bearingcapacity.ppt

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 +/- gradual failure

Punching Loose sands, weak clays (dr.) F. surf. not defined Gradual failure

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)

Moments about point A  B  B M A  (qult  Bb )   ( su  Bb )B    zD  Bb   2 2

qult  2    su   zD

qult  N c su   zD

BC Factor

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 qult  Nc  su *

Nc*

= 5.14 for strip footing = 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

su 1 0.8  sin f '  OCR  'v 2

(Mayne, 1980)

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) Set FS ratio and solve for B Important too: Foundation shape (cost and labor) Moment loads and eccentricity Weight of the foundations

Determine this for various D values…