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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

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Shallow Foundations Bearing Capacity

  • The problems of soil mechanics can be divided into two principal groups - stability problems and elasticity problems

    - Karl Terzaghi, 1943


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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)




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Transcosna Grain Elevator Canada (Oct. 18, 1913)

West side of foundation sank 24-ft


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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?


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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 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




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Terzaghi Bearing Capacity Formulas

For Continuous foundations:

For Square foundations:

For Circular foundations:




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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


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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)


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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


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Vesic Formula Shape Factors


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Vesic Formula Depth Factors


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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



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Groundwater Table Effect; Case I

  • Modify′zD

  • Calculate ′ as follows:


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Groundwater Table Effect; Case II

  • No change in′zD

  • Calculate ′ as follows:


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Groundwater Table Effect; Case III

  • No change in′zD

  • No change in ′


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Allowable Bearing Capacity

  • ….. Allowable Bearing Capacity

  • F…. Factor of safety


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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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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!


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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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Bearing Capacity Spreadsheet

  • Can be downloaded from http://www.prenhall.com/coduto

  • See Appendix B (page 848) for further instructions


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