9. Axial Capacityof Pile Groups

9. Axial Capacityof Pile Groups

CIV4249: Foundation Engineering

Monash University

CIV4249: Foundation Engineering

Monash University

Axial CapacityAxial Capacity

W

Pbase Bearing failure at the pile base

Pshaft Shear failure at pile shaft

Fu Fu + W = Pbase + Pshaft

Pshaft,t Shear failure at pile shaft

Tu - W = Pshaft,t < Pshaft,c

Tension CapacityTension Capacity

ApplicationsApplications

LowWeight

Soft toFirm Clay

Large DistributedWeight

Very Large ConcentratedWeight

Dense Sand

Strong Rock

Group CapacityGroup Capacity

• Overlapping stress fields• Progressive densification• Progressive loosening• Case-by-case basis

• Overlapping stress fields• Progressive densification• Progressive loosening• Case-by-case basis

Pile Cap

Pug

Pug ¹ n.Pup

Pug = e.n.Pup

Pug ¹ n.Pup

Pug = e.n.Pup

Efficiency, eEfficiency, e

Soil Type Soil Type

Clay

SandSand

Rock

Number of Piles, n Number of Piles, n

n = 5 x 5 = 25

Spacing/Diameter Spacing/Diameter

s

d

s/d typically > 2 to 3s/d typically > 2 to 3

Pile Cap

Types of GroupsTypes of Groups

Rigid Cap

Capped GroupsCapped Groups

Flexible Cap

Free-standing GroupsFree-standing Groups

Feld Rule for free-standing piles in clay

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 pile by 1/16 for each adjoing pile

13/16 11/16

8/16

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

Converse-Labarre Formula for free-standing piles in clay

Converse-Labarre Formula for free-standing piles in clay

e = 1 - q (n-1)m + (m-1)n 90 mn

m = # rows = 3

n = # cols = 5

s = 0.75d=0.3

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

Flexible Cap

Pug = min (nPup,PBL)Pug = min (nPup,PBL)

D

L,B

PBL = BLcbNc + 2(B+L)DcsPBL = BLcbNc + 2(B+L)Dcs

cs

cb

Block FailureBlock Failure

Nc incl shape & depth factorsNc incl shape & depth factors

Empirical ModificationEmpirical Modification

nnPupnPup

PBL = BLcbNc + 2(B+L)DcsPBL = BLcbNc + 2(B+L)Dcs

Pug = min (nPup,PBL)Pug = min (nPup,PBL) 1 1 1 P2

ug = n2P2up + P2

BL

1 1 1 P2

ug = n2P2up + P2

BL

1 = 1 + n2P2 up

e2

1 = 1 + n2P2 up

e2

P2

BL

Flexible Cap

D = 20m

L = B = 5m

cs = cb = 50 kPa

Block FailureBlock Failure

d = 0.3m

Rigid Cap

Ptotal = Pgroup + PcapPtotal = Pgroup + Pcap

for group block failure, Pcap = ccapNc [BcLc - BL]for group block failure, Pcap = ccapNc [BcLc - BL]for single pile failure, Pcap = ccapNc [BcLc - nAp ]for single pile failure, Pcap = ccapNc [BcLc - nAp ]

Capped GroupsCapped Groups

B x L

Bc x Lc

Efficiency increasesEfficiency increases

s/d

1 2 3 40.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

72 free-standing

72 capped

Piles in Granular SoilsPiles in Granular Soils

• End bearing - little interaction, e = 1• Shaft - driven

– For loose to medium sands, e > 1– Vesic driven : 1.3 to 2 for s/d = 3 to 2– Dense/V dense - loosening?

• Shaft - bored– Generally minor component, e = 1

Pile SettlementPile Settlement

Elastic Analysis MethodsElastic Analysis Methods

• based on Mindlin’s equations for shear loading within an elastic halfspace

• Poulos and Davis (1980)• assumes elasticity - i.e. immediate and

reversible• OK for settlement at working loads if

reasonable FOS• use small strain modulus

DefinitionsDefinitions

Area Ratio, Ap

RA = Ap / AsRA = Ap / As

Ap

As

Pile Stiffness Factor, K

K = RA.Ep/EsK = RA.Ep/Es

Ep Es

Floating PileFloating Pile

• % load at the base

• Pile top settlement

b = boCKCnb = boCKCn

r = P.IoRKRLRn / Esdr = P.IoRKRLRn / Esdd

Ep Es,n

Rigid Stratum

h

L

Solutions are independentof soil strength and pilecapacity. Why?

Floating pile exampleFloating pile example

0.5

Ep = 35,000 MPa

Es = 35 MPa

Rigid Stratum

32

25

n = 0.3

b = boCKCnb = boCKCn r = P.IoRKRLRn / Esdr = P.IoRKRLRn / Esd

P = 1800 kN

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

Io = 0.043RK = 1.4RL = 0.78Rn = 0.93r = 4.5mm

Effect of :L = 15mdb/d = 2h = 100m

Pile on a stiffer stratumPile on a stiffer stratum

• % load at the base

• Pile top settlement

b = boCKCbCnb = boCKCbCn

r = P.IoRKRbRn / Esdr = P.IoRKRbRn / Esdd

Es,n

Stiffer StratumEb > Es

LEp

Layered SoilsLayered Soils

E1,n1

Stiffer StratumEb > Es

L

d

Ep

E2,n2Es = 1 S Ei hi

L

Es = 1 S Ei hi

L

Stiffer base layer exampleStiffer base layer example

0.5

Ep = 35,000 MPa

Eb = 70 MPa

25

b = boCKCbCnb = boCKCbCn r = P.IoRKRbRn / Esdr = P.IoRKRbRn / Esd

P = 1800 kN

bo = 0.038CK = 0.74Cn = 0.79Cb = 2.1b = .0467Pb = 84 kN

Io = 0.043RK = 1.4Rb = 0.99Rn = 0.93r = 4.5 mm

Es = 35 MPa

n = 0.3

Effect of:Es = 15 MPa to 15m

Movement RatiosMovement Ratios

• MR is ratio of settlement to PL/AE

• Focht (1967) - suggested in general : 0.5 < MR < 2

• See Poulos and Davis Figs 5.23 and 5.24

Pile group settlmentPile group settlment

• Floating Piles• End bearing piles

psg R

Single pile settlement is computed for average working load per pile