CE 632 Bearing Capacity PPT.pdf

CE-632 CE 632 Foundation Analysis and Design

Ultimate Bearing Capacity The load per unit area of the foundation at which shear failure in soil occurs is i called ll d the th ultimate lti t bearing b i capacity. it 1

Foundation Analysis and Design: Dr. Amit Prashant

Principal Modes of Failure: General Shear Failure:

Settlement

Load / Area q

„ „ „ „

qu

Sudden or catastrophic failure Well defined failure surface Bulging on the ground surface adjacent to foundation Common failure mode in dense sand

2

Foundation Analysis and Design: Dr. Amit Prashant

Principal Modes of Failure: Load / Area q

Local Shear Failure:

Setttlement

qu1

„ „ „ „

„

qu

Common in sand or clay with medium compaction Significant settlement upon loading Failure surface first develops p right g below the foundation and then slowly extends outwards with load increments Foundation movement shows sudden jerks first (at qu1) and then after a considerable amount of movement the slip surface may reach h th the ground. d A small amount of bulging may occur next to the foundation. 3

Foundation Analysis and Design: Dr. Amit Prashant

Principal Modes of Failure: Load / Area q

Punching Failure:

Setttlement

qu1

„ „ „

„

qu

Common in fairly loose sand or soft clay Failure surface does not extends beyond the zone right beneath the foundation Extensive settlement with a wedge shaped soil zone in elastic equilibrium beneath the foundation. Vertical shear occurs around the edges of foundation. Aft reaching After hi ffailure il lload-settlement d ttl t curve continues ti att some slope l and mostly linearly. 4

Foundation Analysis and Design: Dr. Amit Prashant

Rela ative dep pth of fou undation n, Df/B*

Principal Modes of Failure: 0

0

Relative density of sand, Dr 0.5 05 Local shear

Vesic (1973) 1.0 10

General shear

2BL B = B+L *

Circular Foundation

5

Punching shear

Long Rectangular Foundation

10 5

Foundation Analysis and Design: Dr. Amit Prashant

g g Capacity p y Theory y Terzaghi’s Bearing B Rough Foundation Surface

Strip Footing k

j Effective Eff ti overburden b d q = γ’.Df

qu

neglected Df a g

45−φ’/2

b

φ’

I

φ’

III Shear Planes

II

II e

d

45−φ’/2 i III c’- φ c φ’ soil f

Assumption „ L/B ratio is large Æ plain strain problem „ Df ≤ B „ Shear resistance of soil for Df depth is neglected „ General shear failure „ Shear strength is governed by Mohr-Coulomb Criterion

B

6

Foundation Analysis and Design: Dr. Amit Prashant

Terzaghi s Bearing Capacity Theory Terzaghi’s B

1 qu .B = 2.Pp + 2.Ca .sin φ ′ − γ ′B 2 tan φ ′ 4 qu

a

b

φ’

Ca= B/2 cosφ’

φ’ Pp

1 qu .B = 2.Pp + B.c′.sin φ ′ − γ ′B 2 tan φ ′ 4

φ’

I

Ca B.tanφ’ d

φ’ Pp

Pp = Ppγ + Ppc + Ppq Ppγ = due to only self weight of soil in shear zone Ppc = due to soil cohesion only (soil is weightless) Ppq = due to surcharge only 7

Foundation Analysis and Design: Dr. Amit Prashant

Terzaghi s Bearing Capacity Theory Terzaghi’s Weight term

Cohesion term

1 ⎛ ⎞ qu .B = ⎜ 2.Ppγ − γ ′B 2 tan φ ′ ⎟ + ( 2.Ppc + B.c′.sin φ ′ ) + 2.Ppq 4 ⎝ ⎠

B. ( 0.5γ ′B.Nγ )

Surcharge term

B.c.N c

qu = c.N c + q.N q + 0.5γ ′B.Nγ

B.q.N q Terzaghi’s bearing capacity equation

Terzaghi’s bearing capacity factors

⎡ K Pγ ⎤ 1 Nγ = tan φ ′ ⎢ 2 − 1⎥ 2 ⎣ cos φ ′ ⎦

N c = ( N q − 1) cot φ ′

e2a Nq = φ′ ⎞ 2⎛ 2 cos ⎜ 45 + ⎟ 2⎠ ⎝ ⎛ 3π φ ′ in rad. ⎞ − a=⎜ ⎟ tan φ ′ 2 ⎝ 4 ⎠

8

Foundation Analysis and Design: Dr. Amit Prashant

9

Foundation Analysis and Design: Dr. Amit Prashant

Terzaghi s Bearing Capacity Theory Terzaghi’s Local Shear Failure: Modify the strength parameters such as:

2 cm′ = c′ 3

⎛2 ⎝

⎞ ⎠

φm′ = tan −1 ⎜ tan φ ′ ⎟ 3

2 qu = c′.N c′ + q.N q′ + 0.5γ ′B.Nγ′ 3

Square and circular footing: qu = 1.3c′.N c + q.N q + 0.4γ ′B.Nγ′

For square

qu = 1.3c′.N c + q.N q + 0.3γ ′B.Nγ′

For circular

10

Foundation Analysis and Design: Dr. Amit Prashant

Terzaghi s Bearing Capacity Theory Terzaghi’s Effect of water table: Case I: Dw ≤ Df

Surcharge, q = γ .Dw + γ ′ ( D f − Dw )

Case II: Df ≤ Dw ≤ (Df + B)

Dw Df

Surcharge, q = γ .DF In bearing capacity equation replace γ by-

⎛ Dw − D f ⎞ ⎟ (γ − γ ′) B ⎝ ⎠ Case III: Dw > (Df + B)

γ =γ′+⎜

B

B Li it off iinfluence Limit fl

No influence of water table.

Another recommendation for Case II: γ = ( 2H + dw )

dw γ 2 sat H

γ′ 2 + 2 ( H − dw ) H

d w = Dw − D f

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

11

Foundation Analysis and Design: Dr. Amit Prashant

p g Capacity p y Analysis y Skempton’s Bearing for cohesive Soils ~ For saturated cohesive soil, φ‘ = 0 Æ N q = 1, and Nγ = 0 Df ⎞ ⎛ For strip footing: N c = 5 ⎜1 + 0.2 ⎟ with limit of N c ≤ 7.5 B ⎠ ⎝

Df ⎞ ⎛ N c = 6 ⎜1 + 0.2 ⎟ with limit of N c ≤ 9.0 B ⎠ ⎝

For square/circular footing: g For rectangular footing:

Df ⎞ ⎛ ⎛ B⎞ + N c = 5 ⎜1 + 0.2 1 0.2 ⎟⎜ ⎟ for D f ≤ 2.5 B ⎠⎝ L⎠ ⎝ B⎞ ⎛ N c = 7.5 ⎜1 + 0.2 ⎟ for D f > 2.5 L⎠ ⎝

qu = c.N c + q Net ultimate bearing capacity,

qnu = qu − γ .D f

qu = c.N c 12

Foundation Analysis and Design: Dr. Amit Prashant

Effective Area Method for Eccentric Loading In case of Moment loading Df

B B’=B-2ey

AF=B’L’

L’=L-2ey ex

ey

ex =

My

ey =

Mx FV

FV

IIn case off Horizontal H i t l Force F att some height but the column is centered on the foundation

M y = FHx .d FH

M x = FHy .d FH 13

Foundation Analysis and Design: Dr. Amit Prashant

General Bearing Capacity Equation: (Meyerhof, 1963)

qu = c.N c .sc .dc .ic + q.N q .sq .d q .iq + 0.5 0 5γ .B.Nγ .sγ .dγ .iγ Shape f t factor

Depth factor

φ′ ⎞ ⎛ N q = tan 2 ⎜ 45 + ⎟ .eπ .tan φ ′ 2⎠ ⎝

inclination f t factor

Empirical p correction factors

N c = ( N q − 1) cot φ ′

Nγ = ( N q − 1) tan (11.4 4φ ′ )

[[Byy Hansen(1970): ( )

N γ = 1.5 ( N q − 1) tan (φ ′ )

[By Vesic(1973):

N γ = 2 ( N q + 1) tan (φ ′ )

qu = c.N c .sc .dc .ic .gc .bc + q.N q .sq .d q .iq .g q .bq + 0.5γ .B.Nγ .sγ .dγ .iγ .gγ .bγ Ground factor

Base factor

14

Foundation Analysis and Design: Dr. Amit Prashant

15

Foundation Analysis and Design: Dr. Amit Prashant

M Meyerhof’s h f’ Correction C i Factors: F Shape Factors

B φ′ ⎞ ⎛ sc = 1 + 0.2 tan 2 ⎜ 45 + ⎟ 2⎠ L ⎝

for φ ′ ≥ 10o

B φ′ ⎞ 2⎛ sq = sγ = 1 + 0.1 tan ⎜ 45 + ⎟ L 2⎠ ⎝ for lower φ ′ value

sq = sγ = 1 Depth Factors

φ′ ⎞ ⎛ d c = 1 + 0.2 tan ⎜ 45 + ⎟ L 2⎠ ⎝ Df

for φ ′ ≥ 10o

d q = dγ = 1 + 0.1

φ′ ⎞ ⎛ tan ⎜ 45 + ⎟ L 2⎠ ⎝

Df

for lower φ ′ value

d q = dγ = 1 Inclination Factors

⎛ βo ⎞ ic = iq = ⎜1 − ⎟ 90 ⎝ ⎠

2

⎛ β⎞ iγ = ⎜1 − ⎟ ⎝ φ′ ⎠

2

16

Foundation Analysis and Design: Dr. Amit Prashant

Hansen’s Correction Factors: Inclination Factors

Depth Factors

FH for φ ′ = 0 ic = 1 − 2 BL.c′ 5 ⎡ ⎤ 0 5F 0.5 FH iq = ⎢1 − ⎥ ′ ′ φ F BL . c .cot + V ⎣ ⎦ For φ = 0

For φ > 0

Df ⎡ for D f ≤ B ⎢ d c = 0.4 B ⎢ Df ⎢ −1 d = 0.4 tan for D f > B ⎢⎣ c B

Df ⎡ for D f ≤ B ⎢ d c = 1 + 0.4 B ⎢ Df ⎢ −1 = 1 + 0.4 tan for D f > B d ⎢⎣ c B

For D f < B

2 ⎛ Df ⎞ d q = 1 + 2 tan φ ′. (1 − sin φ ′ ) ⎜ ⎟ B ⎝ ⎠

Shape Factors

1 ⎡ (1 − FH ) ⎤ ic = ⎢1 + ⎥ for φ ′ > 0 BL.su ⎦ 2⎣ 5 ⎡ ⎤ 0 7F 0.7 FH iγ = ⎢1 − ⎥ ′ ′ + F BL . c .cot φ V ⎣ ⎦ 1/2

sc = 0.2ic .

B L

for φ ′ = 0

sq = 1 + iq . ( B L ) sin i φ′

For D f > B Df ⎞ 2 −1 ⎛ ′ ′ d q = 1 + 2 tan φ . (1 − sin φ ) tan ⎜ ⎟ ⎝ B ⎠

dγ = 1

B for φ ′ > 0 L sγ = 1 − 0.4 0 4iγ . ( B L ) sc = 0.2 (1 − 2ic ) .

Hansen’s Recommendation for cohesive saturated soil, φ'=0 Æ

qu = c.N c . (1 + sc + d c + ic ) + q

Foundation Analysis and Design: Dr. Amit Prashant

Notes: 1. Notice use of “effective” base dimensions B‘, L‘ by H Hansen b butt nott by b Vesic. V i 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 a load HL (and either HB=0 or HB>0) you may have to compute two sets of shape and depth factors si,B, si,L and di,B, di,L. For i,L subscripts use ratio L‘/B‘ or D/L‘. 4. Compute qu independently by using (siB, diB) and (siL, diL) and use min value for design. 18

Foundation Analysis and Design: Dr. Amit Prashant

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 of angles η and β, footing depth D, location of Hi (parallel and at top of base slab; usually also produces eccentricity) eccentricity). Especially notice V = force normal to base and is not the resultant R from combining V and Hi.. 19

Foundation Analysis and Design: Dr. Amit Prashant

20

Foundation Analysis and Design: Dr. Amit Prashant

N t Note: 1. When φ=0 (and β≠0) use Nγ = -2sin(± ( β) in Nγ term. 2. Compute m = mB when Hi = HB (H parallel to B) and m = mL when Hi = HL (H parallel to L). If you have both HB and HL use m = (mB2 + mL2)1/2. Note use of B and L L, not B’ B,L L’. 3. Hi term ≤ 1.0 for computing iq, iγ (always).

21

Foundation Analysis and Design: Dr. Amit Prashant

Suitability of Methods

22

Foundation Analysis and Design: Dr. Amit Prashant

IS:6403-1981 Recommendations Net Ultimate Bearing capacity: For cohesive soils Æ

qnu = c.Nc .sc .dc .ic + q. ( N q − 1) .sq .d q .iq + 0.5γ .B.Nγ .sγ .dγ .iγ

qnu = cu .N c .sc .d c .ic N c , N q , Nγ

Shape Factors

For rectangle,

sc = 1 + 0.2

Inclination Factors

B L

sq = 1 + 0.2

B L

sγ = 1 − 0.4

B L

12 sc = 1.3 1 3 sq = 1.2 sγ = 0.8 for square, sγ = 0.6 for circle

φ′ ⎞ ⎛ tan ⎜ 45 + ⎟ L 2⎠ ⎝ Df φ′ ⎞ ⎛ d q = dγ = 1 + 0.1 tan ⎜ 45 + ⎟ L 2⎠ ⎝ d q = dγ = 1 for φ ′ < 10o

d c = 1 + 0.2

N c = 5.14 5 14

as per Vesic(1973) recommendations

For square and circle,

Depth Factors

where where,

Df

The same as Meyerhof (1963)

for

φ ′ ≥ 10o

23

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity Correlations with S SPT-value a ue Peck, Hansen, and Thornburn (1974) & IS:6403-1981 Recommendation

24

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity Correlations with SPT-value SPT value Teng (1962):

(

)

(

)

For Strip Footing:

1⎡ qnu = ⎣3 N ′′2 .B.Rw′ + 5 100 + N ′′2 .D f .Rw ⎤⎦ 6

For Square F S and d Circular Footing:

1⎡ 2 qnu = ⎣ N ′′ .B.Rw′ + 3 100 + N ′′2 .D f .Rw ⎤⎦ 3 For Df > B, B take Df = B

Dw

Water Table Corrections:

⎛ Dw ⎞ Rw = 0.5 ⎜1 + ⎜ D f ⎟⎟ ⎝ ⎠ ⎛ Dw − D f ⎞ Rw′ = 0.5 ⎜1 + ⎟⎟ ⎜ Df ⎠ ⎝

[ Rw ≤ 1

Df B

[ Rw′ ≤ 1

B Limit of influence

25

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity Correlations with CPT-value 0. 2500

IS:6403-1981 Recommendation: Cohesionless Soil

qnu qc

0

0.1250

Df

B 1.5B to 2.0B

0.1675

qc value is taken as average for this zone

0.0625

=1

0 0

100

200

300

400

B (cm)

Schmertmann (1975):

Nγ ≅ N q ≅

B

0.5

qc 0.8

← in

kg cm 2

26

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity Correlations with CPT-value IS:6403-1981 Recommendation: Cohesive Soil

qnu = cu .N c .sc .dc .ic 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

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footing on Layered Soil Depth of rupture zone =

B φ′ ⎞ ⎛ tan ⎜ 45 + ⎟ or approximately taken as “B” 2 2⎠ ⎝ Case I: Layer-1 is weaker than Layer-2 Design using parameters of Layer -1

Case II: Layer-1 is stronger than Layer-2 1

B Layer-1 B

2

L Layer-2 2

Distribute the stresses to Layer-2 by 2:1 method 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 Layer 1 Choose minimum value for design

Another approximate method for c‘-φ‘ soil: For effective depth

B φ′ ⎞ ⎛ tan ⎜ 45 4 + ⎟≅B 2 2⎠ ⎝

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

cav =

c1 H1 + c2 H 2 + c3 H 3 + .... H1 + H 2 + H 3 + ....

tan φav =

tan φ1 H1 + tan φ2 H 2 + tan φ3 H 3 + .... H1 + H 2 + H 3 + ....

28

Foundation Analysis and Design: Dr. Amit Prashant

g Capacity p y of Stratified Cohesive Soil Bearing IS:6403-1981 Recommendation:

29

Foundation Analysis and Design: Dr. Amit Prashant

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

Depth “H” is relatively small Punching shear failure in top layer General shear failure in bottom layer

„ „

Depth “H” is relatively large Full failure surface develops in top layer y itself

30

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footing on Layered F ti L d Soil: S il Stronger Soil Underlying Weaker ea e So Soil

31

Foundation Analysis and Design: Dr. Amit Prashant

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

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

32

Foundation Analysis and Design: Dr. Amit Prashant

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

2 D f ⎞ K s tan φ1′ 2ca′ H 2⎛ qu = qb + + γ 1H ⎜1 + − γ 1 H ≤ qt ⎟ B H ⎠ B ⎝ Where, qt is the bearing capacity for foundation considering only the top layer to infinite depth

For Rectangular Footing:

⎛ B ⎞ ⎛ 2c ′ H qu = qb + ⎜1 + ⎟ ⎜ a ⎝ L ⎠⎝ B

B ⎞ ⎛ 2 D f ⎞ K s tan φ1′ ⎞ 2⎛ − γ 1 H ≤ qt ⎟ + γ 1H ⎜1 + L ⎟ ⎜1 + H ⎟ B ⎝ ⎠⎝ ⎠ ⎠

Special p Cases: 1. Top layer is strong sand and bottom layer is saturated soft clay

c1′ = 0 φ2 = 0 2. Top layer is strong sand and bottom layer is weaker sand

c1′ = 0

c2′ = 0

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

φ1 = 0

φ2 = 0

33

Foundation Analysis and Design: Dr. Amit Prashant

y Loaded Foundations Eccentrically Q M

e= qmax =

Q 6M + BL B 2 L

qmax =

Q ⎛ 6e ⎞ ⎜1 + ⎟ BL ⎝ B⎠

qmin =

Q 6M − BL B 2 L

qmin =

Q ⎛ 6e ⎞ ⎜1 − ⎟ BL ⎝ B⎠

B

e

M Q

For

e 1 There will be separation > B 6

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

B′ = B − 2e L′ = L

Qu = qu . A′

for

sc , sq , sγ , and B, L for d c , d q , dγ

to obtain qu

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

34

Foundation Analysis and Design: Dr. Amit Prashant

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

eL 1 e 1 ≥ and B ≥ L 6 B 6

⎛ 3 3e ⎞ B1 = B ⎜ − B ⎟ ⎝2 B ⎠

B1 eB L

eL

L1

⎛ 3 3eL ⎞ L1 = L ⎜ − ⎟ 2 L ⎝ ⎠ A′ =

B

1 L1 B1 2

B′ =

L′ = max ( B1 , L1 ) A′ L′

35

Foundation Analysis and Design: Dr. Amit Prashant

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

L2

eL e 1 < 0.5 and 0 < B < L B 6 eB eL

L1

L B

1 ( L1 + L2 ) B 2 L′ = max ( B1 , L1 ) A′ =

A′ B′ = L′ 36

Foundation Analysis and Design: Dr. Amit Prashant

Determination of Effective Dimensions for Eccentrically Loaded foundations (Highter and Anders, Anders 1985) Case III: eL < 1 and 0 < eB < 0.5

L

6

B

B1

eB eL L B B2

1 L ( B1 + B2 ) A′ 2 ′ B = L′ L′ = L

A′ =

37

Foundation Analysis and Design: Dr. Amit Prashant

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

eL 1 eB 1 < < and L 6 B 6 B1

eB eL L B B2

A′ = L2 B + L′ = L

1 ( B1 + B2 )( L + L2 ) 2 A′ B′ = L′

38

Foundation Analysis and Design: Dr. Amit Prashant

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

Case V: Circular foundation

eR

R

L′ =

A′ B′

39

Foundation Analysis and Design: Dr. Amit Prashant

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

40

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footings on Slopes F ti Sl Meyerhof’s (1957) Solution

qu = c′N cq + 0.5 0 5γ BN γ q

Granular Soil

c′ = 0 qu = 0.5γ BN γ q

41

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footings on Slopes F ti Sl Meyerhof’s (1957) Solution Cohesive Soil

φ′ = 0

qu = c′N cq

Ns =

γH c

42

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footings on Slopes Graham et al. (1988), Based on method of characteristics 1000

For

Df 100

10

B

0

10

20

30

40

=0

43

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footings on Slopes Graham et al. (1988), Based on method of characteristics 1000

For

Df 100

10

B

0

10

20

30

40

=0

44

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footings on Slopes G h Graham ett al. l (1988), (1988) Based B d on method th d off characteristics h t i ti

For

Df B

= 0.5

45

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footings on Slopes G h Graham ett al. l (1988), (1988) Based B d on method th d off characteristics h t i ti

For

Df B

= 1.0

46

Foundation Analysis and Design: Dr. Amit Prashant

Bearing Capacity of Footings on Slopes B l (1997): Bowles (1997) A simplified i lifi d approach h B f

B

α = 45+φ’/2 /2

g''

f'

g

qu

qu Df

a

45−φ’/2

e

α

a'

c

α

α e'

45−φ’/2

r

b

d

α

cc'

ro b' b

d' B

„

g' qu

N c′ = N c .

f' a' e'

α

α

45−φ’/2 b' d'

Compute the reduced factor Nc as:

c' „

La′b′d ′e′ Labde

Compute the reduced factor Nq as:

N q′ = N q .

Aa′e′f ′g ′ Aaefg

47

Foundation Analysis and Design: Dr. Amit Prashant

Soil Compressibility Effects on Bearing Capacity Vesic’s (1973) Approach „ „

Use of soil compressibility factors in general bearing capacity equation. These correction factors are function of the rigidity of soil

Rigidity Index of Soil, Ir:

Ir =

Gs ′ tan φ ′ c′ + σ vo

Critical Rigidity Index of Soil, Icr:

I rc = 0.5.e

⎧ B ⎞⎫ ⎛ ⎪⎪ 3.30 − ⎜ 0.45 L ⎟ ⎪⎪ ⎝ ⎠ ⎨ ⎬ ⎪ tan ⎡ 45 − φ ′ ⎤ ⎪ ⎢ ⎪⎩ 2 ⎥⎦ ⎪⎭ ⎣

B B/2

σ vo′ = γ . ( D f + B / 2 )

Compressibility Correction Factors, cc, cg, and cq For

For

I r ≥ I rc

I r < I rc

cc = cq = cγ = 1 cq = cγ = e

⎡⎛ 3.07.sin φ ′.log10 ( 2. I r ) ⎤ B ⎞ ⎢⎜ 0.6 − 4.4 ⎟.tan φ ′ + ⎥ L 1+ sin φ ′ ⎠ ⎣⎝ ⎦

For φ ′ = 0 → cc = 0.32 + 0.12 For φ ′ > 0 → cc = cq −

1 − cq

≤1

B + 0.60.log I r L

N q tan φ ′

48