Shallow Foundations
Bearing Capacity
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The problems of soil mechanics can be
divided into two principal groups stability problems and elasticity
problems
- Karl Terzaghi, 1943
Karl Terzaghi (1883-1963)
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Father of modern soil mechanics
Born in Prague, Czechoslovakia
Wrote “Erdbaumechanick” in 1925
Taught at MIT (1925-1929)
Taught at Harvard (1938 and after)
Karl Terzaghi at Harvard, 1940
Bearing Capacity Failure
Transcosna Grain Elevator Canada
(Oct. 18, 1913)
West side of foundation sank 24-ft
Stability Problem
Bearing Capacity Failure
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Chapter 6. Bearing Capacity Analysis
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How do we estimate the maximum
bearing pressure that the soil can
withstand before failure occurs?
Bearing Capacity Failures
Types/Modes of Failure
general shear failure
 local shear failure
 punching shear failure

General Shear Failure
Punching Shear Failure
Model Tests by Vesic (1973)
General Guidelines

Footings in clays - general shear
 Footings in Dense sands ( D r> 67%)
-general shear
 Footings in Loose to Medium dense
(30%< D r < 67%) - Local Shear
 Footings in Very Loose Sand ( D<
r 30%)punching shear
Bearing Capacity Formulas
qult  Nc su   zD
Terzaghi Bearing Capacity Formulas
Terzaghi Bearing Capacity Formulas
For Continuous foundations:
qult  cNc   zD Nq  0.5 BN
For Square foundations:
qult  1.3cNc   zD Nq  0.4 BN
For Circular foundations:
qult  1.3cNc   zD Nq  0.3 BN
Terzaghi Bearing Capacity Factors
2
a
Nq 
2
2 cos (45    / 2)
a  exp (0.75    / 360) tan 
Nc  5.7
Nq 1
Nc 
tan 
when    0
when    0

tan   K p

N 
 1
2
2  cos   
Bearing Capacity Factors
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

Further Developments
Skempton (1951)
 Meyerhof (1953)
 Brinch Hanson (1961)
 De Beer and Ladanyi (1961)
 Meyerhof (1963)
 Brinch Hanson (1970) See Extra Handout
 Vesic (1973, 1975)

Vesic (1973, 1975) Formulas
qult  cNc sc dcicbc gc   zD Nq sq dqiqbq gq  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
Vesic Formula Shape Factors
 B  N q 
sc  1   

L
N
  c 
B
sq  1    tan 
L
B
s  1  0.4 
L
Vesic Formula Depth Factors
D
k  tan  
B
1
dc  1 0.4k
dq  1 2k tan(1 sin )
d  1
2
Bearing Capacity of
Shallow Foundations
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6.3
6.4
6.5
6.6
6.7
6.8
6.9
Groundwater Effects
Allowable Bearing Capacity
Selection of Soil Strength Parameters
Local & Punching Shear Cases
Bearing Capacity on Layered Soils
Accuracy of Bearing Capacity Analyses
Bearing Capacity Spreadsheet
Groundwater Table Effect
Groundwater Table Effect;
Case I
1. Modify ′zD
2. Calculate ′ as follows:
   b    w
Groundwater Table Effect;
Case II
1. No change in ′zD
2. Calculate ′ as follows:
  Dw  D  
      w 1  
 
  B 
Groundwater Table Effect;
Case III
1. No change in ′zD
2. No change in ′
 
Allowable Bearing Capacity
qult
qa 
F


qa
….. Allowable Bearing Capacity
F …. Factor of safety
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
Minimum Factor of Safety
Selection of Soil Strength
Parameters
 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!
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
Accuracy; Bearing Capacity Analysis
Bearing Capacity Spreadsheet
 Can be downloaded from
http://www.prenhall.com/coduto
 See Appendix B (page 848) for further
instructions