Texas Tech University
Department of Civil and Environmental Engineering
Chapter 6:
Bearing Capacity of Shallow
Foundations
Priyantha Jayawickrama, Ph.D.
Associate Professor
Shallow Foundations
Bearing Capacity
• The problems of soil mechanics can
be divided into two principal groups stability problems and elasticity
problems
- Karl Terzaghi, 1943
CE 4321: Geotechnical Engineering Design
Karl Terzaghi (1883-1963)
•
•
•
•
•
Father of modern soil mechanics
Born in Prague, Czechoslovakia
Wrote “Erdbaumechanick” in 1925
Taught at MIT (1925-1929)
Taught at Harvard (1938 and after)
CE 4321: Geotechnical Engineering Design
Karl Terzaghi at Harvard, 1940
CE 4321: Geotechnical Engineering Design
Bearing Capacity Failure
CE 4321: Geotechnical Engineering Design
Transcosna Grain Elevator
Canada (Oct. 18, 1913)
CE 4321: Geotechnical Engineering Design
West side of foundation sank 24-ft
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?
CE 4321: Geotechnical Engineering Design
Bearing Capacity Failures
Types/Modes of Failure
 general shear failure
 local shear failure
 punching shear failure
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General Shear Failure
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Punching Shear Failure
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Model Tests by Vesic (1973)
CE 4321: Geotechnical Engineering Design
General Guidelines
 Footings in clays - general shear
 Footings in Dense sands ( Dr > 67%)
-general shear
 Footings in Loose to Medium dense
(30%< Dr < 67%) - Local Shear
 Footings in Very Loose Sand (Dr < 30%)punching shear
CE 4321: Geotechnical Engineering Design
Bearing Capacity Formulas
qult  N c su   zD
CE 4321: Geotechnical Engineering Design
Terzaghi Bearing Capacity
Formulas
CE 4321: Geotechnical Engineering Design
Terzaghi Bearing Capacity Formulas
For Continuous foundations:
qult  cN c   zD N q  0.5 BN 
For Square foundations:
qult  1.3cN c   zD N q  0.4 BN 
For Circular foundations:
qult  1.3cN c   zD N q  0.3 BN 
CE 4321: Geotechnical Engineering Design
Terzaghi Bearing Capacity Factors
a2
Nq 
2 cos 2 (45    / 2)
a  exp  (0.75    / 360) tan  
Nc  5.7
Nq 1
Nc 
tan  
when    0
when    0
CE 4321: Geotechnical Engineering Design

tan    K p

N 
 1
2
2  cos   
Bearing Capacity Factors
CE 4321: Geotechnical Engineering Design
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
CE 4321: Geotechnical Engineering Design
Further Developments
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Skempton (1951)
Meyerhof (1953)
Brinch Hanson (1961)
De Beer and Ladanyi (1961)
Meyerhof (1963)
Brinch Hanson (1970) See Extra Handout
Vesic (1973, 1975)
CE 4321: Geotechnical Engineering Design
Vesic (1973, 1975) Formulas
qult  cN c sc d c ic bc g c   zD N q sq d q iq bq g q  0.5 BN  s d i b g
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. 6.25 and 6.26
Ground Inclination Factors….Eq. 6.27 and 6.28
Bearing Capacity Factors …. Eq. 6.29, 6.30 and 6.31
CE 4321: Geotechnical Engineering Design
Vesic Formula Shape Factors
 B  N q 
sc  1   

 L  N c 
B
sq  1    tan  
L
B
s  1  0.4 
L
CE 4321: Geotechnical Engineering Design
Vesic Formula Depth Factors
D
k  tan  
B
1
d c  1 0.4k
d q  1  2k tan  (1  sin  )
d  1
CE 4321: Geotechnical Engineering Design
2
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
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CE 4321: Geotechnical Engineering Design
Groundwater Table Effect
CE 4321: Geotechnical Engineering Design
Groundwater Table Effect;
Case I
1. Modify ′zD
2. Calculate ′ as follows:
   b    w
CE 4321: Geotechnical Engineering Design
Groundwater Table Effect;
Case II
1. No change in ′zD
2. Calculate ′ as follows:
  Dw  D  
      w 1  
 
  B 
CE 4321: Geotechnical Engineering Design
Groundwater Table Effect;
Case III
1. No change in ′zD
2. No change in ′

CE 4321: Geotechnical Engineering Design
Allowable Bearing Capacity
qult
qa 
F


qa
….. Allowable Bearing Capacity
F …. Factor of safety
CE 4321: Geotechnical Engineering Design
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
CE 4321: Geotechnical Engineering Design
Minimum Factor of Safety
CE 4321: Geotechnical Engineering Design
Selection of Soil Strength
Parameters
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
Use Saturated Strength Parameters
Use Undrained Strength in clays (Su)
Use Drained Strength in sands,
c and  
Intermediate soils that where partially
drained conditions exist, engineers
have varying opinions; Undrained
Strength can be used but it will be
conservative!
CE 4321: Geotechnical Engineering Design
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
CE 4321: Geotechnical Engineering Design
Accuracy; Bearing Capacity Analysis
CE 4321: Geotechnical Engineering Design
Bearing Capacity Spreadsheet
 Can be downloaded from
http://www.prenhall.com/coduto
 See Appendix B (page 848) for
further instructions
CE 4321: Geotechnical Engineering Design