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

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

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

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

5. 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

6. 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

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

8. Feld Rule for free-standing piles in clayû
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

9. 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

10. 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)

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

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

13. 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

14. 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

15. 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

16. Pile Settlement

17. 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

18. 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

19. 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

20. 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

21. 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

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

23. 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

24. 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

25. 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