Bearing Capacity of Shallow Foundations

Ch. 6.

B.C. Failures

Local shear

Intermediate case+/- gradual failure

PunchingLoose sands,weak clays (dr.)

F. surf. not definedGradual failure

General shearDense soils,Rock, NC clays

Defined failure surf.Fast failure

B.C. Failures

(Vesic, 1963 and 1973)

Deep foundations

Sand

Circular foundations

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

BC Factor

Bearing Capacity Theory

LIMIT EQUILIBRIUM

Ultimate bearing capacity = qult = ?

(Bearing press. required to cause a BC failure)

Moments about point A

2)(

2)(

BBbBBbs

BBbqM zDuultA

zDucult sNq

zDuult sq 2

Terzaghi’s Bearing Capacity Theory

Assumptions

D < or = B

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

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).

BNNNcq qzDcult '5.0''

BNNNcq qzDcult '4.0''3.1

BNNNcq qzDcult '3.0''3.1

From model tests, he expanded the theory to:

Nc = cohesion factor

Nq = surcharge factor

Nγ = self wt factor

Terzaghi’s Bearing Capacity Theory

= fn (’) See table 6.1 for values

Groundwater level effects

groundwater

1. Reduction in apparent cohesion - cap (sat. soil for lab tests)

2. Decrease in ’

Shear strength

affects

by

Groundwater level effects

D

Groundwater level effects

Case I

w '

Groundwater level effects

B

DDw

11'

Case II

Groundwater level effects

Case III

'

Groundwater level effects

For total stress analysis:

'

regardless of the case

(gw effects are implicit in cT and T)

FS for BC

Allowable BC = qa

FS

qq ult

a

FS = function of soil type

extent of site characterization

soil variability

structure type

uncertainty

BC of shallow foundations in practice (per Mayne ‘97)

Undrained

ucult sNq *

The value of su is taken as the ave. within a depth

= to 1B to 1.5B beneath the foundation base

Nc* = 5.14 for strip footing

= 6.14 for square or circular footing

8.0'sin2

1

'OCR

s

v

u

(Mayne, 1980)

Drained

*'2

1 NBqult

Consider gw cases (I, II, or III to determine ’)

N* = fn (foundation

shape and ’)

BC of shallow foundations in practice (per Mayne ‘97)

SandsPerform drained analysis

ClaysPerform both

BC of shallow foundations in practice (per Mayne ‘97)

1. Find B so that FS = 3

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

Problem formulation – BC design

Consider (drained vs. undrained) and methods for obtaining OCR and ’ ---- CPT?

2. Find B and D so that FS = 3

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

Problem formulation– BC design

Determine this for various D values…

Important too:

Foundation shape (cost and labor)

Moment loads and eccentricity

Weight of the foundations