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Chapter 3
SIMPLIFIED METHOD FOR PILED RAFT FOUNDATION
3.1 Introduction
Simplified method can be used in preliminary design stage for a quick evaluation of
behavior of the foundation and to indicate whether use of piled raft is feasible or not. This
chaper summarizes the thoery of Poulos-Davis-Randolph (PDR) method and
Modifications of Poulos-Davis-Randolph (MPDR) method. PDR method was used to
analysis example 1 where piled raft with 9 and 15 piles and both homogeneous and non-
homogeneous soils were considered. Variations of piled spacing and dimension of the
piles were also considered in the analyses. MDPR method was applied to analysis
example 2 where the raft with 9, 25 and 81 piles and only homogeneous soil was
considered. Only variations of piled spacing were considered in the analyses.
3.2 Solutions for Raft and Single Pile
3.2.1 Solution for raft
Raft foundation is treated as for shallow foundation. For example, vertical capacity,
moment capacity and vertical settlement can be treated as below.
+ Vertical capacity of raft in clay is calculated as
u cs cq F cN = (3.1a)
ult
raft uQ q A= (3.1b)
+ The maximum ultimate moment sustained by the soil below the raft (Poulos, 2000)
2
8
urm
p BLM = (3.2)
+ Vertical settlement of a rigid circle raft (Poulos and Davis, 1974)
Figure 3.1 Symmetrical vertical load on circled raft (after Poulos and Davis, 1974).
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av
s
P aI
E = (3.3)
where = Vertical settlement of raft
Pav= uniformly load on circled raft
a= radius of raft
Es= Youngs modulus of soil
I
= influenced factor for vertical displacement
+ Stiffness of rigid circle raft foundation
From (3.2): [ ]sE
PaI
= (stress) or 2 2( ) [ ] [ ]s sE E
P a a aaI I
= = (force)
saEKI
= (3.4)
h= thickness of soil layer ; = Poissons ratio ;a
h, Figure 3.1 ==> I
Figure 3.2 Influence factors for vertical displacement of rigid circle (Poulos and Davis,
1974).
3.2.2 Solution for single pile
Randolph et al. (1978) was described an analytical method for analysis of a single
vertically loaded pile. The model pile with the soil surrounding the pile is divided into
two layers by a line AB is shown in Figure 3.1. A summary of steps in the solutions willbe presented here.
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Figure 3.3 Uncoupling of effects due to pile shaft and base: (a) upper and lower
soil layers; (b) separate deformation patterns of upper and lower layers (Randolph et
al., 1978)
For rigid pile
+ Assumption of a logarithmic displacement field around the piled shaft as
( )
( )
0 0
0ln ,
0,
m
m
m
r rw r r r r
G rr r
w r
=
> =
(3.5)
where 0 is the shear stress at the pile shaft, r0 is the radius of the pile and rm is the
limiting radius of influence of the pile.+ Deformation of the piled shaft is expressed, using the linear load transfer function, as
0 0s
rw
G
= (3.6)
where
( )0ln /mr r = (3.7)
+ Deformation of the piled base is expressed, using the Boussinesq solution for a rigid
punch acting on an elastic half-space, as
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( )
0
1
4
b
b
Pw
r G
= (3.8)
+ At some distance from the piled base, the load will appear as a point load. The
settlement around a point load decreases inversely with the radius as
( )1( )
2
bP
w rrG
= (3.9)
The ratio of equation (4.2) and (4.3) gives
0( ) 2
b
rw r
w r= (3.10)
From St Venants principle, the settlement caused by the piled base at large radii should
equal that due to a point load. Therefore, settlement profile at the top of the lower layer of
soil in Figure 3.1 is described by
02( )b
rw r w
r= (3.11)
+ The overall load settlement ratio for a rigid pile may be written in dimensionless form
0 0 0 0
4 2
1
t b s
l t l b l s
P P P l
G r w G r w G r w r
= + = +
(3.12)
For general condition
- Randolph (1994) presented an approximate solution based on separate treatment of the
piled shaft and the piled base as below.
+ The piled head response is given by
( )
( )
0
0
0
4 2 tanh
1
1 4 tanh
1 1
t
l t
l l
l rP
l lG r w
l r
+
=
+
(3.13)
where Ptand wtare the load and displacement at the top of the pile
land r0are the length and radius of the pile
Gl is the value of shear modulus at a depth ofz = l (see Figure 3.2)
= rb/r0 (under-reamed piles)
= Poisson ratio of soil
/l bG G =
(end-bearing piles)
Gb= shear modulus of soil below the level of pile base
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/ave l
G G = (heterogeneity of soil modulus)
Gave=average shear modulus of soil along pile length
/p lE G= (pile-soil stiffness ratio)
( )0ln /mr r = (measure of radius of influence of pile)
( ){ }0.25 2.5 1 0.25mr l = + (maximum radius of influence)
( )2.5 1 l = for 1 = (friction pile)
( )02 / /l l r = (pile compressibility)
( )2
2
1tanh
1
l
l
el
e
=
+
+ The proportion of load reaching the piled base is given by
( )
( ) 0
4 1
1 cosh
4 2 tanh
1
b
t
lP
l lP
l r
=
+
(3.14)
where ( )2
1cosh
2
l
l
el
e
+=
(a) Floating pile (b) End-bearing pile
Figure 3.4 Assumed variation of soil shear modulus with depth (Fleming, 1992)
*Discussion:
+ Stiffness of single pile is be derived from equation (3.1) as
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( )
( )
0
0
0
4 2 tanh
1
1 4 tanh1
1
l
l l
l rk G r
l l
l r
+
= +
(3.15)
+ For long piles, or where the stiffness ratio is low, very little load reach the base of the
pile, and the pile response becomes independent of the pile length. Thus, for piles longer
than 0/ 3 /p ll r E G= , the pile head stiffness may be approximated as
0
2 /t
l t
P
G r w = (3.16)
where Gltaken as the shear modulus at a depth of 03 /p lz l r E G= =
+ For stubby piles (such as equivalent piers), / 10l d < , the parameter should be
adjusted as
( ) 0ln 5 2.5 1 / l r = + (3.17)
The addition of the constant term in equation (3.53) makes insignificant difference for
normal piles (with l/d of 10 or more) but increases the piles head flexibility for shorter
piles in keeping with the accurate solution of Poulos and Davis (1980).
+ For very stiff piles, equation (4.1) reduces to
( )0 0
4 2
1
t
l t
P l
G r w r
= +
(3.18)
This expression applies for single piles where / 0.25 /p ll d E G< . For an equivalent
pier, the condition is / 0.1 /eq eq l
l d E G<
3.3 PDR Method for Piled Raft Foundation
3.3.1 Estimation of ultimate geotechnical capacity
3.3.1.1 Vertical loading
The ultimate geotechnical capacity of a piled raft foundation can be estimate as the lesser
of the following two values:
(a) the sum of the ultimate capacities of the raft plus all the piles in the system.
(b)The ultimate capacity of a block containing the piles and raft, plus that of the
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portion of the raft outside the periphery of the pile group.
Thus, the relationship between the ultimate geotechnical capacity and the number of piles
will generally have upper limit once the block mode of failure develops. Conventional
design approaches can be used to estimate the various capacities.
3.3.1.2 Lateral loading
The ultimate lateral capacity is the lesser of the sum of the ultimate lateral capacity of the
raft plus that of all the piles, or the ultimate lateral capacity of a block containing the piles,
raft and the soil, plus the contribution due to that portion of the raft outside the periphery
of the pile group.
The following points need to be noted:
(a) the respone in both orthogonal lateral directions needs to be considered.
(b)the ultimate lateral capacity of the raft may include both shear resistance at the
underside of the raft and passive resistance of the embedded portion of the raft.
(c) for the ultimate lateral capacity of the piles, both short pile (lateral failure of the
supporting soil) and long pile (yield or failure of the pile itself) modes of failure
need to be considered.
(d)for the ultimate lateral capacity of the pile-soil-raft block, it will generally beadequate to consider only the short pile failure of the block.
The generral form of the relationship between ultimate lateral capacity and the number of
piles will be similar to that for vertical loading, with an upper limit being the block
capacity of the group. Converntinal foundation design procedures can be used to assess
the various ultimate capacities.
3.3.1.3 Moment loading
The ultimate moment capacity of the piled raft can be estimated approximately as the
lesser of:
(a) the ultimate moment capacity of the raft (Mur) and the individual piles (Mup)
(b)the ultimate moment capacity of a block containing the piles, raft and soil (Mub)
The ultimate moment capacity of the raft can be estimate using the approach used by
Poulos (2000):
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271
4
ur
m u u
M V V
M V V
=
(3.19)
where Mm= maximum possible moment that soil can support
V = applied vertical loadVu= ultimate centric load on raft when no moment is applied.
Considering loading in the x-direction only, for a rectangular raft, the maximum moment
Mmin the x-direction can be expressed as
2
8
urm
p BLM = (3.20)
where pur= ultimate bearing capacity below raft
B = width of raft (in y-direction)
L = length of raft (in x-direction).
The ultimate moment contributed by the piles can be estimated from
2
1
up uui i
i
M P x=
= (3.21)
where Puui= ultimate uplift capacity of typical pile i
ix = absolute distance of pile I from centre of gravity of group
n = number of piles.The ultimate moment capacity of the block can be estimated (conservatively) from the
theory for short pile failure of a rigid pile subjected to moment loading. Poulos and
Davis (1980) give the solution for ultimate moment capacity Mub(if no harizontal force is
acting) as
2
uB B u B BM p B D= (3.22)
where BB= width of block perpendicular direction of loading
DB= depth of block
up = average ultimate lateral resistance of soil along block
B = factor depending on distribution of ultimate lateral pressure with depth
= 0.25 for constant puwith depth
= o.20 for linearly increasing puwith depth from zero at the surface.
3.3.2 Estimation of load-settlement behavior of piled rafts
PDR method includes the following steps:
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(c)estimation of the load sharing between the raft and the piles, using the
approximate solution of Randolph (1994).
(d)hyperbolic load-deflection relationships for the piles and for the raft, thus
providing a more realistic overall load-settlement response for the piled raft
system than the original tri-linear approach of Poulos and Davis (1980).
Vu
SA
Vru
Vpu
VA
LoadV
Settlement S
Raft
Piles
Total
A
B
Figure 3.5 Construction of load-settlement curve for piled raft
Figure 3.1 shows diagrammatically the load-settlement relationship for the piled raft. The
point A represents the point at which the pile capacity is fully mobilised, when the total
vertical applied load is VA. Up to that point, both the piles and the raft share the load, and
the settlement (S) can be expresses as
pr
VS
K= (3.23)
where V = vertical applied load
Kpr= axial stiffness of piled raft system.
Beyond point A, additional load must be carried by the raft, and the settlement is given by
A A
pr r
V V VS
K K
= + (3.24)
where VA= applied load at which pile capacity is mobilized
Kr= axial stiffness of raft.
The load VAcan be estimated from
pu
A
p
VV
= (3.25)
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where Vpu= ultimate capacity of piles (single pile or block failure mode, whichever is
less)
p = proportion of load carried by piles.
The approximate expressions described by Randolph (1994) are used for Kprin equation
(1) andp
in equation (2), namely
pr pK XK= (3.26)
where Kpdenotes the stiffness of pile group alone and, for fairly large numbers of piles,
( )( )
1 0.6 /
1 0.64 /
r p
r p
K KX
K K
(3.27)
1/ (1 )p
= + (3.28)
0.2
1 0.8( / )
r
r p p
K
K K K
(3.29)
If it is assumed that the pile and raft load-settlemnt relationships are hyperbolic, then the
secant stiffnesses of the piles (Kp) and the raft (Kr) can be expressed as
( )1 /p pi fp p puK K R V V = (3.30)
( )1 /r ri fr r ruK K R V V = (3.31)
where Kpi= initial tangent stiffness of pile group
Rfp= hyperbolic factor for pile group
Vp= load carried by piles
Vpu= ultimate capacity of piles
Kri= initial tangent stiffness of raft
Rfr= hyperbolic factor for raft
Vr= load carried by raft
Vru= ultimate capacity of raft
The load carried by the piles is given by
p p puV V V= (3.32)
and the load carried by the raft is
r pV V V= (3.33)
where V denotes the total vertical applied load.
Substituting equation (3.7) (3.15) in equations (3.5) and (3.6), the following expressionsare obtained for the load-settlement relationship of the piled raft system.
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:A
V V
1fp p
pi
pu
VS
R VXK
V
=
(3.34)
:AV V> ( )1
AA
pu
ri fr
ru
V VS S
V VK R
V
= +
(3.35)
where
( )1A
A
pi fp
VS
XK R=
(3.36)
with VAgiven by equation (3.7).
Equations (3.16) (3.18) are used to estimate the average load-settlement relationship forthe piled raft. Because Krand Kpwill vary with the applied load level, the papameters X
andp
will also generally vary. Therefore, it is necessary to carry out an incremental
analysis, starting with the initial stiffness Kriand Kpi.
3.3.2.1 Immediate and final settlements
The immediate and final settlements of piled raft in clay can be estimated by using the
above procedure.
For immediate settlements, the pile and raft stiffnesses are those relevant to the undrained
case, if using elastic-based theory, are estimated by using undrained values of modulus
and Poissons ratio of the soil.
For long-term settlements (immediate plus consolidation settlements, but excluding creep),
the pile and raft stiffnesses are computed using drained values of modulus and Poissons
ratio. Long-term ultimate capacities of the raft and the pile group are also relevant. Poulos
and Davis (1980) suggested that the consolidation settlement can be calculated as the
difference between the elastic total final and consolidation settlements, and add this to the
immediate settlement computed from a non-linear analysis. The overall total final
settlement STFis then
1 1TF
u e ue
VS V
K K K
= +
(3.37)
where V = applied vertical load on foundation
Ku= undrained foundation stiffness (from non-linear analysis)
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np= number of piles in group
Mx, My = moments about centroid of pile group in direction of x- and y-axes,
respectively
p
= proportion of load carried by piles
Ix, Iy= moment of inertia of pile group with respect to x- and y-axes, respectively
Ixy= product of inertia of pile group about centroid
xi,yi= distance of pile i from y-and x-axes, respectively
*
xM ,
*
yM = effective moments in x- and y-directions, respectively, taking symmetry
of pile layout into account.
For a symmetrical pile group layout, Ixy= 0 and*
x xM M= ,
*
y yM M= . Equation (1) then
reduces to
2 2
1 1
p p
p y ix ii n n
p
i i
i i
V M yM xP
nx y
= =
=
(3.40)
The above approach inherenly makes the following assumptions:
(a) the raft is rigid
(b)the pile heads are pinned to the raft and no moment is transferred from the raft to
the piles i.e. the applied moments are carried by push-pull action of the piles
(c) the piles are vertical.
3.3.4 Estimation of raft moments and shears
Bending moment and shears are significantly affected by the precise nature and
distribution of the loads. Assumpting that the raft is rigid and the contact pressures below
the raft balances only the load carried by the raft, and the piles carrying the remainign
load.
The piled raft can be considered as a series of piled strip foundations (Poulos (1991)),
with the behavior of each piled strip being obtained either on the assumption of the strip
being rigid, or preferably, using solutions for a trip on an elastic foundation, with the piles
being treated as supports (or negative loads).
3.3.5 Worked example 1: PDR method
It is requested to design the foundation for the structure as shown in Figure 3.2. For
comparison, four cases of piled raft foundations listed in Table 3.2 are considered in this
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example. The design criteria for the foundation as following:
a)a minimum overall factor of safety of 2.5 against bearing capacity, overturning and
lateral failure for the ultimate load case.
b)a maximum long-term average settlement of 50 mm and a maximum differential
settlement not exceeding 10 mm.
Table 3.1 Four cases of piled raft foundations in worked example 1
Case 1 Case 2 Case 3 Case 4
d = 0.6 m
L = 15 m
s1= 2, s2= 4
3x3 piles
d = 0.5 m
L = 21.6 m
s1= 2, s2= 4
3x3 piles
d = 0.5 m
L = 21.6 m
s1= 1.67, s2= 3.33
3x3 piles
d = 0.6 m
L = 9 m
s1= 2, s2= 2
3x5 piles
V1= V2= V3= V4(Vi= Total volume of concrete for foundation in Case i)
D
L
d
t
MxV
Hx
S1
Case 4Case 2 Case 3Case 1
L
BS2 x
y
Figure 3.7 Piled raft foundation used in worked example 1
Assuming that the homogeneous soil has a depth of D = 25m and has other parameters as
below: Su= 0.1 MPa,2
18 /sat
kN m = , 216 /unsat
kN m = and, Eu= 30MPa, 0.5u = , E =
15MPa, 0.3 = , 0.6 = (compression) and 0.42 = (tension). The concrete raft has
dimensions of 10 m long, 6 m width and 0.52 m thick. For the concrete, Young modulus
and Poissons ratio are assumed to be 30000 Mpa and 0.2 respectively. The unite weight
of concrete is 24 kN/m
2
. The yield moment of the pile itself is assumed to be 0.45MNm.
Ultimate loading
V = 20 MN
Mx= 25 MNm
Hx= 2 MN
Long-term loading
V = 15 MN
Mx= 0 MNm
Hx= 0 MN
Soil:
,u
S
,u u
E
,E
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Table 3.2 Additional four cases of piled raft foundations in worked example 1
Case 5 Case 6 Case 7
d = 0.6 m, L = 15 m
s1= 2, s2= 4, 3x3 piles
Ultimate loading: V = 13.5MN,M = 17 MNm, H = 1.5MN
Long-term loading: V = 10MN,
M = 0 MNm, H = 0MN
d = 0.6 m, L = 15 m
s1= 2, s2= 4, 3x3 piles
Ultimate loading: V = 35MN,M = 17 MNm, H = 1.5MN
Long-term loading: V = 35MN,
M = 0 MNm, H = 0MN
d = 0.6 m, L = 15 m
s1= 2, s2= 4, 3x3 piles
Su=0.048 MPa, =18kN/m3
Eu= 18 MPa, 0.5u = ,
15.6E MPa = , 0.3 =
Case 8
Undrained Youngs moduli of soils are increased with depth as: 1 15 2 ( )uE z MPa= + and
2 90 2 ( )uE z MPa= + for Layer 1 and Layer 2 respectively. Su2= 0.15 MPa and drained
Youngs moduli are calculated from equation:
2 (1 )
( )3
uE
E MPa
+
= . The properties of
foundation and other parameters of the soils are same as in Case 1.
MxV
Hx15
45 90
110Unit: MPa
D
L
d
t
(a) (b)
Figure 3.8 Piled raft foundation used in Case 8: (a) Foundation, and (b) Profile of Youngs
modulus
Results and Discussions
Table 3.4:
-Maximum central settlement and maximum differential settlement are reasonable
agreement with GARP.
-Load carried by the piles is reasonable agreement with GARP.
-Maximum and minimum piled loads are fair agreement.
-The maximum moments from PDR method are not in agreement with the values
computed by GARP.
==> Need modification or a full 3D FE analysis.
Layer 1
Layer 2
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Table 3.3 Comparison of the results in worked example 1
Verification of method
Table 3.4 Comparison between PDR method and computer analysis (GARP)
Components PDR method GARP
Max. settlement (mm) 49 43.4
Max. differential settlement (mm) 9.8 8.4Max. moment in x-direction (MN.m/m) 0.484 0.499
Min. moment in x-direction (MN.m/m) -0.109 -0.22
Max. moment in y-direction (MN.m/m) 0 0.201
Max. piled load (MN) 1.45 1.64
Min. piled load (MN) 1.45 0.95
Proportion of load carried by piles (%) 87 83*Referenced from Poulos (2000)
Effect of numbers of pile and piled configuration
V1 = V2 = V3= V4 (Vi = Total volume of concrete for foundation in Case i). Piled
configuration as in Figure 3.7
+ Ultimate geotechnical capacity
V (MN)-compression V (MN)-tension H (MN)
Figure 3.9 Ultimate bearing capacities of single pile in cases 1 to 4
(V: vertical load, H: horizontal load)
Factors of study Comparisons between cases
Verification of method 1: PDR to computer analysis
Effect of numbers of pile, piled dimensions,
piled spacing and piled configuration1, 2, 3, 4
Effect of level of loads 1, 5, 6
Effect of Youngs modulus 1, 7, 8
Cases
V,
H(
MN)
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V (MN)-PR V (MN) -Raft
M (MN.m)-PR M (MN.m) - Raft
H (MN)-PR H (MN)-Raft
Figure 3.10 Ultimate bearing capacities of raft alone and piled raft in cases 1 to 4
(V: vertical load, H: horizontal load, M: moment)
V (MN)-PR V (MN)-Raft
M (MN)-PR M (MN)-Raft
H (MN)-PR H (MN)-Raft
Figure 3.11 Comparison of FS of foundations in case 1 to 4
+ Stiffness
K1-s ing le pile (undrained) Kr-raf t (undrained)
Kp-PG (undrained) Kpr-PR(undrained)
Figure 3.12 Comparison of stiffness of raft alone, single pile, piled group and piled raft in
case 1 to 4 (undrained condition)
Cases
FS
Cases
V,
H,
M(
MNo
rMN.m
)
Cases
Stiffness,
K(MN/m
m)
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K1-sing le pile (d rained ) Kr-raf t (d rained)
Kp-PG (drained) Kpr-PR(drained)
Figure 3.13 Comparison of stiffness of raft alone, single pile, piled group and piled raft in
case 1 to 4 (drained condition)
**Effect of undrained and drained conditions
Kpr-PR (undrained) Kp-PG (undrained)
Kp-PG (drained) Kpr-PR(drained)
Figure 3.14 Comparison of stiffness of piled group and piled raft in case 1 to 4
K1-single pile (undrained) K1-single pile (drained)
Kr-Raf t (undrained) Kr-Raft (drained)
Figure 3.15 Comparison of stiffness of raft alone, single pile in case 1 to 4
+ Load distribution
Cases
Stiffness,
K(MN/mm)
Cases
Stiffness,
K(MN/mm)
Cases
Stiffness,K(MN/mm)
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Raft (undrained) Piles (undrained)
Piles (drained) Raft (drained)
Figure 3.16 Comparison of load distribution in piled rafts in case 1 to 4
+ Settlements
Differentia l settlement (Midside to cen tre)
Differentia l settlement (corner to centre)
Average settlement of foundation
Figure 3.17 Comparison of average and differential settlements in piled rafts in case 1 to 4
(case 0: raft alone)
Figure 3.16 and 3.17
For vertically loaded piled rafts, longer piles are preferable to be used to reduce the
settlement of foundation.
Cases
Loadshare,alpha(%)
Cases
Settlements(mm)
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Load carried by piles (drained)
Load carried by raft (drained)
Differential settlement (corner to centre)
Average settlement of foundation
Figure 3.18 Comparison of average, differential settlements and load share in piled rafts
in case 1 to 4 (case 0: raft alone)
*Discussion:
The average long-term settlement of raft alone is 89 mm which exceeds the limited
settlement of 50 mm. The maximum differential settlement (corner and centre) is 18 mm
which exceeds the limited differential settlement of 10 mm. It is need to add piles in the
foundation.
+ Pile load
Ultimate-Max.piled load
Long term-Min.piled load
Long term-Max.piled load
Ultimate-Min.piled load
Figure 3.19 Comparison of piled loads in piled rafts in case 1 to 4
Cases
Settlem
ents(mm)
Loadshare,alpha(%)
Cases
PiledLoad(M
N)
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*Discussion:
Case 1: the maximum axial piled load of 2.51 MN exceeds the ultimate geotechnical piled
load capacity of 1.925 MN, thus implying that the capacity of the outer piles was fully
utilized.
+ Raft bending moments and shears
Max.Mx (positive)
Max .Mx (negative)
Max .My (negative)
Max .My (positive)
Figure 3.20 Comparison of bending moment in rafts in case 1 to 4
Max.shear
Min.shear
Figure 3.21 Comparison of shear forces in rafts in case 1 to 4
+ Load-settlement, bending moment and shear curves
Cases 1 and 2
Cases
BendingMome
nt(MN.m
/m)
Cases
Shearforce(MN/m)
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PR1 PR2
P1 P2
R1 R2
Figure 3.22 Comparison of load-settlement curves of piled raft foundation in Cases 1 and
2 (undrained case), PR: piled raft; P: piled group; R: raft.
M1 M2
Figure 3.23 Comparison of bending moment curves of piled raft foundation in Cases 1
and 2 (undrained case)
Q1 Q2
Figure 3.24 Comparison of shear curves of piled raft foundation in Cases 1 and 2
(undrained case)
Verticalappliedload:MN
Settlement: mm
Bending
Moment(MNm)
Length (m)
Shear(MN)
Length (m)
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Cases 1 and 3
PR1 PR3
P1 P3
R1 R3
Figure 3.25 Comparison of load-settlement curves of piled raft foundation in Cases 1 and
3 (undrained case)
M1 M3
Figure 3.26 Comparison of bending moment curves of piled raft foundation in Cases 1
and 3 (undrained case)
Q1 Q3
Figure 3.27 Comparison of shear curves of piled raft foundation in Cases 1 and 3
(undrained case)
Verticalappliedload:MN
Settlement: mm
Bending
Moment(MNm)
Length (m)
BendingMoment(MNm)
Length (m)
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Cases 1 and 4
PR1 PR4
P1 P4
R1 R4
Figure 3.28 Comparison of load-settlement curves of piled raft foundation in Cases 1 and
4 (undrained case)
M1 M4
Figure 3.29 Comparison of bending moment curves of piled raft foundation in Cases 1
and 4 (undrained case)
Q1 Q4
Figure 3.30 Comparison of shear curves of piled raft foundation in Cases 1 and 4(undrained case)
Verticalappliedlo
ad:MN
Settlement: mm
BendingMoment(MNm)
Length (m)
BendingMoment(MNm)
Length (m)
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More comparisons can be found in Appendix A
*Discussions:
Case 2 and Case 3 have a different piled spacing but Figure 3.96 (Appendix A ) shows the
same lines for those two Cases. It is necessary to modify PDR method so that the
interactions between the piles should be considered.
Effect of levels of load
+ Ultimate geotechnical capacity
V (MN)-compression V (MN)-tension H (MN)
Figure 3.31 Ultimate bearing capacities of single pile in cases 1, 5 & 6
(V: vertical load, H: horizontal load)
V (MN)-PR V (MN) -Raft
M (MN.m)-PR M (MN.m) - Raft
H (MN)-PR H (MN)-Raft
Figure 3.32 Ultimate bearing capacities of raft alone and piled raft in cases 1, 5 & 6
(V: vertical load, H: horizontal load, M: moment)
Cases
V,
H,
M(
MNorMN.m
)
5 6Cases
V,
H(MN)
5 6
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V (MN)-PR V (MN)-Raft
M (MN)-PR M (MN)-Raft
H (MN)-PR H (MN)-Raft
Figure 3.33 Comparison of FS of foundations in case 1, 5 & 6
+ Stiffness
K1-s ing le p ile (undrained) Kr-raf t (undrained)Kp-PG (undrained) Kpr-PR(undrained)
Figure 3.34Comparison of stiffness of raft alone, single pile, piled group and piled raft in
case 1, 5 & 6 (undrained condition)
K1-single pile (d rained ) Kr-raf t (d rained)
Kp-PG (drained) Kpr-PR(drained)
Figure 3.35 Comparison of stiffness of raft alone, single pile, piled group and piled raft in
cases 1, 5 & 6 (drained condition)
Cases
FS
Cases
S
tiffness,
K(MN/mm)
5 6
5 6
5 6Cases
Stiffness,
K(MN/mm
)
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**Effect of undrained and drained conditions
Kpr-PR (undrained) Kp-PG (undrained)
Kp-PG (drained) Kpr-PR(drained)
Figure 3.36 Comparison of stiffness of piled group and piled raft in case 1, 5 & 6
K1-single pile (undrained) K1-single pile (drained)
Kr-Raf t (undrained) Kr-Raf t (drained)
Figure 3.37 Comparison of stiffness of raft alone, single pile in case 1, 5 & 6
+ Load distribution
Raft (undrained) Piles (undrained)
Piles (drained) Raf t (drained)
Figure 3.38 Comparison of load distribution in piled rafts in case 1 to 4
Cases
Stiffness,
K(MN/mm
)
Cases
Stiffness,
K(MN/mm)
5 6
5 6
5 6
Cases
Loadshare,alpha(%)
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+ Settlements
Differential settlement (Midside to centre)
Differential settlement (corner to centre)
Average settlement of founda tion
Figure 3.39 Comparison of average and differential settlements of raft alone in case 1, 5
& 6
Differential settlement (Midside to centre)
Differential settlement (corner to centre)
Average settlement of foundation
Figure 3.40 Comparison of average and differential settlements in piled rafts in case 1, 5
& 6
Cases
Settlements(
mm)
5 6
5 6
Cases
Settlements(mm)
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Load ca rried by piles (drained)
Load ca rried by raft (drained)
Differential settlement (corner to centre)
Average settlement of foundation
Figure 3.41 Comparison of average, differential settlements and load share in piled rafts
in case 1, 5 & 6
+ Pile load
Ult imate-Max.piled load Long term-Min.piled load
Long term-Max.piled load Ultimate-Min.piled load
Figure 3.42 Comparison of piled loads in piled rafts in case 1, 5 & 6
*Discussion:
Case 5: the maximum axial piled load is 1.79 MN and the ultimate geotechnical piled
load capacity is 1.925 MN. This implies that the capacity of the outer piles utilized is
1.79/1.925 = 93 %.
+ Raft bending moments and shears
Cases
PiledLoad
(MN)
5 6
Cases
Settlements(mm)
Loadshare,alpha(%) 5 6
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Max.shear
Min.shear
Figure 3.43 Comparison of bending moment in rafts in case 1, 5 & 6
Max.Mx (positive)
Max.Mx (negative)
Max.My (negative)
Max.My (positive)
Figure 3.44 Comparison of shear forces in rafts in case 1, 5 & 6
+ Load-settlement, bending moment and shear curves
Cases 1 and 5
PR1 PR5
P1 P5
R1 R5
Figure 3.45 Comparison of load-settlement curves of piled raft foundation in Cases 1 and
5 (undrained case)
Cases
BendingMom
ent(MN.m
/m)
Cases
Shearforce(MN/m)
5 6
5 6
Verticalappliedload:MN
Settlement: mm
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M1 M5
Figure 3.46 Comparison of bending moment curves of piled raft foundation in Cases 1
and 5 (undrained case)
Q1 Q5
Figure 3.47 Comparison of shear curves of piled raft foundation in Cases 1 and 5
(undrained case)
Cases 1 and 6
PR1 PR6
P1 P6
R1 R6
Figure 3.48 Comparison of load-settlement curves of piled raft foundation in Cases 1 and6 (undrained case)
BendingMoment(MNm)
Length (m)
BendingMoment(MNm)
Length (m)
Verticalappliedload:MN
Settlement: mm
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M1 M6
Figure 3.49 Comparison of bending moment curves of piled raft foundation in Cases 1
and 6 (undrained case)
Q1 Q6
Figure 3.50 Comparison of shear curves of piled raft foundation in Cases 1 and 6
(undrained case)
More comparisons can be found in Appendix A
Effect of Youngs modulus
+ Ultimate geotechnical capacity
V (MN)-compression
V (MN)-tension
H (MN)
Figure 3.51 Ultimate bearing capacities of single pile in cases 1, 7& 8
7 8Cases
V,
H(MN)
BendingMoment(MNm)
Length (m)
BendingMoment(MNm)
Length (m)
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(V: vertical load, H: horizontal load)
V (MN)-PR V (MN) -Raft
M (MN.m)-PR M (MN.m) - Raft
H (MN)-PR H (MN)-Raft
Figure 3.52 Ultimate bearing capacities of raft alone and piled raft in cases 1, 7 & 8
(V: vertical load, H: horizontal load, M: moment)
V (MN)-PR V (MN)-Raft
M (MN)-PR M (MN)-Raft
H (MN)-PR H (MN)-Raft
Figure 3.53 Comparison of FS of foundations in case 1, 7 & 8
+ Stiffness
K1-s ing le p ile (undrained) Kr-raf t (undrained)
Kp-PG (undrained) Kpr-PR(undrained)
Figure 3.54 Comparison of stiffness of raft alone, single pile, piled group and piled raft in
Cases
FS
Cases
V,
H,
M(
MNorMN
.m)
Cases
Stiffness,
K(MN/mm)
7 8
7 8
7 8
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case 1, 7 & 8(undrained condition)
K1-single pile (drained)
Kr-raft (drained)
Kp-PG (drained)
Kpr-PR(drained)
Figure 3.55 Comparison of stiffness of raft alone, single pile, piled group and piled raft in
cases 1, 7 & 8 (drained condition)
**Effect of undrained and drained conditions
Kpr-PR (undrained) Kp-PG (undrained)
Kp-PG (drained) Kpr-PR(drained)
Figure 3.56 Comparison of stiffness of piled group and piled raft in case 1, 5 & 6
K1-single pile (undrained)
K1-single pile (drained)
Kr-Raft (undrained)
Kr-Raft (drained)
Figure 3.57 Comparison of stiffness of raft alone, single pile in case 1, 7 & 8
Cases
Stiffness,
K(MN/mm)
Cases
Stiffness,
K(MN/mm)
7 8
Cases
Stiffness,
K(MN/mm
)
7 8
7 8
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+ Load distribution
Raf t (undrained) Piles (undrained)
Piles (drained) Raft (drained)
Figure 3.58 Comparison of load distribution in piled rafts in case 1 to 4
+ Settlements
Differential settlement (Midside to centre)
Differential settlement (corner to centre)
Average settlement of foundat ion
Figure 3.59 Comparison of average and differential settlements of raft alone in case 1, 7
& 8
7 8
Cases
Loadshare,alpha(%)
7 8Cases
Settlements(mm
)
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Differential settlement (Midside to centre)
Differential settlement (corner to centre)
Average settlement of foun dation
Figure 3.60 Comparison of average and differential settlements in piled rafts in case 1, 7
& 8
Load carried by piles (drained)
Load carried by raft (drained)
Differential settlement (corner to centre)
Average settlement of foundation
Figure 3.61 Comparison of average, differential settlements and load share in piled rafts
in case 1, 7 & 8
+ Pile load
Cases
Settlements(mm)
7 8
Cases
Settlements(mm)
Loadshare,alpha(%)
7 8
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Ultimate-Max.piled load Long term-Min.piled load
Long term-Max.piled load Ultimate-Min.piled load
Figure 3.62 Comparison of piled loads in piled rafts in case 1, 7 & 8
+ Raft bending moments and shears
Max.Mx (posit ive) Max.Mx (nega tive)
Max.My (nega tive) Max.My (posit ive)
Figure 3.63 Comparison of bending moment in rafts in case 1, 7 & 8
Max.shear Min.shear
Figure 3.64 Comparison of shear forces in rafts in case 1, 7 & 8
+Load settlement, bending moment and shear force curves
Cases
PiledLoad(M
N)
Cases
Bend
ingMoment(MN.m
/m)
Cases
Shearforce(MN/m)
7 8
7 8
7 8
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Cases 1 and 7
PR1 PR7
P1 P7
R1 R7
Figure 3.65 Comparison of load-settlement curves of piled raft foundation in Cases 1 and
7 (undrained case)
M1 M7
Figure 3.66 Comparison of bending moment curves of piled raft foundation in Cases 1
and 7 (undrained case)
Q1 Q7
Figure 3.67 Comparison of shear curves of piled raft foundation in Cases 1 and 7
(undrained case)
Verticalappliedlo
ad:MN
Settlement: mm
BendingMoment(MNm)
Length (m)
BendingMoment(MNm)
Length (m)
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Cases 1 and 8
PR1 PR8
P1 P8
R1 R8
Figure 3.68 Comparison of load-settlement curves of piled raft foundation in Cases 1 and
8 (undrained case)
M1 M8
Figure 3.69 Comparison of bending moment curves of piled raft foundation in Cases 1
and 8 (undrained case)
Q1 Q8
Figure 3.70 Comparison of shear curves of piled raft foundation in Cases 1 and 8
Verticalappliedlo
ad:MN
Settlement: mm
BendingMoment(MNm)
Length (m)
BendingMoment(M
Nm)
Length (m)