# Shallow Foundations Bearing Capacity

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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 Wrote “Erdbaumechanick” in 1925 Taught at MIT ( ) 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

Bearing Capacity Formulas

Terzaghi Bearing Capacity Formulas

Terzaghi Bearing Capacity Formulas
For Continuous foundations: For Square foundations: For Circular foundations:

Terzaghi Bearing Capacity Factors

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

Further Developments Skempton (1951) Meyerhof (1953)
Brinch Hanson (1961) De Beer and Ladanyi (1961) Meyerhof (1963) Brinch Hanson (1970) Vesic (1973, 1975) See Extra Handout

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 and 6.26 Ground Inclination Factors…. Eq and 6.28 Bearing Capacity Factors …. Eq. 6.29, 6.30 and 6.31

Vesic Formula Shape Factors

Vesic Formula Depth Factors

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
Modify ′zD Calculate ′ as follows:

Groundwater Table Effect; Case II
No change in ′zD Calculate ′ as follows:

Groundwater Table Effect; Case III
No change in ′zD No change in ′

Allowable Bearing Capacity
F …. Factor of safety

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!

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