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**9. Axial Capacity of Pile Groups**

CIV4249: Foundation Engineering Monash University

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**Axial Capacity Fu + W = Pbase + Pshaft W Pshaft Fu**

Shear failure at pile shaft Pbase Bearing failure at the pile base

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**Tu - W = Pshaft,t < Pshaft,c**

Tension Capacity Tu - W = Pshaft,t < Pshaft,c Pshaft,t Shear failure at pile shaft

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**Very Large Concentrated**

Applications Very Large Concentrated Weight Large Distributed Weight Low Weight Soft to Firm Clay Dense Sand Strong Rock

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**Group Capacity Pug ¹ n.Pup Pug = e.n.Pup Pile Cap Pug**

Overlapping stress fields Progressive densification Progressive loosening Case-by-case basis Pug ¹ n.Pup Pug = e.n.Pup

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**Efficiency, e Clay Sand Rock Pile Cap n = 5 x 5 = 25 Soil Type**

Number of Piles, n Spacing/Diameter s d s/d typically > 2 to 3

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**Capped Groups Types of Groups**

Flexible Cap Free-standing Groups Rigid Cap Capped Groups Types of Groups

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**Feld Rule for free-standing piles in clay**

û Feld Rule for free-standing piles in clay 13/16 11/16 A B B B A 8/16 reduce capacity of each pile by 1/16 for each adjoing pile B C C C B e = 1/15 * (4 * 13/ * 11/ * 8/16) = 0.683 A B B B A

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**Converse-Labarre Formula for free-standing piles in clay**

n = # cols = 5 m = # rows = 3 e = 1 - q (n-1)m + (m-1)n mn s = 0.75 d=0.3 q = tan-1(d/s) e = 0.645

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**Block Failure PBL = BLcbNc + 2(B+L)Dcs D cs cb L,B**

Flexible Cap D PBL = BLcbNc + 2(B+L)Dcs cs Nc incl shape & depth factors cb L,B Pug = min (nPup,PBL)

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**Empirical Modification**

PBL = BLcbNc + 2(B+L)Dcs Pug = min (nPup,PBL) P2ug = n2P2up + P2BL 1 = n2P2 up e2 P2BL nPup n

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**Block Failure D = 20m cs = cb = 50 kPa d = 0.3m Flexible Cap**

L = B = 5m

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**Capped Groups Ptotal = Pgroup + Pcap Bc x Lc Rigid Cap**

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

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**Efficiency increases s/d 1 2 3 4 72 capped 72 free-standing 1.0 0.9**

0.8 0.7 72 free-standing 0.6 0.5 0.4 s/d 0.3 1 2 3 4

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**Piles 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

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Pile Settlement

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**Elastic 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

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**Definitions Ep Es Area Ratio, Ap Pile Stiffness Factor, K K = RA.Ep/Es**

RA = Ap / As K = RA.Ep/Es Ap As Ep Es

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**Floating Pile Ep Es,n L d h % load at the base b = boCKCn**

Pile top settlement d h r = P.IoRKRLRn / Esd Solutions are independent of soil strength and pile capacity. Why? Rigid Stratum

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**Floating pile example b = boCKCn r = P.IoRKRLRn / Esd P = 1800 kN**

Ep = 35,000 MPa bo = 0.038 CK = 0.74 Cn = 0.79 b = .022 Pb = 40 kN Io = 0.043 RK = 1.4 RL = 0.78 Rn = 0.93 r = 4.5mm 25 32 0.5 Effect of : L = 15m db/d = 2 h = 100m Es = 35 MPa n = 0.3 Rigid Stratum

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**Pile on a stiffer stratum**

% load at the base Ep b = boCKCbCn Es,n L Pile top settlement d r = P.IoRKRbRn / Esd Stiffer Stratum Eb > Es

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**Layered Soils Es = 1 S Ei hi L Ep E1,n1 L E2,n2 d Stiffer Stratum**

Eb > Es d

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**Stiffer base layer example**

P = 1800 kN b = boCKCbCn r = P.IoRKRbRn / Esd Ep = 35,000 MPa n = 0.3 bo = 0.038 CK = 0.74 Cn = 0.79 Cb = 2.1 b = .0467 Pb = 84 kN Io = 0.043 RK = 1.4 Rb = 0.99 Rn = 0.93 r = 4.5 mm 25 Es = 35 MPa 0.5 Eb = 70 MPa Effect of: Es = 15 MPa to 15m

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**Movement Ratios MR is ratio of settlement to PL/AE**

Focht (1967) - suggested in general : < MR < 2 See Poulos and Davis Figs 5.23 and 5.24

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**Single pile settlement is computed for average working load per pile**

Pile group settlment Floating Piles End bearing piles Single pile settlement is computed for average working load per pile

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Prepared by J. P. Singh & Associates in association with Mohamed Ashour, Ph.D., PE West Virginia University Tech and Gary Norris Ph.D., PE University of.

Prepared by J. P. Singh & Associates in association with Mohamed Ashour, Ph.D., PE West Virginia University Tech and Gary Norris Ph.D., PE University of.

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