1

Shallow Foundations

- Bearing Capacity

Reference:

Foundation Design, Principles and Practices,

Donald P. Coduto, Part B, Chapter 6

2

Shallow Foundations

Bearing Capacity

• The problems of soil mechanics can be

divided into two principal groups

- stability problems

and

- elasticity problems

- Karl Terzaghi, 1943

3

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)

4

Karl Terzaghi at Harvard, 1940

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Bearing Capacity Failure

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Transcosna Grain Elevator Canada (Oct. 18, 1913)

West side of foundation sank 24-ft

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Stability Problem

Bearing Capacity Failure

• How do we estimate the maximum bearing

pressure that the soil can withstand before

failure occurs?

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Bearing Capacity Failures

Types/Modes of Failure

general shear failure

local shear failure

punching shear failure

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General Shear Failure

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Punching Shear Failure

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Local Shear Failure

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Model Tests by Vesic (1973)

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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

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Bearing Capacity Formulas- Consider a continuous footing and assume;

- Footing experiences a bearing capacity failure,

- Failure occurs along a circular shear surface,

- Soil is an undrained clay with a shear strength su-Neglect the shear strength between ground surface and a Depth D

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Bearing Capacity Formulas

Considering a slice of the foundation of length b and taking

moments about Point A

)2/())(()2/()( BbBBbBsBbBqM zDuultA

zDuult sq 2

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Bearing Capacity Formulas

zDucult sNq

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Terzaghi Bearing Capacity Formulas

D B

no sliding between footing and soil

soil is a homogeneous semi-infinite mass

shear strength of soil s = c' + σ' tan φ'

general shear failure occurs

no consolidation of soil occurs

settlement is due to the shearing and lateral movement of soil

footing is very rigid compared to soil

soil to depth D has no shear strength, and serves as surcharge

applied load is compressive applied vertically to the centroid of foundation

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Terzaghi Bearing Capacity FormulasTerzaghi considered three zones in the soil :

* Immediately beneath the foundation, a wedge zone that

remains intact and moves downward with the foundation

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Terzaghi Bearing Capacity Formulas* A radial shear zone extends from each side of the wedge, where

the shape of the shear planes is considered to be logarithmic

spirals

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Terzaghi Bearing Capacity Formulas* Outer portion, the linear shear zone in which the soil shears

along planar surfaces.

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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

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Terzaghi Bearing Capacity Factors

07.5 whenNc

0tan

1

when

NN

q

c

)2/45(cos2 2

2

aNq

tan)360/75.0(expa

1

cos2

tan2

pKN

)4sin(4.01

tan)1(2

qNN

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Bearing Capacity Factors

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Example 6.1

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Example 6.2

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Further Developments

Skempton (1951)

Meyerhof (1953)

Brinch Hanson (1961)

De Beer and Ladanyi (1961)

Meyerhof (1963)

Brinch Hanson (1970)

Vesic (1973, 1975)

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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

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Vesic Formula Shape Factors

c

q

cN

N

L

Bs 1

tan1

L

Bsq

L

Bs 4.01

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Vesic Formula Load Inclination Factors

0'

1

c

cNcA

Vmi

0

'tan

1'

m

qcA

P

Vi

0

'tan

1

1

'

m

cAP

Vi

LB

LBm

/1

/2

For loads inclined in B direction

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Vesic Formula Depth Factors

B

Dk 1tan

2)sin1(tan21 kdq

1d

kdc 4.01

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Groundwater Table Effect

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Groundwater Table Effect;

Case I

1. Modify ′zD

2. Calculate ′ as follows:

wb

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Groundwater Table Effect;

Case II

1. No change in ′zD

2. Calculate ′ as follows:

B

DDww 1

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Groundwater Table Effect;

Case III

1. No change in ′zD

2. No change in ′

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Example 6.3

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Allowable Bearing Capacity

F

qq ulta

….. Allowable Bearing Capacity

F …. Factor of safety

aq

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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

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Factor of Safety

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Factor of Safety

• Shear strength data are normally interpreted

conservatively, so the design values of c and ø implicitly

contain another factor of safety.

• Service loads are probably less than the design loads.

• Settlement, not bearing capacity, often controls the

final design, so the footing will likely be larger than that

required to satisfy bearing capacity criteria.

• Spread footings are commonly built somewhat larger

than the plan dimensions.

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Minimum Factor of Safety

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BEARING CAPACITY ON LAYERED SOILS

Three primary ways

1. Evaluate the bearing capacity using the lowest

values of c‘ and ø’ in the zone between the bottom

of the foundation and a depth B below the bottom.

2. Use weighted average values of of c‘ and ø’

based on the relative thicknesses of each stratum.

3. Consider a series of trial failure surfaces beneath

the footing and evaluate the stresses on each

surface using methods similar to those employed in

slope stability analyses.

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Example 6-5

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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

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Accuracy; Bearing Capacity Analysis