16.1_Bearing Capacity - Terzaghi

7/28/2019 16.1_Bearing Capacity - Terzaghi

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BC1

BEARING CAPACITY: (BC)

Recall the requirements for a satisfactory foundation:

1. Future influences (frost, shrink-swell clay, sinkholes, etc.)2. Bearing capacity failure (catastrophic, not very common in modern times)3. Excessive settlements (long term, still a too-frequent problem)

Bearing Capacity Design Criteria:

o Bearing Stress (qs) - the bearing stress actually appliedto the soil by a foundation, force per unit area (Q s/A).

o Allowable Bearing Stress (qa) - the bearing stress usedas a design limit after consideration of stability, failurecriteria, soil layering and variability, influence of otherstructures/footings, and risk tolerance - typically divide

the ultimate bearing capacity by a factor of safety (F.S.

3).o

Local Shear Bearing Capacity (qls) - the bearing stressat which local shear failure occurs, typically where thebearing stress vs. movement plot becomes significantlynonlinear.

o Ultimate Bearing Capacity (qu) - the bearing stress atwhich there is catastrophic movement, usually a generalshear failure

Factors Affecting Mode of BC Failure:

o Depth of embedment, Df

o Stiffness or relative density, %100xeeeeDminmax

maxr

=

o Geometry of foundation (B/L), shapeo Inclination or eccentricity of applied load

BC Failure Modes:

o General shear failure

(qu)- abrupt, sudden. Failure surfaceextends to ground surface(dense sand).

o Local shear failure (qls)- occurs slowly,with substantialsettlement. Failure surface does

DenStiff

Loose orSoft Soil

qs

qa

Settlement,

Bearing Stre

qls

FailureSurface

Qq

s

qu

FailureSurface

Q

qs

qu

qls


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not extend to ground surface. Progresses to general shear failure (medium compactedsand, clayey soil)


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o Punching shear failure (qps)- continuous punching failure andsettlement with gradual increase in qsdue to compaction (loose sands), morelikely to occur at depth.

o Estimate type of failurefrom geometry & Dr:

general shear failure, qu will

occur at = (4-10%) x B

local shear failure(or punching), qu will

occur at = (1525%) x B

(figure by Vesic, 1963)

Terzaghi Bearing Capacity (1943): B.C. still a real problem in Terzaghis era,

Prandtl B.C. (1920) for metals assumed weight forces small compared to material strength

o Depth of foundation width (i.e. Df B)

o Rough bottom, foundation does not slide

o homogeneous, semi-infinite, isotropic soil masso Mohr-Coulomb failure criteria, = c + tan , (usu. effective stress analysis w/ c & )

o General shear failure modeo Movement due only to shear, no settlemento Rigid foundation in comparison to soil stiffnesso Soil above bottom of footing acts as surcharge only and has no strengtho Applied load vertical, in compression, through footing centroid, no momento Radial shear zone, governed by passive pressureo Started with plane strain (strip footing), then extended to square & round footings

Radial Shear Zone

FailureSurface

Q

qs

qu?

qps

c

I

II

III

Df

=

45- /2 = D

f= q

Q

Passive Failure Zone

qs

W

PpPp

c

Superimpose effects of c, , q: qu

= qc

+ qq

+ q


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Terzaghi Bearing Capacity Equation: (basically conservative)

for general shear failure:

strip: ++= NB5.0NDcN0.1q qfcu

square: ++= NB4.0NDcN3.1q qfcu

circular:

++= NB3.0NDcN3.1qqfcu

bearing factors:)2/45(cos2

aN

2

2

q +=

=tan)2/75.0(ea ( in radians)

=

tan

1NN

q

c , Nc = 5.70 for = 0)4sin(4.01

tan)1N(2N

q

+

+ (Coduto)

(rigorous calculation for N in chart below or table on next page )

for local shear failure:

strip: ++= 'NB5.0'ND'Nc0.1q qfcu

square: ++= 'NB4.0'ND'Nc3.1q qfcu

circular: ++= 'NB3.0'ND'Nc3.1q qfcu

where: c)3/2(c = and use in table/chart to get N' bearing factors

or use = [ ]= tan)3/2(tan 1 to get N in above equations

B

Q

DfDf

Soil:

, c,

0.01

0.1

1

10

100

1000

0 10 20 30 40 50

Friction Angle, degrees

Bearing

CapacityFactor,

N

Local

Shear

Failure

GeneralShear

Failure

0.01

0.1

1

10

100

1000

0 10 20 30 40 50


Bearing

CapacityFactor,

N

Local

Shear

Failure

General

Shear

Failure

0.01

0.1

1

10

100

1000

0 10 20 30 40 50


Bearing

CapacityFactor,

N

Local

Shear

Failure

General

Shear

Failure

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16.1_Bearing Capacity - Terzaghi