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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


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)


case 1 to 4 (drained condition)

**Effect of undrained and drained conditions

Kpr-PR (undrained) Kp-PG (undrained)


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)


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


3 (undrained case)

M1 M3



Q1 Q3


(undrained case)


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


4 (undrained case)

M1 M4



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


V (MN)-compression V (MN)-tension H (MN)

Figure 3.31 Ultimate bearing capacities of single pile in cases 1, 5 & 6





Figure 3.32 Ultimate bearing capacities of raft alone and piled raft in cases 1, 5 & 6


Cases

V,

H,

M(

MNorMN.m

)

5 6Cases

V,

H(MN)

5 6

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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)



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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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)


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)


Average settlement of founda tion

Figure 3.39 Comparison of average and differential settlements of raft alone in case 1, 5

& 6




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)




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 %.


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


5 (undrained case)

Cases

BendingMom

ent(MN.m

/m)

Cases

Shearforce(MN/m)

5 6

5 6


Settlement: mm

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M1 M5



Q1 Q5


(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)


Settlement: mm

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M1 M6



Q1 Q6


(undrained case)

More comparisons can be found in Appendix A

Effect of Youngs modulus


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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Figure 3.52 Ultimate bearing capacities of raft alone and piled raft in cases 1, 7 & 8





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)


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)


cases 1, 7 & 8 (drained condition)




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)


+ Settlements



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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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)




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


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


7 (undrained case)

M1 M7



Q1 Q7


(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


8 (undrained case)

M1 M8



Q1 Q8


Verticalappliedlo

ad:MN

Settlement: mm

BendingMoment(MNm)

Length (m)

BendingMoment(M

Nm)

Length (m)

13chapter 3a

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