Effect Of Using Stone Columns On The Behavior Of the Raft Foundation.

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 10 | Oct 2022 www.irjet.net p-ISSN: 2395-0072
© 2022, IRJET | Impact Factor value: 7.529 | ISO 9001:2008 Certified Journal | Page 245
Effect Of Using Stone Columns On The Behavior Of the Raft Foundation.
Salma Amr Ezzat1, Ahmed Fathy Zidan2, Mohamed Sayed Gomaa3
1Post graduate Student, Civil Engineering Dept., Faculty of Engineering, Fayoum University, Egypt
2 Professor, Civil Engineering Dept., Faculty of Engineering, Beni sueif University, Egypt
3 Associate professor, Civil Engineering Dept., Faculty of Engineering, Fayoum University, Egypt
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Abstract- A series of axis-symmetry models using finite
element analyses (PLAXIS 3D) were performed to investigate
the behavior of a raft foundation over clayey soil improved by
stone columns (SC). Clayey soil and stone columns were
modelled using hardening soil model, which uses an elastic-
plastic hyperbolic stress–strain relation, and the raft
foundation was modelled as an elastic element. Several
parameters, including number of stone columns (n), length of
stone columns (L), young’s modulus of stone columns ( ),
thickness of raft foundation (t), and diameter ofstonecolumns
(D), are selected in this paper to investigate the influence of
these parameters on the settlement, bearing capacity of soil,
flexural behavior and shear of raft foundation. Finally, the
results indicate that by increasing all parametric studies,
bearing capacity of soil increased and settlement decreased,
while the flexural behavior and shear of the raft foundation
decreased in some sections. The most effective parameters for
decreasing flexural behavior and settlement are diameter of
stone columns (D) andYoung’smodulusofstonecolumns ;
for decreasing shear is (Young’s modulus of stone
columns) . Some significant observations on the
performance of raft-stone column systems with changes inthe
values of parametric study are presented in this paper.
Keywords: stone columns, shear, flexural behavior, and
bearing capacity
1. INTRODUCTION
The use of stone columns under raft foundation to improve
the settlement behavior became an important topic in the
last decade. Both theoretical and experimental studies have
been performed by several previous researchers to
investigate the benefits of stone column system (JAN (2011)
[1], Ng. (2018) [2], Nav et al. (2020) [3], Danish et al. (2021)
[4], Znamenskii et al. (2021) [5] and Shehata et al. (2021)
[6]). This paper discusses the behavior of a raft foundation
constructed on clayey soil improved by stonecolumnsunder
the influence of some factors including number of stone
columns (n), length of stone columns (L),young’smodulus of
stone columns ( ), thickness of raft foundation (t) and
diameter of stone columns (D). Stone columns are ideally
suited for sandy soils, according to Law et al. (2015) [7].
Clayey soils necessitate a greater number of stone columns.
Due to the necessity for large machinery and a stone storage
area, this method may not be ideal for those with limited
mobility. Stone column ground improvement istheinsertion
of vertical stone columns to the ground to a depth of at least
4 meters below the ground surface. The columns canthen be
covered with compacted gravel in preparation for the
construction of new housing foundations. In columns
arranged with spacing bigger than three times diameter,
Ambily et al. (2007) [8] demonstrated that the diameter of
the column does not provide a significant advantage.Whena
single column is loaded, it fails by bulging with a maximum
bulging intensity of approximately 0.5 times the diameter of
a stone column. The ratio of limiting axial stress on the
column to the equivalent shear of surrounding clay is found
to be constant for any given s/d and angle of internal friction
of stones, and is independent of the sheer strength of the
surrounding clay, Killeen et al (2010) [9]. Due to the
enhanced stiffness of the stone backfill, [9] discovered that a
footing supported by a high number of stone columns had a
substantial effect on the settlement improvement factor. A
reduction in the distancebetweenstonecolumnsboosted the
effectiveness of footing settlement. Al-Waily et al. (2012)
[10] demonstrated that as the number of stone columns
increased, the group efficiencydecreased;additionally,stone
columns were more effective than lime columns in shear
(cu= 8 KPA) soil, but lime columns were more effective than
stone columns in shear (cu= 14 KPA) soil. Chauhan et al
(2017) [11]. According to [11],thereisaninverseproportion
between the diameter of the stone column and the
settlement of the clayey soil, which can be attributed to the
confining stresses, which are greater instonecolumnswitha
smaller diameter. Due to confinement stresses, the failure
load of the reinforced clay bed is approximately six times
that of the unreinforced one, and its ultimate bearing
capacity decreases by 40 percent for 100mmdiameterand6
percent for 70 mm diameter compared to the 50 mm
diameter of the stone column. Still, the earth's bearing
capability was enhanced in comparison to untreated soil.
Reza et al (2019) [12]. These tests demonstratethevariation
of ultimate bearing capacity ratio (BCR), settlement
reduction factor (SRF), and stiffness improvement factor
(SIF) for stone columns with varying lengths, numbers, and

diameters. According to the data, increasing the numberand
length of stone columns will enhance the BCR,but reduce the
SRF. The increase in the diameter of stone columns will
increase the BCR and reduce (SIF), the increase in lengths,
diameter, and a number of stone columns leads to an
increase in high ultimate bearing capacity, which reached
2.75 times of untreated soil. Samuel et al. (2019) [13]
indicated that using stone columns leads to improvement in
ultimate bearing capacity. The most effective material in
maximum bearing capacity was hard blue granite aggregate,
pebbles, and finally marble waste. Vladimir et al. (2019)[14]
indicated that as the length of the stone columns grows
longer, the clay layer's settlement normalized tothewidthof
footing dimension (Δ/D) decreases. This decline in the
settlement is significant until the length of the stone column
is normalized to the diameter of the stonecolumn(L/d)=10.
Nitin et al. (2021) [15] showed that using stone columns to
reinforce black cotton soil increases its strength,
consolidation, permeability, and swelling qualities simply
and cost-effectively. Stone columns increase the load-
carrying capacity of black cotton soil significantly. End
bearing and floating stone columns are strengthened by
increasing the diameter and the length ratio of the stone
columns.
The aim of this study is to address the aspects of
enhancement of the bearing capacity, settlement reduction,
flexural behavior and shear of raft foundation reduction
through the use of raft-stone column system. The
improvement of bearing capacity, settlement, flexural
behavior and shear of a raft improved by a stone column
system is studied here to investigate the change of this
enhancement when the point displacement is applied.
2. NUMERICAL MODELLING
The numerical models in this investigation were modelled
using the PLAXIS 3-D finite element computer software. The
program's results have been validated bycomparingthemto
measures gathered fromgenuinecasehistoriesand research.
The program can simulate stone columns, soil, footings, and
foundation behavior.
2.1. Problem definition and parametric studies
An axisymmetric model is used to replicate the model shape,
with a 9 x 9 m raft foundation and a 0.06 m point
displacement load positionedalongtheaxisofsymmetry.The
depth and width of clayey soil are taken 27 m and 38 m
respectively with square dimensionsas showninFig1.These
model dimensions were set such that the amplitude of the
collapse load remains constant even when depth and width
are raised beyond the selected values. The model's vertical
borders were restraint horizontally and free vertically,
whereas the bottom boundary was constrained in both
horizontal and verticaldirections.Inallfiniteelementstudies,
the parameters given to the clayey soil, stone columns, sand
pad, sandy soil, and raft foundation were assumed to remain
constant. Various parameters affect the system's behavior.In
this analysis, number of stone columns (n) =13 and 25 stone
columns as it examines how stone column numbers affect
system behavior. To simulate floating and end-bearing stone
columns, the column length is normalized to the clay layer
thickness. In order to measure the enhancement, (L/H) is
varied (0.4, 0.6, and 0.8). The Young’s modulus of stone
column =30, 70, 90 mPa, stone column's diameter
(D=0.4, 0.6, 0.8 m) and the thickness of raft foundation (t)
(0.5, 0.8, 1 m) are parametric studies in this current study.
3. MATERIAL MODELLING AND MESH
GENERATION
3.1. The clayey soil and stone columns.
In this numerical investigation, a hardening-soil model was
employed to represent the non-linear behavior of clay and
stone columns. The Hardening-Soil model represents the
hyperbolic relationship between vertical strain, (e1), and
deviator stress, (q). A hyperbola can adequately reflect the
observed relation between axial strain and deviator stress in
the current situation of a drainedtriaxletest.Inthisstudy,the
limiting state of stress is described by the secant Young's
modulus , the odometer modulus as as being
( according to (Elshazly et al., 2009)[16],
Poisson's ratio( ), unloading reloading modulus(
3 ),effective cohesion ( ), angle of internal
friction ( ), angle of dilatancy (Ѱ) which is ( -30)
according to McCabe et al. (2009) [17] forstone columns and
(Ѱ=- ) using 0.0564 as the value for d) for clayey
soil according to Salah et al. (2021)[18],andfailureratio(Rf).
The parameters of hardening soil model for clay soil and
stone columns in this current study are selected according to
Salah et al. (2021) [18] and Killeen et al. (2010) [9]
respectively and shown in Table -1.

(a)
(b)
Fig -1 : Raft . stone column system and soil layer
(a) 3D. View (b) Side view.
Table -1: Clayey soil and stone column dates.
Material
name
Clayey soil Stone column
Material
model
Hardening soil
model
Hardening soil
model
Drainage
type
Drained Drained
ꙋ unsat 20 KN/ 19 KN/
ꙋ sat 22 KN/ 21 KN/
3400 KN/ 70000 KN/
3600 KN/ 70000 KN/
12000 KN/ 210000 KN/
33.58 KN/ 1 KN/
17.51◦ 45◦
Ѱ 1.6◦ 15◦
0.9 -
Power (m) 0.7 0.3
0.2 -
0.6991 0.3
3.2. Sand pad soil.
The Mohr-Coulomb failure criteria are commonly used to
describe the strength of soils. A failure theory is required to
relate the available strength of soil as a function of measured
attributes and applied stress conditions. Its primary premise
is that combining normal and shears leads to a more critical
limiting condition than would be reached if either the major
principle stress or maximum shear were considered
individually. The major stresses caused failure, while the
normal and shears produced the failure plane. Linear elastic
that is perfectly elastic The Mohr-Coulomb model takes five
input factors into account:young’smodulus(E) andPoisson’s
ratio (v) for soil elasticity; cohesion (c) for soil plasticity; an
angle of friction ( ) and an angle of dilatancy (Ѱ) which is
( -30) according to McCabe et al. (2009) [17]. Sand pad is
modelled as a Mohr Coulombfailurein thisstudybecauseitis
used to distribute load in all stone columns. All data for the

sand pad is taken from Samanta et al. (2017) [19] and shown
in Table -2.
3.3. Sandy soil.
In this research, sand represents the element volume (15-
node). The sand pad is drained soil. The sand pad is modelled
as a Mohr Coulomb. Table -2 shows all date for sandy soil.
Table -2: Sand Pad and sandy soil dates
Material name Sand pad Sandy soil
Material model Mohr_ Coulomb Mohr_ Coulomb
Drainage type Drained Drained
ꙋ unsat 20 KN/ 19 KN/
ꙋ sat 20 KN/ 19 KN/
45000 KN/ 25000 KN/
0 KN/ 0 KN/
40◦ 35◦
Ѱ 10◦ 5◦
0.3 0.3
3.4. Concrete raft foundation.
A linear elastic model considers a material to be an idealized
linear-elastic material that does not deform, which prevents
irreversible stresses from forming during loading and
unloading. The model requires two factors to simulate the
behavior: Young's elastic modulus, E, and Poisson's ratio, v.
The model was used to model the concrete raft foundation
behavior in this study and all the data is shown in Table -3.
Table -3: Concrete raft foundation date.
Material name Concrete raft
Material model Elastic
ꙋ 25 KN/
E1 25000000 KN/
U12 0.2
4. MESH SENSITIVITY
In order to remain analysis and collapsing load constant,
mesh is getting smaller and smaller.
5. VALIDATION
In order to support this study, the current numerical models
are compared with the results obtained by Reza et al. (2019)
[12]. Reza et al. (2019) [12] examined a model with a
0.4x0.4x0.02 m steel plate as a footing was loaded by 0.06 m
a point displacement, sandy soil and stone columns were
modelled as Mohr coulomb model and all date is shown in
Table -4. Reza et al. (2019) [12] parametric studies were
variation of stone column lengths such as 30, 40 and 50 cm
for 5 stone columns and different stone column numbers for
the same length such as 4 and 5 stone columns. The results
are compared to Reza et al. (2019) [12] envelope
improvementin(settlement/widthoffooting)versusapplied
load curve. The identical experimental model is modelled
using the finite element method in PLAXIS 3D. Fig -2 shows
that the ultimate bearing capacity of 30 cm stone columns
from FE modeling is 34 KN and from experimental results is
32.5 KN and from FE modeling is 36.5 KN and from
experimental results is 36.5 KN for 40cm in length. Fig -3
shows that the ultimate bearing capacity for 4 for the same
length from FE modeling is 37 KN, and from experimental
results is 33 KN for 4 stone columns and from FE modelingis
37.5 KN and from experimental results is 37.6 KN for5stone
columns. This study's finite element results and Reza et al.
(2019) [12] agree well.
Table -4: Reza et al. (2019) [12] date
parameter Sand
bed
Sand
pad
Stone
column
steel
Young’s
Modulus(mPa)
11 25 45 2x
Poisson’s ratio 0.3 0.3 0.25 0.2
Density
(kN/m3)
14.5 15.8 17.25 78.5
Internal
friction angle
31 41 45 -

Fig -2: Envelop settlement-load curve for present work
and experimental results Reza et al (2019) for different
lengths.
Fig -3: Envelop settlement-load curve for present work
and experimental results Reza et al. (2019) for numbers of
stone columns.
6. ANALYSIS CASES
Figure 1 illustrates the geometry of the model used in this
analysis. The parametric study included young’s modulus of
stone columns ( , thickness of raft foundation (t) and
diameter of stone columns (D). This Parameters is
normalized (non-dimensional) to thickness of claylayerL/H
to describe the effect of the length of stone columns. Table -5
shows parametric studies in this study.
7. RESULTS AND DISCUSSIONS
A series of axis-symmetric finite element analyses were
performed to investigate the improvement in bearing
capacity, settlement reduction, flexural behavior, and
induced shear on the raft foundation caused by the use of
stone columns under a raft foundation exposed to a point
displacement as load. The bearing capacity increasing factor
(BIF) is used to express the increase in the bearing capacity
of the raft stone column system compared to the raft
foundation without stone column and is defined in Eq 1 The
moment reduction factor (MRF) is used to express the
decrease in the flexural behavior of the raft stone column
system compared to the raft foundation without stone
column and is defined in Eq 2. The shear reduction factor
(SRF) is used to express the decrease in the shear of the raft
stone column system compared to the raft foundation
without stone column and is defined in Eq 3. In this paper,
the raft foundation is symmetry, so shear is skew symmetry
and moment is symmetry. Shear is drawn for half-sections in
the other side moment for full sections. Flexural behavior
and shear on the raft foundation analyses are divided into
two sections, shown in Fig 4 and 5.
. (1)
(2)
(3)
Table -5: Parametric studies
Group Constant parameters Variable parameters Remarks
1 Untreated soil (raft foundation without
stone columns)
2
=70 mPa, t= 0.8m, D=0.6 m, n=13 SC
L/H= 0.4 , 0.6, 0.8 Influence of length of
stone columns
=70 mPa, t= 0.8m, D=0.6 m, n=25 SC
L/H= 0.6, t=0.8m, D=0.6m, n=13 SC Influence young’s

3 L/H= 0.6, t=0.8m, D=0.6m, n=25 SC = 30, 70, 90 mPa modulus of stone
columns
4
L/H= 0.8, =70 mPa, D=0.6 m, n=13
SC
t=0.5, 0.8, 1 m Influence thickness of
raft foundation
L/H= 0.8, =70 mPa, D=0.6 m, n=25
SC
5
L/H= 0.8, =70 mPa, t=0.8 m, n=13 SC
D=0.4, 0.6, 0.8 m Influence of diameter of
stone columns
L/H= 0.8, =70 mPa, t=0.8 m, n=25 SC
Fig -4: sections for 13 stone columns
Fig -5: sections for 25 stone columns
7.1 Influence of length of stone columns
Six analytical cases are included using the axis-symmetric
finite element method to explore the behavior of the raft-
stone column system under point displacement. Group 2 is
examined in Table -5 to determine the effect of variation of
stone column lengths on the performance of the raft-stone
column system for 13 and 25 stone columns while keeping
the young's modulusofstonecolumns ,raftfoundation
thickness (t), and stone column diameter (D) constant.
7.1.1 Load – settlement behavior of clayey soil
Fig -6 depicts an example of load settlement curves for both
raft-stone column systems and untreated soil without stone
columns. It can be noted from Fig 6 that there is a light effect
of variation in stone column lengths/thickness of clayey soil
(L/H). When stone column lengths/thickness of clayey soil
(L/H) increased by 0.4, 0.6, and 0.8, bearing capacity
increasing factor (BIF) increases for 13 stone columns by
33.24%, 36.7%, and 37.3% respectively and for 25 stone
columnsby53.02%,58.7%,and60.08%respectively.Bearing
capacity increasing factor (BIF) increases with an increasing
number of stone columns.
Fig -6 : Comparison between load and settlement for 13
and 25 stone columns for variation length with respect to
thickness of clayey soil.
7.1.2 Flexural behavior of the raft foundation
(M1-1) and shear (Q2-3).
Figs 7 and 8 show the flexural behavior of the raft-stone
column system and raft foundation without stone columns
for sections 1 and 2 respectively with different values of
stone column lengths/thickness of clayey soil (L/H) such as
0.4, 0.6, and 0.8 and with differentnumbersofstonecolumns.

Fig -7: Flexural behavior of the raft foundation (M1-1) of
section 1 for 13 and 25 stone columns (variation of stone
column lengths with respect to the thickness of clayey soil
(L/H))
By increasing the length (L/H), moment reduction factor
(MRF) increases. For 13 stone columns, the moment
reduction factor (MRF) increases for section 1 by 1.98%,
2.15%, and 2.25% respectively, and for section 2 by 6.69%,
6.27%, and 7.58% respectively.Fora25-stonecolumngroup,
moment reduction factor (MRF) reduces by increasing(L/H)
for section 1, 2.5%, 2.42% and 2.29% respectively and for
section 2, up to 10.25%, 9.46% and 9.43% respectively
section 2 for 13 and 25 stone columns (variation of stone
column lengths with respect to the thickness of clayey soil
(L/H))
Figures 9 and 10 illustrate the shear of the raft-stone column
system and the raft foundation without stone columns for
sections 1 and 2 with different values of stone column
lengths/thickness of clayey soil(L/H)suchas0.4,0.6,and0.8
and with varied numbers of stone columns. By increasingthe
length (L/H), shear reduction factor (SRF) increases. For 13
stonecolumns, the shear reductionfactor(SRF)increasesfor
section 1 by 3.88%, 4.32% and 3.91% respectively, and for
Fig -9: Shear of the raft foundation (Q2-3) of section 1for
13 and 25 stone columns (variation of stone column
lengths with respect to the thickness of clayey soil (L/H))
section 2 by 16.84%, 19.67% and 17.53% respectively.
For 25 stone columns, shear reduction factor (SRF)
reduces for section 1 up to 2.82%, 2.76% and 2.74%
respectively, and for section 2 up to 28.4%, 25.8% and
27.02%respectively.While stone column numbers increase,
(MRF) and (SRF) increase.
Fig -10: Shear of the raft foundation (Q2-3) of section 2 for
lengths with respect to the thickness of clayey soil (L/H))
7.2 Young’s modulus of stone columns ).
To investigate the behavior of the raft-stone column system
under point displacement, six analytical examples are
conductedusingtheaxis-symmetricfiniteelementmethod.In
Table -5, for group 3, the effect of varying the young's
modulus of stone columns ( )) on the performance of the
raft-stone column system for 13 and 25 stone columns is
investigated, whilekeepingstonecolumnlength/thicknessof
clayey soil (L/H), raft foundation thickness (t), and stone
column diameter (D) constant.

Figure 11 depicts an example of load settlement curves for
both raft-stone column systems and untreated soil without
stone columns. Figure 11 shows that variation in the young's
modulus of stone columns ( ) and the number of stone
columns has a significant influence. When the young's
modulus of stone columns increases by 30, 70, and 90 mPa,
bearing capacity increasing factor (BIF)for13stonecolumns
exceeds by 26.19%, 37.3%, and 39.42% respectively, and
41.82%, 60.08%, and 63.54% respectively for 25 stone
columns. Bearing capacity increasing factor (BIF) rises
significantly as the number of stone columns increases.
Fig -11: Comparison between load and settlement for 13
and 25 stone columns for variation of young’s modulus of
stone columns.
Figures 12 and 13 depict the flexural behavior of a raft-stone
column system and a raft foundation without stone columns
for sections 1 and 2 respectively with different values of the
young's modulus of stone columns ( ) such as 30, 70, and
90 mPa and varying numbers of stone columns. For 13 stone
columns, the moment reduction factor (MRF) rises by 0.7%,
1.7%, and 0.75% respectively for section 1 and up to 4.69%,
7.58%, and 5.8% respectively for section 2. For a 25-stone
column group, moment reduction factor (MRF) increases by
increasing ( ) for section 1 by 1.95%, 2.41%, and 2.37%
respectively and for section 2 by up to 8.17%, 9.43%, and
9.54% respectively.
section 1for 13 and 25 stone columns (variation of Young’s
modulus of stone columns )
section 2 for 13 and 25 stone columns (variation of
Young’s modulus of stone columns )
Figs 14 and 15 show the shear of the raft-stone column
system and raft foundation without stone columns for
sections 1 and 2 respectivelywith different valuesofYoung's
modulus of stone columns and with a different number of
stone columns. For 13 stone columns, the shear reduction
factor (SRF) increases for section 1 by 2.78%, 3.91%, and
3.39% respectively, and for section 2 up to 15.08%, 17.53%,
and 18.14% respectively. For 25 stone columns, shear
reduction factor (SRF) increases for section 1 up to 2.66%,
2.74% and 2.75% respectively, and for section 2 up to
24.42%, 27.02%and 27.03% respectively.Whilethenumber
of stone columns raises, the moment reduction factor (MRF)
and the shear reduction factor (SRF) increase.

13 and 25 stone columns (Young’s modulus of stone
columns )
13 and 25 stone columns (Young’s modulus of stone
columns .
7.3 Thickness of raft footing (t).
Six analytical cases are performed using the axis-symmetric
finite element method to explore the behavior of the raft-
stone column system under point displacement. The impact
of modification in raft footing thickness (t) on the
performance of the raft-stone column system is explored in
Table -5 for group 4 as various thickness of raft foundation
values for 13 and 25 stone columns while keeping stone
column length/thickness of clayey soil (L/H), young's
modulus of stonecolumns( ),andstonecolumndiameter
(D) constant.
7.3.1 Load – settlement behavior of clayey soil.
The effect of the thickness of the raft foundation on the
performance of the raft-stone column system is presented in
Fig -16. It shows the general trend of load settlement
relations for different values of (t) and the number of stone
columns. Fig -16 presents the results of the analyses for
Group 4. The results show that there is a significant effect of
the variation of the thickness of the raft foundation on the
load-settlement behavior of the raft-stone column system,
and by increasing the number of stone columns, bearing
capacity increases.
Fig -16: Comparison between load and settlement for 13
and 25 stone columns for variation of raft foundation
thickness
Figures 17 and 18 show the flexural behavior of a raft-stone
for sections 1 and 2 respectively with various values of
thickness of raft foundation (t) such as 0.5, 0.8, and 1 m and
varying numbers of stone columns. Figs. 19 and 20 show the
shear of the raft-stone column system and raft foundation
without stone columns forsections 1 and 2 respectively with
different values of the thickness of the raft foundation(t)and
with different numbers of stone columns. It can be seen that
flexural behavior and shear on the raft-stone column system
increase by increasing (t). By increasing stone columns
numbers, flexural behavior and shear on the raft-stone
column system reduce.
section 1for 13 and 25 stone columns (thickness of raft
footing (t))

section 2 for 13 and 25 stone columns (thickness of raft
footing (t))
Fig -19: Shear of the raft foundation (Q2-3) of section 1for
13 and 25 stone columns (variation of thickness of raft
footing (t))
13 and 25 stone columns (variation of thickness of raft
footing (t))
7.4 Diameter of stone columns (D).
Six analytical scenarios are conducted using the axis-
symmetric finite element method to explore the behavior of
the raft-stone column systemunder point displacement. The
effect of changing the diameter of stone columns on the
performance of the raft-stone column system is investigated
in Table -5 forgroup 5 as different diameterofstonecolumns
values for 13 and 25 stone columns while keeping the stone
column length/thickness of clayey soil (L/H), young's
modulus of stone columns ( , and raft foundation
thickness (t) constant.
Figure 21 shows the relationship between the load-
settlement fordifferent casesof stone column diametersand
the number of stone columns. It has been discovered that
raising the area replacement ratio or the diameter of the
stone column by 0.4, 0.6, and 0.8 m results in an enhanced
bearing capacity increasing factor (BIF). Bearing capacity
increasing factor (BIF) exceeds by 19.21%, 37.3%, and
56.16%, respectively, for 13 stone columns and by 27.55%,
60.08%, and 94.35%, respectively, for25 stone columns. Itis
observed that an increasing number of stone columns has a
significant effect on (BIF).
Fig -21: comparison between load and settlement for 13
and 25 stone columns for variation of diameter of stone
columns
Figures 22 and 23 present the flexural behavior of a raft-
stone column system and a raft foundation without stone
columns for sections 1 and 2 when stone column diameters
are 0.4, 0.6, and 0.8 m and the number of stone columns is
varied. By increasing(D),themomentreductionfactor(MRF)
increases. Although there is some scatter, there is an
improvement for flexural behavior and shear of raft

section 1 for 13 and 25 stone columns (stone column
diameters (D))
foundation. The moment reduction factor(MRF)for13stone
columns increases by 0.55%, 1.7%, and 2% respectively for
section 1 and up to 6.42%, 7.58%, and 9.63%respectivelyfor
section 2. For the 25 stone column group, moment reduction
factor (MRF) reduces by increasing (D) only for section 1 by
6.15%, 2.41%, and 3.3% respectively, but for section 2 The
moment reduction factor (MRF) increases by 6.8%, 9.43%,
and 13.05% respectively.
section 2 for 13 and 25 stone columns (stone column
diameters (D))
Figures 24 and 25 summarize the shear of a raft-stone
for sections 1 and 2 when stone column diameters (D) and
the number of stone columns are varied. Shear reduction
factor (SRF) increases as (D) grows,whereasshearreduction
factor (SRF) increases for section 2 for 13 and 25 stone
columns by 14.11%,17.53%,and23.65%respectivelyandby
18.91%, 27.02%, and 30.32% respectively, but for section 1
for13 and 25 stone columns,theshearreductionfactor(SRF)
reduces by 34.37%, 3.91%, and 0.5% respectively and by
50.79%, 2.74% respectively. While the number of
stone columns raises, the moment reduction factor (MRF)
and the shear reduction factor (SRF) increase.
diameters (D))
diameters (D))
8. CONCLUSIONS
1. 13 and 25 stone columns have better load-settlement
behavior compared with untreated soil. The settlement
decreases and bearing capacity increases as (length of
stone columns/thickness of clay layer) (L/H) increases
from 0.4 to 0.8, (young’s modulus of stone columns)
from 30 to 90 mPa, (thickness of raft foundation)(t)from
0.5 to 1 m, and (diameter of stone columns) (D) from 0.4
to 0.8 m.

2. Increasing number of stone columns resultsinincreasing
bearing capacity and settlement decreasing. Most
effective are (D), , (t), and (L/H).
3. For all parametric studies for 13 and 25 stone column
groups, maximum moment (M1-1) is forsection1andthe
minimum moment is for section 2. The maximum
improvement is for section 2 and The minimum
improvement is for section 1, for all parametric studies.
4. For all parametric studies for 13 and 25 stone column
groups, maximum shear (Q2-3) is for section 1and the
minimum shear (Q2-3) is for section 2. The maximum
improvement is for section 2 and The minimum
improvement is for section 1, for all parametric studies.
5. The increasing in (length of stone columns/thickness of
clay layer) (L/H) from 0.4 to 0.8, there is a decrease in
moment and shear.
6. The increasing in (young’s modulus of stone columns
from 30 to 90 mPa, there is a decrease in moment
and shear.
7. The increasing in (diameter of stone columns) (D) from
0.4 to 0.8 m, there is a decrease in moment and shear.
8. The increasing in (thicknessofraftfoundation)(t)from
0.5 to 1 m, there is an increasing in moment and shear.
9. With The increase in the number of stone columns,
shear (Q2-3) on the raft was reduced. The most
influential parameter, in this case, is (D), then (L/H), (t)
and finally .
10. The increase in numbers of stone columns, M1-1
reduces. The most effective parameterinthiscaseis(D),
then , (t) and finally (L/H).
11. Variation of (L/H) for 25 stone column groups has an
insignificant improvement for momentandshearonthe
raft.
12. Variation of and (t) for 25 stone column group has
a slight improvement for shear on the raft only for
section 1.
13. Variation of (D) for 25 stone column group has an
insignificant improvement for moment on the raft only
for section 1.
14. Increasing of (D) for 13 and 25 stone column groups,
increase shears on the raft only for section 1.
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