CE 632 Bearing Capacity PPT

CE-632CE 632Foundation Analysis and DesignDesign

Ultimate Bearing CapacityThe load per unit area of the foundation at which shear failure in soil

i ll d th lti t b i it

Ultimate Bearing Capacity

1

occurs is called the ultimate bearing capacity.

Foundation Analysis and Design: Dr. Amit Prashant

Principal Modes of Failure:Principal Modes of Failure:

General Shear Failure: Load / AreaLoad / Areaq

men

t qu

Set

tle

Sudden or catastrophic failureWell defined failure surfaceWell defined failure surfaceBulging on the ground surface adjacent to foundationCommon failure mode in dense sand

2



Local Shear Failure: Load / Areaqq

qu1

ttlem

ent

qu

Set

Common in sand or clay with medium compactionSignificant settlement upon loadingFailure surface first develops right below the foundation and then p gslowly extends outwards with load incrementsFoundation movement shows sudden jerks first (at qu1) and then after a considerable amount of movement the slip surface may

h th d

3

reach the ground.A small amount of bulging may occur next to the foundation.



Punching Failure:Load / Area

q

q

qu1

ttlem

ent qu

Set

Common in fairly loose sand or soft clay Failure surface does not extends beyond the zone right beneath the foundationExtensive settlement with a wedge shaped soil zone in elastic equilibrium beneath the foundation. Vertical shear occurs around the edges of foundation.Aft hi f il l d ttl t ti t l

4

After reaching failure load-settlement curve continues at some slope and mostly linearly.


Principal Modes of Failure:Principal Modes of Failure:Relative density of sand, Dr

0 0 5 1 0Vesic (1973)

Local General shearn, D

f/B* 00 0.5 1.0

* 2BLB =shear

unda

tion B

B L=

+

Circular Foundation

pth

of fo

u

5

Punchingativ

e de

p

Long Rectangular Foundation

Punching shear

Rel

a

5

10


Terzaghi’s Bearing Capacity Theoryg g p y yB

Eff ti b d

Strip Footing

j k

Rough Foundation Surface

Df

neglected Effective overburdenq = γ’.Df

a b

qu

φ’ φ’45−φ’/2 45−φ’/2

Shear

g i

c’- φ’ soilB

I

II IIIII III

Assumption

Planes de fc φ soilII

Assumption L/B ratio is large plain strain problemDf ≤ BShear resistance of soil for D depth is neglected

6

Shear resistance of soil for Df depth is neglectedGeneral shear failureShear strength is governed by Mohr-Coulomb Criterion


Terzaghi’s Bearing Capacity TheoryTerzaghi s Bearing Capacity TheoryB

21. 2. 2. .sin tan4u p aq B P C Bφ γ φ′ ′ ′= + −

21. 2. . .sin tan4u pq B P B c Bφ γ φ′ ′ ′ ′= + −

qu

4p

Iφ’ φ’

ab

C = B/2 P P P P= + +I

dφ’ φ’

Ca= B/2cosφ’

Ca B.tanφ’Ppγ = due to only self weight of soil

in shear zone

p p pc pqP P P Pγ + +

dφ φPp Pp

in shear zone

Ppc = due to soil cohesion only (soil is weightless)

7

Ppq = due to surcharge only


Terzaghi’s Bearing Capacity TheoryTerzaghi s Bearing Capacity Theory

⎛ ⎞

Weight term Cohesion term

( )21. 2. tan 2. . .sin 2.4u p pc pqq B P B P B c Pγ γ φ φ⎛ ⎞′ ′ ′ ′= − + + +⎜ ⎟

⎝ ⎠SSurcharge term

( ). 0.5 .B B Nγγ ′ . . cB c N . . qB q N

. . 0.5 .u c qq c N q N B Nγγ ′= + +Terzaghi’s bearing capacity equation

1 PK⎡ ⎤2aeN

Terzaghi’s bearing capacity factors

2

1 tan 12 cos

PKN γ

γ φφ

⎡ ⎤′= −⎢ ⎥′⎣ ⎦ 22cos 45

2

qNφ

=′⎛ ⎞+⎜ ⎟

⎝ ⎠⎛ ⎞

8

3 in rad. tan4 2

a π φ φ′⎛ ⎞ ′= −⎜ ⎟

⎝ ⎠( )1 cotc qN N φ′= −


9


Terzaghi’s Bearing Capacity TheoryTerzaghi s Bearing Capacity Theory

Local Shear Failure:Local Shear Failure:Modify the strength parameters such as: 2

3mc c′ ′= 1 2tan tan3mφ φ− ⎛ ⎞′ ′= ⎜ ⎟

⎝ ⎠2 . . 0.5 .3u c qq c N q N B Nγγ′ ′ ′ ′ ′= + +

⎝ ⎠

Square and circular footing:Square and circular footing:

1.3 . . 0.4 .u c qq c N q N B Nγγ′ ′ ′= + + For square

1.3 . . 0.3 .u c qq c N q N B Nγγ′ ′ ′= + + For circular

10


Terzaghi’s Bearing Capacity TheoryTerzaghi s Bearing Capacity TheoryEffect of water table:

Dw

Case I: Dw ≤ Df

Surcharge, ( ). w f wq D D Dγ γ ′= + −

DfCase II: Df ≤ Dw ≤ (Df + B)

Surcharge, . Fq Dγ=

BIn bearing capacity equation replace γ by-

( )fD D−⎛ ⎞B

Li it f i fl

( )w fD DB

γ γ γ γ⎛ ⎞

′ ′= + −⎜ ⎟⎝ ⎠

Case III: Dw > (Df + B)Limit of influenceNo influence of water table.

Another recommendation for Case II:d D D=

11

( ) ( )22 22 w

w sat wdH d H dH H

γγ γ′

= + + −w w fd D D= −

( )0.5 tan 45 2H B φ′= +Rupture depth:


Skempton’s Bearing Capacity Analysis for p g p y ycohesive Soils

~ For saturated cohesive soil, φ‘ = 0 1, and 0qN Nγ= =

For strip footing: 5 1 0.2 with limit of 7.5fc c

DN N

B⎛ ⎞

= + ≤⎜ ⎟⎝ ⎠⎝ ⎠

For square/circular footing:

6 1 0.2 with limit of 9.0fc c

DN N

B⎛ ⎞

= + ≤⎜ ⎟⎝ ⎠g

For rectangular footing: 5 1 0.2 1 0.2 for 2.5fc f

D BN DB L

⎛ ⎞⎛ ⎞= + + ≤⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

7.5 1 0.2 for 2.5c fBN DL

⎛ ⎞= + >⎜ ⎟⎝ ⎠

.u cq c N q= +q c N

12

Net ultimate bearing capacity, .nu u fq q Dγ= − .u cq c N=


Effective Area Method for Eccentric LoadingEffective Area Method for Eccentric Loading

Dy

x

Me =

In case of Moment loading

B

Dfx

VF

xMeBB’=B-2ey

AF=B’L’x

yV

eF

=

I f H i t l F t

eyex

L’=L-2ey

In case of Horizontal Force at some height but the column is

centered on the foundationx

.y Hx FHM F d=

M F d=

13

.x Hy FHM F d=


General Bearing Capacity Equation: (Meyerhof, 1963)

0 5q c N s d i q N s d i B N s d iγ= + +. . . . . . . . 0.5 . . . . .u c c c c q q q qq c N s d i q N s d i B N s d iγ γ γ γγ+ +

Shape f t

Depth factor

inclination f t

Empirical correction factor factor factor

pfactors

2 φφ ′′⎛ ⎞ ( )1N N φ′ ( ) ( )1 1 4N N φ′2 .tantan 45 .2qN eπ φφ ′⎛ ⎞= +⎜ ⎟

⎝ ⎠( )1 cotc qN N φ′= − ( ) ( )1 tan 1.4qN Nγ φ′= −

( ) ( )1.5 1 tanqN Nγ φ′= −[By Hansen(1970):

( ) ( )2 1 tanqN Nγ φ′= +

( ) ( )qγ φ

[By Vesic(1973):

[ y ( )

. . . . . . . . . . . . 0.5 . . . . . . .u c c c c c c q q q q q qq c N s d i g b q N s d i g b B N s d i g bγ γ γ γ γ γγ= + +

14Ground factor Base factor


15


M h f’ C i FMeyerhof’s Correction Factors:

2B φ′⎛ ⎞ B φ′⎛ ⎞for 10oφ′ ≥

Shape Factors

21 0.2 tan 452c

BsL

φ⎛ ⎞= + +⎜ ⎟⎝ ⎠

21 0.1 tan 452q

Bs sLγ

φ′⎛ ⎞= = + +⎜ ⎟⎝ ⎠

φ

for lower valueφ′

1qs sγ= =for lower valueφ

Depth Factors 1 0.2 tan 45

2f

c

Dd

Lφ′⎛ ⎞= + +⎜ ⎟

⎝ ⎠ 1 0.1 tan 452

fq

Dd d

Lγφ′⎛ ⎞= = + +⎜ ⎟

⎝ ⎠

for 10oφ′ ≥

2L ⎝ ⎠

1d dγ= =for lower valueφ′

1qd dγ

Inclination 2

1o

i i β⎛ ⎞⎜ ⎟

2

1i β⎛ ⎞⎜ ⎟

16

Factors 190c qi i β

= = −⎜ ⎟⎝ ⎠

1iγβφ

= −⎜ ⎟′⎝ ⎠


Hansen’s Correction Factors:( ) 1/2

⎡ ⎤1 for 0

2 .H

cFiBL c

φ′= − =′

( ) 1/211 1 for 0

2 .H

cu

Fi

BL sφ

⎡ ⎤−′= + >⎢ ⎥

⎣ ⎦Inclination Factors

50 5F⎡ ⎤ 5

0 7F⎡ ⎤

For 0φ = For 0φ >

0.51. .cot

Hq

V

FiF BL c φ

⎡ ⎤= −⎢ ⎥′ ′+⎣ ⎦

0.71. .cot

H

V

FiF BL cγ φ

⎡ ⎤= −⎢ ⎥′ ′+⎣ ⎦

For 0

0.4 for fc f

Dd D B

B

φ =

⎡= ≤⎢

⎢

For 0

1 0.4 for fc f

Dd D B

B

φ >

⎡= + ≤⎢

⎢

Depth Factors

10.4 tan for fc f

Dd D B

B−

⎢⎢

= >⎢⎣11 0.4 tan for f

c f

Dd D B

B−

⎢⎢

= + >⎢⎣

For D B< For D B>For fD B< For fD B>1dγ =( )21 2 tan . 1 sin f

q

Dd

Bφ φ

⎛ ⎞′ ′= + − ⎜ ⎟

⎝ ⎠( )2 11 2 tan . 1 sin tan f

q

Dd

Bφ φ − ⎛ ⎞

′ ′= + − ⎜ ⎟⎝ ⎠

Shape Factors 0.2 . for 0c c

Bs iL

φ′= =

( )1 i φ′

( )0.2 1 2 . for 0c cBs iL

φ′= − >

( )1 0 4( )1 . sinq qs i B L φ′= + ( )1 0.4 .s i B Lγ γ= −

Hansen’s Recommendation for cohesive saturated soil, φ'=0 ( ). . 1u c c c cq c N s d i q= + + + +


Notes:Notes:

1. Notice use of “effective” base dimensions B‘, L‘ by H b t t b V iHansen but not by Vesic.

2. The values are consistent with a vertical load or a vertical load accompanied by a horizontal load HB.

3. With a vertical load and a3. With a vertical load and a load HL (and either HB=0 or HB>0) you may have to compute two sets of shape and depth factors s sand depth factors si,B, si,Land di,B, di,L. For i,Lsubscripts use ratio L‘/B‘ or D/L‘.

4. Compute qu independently by using (siB, diB) and (siL, diL) and use min value for

18

design.


Notes:Notes:

1. Use Hi as either HB or HL, or both if HL>0.

2. Hansen (1970) did not give an ic for φ>0. The value given here is from Hansen (1961) and also used by Vesic.

3. Variable ca = base adhesion, on the order of 0.6 to 1.0 x base cohesion.

4. Refer to sketch on next slide for identification ofslide for identification of angles η and β, footing depth D, location of Hi (parallel and at top of base slab; usually also produces eccentricity)also produces eccentricity). Especially notice V = force normal to base and is not the resultant R from combining V

19

and Hi..


20


N tNote:

1. When φ=0 (and β≠0) use Nγ = -2sin(±β) in Nγ term.γ ( β) γ

2. Compute m = mB when Hi = HB (H parallel to B) and m = mL when Hi = HL (Hm mL when Hi HL (H parallel to L). If you have both HB and HL use m = (mB

2 + mL2)1/2. Note use

of B and L not B’ L’of B and L, not B , L .

3. Hi term ≤ 1.0 for computing iq, iγ (always).

21


Suitability of MethodsSuitability of Methods

22


IS:6403-1981 RecommendationsNet Ultimate Bearing capacity: ( ). . . . . 1 . . . 0.5 . . . . .nu c c c c q q q qq c N s d i q N s d i B N s d iγ γ γ γγ= + − +

q c N s d i= 5 14NFor cohesive soils where. . . .nu u c c c cq c N s d i= 5.14cN =For cohesive soils where,

, ,c qN N Nγ as per Vesic(1973) recommendations

Shape Factors

1 0.2cBsL

= + 1 0.2qBsL

= + 1 0.4 BsLγ = −For rectangle,

1 3 1 2

D φ′⎛ ⎞

1.3cs = 1.2qs =0.8 for square, 0.6 for circles sγ γ= =

For square and circle,

1 0.2 tan 452

fc

Dd

Lφ′⎛ ⎞= + +⎜ ⎟

⎝ ⎠fD φ′⎛ ⎞

Depth Factors

1 0.1 tan 452

fq

Dd d

Lγφ⎛ ⎞= = + +⎜ ⎟

⎝ ⎠for 10oφ′ ≥

1qd dγ= = for 10oφ′ <

23

Inclination Factors

q γ φ

The same as Meyerhof (1963)


Bearing CapacityBearing Capacity Correlations with SPT-valueS a ue

Peck, Hansen, and Thornburn (1974)Thornburn (1974)

&

IS:6403-1981 Recommendation

24


Bearing Capacity Correlations with SPT-valueBearing Capacity Correlations with SPT value

Teng (1962):1 ( )2 21 3 . . 5 100 . .6nu w f wq N B R N D R⎡ ⎤′′ ′ ′′= + +⎣ ⎦

For Strip Footing:

1F S d ( )2 21 . . 3 100 . .3nu w f wq N B R N D R⎡ ⎤′′ ′ ′′= + +⎣ ⎦

For Square and Circular Footing:

For Df > B take Df = BFor Df > B, take Df B

Water Table Corrections: Dw

[0.5 1 1ww w

DR RD

⎛ ⎞= + ≤⎜ ⎟⎜ ⎟

Water Table Corrections: w

Df

[w wfD⎜ ⎟

⎝ ⎠

[0.5 1 1w fD DR R

⎛ ⎞−′ ′= + ≤⎜ ⎟⎜ ⎟ B

B

25

[0.5 1 1w wf

R RD

+ ≤⎜ ⎟⎜ ⎟⎝ ⎠

B

Limit of influence


Bearing Capacity Correlations with CPT-valueBearing Capacity Correlations with CPT-value0. 2500IS:6403-1981 Recommendation:

0.1675nuq

Cohesionless Soil

0.1250

nu

qc

D0.5

0

0.06251fD

B=

1.5B to

Bqc value is taken as

0 100 200 300 4000

to 2.0B

taken as average for this zone

B (cm)Schmertmann (1975):

kgq

26

2

kg in 0.8 cm

cq

qN Nγ ≅ ≅ ←


Bearing Capacity Correlations with CPT-valueBearing Capacity Correlations with CPT-value

IS:6403-1981 Recommendation:

Cohesive Soil

q c N s d i= . . . .nu u c c c cq c N s d i=

Soil Type Point Resistance Values( qc ) kgf/cm2

Range of Undrained Cohesion (kgf/cm2)

Normally consolidated clays qc < 20 qc/18 to qc/15

Over consolidated clays qc > 20 qc/26 to qc/22

27


Bearing Capacity of Footing on Layered SoilDepth of rupture zone tan 45

2 2B φ′⎛ ⎞= +⎜ ⎟

⎝ ⎠or approximately taken as “B”

Case I: Layer-1 is weaker than Layer-2Design using parameters of Layer -1

B 1

Case II: Layer-1 is stronger than Layer-2Distribute the stresses to Layer-2 by 2:1 method and check the bearing capacity at this level forB

2

1

Layer-1

L 2

and check the bearing capacity at this level for limit state.

Also check the bearing capacity for original foundation level using parameters of Layer-1

B Layer-2 foundation level using parameters of Layer 1

Choose minimum value for design

4B φ′⎛ ⎞Another approximate method for c‘-φ‘ soil: For effective depth tan 45

2 2B Bφ⎛ ⎞+ ≅⎜ ⎟

⎝ ⎠Find average c‘ and φ‘ and use them for ultimate bearing capacity calculation

28

1 1 2 2 3 3

1 2 3

........av

c H c H c HcH H H

+ + +=

+ + +1 1 2 2 3 3

1 2 3

tan tan tan ....tan....av

H H HH H H

φ φ φφ + + +=

+ + +


Bearing Capacity of Stratified Cohesive Soilg p yIS:6403-1981 Recommendation:

29


Bearing Capacity of Footing on Layered Soil:g y g yStronger Soil Underlying Weaker Soil

Depth “H” is relatively smallPunching shear failure in top layerGeneral shear failure in bottom

Depth “H” is relatively largeFull failure surface develops in top layer itselfGeneral shear failure in bottom

layery

30


Bearing Capacity of F ti L d S ilFooting on Layered Soil:Stronger Soil Underlying Weaker Soilea e So

31


Bearing Capacity of Footing on Layered Soil:St S il U d l i W k S ilStronger Soil Underlying Weaker Soil

Bearing capacities of continuous footing of with B under vertical load on the surface of homogeneousunder vertical load on the surface of homogeneous thick bed of upper and lower soil

32


Bearing Capacity of Footing on Layered Soil:Stronger Soil Underlying Weaker Soil

For Strip Footing: 2 122 tan1 fa sDc H Kq q H H qφγ γ′ ′⎛ ⎞

+ + + ≤⎜ ⎟For Strip Footing:

Where, qt is the bearing capacity for foundation considering only the top layer to infinite depth

11 11 fa s

u b tq q H H qB H B

γ γ= + + + − ≤⎜ ⎟⎝ ⎠

only the top layer to infinite depth

For Rectangular Footing:

2 22 tanfDc H KB B φ′ ′⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞2 11 1

22 tan1 1 1 fa su b t

Dc H KB Bq q H H qL B L H B

φγ γ⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞= + + + + + − ≤⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠Special Cases:p

1. Top layer is strong sand and bottom layer is saturated soft clay

2 0φ =1 0c′ =

2. Top layer is strong sand and bottom layer is weaker sand

1 0c′ = 2 0c′ =2 Top layer is strong saturated clay and bottom layer is weaker saturated clay

33

2. Top layer is strong saturated clay and bottom layer is weaker saturated clay

2 0φ =1 0φ =


Eccentrically Loaded FoundationsyM

QMeQ

=

Bmax 2

6Q MqBL B L

= +

Q

max61Q eq

BL B⎛ ⎞= +⎜ ⎟⎝ ⎠B BL B L

min 2

6Q MqBL B L

= −

BL B⎝ ⎠

min61Q eq

BL B⎛ ⎞= −⎜ ⎟⎝ ⎠

e

⎝ ⎠

16

eB

>For There will be separation e 6B

of foundation from the soil beneath and stresses will be redistributed.

Use for , and B, L for to obtain qu, ,c qd d dγ2B B e′ = −

L L′ =, ,c qs s sγ

34.u uQ q A′=

The effective area method for two way eccentricity becomes a little more complex than what is suggested above.

It is discussed in the subsequent slides


Determination of Effective Dimensions for Eccentrically L d d f d ti (Hi ht d A d 1985)Loaded foundations (Highter and Anders, 1985)

C I 1 1e eCase I: 1 1 and 6 6

L Be eL B

≥ ≥

33 BeB B ⎛ ⎞⎜ ⎟1

332

BeB BB

⎛ ⎞= −⎜ ⎟⎝ ⎠

33⎛ ⎞eB

B1

133

2LeL L

L⎛ ⎞= −⎜ ⎟⎝ ⎠eL

eB

L1L

1 112

A L B′ = ( )1 1max ,L B L′ =

ABL

′′ =

′B

35


Determination of Effective Dimensions for Eccentrically Loaded foundations (Highter and Anders 1985)

Case II: 10.5 and 0L Be e< < <

foundations (Highter and Anders, 1985)

0.5 and 06L B

< < <

eL2

eL

eB

L1

2

L

B

( )1 212

A L L B′ = + AB′

′ =

36

BL′( )1 1max ,L B L′ =


Determination of Effective Dimensions for Eccentrically Loaded foundations (Highter and Anders 1985)foundations (Highter and Anders, 1985)

Case III: 1 and 0 0.56

L Be eL B

< < <6L B

B1

eB

eL

L

B

( )1 21A L B B′ = + A′

B2

37

( )1 22 ABL

′′ =

′L L′ =



Case IV: 1 1 and 6 6

L Be eL B

< <

B1

e

eB

eL

L

B

BB2

( )( )2 1 2 212

A L B B B L L′ = + + +

38

ABL

′′ =

′L L′ =

2



Case V: Circular foundationCase V: Circular foundation

eRR

R

A′′ AL

B′ =

′

39


Meyerhof’s (1953) area correction based on empirical l ti (A i P t l I tit t 1987)correlations: (American Petroleum Institute, 1987)

40


Bearing Capacity of F ti SlFootings on SlopesMeyerhof’s (1957) SolutionSolution

0 5q c N BNγ′ + 0.5u cq qq c N BNγγ= +

0c′ =Granular Soil

0.5u qq BNγγ=

41


Bearing Capacity of F ti SlFootings on SlopesMeyerhof’s (1957) SolutionSolution

Cohesive Soil

0φ′ =

u cqq c N′=u cqq

H

42s

HNc

γ=


Bearing Capacity of Footings on SlopesFootings on SlopesGraham et al. (1988), Based on method of characteristics

1000

For

0fDB

=100 B100

43

100 10 20 30 40


Bearing Capacity of Footings on SlopesFootings on SlopesGraham et al. (1988), Based on method of characteristics

1000

100

For

0fDB

=100 B

44

100 10 20 30 40


Bearing Capacity of Footings on SlopesG h t l (1988) B d th d f h t i tiGraham et al. (1988), Based on method of characteristics

For

D0.5fD

B=

45


Bearing Capacity of Footings on SlopesG h t l (1988) B d th d f h t i tiGraham et al. (1988), Based on method of characteristics

For

D1.0fD

B=

46


Bearing Capacity of Footings on SlopesB l (1997) A i lifi d hBowles (1997): A simplified approach

B α = 45+φ’/2B

'

Df a

fqu

gα = 45+φ /2

a' c'

g'qu

f'

α α45−φ’/2a c

eα α

45−φ’/2b'

c

e' rorbd

B

b

d'

Compute the reduced factor Nc as:

. a b d ec c

LN NL

′ ′ ′ ′′ =

Bg'

quf'

Compute the reduced factor Nq as:

c cabdeL

α α45−φ’/2

a' c'e'

47

. a e f gq q

aefg

AN N

A′ ′ ′ ′′ =b'

d'


Soil Compressibility Effects on Bearing CapacityVesic’s (1973) ApproachUse of soil compressibility factors in general bearing capacity equation.These correction factors are function of the rigidity of soilThese correction factors are function of the rigidity of soil

tans

rvo

GIc σ φ

=′ ′ ′+

Rigidity Index of Soil, Ir:

BCritical Rigidity Index of Soil, Icr:

3.30 0.45

tan 452

BL

φ

⎧ ⎫⎛ ⎞−⎜ ⎟⎪ ⎪⎪ ⎪⎝ ⎠⎨ ⎬′⎡ ⎤⎪ ⎪−⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭

B/2

( ). / 2vo fD Bσ γ′ = +

20.5.rcI e⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭=

Compressibility Correction Factors, cc, cg, and cq ( )vo fγr rcI I≥For 1c qc c cγ= = =

( )103.07.sin .log 2.0.6 4.4 .tan rIB φ

φ′⎡ ⎤⎛ ⎞ ′− +⎢ ⎥⎜ ⎟ ′⎝ ⎠

r rcI I< 1 sin 1Lqc c e

φφ

γ

⎢ ⎥⎜ ⎟ ′+⎝ ⎠⎣ ⎦= = ≤For

For 0 0.32 0.12 0.60.logc rBc IL

φ′ = → = + +

48

L1

For 0 tan

qc q

q

cc c

Nφ

φ−

′ > → = −′

CE 632 Bearing Capacity PPT

Documents

Transcript of CE 632 Bearing Capacity PPT