Bearing Capacity Lecture 2014

7/23/2019 Bearing Capacity Lecture 2014

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SI 3221 2014

References:

1. Joseph E. Bowles, Foundation Analysis and Design, McGraw Hill, 1997

2. Braja M. Das, Principles of Foundation Engineering, ITP, 1995.

3. Tien HsingWu, Soil Mechanics, Allyn Bacon, 1976

earing Capacity

of

Shallow Foundations

Bearing Capacity Failures


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Lab Model Test

Lateral Earth Pressure (Review)

ITB Lecture

2011

Reference:1. Das, Braja M., Principles of Geotechnical Engineering, Brooks/Cole, USA,

2002. CHAPTER 12

2. The Canadian Foundation Engineering Manual, 2006


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h = K v

h = Kov

v v v

h = Kav h = Kpv

Note: All stresses in effective stress , NOT in total stress

Lp >>La


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At Rest, Ko

Jaky, 1944 (good for loose sand)

Ko = 1 sin Sherif, Fang, 1984 (dense sand)

Ko = 1 sin + 5.5 [ (d/d min) - 1 ] Massarsch, 1979 (NC clays)

Ko = 0.44 + 0.42 [PI(%)/100]

OC Clays: Ko, OC = Ko NCOCR

The Pole Method

b

a

ab

POLE a

b =a

b

a

(p,p)

(q,q)


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Rankine Ka The Pole Method

h

v

vhhh

ff

ff

A

A

POLE

A

Rankine Kp The Pole Method

h

v

vh h h

ff

ff

A

A

POLE

A


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Rankine Ka

h

v

vh

ff

ff POLE

C

(

v + h)/2c/tan

45o + /2

(90o-)

(90o+)/2

sin =(v -h)/2

c/tan (v + h)/2+

h = v Ka 2c Ka

Ka = tan2 (45o - /2)

Rankine Kp

h

v

v h

ff

ff POLE

C

(v + h)/2c/tan

45o -/2

(90o-)

sin =(

h-

v)/2

c/tan (v + h)/2+

h = v Kp + 2c Kp

Kp = tan2 (45o + /2)


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Simplified BC Equation ( - soil)

(45 + /2) (45 -/2)

Q

Pp

N

W

q = f(D)

Pp = 0.5 H2 Kp + q H Kp

Kp = tan2 (45 + /2)

H = B tan (45 + /2)

H

B

W = 0.5 B H

PpW

NQ

Q = F (, , , B, D)

Q/B = q ult= B N + .. D Nq

N & Nq = f (, )

Simplified BC Equation (c soil)

Moment against A, for b length and mass less soil:

MA = (qult Bb)(B/2) (cu Bb) B - zD Bb (B/2)

qult = 2 cu + zD = c Nc + zD Nq

If K 0, we will have a N term


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Other simplified formulations

Pp

(90--)

W

cA

Qu

N


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Equilibrium

of adg wedge,

example

ignores the

friction in gf


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Terzaghi (1943a) BC Equation:

(See copy of Wu (1976), pp. 232 236)


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log spiral eq:

r = a e tan

c ds cos

c ds

r dFailure plane


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Other BC Equations

See Bowles 5th Ed. (1997) , pp. 220 -231

Kp is

Terzaghis

passive

pressure

coefficient,K KpRankine


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Always check other sources to eliminate typo errors!!!


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2e, see

Bowles

p 237


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Which formula to use?

ps = plane starin

tr = triaxial

Which soil parameters to use??

See and review Soil Mechanics Shear Strength Theory

VERY IMPORTANT, error due to wrong soil parameters

often much more significant than variations in formula choice

Examples of case studies

a. RangsitThailand, Bangkok Clay

b. Menara Jakarta


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Rangsit (Bangkok Clay Site)


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Field vane Su

correction

(Bjerrum)

Modified Terzaghis, c = 2/3 c , tan = 2/3 tan

Field vane Su

correction

(Bjerrum)


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Menara Jakarta


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Beban max per

kolom

Mmax = 387 MN-m

Pmax = 150 MN

Hmax = 8.65 MN


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UU Triaxial


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CU Triaxial

Additional Considerations

N factors are sensitive to , especially for 35o. Do notinterpolate over more than 2o

Most of the times, BC equations are conservative due to

safe choice of parameters.

Terzaghi considered other modes of failures , e.g. local shear

failure with c = 0.67 c and tan = 0.67 tan

B N must be corrected by:r = 1 0.25 log (B/2) , for B > 2 m, and B is in meters.

See next slide


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For c soils, c Nc is the predominant portion of BC For soils, q Nq is the predominant portion of BC For B < 3 to 4 m, N is small and often neglected No one would place a footing at the surface of cohesionless

soil.

In case of uncertain overburden quality, Vesic does notrecommend using di correction factors

BC equations are generally used with SF = 2.5 to 3.5


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Effect of water table to BC

Use effective unit weight for q Nq and N terms whenwater table is above foundation base.

Ignore effect if water table is below wedge zone

If water table is below base and within (triangle) wedge zone,

use:

e = (2H-dw) dwwet/H + (H-dw)2/H2

H = 0.5 B tan (45o+/2)

dw = depth of GWT from base

From the term 0.5 B N Wedge

under BArea above water Area under water

BC in layered soils (See also other texts)


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See slide 17

for H

Then qult = c1 Nc

2.5?


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Then qult = c1 Nc

See Next Slide

Table 4.1


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See previous slide


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Meyerhoff & Hannas (1974, 1978)


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= -

Super positions

qt qt

H

Hf(HfH)

qt (1- H/Hf)2


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= -

Super positions

qb qb

H

Hf(HfH)

qb -qb (1- H/Hf)2


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BC formulas from SPT

Terzaghi & Peck (1967); Meyerhof (1956, 1974):

qa = N Kd/F1 BOF4qa = N (B + F3)

2 Kd / (F2 B2) B>F4

qa = allowable at 25 mm settlement

Kd = 1 + 0.33 D/BO1.33

Formula above (1950-60s), therefore applicable to N55 . F1 and F2corrected these.

B (m)


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BC from CPT (Schmertmann, 1978)

0.8 Nqz 0.8 Nz qc for D/B 1.5 and qc averaged from B/2

above to 1.1 B below base.

Cohesionless:

Strip : qult = 28 0.0052 (300 qc)1.5 kg/cm2

Square : qult = 48 0.009(300 qc)1.5 kg/cm2

Cohesive:

Strip : qult = 2 + 0.28 qc kg/cm2

Square : qult = 5 + 0.34 qc kg/cm2

Example Problems

See problems in Shallow Foundation Example Problems

Documents

Bearing Capacity Lecture 2014