Terzaghi bearing capacity

8/13/2019 Terzaghi bearing capacity

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Content

Bearing Capacity Concepts

Analysis for Shallow Foundations

2


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Bearing Capacity Failures

Modes of Soil Failure:

General shear failure

Local shear failure

Punching shear failure

3


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Terzaghi Bearing Capacity Formulas

4


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General Shear Failure

5


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Local Shear Failure

6


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Punching Shear Failure

7


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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

9


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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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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


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13


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

14


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15


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


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


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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18


Capacity Formula

calthe vertirespect toload with

iedf the appllination ois the inc

F

FF

i

qici

)(

1

901

2

2


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19

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

22

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

26

Factor of Safety


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27

Factor of Safety


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28

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.

29

Example 1


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30

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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32


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.

33

Example 3


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34


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.

35

Example 4


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36


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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38


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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39


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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40


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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41


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(

2


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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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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

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Terzaghi bearing capacity