# Bearing Capacity of Shallow Foundations - PowerPoint

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```					Bearing Capacity of Shallow
Foundations
Ch. 6.
B.C. Failures
General shear
Dense soils,
Rock, NC clays

Defined failure surf.
Fast failure

Local shear

Intermediate case

Punching
Loose sands,
weak clays (dr.)

F. surf. not defined
B.C. Failures

Sand
Circular foundations

Deep
foundations

(Vesic, 1963 and 1973)
We design for the general shear case
(for shallow foundations)
Bearing Capacity Theory
LIMIT EQUILIBRIUM
1. Define the shape of a failure surface
2. Evaluate stresses vs. strengths along this surface
Bearing Capacity Theory
LIMIT EQUILIBRIUM

Ultimate bearing capacity = qult = ?
(Bearing press. required to cause a BC failure)

 B                                  B
M A  (qult  Bb )   ( su  Bb )B    zD  Bb  
2                                  2
qult  2    su   zD
BC Factor

qult  N c su   zD
Terzaghi’s Bearing Capacity Theory
Assumptions

D < or = B

Homogenous and isotropic s = c’ + ’tan(f’)

level ground

rigid foundation

full adhesion between soil and base of footing

general shear failure develops
Terzaghi’s Bearing Capacity Theory
Terzaghi’s Bearing Capacity Theory
Terzaghi developed the theory for continuous foundations
(simplest, 2D problem).

qult  c' N c   ' zD N q  0.5 ' BN 
From model tests, he expanded the theory to:

qult  1.3c' N c   ' zD N q  0.4 ' BN 

qult  1.3c' N c   ' zD N q  0.3 ' BN 
Terzaghi’s Bearing Capacity Theory

Nc = cohesion factor
Nq = surcharge factor
Nγ = self wt factor

= fn (f’) See table 6.1 for values
Groundwater level effects

groundwater

affects

Shear strength

by

1. Reduction in apparent cohesion - cap (sat. soil for lab tests)
2. Decrease in ’
Groundwater level effects

D
Groundwater level effects

Case I

 '   w
Groundwater level effects

Case II

  D1  D  
 '     w 1  
          
  B 
Groundwater level effects

Case III

 ' 
Groundwater level effects

For total stress analysis:

 ' 
regardless of the case

(gw effects are implicit in cT and fT)
FS for BC

Allowable BC = qa

qult
qa 
FS
FS = function of    soil type
structure type
soil variability
uncertainty          extent of site characterization
BC of shallow foundations in practice
(per Mayne ‘97)

Undrained
Nc*    = 5.14 for strip footing
qult  Nc  su
*
= 6.14 for square or
circular footing

The value of su is taken as the ave. within a depth
= to 1B to 1.5B beneath the foundation base

 sin f '  OCR
su  1                0.8
(Mayne, 1980)
 'v 2
BC of shallow foundations in practice
(per Mayne ‘97)

Drained
1
qult   B   'N
*

2

N*    = fn (foundation
shape and f’)

Consider gw cases
(I, II, or III to determine ’)
BC of shallow foundations in practice
(per Mayne ‘97)

Sands
Perform drained analysis

Clays
Perform both
Problem formulation – BC design

1. Find B so that FS = 3

Get q
Get q ult (by BC analysis)
Set FS ratio and solve for B

Consider (drained vs. undrained) and methods
for obtaining OCR and f’ ---- CPT?
Problem formulation– BC design

2. Find B and D so that FS = 3

Get q
Get q ult (by BC analysis)            Determine this
for various D
Set FS ratio and solve for B          values…

Important too:
Foundation shape (cost and labor)