shallow foundations bearing capacity the problems of soil mechanics can be divided into two...
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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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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 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 Shear Failure
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Punching 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
zDucult sNq
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Terzaghi Bearing Capacity Formulas
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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
)2/45(cos2 2
2
aNq
tan)360/75.0(expa
1cos2
tan2
pKN
0tan
1
whenN
N qc
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Bearing Capacity Factors
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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
gbidsBNgbidsNgbidsNcq qqqqqqzDccccccult 5.0
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Vesic Formula Shape Factors
c
qc N
N
L
Bs 1
tan1
L
Bsq
L
Bs 4.01
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Vesic Formula Depth Factors
B
Dk 1tan
2)sin1(tan21 kdq
1d
kdc 4.01
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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
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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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Allowable Bearing Capacity
F
qq ult
a
….. 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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Minimum Factor of Safety
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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!
and c
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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
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Bearing Capacity Spreadsheet
Can be downloaded from http://www.prenhall.com/coduto
See Appendix B (page 848) for further instructions