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Soils and Foundations 59 (2019) 1579–1590
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Technical Paper
Short-term and long-term behavior of geosynthetic-reinforced
stone columns
Ahad Ehsaniyamchi ⇑, Mahmoud Ghazavi
Civil Engineering Department, K.N. Toosi University of Technology, Tehran, Iran
Received 28 December 2018; received in revised form 10 May 2019; accepted 31 July 2019
Available online 14 September 2019
Abstract
Stone columns are often used to improve the load-carrying characteristics of weak soils. In very soft soils, however, the bearing capacity of stone columns may not significantly improve the load-carrying characteristics due to the very low confinement of the surrounding
soil. In such cases, encased stone columns (ESCs) or horizontally reinforced stone columns (HRSCs) may be used. Although ESCs have
been studied extensively, few studies have been done on HRSCs. In addition, very limited studies are available on ESCs and HRSCs
under the same conditions. Moreover, no studies have been carried out to compare the long-term and short-term behavior of HRSCs
with that of ESCs. In this research, therefore, numerical analyses are performed on various types of reinforced end-bearing stone
columns to compare their behavior under both long-term and short-term conditions under various loading conditions. The Advanced
Modified Cam-clay model for clay and the Hardening Soil model for stone column materials are used. The results show that with proper
reinforcing stone columns, in addition to a considerable reduction in settlement, the consolidation time can be greatly decreased and
most of the settlement will occur during the loading period. Also, the consolidation settlement rate may be increased by using a smaller
column diameter and a larger area replacement ratio for the unit cell, stiffer geosynthetic reinforcements, and greater values for the
internal friction angle of the stone column materials.
Ó 2019 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Geosynthetics; Reinforced stone columns; Numerical analysis; Short-term and long-term behavior; Consolidation settlement
1. Introduction
Stone columns are often used as a ground-improvement
method to improve the bearing capacity, to reduce the settlement of saturated clayey soil, to increase the consolidation rate of fine soils, and to decrease the liquefaction
potential. In very soft soils, however, the bearing capacity
of ordinary stone columns (OSCs) is small due to the very
low lateral confinement of the surrounding soil that leads
to bulging failure at a depth of D-2.5D (Nazariafshar
Peer review under responsibility of The Japanese Geotechnical Society.
⇑ Corresponding author.
E-mail addresses: aehsani@mail.kntu.ac.ir (A. Ehsaniyamchi),
ghazavi_ma@kntu.ac.ir (M. Ghazavi).
and Ghazavi, 2014). In such situations, the loadsettlement behavior of the stone columns can be improved
by geosynthetic reinforcements. Fig. 1 shows two main
reinforcing methods of stone columns. As seen in the figure, a stone column may be reinforced by an encasement,
called an encased stone column (ESC), wrapped with a
geosynthetic like a wick drain, or by placing horizontal
sheets of a geosynthetic within the column body at regular
intervals, called a horizontally reinforced stone column
(HRSC). The encasement may be wrapped around the
whole length of the stone column (Le = L), called a fulllength ESC, or just wrapped around the upper portion of
the stone column, for example, the half-length of the column (Le = 0.5L), where Le is the encased length of the
ESC.
https://doi.org/10.1016/j.sandf.2019.07.007
0038-0806/Ó 2019 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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Applied pressure
Le=0.5L
Soft soil
Geosynthetic encasement
Le=L
Soft soil
Stone column
(a)
Sr
(b)
Horizontal
reinforcing layers
(c)
(d)
(e)
Fig. 1. Examples of various models used in numerical analyses. Unit cell models of: (a) OSC, (b) full-length ESC, (c) half-length ESC, (d) HRSC with
Sr = 0.5D, and (e) single HRSC with Sr = 0.25D.
The encasing of stone columns has been studied using
analytical solutions (Pulko et al., 2011; Zhang and Zhao,
2015), experiments (Gniel and Bouazza, 2009; Murugesan
and Rajagopal, 2010; Ghazavi and Nazariafshar, 2013;
Ali et al., 2012, 2014; Miranda and Da Costa, 2016;
Hong et al., 2016), and numerical methods (Murugesan
and Rajagopal, 2006; Khabbazian et al., 2010;
Keykhosropur et al., 2012; Elsawy, 2013; Hosseinpour
et al., 2014; Yu et al., 2016). Most of the analytical and
numerical studies used the unit cell concept, assuming an
infinitely wide loaded area with end-bearing stone columns
having a constant diameter and spacing, where the stone
column and the surrounding soil were treated as axisymmetric forms (Pulko et al., 2011). Murugesan and
Rajagopal (2006) and Khabbazian et al. (2010) reported
that encasing the top portion of ESCs may be sufficient
for preventing bulging failure and enhancing the bearing
capacity. However, Gniel and Bouazza (2009) and
Ghazavi and Nazariafshar (2013) reported that, in very
soft soils, reinforcing the upper half part of ESCs may lead
to the relocation of the bulging failure to the lower unencased parts of the columns; and thus, it may be more useful to encase the full length of the ESCs.
HRSCs have been studied by Sharma et al. (2004), Wu
and Hong (2008), Ali et al. (2012, 2014), Nazariafshar and
Ghazavi (2014), Hosseinpour et al. (2014) and Ghazavi
et al. (2018). Their results showed that the beneficial effect
of HRSCs mainly depends on the vertical spacing between
the horizontal reinforcing sheets and that the bearing
capacity of HRSCs increases with a decrease in the spacing
between the reinforcing layers (Ghazavi et al., 2018).
Although various studies have been conducted on ESCs
and HRSCs, only a very limited number of studies have
compared the two methods under the same conditions
(Ali et al., 2012, 2014; Hosseinpour et al., 2014). Moreover,
although several studies have been conducted on the con-
solidation of OSCs (Wang, 2009; Cimentada et al., 2011;
Ng and Tan, 2014; Lu et al., 2017; Deb and Behera,
2017), most of the studies on ESCs have been focused on
either the short-term or the long-term behavior and only
a few studies investigated the consolidation of ESCs
(Castro and Sagaseta, 2011; Zhang et al., 2012; Castro
et al., 2013; Pulko and Logar, 2017). Castro and Sagaseta
(2011) presented an advanced analytical method for predicting the consolidation settlement of ESCs based on Barron’s solution. Pulko and Logar (2017) used Biot’s theory
and presented a fully coupled semi-analytical solution in
order to account for the consolidation settlement of ESCs.
In addition, to the best knowledge of the authors, there
have been no studies that compared the long-term behavior
and the consolidation settlement of HRSCs with those of
ESCs.
Although the behavior of the granular aggregates and
geosynthetic reinforcements of stone columns is almost
independent of the loading speed, due to the presence of
soft compressible clay around columns with very low permeability, after applying the initial loading on the stone
columns and the surrounding soil, horizontal and vertical
consolidation deformation is generated in the soil around
the stone columns. This will cause additional deformation
and the regeneration of stress in both the stone columns
and the reinforcements. Therefore, the effects of consolidation on the soft clay surrounding the columns should be
taken into account when calculating the stress and deformation of the various elements of the stone columns. This
paper performs numerical analyses to compare both the
long-term and short-term behavior and the consolidation
settlements of end-bearing ESCs and HRSCs. To this
aim, advanced constitutive models are used to compare
the long-term and short-term behavior of ESCs and
HRSCs. The present results may assist practicing engineers
in choosing the best reinforcement method for stone
A. Ehsaniyamchi, M. Ghazavi / Soils and Foundations 59 (2019) 1579–1590
columns with respect to the site, the loading conditions, the
available materials, and the soil-improvement target.
2. Finite element analyses
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linear-elastic behavior was used for reinforcing the material
simulation. To allow the mobilization between the reinforcement and the soil materials, interface elements were
used by applying a strength reduction factor of 0.67, as
suggested by the PLAXIS manual and used by
Khabbazian et al. (2010).
2.1. Model description and boundary conditions
2.2. Numerical analysis validation
The finite element model was verified for both reinforcing methods using data reported by others in the literature
(Figs. 2 and 3). The predicted ESC data were verified by the
data reported by Khabbazian et al. (2010) for an OSC and
a full-length ESC, both with a diameter of 80 cm and a
length of 5 m. The predicted HRSC data were verified by
the experimental data reported by Ghazavi et al. (2018)
for an OSC and an HRSC, both with a diameter of
10 cm and a length of 50 cm. As seen in Fig. 3, there is a
good agreement between the test data and the simulations.
Therefore, the adopted numerical analysis methods can be
used to further discover the behavior of HRSCs and ESCs.
Fig. 2. Validation of numerical analysis for ESCs.
Vertical stress (kPa)
0
100
200
300
400
500
600
700
800
0
10
Settlement (mm)
Finite element analyses were performed using PLAXIS
2D in an axisymmetric condition. In the numerical analyses, two configurations of full-length ESCs and halflength ESCs were adopted, and their characteristics were
compared with HRSCs with Sr = 0.25D and Sr = 0.5D,
where Sr is the spacing of the horizontal reinforcing strips
(Fig. 1d) and D denotes the stone column diameter. The
reinforcing material used for the two cases of full-length
ESC and HRSC with Sr = 0.25D was the same and equal
to p.D.L, where L is the column length. In the same way,
the area of the reinforcing material used for the two cases
of half-length ESC and HRSC with Sr = 0.5D was equal
to p.D.L/2. This facilitated a comparison between ESCs
and HRSCs in terms of the consumption of the reinforcing
material. Two types of stone column configurations for a
single column and the unit cell concept, representing the
stone column group, were studied by means of various
numerical parametric analyses (Fig. 1). The length of all
the stone columns was assumed to be 5 m. All the stone
columns were located on a rigid stratum.
Fig. 1 also shows some examples of the geometric models adopted for various types of stone columns with various
loading conditions. Fig. 1a to 1d show the configurations
of the unit cell conditions for the interior column conditions in the group of stone columns supporting a rigid
spread footing. Fig. 1e shows a single HRSC supporting
a rigid footing. In all the numerical analyses, the initial
in-situ stress levels were predicted by considering a value
of 0.5 for the at-rest pressure coefficient. Then, the analyses
were carried out by removing the hole, replacing the column materials, and applying vertical pressure on the top
of the rigid footing or adopting a prescribed displacement
on the top of the model to simulate the rigid footing condition on the top of the stone column and the tributary
area. To remove the effects of the element size, a fine mesh
discretization was considered for all the models. As seen in
Fig. 1, the boundary conditions in modeling single stone
column loading were sufficiently extended. However, the
boundary conditions of the unit cell models were adopted
according to three assumed area replacement ratios,
namely, 0.15, 0.25, and 0.35, which are the ratios normally
used in practice.
The soft soil and stone column materials were modeled
using 15-noded triangular elements, and the geosynthetic
reinforcements were simulated using 5-noded geogridtype elements. The Modified Cam-Clay (MCC) model
and the Hardening Soil (HS) model were used for the clay
and stone column materials, respectively. Moreover, a
20
PLAXIS, OSC, D=100 mm
30
PLAXIS, HRSC, D=100 mm,
S =D
40
Experiment by Ghazavi et al.
(2018), OSC, D=100 mm
Experiment by Ghazavi et al.
(2018), HRSC, D=100 mm, S =D
50
Fig. 3. Validation of numerical analysis for HRSCs.
900
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3. Numerical results
In the literature, most of the tests performed on ordinary or reinforced stone columns were under quick
undrained loading conditions for soft clay materials. However, the presence of a stone column causes the rapid dissipation of the excess pore pressure that is generated due to
the undrained loading conditions. As a result, the insufficient column-bearing capacity and the changes in settlement are due to the consolidation of the surrounding
clay. In this research, the Advanced Modified Cam-Clay
and Hardening Soil constitutive models for clay and stone
column materials, respectively, were used in the numerical
analyses to study the long-term and short-term behavior of
both HRSCs and ESCs. Also, to consider the free drainage
effects of the stone column materials, a fully coupled flowdeformation analysis was used to simulate quick loading
conditions and free drainage was assumed for the geosynthetic reinforcements. The clay parameters in the numerical
analyses were the same as those used by Khabbazian et al.
(2010) for Bangkok clay. For the stone column material,
typical values were used (Table 1). For the various types
of reinforced stone columns in the unit cell, various series
of numerical analyses were conducted, details of which
are given Table 2. To assess the effect of each parameter,
all other parameters were kept constant according to the
underlined values given in Table 2.
Table 1
Material parameters for numerical models.
Property name
Soft soil
Stone column
Behavior
Model
csat (kN/m3)
/ (deg)
c (kPa)
w (deg)
Eref
50 (MPa)
Eref
oed (MPa)
Eref
ur (MPa)
M
Ν
Κ
K
eint
kx (m/day)
Ky (m/day)
undrained
MCC
20
–
–
–
–
–
–
1.00
0.2
0.09
0.5
2
0.0003
0.0001
drained
HS
20
40
1
0
150
150
450
0.5
0.2
–
–
–
3
1
Two different series of numerical analyses were performed to study the short-term bearing capacity and the
long-term consolidation settlement of various types of single stone columns. The first series of analyses consisted of a
short-term two-day coupled loading, performed by applying a prescribed settlement of 20 cm. However, the second
series of analyses included a short-term two-day coupled
loading performed by applying vertical stress that caused
a 20-cm settlement at the end of the two-day loading period
determined from the first series of analyses that was followed by a 100-day consolidation period. In all the analyses, constant values of 80 cm and 500 cm were considered
for the diameter and the length of the stone columns,
respectively. However, three different ratios of footing
diameter (D0 ) to stone column diameter (D), namely, D0 /
D = 1, 2, and 3, were adopted for the single stone columns.
To determine the efficiency of the geosynthetic reinforcement on the load-bearing capacity of the stone columns,
the bearing improvement factor (B.I.F.) is defined as the
ratio of the bearing capacity of a reinforced stone column
to the bearing capacity of an ordinary stone column with
the same conditions at the same settlement values. In addition, to evaluate the settlement improvement of the reinforcements, the settlement improvement factor (S.I.F.) is
defined as the ratio of the settlement caused by an ordinary
stone column to the settlement caused by a reinforced stone
column with the same conditions. The definition of both
parameters, B.I.F. and S.I.F., are illustrated in Fig. 4.
Moreover, as shown in Fig. 4b, parameter SEOL is defined
as the settlement value of a stone column at the end of the
loading stage, while parameter SF is defined as the final settlement value of a stone column at end of the consolidation
process.
3.1. Unit cell modeling
3.1.1. Influence of loading rate and consolidation time
To study the behavior of various types of reinforced
stone columns at various loading rates, 15 coupled numerical analyses were carried out using three loading durations, namely, 2, 20, and 100 days, for applying 200 kPa
of vertical stress on the top of the unit cell. These durations
were selected to simulate rapid, medium, and slow loading
rates, respectively. All analyses were followed by a consolidation analysis until 200 days had passed from the start of
the loading period, in order to assess and compare the
long-term behavior of all the stone column types.
Table 2
Various numerical parametric analyses for unit cell concept of stone column.
Series of parametric
analyses
Parameter details
1
Loading duration and consolidation time = 2 days of loading + 198 days of consolidation, 20 days of loading + 180 days of
consolidation, 100 days of loading + 100 days of consolidation
Column diameter = 50, 80, and 110 cm
Area replacement ratio = 0.15, 0.25, and 0.35
Reinforcement stiffness = 1000, 3000, and 5000 kN/m
Internal friction angle of stone column materials = 35, 40, and 45°
2
3
4
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Fig. 4. Definition of reinforcement improvement parameters: (a) B.I.F.
and (b) S.I.F.
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Fig. 5 shows the variation in the time-settlement behavior at the top of the unit cell in the OSC and various types
of reinforced stone columns, while Fig. 6 compares the
final settlement (sF) and the S.I.F. values at the end of
200 days. As seen in Figs. 5 and 6, all types of reinforcements were able to reduce the settlement of the OSC. The
HRSC with Sr = 0.25D and the full-length ESC show the
best reinforcement performances, providing high confining
effects on the stone column materials. However, the halflength ESC and the HRSC with Sr = 0.5D show smaller
improvement effects with low confining effects on the stone
column material. Also, as seen in Fig. 6, the final long-term
settlement of the OSC or the reinforced stone columns is
independent of the column loading rate. In fact, the
amount of final settlement of the loaded stone columns is
seen to depend on the soil and the stone column material
properties, the reinforcement stiffness, and the geometric
conditions, and it is independent of the loading rate.
Fig. 7 shows the excess pore water pressure levels at the
end of the 2-day loading duration. As seen in the figure, by
reinforcing the columns, the excess pore pressure decreases
and the greatest decreases in excess pore pressure occur for
the full-length ESC and the HRSC with Sr = 0.25D. Therefore, due to the small excess pore pressure generation with
these types of reinforcements, minimum consolidation settlement is expected. Fig. 8 shows the variation in the ratio
of the settlement at the end of the loading time (sEOL) to
the final settlement at the end of consolidation (sF). As seen
from Figs. 6 and 8, the loading rate has a very minimal
effect on the final long-term settlements for all types of
stone columns. However, the ratio of sEOL/sF varies greatly
Fig. 5. Time-settlement behavior of various stone columns with different loading rates.
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Fig. 6. Variation in (a) final settlement (sF) and (b) S.I.F. values at end consolidation vs loading duration.
for the various types of stone columns and the various
loading rates. For example, for the 2-day loading rate,
the value of sEOL/sF for both the full-length ESC and the
HRSC with Sr = 0.25D is about 0.66. This indicates that
these reinforcing types can reduce the consolidation settlement to the minimum value, even with very rapid loading.
It is also seen that, by using the moderate time of 20 days
of loading, the value of sEOL/sF for both the full-length
ESC and the HRSC with Sr = 0.25D is more than 0.93.
This means that most of consolidation settlement occurs
within the first 20 days for these stone columns. However,
the consolidation settlement rates for the half-length ESC
and the HRSC with Sr = 0.5D are remarkably lower than
those in the above cases, especially at rapid loading rates.
Fig. 7. Excess pore pressure generated in various stone columns at end of
2-day loading duration: (a) OSC, (b) full-length ESC, (c) half-length ESC,
(d) HRSC with Sr = 0.25D, and (e) HRSC with Sr = 0. 5D.
Fig. 8. Variation in (sEOL/sF) vs loading duration for various stone
columns.
3.1.2. Influence of stone column diameter
Fig. 9 shows the time-settlement behavior of various
diameters of 50, 80, and 110 cm for stone columns loaded
up to 200 kPa of vertical stress in 2 days, followed by
198 days of consolidation time. As seen in the figure, with
an increase in the diameter of all types of stone columns in
the unit cell with a constant area replacement ratio, the
consolidation settlement rate decreases and more time is
required to reach the final settlement for larger diameters.
The difference in the consolidation time for various diameters of the full-length ESC and the HRSC with Sr = 0.25D
is very small, ranging from 2 days for D = 50 cm to 10 days
for D = 110 cm. However, the consolidation time for the
half-length ESC increases from 4 days for D = 50 cm to
20 days for D = 110 cm. Moreover, for the OSC and the
HRSC with Sr = 0.5D, the consolidation time has the largest increase from about 15 days for D = 50 cm to about
60 days for D = 110 cm. In fact, the load-bearing behavior
of the full-length ESC and the HRSC with Sr = 0.25D has
minimum dependency on the surrounding clay behavior,
and a minimum amount of excess pore pressure is generated for these types of reinforced stone columns. As a
result, they experience minimum consolidation settlements.
Fig. 10 shows the variation in the S.I.F. versus the diameter of the stone columns for various reinforcement types.
A. Ehsaniyamchi, M. Ghazavi / Soils and Foundations 59 (2019) 1579–1590
1585
Fig. 9. Time-settlement behavior of various stone columns with different column diameters: (a) D = 50 cm, (b) D = 80 cm, and (c) D = 110 cm.
the benefit of the encasement decreases with an increase
in the diameter of these columns.
It should be noted that, with an increase in the stone column diameter from 50 to 80 and 110 cm, the area ratio of
the reinforcing material to the volume for the unit cell
decreases from 2 to 1.25 and 0.91, respectively. In other
words, with an increase in the diameter of the full-length
ESC and the HRSC with Sr = 0.25D from 50 to 110 cm,
the use of reinforcement material brings about a two-fold
decrease. However, the S.I.F. decreases just about 19%
for the HRSC with Sr = 0.25D. Therefore, from the viewpoint of the amount of consumption of the reinforcing
material, the best reinforcement type is the HRSC with
Sr = 0.25D for larger stone column diameters.
Fig. 10. Variation in S.I.F. with column diameter for various stone
columns.
As shown in the figure, for all reinforcement types, the S.I.
F. value decreases with an increase in the stone column
diameter. However, the rate of decrease is much larger
for the full-length ESC than for the HRSCs. Murugesan
and Rajagopal (2010) and Castro and Sagaseta (2011)
reported the same results for ESCs and concluded that
3.1.3. Influence of area reinforcement ratio
Fig. 11 shows the time-settlement behavior of stone columns with various area replacement ratios. As seen in the
figure, the rate of consolidation increases with an increase
in the area replacement ratio for all types of stone columns.
This is due to a reduction in the drainage path length and
to bearing a larger part of the applied load by the stiffer
stone column. In addition, the time it takes to reach the
final settlement for the full-length ESC and the HRSC with
Fig. 11. Time-settlement behavior of stone columns with different area replacement ratios: (a) 0.15, (b) 0.25, and (c) 0.35.
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Fig. 12. Variation in S.I.F. with area replacement ratio for various stone
columns.
Sr = 0.25D is minimum. This is because their behavior has
only minimum dependency on the surrounding clay.
Fig. 12 shows the variation in the S.I.F. with the area
replacement ratio for various reinforced stone columns.
As seen in the figure, the S.I.F. increases with an increase
in the area replacement ratio for all cases. However, the
rate of increase in the S.I.F. decreases for larger area
replacement ratios.
3.1.4. Influence of reinforcement stiffness
Fig. 13 shows the time-settlement behavior of various
stone columns with reinforcement stiffness. As seen in the
figure, for the full-length ESC and the HRSC with
Sr = 0.25D, the total consolidation time decreases from
about 10 days for J = 1000 kN/m to about 3 days for
J = 5000 kN/m. However, the variation in reinforcement
stiffness has no sensitive effect on the total consolidation
time in the half-length ESC and or the HRSC with
Sr = 0.5D. Fig. 14 shows the variation in the S.I.F. with
reinforcement stiffness for various types of stone columns.
As seen in the figure, the S.I.F. values increase with an
increase in the reinforcement stiffness for all reinforcement
types. However, the increases in the S.I.F. for the
Fig. 14. Variation in S.I.F. with reinforcement stiffness for various stone
columns.
full-length ESC and the HRSC with Sr = 0.25D are much
larger than those for the half-length ESC and the HRSC
with Sr = 0.5D. In fact, the loading behavior of the fulllength ESC and the HRSC with Sr = 0.25D has a strong
dependency on the reinforcement material stiffness and
has much less dependency on the properties of the
surrounding clay. However, the loading behavior of the
half-length ESC and the HRSC with Sr = 0.5D not only
depends on the reinforcement material stiffness, but also
on the properties of the surrounding clay. Moreover, for
the half-length ESC and the HRSCs, the rates of increase
in the S.I.F. decrease with an increase in the reinforcement
stiffness. This is because, with these reinforcement types, a
moderate level of reinforcement stiffness of about 3000 kN/
m can produce a sufficient level of confinement effect on the
column material in the reinforced parts of these columns
and, by increasing the reinforcement stiffness from 3000
kN/m to 5000 kN/m, the main effective parameter on the
behavior of stone columns is the bulging of the column
materials at the unreinforced parts located between the
horizontal layers of the HRSCs or at the lower unreinforced part of the half-length ESC. Therefore, the use of
high stiffness for the reinforcements cannot bring about
Fig. 13. Time-settlement behavior of various stone columns with reinforcement stiffness: (a) J = 1000 kN/m, (b) J = 3000 kN/m, and (c) J = 5000 kN/m.
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greater improvement for either the half-length ESCs or the
HRSC with Sr = 0.5D. However, in the cases of the fulllength ESCs and the HRSC with Sr = 0.25D, due to the full
confinement of all parts of the columns, the horizontal displacements of the columns of all lengths were limited and
the behavior of the stone columns was seen to mainly
depend on the reinforcement stiffness. Therefore, with an
increase in the stiffness of the reinforcements, even for high
stiffness values, the S.I.F. value will increase.
3.2. Single stone column loading
3.2.1. Short-term bearing capacity of single stone columns
To study the short-term bearing capacity of single reinforced stone columns and to predict the B.I.F. of various
types of reinforcements, some coupled flow-deformation
Fig. 16. Variation in S.I.F. with internal friction angle of column material
for various stone columns.
Vertical stress (kPa)
0
50
100
150
200
0
OSC
Settlement (mm)
3.1.5. Influence of internal friction angle (/) of stone column
materials
Fig. 15 shows the time-settlement behavior of various
stone columns with three values of 35, 40, and 45° for
the internal friction angle of the stone column material.
As seen in the figure, with an increasing /, the consolidation settlement rate increases slightly for all types of stone
columns. In fact, by using a stronger material for the stone
columns, a greater part of the load is tolerated by the column material, leading to a lower generation of excess pore
pressure in the surrounding clay, and thus, the occurrence
of lower consolidation settlement.
Fig. 16 shows the variation in the S.I.F. with the internal
friction angle of the column material for various types of
reinforced stone columns. As seen in the figure, the S.I.F.
value for all the stone columns increases with an increase
in the internal friction. However, the rate of increase for
the HRSCs is greater than that for the ESCs. This is due
to the interlocking effect between the horizontal reinforcement layers and the column materials. In practice, this may
help in choosing the type of reinforcement. Thus, HRSCs
may be used when stronger column materials are available.
Also, ESCs are preferable when poor materials are present
in the stone columns.
40
HRSC, S =0.5D
Half-length ESC
80
Full-length ESC
HRSC, S =0.25D
120
160
200
Fig. 17. Variation in vertical stress-settlement behavior of various types of
single stone columns.
analyses were performed by applying a prescribed settlement of 20 cm for the duration of one day. In these analyses, three ratios, namely, D0 /D = 1, 2, and 3, and
D = 80 cm, were considered for all cases. Figs. 17 and 18
show the variations in the vertical stress-settlement
behavior and the excess pore pressure generated under
Fig. 15. Time-settlement behavior of various stone columns with internal friction angle for stone column material: (a) 35°, (b) 40°, and (c) 45°.
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Fig. 18. Excess pore pressure under footing area for case of D0 /D = 2, due to 20-cm settlement of footing for various stone columns: (a) OSC, (b) HRSC
with Sr = 0.5D, (c) half-length ESC, (d) full-length ESC, and (e) HRSC with Sr = 0.25D.
the footing area, respectively, of various types of stone columns for D0 /D = 2. Table 3 presents the bearing capacity
and the B.I.F. values at the end of 1 day of loading for various cases. As seen in Fig. 17 and Table 3, for all the D0 /D
values, the HRSC with Sr = 0.25D and the full-length ESC
have the best B.I.F., while the HRSC with Sr = 0.5D has
the lowest B.I.F. value. In addition, the half-length ESC
has a moderate effect on the B.I.F. In fact, as shown in
Fig. 18, using a full encasement along the column or horizontal reinforcing layers with a low interval spacing provides a full confining effect on the stone column material.
As a result, most of the applied load on the footing is tolerated by the stone column and a minimum amount of vertical stress is transferred to the surrounding clay. Thus, low
excess pore pressure is generated in the soft soil. However,
for the cases of the half-length ESC and the HRSC with
Sr = 0.5D, no sufficient confinement is provided for the
stone column materials. As a result, greater vertical stress
is transferred to the surrounding clay; and thus, greater
excess pore pressure is generated. This leads to an increase
in the long-term consolidation settlement in such types of
reinforced stone columns compared with the other cases.
3.2.2. Long-term consolidation settlement of single stone
columns
To investigate the long-term behavior, various types of
single reinforced stone columns were initially modeled
using a rigid plate on the top of the stone columns with various D0 /D and applying the amount of vertical stress that
would lead to the same 20-cm settlement for all cases,
according to bearing capacity values mentioned in Table 3.
The vertical stress is applied for 1 day with a coupled analysis and, after that, a consolidation analysis is conducted to
dissipate the excess pore pressure in the clay medium and
to reach a steady state condition of the settlements.
1. The results of the time-settlement analysis for D0 /D = 2
are shown in Fig. 19. As seen in the figure, a maximum
settlement of 4 cm occurs during consolidation for the
HRSC with Sr = 0.5D. This is approximately equal to
the consolidation settlement of an OSC. However, for
the full-length ESC and the HRSC with Sr = 0.25D,
the minimum consolidation settlements of 0.4 cm and
1.2 cm, respectively, occur. Therefore, by using fulllength ESCs or HRSCs with Sr = 0.25D, the long-term
settlement of single stone columns can be significantly
reduced, in addition to there being an improvement in
the short-term load-bearing behavior.
Fig. 19. Time-settlement variations for various types of single-stone
columns during short-term, 1-day of loading, and long-term consolidation
time to 200 days.
Table 3
Bearing capacity and B.I.F. values at end of two days of loading for various single stone columns.
D0 /D (D = 80 cm)
OSC
Bearing capacity (kPa)
HRSC, Sr = 0.5D
B.I.F.
Half-length ESC
B.I.F.
Full-length ESC
B.I.F.
HRSC, Sr = 0.25D
B.I.F.
1
2
3
63.5
25.9
19.9
2.87
2.97
2.4
6.53
4.14
2.71
10.74
6.8
4.34
9.88
7.07
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4. Conclusions
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In this paper, various short-term coupled flowdeformation analyses and long-term consolidation analyses
have been performed to investigate the behavior of various
types of reinforced stone columns. Based on the numerical
analyses, the following concluding remarks can be made:
2. All types of reinforcements can improve the short-term
load-settlement behavior of OSCs and reduce their
long-term consolidation settlement in both the unit cell
configuration and the single stone column configuration.
3. The final long-term settlement of OSCs or reinforced
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4. By considering the results of the parametric analyses
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HRSC with Sr = 0.25D is the most efficient type of reinforcement for stone columns with the greatest B.I.F. and
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5. With proper reinforcements, such as full-length ESCs or
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9. The bearing capacity of full-length ESCs and HRSCs
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