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Lecture 3 Shallow Foundations: Ultimate Bearing Capacity

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lecture_03_shallow_foundation_capacity

Lecture 4 Ultimate Bearing Capacity

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lecture_03_shallow_foundation_capacity

Lecture 4 Shallow Foundations: Ultimate Bearing Capacity

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Types of Failure

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Relationship between Dr, Df/B & mode of failure

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토질역학 Review - 전단강도

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lecture_03_shallow_foundation_capacity

토질역학 Review - 전단강도

Ultimate Bearing Capacity: The load per unit area of the foundation at whichshear failure in soil occurs (Resistance > Load)

Design Criteria: Settlement(Expected settlement < Tolerable settlement)

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lecture_03_shallow_foundation_capacity

Lecture 4 Ultimate Bearing Capacity

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Lecture 4 Ultimate Bearing Capacity

qu

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lecture_03_shallow_foundation_capacity

Lecture 4 Ultimate Bearing Capacity

Lecture Outline

•Terzaghi’s Bearing Capacity Equation

•Modified Bearing Capacity Equation

•Shape, Depth, Inclination Factors

•Bearing Capacity in Clays (’=0)

•Bearing Capacity in Sands (c’=0)

•Estimation of Strength Parameters

•Eccentric Loads

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lecture_03_shallow_foundation_capacity

Terzaghi’s Bearing Capacity Theory

45-’/2

Shallow if Df ≤ B

A C

D EF

GH

IJ

3 Zones1. Triangular Zone: ACD2. Radial Shear Zone: ADF and CDE (DE and DF are arcs of a logarithmic spiral)3. Rankine Passive Zone: AFH and CEG

Another Assumption: = ’

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lecture_03_shallow_foundation_capacity

Terzaghi’s Bearing Capacity Theory

)(21' foundationstripBNqNNcq qcu

)(3.0'3.1 foundationcircularBNqNNcq qcu

)(4.0'3.1 foundationsquareBNqNNcq qcu

2(3 /4 '/2) tan '

2 '2cos 452

qeN

'cot1 qc NN

2

1 1 tan '2 cos '

prKN

Mathematically Exact Solutions

Non analytical solution

General shear failure mode

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lecture_03_shallow_foundation_capacity

Terzaghi’s Bearing Capacity Theory

)('21'''

32 foundationstripBNqNNcq qcu

)('3.0'''867.0 foundationcircularBNqNNcq qcu

)('4.0'''867.0 foundationsquareBNqNNcq qcu

Local shear failure mode

Nc’, Nq’, N’

Replace ’ in Nc’, Nq’, N’ with

'tan

32tan' 1

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lecture_03_shallow_foundation_capacity

Terzaghi’s Bearing Capacity Theory

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Modified Bearing Capacity EquationTerzaghi’s Assumption: = ’

New Assumption: = 45 + ’/2

'cot1 qc NN

'tan2

2'45tan eNq

q

q

q

N 2 N 1 tan ' Caquot and Kerisel (1953), Vesic (1973)

N N 1 tan 1.4 ' Meyerhof 1963

N 1.5 N 1 tan ' Hansen 1970

Mathematically Exact SolutionsNot analytical

solution

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Check page 139

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General Bearing Capacity Equation

idsqiqdqsqcicdcscu FFFBNFFFqNFFFNcq 21'

Shape FactorsFcs, Fqs, Fs

Depth FactorsFcd, Fqd, Fd

Inclination FactorsFci, Fqi, Fi

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