on settlement prediction of soft clay reinforced by a … paper on settlement prediction of soft...
TRANSCRIPT
TECHNICAL PAPER
On settlement prediction of soft clay reinforced by a groupof stone columns
Seifeddine Tabchouche1 • Mekki Mellas1 • Mounir Bouassida2
Received: 23 August 2016 / Accepted: 24 December 2016 / Published online: 19 January 2017
� Springer International Publishing Switzerland 2017
Abstract This paper studies the behavior of a foundation
on a soil reinforced by a group of end-bearing stone col-
umns in terms of settlement reduction in oedometer con-
dition. The group of stone columns has been reduced to
equivalent concentric crowns using a finite-difference
FLAC3D modeling. The obtained numerical results were
compared to existing analytical and numerical methods for
the prediction of the settlement of reinforced soil. It was
found that the prediction of the settlement by the 3D
numerical modeling of equivalent concentric crowns is less
than that obtained by the actual 3D model of group of stone
columns. These results have been validated through com-
parison between numerical, analytical, and in situ mea-
surements collected from full-scale loading tests of stone
column from recent case history.
Keywords Soft soils � Stone columns � Settlement
reduction � Numerical method � Loading tests
Introduction
The need of construction on soft soils remains a big challenge
for geotechnical engineers. Several ground improvement
techniqueswere developed to render soft soils able to support
a variety of constructions with suitable stability conditions.
The stone columns revealed one of those techniques that
were widely practiced since the 70s.
The improvement by stone columns increases the
bearing capacity of weak soils, decreases their settlement,
and accelerates their consolidation. Hence, the prediction
of performances provided by stone columns should be
addressed with respect to all those benefits.
The vibro displacement technique represents a process that
contributes in the improvement of properties of soft clays
upon the installation of stone columns. The laterally expanded
stone material increases both the Young modulus and
undrained shear strength of soft clays as a result of the induced
horizontal consolidation favored by enhanced permeability of
stone material [15, 16]. However, the applicability of stone
columns technique can be sometimes subjected to restrictions.
As an example, after Bowles [8], granular piles are prohibited
in thick deposits of pears or highly organic silts or clays due to
the low degree of stiffening achieved in those soils. Wood-
ward [22] reported that theminimumundrained shear strength
of soft soil to be treated should equal 20 kN/m2.
The design of foundation on soils reinforced by col-
umns, first, involves two verifications [5]:
– Bearing capacity To check if the allowable bearing
capacity of reinforced soil complies with the applied
load.
– Settlement To check whether the predicted settlement
of reinforced soil subjected to the applied load verifies
the allowable settlement.
& Mounir Bouassida
Seifeddine Tabchouche
Mekki Mellas
1 Faculty of sciences and technology, Laboratory of research in
civil engineering - LRGC, University of Biskra, BP 145,
07000 Biskra, Algeria
2 Universite de Tunis El Manar, Ecole Nationale d’Ingenieurs
de Tunis, LR14ES03-Ingenierie Geotechnique, BP 37 Le
Belvedere, 1002 Tunis, Tunisia
123
Innov. Infrastruct. Solut. (2017) 2:1
DOI 10.1007/s41062-016-0049-0
Handling both the bearing capacity and settlement ver-
ifications, an optimized area ratio can be determined.
Second, adopting the optimized area ratio, the study of
the behavior of foundation on reinforced soil can be tackled
by considering the acceleration of consolidation provided
by the stone columns, which play the role of vertical drains
[4].
Using numerical codes, the prediction of long-term
settlement, especially when reinforcement by floating col-
umns is decided, of unreinforced compressible layers is
crucial [7].
In this paper, the prediction of settlement of a founda-
tion resting on a soil reinforced by a group of end-bearing
stone columns in oedometer condition is investigated. The
oedometer condition fairly applies for foundations having
dimensions (width and length) quite greater than the
thickness of compressible layer(s).
The statement of the problem is presented with focus on
numerical modeling, the design parameters of reinforced
soil by columns, and enriched literature review from recent
contributions.
First, the numerical modeling using FLAC 3D code of
soil reinforced by end-bearing stone columns at constant
area ratio are presented: the unit cell model (UCM) as
reference case, the group of stone columns (GSC), and the
equivalent concentric crowns (ECC) with boundary con-
ditions. Obtained results are presented and compared. The
predictions made by the FLAC 3D code of settlement of a
large tank diameter in oedometer condition are compared
to results obtained by existing methods of design. Their
interpretation and synthesis are addressed in details. In
particular, due to their simple numerical implementation,
compared to actual group of stone columns, it is aimed to
quantify the efficiency of annular concentric approach, in
oedometer condition, for the prediction of settlement of
reinforced soil.
Second, the Algiers harbor case history is presented,
from which the recorded data are used for the validation of
numerical predictions by FLAC 3D code.
The effectiveness of two 3D modeling of column-rein-
forced foundation (CRF) is discussed by comparing
numerical predictions with measurements recorded from a
full-scale load test carried out in the framework of Algiers
harbor case history.
Statement of the problem
The settlement of a reinforced soil by stone columns occurs
when the foundation is subjected to its final loading. The
study of the behavior of foundations on a soil reinforced by
columns is carried out using two parameters, i.e., the area
ratio (g) and the settlement reduction factor (b) defined,
respectively, as follows:
g ¼ Ac=A ð1Þb ¼ SunreinfðpÞ=SreinfðpÞ: ð2Þ
Here, Ac denotes the total cross section of stone columns all
located under the loaded foundation of area A.
Sunreinf and Sreinf denote the settlement of the foundation
on unreinforced soil and reinforced soil, respectively,
subjected to the same allowable surcharge load p.
Several methods for predicting the settlements of a
reinforced foundation by stone columns have been devel-
oped [4].
The study of behavior of stone columns, with focus on
settlement prediction, has been investigated by several
researchers in the literature, Balaam and Booker [2].
Barksdale and Bachus [3] carried out a series of scaled
laboratory tests conducted on an isolated stone column in
undrained conditions from which the load-settlement
response was analyzed. This experimental investigation
evidenced that the bearing capacity and the settlement
behavior of a single stone column are significantly influ-
enced by the type of applied load and the support provided
by the surrounding soil.
Wehr [21] performed a finite-element analysis in plane
strain condition to simulate the observed behavior from
laboratory tests of loaded footing on soil reinforced by a
group of columns. The author suggested that beyond a
depth equals 1.5 the diameter of the footing, the expansion
behavior of columns is noticed. Beneath that critical depth,
central columns behave in punching failure, whilst edge
columns behave in buckling failure.
Serridge [20] conducted a series of field trial of partially
penetrating dry bottom-feed vibro stone columns support-
ing shallow narrow footings. The author investigated the
behavior and the settlement performance of vibro stone
columns installed within a deep soft clay deposit. In this
study, focus was made on the response of sensitive soft
clay to the method of installation of stone columns.
Killeen and McCabe [17] conducted a finite-element
analysis on small groups of stone columns loaded by pad
and strip footings. Authors have studied the influence of the
column stiffness and strength on the settlement behavior of
small loaded areas.
Castro [9] proposed an approximated solution to predict
the settlement of rigid footings resting on soft soil improved
by a group of stone columns. The proposed analytical solu-
tion converts the group of stone columns to equivalent single
column with the same cross-sectional area. The author aims
to convert the problem to be axially symmetric.
McCabe and Killeen [19] studied the behavior of small
groups of stone columns. Authors indicate that the mode of
1 Page 2 of 12 Innov. Infrastruct. Solut. (2017) 2:1
123
deformation of a column-reinforced foundation is governed
by the column spacing and length rather than the number of
columns. Authors also discussed the influence of a critical
length on the settlement performance of a CRF.
Consider the effect of stone column installation by lat-
eral expansion, Ellouze et al. [12] reported that an
improvement in the Young’s modulus of the initial soil
takes place due to the horizontal consolidation owed to the
presence of stone columns. Then, prior to the final loading
due to the construction of oil tank, the averaged improve-
ment in Young’s modulus of loose silt sand can attain by
30% around each stone column over a horizontal distance
of about 1.5 times its diameter.
In the following, focus is made on numerical settlement
predictions by the FLAC 3D code in oedometer condition
and their assessment with data collected from the very
recent Algiers harbor stone columns project.
The improvement in Young’s modulus of the initial soil
due to the installation of stone columns is not considered.
Investigated 3D numerical modeling
Three modeling in oedometer condition of soil reinforced
by stone columns is investigated by performing a three-
dimensional explicit finite-difference method (FDM),
incorporated in Fast Lagrangian Analysis of Continua
(FLAC). Those numerical models are considered for the
study of the behavior of loose sandy silt layer reinforced by
a group of end-bearing stone columns subjected to an oil
tank uniform load of 120 kPa having large diameter. The
properties of the initial soil and constitutive material of
end-bearing column are taken from a real stone column
project built at Zarzis terminal (Tunisia). The column’s
diameter is equal to 1.2 m and length of Hc = 7 m. As
reported by Bouassida and Hazzar [7], the related data of
this case history are given in Table 1.
The reinforcement is controlled by an area ratio of
g = 20% that was adopted after the method of design of
column-reinforced foundations proposed by Bouassida and
Carter [5]. This reinforcement is kept constant, while the
number of stone columns (modeled by a stone crown) and
the area of loaded foundation are varied. The settlement of
reinforced soil is, first, predicted by the unit cell model
(UCM) and, then, by the group of stone columns modeling.
Then, the load-settlement curves are predicted using
different reinforcement configurations where the number of
stone columns and equivalent concentric stone crowns is
increased.
The predictions obtained by the reinforcement using the
concentric crowns are compared to the one predicted by the
actual group of columns modelings.
Unit cell model (UCM)
According to Bouassida [4], the UCM is built from the
distribution of a group of columns installed in a regular
pattern. Geometrically, the UCM is a reproducible volume
which includes a single column with a circular cross sec-
tion surrounded by a given volume of the initial soil. In
case the columns are installed in squared pattern, the
periodic volume of UCM corresponds to a parallelepiped
cylinder. The axisymmetric condition is, then, adopted by
an equivalent unit cell with circular cross section. The area
ratio is written as follows:
g ¼ 4a2
D2eq
: ð3Þ
The diameter of unit cell model, Deq, is expressed as a
function of the axis-to-axis spacing between columns ‘‘Sp’’,
‘‘a’’ denotes the stone column’s radius, [1].
Figure 1 shows the considered UCM with zero hori-
zontal displacement at the lateral border as required in
oedometer condition.
Under the central axis of the loaded foundation, it is
obvious to assume that horizontal displacement within the
reinforced soil layer(s) is almost zero, in particular when
end-bearing columns are designed. Consequently, in the
central zone of loaded foundation, the settlement is quasi
uniform as usually assumed in the design of column-rein-
forced foundations [4].
The study of the behavior of the UCM is undertaken
using the FLAC 3D code by assuming the elastic perfectly
plastic Mohr–Coulomb model for the initial soil. This
model is still current to describe approximately the
behavior of granular soils (sands), cohesive soils (clay and
silt soils), and rocks. In very recent numerical investiga-
tions conducted by the FLAC 3D code, the Mohr–Coulomb
behavior model revealed satisfactory when predicting the
Table 1 Geotechnical parameters of the stone columns reinforced
foundation described by the Mohr–Coulomb model
Parameter Unit Soft soil Stone column
ch kN/m3 17 18
u Degree 0 42
C kPa 25 0
E kPa 3600 36,000
v – 0.33 0.33
G MPa 1.35 13.53
K MPa 3.53 35.29
Dc m – 1.2
ch unit weight, u friction angle, C cohesion, E Young’s modulus, mPoisson’s ratio, G shear modulus, K bulk modulus, Dc stone column
diameter
Innov. Infrastruct. Solut. (2017) 2:1 Page 3 of 12 1
123
behavior of loose silt soil reinforced by stone column, Klai
et al. [18] and Bouassida [4].
The numerical FLAC 3D model, sketched in Fig. 1,
comprises 672 finite-difference zones and 735 grid points
(at cycle 6609).
The settlements of unreinforced soil and reinforced soil
were predicted, by different methods, as a function of the
applied surcharge load at the surface of UCM. Figure 2
displays the variation of settlements as a function of the
applied load.
The settlement predicted by the GSC modeling UCM
and the analytical variational approach [6] appears identi-
cal. In turn, the French method [13] led to lower prediction
of the settlement of reinforced soil. Indeed, by this method,
the oedometer Young modulus of the initial soil is adopted
which provides more settlement reduction.
It is worth mentioning that Chow’s method [11] predicts
the lowest settlement, because it assumes the composite
ground deforms in one-dimensional compression condition,
i.e., horizontal deformation is zero, and therefore, the
oedometer Young modulus is both used for the initial soil
and column material.
The UCM was also adopted to predict the consolidation
of soft soil reinforced by stone column. Guetif and
Bouassida [14] and Castro and Sagaseta [10] used different
constitutive laws for the constituents of reinforced soil to
predict the evolution of settlement due to horizontal con-
solidation as the stone column behaves like vertical drains.
Group of stone columns (GSC)
The prediction of settlement is investigated by three
equivalent numerical modeling of soil reinforced by a
group of end-bearing stone columns. The 3D finite-differ-
ence analysis has been carried out by the FLAC 3D code to
analyze the variation of settlement reduction factor b ver-
sus the applied load using different configurations of stone
columns in triangular pattern. Figure 3 displays the three
numerical 3D modeling 1a, 2a, and 3a performed by FLAC
3D code.
The same area ratio adopted for the UCM is considered:
g = 20%; the stone columns of diameter Dc = 1.2 m are
installed along an average depth of Hc = 7 m in a trian-
gular pattern with an axis-to-axis spacing of 2.06 m
(Fig. 3). The characteristics of generated meshes for the
three numerical FLAC3D modeling are summarized in
Table 2.
Figure 4 shows the settlement reduction predicted by the
Chow and French methods which adopt the UCM and the
three modeling performed by FLAC 3D code and Bouas-
sida et al. [6] method which adopt the 3D modeling of soil
reinforced a group of stone columns.
The installation of stone columns with an area ratio
g = 20% provides a settlement reduction in the range of
3.5–3.9 times, this relatively significant reduction of set-
tlement is affected by the oedometer condition as consid-
ered by the studied three numerical FLAC 3D modeling.
The predicted settlement reduction by the numerical
modeling of soil reinforced by a group of 7, 19, and 37
stone columns appears almost identical with negligible
relative difference, of ±2.5%, of the settlement reduction
factor. Analytical predictions made by Bouassida et al. [6]
method fit well with those obtained from modeling 3a
Fig. 1 Numerical FLAC3D modeling of adopted UCM
0 20 40 60 80 100 120 1400
2
4
6
8
Set
tlem
ent (cm
)
Working Load (kPa)
Chow's method (1996) French method - CFMS (2011) Bouassida et al. (2003) FLAC 3D - Unit Cell Model Unreinforced soil
Fig. 2 Settlement predictions by the UCM
1 Page 4 of 12 Innov. Infrastruct. Solut. (2017) 2:1
123
using the reinforcement by a group of 37 columns. As
shown from the settlement predictions in Fig. 2, it is well
noted the significant overestimation of settlement reduction
by the Chow’s method.
Therefore, in oedometer condition, it is concluded that
increasing the number of stone columns, as shown in
Fig. 3, for the generated 3D numerical modeling does not
significantly affect the settlement prediction of reinforced
soil up to surcharge loads of 120 kPa.
Equivalent concentric crowns (ECC)
The group of stone columns has been reduced to equivalent
concentric crowns (ECC) using a full 3D finite-difference
FLAC3D modeling. The equivalent co-centric crowns
(ECC) modeling can be adopted, in case the reinforcing
columns are located in a regular pattern as investigated by
Ellouze and Bouassida (2009) and Ellouze et al. [12].
Major advantage of this geometrical transformation con-
sists in carrying numerical computations in axisymmetric
condition that is timeless consuming than 3D modeling.
Equaling between the area of columns, located at equal
distance from the axis of loaded foundation, and the area of
ECC, then the equivalent thickness of ECC, eCr, is calcu-
lated from Eq (4):
Modeling 3aModeling 2a
y z
14 m10 m6 m
10 m
7 m
14 m14 m
Triangular patternSp = 2,06 mDc = 1,2 m
= 20 %
x
7 m7 m
6 m
Modeling 1a
η
Fig. 3 Finite-difference discretization of a group of 7, 19, and 37 stone columns
Table 2 Characteristics of numerical modeling of group of stone
columns as implemented by the FLAC 3D code
Modeling of group of stone
columns
FD
zones
Grid
points
Cycle
1a 1680 1575 2722
2a 4592 4215 3146
3a 8960 7815 5926
0 20 40 60 80 100 120 1400
2
4
6
8
10
Set
tlem
ent r
educ
tion
fact
or β
Applied load (kPa)
Chow's method (1996) French method - CFMS (2011) Bouassida et al. (2003) FLAC 3D - Group of 07 columns FLAC 3D - Group of 19 columns FLAC 3D - Group of 37 columns
Fig. 4 Estimation of settlement reduction factors
Innov. Infrastruct. Solut. (2017) 2:1 Page 5 of 12 1
123
eCrðiÞ ¼ ðNðiÞ � AcÞ=ð2p� SpÞ: ð4Þ
Sp spacing between columns. N(i) number of columns
located on the circumference of the crown i.
Figure 5 illustrates the finite-difference discretization of
group of stone columns and its equivalent concentric
crowns as generated by the FLAC 3D code.
Table 2 presents the characteristics of three numerical
modeling implemented by the FLAC 3D code when the
group of stone columns is adopted.
Table 3 presents the characteristics of three numerical
modeling implemented by the FLAC 3D code when
adopting the ECC.
The interpretation of numerical predictions by the FLAC
3D code is given below.
(a) Group of stone columns (GSC)
Figure 6 compares between the settlement predictions
obtained by the three modeling 1a, 2a, and 3a of a
group of stone columns. From Fig. 6, when the
applied load is equal to or greater than 100 kPa,
Modeling 1a (7 stone columns) overestimates the
settlement of reinforced soil by 14.6–15% compared
to predictions byModeling 2a and 3a (19 and 37 stone
columns). The difference in predictions by Modeling
2a and 3a remains insignificant (less than 5%).
Fig. 5 Finite-difference
discretizations generated using
the FLAC 3D code-A zoomed
view: a group of stone columns;
b equivalent concentric stone
crowns
Table 3 Characteristics of numerical modeling of equivalent con-
centric crowns as implemented by the FLAC 3D code
Modeling of equivalent concentric
crowns
FD
zones
Grid
points
Cycle
1b 3136 3375 5644
2b 4928 5295 6237
3b 8512 9135 8560
1 Page 6 of 12 Innov. Infrastruct. Solut. (2017) 2:1
123
(b) Equivalent concentric crowns (ECC)
Figure 7 compares between the settlement predic-
tions when adopting the three ECC modeling. From
Fig. 7, the predictions of settlement of reinforced
soil are quasi similar by Modeling 2b and 3b (2 and 3
ECC), up to load of 130 kPa. Whilst the use of
modeling 2a (1 ECC) significantly overestimates the
settlement prediction from load of 60 kPa.
From Fig. 7, it is also noted the settlement prediction
by one ECC modeling is greater than those predicted
by the 2 and 3 ECC modeling.
(c) Comparing between GSC and ECC modeling
First, it is worth noted that the GSC represents the
more realistic modeling as the columns are usually
installed in regular pattern to cover the completely
loaded area.
0 20 40 60 80 100 120 1400
2
4
6
8
Set
tlem
ent (cm
)Load (kPa)
group of 37 columns group of 07 columns group of 19 columns
Fig. 6 Soil behavior of columns reinforced foundation with a group
of 7, 19, and 37 stone columns
0 20 40 60 80 100 120 1400
2
4
6
8
10
12
Set
tlem
ent (cm
)
Load (kPa)
1 concenrtric crown 2 concenrtric crown 3 concenrtric crown
Fig. 7 Soil behavior of columns reinforced foundation with 1, 2, and
3 equivalent concentric crowns (ECC)
0 20 40 60 80 100 1200
a
b
c
2
4
6
8
10
12
Set
tlem
ent (cm
)
Load (kPa)
Unreinforced soil group of 07 columns 1 concentric crown
0 20 40 60 80 100 1200
2
4
6
8
10
12
Set
tlem
ent (cm
)
Load (kPa)
Unreinforced soil group of 19 columns 2 concentric crowns
0 20 40 60 80 100 1200
2
4
6
8
10
12
Set
tlem
ent (cm
)
Load (kPa)
Unreinforced soil group of 37 columns 3 concentric crowns
Fig. 8 a Variation of applied load versus settlement using a group of
07 stone columns and ECC. b Variation of applied load versus
settlement using a group of 19 stone columns and two ECC.
c Variation of applied load versus settlement using a group of 37
stone columns and three ECC
Innov. Infrastruct. Solut. (2017) 2:1 Page 7 of 12 1
123
The predictions of settlement using the three ECC
modeling and respective GSC modeling are com-
pared from Fig. 8a–c.
Figure 8a shows that quasi-identical predictions of the
settlement of reinforced soil are obtained by adopting
either the modeling using a group of seven columns or the
respective one ECC modeling. The maximum difference of
settlement prediction between the two modeling equals
0.49 cm that is negligible for predicting the settlement
under surcharge load of 120 kPa.
In turn, Fig. 8b, c clearly shows that when the number of
stone columns increases, as well as for the number of
respective ECC, the difference between the settlement
predictions also increases, especially when the surcharge
load exceeds 80 kPa. Furthermore, an opposite trend is
marked for the difference between the two settlement
predictions, i.e., the two ECC modeling provides lower
settlement than that obtained by a group of 19 columns.
Figure 8 shows that Modeling 3b (three ECC) predicts
less settlement than that obtained by Modeling 3a (37 stone
columns) especiallywhen the applied load is beyond or equal
to 100 kPa. Such prediction is explained by the fact that the
ECC, as continuous walls having much higher stiffness than
that of soft soil, provides much better confining effect within
the surrounding soil in particular in the central part of the
loaded foundation. Hence, the settlement prediction by the
group of columns, which provides lesser confining effect, is
higher than that predicted by the 3 ECC modeling.
Algiers harbor case history—full-scale load testson a column-reinforced foundation
Local ground conditions of Algiers Harbor area
In the framework of the Algiers Harbor extension project,
the consolidation of the quays and creation of new docks
were recently launched at the end of 2015. After the
Algerian seismic standards RPA 2003, Algiers City
belongs to zone 1 that is classified with high potential
seismic risk. Furthermore, the soil profile of Algiers Harbor
comprises an intermediate sand layer that might be sub-
jected to the liquefaction phenomena. Hence, a ground
improvement solution of existing soil layers was decided to
mitigate the liquefaction risk and to reduce settlements of
compressible soil layers.
The investigation of underground conditions at the site
of project showed the ability in using the improvement by
the deep vibro-techniques. After Fig. 9, the grain size
distribution of the soil layers matches well with the known
recommendations in regard to the limits of applications of
deep vibro-techniques.
The soil profile illustrated in Fig. 10 shows a 1-m-thick
clay layer sandwiched between silt clayey sand and fine
sand layers. Several undisturbed samples were extracted
within the soil profile at various depths and then subjected
to laboratory tests.
0,001 0,01 0,1 1 10 1000
10
20
30
40
50
60
70
80
90
100
0
10
20
30
40
50
60
70
80
90
100
Depth 3,50m-3,95m Depth 5,85m-6,30m Depth 9,45m-9,90m Depth 11,50m-12,10m Depth 12,10m-12,55m Depth 14,55m-15m Depth 18,20m-18,65m
Per
cent
age
pass
ing
[by
wei
ght]
(%)
Particle size (mm)
limits of application for stone columns technique
Clay Silt Fine Sand Coarse Sand Gravel CobblesFig. 9 Grain size distribution
curves of the different layers in
Algiers harbor region
1 Page 8 of 12 Innov. Infrastruct. Solut. (2017) 2:1
123
Full-scale loading tests on soil reinforced by stone
columns
A series of full-scale load tests was undertaken to capture
the behavior of soil layers reinforced by stone columns.
Figure 11 displays: (a) the excavation at the top side of
installed stone columns confirms a diameter of 84 cm;
(b) stone columns were installed in triangular pattern with
axis-to-axis spacing equals to 1.8 m. The area ratio of this
trial test is 100%. The length of the installed stone columns
was 7.5 m. About the properties of sand layers and marl
stone layer underneath, the installed stone columns are of
end-bearing type.
The plot tests included the installation of 28 stone
columns, a single column is loaded. The column subjected
to the loading test is located at the center of area where the
28 SCs were installed. The full-scale loading test consisted
of incremental applied load with measurement of settle-
ment using three sensors. As such, the loaded stone column
surrounded by the 27 installed stone columns is assumed to
behave in oedometer condition due to the confinement
provided by those columns.
Load-settlement curves drawn from those loading tests
represent the best indicator to assess the predictions by the
FLAC 3D code to simulate the real behavior of CRF. The
unit cell model was, first, investigated by the finite-differ-
ence method implemented by the FLAC 3D code. The soil
layers and column material have been modeled by the
Mohr–Coulomb constitutive law with the properties sum-
marized in Table 4.
Figure 12a–c shows the respective numerical predic-
tions by the FLAC 3D code compared to measured load-
settlement data. It should be noted that the two numerical
modeling do not consider the improvement of mechanical
characteristics of the initial soil due to the installation of
stone columns.
In a second attempt, the simulation of numerical mod-
eling that comprises 28 installed stone columns with loaded
central stone column has been studied (Fig. 12b). Two
numerical models generated by the FLAC 3D code have
been tested to predict the load-settlement curve. Fig-
ure 12b, c shows that the real behavior of loaded single
stone column belonging to a group of stone columns is
much better predicted than the behavior of an isolated
column.
Fig. 10 Typical ground cross section of Algiers harbor area
Fig. 11 Stone column viewed
after installation
Innov. Infrastruct. Solut. (2017) 2:1 Page 9 of 12 1
123
The two FLAC 3D well illustrates the importance of the
group effect on the settlement reduction that results from
the installation of a group of stone columns.
Figure 13 shows the settlement predictions obtained
from the 3D group of stone columns and the equivalent
concentric crowns. As seen from this figure, the two gen-
erated FLAC 3D numerical modelings (GSC and ECC)
predict similar results up to uniform load of 120 kPa. In
this range of applied load, it is agreed that the ECC mod-
eling is favored because of its simplest numerical handling
Table 4 Geotechnical
parameters of soil layers at
Algiers harbor region
Parameters Unit Soil 1 Soil 2 Soil 3 Soil 4 Stone columns
c kN/m2 16.68 16 17.66 15.20 21
u Degree 32 0 32 15.04 40
C kPa 0 4.325 0 298 0
Pressure meter modulus EM MPa 10.27 13.39 44.1 62.9 60
v – 0.27 0.27 0.27 0.30 0.33
Constitutive model – Mohr
Dc m – – – – 0.84
(a)
(b) (c)
Fig. 12 Load vs settlement of the full loaded stone column: a FDM—isolated SC; b FDM—group of SC; c predicted vs measured settlement of
the loaded stone column
1 Page 10 of 12 Innov. Infrastruct. Solut. (2017) 2:1
123
about that required by the GSC modeling. However, for all
applied loads, the predictions made by the GSC modeling
fit well with full-scale load test measurements from the
Algiers harbor case history.
Summary and conclusions
The settlement prediction of a foundation on a soil rein-
forced by stone columns has been investigated in
oedometer condition. Three numerical modelings were
implemented by the FLAC 3D code: unit cell model
(UCM), group of stone columns (GSC), and equivalent
concentric crowns (ECC). The data from the Zarzis case
history (Tunisia) served for the validation of predictions
given by the UCM.
The data collected from the recent Algiers harbor stone
columns project were considered to validate the predictions
obtained by three configurations of the GSC and ECC
modeling at constant area ratio. The main findings from
this research work are summarized as follows.
• Settlements predicted in case of uniform stress load
with an isolated stone column (unit cell model) were
underestimated compared to those obtained by a group
of stone columns modeling. This is due to the
confinement imposed on the lateral border of the
UCM resulting from zero horizontal displacement.
• In oedometer condition and with identical area ratio, it
is concluded that increasing the number of stone
columns by the generated 3D numerical modeling does
not significantly affect the settlement prediction of
reinforced soil up to surcharge loads of 120 kPa.
Therefore, the behavior of a CRF is not greatly affected
by the variation of stone columns number.
• Predictions obtained by the UCM showed that the
settlement by Bouassida et al. [6]’s linear elastic
method fits well with predicted results by the GSC
modeling 3a.
• By comparing 3D settlement predictions, a good
agreement has been shown between the reduced
equivalent concentric stone crowns and the group of
vibro-replacement end-bearing stone columns. Indeed,
the maximum relative error of 9, 27, and 20% has been
registered in the case of 7, 19, and 37 stone columns
equivalent to 1, 2, and 3 concentric stone crowns,
respectively.
• From the Algiers harbor case history, the measurements
of settlement during the full-scale load test conducted
on soil reinforced by stone columns permitted the
validation of predicted settlement by the three equiv-
alent concentric crown FLAC 3D modeling.
Acknowledgements The authors would like to appreciate Professor
Ali Bouafia (University of Blida, Algeria) for his kind support in
providing the data of stone columns project at Algiers Harbor.
References
1. Balaam NP, Booker JR (1981) Analysis of rigid rafts supported
by granular piles. Int J Numer Anal Methods Geomech
5:379–403
2. Balaam NP, Booker JR (1985) Effect of stone column yield on
the settlement of rigid foundations in stabilized clay. Int J Numer
Anal Methods Geomech 9(4):331–351
3. Barksdale RD, Bachus RC (1983) Design and construction of
stone columns. Federal highway administration office of engi-
neering and highway operations. National Technical Information
Service, Springfield, p 22161
4. Bouassida M (2016) Design of column-reinforced foundations.
J Ross Publ, USA p 224, ISBN: 978-1-60427-072-3
5. Bouassida M, Carter JP (2014) Optimization design of column-
reinforced foundations. Int J Geomech ASCE 14(6):04014031
6. Bouassida M, Guetif Z, de Buhan P, Dormieux L (2003) Esti-
mation par une approche variationnelle du tassement d’une fon-
dation sur sol renforce par colonnes ballastees. Revue Francaise
de Geotechnique 102(1), 21–29
7. Ellouze S, Bouassida M, Ben Salem Z, Znaidi MN (2016)
Numerical Analysis of the Installation Effects on the Behavior of
Soft Clay Improved by Stone Columns. Geomech Geoengineer-
ing: Int J. doi:10.1080/17486025.2016.1164903
8. Bowles JE (1997) Foundation analysis and design, 5th edn.
McGraw-Hill Book Co., Singapore
9. Castro J (2016) An analytical solution for the settlement of stone
columns beneath rigid footings. Acta Geotech 11(2):309–324
10. Castro J, Sagaseta C (2009) Consolidation around stone columns.
Influence of column deformation. Int J Numer Anal Methods
Geomech 33(7):851–877
11. Chow YK (1996) Settlement analysis of sand compaction pile.
Soils Found 36(1):111–113
12. Ellouze S, Bouassida M, Hazzar L, Mroueh H (2010) On set-
tlement of stone column foundation by Priebe’s method. Proc Inst
Civ Eng Ground Improv 163(2):101–107
0 50 100 150 200
0 50 100 150 200
-7
-6
-5
-4
-3
-2
-1
0
-7
-6
-5
-4
-3
-2
-1
0
Load (kPa)S
ettle
men
t (mm
)
Group of stone columns Equivalent Concentric crown Full loading test
Fig. 13 Settlement predictions of the full loaded stone column—
GSC vs ECC
Innov. Infrastruct. Solut. (2017) 2:1 Page 11 of 12 1
123
13. French Committee for Soil Mechanics and Foundations (CFMS)
(2011) Recommendations for the design, calculation, construc-
tion and quality control of stone columns under buildings and
sensitive structure. RFG No 111, Version No 2, France
14. Guetif Z, Bouassida M (2005) Analytical estimate of settlement
evolution of soft soil reinforced by stone columns. In: Proceed-
ings of the 16th International conference of soil mechanics and
geotechnical engineering, vol. 3, 12–16 September, Osaka. IOS
Millpress, Lansdale, pp 1355–1358
15. Guetif Z, Bouassida M, Debats JM (2007) Improved soft clay
characteristics due to stone column installation. Comput Geotech
34(2):104–111
16. Greenwood DA (1970) Mechanical improvement of soils below
ground surface. In: Proceedings of the conference on ground
engineering, paper II. Institution of Civil Engineers, London,
pp 11–22
17. Killeen MM, McCabe BA (2014) Settlement performance of pad
footings on soft clay supported by stone columns: a numerical
study. Soils Found 54(4):760–776
18. Klai M, Bouassida M, Tabchouche S (2015) Numerical mod-
elling of Tunis soft clay. Geotech Eng J SEAGS AGSSEA
46(4):87–95
19. McCabe BA, Killeen MM (2016) Small stone column groups:
mechanisms of deformation at serviceability limit state. ASCE Int
J Geomech. doi:10.1061/(ASCE)GM.1943-5622.0000700
20 Serridge CJ (2013) An evaluation of partial depth dry bottom-feed
vibro stone columns to support shallow footings in deep soft clay
deposits. Doctoral thesis, Anglia Ruskin University
21 Wehr W (2004) Stone columns-single columns and group
behavior. In: Proceedings of the 5th international conference on
ground improvement techniques, Kuala Lumpur, Malaysia, 22–23
March 2004, pp 329–340
22 Woodward J (2005) An introduction to geotechnical processes, 1st
edn. Spon Press–Taylor and Francis Group, USA
23 Ellouze S, Bouassida M (2009) Prediction of the settlement of
reinforced soft soil clay by a group of stone columns. In: Pro-
ceeding 2nd International Conference New Development in
SMGE. Edit. Atalar et al. 28–30 May NEU Nicosia, pp 182–187
1 Page 12 of 12 Innov. Infrastruct. Solut. (2017) 2:1
123