Journal of GeoEngineering, Vol. 12, No. 4, pp.

157-166, December
Maryam 2017 the Strength of Non-Homogenous Soils Using the Stone Column Technique
et al.: Improving 157
http://dx.doi.org/10.6310/jog.2017.12(4).3

IMPROVING THE STRENGTH OF NON-HOMOGENOUS SOILS

USING THE STONE COLUMN TECHNIQUE
Maryam Gaber 1, Anuar Kasa 2, and Norinah Abdul Rahman 3

ABSTRACT
A numerical solution was provided in order to improve the understanding of the behaviour of stone columns in an
embankment system. A two-dimensional finite element method was adopted in this study to estimate the bearing capacity and
safety factor against the deep-seated failure of an embankment over stone column-improved non-homogenous soft soil. The
factors influencing the behaviour of stone columns were investigated, including the spacing ratio, diameter, friction angle, unit
weight, elastic modulus and Poisson’s ratio of the stone columns and the height of the embankment fill. 15-node triangular
elements in the Plaxis 2D (v8.2) software based on the plane strain concept were used to examine these features. According to the
results of this study, it was observed that the load carrying capacity was developed as the diameter and the stiffness of the stone
columns were enhanced, where the internal friction angle of the stone columns exerted the greatest influence compared to all the
other parameters. The safety factor for most of the cases ranged between 2.2 to 2.6, whereby the lower value was recommended.

Key words: Finite element method, stone columns, bearing capacity, safety factor.

1. INTRODUCTION where

The seating of embankment foundations on weak soil may s  stress in the column
cause the embankment to undergo large vertical and horizontal c  stress in the surrounding soil
displacements. Some of the ground improvement techniques that
The stress concentration ratio is one of the most important
have been adopted to relieve settlement are stone columns
factors to be considered when designing stone columns. Since
(Greenwood 1970; Hughes et al. 1975), pre-consolidation with
there is no accurate method for obtaining a rational estimate of
prefabricated vertical drains (Yeung 1997; Shen et al. 2005),
this ratio, it has to be determined either through an empirical
vacuum pre-consolidation (Chu et al. 2000; Indraratna et al.
2004), and deep mixed columns (Krenn and Karstunen 2008; estimation of the field measurements or based on the engineer’s
Huang and Han 2009). previous experience. This ratio is crucial in predicting the benefi-
Stone column is a common ground improvement technique cial effects of stone column-reinforced grounds, especially in
used to alter the condition of the subsoil. The advantages of using settlement and stability analyses.
stone columns to support embankments are: (i) increased bearing Theories of the predicted settlement of stone columns, the
capacity, (ii) reduced settlement, and (iii) accelerated consolida- load transfer, and evaluation of the ultimate bearing capacity
tion settlement. This method requires the replacement, typically were developed over a period of four decades by numerous
between 10 ~ 40%, of a weak subsoil with stiffer granular mate- researchers (Greenwood 1970; Hughes and Withers 1974; Ab-
rials. Due to the higher stiffness of the stone column in compari- oshi et al. 1979; Priebe 1976; van Impe and de Beer 1983; Ba-
son to the native soil, the stress will be concentrated in the stone laam and Poulos 1983).
column, thereby reducing the stress in the surrounding soil (Ab- Several publications have shown that the stress concentra-
oshi et al. 1979). The distribution of stress is generally defined in tion ratio for stone column-reinforced foundations range between
terms of the stress concentration ratio (SCR), which is expressed 2 to 6, with typical values being between 3 to 4 (Goughnour and
as: Bayuk 1979; Ambily and Gandhi 2007). Greenwood (1991) re-
ported a much higher ratio of 25, which was measured in very
s soft clay at a low stress level. Most previous studies focused on
SCR  (1) designs of isolated stone columns seated only in homogenous
c
soils (Baumann and Bauer 1974; Ng and Tan 2014). Since very
few researchers have studied the behaviour of stone columns that
penetrate non-homogenous soils under long-term loading condi-
Manuscript received May 26, 2017; revised August 18, 2017; ac- tions using a plane strain model, this paper focused on this novel
cepted October 12, 2017. approach.
1
Ph.D. student (corresponding author), Department Civil and
Structural Engineering, Universiti Kebangsaan Malaysia, Selan-
gor, Malaysia (e-mail: mm_gaber@yahoo. com). 2. PARAMETRIC STUDY
2
Senior Lecturer, Faculty of Engineering and Built Environment,
Universiti Kebangsaan Malaysia, Selangor, Malaysia. In the parametric study of the construction of embankments
3
Senior Lecturer, Faculty of Engineering and Built Environment, on stone columns, one parameter was varied at a time, while all
Universiti Kebangsaan Malaysia, Selangor, Malaysia. the other parameters were kept constant. The following section
158 Journal of GeoEngineering, Vol. 12, No. 4, December 2017

presents a detailed discussion of the geometry of the embank- 4. SUBSOIL PROFILE

ment along with the stone column-reinforced ground. In the
analysis, the diameter of the stone column (d), spacing ratio (S/d), Ground improvement works were necessary for about 32 km
deformation modulus and other properties of the stone column of the IRDT project. The new track passes through highly varia-
material (friction angle , Poisson’s ratio  and unit weight ), ble poor soils, with a mixture of very soft silts, soft clays and
and the height of the embankment (H) were varied, as summa- loose sand up to a depth of 24 m. The cone tip resistance (qc)
rized in Table 1. values of the very soft silts and clays often range between 150 to
250 kPa. Vibro stone columns were installed to depths of 8 m
until 18 m to support the embankments, with heights varying
3. DESCRIPTION OF STONE
from 2 to 11 m. Figure 2 shows the constructed embankment
COLUMN-REINFORCED EMBANKMENT with time as well as the settlement over 1,231 days measured in
FOUNDATION field and FEM estimation. The settlement increased at a rapid
rate with time until approximately 380 and 150 days based on
The properties of the stone columns, soil and embankment field and FEM respectively, after which, a very small rate of
fill were chosen from the Ipoh-Rawang Double Track (IRDT- increase in the settlement with time was recorded, and the
MALAYSIA) project. The site location of this project is shown settlement did not exhibit any increase after 650 days in field
in Fig. 1. Vibro replacements (vibro stone columns) were in- measurement. This indicated that the consolidation had ended.
stalled at 23 separate locations covering a total track length of The total final settlement was 48 mm measured in the field and
about 7 km. 44 mm according to the FEM calculation.
The embankment top had a minimum width of 14.9 m with a
side slope of 1V:2H constructed on 9.5 metres of non-
homogeneous soil. In ordinary cases of embankment construc-
tions, the stone column has a diameter of 0.8 m with a center to
center spacing of 1.8 m and a height of 2 m. Proposed double
track stations

Table 1 Values of influencing factors

Parameter Range
Stone column diameter (m): d 0.8, 0.9, 1.0, 1.2
Spacing ratio: S/d 1.875, 2.25, 2.5, 2.75, 3.125
Stone column material:
Deformation modulus (MPa) E 50, 65, 80,100,130, 150
Angle of internal friction ()  35, 38, 40, 43, 45
Poisson’s ratio (-)  0.25, 0.35, 0.4, 0.45, 0.49
Unit weight (kN/m3)  15, 17, 20, 23, 25
Height of embankment (m): H 1.8, 2, 2.2, 2.5, 3, 3.5 Fig. 1 Site location

Time (days)
Embankment height (m)
Settlement (mm)

FEM settlement = 44 mm
Field measurement settlement = 48 mm

Field settlement FEM settlement Fill height

Fig. 2 Typical settlement data with applied 2 meters height embankment

 Maryam et al.: Improving the Strength of Non-Homogenous Soils Using the Stone Column Technique 159

5. NUMERICAL MODEL AND ANALYSIS the embankment. The stone columns were modelled using a
linear elastic perfectly plastic model based on the Mohr-Coulomb
In this study, a finite element analysis approach was selected failure criterion. The Mohr-Coulomb model is defined by five
to numerically simulate the behaviour of the stone columns and
parameters: friction angle (), effective cohesion (c), dilatancy
the foundation soils. A commercial analysis was performed using
angle (    30, as given in Brinkgreve (2008)), effective
the finite element program, PLAXIS 2D (v8.2). For the purpose
Young’s modulus (E), and Poisson’s ratio (). The parameters of
of symmetry, only half of the embankment was modelled to
the Mohr-Coulomb model used in the numerical analysis are
reduce the computation time. A plane strain model with 15-node
summarized in Table 2.
triangular elements was built. A relatively refined mesh
arrangement was used to achieve greater accuracy during the Figure 3 shows the 2D model with a refining mesh that was
initial consolidation process (the average size of the elements used in the analysis. Interface elements were used to simulate the
was about 630  103 m). interaction between the stone columns and the soil; without the
The columns were installed in a square grid with spacings, S, interface, there would be no slipping and gapping between the
supporting an embankment with a height, H. The 9.5 m long stone columns and the surrounding soil. In this study, the
column penetrated the entire non-homogenous soil and rested interfaces are set rigid (Rinter  1.0) which mean the interface
on a rigid stratum. Standard fixities were used for the horizontal elements have same strength properties of surrounding soil
and vertical boundaries. The boundary effect was investigated to (Brinkgreve 2002).
extend the right boundary successively up to 40 m from the toe of

Table 2 Soil parameters

Mohr-Coulomb Fill material Soft clay (layer1) Silty sand (layer2) Firm clay (layer3) Sand (layer4) Stone column Firm clay
Type Drained Undrained Undrained Undrained Undrained Drained Undrained
unsat kN/m³ 17 14 17 16 17 16 16
sat kN/m³ 18 16 20 18 18 17 17
kx m/day 1.00 7.36E5 0.10 7.36E5 1.00 1.00 7.36E5
ky m/day 1.00 3.68E5 0.10 3.68E5 1.00 0.50 3.68E5
Eref kN/m² 20,000 1,000 3,000 2,400 3,600 15,000 15,000
  0.3 0.4 0.333 0.333 0.333 0.4 0.4
cref kN/m² 5.0 10.0 1.0 30.0 0.1 23.0 23.0
  30 0 28 0 28 28 28
  0 0 0 0 0 0 0
Note: To avoid numerical instability, a cohesion value of 0.1 kN/m2 was used

Fig. 3 Numerical model used in the 2D analysis

160 Journal of GeoEngineering, Vol. 12, No. 4, December 2017

The soil was assumed to be normally consolidated with an stone columns when the applied load was higher than the confin-
overconsolidation ratio (OCR) of 1. On the other hand, the initial ing stress. The surrounding soil provided some lateral support to
stress was generated by Ko, which was calculated using the for- prevent further expansion of the columns. As the confining stress
mula by Jaky (1944), namely Ko = 1  sin , since the installation increased with depth, bulging occurred in the upper part of the
effects of the stone columns were not taken into account in the stone column (Madhav and Miura 1994). Shivashankar et al.
current work. The water pressure was fully hydrostatic and, based (2011) studied the behaviour of a stone column installed in
on the general phreatic level, was set at 1 metre below the ground layered soils. Maximum bulging was noted at a depth of one
surface to consider the impact of ground water on embankment column diameter from the top, and the total length of the stone
stability during the analysis. However, the boundary conditions for column exhibiting bulging was observed to be 2 ~ 3 times the
the consolidation analysis had to be closed at the left vertical boundary column diameter. According to Mohanty, and Samanta (2015)
to take into consideration the line of symmetry or the fact that no the vertical extent of the bulging increases with increase in the
thickness of the top soft clay up to two times the diameter of the
flow entered, thereby preventing a horizontal flow. The right vertical
stone column.
boundary also had to be closed since it was far enough from the
embankment to have any significant impact on the results. The Ambily and Gandhi (2007) investigated the performance of
bottom was open to allow a free flow of excess pore pressure. A single and group columns. They reported that the bending of a
consolidation analysis was performed in which the embankment column is dependent on its position in the group. In addition,
fill was assumed to be constructed in one stage, and it took 21 bending increases further away from the center of the column.
However, Fig. 4 clearly shows that bulging does not occur along
days to be completed, while the second phase of the model
the depth of the column, and that the failure at the edge of the
analysis took a period equal to 1,000 days to take into considera-
column is not caused only by the bulging, but can also be due to
tion long-term conditions. In addition, the (Phi-c) reduction
the sliding that occurs far from the group. On the other hand,
calculation was selected to find the safety factor (SF) against the
Priebe (1995) assumed that constant bulging occurs along the
stability of the embankment after each phase. column, and used the cavity expansion theory to estimate the
settlement improvement factor. As mentioned above, the bulging
6. RESULTS AND DISCUSSION along the column length that was observed in this study was not
6.1 Deformation Modes constant. The horizontal displacement profile along the edge of
the column, as shown in Fig. 5, revealed that the maximum
The deformation mode of the stone columns is shown in displacement in the model occurred at about 1.0 m below the
Fig. 4. The formation of internal bulging was observed close to surface of the ground. This magnitude was observed in most of
the upper part of the inner columns. Bulging occurred in the the cases that were studied.

Fig. 4 D eformation mode

Horizontal distance from center line (m)

Column depth (m)

Fig. 5 Horizontal displacement profile at 5.8 m from the center line

 Maryam et al.: Improving the Strength of Non-Homogenous Soils Using the Stone Column Technique 161

6.2 Bearing Capacity 0.0

Load cycle to allowable design load
0.5 Load cycle to 1.5 of allowable design
The ultimate bearing capacity of a stone column depends on
1.0
the geometry of the stone column and the properties of the material

Settlement (mm)
1.5
as well as those of the native soil. On the other hand, the effect of
the column length on the ultimate bearing capacity of a long 2.0

column is negligible. Since the applied load is transferred from the 2.5
column to the surrounding soil, only a small amount of the load 3.0
will be transferred to the base of the column (Pitt et al. 2003). 3.5
Several researchers adopted different approaches to estimate 4.0
the bearing capacity of a single column and a group of columns, 4.5
(Hughes and Withers 1974). Etezad et al. (2006) published a 5.0
report on the analytical treatment of the bearing capacity and 0 40 80 120 160 200 240 280 320
failure mechanisms. They depended on the results of the output Applied load (kN)
from a combination of finite element analyses and field trials for
the adoption of failure mechanisms.
In this paper, the finite element method based on PLAXIS Fig. 6 Sample of load-settlement curves of a single column
was carried out to compute the bearing capacity of the stone plate-load test (chain 352066-IRDT project)
columns. Several criteria have been proposed to define the ulti-
mate bearing capacity of foundations based on the load-
settlement curves. Some of these criteria are described by
Lutenegge and Adams 1998; including the 0.1B, the tangent in- Applied stress (kPa)
tersection, the Log-Log and the Hyperbolic methods. During this
study, Tangent method has been selected to evaluate the bearing
qult = 17.2 kPa
capacity of stone column.
Figure 6 presents the results of a typical single column plate-
Settlement (m)

load test carried out in (IRDT) project. In the first cycle loading,
the allowable design load was applied and maintained for a 24 h
duration while, in the second cycle, a maximum load of 1.5 times
of the design load has been applied. The acceptance requirement
of the load test was that the settlement should not exceed 50 mm
under the allowable load design and 80 mm under 150% of the
allowable design load (Arulrajah et al. 2009).
Figure 7 shows the load-settlement curve of the untreated
embankment. The final settlement was recorded as 56.54 mm
under a stress of 31 kPa and the ultimate bearing capacity (qult) Fig. 7 Load-settlement curve for the foundation of unimproved
was adopted about 17.2 kPa . On the other hand, Figs. 8 and 9 embankment at point A
show the results of the load-settlement curve for all the treated
cases in the study that were calculated at point A.
Improving the characteristics of the stone columns, such as
Increasing the diameter of the stone columns clearly resulted in terms of the internal friction angle and unit weight under the
in an improvement in the bearing capacity compared to the embankments, significantly improved the bearing capacity of the
untreated state. The load-settlement relationships for four differ- foundation soil, as can be seen in Figs. 8(d) and 8(e). Increasing
ent diameters that were examined showed the same development, the friction angle of crushed stone column from 35 to 45 led to
with a slight increase in the bearing capacity when the diameter increase the bearing capacity of stone column up to 30%. The
was increased (Fig. 8(a)). The stone column with a diameter of graph in Fig. 9(a) shows that the elastic modulus of the stone
1.2 m had the highest bearing capacity of about 37 kPa. The columns had less of an effect on the bearing capacity compared
stress-settlement behaviour of the stone columns for all the spac- to the factors that were previously studied, although increasing
ing ratios (S/d) was the same, as shown in Fig. 8(b). The load- the elastic modulus of the stone columns contributed to an
settlement curve indicated that the spacing ratio (S/d) of 1.875 increase in the bearing capacity. This result was in agreement
was better than the greater spacing ratios in increasing the bear- with the report by Reihani and Dehghani (2014). On the other
ing capacity of the stone columns. More than 20% improvement hand, Poisson’s ratio did not seem to have a noticeable effect on
achieved when the spacing ratio was reduced from 3.125 to 1.875. the bearing capacity of the soil or on any of the other factors that
The results indicated that the bearing capacity of the ordinary were studied, as can be seen in Fig. 9(b). Falsafi, and Motahari
stone columns increased with a decrease in the spacing distance (2015) reported that increasing the stone material’s Poisson
between the columns as well as with an increase in the stone coefficient has a slight influence on the stone column behavior
column diameter, which was similar to the behaviour reported by which is agree with this study’s results.
Afshar and Ghazavi (2014). Figure 8(c) shows the impact of the
embankment height on the bearing capacity of the column. The
6.3 Safety Factor (SF)
load-settlement graph shows that reinforcing the weak soil with
stone columns at a lower embankment height provided the best A safety (Phi-c) analysis was conducted in this study to
bearing capacity amongst all the investigated cases. assess the global safety factor (SF) against a deep-seated failure
162 Journal of GeoEngineering, Vol. 12, No. 4, December 2017

of embankments over stone column-improved non-homogenous occurs which at this point the safety factor is given by the follow
soil based on the plane strain model. This option is available in expression:
the Plaxis 2D, where the safety factor is computed by reducing
the strength parameters of the soil until failure occurs. The total available strength
multiplier Msf defines the magnitude of soil strength parameters
SF   M sf at failure (3)
strength at failure
at given stage in the analysis. The strength parameters are con-
secutively reduced automatically until failure of the structure

Applied stress (kPa) Applied stress (kPa)

Settlement (m)

Settlement (m)

S/d = 1.875 S/d = 2.25 S/d = 2.5

d = 0.8 m d = 0.9 m d = 1.0 m d = 1.2 m S/d = 2.75 S/d = 3.125

(a) Size of stone column (b) Spacing of stone column

Applied stress (kPa) Applied stress (kPa)

Settlement (m)
Settlement (m)

H = 1.8 m H = 2.0 m H = 2.2 m

 = 35  = 38  = 40  = 43  = 45
H = 2.5 m H = 3.0 m H = 3.5 m

(c) Height of embankment fill (d) Friction angle of stone column

Applied stress (kPa)

Settlement (m)

 = 15 kN/m3  = 17 kN/m3  = 20 kN/m3

 = 23 kN/m3  = 25 kN/m3

(e) Unit weight of stone column

Fig. 8 Factors influencing the bearing capacity of reinforced soil foundation at point A
 Maryam et al.: Improving the Strength of Non-Homogenous Soils Using the Stone Column Technique 163

Applied stress (kPa) Applied stress (kPa)

Settlement (m)

Settlement (m)
E = 50 MPa E = 65 MPa E = 80 MPa
E = 110 MPa E = 130 MPa E = 150 MPa  = 0.25  = 0.35  = 0.4  = 0.45  = 0.49

(a) Elastic modulus of stone column (b) Poisson’s ratio of stone column

Fig. 9 Factors influencing the bearing capacity of reinforced soil foundation at point A

A safety analysis was conducted after each stage of con- Figures 11(e) to 11(g) show the effect of the elastic modulus
struction. The safety factor was evaluated by plotting the dis- (E), unit weight () and Poisson’s ratio () of the stone columns
placement against the parameter, Msf, at a selection point on the on the safety factor. The benefit of increasing these parameters
slope head (point B), as shown in Fig. 10. Since the displacement was less significant compared with the other parameters investi-
was set at zero at the beginning of each Phi-c reduction analysis gated in this study. However, a slight change in the safety factor
so the total displacement seen in this graph is not relevant and it was observed when the values of these parameters were changed.
indicates whether or not a failure mechanism has developed Figure 12 illustrates an example of the maximum shear-
(Brinkgreve 2002). strain rates with a critical slip surface. It shows the critical slip
This study investigated several factors influencing the safety surface and safety factor in the untreated case (before the use of a
factor against deep-seated embankment failure over the group of stone column) and the treated case in the study, where a stone
stone columns during construction and service conditions, as column with a friction angle of 45 was used. The figure shows
stated in Table 1. The impact of each factor on the safety factor that the safety factor increased from 1.834 to 2.401 when the
under both conditions is presented in Fig. 11. ground was improved through the use of the stone columns.
The effect of the diameter of the stone column on the safety As a result, if a higher safety factor is used, then unneces-
factor is shown in Fig. 11(a). The value of the safety factor sary and costly ground improvement works will have to be
increased gradually as the value of d was increased in both the undertaken. It is more significant to carry out an appropriate
short and long-terms conditions. Figure 11(b) illustrates the planning analysis and design rather than to employ a higher
effect of the spacing ratio of the stone columns on the value of safety factor to cover weaknesses in the design methodology.
the safety factor. The value of the spacing ratio in the investiga-
tion was between 1.875 and 3.125. The result showed that the
behaviour of the safety factor decreased gradually as the spacing
ratio (S/d) was increased. The maximum safety factor of 2.465
was observed during the serviceability stage, when the spacing
ratio was 1.875, while the minimum safety factor was 2.218
during the construction stage when the spacing ratio was 3.125. SF = 1.834 (During serviceability)

The effect of the internal friction angle of the stone column

material on the safety factor of the embankment over the stone SF = 1.721 (During construction)
SF [Msf]

column-improved soil is shown in Fig. 11(c). It indicated that a

superior stone column material resulted in a higher safety factor
for the embankment system. Figure 11(d) shows the plot of the
effect of the embankment height on the safety factor. The stabil-
ity of the embankment is most critical when the embankment is
at its highest during the construction and serviceability stages
(short and long-term), as the subsoil will become stronger over
time when the excess pore pressure dissipates. Therefore, lower Settlement (m)
safety factors of 1.77 and 1.88 were adopted in the stability Note: Settlement in this graph is irrelevant
analyses for the construction and serviceability stages,
respectively. Fig. 10 SF graph of untreated soil foundation of two phases
164 Journal of GeoEngineering, Vol. 12, No. 4, December 2017

d = 0.8 m d = 0.9 m d = 1.0 m d = 1.2 m S/d = 1.875 S/d = 2.25 S/d = 2.5 S/d = 2.75 S/d = 3.125

(a) Size of stone column (b) Spacing of stone column

 = 35  = 38  = 40  = 43  = 45 H = 1.8 m H = 2.0 m H = 2.2 m H = 2.5 m H = 3.0 m H = 3.5 m

(c) Friction angle of stone column (d) Height of embankment fill

(e) Elastic modulus of stone column (f) Unit weight of stone column

 = 0.25  = 0.35  = 0.4  = 0.45  = 0.49

(g) Poisson’s ratio of stone column

Fig. 11 Factors influencing FS behavior

 Maryam et al.: Improving the Strength of Non-Homogenous Soils Using the Stone Column Technique 165

Failure surface

SF = 1.834 SF = 2.401
(a) Untreated embankment (b) Treated embankment using SC of  = 40

Fig. 12 Embankment stability over untreated and treated models of stone columns

7. CONCLUSIONS 1525.
Ambily, A.P. and Gandhi, S.R. (2007). “Behavior of stone columns
A series of 2D numerical analyses was carried out to evalu- based on experimental and FEM analysis.” Journal of Geotech-
ate the bearing capacity and safety factor with regard to a soil nical and Geoenvironmental Engineering, ASCE, 133(4),
405415.
foundation reinforced with a group of stone columns. The soil
Arulrajah, A., Abdullah, A., Bo, M.W., and Bouazza, A. (2009).
foundation was non-homogeneous, and the analyses employed an “Ground improvement techniques for railway embankments.”
elastic, perfectly plastic, constitutive model that was based on the Proceedings of the ICE  Ground Improvement, 162(1), 314.
Mohr-Coulomb failure criterion. The following conclusions were Balaam, N.P. and Poulos, H.G. (1983). “The behaviour of foundations
made based on the results obtained in this study. supported by clay stabilised stone columns.” Proceedings of the
1. This study highlighted some of the variables that had Eight European Conference on Soil Mechanics and Foundation
been taken into account in a few previous studies, such Engineering, Helsinki, 199204.
as Poisson’s ratio and the unit weight of the stone Baumann, V. and Bauer, G.E.A. (1974). “The performance of foun-
dations on various soils stabilized by the vibro-compaction
columns, to verify the impact of most of the characteris- method.” Canadian Geotechnical Journal, 11(4), 509530.
tics of the columns. Brinkgreve, R. (2002). PLAXIS 2D Version 8.2. Delft University of
2. Improving the characteristics and geometries of the stone Technology and PLAXIS BV, the Netherlands.
columns resulted in a significant increase in the bearing Chu, J., Yan, S.W., and Yang, H. (2000). “Soil improvement by the
capacity of the stone columns. vacuum preloading method for an oil storage station.” Geotech-
3. The size, spacing and friction angle of the stone columns, nique, 50(6), 625632.
the stone column material, and height of the embankment fill Etezad, M., Hanna, A.M., and Ayadat, T. (2006). “Bearing capacity of
affected the safety factor values against the deep-seated groups of stone columns.” Proceedings of the 6th European
Conference on Numerical Methods in Geotechnical Engineering,
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Graz, 781786.
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Falsafi, A. and Motahari, M.R. (2015). “Improving the bearing ca-
4. One important point that emerged from this numerical study pacity of footing on soft soils using stone columns.” Interna-
was that the friction angle, diameter of the stone columns, tional Journal of Current World Environment, 10(1),
spacing of the columns, height of the embankment and 10371042.
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determining the performance of an embankment with stone modeling of vacuum preloading and field applications.” Cana-
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ACKNOWLEDGMENTS Institution of Civil Engineering, London, UK, 920.
The authors gratefully acknowledge the financial support Greenwood, D.A. (1991). “Load tests on stone columns.” Deep
Foundation Improvements: Design, Construction and Testing,
provided by Universiti Kabangsaan Malaysia UKM under 148171.
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