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9. Axial Capacity

of Pile Groups

CIV4249: Foundation Eng ineering

Monash Univers i ty

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Axial Capacity

W

Pbase Bearing failure at the pi le base

PshaftShear fai lure at pile sh aft

Fu Fu+ W = Pbase+ Pshaft

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Pshaft, tShear failur e at pil e shaft

Tu - W = Pshaft, t < Pshaft,c

Tension Capacity

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Applications

Low

Weight

Soft toFirm Clay

Large Distr ibu ted

Weight

Very Large ConcentratedWeight

Dense Sand

Strong Rock

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Group Capacity

Overlapping stress f ields

Progressive densi f ication

Progressive loosening

Case-by-case bas is

Pile Cap

Pug

Pugn .PupPug= en.Pup

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Efficiency, e

Soil Type

Clay

Sand

Rock

Number of Pi les, n

n = 5 x 5 = 25

Spacing/Diameter

s

d

s/d typ ical ly > 2 to 3

Pile Cap

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Types of Groups

Rigid Cap

Capped Groups

Flexib le Cap

Free-standing Groups

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Feld Rule for free-standing

piles in clay

A

B

A

B

C

B

B

C

B

B

C

B

A

B

A

reduce capacity of each p i le by 1/16 for each adjo ing p i le

13/16 11/16

8/16

e = 1/15 * (4* 13/16 + 8 * 11/16 + 3 * 8/16) = 0.683

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Converse-Labarre Formula for

free-standing piles in clay

e= 1 - q (n-1)m + (m-1)n90 mn

m = # row s = 3

n = # co ls = 5

s = 0.75d=0.3

q = tan-1(d/s) e = 0.645

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Flexib le Cap

Pug

= m in (nPup

,PBL

)

D

L,B

PBL= BLcbNc+ 2(B+L )Dcs

cs

cb

Block Failure

Ncincl shape & depth factors

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Empir ical Mod i f ication

nnPup

PBL= BLcbNc+ 2(B+L )Dcs

Pug

= min (nPup

,PBL

)1 1 1

P2ug= n2P2up+ P

2BL

1 = 1 + n

2

P

2

upe2 P2BL

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Flexib le Cap

D = 20m

L = B = 5m

cs= cb= 50 kPa

Block Failure

d = 0.3m

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Rigid Cap

Ptotal= Pgroup+ Pcap

for group block fai lure, Pcap= ccapNc[BcL c- BL ]for single pi le failure, Pcap= ccapNc[BcL c- nA p]

Capped Groups

B x L

Bcx L c

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Piles in Granular Soils

End bearing - l i t t le interact ion , e= 1 Shaft - dr iven

For loose to medium sands, e> 1 Vesic driven : 1.3 to 2 for s /d = 3 to 2

Dense/V dense - loosening?

Shaft - bo red

General ly m ino r component, e= 1

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Pile Settlement

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Elastic Analysis Methods

based on Mindlins equations for shear

loading w ithin an elast ic hal fspace

Poulos and Davis (1980)

assumes elast ic i ty - i .e. immediate and

reversible

OK for sett lement at wo rking loads i f

reasonable FOS

use smal l st rain modulus

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Definitions

Area Ratio, A p

RA= A p/ A s

A p

A s

Pile Stif fness Facto r, K

K = RA .Ep/Es

Ep Es

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Floating Pile

% load at the base

Pile top settlement

b= boCKCn

r= P.IoRKRLRn/ EsddEp Es,n

Rigid Stratum

h

L

Solut ions are independent

of so i l strength and pi le

capacity. Why?

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Floating pile example

0.5

Ep= 35,000 MPa

Es= 35 MPa

Rigid Stratum

32

25

n = 0.3

b= boCKCn r= P.IoRKRLRn/ EsdP = 1800 kN

bo= 0.038CK= 0.74Cn= 0.79b= .022Pb= 40 kN

Io= 0.043

RK= 1.4RL= 0.78

Rn= 0.93r= 4.5mmEffect of :

L = 15m

db/d = 2

h = 100m

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Pile on a stiffer stratum

% load at the base

Pile top settlement

b= boCKCbCn

r= P.IoRKRbRn/ EsddEs,n

Sti ffer Stratum

Eb> Es

LEp

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Layered Soils

E1,n1

Sti ffer Stratum

Eb> Es

L

d

EpE2,n2 Es= 1 Ei hi

L

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Stiffer base layer example

0.5

Ep= 35,000 MPa

Eb= 70 MPa

25

b= boCKCbCn r= P.IoRKRbRn/ EsdP = 1800 kN

bo= 0.038CK= 0.74

Cn= 0.79Cb= 2.1b= .0467Pb= 84 kN

Io= 0.043

RK= 1.4

Rb= 0.99

Rn= 0.93r= 4.5 mm

Es= 35 MPa

n = 0.3

Effect o f:

Es= 15 MPa to 15m

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Movement Ratios

MR is rat io of sett lement to PL/AE

Foch t (1967) - suggested in general :

0.5 < MR < 2 See Pou los and Davis Figs 5.23 and 5.24

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Pile group settlment

Floating Piles End bearing piles

psg R rr

Single pile settlement is computedfor average working load per pile