Pile Group (2)
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Transcript of Pile Group (2)
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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