32.three dimensional analysis of piled-raft foundation in clay soils

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Three Dimensional Analysis of Piled Raft Foundation in Clay Soils

Sangseom Jeong1* ･ Jaeyeon Cho2

1 Professor, School of Civil and Environmental Engineering, Yonsei University, Seoul 120 749, Korea

2Graduate student, School of Civil and Environmental Engineering, Yonsei University, Seoul 120 749, Korea

❚ Abstract❚

The settlement behavior of a square piled raft in clay soil was investigated using numerical analysis. The emphasis

was on quantifying the reduction of the average and differential settlements in soft and stiff clay soils. To obtain the

detailed information on the piled raft, nonlinear three dimensional finite element analyses with pile-soil slip interface

model were performed for various pile positions, pile numbers, pile lengths under the raft and different loading types.

Based on the results obtained, design considerations concerning the settlement of piled rafts subjected to vertical loading

are discussed. It is found that the variation of reduction ratio of soft clay was relatively greater than that of stiff clay,

whereas the reduction ratio of soft clay was relatively smaller than that of stiff clays. It is also found that the required

pile group-raft area ratio for minimizing differential settlement in soft clay was slightly larger than that of stiff clay

in the same pile array.

Keywords : Piled raft, Average and differential settlement, Three dimensional finite element analysis, Pile-soil slip

interface

*Corresponding author to Sangseom Jeong, Professor, School

of Civil and Environmental Engineering, Yonsei University,

Seoul 120 749, KoreaTel : +82-2-2123-2807, Fax : +82-2-364-5300

E-mail : [email protected]

Received 25 January 2012; Accepted 12 March 2012

International Journal of Geo-Engineering 4(1) : 11-22 (2012)

1. INTRODUCTION

In South Korea, a number of large projects involving

land reclamation are being undertaken. An increasing

number of structures are constructed on soft ground, and

the application of piled rafts on soft ground is becoming

an important issue in foundation design. However, it is

known for an unfavorable foundation type in soft clay,

which may be associated with excessive settlement andinsufficient bearing capacity (Cooke, 1986; Lee et al. 2010;

Poulos, 2001, 2005). Despite these concerns, a few successful

applications of piled rafts on soft clay have been reported

(Kakurai et al. 1987; Poulos, 2005; Tan et al. 2006;

Yamashita et al. 1998).

A piled raft comprises three elements of pile, raft and

subsoil. And the behavior of a piled raft is affected by

the 3D interaction between the subsoil, piles and raft. In

addition, for soft clay conditions, the magnitude of settlement

is larger than for stiff clay conditions under the same vertical

applied load, so soil-structure (piles and raft) interaction

is much more complicated. In this case, a contribution

of the raft, which is contact with soil, is considered and

the loads are carried by the raft and the piles. However,

the piles are usually required to reduce the average and/ordifferential settlements of the foundation to an acceptable

level rather than to carry the major portion of the load.

Therefore, a major design concept is that the settlement

of foundation is permitted within serviceability criterion.

This has affected how piles are designed optimally to reduce

the settlements of the foundation. There are several design

approaches available for predicting the settlement behavior

of piled raft in clay soils subject to vertical loading, using

numerical methods (de Sanctis et al. 2002; Horikoshi and

Randolph, 1997; Katzenbach et al. 2005; Poulos, 1994;Prakoso and Kulhawy, 2001; Randoph, 2003; Reul and

Randolph, 2004). It is recognized, however, that the three

11



12 Sangseom Jeong and Jaeyeon Cho

(a) (b)

Fig. 1. Representative finite element mesh used in the analysis (ex. 3x3 array, Lp=16 m): (a) Typical 3D FE mesh and boundary

condition; (b) Side view

Table 1. Summary of pile configurations of numerical analyses conducted

Pile array Pile spacing (s)* Pile length (Lp, m)** Remarks

33 3d, 6d, 9d 8f

, 12f

16f , 20

e1) *d (pile diameter): 0.5 m2) **f: floating; e: end bearing44 3d, 4d, 6d

■ Square raft: width (B) = 10 m, thickness (t) = 1 m

dimensional (3D) Finite Element (FE) analysis is the most

appropriate method (Poulos, 2001); additionally 3D FE

analysis which consider pile-soil slip interface offer a better

estimation of the behavior of piled raft in clay soils (Lee

et al. 2010).Therefore, the overall objective of this study focuses

on investigating the settlement behavior of a piled raft on

clay soils under vertical loading by using 3D FE analysis

considering the pile-soil slip interface model. Furthermore,

the comparison of behavior for relatively stiff soil properties

was also carried out for different pile configurations and

loading types then, the settlement behavior of piled rafts

was investigated.

2. THREE DIMENSIONAL FEM MODELING

2.1 Finite Element Mesh and Boundary Conditions

The behavior of a square piled raft (PR) was investigated

using 3D FE analyses. The FE package ABAQUS was

used. The 3D model included a rigorous treatment of the

soil and piled raft which were represented by 27 noded

2nd

order hexahedral elements. The mesh was assumed

to be resting on a rigid layer, and the vertical boundaries

at the left- and right- hand sides were assumed to be on

rollers to allow downward movement of soil layers. The

pile head was connected to the raft rigidly. Due to symmetry,

a quarter of a whole mesh was used in the 3D analyses.

Since modeling of the entire pile installation process israther complicated, the pile was assumed to be in a stress-

free state at the start of the analysis (Jeong et al. 2004).

The stress change in the soil during pile installation was

therefore not included. A summary of the analyses is

shown in Table 1. Fig. 1 shows a typical 3D FE mesh

used in this analysis. In addition, as a reference for the

behavior of a piled raft, an unpiled raft (UR) was also

analyzed.

2.2 Constitutive Modeling

Table 2 summarizes the material parameters used in

the analyses. The soft clay, stiff clay and bearing layer

were modeled with a Mohr-Coulomb model. Attention was

focused on the drained response of a piled raft resting

on a soft and stiff clay layer, so that the soil layer was

idealized using drained properties with the groundwater

table located on the top of the clay layer, assuming a

hydrostatic water pressure distribution. Thus, consolidation



Three Dimensional Analysis of Piled Raft Foundation in Clay Soils 13

Table 2. Material parameters used in the analyses

Model E ' (MPa) c' (kPa) ' (°) ν' K 0 t (kN/m3)

PileElastic

12,500 - - 0.25 0.01 25

Raft 30,000 - - 0.2 0 25

Clay (soft)Mohr-

Coulomb

5 3 20 0.3 0.65 18

Clay (stiff) 45 20 20 0.3 0.65 19

Bearing 500 0.1 45 0.3 0.5 20

Fig. 2. Behavior at the interface

Fig. 3. Coulomb’s friction laweffects were neglected. Also, to simplify the analysis

process, constant material parameters were adopted for

the soil layer. The raft and piles were modeled with an

isotropic elastic element. The pile was selected as a typical

steel pipe pile which was modeled with a solid section.

The Young’s modulus of the solid pile section was chosen

so that the axial stiffness would be equivalent to that of

a steel pipe pile. The material properties were adopted

from reference values as reported by Lee et al. (2010).

A slip model was used to describe the pile-soil interface

behavior. This model was selected from the contact model

of ABAQUS and the interface modeling was carried out

by specifying a limiting shear displacement of 5 mm (Lee

et al. 2002) and an interface friction coefficient μ=0.3

(Jeong et al. 2004). The raft-soil interface was considered

smooth with contact only. The schematic diagram is shown

in Fig. 2. The interface elements were composed of 2D

quadratic 18-node elements, each element of two nine-node

surfaces compatible with the adjacent solid elements (the

two surfaces coincide initially). In case of “no sliding”

occurred, nodes at the interface have identical coordinates

and the distance between the two surfaces is zero, through

the surfaces, shear stress was transferred as well as normal

forces when two surfaces are attached each other. In the

case that pile element moves along the surface, shear

stress (τ) occurs in the interface. The frictional constitutive

model for interface used is a Coulomb’s frictional model

which is shown in Fig. 3. The shear behavior in the

interface is that elastic behavior occurs until critical shear

stress (τcrit ) in Eq. (1) reached and after that only shear

displacement increases without increase of shear stress.

pcrit ⋅= µ τ (1)

After initial equilibrium, the vertical uniformly distributed

loading (P) was applied on the top of the raft. In this

analysis, the pile installation effect and the settlement due

to the weight of the raft were not considered.

2.3 Post Analysis

The vertical settlements from the 3D FE analyses were

used directly, and the average settlement ( savg ) was calculated

by Eq. (2) (Reul and Randolph, 2004).

3/)2( corner center avg s s s += (2)

where scenter = settlement of raft center, scorner = settlement

of raft corner.

The center to corner differential settlement was calculated

based on Eq. (3).

corner center cc s s s −=∆ − (3)




(a) (b)

(c) (d)

Fig. 4. Typical Finite element mesh: (a) 3D FE mesh; (b) Plan view; (c) Profile view of Torhaus Der Messe; (d) Side view

The rectangular raft-soil stiffness ratio ( K rs) was calculated

at 31.7, using Eq. (4), which can be assumed to represent

a relatively rigid raft because Horikoshi and Randolph

(1997) reported K rs of 0.001 is fully flexible, while K rs

of 1000 is essentially rigid.

35.0

2

2

1

157.5 ⎟

⎠

⎞⎜⎝

⎛ ⎟ ⎠

⎞⎜⎝

⎛

−

−=

L

t

L

B

E

E K r

r

s

s

r rs

ν

ν

(4)

where E r and E s = Young’s modulus of the raft and the

soil, ν r and ν s = Poisson’s ratio of the raft and the soil

respectively, t r = thickness of the raft, B and L = breadth

and the length of the rectangular raft, respectively.

The piled raft coefficient described the ratio of the sum

of all pile load (R pile) to the total load of the foundation

(R tot) using Eq. (5).

tot

pile pr

R

RΣ=α

(5)

2.4 Validation

The validation of the 3D FE model was examined by a

comparison of the analyzed results with the field measure-

ment for vertically loaded piled rafts on the Frankfurt

clay, which was carried out by Sommer (1991). A total

number of 84 bored piles with a length of 20 m and

diameter of 0.9 m were located under two 17.5 m × 24.5

m large rafts with 2.5 m thickness. Fig. 4 (a) shows a




Table 3. Material properties used for 3D FE analysis

Clay Sand Raft Piles

Young’s modulus, E’: MPa 47 75 34000 23500

Poisson’s ratio, ν’ 0.15 0.25 0.2 0.2

Total unit weight, : kN/m3 19 18 15 15

Angle of internal friction, ’ 20 32.5 - -

Cohesion, c’: kPa 20 0 - -

Table 4. Comparison of the results

Results scenter (mm) Piled raft coefficient (pr)

Measured (Sommer, 1991) 124 0.67

Reul & Randolph (2003) 96 0.76

Present study

(Frankfurt clay)

Slip analysis 114 0.65

No-slip analysis 92 0.81

Present study

(Soft clay)

Slip analysis 743* 0.96

No-slip analysis 640* 1.0

Scenter* =Max. Settlement

Fig. 5. Calculated load-settlement curve

3D FE mesh used in this analysis. The subsoil comprises

quaternary sand up to 2.5 m below the bottom of the raft,

followed by the Frankfurt clay. The material properties

of the soil and piled raft, which were adopted from the

values as reported by Reul & Randolph (2004), are shown

in Table 3. And the constant (average) values of the drainedYoung’s modulus and drained shear strength parameters

were adopted to simplify the analysis for the soil layer.

The interface friction coefficient was estimated from the

soil friction angle using Eq. (6) and (7). Therefore, the

interface friction coefficient of 0.3 was used. An applied

load of 200 MN for each raft (Sommer, 1991) was applied

as a uniform load over the whole raft area.

0

)tan(

K

β δ µ ==

(6)

where δ is interface angle and K 0 is an earth pressure

coefficient at rest.

))sin1(/cos(sintan 21 φ φ φ δ +×= −

(7)

where is soil friction angle.

For this case, the comparative results of 3D FE analysis

and field measurements are shown in Fig. 5. In addition,

the 3D FE analysis result reported by Reul and Randolph

(2004) and relatively soft soil properties were compared. The

calculated and measured center settlements were summarized

in Table 4. All values of 3D FE analyses are smaller than

the measured one. However, there was reasonably good

agreement between the result of 3D FE model with an

interface and that from the measured. In addition, the

trends of results of no-slip analysis were similar to those

obtained by the thin-layer interface analysis of Reul and

Randolph (2004). For a soft clay on the piled raft, the

settlement of the raft was larger than that of a Frankfurt

clay (=stiff clay), and the piled raft coefficient (α pr ) was

significantly affected by soil properties. The coefficient




(a) 3x3, s=3d (b) 3x3, s=9d

(c) 4x4, s=3d (d) 4x4, s=6d

Fig. 6. Effect of loading types on load-average settlement curves for soft clay

value was mostly higher for soft clay than for stiff clay.

And the non-slip analysis was also higher than the value

from the slip analysis. This difference in the piled raft

coefficient was caused by the contribution of the raft,

which was more efficient with stiff clay (Lee et al. 2010).

3. RESULTS AND DISCUSSION

3.1 Effect of Loading Types

Fig. 6 and Fig. 7 show general load-average settlement

curves of piled raft with various pile configurations and

different raft-soil stiffness ratio under uniform and point

loading. The raft on stiff clay (K rs = 3.5) was relatively

more flexible than that for soft clay (K rs = 31.7). The

pile lengths (L p) ranged from zero (UR) to 20 m (end

bearing). By comparing the load-settlement curves of the

uniform loading and point loading, the behaviors of load-

settlement were similar and the effects of the different

loading types on the average settlements were insignificant

in soft clay. For stiff clay, the average settlement for

point loading was larger than for uniform loading, but

the difference became very small and an effect of loading

type could be negligible. This was similar to results

reported by Poulos (2001).

Fig. 8 and Fig. 9 show a load-center to corner differential

settlement curves. In contrast with average settlements,the load-differential settlement behavior was affected by

not only pile configuration but also loading type. For point

loading, the settlement profiles appeared concave and the

settlement increased with increasing load level. For uniform

loading, according to pile configurations, the deformed shape

of the raft was changed according to pile configurations.

3.2 Average Settlements

Fig. 10 shows the typical load-normalized average settle-

ment curves of a piled raft and an unpiled raft. Additionally,

The ultimate bearing capacity of a square unpiled raft

(QUR_ult), which was used to normalize the applied load

level (P/QUR_ult), was estimated by the load of settlement

of 10% B (Cooke, 1986; de Sanctis and Mandolini, 2003,

2006) from the ABAQUS analysis of the unpiled raft

load-settlement relationships reported by Lee (2007). The




(a) 3x3, s=3d (b) 3x3, s=9d

(c) 4x4, s=3d (d) 4x4, s=6d

Fig. 7. Effect of loading types on load-average settlement curves for stiff clay

(a) 3x3 3d (b) 3x3 9d

(c) 4x4 3d (d) 4x4 6d

Fig. 8. Effect of loading types on load-differential settlement curves for soft clay




(a) 3x3 3d (b) 3x3 9d

(c) 4x4 3d (d) 4x4 6d

Fig. 9. Effect of loading types on load-differential settlement curves for stiff clay

(a) Soft clay (b) Stiff clay

Fig. 10. Normalized load-average settlement of UR, PR

ratio of pile lengths L p/Ls ranged from zero (UR) to 1.0

(PR-end bearing). The settlement increased with the increasing

load level, and the settlement decreased as the pile length

increased in soft and stiff clay. Additionally, the effects

of pile lengths on the reducing the average settlements

of soft clay were much greater than that of stiff clay

under the same load level.Fig. 11 shows the load (P/QUR,ult)-reduction ratio (sPR,avg/

sUR,avg) of a piled raft with various pile configurations.

The reduction ratio means the average settlement of a

piled raft divided by the average settlement of an unpiled

raft. The settlement of the unpiled raft (sUR,avg) was taken

as reference for the settlement of the piled raft (sPR,avg).

Therefore, the reduction ratios of 1.0, in this figure, mean

that the settlement of the piled raft is same as the settle-

ment of the unpiled raft.As expected, the average settlement decreased with

increasing pile length and pile spacing of the same number




(a) 3×3 array (b) 4×4 array

Fig. 11. Normalized average settlements with load levels of soft clay


Fig. 12. Normalized average settlements with load levels of stiff clay

of piles. This was due to the fact that, for closely spaced

piles, the bearing capacity of pile groups in a piled raft is

decreased by the group effect. The reduction ratio decreased

until certain inflection points and then increased with

increasing load level, though the actual average settlements

of a piled raft generally increased with the increasing load

levels. These inflection points were estimated bearing capacityof a Single Pile (SP) multiplied by the number of piles

from the ABAQUS analysis of single pile load-settlement

relationships (Lee, 2007). For wide pile spacing (ex. 3×3,

s=9d; 4×4, s=6d), the location of inflection points were

similar to the sum of the ultimate bearing capacity of single

piles. However, for narrow pile spacing, these points were

slightly larger than the sum of the ultimate bearing capacity

of single piles. It was estimated that the behavior of piles

in a piled raft with wide pile spacing was similar to the

behavior of single pile. Likewise, for narrow pile spacing,the yielding point of pile groups in a piled raft was slightly

smaller than that of wide pile spacing cases; this is due to

the effect of block mode of failure of pile groups, though the

bearing capacity of pile groups in piled raft was decreased

by the group effect of pile group. For the cases considered,

the efficiency for reducing average settlement was maximized

when the point was similar to the ultimate capacity of

pile groups in a piled raft.

For stiff clay, as shown in Fig. 12, as soft clay, thereduction ratio decreased with increasing pile length and

pile spacing of the same number of piles. Also, it was

shown that the variation of reduction ratio of soft clay

was relatively greater than that of stiff clay, and the

reduction ratio was relatively smaller than that of stiff

clay, although the real average settlement of soft clay

was larger than that of stiff clay.

The efficiency for reducing average settlement increased

when the point was similar to the ultimate capacity of pile

groups in piled raft and after then, efficiency decreased.The bearing capacity developed by piles within a piled

raft can be significantly greater than that for a pile in





Fig. 13. Normalized differential settlements with pile group-raft raft area ratio (soft clay)


Fig. 14. Normalized differential settlements with pile group-raft raft area ratio (stiff clay)

a conventional pile group. This is because the increased

normal stresses generated between the soil and the pile

shaft by the loading on the raft (Poulos, 2001). This

effect of stiff clay is much larger than that of soft clay.

3.3 Differential Settlement

Fig. 13 shows the normalized differential settlement (Δ

sPR,c-c/ΔsUR,c-c) with the pile group-raft area ratio (Ag/Ar ),

defined as Eq. (8) (Randolph, 1994), and pile length. In

this Figure, (+) value in y-axis means the sagging of the

raft and (-) value means the hogging of the raft.

r r g A sn A A /])1[(/ 2−= (8)

where n is the number of piles in piled raft, s is thecenter to center pile spacing, Ar is the area of the raft.

As expected, an effective way of minimizing differential

settlement was achieved by placing a pile group over the

central area of the raft. But this area, which is defined

as the pile group-raft area ratio (Ag/Ar ), was affected by

not only the pile number and the pile length, but also

load level. For a 3×3 array (pile number=9), as shownin Fig. 13 (a), the differential settlement was minimized

by the Ag/Ar of about 0.25 with relative pile length (L p/Ls)

of 0.4 under load level (P/QUR,ult) of 0.2. Likewise, the

required Ag/Ar for minimizing differential settlement under

the relative pile length (L p/Ls) of 0.4 was increased from

0.25 to 0.4 after increasing load level of from 0.2 to 0.4.

Also, the required Ag/Ar under load level of 0.2, slightly

increased with increasing pile length from 0.25 (L p/Ls=0.4)

to 0.4 (L p/Ls=0.8). However, the effect of pile length was

reduced according to increasing load level and the differentialsettlement approximately minimized at Ag/Ar of about

0.4. Moreover, the required Ag/Ar was increased with

increasing pile number, as shown in Fig. 13 (b). The




required Ag/Ar of 4×4 arrays was about 0.45, with pile

length of 0.4 under load level of 0.2. In these cases, the

required Ag/Ar increased with increasing load levels from

0.45 to 0.5 (4×4), respectively, after increasing load level

of from 0.2 to 0.4, as well. By contrast with the 3×3 array,however, the pile length had less affected the required

Ag/Ar for minimizing differential settlement under low

load level of 0.2, according to increasing pile number.

The results showed that the required Ag/Ar for minimizing

differential settlement tends to be about 0.25～0.4 parti-

cularly in 3×3 pile groups in piled raft according to pile

length and load level. As pile numbers are increased, the

minimum required Ag/Ar increased to 0.45～0.5 of 4×4

pile group.

For the stiff clay, as shown in Figure 14, similar resultsdeveloped as with soft clay. However, the effect of pile

length was larger than that of soft clay for the required

Ag/Ar of minimizing differential settlement. The differential

settlement could be minimized effectively when the smallest

number of piles (3×3 array) is located below the Ag/Ar

of approximately 0.2 (load level=0.2), 0.35 (load level=0.4).

As same as soft clay, the required Ag/Ar was increased

with increasing pile number, as shown in Fig. 14 (b). The

required Ag/Ar of 4×4 arrays was about 0.3, with pile

length of 0.4 under load level of 0.2.The optimum Ag/Ar was similar in both soil conditions

but the optimum Ag/Ar of soft clay was slightly larger

than stiff clay for low load level and the optimum Ag/Ar

was changed according to load levels. Furthermore, the

optimum Ag/Ar was affected by pile length and piles

numbers. Consequently, an optimum Ag/Ar should accompany

a pile length, numbers and load levels. The required

Ag/Ar for minimizing differential settlement in soft clay

is larger than that of stiff clay and in both cases of soil

condition, the required Ag/Ar for inducing differentialsettlement of unpiled raft (ΔsPR,c-c/ΔsUR,c-c=1.0) was similar

in the same pile array.

Similar studies on required pile geometry in stiff clay

under uniform loading have been reported by Horikoshi

and Randolph (1998), Prakoso and Kulhawy (2001), de

Sanctis et al. (2002). They suggested that the piles of

length greater than about 70% of the width of the raft

are required and they conclude that the piles should be

situated over the central 16-25%, 16-36% and 25-45% of

raft area, respectively. For soft clay, Randolph (2003)

reported that the most significant factors were the short

pile installed extending through that layer over the full

raft area, or longer piles used in the central 25-40% of

the raft area. This is similar to the results of this study.

However, previous studies did not consider the effect of

pile numbers or load level in detail, which they generally

take to be about 0.3. However, as investigated, the requiredAg/Ar should be accompanied a pile length, pile numbers

and load level, in this study.

4. CONCLUSIONS

A series of numerical analysis were conducted to investi-

gate the behavior of a square piled raft subjected to vertical

loading. In this study, the 3D elasto-plastic FE analyses

with slip interface model of pile-soil contact were carried

out with drained shear parameters and no consolidationeffect for a clay layer. Pile positions, pile number, pile

length and load distribution on the raft were varied and

the effects of pile geometries, load levels and loading types

were examined. Based on the results, the validity of the

3D elasto-plastic FE analyses with slip interface model

at the pile-soil contact was evaluated and the settlement

behavior of piled raft was examined. From this study, the

following conclusions can be drawn;

(1) The average settlement could be reduced effectivelywith wider spaced pile groups with the same number

of piles. Furthermore, the efficiency of piles in a piled

raft was maximized when the magnitude of the applied

load of the piled raft was similar to the ultimate

capacity of pile groups in the piled raft. It was shown

that the reduction ratio was relatively smaller than

that of stiff clay, although the real average settlement

of soft clay was larger than that of stiff clay.

(2) The differential settlement of the piled rafts can be

minimized when the central area of the raft is supported by piles. The required (install) area The required install

area of pile group for minimizing differential settlement

was affected by not only the pile number and length,

but also the load level. The required Ag/Ar was generally

increased with increasing load level and pile number,

but the pile length had less influence compared with

the effect of pile number. And the required Ag/Ar for

minimizing differential settlement in soft clay is slightly

larger than that of stiff clay in the same pile array.

(3) The average and differential settlements of the raft

are dependent on the combination of pile geometries;

thus the design of pile geometries should be carefully




considered to satisfy the both settlement criterion. The

loading type (uniform or point load) greatly influences

the differential settlement rather than the average

settlement.

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