9. Axial Capacity of Pile Groups

9. Axial Capacityof Pile Groups CIV4249: Foundation Engineering Monash University

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

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

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

Pug Group Capacity Pile Cap • Overlapping stress fields • Progressive densification • Progressive loosening • Case-by-case basis Pug¹n.Pup Pug = e.n.Pup

Clay Sand d s Rock Efficiency, e Pile Cap n = 5 x 5 = 25 Soil Type Number of Piles, n Spacing/Diameter s/d typically > 2 to 3

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

13/16 11/16 8/16 û Feld Rule for free-standing piles in clay A B B B A 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

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

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

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

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

Capped Groups Bc x Lc Rigid Cap Ptotal = Pgroup + Pcap for single pile failure, Pcap = ccapNc [BcLc - nAp] for group block failure, Pcap = ccapNc [BcLc - BL] B x L

Efficiency increases 1.0 72 capped 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

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

% load at the base Pile top settlement d Floating Pile Ep b = boCKCn Es,n L h r = P.IoRKRLRn / Esd Solutions are independent of soil strength and pile capacity. Why? Rigid Stratum

0.5 Floating pile example P = 1800 kN b = boCKCn r = P.IoRKRLRn / Esd Ep = 35,000 MPa Io = 0.043 RK = 1.4 RL = 0.78 Rn = 0.93 r = 4.5mm bo = 0.038 CK = 0.74 Cn = 0.79 b = .022 Pb = 40 kN 25 32 Effect of : L = 15m db/d = 2 h = 100m n = 0.3 Es = 35 MPa Rigid Stratum

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

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

0.5 Stiffer base layer example P = 1800 kN b = boCKCbCn r = P.IoRKRbRn / Esd Ep = 35,000 MPa n = 0.3 Io = 0.043 RK = 1.4 Rb = 0.99 Rn = 0.93 r = 4.5 mm bo = 0.038 CK = 0.74 Cn = 0.79 Cb = 2.1 b = .0467 Pb = 84 kN 25 Es = 35 MPa 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

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

9. Axial Capacity of Pile Groups