9. Axial Capacity
of Pile Groups
CIV4249: Foundation Engineering
Monash University
Fu
Fu + WCapacity
= Pbase + Pshaft
Axial
Pshaft
Shear failure at pile shaft
W
Pbase
Bearing failure at the pile base
Tension Capacity
Tu - W = Pshaft,t < Pshaft,c
Pshaft,t
Shear failure at pile shaft
Applications
Large Distributed
Weight
Very Large Concentrated
Weight
Low
Weight
Soft to
Firm Clay
Dense Sand
Strong Rock
ug
Group PCapacity
Pile Cap
•
•
•
•
Overlapping stress fields
Progressive densification
Progressive loosening
Case-by-case basis
Pug  n.Pup
Pug = e.n.Pup
Efficiency, e
Pile Cap
n = 5 x 5 = 25
Clay
Soil
Type of Piles, n
Number
Spacing/Diameter
d
Sand
s
s/d typically > 2 to 3
Rock
Types
of Groups
Free-standing
Capped
Flexible Cap
Rigid Cap
Feld Rule for free-standing
piles in clay
13/16
11/16
A
B
B
B
A
reduce capacity of each pile by 1/16 for each adjoing pile
B
8/16
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
e = 1 - q (n-1)m + (m-1)n
90
mn
q=
d=0.3
tan-1(d/s)
s = 0.75
e = 0.645
m = # rows = 3
Block Failure
Flexible Cap
PBL = BLcbNc + 2(B+L)Dcs
D
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
nPup
1 = 1 + n2P2 up
e2
P2BL
n
Block Failure
Flexible Cap
D = 20m
d = 0.3m
L = B = 5m
cs = cb = 50 kPa
Capped Groups
Bc x Lc
Rigid Cap
Ptotal = Pgroup + Pcap
for single
group pile
block
failure,
failure,PP
= =ccap
ccap
NN
[B[B
Lc- nA
- BL]
cap
cap
cc
cL
cc
p ]
BxL
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
Definitions
Area Ratio, Ap
Pile Stiffness Factor, K
RA = Ap / As
K = RA.Ep/Es
Ap
Ep
As
Es
Floating Pile
• % load at the base
b = boCKCn
L
Ep
Es,n
d
Rigid Stratum
• Pile top settlement
h
r = P.IoRKRLRn / Esd
Solutions are independent
of soil strength and pile
capacity. Why?
P = 1800 kN
Floating pile example
b = boCKCn
Ep = 35,000 MPa
25
0.5 32
Es = 35 MPa n = 0.3
Rigid Stratum
r = P.IoRKRLRn / Esd
bo = 0.038
CK = 0.74
Cn = 0.79
b = .022
Pb = 40 kN
Effect of :
L = 15m
db/d = 2
h = 100m
Io = 0.043
RK = 1.4
RL = 0.78
Rn = 0.93
r = 4.5mm
Pile on a stiffer stratum
• % load at the base
b = boCKCbCn
L
Ep
Es,n
d
Stiffer Stratum
Eb > Es
• Pile top settlement
r = P.IoRKRbRn / Esd
Layered Soils
L
Ep
E1,n1
E2,n2
d
Stiffer Stratum
Eb > Es
Es = 1
L
S Ei hi
P = 1800 kN
Stiffer base layer example
b = boCKCbCn
r = P.IoRKRbRn / Esd
n = 0.3
Ep = 35,000 MPa
25
Es = 35 MPa
0.5
Eb = 70 MPa
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
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
Pile group settlment
• Floating Piles
• End bearing piles
r g  Rs r p
Single pile settlement is computed
for average working load per pile