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 ProblemBearing 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

1cos2

tan2

pKN

0tan

1

whenN

N qc

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

qc N

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