one vibro-compacted stone column was evaluated. Guetif et al., (2007). In this paper is investigated simulate the installation of a stone column surrounded by a.
International Conference on Numerical Computation in Geotechnical Engineering NUCGE'08
Parametric study of improved soft clay due to installation of a group of stone columns M. Bouassida (*) & S. Ellouze Geotechnical Engineering Research Team. Ecole Nationale d’Ingénieurs de Tunis, BP 37 Le Belvédère, 1002 Tunis. Tunisia
J.M. Debats The Vibroflotation Group, Aix en Provence, Bouches du Rhône, France
(*) Corresponding author
ABSTRACT: A method is proposed for evaluating the improvement of the Young modulus of soft clay in which a group of vibrocompacted stone columns is installed. Using axisymmetric modeling, a finite-element analysis has been performed, using 15-noded triangular elements, with the software package PLAXIS. MohrCoulomb's constitutive law has been adopted for constituents of tow layers soil profile. A sub soft clay layer is reinforced by stone material and an upper sand layer is improved by the vibro compaction technique. The extent of the influence zone by stone column reinforcement is localized and the reduction of settlement of soft clay reinforced by a group of stone columns is predicted. The influence of parameters such as Poisson’s ratio of soft clay, friction angle and Young modulus of ballast is studied through analysis of the state of stress in the soft clay surrounding the columns where a primary consolidation occurred after eleven months. The improvement of soft soil Young modulus varies with the parameters in question.
1 INTRODUCTION This procedure, compared to the execution of a group of columns, is more realistic than that carried out with a single column. However, the latency between the installations of all columns is neglected. Our investigation aims at the conditions of installation so that the zones of influence of the column, on one hand, and of the crown of columns, on the other hand, do not overlap. The criterion making it possible to check this type of installation is a horizontal displacement near to zero in extreme cases of the zones of influence. As second goal, the settlement of the improved ground by a group of columns under a distributed loading of 100 kPa is examined. Further, is studied the influence of drained mechanical characteristics (as Poisson’s ratio of soft soil, friction angle and Young modulus of stone material) on soft soil improvement and reduction of the settlement of reinforced soil.
Many researchers have developed theoretical solutions for estimating the bearing capacity and settlement of foundations on reinforced soils by stone columns (Greenwood 1970; Hughes et al. 1976, Aboshi et al. 1979, Bouassida et al. 1995, Jellali et al. 2007). When designing foundations on reinforced soils by stone columns, settlements are basically estimated using the characteristics of the incorporated material and those of ambient soil before column installation. Meanwhile, the efficiency of the soil improvement is usually controlled after results from in-situ tests which are executed, both within columns and in the surrounding soil. Such controls have made it possible to reveal improvements on failure characteristics such as standard penetration resistance Sanglerat (2002), Alamgir & Zaher (2001), undrained shear resistance from vane tests Vautrain (1980). Considering a unit cell model, the increase of modulus of soft clay after installation of one vibro-compacted stone column was evaluated Guetif et al., (2007). In this paper is investigated simulate the installation of a stone column surrounded by a crown of stone columns.
2 REINFORCED SOIL MODEL The data are taken from a real stone column project Naama Engineering (2001). The soil profile is formed by a soft clay layer with 12,25 m thickness overlaid by a sandy layer of 12,75 m thickness. The soft 14
International Conference on Numerical Computation in Geotechnical Engineering NUCGE'08
clay is reinforced with vibro-displacement stone columns with 1.1m diameter and 2.7m triangular grid spacing (improvement area ratio is 15%). The parameters of the two soil layers and column material are given in table 1. This model has been considered by Guetif et al (2007) for studying the improvement of soft clay Young modulus.
Soils
Sand
Column material
Compacted sand
E’ (kPa) 25000 4000
32000
50000
ν’
0.33
0.3
0.33
0.33
ϕ’ (°)
35
21
38
38
c’ (kPa) 1
5
10
1
γh kN/m3
17
20
20
18
Soft clay
-05
kh m/day
10
1.8 10
kv m/day
10
0.94 10-05
100
10
100
10
The equivalent thickness of the stone’s crown is determined by:
N
π D2 4
= 2π Re
(1)
D = diameter of stone column N = number of columns simulated to a crown of stone R = mean radius of the stone’s crown e = thickness of the crown When adopting a triangular column’s pattern the radius of the zone of influence is 1.05R/2 (R is also the spacing between two columns). 2.2 The geometry The impact of reinforcement of soft clay by a group of vibro compacted stone columns is studied by the axisymmetric model shown in Fig.2. After the project data the area replacement ratio is η=0.15, using Equation (1) the crown’s thickness is deduced.
Table 1. Parameters of reinforced soil constituents
γ h = total unit weight; kh (respectively kv ) = horizontal (respectively vertical) permeability. E ';ν ' = respectively drained Young modulus and Poisson’s ratio. c '; ϕ ' = respectively drained cohesion and friction angle.
Compacted Sand
12.75m
2.1 Statement of the problem Stone Column
Considering the reinforced soil model described above, is intended the simulation of the installation of seven stone columns in triangular pattern as depicted in fig 1. For this an axisymmetric analysis is undertaken of a stone column surrounded by six columns assimilated to a crown of stone (Fig. 1).
Soft Clay
Z
Impervious conditions
Crown 12.25m
55cm
2.7m
16.8cm
1.41 m
Figure 2: Axisymmetric model of stone column surrounded by a crown of stone.
R
To make this model as representative of several co centric crowns of stone boundary conditions are those of oedometric test. The interface between columns and soft clay is assumed to be with perfect contact (total adhesion). Since stone columns are installed in a very short period of time the expansion process is considered to occur in undrained conditions. Along the thickness of soft clay layer a
e
Figure.1 Equivalent crown of stone columns
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International Conference on Numerical Computation in Geotechnical Engineering NUCGE'08
numerical procedure called « Dummy material » is adopted to simulate this expansion of soft clay. The procedure “Dummy material” (Guetif et al, 2007), firstly, consists in modeling the cylindrical hole occupied by the vibro probe with radius of 0.25 m by a fictious material having a weakest Young’s modulus i.e. E dm = 20kPa . Then, along the border of hole in soft clay is subjected to radial displacement that simulates the vibro compaction installation in soft clay until the horizontal expansion reaches the final column radius of 0.55m. The second stage of “Dummy material” procedure aims the simulation of installation of the stone’s crown with initial thickness of 0.095m. Then, along the hole's border the soft clay is subjected to radial displacement that simulates the vibro compaction installation in soft clay until the end of horizontal expansion which corresponds to the equivalent crown’s thickness e= 0.168m (Fig. 2). Finally, the actual characteristics of column material are introduced to start, with Plaxis Software, the numerical computation of eleven months primary consolidation (335days) of soft clay.
3 RESULTS 3.1 Horizontal displacement A unique profile of horizontal displacement is predicted during all steps of columns installation and after primary consolidation of soft clay. From Fig.3 it is, therefore, by assumed no overlap occurs between zones of influence of central columns and the surrounding crown columns during columns installation. It is then concluded from this study case the extent of soft clay improvement is about 1.4m. 3.2 Vertical displacement The installation of seven columns generates a significant uplift at the surface of improved soil model. This is due to a large incorporated quantity of ballast, in short period of time, in quasiincompressible soft clay. To show up the reduction of the settlement resulting from columns installation the computation settlement for improved soil has been predicted by Plaxis software. For uniform load of 100kPa the predicted settlement (after 405 days) is 16 cm at the surface (Fig. 4). The settlement of unimproved soft clay is of about 50 cm. The coefficient of settlement reduction which is the ratio between settlements of unimproved soil to that of improved soil is of 3.12. This reduction of soft clay’s settlement is, then, predicted by taking account of the consolidation of soft clay due to columns installation that is quite different if an improved Young modulus of soft clay was considered for direct settlement prediction. In the following section the evolution, within soft clay, of effective mean stresses is analyzed.
After the end of consolidation of soft clay due to column installation is ended, a uniform load of 100kPa is applied to the model of reinforced soil to follow up with a complete primary consolidation for 405 days.
The improved soil is modeled by the use of fifteen nodes triangular finite elements. 2.3 Behavior of improved soil Based on experimental observations, the improvement of Young modulus of the soil could be deduced from laboratory tests in which the stress modulus dependency is correlated by the following power law, Biarez et al (1998). E ⎛ σ m' ⎞ =⎜ ⎟ E0 ⎝ σ m' 0 ⎠
p
12
(2)
10 8
Where E (E0) and σ’m (σ’m0) designate respectively the Young modulus and effective mean stress (that equals the third of first stress invariant) of the soil. Subscript “0” in Eq (2) refers to an initial state. The exponent p basically characterizes the non linearity between normalized Young modulus and effective mean stress. In Plaxis users' manual, this was obviously assumed. Particularly, it is recommended to take p = 1 for soft clay.
6 4 2 0 Ux(m ) -0,05 -0,04 -0,03 -0,02 -0,01 0
0,01 0,02 0,03 0,04 0,05
after expansion after consolidation loaded loaded afterconsolidation
Figure 3: Evolution of horizontal displacement in soft clay layer with depth at r=1.41m 16
International Conference on Numerical Computation in Geotechnical Engineering NUCGE'08
4 PARAMETRIC STUDY 1
As presented in Table 1 the parameters of reinforced soil could not be exactly representing the investigated area. In this way a parametric study is undertaken to predict how the soft clay improvement will be when its parameters vary? Then, the influence of drained friction angle and Young modulus of ballast and drained Poisson’s ratio of soft clay is looked for by analyzing the states of stress in the area surrounding the column and the settlement reduction under a uniform distributed load of 100 kPa.
0,8 0,6
Uz
0,4 0,2 r(m )
0 -0,2
0
0,5
1
1,5
2
2,5
-0,4 -0,6 after expansion after consolidation loaded loaded after consolidation unimproved soft clay
4.1 Ballast drained friction angle The increase of ballast friction angle from 38° to 45° seems to be insignificant on the improvement due to the installation of columns in soft clay after a consolidation of 11 months (Fig.6). Indeed the expansion of columns is simulated by using “Dummy material”. The influence of the friction angle of columns is shown in the reduction of improved soil’s settlement (Fig. 7). Settlement reduction is more significant when columns friction angle is too.
Figure 4: Evolution of vertical displacement at the surface of improved soft soil model
3.3 Effective stress analysis Immediately after the group of columns installation the states of stress vary at the middle depth of soft clay layer. Columns installation immediately generates too significant excess pore pressure. During the consolidation period of eleven months the excess pore pressures dissipate from the soft clay into the free-draining stone columns material. The effective mean stress increases about 30% at radius of 1.41m on both sides i.e. on the right of central column: 33% and on the left of the crown’s columns: 27% (Fig. 5).
0,5 0,7 0,9
1,1 1,3 1,5 1,7 1,9 2,1
-80
4.2 Ballast Young modulus The evolution of the ratio of oedometric Young modulus of columns and soft clay Ec,oed/Es,oed from 8 to 20 shows up insignificant change of the state of mean effective stress at midth depth of soft clay after installation of columns and a consolidation of 11 months (Fig. 8). Similar to the effect of evolution of settlement reduction as a function of ballast’s friction angle, it is obviously noticed a better reduction of settlement of improved soil loaded under 100 kPa when the ratio Ec,oed/Es,oed is more important (Fig.9)
2,3 2,5 2,7 r(m )
effective mean stress
-100 -120 -140
It is then concluded that when varying the characteristics of ballast (stone material), it influences the reduction of settlement rather the improvement of soft clay due to columns installation. This result is comparable to that obtained by Priebe (1995) where three improvement factors (n0: basic improvement factor, n1: improvement factor taking account of the column compressibility, n2: improvement factor taking account of the overburden) are proportional to the friction angle. Priebe’s method determines a homogeneous modulus which is a function of the ballast modulus then if this latter increases the homogeneous modulus does too. As consequence the predicted settlement reduction is better.
-160 -180 -200 -220 after expansion after consolidation loaded after consolidation unimproved soft clay
Figure 5: Evolution of effective mean stress (kPa) at midth depth of soft clay layer
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International Conference on Numerical Computation in Geotechnical Engineering NUCGE'08
0,5
2,2
1,5
2
2,5 r(m )
-110 Effective mean stress(kPa)
2 Normalized effective stress
1
-100
1,8 1,6 1,4
-120 -130 -140 -150 -160 -170 -180
1,2
-190
1 0,5
1
1,5
phi=38
2
2,5 r(m )
phi=42
Ec/Es= 20
phi=45
0,5
0,5
1
1,5
2
2,5
Ec/Es= 8
Figure 8: Evolution of effective mean stress ratio at the middle of depth of soft clay layer after consolidation vs oedometric Young modulus
Figure 6: Evolution of normalized effective mean stress at midth depth of soft clay layer after consolidation vs drained friction angle
0
Ec/Es= 15
1
1,5
2
2,5
-10
r(m )
-13
r(m )
-11
Settlement (cm)
-12
Settlement (cm)
-14
-15
-13 -14 -15 -16
-16
-17 Ec/Es= 8
-17
phi=38
phi=42
Ec/Es= 15
Ec/Es= 20
Figure 9: Evolution of settlement at the surface of improved soft soil model loaded under 100 kPa vs oedometric Young modulus
phi=45
Figure 7: Evolution of settlement at the surface of improved soft clay model loaded under 100 kPa vs drained friction angle
4.3 Drained Poisson ratio of soft clay The variation of the drained Poisson’s ratio was from ν’= 0.2 to ν’= 0.35. It led to a significant increase of the normalized effective mean stress (Fig.10). It should be reminded that for Plaxis software the drained Poisson’s ratio considered for incompressibility conditions is ν’= 0.35. The settlement reduction can not be neglected (19%) when comparing the predictions for ν’= 0.3 andν’ = 0.35 (Fig.11). It is concluded that the more friction angle is important more the soil is incompressible so 18
International Conference on Numerical Computation in Geotechnical Engineering NUCGE'08
5 CONCLUSION
effective mean stress increases due to columns installation. Besides, settlement reduction is more important when the soil is more incompressible. This result is also confirmed by the semi empirical Priebe’s method (n0: basic improvement factor > n1:
The installation of a group of stone columns in soft clay was simulated numerically by adopting a model of central column surrounded by a crown of stone in axisymmetric condition. The inherent computations are conducted by the use of Plaxis software. The simulation showed up a significant improvement of soft clay characteristics after vibrocompacted group of columns installation. Based on Mohr Coulomb's behavior considered for the constituents of improved soil, the main conclusions are drawn below.
improvement factor taking account of the column compressibility n1).
Normalized effective mean stress
2,2
Young modulus improvement of about 30% is predicted on both sides (of central column and of stone crown) due to the installation procedure of columns. A reduction of settlement of improved soft clay under uniform load of 100 kPa is predicted which is more significant than that predicted by the composite cell model (settlement of 16 cm for the proposed model of improved soft clay and 23 cm for the composite cell model.
2 1,8 1,6 1,4 1,2
A negligible radial displacement at r=1,41m (extent of influenced zone deduced from the triangle pattern model) which means no overlap occurs between respective zones of influence (of central column and stone crown). The parametric study, here presented, showed up the influence of parameters such the Poisson’s ratio, ballast’s Young modulus and its friction angle in soft clay improvement. Further developments aimed at the influence of other parameters, such as the spacing between columns or the use of a hardening soil model for improved soft soil constituents, are in progress.
1 0,5
0,9 nu=0,2
1,3
1,7
nu=0,3
2,1 nu=0,35
2,5 r(m ) nu=0,25
Figure 10 Evolution of normalized effective mean stress at midth depth of soft clay layer after consolidation vs drained Poisson ratio
0
0,5
1
1,5
2
2,5
r(m )
-10
REFERENCES
Settlement (cm)
-12
Aboshi H., Ichimoto E., Harada K., and Enoki M. 1979."The composer A method to improve the characteristics of soft clay by inclusion of large diameter sand columns".Proc. Int. Conf. on Soil Reinforcement; E.N.P.C, Paris, 211-216 Alamgir M., and Zaher SM. 2001. Field investigation on a soft ground of Bangladesh reinforced by granular piles. Proc. Int. Symposium "Earth Reinforcement", 14-16 November. Landmarks in earth Reinforcement. Ochiai et al Editors, p. 517-522. Biarez J., Gambin M., Gomes-Corriea A., Falvigny E., and Branque D. 1998. Using pressuremeter to obtain parameters of elastoplastic models for sands. Proceedings of the first international conference on site Characterization, ISC’98, Atlanta, Georgia, USA, 19-22, 747-752. Bouassida M., de Buhan P., and Dormieux L. 1995. Bearing capacity of a foundation resting on a soil reinforced by a group of columns. Géotechnique, 45, (1): 25-34. Greenwood DA. 1970. Mechanical improvement of soils below ground surface. Proceedings of the conference on Ground Engineering, Institution of Civil Engineers, London, paper II, p 11-22. Guetif, Z., Bouassida, M. and Debats, J.M. 2007. Improved Soft Clay Characteristics Due to Stone Column Installation. Computers & Geotechnics, (34) 104-111.
-14
-16
-18
-20 nu=0,2
nu=0,3
nu=0,35
nu=0,25
Figure 11: Evolution of vertical displacement at the surface of improved soft soil model loaded under 100 kPa vs drained Poisson ratio
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Hughes J.M.O. Withers N.J., and Greenwood D.A. 1976. "A Field trial of reinforcing effect of stone column in soil" Proc. Ground Treatment by Deep Compaction, Institution of Civil Engineers, London, , 32-44. Jellali B., Bouassida M., and de Buhan P. 2007. A homogenization approach to estimate the ultimate bearing capacity of a stone column reinforced foundation. In press International Journal of Geotechnical Engineering., (1), 6169. Namaa Engineering & Consultation (SAE). 2001, Rapport géotechnique du projet “Damiette LNG tanks. Vibroflotation Europe. Priebe H. 1995. The design of vibro replacement. Ground Engineering: 31-37. Sanglerat G. 2002. Contrôle des colonnes ballastées à l’aide du pénétromètre statique AMAP’sols. Jubilé Jimenez Salas, Madrid. Vautrain J. 1980 Comportement et dimensionnement des colonnes ballastées. Revue Française de Géotechnique, 11: 59-73.
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