9. Axial Capacity of Pile Groups CIV4249: Foundation Engineering Monash University

Axial Capacity Fu + W = Pbase + Pshaft W Pshaft Fu Shear failure at pile shaft Pbase Bearing failure at the pile base

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

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

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

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

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

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 * 13/16 + 8 * 11/16 + 3 * 8/16) = 0.683 A B B B A

Converse-Labarre Formula for free-standing piles in clay n = # cols = 5 m = # rows = 3 e = 1 - q (n-1)m + (m-1)n 90 mn s = 0.75 d=0.3 q = tan-1(d/s) e = 0.645

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)

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

Block Failure D = 20m cs = cb = 50 kPa d = 0.3m Flexible Cap L = B = 5m

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

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

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

Pile Settlement

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

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

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

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

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

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

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

Movement 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

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