Shallow Foundations

Bearing Capacity

• The problems of soil mechanics can be

divided into two principal groups -

stability problems and elasticity

problems

- Karl Terzaghi, 1943

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)

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

• Chapter 6. Bearing Capacity Analysis

• 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 ( > 67%)

-general shear

Footings in Loose to Medium dense

(30%< < 67%) - Local Shear

Footings in Very Loose Sand ( < 30%)-

punching shear

rD

rD

rD

Bearing Capacity Formulas

zDucult sNq

Terzaghi Bearing Capacity Formulas

Terzaghi Bearing Capacity Formulas

BNNNcq qzDcult 5.0

For Square foundations:

For Continuous foundations:

BNNNcq qzDcult 4.03.1

For Circular foundations:

BNNNcq qzDcult 3.03.1

Terzaghi Bearing Capacity Factors

07.5 whenNc

)2/45(cos2 2

2

aNq

tan)360/75.0(expa

1

cos2

tan2

pKN

0tan

1

when

NN

q

c

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

See Extra Handout

Further Developments

Skempton (1951)

Meyerhof (1953)

Brinch Hanson (1961)

De Beer and Ladanyi (1961)

Meyerhof (1963)

Brinch Hanson (1970)

Vesic (1973, 1975)

Vesic (1973, 1975) Formulas

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

gbidsBNgbidsNgbidsNcq qqqqqqzDccccccult 5.0

Vesic Formula Shape Factors

c

q

cN

N

L

Bs 1

tan1

L

Bsq

L

Bs 4.01

Vesic Formula Depth Factors

B

Dk 1tan

2)sin1(tan21 kdq

1d

kdc 4.01

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

Groundwater Table Effect

Groundwater Table Effect;

Case I

1. Modify ′zD

2. Calculate ′ as follows:

wb

Groundwater Table Effect;

Case II

1. No change in ′zD

2. Calculate ′ as follows:

B

DDww 1

Groundwater Table Effect;

Case III

1. No change in ′zD

2. No change in ′

Allowable Bearing Capacity

F

qq ult

a

….. Allowable Bearing Capacity

F …. Factor of safety

aq

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,

Intermediate soils that where partially

drained conditions exist, engineers have

varying opinions; Undrained Strength can

be used but it will be conservative!

and c

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