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10/23/08
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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected]
Lecture 12 – Bearing Capacity
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Lecture Goals
Students will be able to: recognize types of shallow foundations, examine the limits of foundation settlement, estimate the ultimate bearing capacity of
shallow foundations, and estimate the influence of groundwater on the
bearing capacity of shallow foundations.
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ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Reading List
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Das (2006). Principles of Geotechnical Engineering. 6th Edition Section Title 15.1 Ultimate Soil-Bearing Capacity for Shallow Foundations 15.2 Terzaghi’s Ultimate Bearing Capacity Equation 15.3 Effect of Groundwater Table 15.4 Factor of Safety 15.5 General Bearing Capacity Equation
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ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Shallow Foundations Purpose
Redistribute structural loads over an area
Type Strip footing Pad footing Combined footing Raft or mat foundation
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Rowe (2001)
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Foundation Settlement Limits on uniform
displacement Concern for buried
infrastructure and utilities Limits on non-uniform
displacement Structural serviceability
concerns Typically Controls Design
Total settlement 25mm to 50mm
Differential settlement Δ / span length = 1/500 to
1/150
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Handy and Spangler (2007)
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Foundation Settlement Calculations Cohesionless Soil
Elastic deformation Pore pressures can
dissipate SPT
Cohesive Soil Elastic deformation Pore pressure, deformation
at constant volume Consolidation methods
Settlement Analysis One-dimensional Three-dimensional
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ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Bearing Capacity Limit State
Capacity and stability Failure Mechanisms
General Dense sand, stiff clay UU & CU conditions
Local Transitional mode
Punching Compressible soil Loose sand, sensitive
clay CD conditions
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Handy and Spangler (2007)
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Bearing Capacity – Terzaghi Considerations
Strip Footing Infinite soil layer depth Uniform soil strength
properties Extended Applications
Square footing
Circular footing
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qu = 1.3 ′c Nc + qNq + 0.4 ′γ BNγ
qu = 1.3 ′c Nc + qNq + 0.3 ′γ BNγ
qu = cohesion + surcharge + density
qu = ′c Nc + qNq +12
′γ BNγ
Das (2006)
qu = cohesion + depth + width
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Bearing Capacity Factors Smooth Base
Cohesion Exact
Surcharge Exact
Soil density Vesic (1975)
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Nq = eπ tan ′φ tan2 45 + ′φ
2⎛⎝⎜
⎞⎠⎟
Nc = Nq −1( )cot ′φ
Nγ = 2 Nq +1( ) tan ′φ( )
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ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Bearing Capacity Factors Rough Base
Cohesion Exact
Surcharge Exact
Soil density Bowles (1968)
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Nq = e1.5π − ′φ( ) tan ′φ 2cos2 45 + ′φ
2⎛⎝⎜
⎞⎠⎟
⎡⎣⎢
⎤⎦⎥
−1
Nc = Nq −1( )cot ′φ
Nγ = 1.1 Nq −1( ) tan 1.3 ′φ( )
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Bearing Capacity Factors General shear
failure
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ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
General Bearing Capacity – Meyerhof’s Factors
Additional Considerations Footing shape Footing depth Footing inclination
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qu = λcs λcd λci ′c Nc + λqs λqd λqi q Nq +12λγ s λγ d λγ i ′γ BNγ
Das (2006)
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ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Bearing Capacity – Undrained Conditions
Terzaghi ϕ′ = 0° τ = su
Nϒ = 0 Nq = 1 Nc = 5.70
Meyerhof ϕ′ = 0° τ = su
Nϒ = 0 Nq = 1 Nc = 5.14 λqs = λϒs = 1 λqd = λϒd = 1
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qu = ′c Nc + qNq +12
′γ BNγ
qu = 5.70su + q
qu = λcs λcd λci ′c Nc + λqs λqd λqi q Nq +12λγ s λγ d λγ i ′γ BNγ
qu = 5.14λcs λcd su +q
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Factor of Safety – Bearing Capacity Gross Allowable
Capacity FS = 2.5 or 3.0
Net Allowable Capacity
Design Capacity
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qall =quFS
qnet = qu − q = qu − ′γ Df
qdesign =qnetFS
Das (2006)
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Design Considerations Unequal Surcharge
Use lesser value High Water Table
More complex loading
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qu = ′c Nc + qNq +12
′γ BNγ
Handy and Spangler (2007)
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ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Design Considerations Footing on a Slope
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Handy and Spangler (2007)
ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
Design Considerations Non-Uniform Soil
Properties Strength variation with
depth Fissured clays Layered soils
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ENGI 6723 Geotechnical Engineering II – Lecture 12 © 2008 S. Kenny, Ph.D., P.Eng.
References Das, B.M. (2006). Principles of Geotechnical
Engineering, 6th Edition. ISBN 0534551440 Handy, R.L. and Spangler, M.G. (2007).
Geotechnical Engineering: Soil Foundation Principles and Practice, 5th Edition, ISBN 0071481206
Rowe, R.K. (2001). Geotechnical and Geoenvironmental Engineering Handbook. ISBN 0792386132
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