Designing Stone Columns using 2D FEA with ...

International Conference on Ground Improvement and Ground Control (ICGI 2012), 30 Oct. – 2 Nov. 2012, University of Wollongong, Australia K. Chan and B. Poon

Designing Stone Columns using 2D FEA with Equivalent Strips KIM CHAN1 and BOSCO POON2 1,2

GHD, 57-63, Herbert Street, Artarmon, NSW, Australia. E-mail: [email protected], [email protected]

This paper presents an approach for the prediction of both vertical and horizontal displacements of soft ground treatment using stone columns in a 2D finite element analysis (FEA). This involved the modeling of stone columns as strips with appropriate strip width, spacing and smeared properties. Design charts to assess the equivalent 2D column stress concentration parameters are also provided for the design of fully penetrating columns under the influences of various key parameters. The accuracy of the proposed 2D strip model is investigated by comparing the results with the baseline 3D and axi-symmetric FEA. It is found that the proposed strip model is preferable over the conventional 2D approach using composite block material to represent the entire improved soil. Finally, comparisons are presented between measurements from two case studies and that predicted from the proposed design method, and reasonably good agreement is found between them. Keywords: Stone column, stress concentration, ground improvement, numerical analysis

1

Introduction

Conventionally, the design of stone columns involves the prediction of settlements using either a simplistic theoretical method (e.g. Priebe,1995) or a composite material approach in which equivalent strength and deformation parameters are derived using semi-empirical correlation to represent the entire reinforced soil. While these approaches have been accepted as reasonable methods for vertical displacement prediction, they are less certain for the prediction of horizontal displacement. This paper presents a design approach where stone columns are idealized as equivalent strips in 2D finite element analysis (FEA). The stress distribution between the stone column and surrounding soil is essential for calculating the strength parameter of the equivalent strips. A series of design curves for the stress concentration are presented to facilitate parameter derivation in practice. The accuracy of the 2D strip model is investigated by comparing the results with the baseline 3D and axi-symmetric FE solutions. Two case studies are then described to demonstrate the applicability of the present method. 2

Idealized 2D Modeling Approach for Stone Columns

For the modeling of stone columns in 2D FEA, the width of the stone column strips can be made to be equal to the width of an equivalent square for the cross-sectional area (Figure 1). The spacing of the strips is equal to the actual spacing, b, for square column arrangement and b/2 for equilateral triangular arrangement. The stone column strips are modeled as Mohr-Coulomb materials with Poisson’s ratio of 0.3, which was taken to be the value of the soil itself. The equivalent Young’s modulus Eeq and the cohesion ceq of the strips can be calculated based on weighted average approach as given by Equation 1: (

)=

(

)

+

1

+

(

)

(1)

K. Chan, B. Poon where Asoil and Acolumn are the areas of the soil and column inside a unit cell within the 2D strip

as shown in Figure 1.

b cos30º 2D strip

d = diameter of stone column

a = width of equivalent strip in 2D FEA

d

=

Asoil

a

4

Acolumn

b

Figure 1. 2D Stone Column Strips

The equivalent friction angle approach as given by tan

=

eq

of the strips can be derived based on force equilibrium tan(

)+ +

tan(

)

(2)

Note that the determination of eq in Eq. (2) requires a presumption of stress concentration factor, n, of the stone column, which is defined as the ratio of the vertical stress within stone column to the vertical stress of the surrounding soil at the same depth level. Section 3 presents an appraisal for this important parameter. Also, the present 2D FEA is an elasto-plastic analysis for the assessment of long term deformation in which the decay of excess pore pressure with time was not taken into account. 3

Stress Concentration of Stone Column under Flexible Embankment Loading

This section devotes to the discussion of stress concentration of stone column under the influences of various parameters including the column spacing ratio, plastic yielding and internal friction within the stone columns, the load level, and the modulus ratio of stone column and surrounding soil. The parametric study was carried out based on axisymmetric finite element analysis of a “unit cell” consisting of a stone column and the surrounding soil within a column’s zone of influence. Interface elements were introduced at the soil-column contact to allow for slippage. The roughness of the interface was assumed to be 70% of the original soil strength. Figure 2b presents the calculated stress concentration with depth for a particular case where a flexible embankment load is applied on stone columns that are founded on a rigid base. The selected column configuration and parameters are shown in Figure 2a. As would be expected, the stress concentration (n) is lower at the top of the column under uniform pressure condition, as compared to that for greater depth where equal strain condition occurs between column and the surrounding soil. If the column and soil were appraised as elastic material, the calculated n (dash line in Figure 2b) increases from 5 at the top of column, which is consistent with the value obtained from design chart published in FHWA (1983) for flexible footing, to about 14 at depth, which is commensurate with the solution obtained by Balaam and Poulos (1982) for rigid foundation over column and clay under elastic condition, and with the same configurations of b/a = 2 and Ecolumn / E soil = 20. When the column and clay are modeled as Mohr-Coulomb material, it is observed that yielding elements begin to form at the column top soon after a small load (~40kPa) is applied,

2

International Conference on Ground Improvement and Ground Control (ICGI 2012)

leading to a reduction of stress concentration. The yielding of the column (and hence the reduction of n) progresses downwards through the column as the applied load level increases, as shown by the solid curves in Figure 2b. Note that the oscillatory trend of the curves is due to some instability with the numerical solution, which is common for the current adoption of highly non-associated flow rule (dilation angle = 0°) in the Mohr-Coulomb model (Carter et al, 2005). Stress Concentration ratio n 0 2 4 6 8 10 12 14 16

Stone Column Clay Depth z Rigid Boundary a Clay: E´=3MPa, ´=26°, c´=2kPa, total = 17kN/m3 Column: E´= 60MPa, ´= 40°, c´= 0kPa, total = 22kN/m3 ´clay = ´column = 0.3; b/a = 2

(a)

Definition of Terms

Depth z below top of stone column (m)

Uniform Pressure qa

0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 Elasto-22 plastic -24 solution

(b)

Embankment load = 20kPa

0 Elastic solution 1 2 3

40kPa

B 60kPa

80kPa

Stress Concentration n 0 2 4 6 8 10 12 14 16

z / qa

b

5 6

C

7 8

100kPa

9

120kPa 140kPa

A

4 40kPa 60kPa 80kPa 100kPa 120kPa 140kPa

10

n with depth z

(c) n with depth z· /qa

Figure 2. Stress Concentration with Depth

Figure 2c shows a normalized plot in which the depth of the column, z, were normalized by qa/ , where qa is the applied pressure and is the total unit weight of the soil. It is found that the normalized stress concentration curves for the different load levels ( 40kPa) lie on a single curve. One application of the normalized curve can be illustrated by considering the position of the turning point within the column where the upper yielding zone transition to the lower nonyielding zone. The transition point (Point A) on the normalized curve occurs at about z· /qa = 4. For qa = 40kPa and = 17kN/m3, the position of the transition point is at about 9.5m depth below top of the column (see point B in Figure 2b). Conversely, when qa increases to 60kPa, z 14m (point C in Figure 2b). To illustrate further, a typical 7m high embankment (i.e. 140kPa) constructed over 15m depth of stone columns is considered. For the same configuration and properties of the soil and columns as per Figure 2a, the z· /qa is calculated to be ranging from 0 at the top of the column to 1.8 at the column base. The corresponding n, as indicated in Figure 2c, varies between 3 and 6. These stress concentration values compare well with field measurements quoted in the literature. Mitchell (1981) quotes values of n between 2 and 6, although values of 3 to 4 are stated to be more usual. It is also worthwhile to point out that the likelihood of having the maximum stress concentration of 14 within the stone column is low. It occurs either at a conceivable depth (e.g. 9m) at low embankment stress of 40kPa or at a much deeper level (e.g. 33m) under a typical embankment load of 140kPa. In reality however only a proportion of the total embankment stress will be felt by the stone column and clay at great depth due to load spreading. Results similar to those given in Figure 2c are given in Figure 3 to show the effect of modulus ratio and spacing ratio while the internal friction angle of stone columns remains constant. For a given column spacing ratio the proportion of vertical load carried by the

3

K. Chan, B. Poon

columns, and hence the stress concentration, is higher for higher modulus ratio E column/Esoil. This of course implies that at a given load level the extent of yielded zone within the column is also greater for stiffer stone column. Conversely, for the columns with a given modulus ratio, the extent of the yielding zone, and hence the reduction of stress concentration, is greater as the spacing ratio increases even though the maximum stress ratio in the columns is ultimately similar. This occurs because there is less confinement for the spaced columns, leading to greater yielding zone and stress reduction within columns. A comparison of the corresponding curves in Figures 3a and 3b shows that the loss of stress concentration due to yielding is more severe for column material having a lower angle of internal friction. Stress Concentration n 0 2 4 6 8 10 12 14 16 18 20 22 24

Stress Concentration n 0 2 4 6 8 10 12 14 16 18 20 22 24 0 2 6

z / qa

z · / qa

4 8 10 12 14 16 18

(a) n with z· /qa for ’column = 40°

0 2 4 6 8 10 12 14 16 18 20

b/a = 2; Ec/Es = 10 b/a = 2; Ec/Es = 20 b/a = 2; Ec/Es = 30 b/a = 2.5; Ec/Es = 10 b/a = 2.5; Ec/Es = 20 b/a = 2.5; Ec/Es = 30 b/a = 3; Ec/Es = 10 b/a = 3; Ec/Es = 10 b/a = 3; Ec/Es = 10

(b) n with z· /qa for ’column = 35°

Figure 3. Variation of Stress Concentration n in Column with z· / qa

4

Modeling of Fill Embankment over Soft Clay Treated with Stone Columns

The accuracy of plane strain idealization of stone column using equivalent strips in 2D FEA was investigated under self-weight load imparted by a 6m high embankment with 2H:1V batter. The analyses undertaken for the investigation include: Analysis 1 – Full 3D FEA of embankment over stone columns modeled by solid elements Analysis 2 – Axisymmetric FEA of a unit cell consisting stone column Analysis 3 – 2D plane strain FEA with the stone columns modeled as strips Analysis 4 – 2D FEA with the entire soil and columns modeled as equivalent block The adopted parameters for all of the analyses are summarized in Table 1. The full 3D FEA (Analysis 1) is considered a baseline model that comprises a 13m long segment of embankment over soft clay foundation treated with stone columns in a triangular grid formation. The analysis was repeated with the 0.9m diameter stone columns spaced at 1.7m, 2m and 2.5m. The 3D FE mesh is shown in Figure 4. Only half of the embankment segment was modeled because of symmetry. The 3D FEA utilizes solid elements (15 nodes wedge element) for stone columns and interface elements sandwiched between the stone columns and surrounding soil. The roughness of the interface is assumed to be 70% of the original soil strength. The axisymmetric 3D FEA (Analysis 2) is also considered a baseline model for embankment settlement under axially axisymmetic loading condition that occurs in the zone away from the embankment batter. The influence radius of the axisymmetric unit cell was varied so to be equivalent to the actual spacing as adopted in the full 3D Analysis 1.

4

International Conference on Ground Improvement and Ground Control (ICGI 2012)

In Analysis 3, a 2D plane strain idealization of the stone columns using equivalent strips was investigated. The dimension and spacing of the 2D strips and their equivalent properties were derived as per the procedure outlined in Section 2 and stress concentration factors from Figure 3. Analysis 4 presents the conventional 2D approach in which the entire treated soil is represented by a single block with the equivalent strengths, block , cblock and Young’s modulus Eblock derived based on semi-empirical relationship given by Madhav, 1996: 2

45 +

2 (45

=

=

[

=

2

2 (45 +

2 (45

+

+

/

+

/2) + (1

/2 + /2) + (1 (1

)2 ]

(1 )

2

)

)

2 (45

+

45 +

2 (45

(4)

/2

+ /2)

/2

(5)

(6)

Note that ar is the area replacement ratio and is defined as the ratio of the cross-sectional area of one column to the total area of the ‘unit cell’. Table 1. FEA model parameters for stone column Analysis 1,2 baseline FEA 3 - 2D FEA with strips 4 - 2D FEA with equiv. block

b/a 2.0, 2.3,2.9 2.0 2.3 2.9 2.0 2.3 2.9

ar 0.26, 0.19, 0.12 0.26 0.19 0.12 0.26 0.19 0.12

Stone Column Parameters col=50MPa, strip=26MPa,

c col=0kPa,

c strip~1kPa, strip=22MPa, c strip~1kPa, strip=18MPa, c strip~1kPa, block=6MPa, c block~1kPa, block=6MPa, c block~1kPa, block=6MPa, c block~1kPa,

col

Comment

= 40º

= 37º strip = 35º strip = 33º block = 30º block = 30º block = 30º strip

Note: The adopted soil parameters for all analyses are E soil = 30MPa, c soil = 2kPa,

soil

n 4 to 5 n 4 n 3.5 - 4

= 26º

Embankment with 2H:1V batter 6m

10m

~13m Soft Soil without treatment

Soft Soil (not shown) treated with stone columns

Figure 4. 3D FEA Mesh for with 2D FEA using Idealized Stone Column Strips

Before considering the numerical results in details, it is illuminating to discuss the deformation mechanism of the stone column under the loading of a flexible fill embankment. Figures 5a and 5b have indicated that the deformation of the stone columns as given by the 2D strip model (Analysis 3) is similar to that of the baseline 3D (Analysis1) result, in which the stone columns can be broadly divided into three zones: namely, at Zone 1 away from the fill

5

K. Chan, B. Poon

batter where columns underwent vertical deformation by “bulging”; at a localized Zone 2 just behind the crest of the fill batter where columns underwent both vertical and horizontal deformation by “bulging” and “leaning”; and at Zone 3 beneath the fill batter where columns underwent mainly tilting. This numerical prediction for the deformation appears to be consistent with the results of the centrifuge model test carried out by Stewart and Fahey (1994) for a stone column foundation system supporting stockpile and railway embankment. Away from the fill batter in Zone 1, the stone columns are subject to axially symmetric loading condition and thus the axisymmetric FEA (Analysis 2) is also considered as the baseline solution for this zone. At the localized Zone 2 just before the crest of the fill batter, it is observed from the FEA results (see Figures 5b and 5d) that the stone columns exhibit the greatest vertical displacement (more than those at Zone 1). This is presumably due to the concurrence of bulging and leaning deformation mechanisms of the stone columns. Conversely, the columns in Zone 3 exhibit a maximum horizontal displacement mechanism (Figure 5e) and this is likely due to the prevailing leaning deformation of the stone columns. Figure 5c presents the deformation mechanism given by the 2D FEA using the conventional composite block material (Analysis 4). It can be seen that this method is unable to capture the bulging and leaning deformation of the stone columns. Moreover, the maximum vertical displacement is predicted to occur at the centre of the embankment (i.e. at Zone 1, see Figure 5f), as opposed to occurring in Zone 2 predicted by the baseline 3D FEA (Analysis 1) and the proposed 2D FEA approach using equivalent strips (Analysis 3). In Figure 6, predicted displacements at points O, P and Q at the base of the embankment (see Figure 5b for locations) are plotted against the area replacement ratio for the different FE analyses. Figures 6a shows that all analyses give comparable results for vertical displacement at point O in Zone 1. This indicates that all the different FE methods are commensurable in terms of predicting the vertical displacement under axially symmetric loading condition. The predictions for the vertical displacements at point P in Zone 2 and the horizontal displacement at point Q in Zone 3 are presented in Figure 6b and 6c, respectively. Two important observations are drawn following the inspection of the results: The predictions from the 2D strip model (Analysis 3) for the displacements at the fill batter compare reasonably well with the 3D baseline model results. The solutions from the 2D block model (Analysis 4) however under-predict the displacements when compared with the 3D baseline predictions. While stone columns serve to reduce vertical settlement under axially symmetric loading (i.e. at Zone 1 away from the batter), they are less effective in reducing lateral deformation at the embankment batter. In fact, the lateral movement is shown to be slightly higher for columns with closer spacing. Closer inspection of the numerical results indicates that stone columns beneath the embankment batter did not failed by shearing. The columns, which have little bending stiffness, are simply leaning slightly more forward as the column spacing reduces. Stewart and Fahey (1994) arrived at similar conclusions based on their centrifuge test results. The first observation has indicated that the use of the isotropic soil properties in the 2D block model, which were derived based on semi-empirical relationships originally for settlement prediction under axially loading condition, have overestimated the reduction in lateral spreading underneath the embankment batter. The use of equivalent strips in the 2D strip model, however, is able to capture the interaction between the soil and the stone column, leading to a better agreement for the lateral deformation with the 3D baseline solution. The second observation has implied that in order to utilize the stone columns more efficiently at the embankment batter, some form of head restraint is preferable to reduce the column inclination. This can be achieved by the placement of structural geofabric above the foundation soil and stone columns at the embankment interface, or simply by installing the stone

6

International Conference on Ground Improvement and Ground Control (ICGI 2012)

columns to the top of a compacted construction platform. Case Study 1 in Section 5 below illustrates another form of head restraint using dead-man anchors.

Bulging & leaning of stone column

Bulging of stone column

Zone 2 Bulging & Leaning

Zone 1 Bulging

Zone 3 Leaning

(a) 3D FEA (Baseline Analysis 1) with cylindrical stone columns Max. vert. disp.

Max. vert. disp.

O

Q P

(c) 2D FEA (Analysis 4) with equivalent composite block

(b) 2D FEA (Analysis 3) with equivalent stone column strips

(e) Horizontal displacement from (f) Vertical displacement from Analysis 1 and Analysis 3 Analysis 4

(d) Vertical displacement from Analysis 1 and Analysis 3

Figure 5. Comparison of 3D FEA with 2D FEA using Idealized Stone Column Strips Settlement (mm) at point P in Zone 2

Settlement (mm) at point O in Zone 1

250 230 210 190 170 150

0 10 20 30 Area replacement ratio ar

(a) Settlement at Point O Axi-symmetry (baseline)

Hori. displ. (mm) at point Q in Zone 3

280

270

260 240 220 200 180 160 140 120

120 100 80 60 40 Untreated soil

20 0

100 0

10

20

30

Area replacement ratio ar

(b) Settlementb/a at Point P 3D (baseline)

2D_Strip (proposed)

Figure 6. Comparison of FEA results

7

0

10

20

Area replacement ratio ar

(c) Hori. Disp. at Point Q 2D_Block (conventional)

30

K. Chan, B. Poon

5

Application to Case Studies

To demonstrate the ability of the present 2D FE strip model for the design of stone column, two case studies are described briefly as follows. Case 1. Poon et al. (2011) described the design of a reinforced soil wing wall (RSW) over 6m soft ground treated with dynamic replacement (DR) columns on Ballina Bypass Project. Prior to the RSW construction, a post-DR investigation indicated that many of the DR columns at the RSW location were not installed to their design depth. The untreated soft soil thickness beneath the columns was in excess of 0.5m. Re-designs of the soft ground treatment were subsequently implemented, which involved the installation of remedial full depth stone columns (SC). The design configuration of the RSW is outlined in Figure 7a. In essence, the design wall height is 7m while the total embankment height is 10.5m. The RSW block is 12m wide and is built upon a stripped 0.75m thick working platform that was constructed over the DR and SC columns. The DR and SC are 2.5m and 1m in diameter respectively at 5m triangular spacing. To limit the differential settlements of the wall facing, a ground beam spanning over a row of remedial SC is provided to support the wall panels. To limit the applied horizontal force on the front row of SC, a dead-man anchor is adopted to tie back the ground beam into the platform fill. The modeling of the RSW over ground treatment was carried out based on 2D FEA using equivalent column strips. Details of the FE modeling including the adopted soil and column properties are given in Poon et al. (2011). The FEA results have shown that the DR and SC columns were ineffective in reducing the lateral spreading under the imparted load of the reinforced soil block. The dead-man anchor was therefore considered to be an essential component in the RSW design for its role to limit the applied shear force on the SC, thus greatly reducing the outward movement of the RSW facing. 12m

Wingwall A (Nth) Settlement

Surcharge level

Date 14/10/09 3/12/09 22/1/10 13/3/10

Settlement (mm)

Design level RSW 6.7m

RSW ground beam

Anchor bar

2/5/10

21/6/10 10/8/10

0

Construction platform Dead-man anchor Ground surface

-0.05 -0.1

2D FEA Prediction of 210mm at the ground beam level of the RSW facing

-0.15 -0.2 -0.25 Settlement at Monument #19

(b) Measured and predicted Settlement

0.5m DR

5m

4m

Full depth SC

1m untreated soft soil

Wick drains at 1.2m triangular spacing

Hori. Movement (mm)

Base of soft soil

Wingwall A (Nth) Ground Beam Hori. Movement 0.16 0.14 0.12 0.1 0.08

2D FEA Prediction of 130mm at the ground beam level of the RSW facing

0.06 0.04 0.02

(a) RSW design

0 14/10/09 3/12/09 22/01/10 13/03/10 2/05/10 21/06/10 10/08/10 Date Ho riz. Movement at Monument #19

(c) Measured and Predicted horizontal movement

(a) RSW design outline for Case 1

Figure 7. Case Study 1 – RSW over soft ground treated with DR and SC on Ballina Bypass Project

Figure 7b shows that the FE predictions for the vertical settlements are in good agreement with the field measurements at the wall facing. The prediction for the horizontal movement at the wall facing, as shown in Figure 7c, is however erring on the conservative side, but remains

8

International Conference on Ground Improvement and Ground Control (ICGI 2012)

within the design limit of 150mm. Poon et al. (2011) indicated that this could be due to: (i) column installation effect; (ii) anisotropy of the column stiffness; and (iii) adoption of conservative design parameter for the anchor design. Case 2. Chan et al. (2008) reported the design of a new coal pad and an associated machinery berm that were constructed for Project 3D of the Kooragang Coal Terminal stockyard expansion project. The site is underlain by soft soil strata of variable thickness. Prior to the construction of the coal pad and berm, part of the proposed new stockyard was preload, while the remaining sections were treated by the installation of stone columns. One key aspect of the stone column design was to limit the transverse tilting of the berm to be no more than 0.3%. The modeling of the stockpile and berm over stone column reinforced foundation was carried out based on 2D FEA using equivalent column strips. A typical FE model showing variable stone column strip spacing is shown on Figure 8. The berm was 4m high with equivalent loading of 95kPa, while the coal pad was 20m high with equivalent loading of 180kPa. A live load of 20kPa was considered above the berm. Details of the FE modeling including the adopted soil and column properties are given in Chan et al. (2008). The FE results showed that the post-construction differential settlement under the berm will be some 115mm and 20mm over the (19m) width of the berm without and with stone columns (for the lower bound cases) respectively. The tilting of the berm is therefore 0.6% and 0.11% using the lower bound model. The tilting with the stone column improvement is thus well within the design criterion.

Figure 8. Case Study 2 – Typical numerical model for stone column design

To verify the design, a large scale area load test was performed on working columns in the region of the deepest soft clay zone. A 5 metre high embankment was built over an area of 40 metres square. To further simulate the working conditions additional load was imparted by the use of sand filled shipping containers placed on top of the embankment. The test was instrumented and monitored, including settlement plates, hydrostatic profile gauge, load cells, inclinometers, and survey monuments. In summary, the FE modeling results predicted maximum test pad settlement and maximum horizontal displacement of some 185mm and 40mm respectively for the “as constructed” case. These predictions compare with the measured maximum values of 168mm and 30mm. Similarly, the FE predictions of the vertical stresses below the containers, at the original ground surface level, are about 150kPa and 120kPa at the columns and in-between column respectively. These values again compare (favorably) with the corresponding measured results of 152kPa and 111kPa. The actual monitoring results were thus considered to be in reasonably good agreement with (but slightly lower than) the predicted results.

9

K. Chan, B. Poon

6

Conclusion

This paper presents a 2D finite element approach for analyzing the response of stone columns under embankment loading. One of the key features in the 2D FEA is the modeling of the stone columns as equivalent strips. The equivalent cohesion and Young’s modulus of the strips can be calculated based on weighted average approach, whereas the equivalent friction angle can be derived based on force equilibrium method, which requires a presumption of the stress concentration factor of the stone column (defined as the ratio of vertical stress within the stone column to the vertical stress of the surrounding soil). For convenience, a number of elasto-plastic solutions for the stress concentration factor of fully penetrating stone column are generated using axi-symmetric FEA that utilized MohrCoulomb model to represent the soil and the stone column within a unit cell. The solutions are presented in charts and may be useful for preliminary design when there is lack of detailed site information. The design charts cover the variation of stress concentration factor under the influence of various key parameters including (i) load levels; (ii) column spacing ratio; (iii) modulus ratio of stone column and surrounding soil; and (iv) friction angle of the stone column. The accuracy of the proposed 2D FE strip model was investigated by comparing the results with the baseline solutions obtained from the full 3D and axi-symmetric FEA. The results have indicated that the 2D strip model is able to capture the ‘bulging’ mechanism of the stone columns under axially symmetric loading condition away from the embankment fill batter, and the ‘bulging’ and ‘leaning’ deformation towards the fill batter. The predictions of vertical and horizontal displacement at various positions across the embankment agreed reasonably well with baseline solutions. Conversely, the 2D FE model using conventional composite block material is unable to capture the bulging and leaning of the stone columns. The solution grossly under predicted the vertical and horizontal displacements near the embankment batter when compared with the baseline solutions, although it gives comparable vertical displacement result under axially symmetric loading condition. Thus the 2D strip FE model is preferable over the 2D block model for stone column design. Stone columns tend to lean forward and are ineffective in reducing lateral deformation at the embankment batter. Some form of head restraint is essential to reduce the column inclination. The ability of the present 2D FE approach using equivalent stone column strips have been demonstrated in the two presented case studies. In general, the predictions given by this method are in reasonably good agreement with the actual monitoring results. References Balaam, N.P. and Poulos, H.G. (1983). The behavior of foundations supported by clay stabilized by stone columns. Proc. 8th European Conference on Soil Mechanics and Foundation Engineering, Helsinki. Carter, J.P., Poon, B., and Airey, D.W. (2005). Numerical and semi-analytical techniques for footings subjected to combined loading. Proc. 11th International Conference on Computer Methods and Advances in Geomechanics, Torino/Italy, Vol.4, pp. 163-176 Chan, K., Raj, D., Hoffmann, G. and Stone, P. (2007) "Designing stone columns to control horizontal and vertical displacements", Proc 10th ANZ Conference on Geomechanics 2007, Brisbane, Vol 2, pp 48-53. FHWA (1983) U.S. Department of Transportation Federal Highway Administration (Dec, 1983) – Design and Construction of Stone Columns, Vol 1. Report No. FHWA/RD-83/026. Mitchell, J.K. (1981). Soil improvement state-of-the-art. Proc.10th ICSMFE, Stockholm,Vol.4, 509 – 565. Priebe, HeinzJ. (1995) – The Design of Vibro Replacement, Keller Grundbau GmbH Publication. Poon, B., Chan, K. and Kelly, R. (2011) "Analysis and Performance of a Reinforced Soil Wing Wall Constructed over Treated Soft Ground", Proc.14th Pan-American Conference on Soil Mechanics and Geotechnical Engineering, Toronto, Canada, Paper 247. Stewart, D.P. and Fahey, M. (1994). Centrifuge modelling of a stone column foundation system, Seminar on ground improvement techniques, Perth, Curtin Printing Services, 1: pp 101-111.

10