terzaghi bearing capacity
TRANSCRIPT
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Content
Bearing Capacity Concepts
Analysis for Shallow Foundations
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Bearing Capacity Failures
Modes of Soil Failure:
General shear failure
Local shear failure
Punching shear failure
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Terzaghi Bearing Capacity Formulas
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General Shear Failure
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Local Shear Failure
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Punching Shear Failure
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Model Tests - Vesic (1973)
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General Guidelines
Footings on clays - general shear
Footings on dense sands (> 70%) - general
shear
Footings on loose to medium dense - local
shear
Footings on very loose sand (< 35%) -
punching shear
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Terzaghis Basic Assumptions
D B
No sliding between footing and soil
Soil is a homogeneous semi-infinite mass
General shear failure
Footing is very rigid compared to soil
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Terzaghi Bearing Capacity Formulas
General Shear Failure
BNqNcNq qcult 5.0
For Square foundations:
For Continuous foundations:
BNqNcNq qcult 4.03.1
For Circular foundations:
BNqNcNq qcult 3.03.1
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Terzaghi Bearing Capacity Factors
General Shear Failure
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Terzaghi Bearing Capacity Formulas
Local Shear Failure
cc
3
2
)tan3
2(tan
tan3
2tan
1
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Modified General Ultimate Bearing
Capacity Formula
ids
qiqdqsq
cicdcscult
FFFBN
FFFqN
FFFcNq
5.0
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15
Modified General Ultimate Bearing
Capacity Formula
1
4.01
tan1
1
L
B
L
BF
L
BF
N
N
L
BF
s
qs
c
q
cs
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16
Modified General Ultimate Bearing
Capacity Formula
1
1
tan)sin1(21
4.01
2
B
D
F
B
DF
B
DF
f
d
f
qd
f
cd
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17
Modified General Ultimate Bearing
Capacity Formula
1
1
tantan)sin1(21
tan4.01
12
1
B
D
F
B
DF
B
DF
f
d
f
qd
f
cd
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Modified General Ultimate Bearing
Capacity Formula
calthe vertirespect toload with
iedf the appllination ois the inc
F
FF
i
qici
)(
1
901
2
2
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Effect of GWT Level
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Case I: 0 D1D
f
'21 DDq
'
20
Effect of GWT Level
wsat
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Case II: 0 d B
fDq
B
d'
21
Effect of GWT Level
wsat
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Case III: d > B
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Effect of GWT Level
fDq
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Selection of Soil Strength
Parameters
Use saturated strength parameters
Use undrained strength in clays (cu)
Use drained strength in sands
For intermediate soils with partially drained
conditions, undrained shear strength can be
used but it will be conservative
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Other Approaching Methods
Skempton (1951)
Meyerhof (1953, 1963)
De Beer and Ladanyi (1961)
Brinch Hanson (1961, 1970)
Vesic(1973, 1975) Others
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Factor of Safety
Depends on:
Type of soil
Level of uncertainty in soil strength
Importance of structure
Consequences of failure
Likelihood of design load occurrence
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Gross Allowable Bearing Capacity
Net Allowable Bearing Capacity
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Factor of Safety
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Factor of Safety
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Design Factor of Safety
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Use Terzaghis formula to determine the gross
allowable load for the square footing shown
below at a general shear failure condition with
no GWT effect. Take Nc = 17.69, Nq = 7.44, N =3.64, and FS= 3.0.
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Example 1
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Example 1 - Solution
lbAqQ
ftlbF
qq
ftlb
BNqNNcq
allall
S
ultall
qcult
28.41041)4)(4)(08.2565(
/08.25653
24.7659
/24.7659
)64.3)(4)(110(4.0)44.7)(110)(3()69.17)(200(3.1
4.0'3.1
2
2
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Redo the previuos example under a local shear
failure condition with no GWT effect. Use
Terzaghisformula. Take Nc= 11.85, Nq= 3.88, N= 1.12, and FS= 3.0.
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Example 2
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Example 2 - Solution
lbAqQ
ftlbF
qq
ftlb
BNqNNcq
ftlbcc
allall
S
ultall
qcult
72.18834)4)(4)(17.1177(
/17.11773
52.3531
/52.3531
)12.1)(4)(110(4.0)88.3)(110)(3()85.11)(200)(3
2(3.1
4.0'3.1
64.13))20tan(
3
2(tan)'tan
3
2(tan'
/)200(3
2'
3
2'
2
2
11
2
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Refer to the previous example to determine the
net allowable load. Use Terzaghisformula. Take
FS= 3.0.
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Example 3
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Example 3 - Solution
lbAqQ
ftlbF
qq
ftlb
qqq
netallnetall
S
netnetall
ultnet
72.17074)4)(4)(17.1067(
/17.10673
52.3201
/52.3201
)110)(3(52.3531
)()(
2
)(
2
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Determine the breadth of the square footing
shown below using Terzaghis formula to
withstand a gross mass of 30 tons with no GWT
level effects. Nc = 57.75, Nq = 41.44, N = 45.41,and FS= 3.0.
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Example 4
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Example 4 - Solution
cmB
BforSolving
BB
B
BNqNNcq
BAQq
kNFQQ
mkN
qcult
ultult
Sallult
50.91
/90.88268.32914.752
)41.45)()(15.18(4.0)44.41)(15.18)(1()75.57)(0(3.1
4.0'3.1
/90.882/
90.882)1000/()3)(81.9)(30000(
/15.18)1000/()81.9)(1850(
2
2
3
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Determine the required breadth of a square
footing using the general bearing capacity
formula to withstand a gross load of 150 kN at adepth of 0.7 m with no GWT level effects. The
applied load is inclined at angle of 20 to the
vertical. c= 0, = 30, = 18 kN/m3, Nq = 18.40,
N = 22.40, and FS= 3.0.
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Example 5
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Example 5 - Solution
60.04.014.01
58.130tan1'tan1
5.0
'
B
B
L
BF
B
B
L
BF
FFFBN
FFFqN
FFFNcq
s
qs
ids
qiqdqsq
cicdcscult
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Example 5 - Solution
1
1
2021.0
1
30tan)30sin1(7.0
21
'tan)'sin1(21
2
2
B
D
F
B
B
B
DF
f
d
f
qd
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Example 5 - Solution
2
22
22
/450/
450)3)(150(
111.030
2011
605.0
90
201
90
1
BAQq
kNFQQ
F
FF
ultult
Sallult
i
qici
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Example 5 - Solution
OKB
D
cmB
BforSolving
BBB
B
Bq
f
ult
1282.1
7.0
20.128
/45044.13)2021.0
1)(62.221(
)111.0)(1)(60.0)(4.22)()(18)(5.0(
)605.0)(2021.0
1)(58.1)(4.18)(18)(7.0(
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Determine the safe gross vertical loading for the
square footing shown below using Terzaghis
formula. Take Nq = 23.18, N = 22.02, and FS= 3.0.
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Example 6
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Example 6 - Solution
tonskNAqQ
mkNFqq
mkNq
mkN
mkN
DDq
BNqNNcq
allall
S
ultall
ult
qcult
59.1913.192)2.1)(2.1)(43.133(
/43.133328.400
/28.400)02.22)(2.1)(69.9(4.0)18.23)(85.12(
/69.981.95.19'
/85.12)81.95.19)(5.0()16)(5.0(
'
4.0'3.1
3
3
3
3
21