This document discusses bearing capacity of shallow foundations. It defines bearing capacity as the ability of soil to safely carry pressure without shear failure. Terzaghi's bearing capacity theory from 1943 is described, including his assumptions of three soil zones and equations for calculating ultimate bearing capacity. The effects of foundation shape, inclined loads, soil type (clay vs. sand), and water table are explained. Settlement analysis is also important to determine allowable bearing capacity. An example problem demonstrates calculating the net allowable bearing capacity of a footing in clay.

1. 4th Year Civil
FOUNDATION ENGINEERING
BEARING CAPACITY
OF SHALLOW
FOUNDATIONS
Dr. Tarek Nageeb Salem
Associate Professor
April 5, 2012 Bearing Capacity 1

2. DEFINITION OF SOIL
Soil is a mixture of irregularly shaped mineral
particles of various sizes containing voids between
particles. The particles are a by-product of
mechanical and chemical weathering of rock and
described as gravels, sands, silts, and clays..
Any manmade structure should, one way or
another, rest and/or transmit its load to the
underlying soil
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3. BEARING CAPACITY OF SOILS
Bearing capacity is the ability of soil to safely carry
the pressure placed on the soil from any engineered
structure without undergoing a shear failure with
accompanying large settlements.
Therefore, settlement analysis should generally be
performed since most structures are sensitive to
excessive settlement.
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4. Bearing Capacity of Shallow
Foundations
s Soil Bearing Capacity is Controlled by:
– Bearing Capacity Analysis:
» Terzaghi’s Theory (1943), based on Prandtl theory
(1920).
» General B.C. Equation.
– Settlement Analysis:
» Immediate Settlement
» Consolidation Settlement
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5. Types of Foundations
Shallow
Foundations
Spread
Mat or Raft
Deep
Foundations
Belled Pier
Friction Piles
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6. Failure Modes for Shallow Foundations
General Shear
Failure,
Zones I, II, III,
Dense Sand
Local Shear
Failure,
Zones I, II,
Medium Dense
Sand
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7. Failure Modes, Continued
Punching Failure, Zone I Only,
Loose Sand and Soft Clay
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8. Terzaghi’s Assumptions
Zone I, Active.
Zones II, Transition.
Zones III, Passive.
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9. Terzaghi B/C Assumptions
Three zones do exist:
1- Active zone, just below the foundation.
2- Transition zone, between the active and passive zones.
3- Passive zone, near the ground surface, just beside the
foundation.
passive active
Transition
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10. Terzaghi Bearing Equation for
Strip Footing
qu net = c Nc + γ 1 D (Nq - 1) + 0.5 B γ 2 Nγ
Overburden
γ1 D
B
Failure Zone (depth ≈ 2B)
Generalized soil strength : c, φ Soil unit weight : γ 2 (total or
(drainage as applicable) effective as applicable)
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11. Terzaghi Bearing Equation
qult =
qult = c Nc Cohesion Term
qult = c Nc + γ 1 D Nq Above F.L.
qult = c Nc + γ 1 D Nq + 0.5B γ 2 Nγ
Below F.L.
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12. Terzaghi Bearing Equation
Nc, Nq, Nγ are Terzaghi B/C Coefficients, f(φ )
C, φ are the soil shear strength parameters
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13. Bearing Capacity Factors
qult = c Nc + γ 1 D Nq + 0.5 B γ 2 N γ
Nc Nq Nγ
40
Ø – in Degrees
30
20
10
0
70 60 50 40 30 20 10 0 10 20 40 60 80
Nc and Nq 5.7 1.0 Nγ
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14. Terzaghi Bearing Equation
B
L P
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15. Foundation Shape Factors
qult = c.Nc λ c + γ 1 D Nq λ q + 0.5B γ 2 Nγ λ γ
For Rectangular or Square Footing
λ c = 1.0 + 0.30 B/L
λ q = 1.0 Egyptian Code of Practice
λ γ = 1.0 – 0.30 B/L
For Circular Footing
λ c = 1.30
λ q = 1.00 Egyptian Code of Practice
λ γ = 0.70
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16. Terzaghi’s Equation for Different
Foundation Shapes
Continuous (Strip) Footing:
qu = c Nc + γ 1 D Nq + 0.5 B γ 2 Nγ
qu-net = c Nc + γ 1 D (Nq - 1) + 0.5 B γ 2 Nγ
Square Footing:
qu-net = 1.3 c Nc + γ 1 D (Nq - 1) + 0.35 B γ 2 Nγ
Circular Footing:
qu-net = 1.3 c Nc + γ 1 D (Nq - 1) + 0.35 B γ 2 Nγ
N , Nq, Nγ = B.C. Factors
c
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17. Footings with inclined loads
β
P P
Inclined Load Factors λ ci, λ qi, λ gi
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18. Inclined Loads
λ ci = λ qi = (1.0 - β / 90) 2
λ γ i = (1.0 - β / φ )2
Correction Factors, λ ci, λ qi, and λ γ i are
empirically determined from experiments
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19. Inclined Load Factors
qult = c Nc λ c λ ci + γ 1 D Nq λ q λ qi + 0.5B γ 2 Nγ λ γ λ γ i
Inclined Load Factors:
λ ci = λ qi = (1.0 – β /90)2
λ γ i = (1.0 – β /φ )2
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20. Bearing Capacity of Clay, φ = 0
qult = c Nc + γ 1 D Nq + 0.50 B γ 2 N γ
For Clay:
Nc = 5.70, Nq = 1.0, Nγ = 0.0
qult = 5.70 cu + γ 1 D
qult net = 5.70 cu qall net = 1.90 cu
cu = qu/2 qu Unconfined compressive strength
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21. Bearing Capacity of Sand, cu = 0
qult = c Nc + γ 1 D Nq + 0.50 B γ 2 N γ
For Sand:
Nc, Nq, Nγ are determined from curve, and cu = 0,
then:
qult = γ 1 D Nq + 0.50 B γ 2 N γ
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22. Gross and Net Bearing Capacity
qult
qall = Gross allowable bearing capacity
F .S .
qult = qult net + γ 1 D Gross ultimate B/C
qult net
qall = + γ1 D Gross allowable B/C
F .S .
qult net
qall net = Net allowable B/C
F .S .
γ 1 D is the overburden pressure
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23. Effect of Water Table on B/C
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24. Effect of Water Table on B/C
qult = c Nc + γ 1 D Nq + 0.5B γ 2 Nγ
Case (a): Case (b):
γ 1 D = γ b (Df-d) + γ sub d, γ 1 D = γ b Df,
γ 2 = γ sub γ 2 = γ sub
Case (c):
γ 1 D = γ b Df, γ b = Bulk unit weight
If , d ≤ B, then γ 2 = γ sub γ sub = Submerged Unit weight,
If , d > B, then γ 2 = γ b γ sub = γ sat - γ water
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25. Settlement Analysis
Allowable bearing capacity, as calculated from the
settlement analysis, usually controls the soil
bearing capacity, especially in clay and silt.
The maximum allowable settlement is set first,
then the stress (bearing pressure) that will induce
that settlement will be the allowable bearing
capacity.
For stratified soils, 2:1 stress distribution is used to
determine the stresses at the top of each layer.
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26. Bearing Capacity in Stratified Deposits
P P = q1 A1 = q1 B1 L1
B1
soft clay P = q2 A2 = q2 B2 L2
q1
q1 is the allowable
q2 bearing capacity
for layer 1
2B q is the allowable
B2 2
bearing capacity
stiff clay or for layer 2, and
dense sand so on
The allowable bearing capacity as determined from either
the shear strength parameters or the settlement analysis.
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27. Settlement Analysis
Total Settlement =
Immediate Settlement +
Primary Consolidation Settlement +
Secondary Consolidation Settlement
In Sand:
Total Settlement ≈ Immediate settlement
In Silts, Stiff and Medium Clays:
Total Settlement ≈ Immediate Settlement +
Primary Consolidation Capacity
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Settlement 27

28. Settlement Analysis
In Soft Clays, Silts and Organic Soils:
Total Settlement = Immediate Settlement +
Primary Consolidation Settlement +
Secondary Consolidation Settlement
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29. Example
A footing 1.8 m x 2.5 m is located at a depth of
1.5 m below the ground surface, in an over-
consolidated clay layer. The groundwater level is
2 m below the ground surface. The unconfined
compressive strength of that clay is 120 kPa, γ bulk
= 18 kN/m3, and γ sat = 20 kN/m3. Determine the
net allowable bearing capacity, assuming a factor
of safety of 3.
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30. Solution
qult = c Nc λ c + γ 1 D Nq λ q + 0.5B γ 2 Nγ λ γ
For Clay: Nc = 5.7, Nq = 1.0, Nγ = 0.0
For Rectangular Footing:
λ c = 1.0 + 0.30 B/L = 1.0 + 0.30 x 1.8/2.5 = 1.22
λ q = 1.0
qult net = c Nc λ c + γ 1 D (Nq -1) λ q
qu = 120 kPa, cu = 60 kPa
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31. qult net = 60 x 5.7 x 1.22 = 417.20
qult net 417.2
qall net = = = 139.08 kN/m 2
F .S . 3
qall net = 13.91 t/m2 = 1.39 kg/cm2
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32. April 5, 2012 Bearing Capacity 32