .
The shear strength parameters of the soil are, c = 80 kPa and Φ = 15˚. The depth of embedment is 1.2 m and the size of foundation is 1.5 x 2 m. Determine the ultimate bearing capacity of the foundation and the allowable load if factor of safety is 3.

61. Solution: Example #6 Given: Df = 1.2 m, B = 1.5 m, L = 2 m
Use general bearing capacity equation;
From Table 2 (Meyerhoff Bearing Capacity Factors); for Φ = 15˚, we get
Nc = 10.98, Nq = 3.94 and Nγ = 1.13

62. Solution: Example #6
Calculate the shape factors;

63. Solution: Example #6 Use, (There are no groundwater effect)
Then, the ultimate bearing capacity is

64. Solution: Example #6
With safety factor, Fs = 3
The allowable load is

65. Depth factors (Hansen, 1970)
The depth of embedment influences the shear strength at failure plane.
This factor can be neglected if the soil above foundation base is not stable or not compacted.

66. Depth factors (Hansen, 1970)

67. Example #7: Do Example #6 by taking into account the depth factor.
Solution:
Use general bearing capacity equation;
From Table 2 (Meyerhoff Bearing Capacity Factors);
for Φ = 15˚, we get
Nc = 10.98, Nq = 3.94 and Nγ = 1.13

68. Solution: Example #7
Shape factor;
Depth factor;

69. Solution: Example #7
Then, the ultimate bearing capacity is

70. Solution: Example #7
With safety factor, Fs = 3
The allowable load is

71. Inclination Factor Footing may be subjected to inclined load.
The effect of load inclination is proposed by Meyerhoff (1963) and Hanna and Meyerhoff (1981).
Where, is the angle of loading with vertical axis
Q (Load) B

72. Example #8:
A foundation of size 2 x 2 m carrying a column load that form an angle of 10˚ to the vertical. The depth of the foundation is 2 m. The internal friction angle is 34˚ and the unit weight of the soil is 20.8 kN/m3. Find the allowable column load for a factor of safety 4.
Given: Df = 2 m
B = L = 2 m

73. Solution: Example #8 For c = 0 then,
The general bearing capacity equation;
From Table 2 (Meyerhoff Bearing Capacity Factors);
for Φ = 34˚, we get
Nq = and Nγ = 31.15

74. Solution: Example #8 For square footing; shape factor
Inclination factors:
Q (Load)
2 x 2 m

75. Solution: Example #8
For depth factors:

76. Solution: Example #8
Then, the ultimate bearing capacity is

77. Solution: Example #8
With safety factor, Fs = 4
The allowable load is

78. THANK YOU