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3D numerical analyses of geosynthetic encased stone columns
Geotextiles and Geomembranes 35 (2012) 61e68
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3D numerical analyses of geosynthetic encased stone columns L. Keykhosropur*, A. Soroush, R. Imam Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran 15875-4413, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 May 2011 Received in revised form 26 May 2012 Accepted 21 July 2012 Available online 3 August 2012
Stone columns are commonly used as ground improvement elements since they act as reinforcing inclusions. However, due to the lack of sufficient lateral confinement for the columns, this technique is not applicable for the improvement of grounds that consist of very soft soils. In order to provide lateral confinement and increase the load bearing capacity of stone columns installed in very soft clay soils, they are usually encased with suitable geosynthetic materials, forming geosynthetic-encased columns (GECs). In this paper, a 3D numerical approach is used to study the effect of varying the encasement length of different columns of a group of GECs on the overall group behavior. These results are compared with those obtained from a group of fully encased columns, through comparison of the settlements and lateral deformations (bulging) of the columns. The analyses are calibrated through modeling the behavior of GECs used in a ground reclamation project in Hamburg, Germany. Parametric studies are also carried out to investigate the effects of factors such as stiffness of the geosynthetic encasement, column diameter, and modulus of elasticity and friction angle of the column material on the overall behavior of the GEC group. The results indicated that encasing only the outer columns of the stone column group is sufficient in providing an optimal design. It was also shown that increasing the stiffness of the encasement and the column diameter enhance the overall behavior of the GEC group through increasing the overall stiffness of the stone columns and the ratio of the soft soil replaced by the stone columns (i.e. the area replacement ratio), respectively. Moreover, it was observed that the performance of GECs is comparatively less sensitive to the internal friction angle of the column material, and that, in general, the modulus of elasticity of the column material has only a small effect on the group behavior. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Ground improvement Stone column Geosynthetic encased columns Finite element method 3D analysis
1. Introduction Stone columns are being increasingly used as a cost-effective and environmentally friendly method for improvement of weak soils such as clays, silts and silty sands. The main functions of the stone columns are: the increase in the soil bearing capacity, the reduction in the soil total settlement, and the increase in the soil drainage capacity. This method involves replacement of a portion of the soft or loose soil by vertical columns made of compacted aggregates, turning the in-situ soil into a composite material that exhibits higher shear strength and permeability, and lower compressibility. Stone columns are normally expected to derive their strength and stiffness primarily from the confining stresses provided by the surrounding soil. However, in very soft soils (cu < 15 kPa), the confining stresses developed may not be sufficient; and, although some additional confinement is expected to be
* Corresponding author. Tel.: þ98 21 64543009. E-mail addresses: [email protected] (L. Keykhosropur), Soroush@ aut.ac.ir (A. Soroush), [email protected] (R. Imam). 0266-1144/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.geotexmem.2012.07.005
mobilized due to the application of the structural loads, in weak soils, generation of the necessary confinement requires high radial deformations of the stone column, and this may lead to it’s failure. In order to provide the required lateral column confinement and enhance the bearing capacity in soft soils, the columns may be encased with high stiffness, creep-resistant geosynthetics, resulting in “Geosynthetic Encased Columns (GECs)”. The main advantage of GECs in comparison with ordinary stone columns is that the low confining stresses developed in the soft soil are compensated by the radial confinement provided by the encasement. The geosynthetic encasement also prevents the aggregates from laterally squeezing out of the columns in very soft soils. This results in a minimal loss of aggregates and quicker installation of the columns (Murugesan and Rajagopal, 2006). The idea of encasing stone columns was first proposed by Van Impe in 1985 (see also Van Impe, 1989). Bauer and Al-Joulani (1994) investigated the behavior of sleeved stone columns using uni-axial and tri-axial compression tests. Ayadat and Hanna (2005) studied the advantages of encasing stone columns in collapsible soils. Murugesan and Rajagopal (2006) compared the performance of ordinary and encased stone columns using numerical analyses.
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They later performed some laboratory tests on stone columns installed in a unit-cell tank and reported that the tensile modulus of the encasement has the most important role in the strength of the GECs (Murugesan and Rajagopal, 2007). Gniel and Bouazza (2009) evaluated experimentally and numerically the effects of encasement length on the behavior of GECs, based on the Unit-Cell concept. Wu and Hong (2008) investigated the axial stressestrain relations of embedded granular columns encapsulated with flexible reinforcement, using an analytical procedure based on the concept of cavity expansion. The results were validated by tri-axial testing of a reinforced sand specimen. Murugesan and Rajagopal (2010) carried out laboratory tests to compare the shear load capacity of stone columns with and without encasement by inducing lateral soil movements in a soft soil treated with stone columns. Lo et al. (2010) and Khabazian et al. (2010) also investigated the performance of GECs through numerical studies. This paper presents the results of 3D numerical analyses of different aspects of the performance of GECs using the finite element code ABAQUS. Calibration of the procedures used in the numerical analyses is carried out by modeling a ground reclamation project in Hamburg, Germany, reported by Kempfert and Raithel (2002). Effects of varying the encasement length of different columns of a group of GECs on the group performance are then examined. Parametric analyses are later carried out to evaluate the influence of different factors such as stiffness of the encasement, column diameter, and friction angle and elastic modulus of the stone column material, on the behavior of the GEC group. 2. Three dimensional numerical analyses The analysis procedure was calibrated by modeling a land reclamation project implemented as part of an area extension for the airplane dockyard at the Elbe River in Hamburg, Germany. In this project, the area extension was carried out by enclosing the polder with a 2.4 km long dike constructed on very soft sludge with undrained shear strength of 0.4 kPae10 kPa. A total of 60,000 geotextile encased columns with a diameter of 800 mm was used as part of the foundation for the dike. The project data including its plan, dike sections, and geometric and mechanical properties of the GECs are reported by Kempfert and Raithel (2002). In order to calibrate the analytical procedure used in the current study, Section VI of the dike, shown in Fig. 1, was modeled, and its measured settlements during construction were compared with the settlement results obtained from the current FEM analyses. The
subsoil conditions shown in Fig. 1 are those reported by Kempfert and Raithel (2002) for Section VI of the dike. Based on the actual project information, the 800 mm diameter stone columns were modeled with 2 m spacing in the middle of the dike section (total of 13 columns in each row) and 3 m spacing on each side (28 columns in each row), as shown in Fig. 1. The length of the columns is 11.2 m, which is the same as the thickness of the soft soil layer as reported by Kempfert and Raithel (2002). It should be noted that because of computational limitations, it was not possible to model the dike over its full length.; Instead, a representative 10 m of its length, which includes 5 rows of the encased stone columns along the dike length, were simulated as shown in Fig. 2. Due to similar limitations, the circular section of the stone columns was replaced by a square section with an equivalent circumference (0.63 m side length). Analyses of the behavior of the equivalent square section showed settlements and variations of stresses over column length very close to those of the actual circular section. Due to the large length of the dike, boundary conditions were selected such that no movement along the longitudinal axis of the dike (Y axis in Fig. 2) was allowed. The 9 m high dike was modeled using 6 layers with equal thickness. Due to the symmetry in geometry and loading conditions with respect to the YeZ plane, only half of the dyke section was modeled. Since the parameters provided by Kempfert and Raithel (2002) were those of the Mohr-Coulomb constitutive model, this model was used for simulating the behavior of the soft soil and stone column materials. These parameters are shown in Table 1. The dike was constructed during 9 months and, therefore, loading condition of the soft soil was considered to be undrained. The geotextile encasement was modeled as a linear elastic material using 3-node triangular membrane elements with a J ¼ 2000 kN/m stiffness. Values of the elastic modulus and thickness of the encasement were selected to satisfy the equation J ¼ E t. The finite element mesh for the foundation soil was constructed using 8-node linear brick elements for the stone columns and the soft soil. The dike was modeled using 6-node linear triangular prism elements. In the numerical model, due to the limitations in modeling the multilayer soil in contact with the stone columns by the software used, the various layers of the soil in the actual project were replaced by a single layer with mechanical properties equivalent to the average properties of the actual soil layers. A comparison between the measured maximum settlements reported by Kempfert and Raithel (2002) for the various construction stages and those obtained from the current numerical analyses is shown in Fig. 3. Although there is an 110.7 mm difference between the numerical results and the field measurements in
Fig. 1. Section VI of the dyke, (Kempfert and Raithel, 2002).
L. Keykhosropur et al. / Geotextiles and Geomembranes 35 (2012) 61e68
Fig. 2. The geometry and boundary conditions of the model.
the first stage of loading, the overall match for the subsequent loading stages is reasonable. 3. Flexible and concrete foundations supported by GECs In this section, effects of arrangements of encased columns in a group of stone columns installed under a flexible foundation are examined. Effects of encasing various portions of length of the stone columns installed under a concrete foundation on the behavior of the GEC group are also investigated. The settlement and lateral deformation of stone columns are used as criteria for comparison of behaviors of the various GEC configurations. 3.1. Effects of arrangement of encased columns installed under a flexible foundation Effects of configuration of GEC groups installed under a flexible foundation were first evaluated by analyzing 3 numerical models similar to the dike modeled in the previous section and with different arrangement of encased stone columns which are shown in Fig. 4. It should be noted that the encased stone columns in this figure are denoted by circles with thick borders. In order to simplify the problem description, stone column rows were numbered as shown in Fig. 4 and, considering symmetry of the system, only half of the columns in each row (21 columns) are presented. In the first model, only the columns located in the perimeter of each of the 5 stone column rows were encased. In the second model, the 23 middle columns of each of the 5 stone column rows were encased and in the third model a combination of the encased stone columns used in the first and second models was assumed. The geometric and material properties, the load conditions and the element types used in the finite element analyses of these three models were the same as those previously used in Section 2. Comparisons between the final settlements of the stone columns in row 1 (the middle row) of the three models analyzed are presented in Fig. 5. It is observed that stone columns of model 1, especially the middle columns, experienced much more settlements than the initial model, in which all the stone columns were encased. In the second model, in which the 23 middle columns of each row were encased, settlements of the non-encased side columns were more than their counterparts in the initial model.
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However, final settlements of all of the stone columns were approximately equal or less than the maximum settlement obtained from the initial model. Finally, in the third model, the settlement of the stone columns has almost the same trend as the initial model, but a maximum difference of about 140 mm between the settlements of the two models is obtained. This maximum difference occurs in the areas of columns number 14 to 16. Maximum lateral deformation of the 6th, 11th and last columns of Row 1 of the analyzed models are shown in Fig. 6, in which the initial model was referred to as model number 4. As shown in this and the previous figures, maximum lateral deformations and stone column settlements of Model 3 and the initial model are very similar, indicating that there is only a small difference between the performances of the two models. Variations of final settlements of the 1st, 2nd, 6th, 11th and 19th columns of row 1 with the amount of geosynthetic consumption are shown in Fig. 7. The amount of geosynthetic consumption was calculated to be 5785.184 m2 for the initial model and 2483.712 m2, 3245.67 m2, 4431.168 m2 for models 1 to 3, respectively. It is obvious that in spite of the use of 23% less geosynthetic material in model No. 3 compared to the initial model, settlements of both models are almost the same. Considering the settlement and bulging results discussed before, it may be concluded that due to the greater height of the middle part of the dike section, the stone columns installed in this part should all be encased. However, due to the decrease in the height of the dike section on its sides, only the circumferential columns may need to be encased in these areas and, therefore, without losing a significant percentage of the load carrying capacity and performance of the GEC group, construction costs may be reduced by about 23% by selectively encasing the stone columns. 3.2. Effect of encasement length combinations for columns under a concrete foundation In order to study the effect of encasement length combinations on the behavior of a group of GECs installed under a concrete foundation, a group of 25 encased stone columns having 800 mm diameter and arranged in a 2 m c/c square pattern was analyzed. Thickness of the soft soil and length of the stone columns were assumed to be 10 m. A 500 kPa surcharge pressure was applied in 100 increments on the GEC group through a 1 m thick, linear elastic concrete foundation. The soft soil and the stone column material behaviors were simulated using the Modified Cam Clay and DruckerePrager Cap constitutive models respectively. The finite element mesh was developed using 8-node linear brick elements for the stone columns, the concrete foundation and the soft soil. The geosynthetic encasement was also modeled as a linear elastic material using 3-node triangular membrane elements. Material properties selected in the analyses were based on the material properties that Gniel and Bouazza (2009) used in their tests, and are presented in Table 2. According to Alexiew et al. (2005), the most common range of tensile stiffness J of the encasement is between 2000 kN/m and 4000 kN/m; therefore, a tensile stiffness of 3000 kN/m was used in the analyses. Thickness of the encasement was assumed to be 5 mm in all models.
Table 1 Material properties used in numerical models (Kempfert and Raithel, 2002). Material
Density, (kg/m3)
Internal friction angle, ( )
Dilation angle, ( )
Cohesion, (KPa)
Elastic modulus, (MPa)
Poisson’s ratio, (y)
Soft soil Stone column material Geotextile encasement
1500 1900 e
0 32.5 e
0 2.5 e
7 1 e
0.6 50 400
0.3 0.3 0.3
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Dike Height (m)
Settlement (mm)
Settlement results reported by (Kempfert and Raithel, 2002) Numerical results
Fig. 3. Comparison of maximum settlements for the calibration analyses.
The various stone columns are referred to using the column numbers shown in Fig. 8. In order to study the effect of encasement length combinations on the behavior of the modeled GEC group, a total of 20 numerical models with various encasement length combinations as shown in Table 3 were analyzed. Column number 13 is introduced as the “central column” in this table. Similarly, columns 7, 8, 9, 12, 14, 17, 18, 19 are referred to as the “Central Ring Columns” and columns 1, 2, 3, 4, 5, 6, 10, 11, 15, 16, 20, 21, 22, 23, 24, 25 are defined as the “circumferential ring columns”. In each of model descriptions presented in Table 3, not mentioned stone columns are assumed to be fully encased. Final settlement of column number 13 and final maximum lateral deformation of column number 25 obtained from the analyzed models are presented in Figs. 9 and 10, respectively. Based on the results shown in Figs. 9 and 10, it may be noticed that encasement of the central columns and the central ring columns have small effects on the behavior of the group; and, the increase in the settlement and bulging of the selected columns due to the removal of the encasement of these groups of columns from models No. 1 to 15 is negligible. However, encasement of the circumferential ring columns is so important in improving the performance of the group that removing the encasement of these columns results in an increase of up to 74.8% and 150% in the settlement and bulging of the selected columns, respectively, as compared to the initial model with all its columns encased. Based
on the results obtained from the current analyses, it can be concluded that in practical projects involving the use of GECs under relatively rigid foundations, it may be possible to encase only the outer columns, without losing a significant percentage of the foundation bearing capacity. 4. Factors affecting performance of GECs under a concrete foundation In order to examine the effects of various design parameters on the performance of GEC groups installed under a concrete foundation, analyses were carried out using a finite element model with the same geometric and material properties, load conditions and element types used in Section 3.2. Settlement of column number 13 and lateral deformation of column number 25 obtained from the analyses were selected as representatives of the group behavior. Effects of encasement stiffness, stone column material friction angle and stiffness, and stone column diameter were investigated. 4.1. Encasement stiffness For this study, the tensile stiffness J of the geosynthetic encasement was varied between 300 and 10000 kN/m Figs. 11 and 12 show the settlements of Column 13 and the lateral deformations of Column 25, respectively, as obtained from the analyses in each case. An increase in the stiffness of the geosynthetic results in the increase in its mobilized hoop tension force and lateral confining action, leading to a higher overall stiffness for the stone columns. Therefore, the lateral deformation and the resultant settlement of the GEC group decrease, such that with an increase in the encasement tensile stiffness J to 10000 kN/m, the amounts of settlement and lateral deformation of the aforementioned columns decrease by up to 62% and 79%, respectively, compared to the model with the un-encased (ordinary) columns. 4.2. Internal friction angle of the stone column material The geosynthetic encasement was modeled as a linear elastic material with J ¼ 2000 kN/m. The internal friction angle of the stone column material, 4s, was varied from 30 to 45 to evaluate its effect on the performance of the GEC group. It should be noted that since the stone column material was modeled using the
Fig. 4. Arrangement of encased stone columns in: a) Initial model, b) Model 1, c) Model 2, d) Model 3.
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65 1st column
Column Number
2nd column
Initial model Model No. (1)
Settlement (m)
Settlement (m)
6th column 11th column 19th column
Model No. (2) Model No. (3)
Geosynthetic Consumption (m2)
Fig. 5. Final settlements of row 1 of stone columns in the models analyzed.
Fig. 7. Settlement of different columns versus geosynthetic consumption.
DruckerePrager Cap model, 4s was converted to the parameter b used in this model, through the equation.
tanb ¼
6sin4 3 sin4
Settlement of column number 13 and lateral deformation of column number 25 obtained from the analyzed models are presented in Figs. 13 and 14, respectively. As expected, increasing the internal friction angle of the column material increases the strength of the column and decreases its potential for failure, leading to the decrease in the size of the zones in which the stone column material may fail. As a result, lateral deformation and settlement of the stone column decrease, resulting in the reduction in the hoop tension force induced in the encasement. The results shown also indicate that the effect of the increase in friction angle is more pronounced in the higher range of the applied loads when settlements are considered (Fig. 13); and, around the mid-height of the columns when lateral deformations are considered (Fig. 14). These are conditions in which higher stresses and strains develop, and greater potential for failure of the material exists. Such increase in the size of the yielding zone in the stone column material leads to a decrease in the settlement and lateral deformation of the column. Based on the results shown, an increase in 4s from 30 to 45 can result in up to 20% decrease in both settlement and lateral deformation of the stone columns considered. 4.3. Elastic modulus of the stone column material The geosynthetic encasement was modeled as a linear elastic material with J ¼ 2000 kN/m. Elastic modulus of the stone column material, Es, was varied from 30 MPa to 100 MPa, and its effect on the performance of the GEC group was investigated. Settlement of column number 13 and lateral deformation of columns number 13 and 25 obtained from the analyzed models are presented in Figs. 15 and 16. A decrease in Es results in a decrease in the portion of the load carried by the stone columns, compared to that carried by the Maximum lateral deformation of the 6th column
Maximum Lateral Deformation (m)
Maximum lateral deformation of the 11th column Maximum lateral deformation of the last column
surrounding soil; and, because of the decrease in the stone column stiffness compared to that of the encasement, it leads to an increase in the hoop tension force induced in the encasement. Settlement of stone columns may be considered to occur due to contributions from three components: the elastic compression of the column due to axial loading, the settlement caused by the downdrag force caused by the consolidation of the surrounding soil, and the settlement due to the lateral deformation of the stone column (Ayadat and Hanna, 2005). It should be mentioned that due to the loading method and analysis procedure the consolidation settlements were not considered in the analyses. If the load carried by the stone column remains unchanged, a decrease in Es is expected to result in an increase in the first and third of the aforementioned settlement components, while the effect of the second component is expected to be small as a result of the uniform settlement of the columns and the surrounding soil under the relatively rigid foundation. However, a decrease in Es also leads to a decrease in the load portion carried by the GEC group compared to its surrounding soil and a decrease in the stone column settlement. Therefore, as shown in Fig. 15, the overall increase in settlement due to decrease in Es for the case considered is small. On the other hand, Raithel (1999) indicates that application of an external vertical pressure (Ds) to a unit cell induces vertical reaction stresses in both the stone column (Dsv, c) and the soil (Dsv, s), the values of which depend on the ratios of the areas of the stone Table 2 Material properties used in the numerical models. Material properties
Soft soil
Stone column material
Geosynthetic
Concrete
Friction angle, ( ) Cohesion, (kPa) Saturated density, (kg/m3) Compression index, (Cc) Recompression index, (Cr) Elastic modulus, (MPa) Poisson ratio, (y) (M)a Preconsolidation pressure, (kPa) Initial void ratio (R)b (a)c
e e 1620
35 0 2020
e e e
e e e
0.8
0.011
e
e
0.09
0.003
e
e
e
60
1650
20000
0.35 0.7 50
0.3 e e
0.3 e e
0.3 e e
2 e e
0.595 0.4 0.05
e e e
e e e
Slope of critical-state line in p0 -q plane. Eccentricity of the cap yield surface in DruckerePrager Cap model. c Small number which is used to define a smooth transition surface between the DruckerePrager shear failure surface and the cap. a
Model Number Fig. 6. Maximum lateral deformations obtained from the analyzed models.
b
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Final Settlement (m)
66
Model No.
Fig. 8. Stone column numbers used in numerical modeling.
columns and the surrounding soil. Corresponding horizontal stresses (Dsh, c) and (Dsh, s) also develop due to the aforementioned vertical stresses. The change in the hoop tension force (DFr) due to the external pressure in an encasement having a radius (rgeo), can be converted to an equivalent horizontal stress (Dsh, geo) using the equation (Dsh, geo ¼ DFr/rgeo). Equilibrium of stresses in the horizontal direction leads to the following relationship between the aforementioned stresses and a horizontal stress difference (Dsh, diff) defined as:
Dsh;diff ¼ Dsh;c Dsh;s þ Dsh;geo
A decrease in Es relative to the encasement stiffness leads to an increase in the hoop tension force induced in the encasement and, consequently, the radial strain and lateral deformation of the GEC increase. But the horizontal stress difference (Dsh, diff) results in a horizontal deformation in the soft soil such that a corresponding additional earth pressure is mobilized in the soil which brings the horizontal stresses to equilibrium (Kempfert and Gebreselassie,
Final Lateral Deformation , (m)
Fig. 9. Comparison of final settlement results of stone column number 13 obtained from the analyses.
Model Noo.
Fig. 10. Final maximum lateral deformations of stone column number 25 obtained from the analyses.
2006). A decrease in Es leads to increases in both (Dsh, geo) and (Dsh, s), resulting in a decrease in the value of (Dsh, diff), and its associated bulging of the GEC. In the middle columns of a group such as in column 13 shown in Fig. 8, due to the higher confinement provided by the surrounding columns, the decrease in (Dsh, diff) has more effect on bulging than the increase in the hoop tension force and, therefore, the decrease in Es results in a very slight decrease in
Table 3 Encasement length combinations of the analyzed models. Model no.
Encasement length formation
Model no.
Encasement length formation
1
All columns encased 100%
11
2
Central column length 75% encased
12
3
Central column length 75% encased - Central ring columns lengths 75% encased
13
4
Central column length 50% encased
14
5
Central column length 50% encased - Central ring columns lengths 75% encased
15
6
Central column length 25% encased
16
7
Central column without encasement
17
8
Central column length 25% encased - Central ring columns lengths 75% encased
18
9
Central column without encasement - Central ring columns lengths 75% encased
19
10
Central column length 50% encased - Central ring columns lengths 50% encased
20
Central column length 25% encased - Central ring columns lengths 50% encased Central column length 75% encased - Central ring columns lengths 50% encased Central column without encasement- Central ring columns lengths 50% encased Central column length 25% encased - Central ring columns lengths 25% encased Central column and Central ring columns without encasement Central column and Central ring columns without encasement - circumferential ring columns lengths 90% encased Central column and Central ring columns without encasement - circumferential ring columns lengths 75% encased Central column and Central ring columns without encasement - circumferential ring columns lengths 50% encased Central column and Central ring columns without encasement - circumferential ring columns lengths 25% encased All columns without encasement
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Lateral Deformation (m)
Column Length (m)
Settlement (m)
Load (kPa)
67
J=10000kN/m J=6000kN/m J=3000kN/m J=1500kN/m J=300kN/m Ordinary stone column
Fig. 11. Settlements of stone column 13 obtained from models with various encasement stiffnesses.
Fig. 14. Lateral deformations of stone column 25 obtained from the analyses with various 4s.
Lateral Deformation (m) 0
0
100
200
Load (kPa) 300
400
Settlement (m)
Column Length (m)
ES=40MPa
0.2
ES=60MPa
0.3
ES=80MPa
0.4
ES=100MPa
0.5 0.6
Fig. 15. Settlements of stone column 13 for various values of Es.
Fig. 12. Lateral deformations of stone column 25 obtained from models with various encasement stiffnesses.
bulging of this column. On the other hand, in circumferential columns such as column 25, less confinement stresses are provided by the soft soil, and the situation is opposite such that a decrease in Es results in a slight increase in bulging of the stone columns. 4.4. Stone column diameter Unlike the laboratory tests carried out by Murugesan and Rajagopal (2006) and the numerical analyses performed by Murugesan and Rajagopal (2007) and Khabazian et al. (2010), in which the influence of the stone column diameter, Ds, on the behavior of GECs was examined by applying the load directly to the column, in the current study, the load was applied to the whole stone column group and the surrounding soil through a concrete foundation. In order to evaluate the effects of the stone column diameter on the performance of the GEC group, the value of Ds, was varied from 0.5 m to 1.5 m to, while the center to center spacing between the stone columns was kept constant. Therefore, the changes in Ds from 0.5 m to 1.5 m are equivalent to changes in the area replacement ratio from 0.049 to 0.441. The “Area Replacement Ratio” or ARR is defined as the ratio of the area of the ground surface that is
600
ES=30MPa
0.1
J=10000kN/m J=6000kN/m J=3000kN/m J=1500kN/m J=300kN/m Ordinary stone column
500
replaced by the stone columns to the original area of the ground surface prior to installation of the columns. It is noted that in this section, because GECs with different diameters were analyzed, lateral deformations were replaced by lateral strains of the stone columns as criteria for comparison of the lateral behavior. Settlements of column 13 and lateral strains of column 25 obtained from the analyzed models are presented in Figs. 17 and 18. As shown in these figures, increases in Ds from 0.5 m to 1.5 m lead to decreases in the settlement and lateral strain of the selected columns by 53.6% and 84%, respectively. It is noted that, in general, increase in the column diameter leads to increase in the total load carried by the columns and decrease in the lateral confinement provided by the encasement. However, while the increase in Ds has a negative effect on the performance of each single GEC due to the decrease in the effectiveness of its encasement, it leads to an increase in the ARR, which has a larger influence on the performance of the GEC and results in an improvement in the overall performance of the GEC group. Applying the load only on the stone columns, as assumed in the aforementioned studies, ignores the positive effect of the increase in the ARR on the overall performance.
0
0.01
0.02
Lateral Deformation (m) 0.03 0.04
0.05
0.06
0.07
0
Load (kPa)
1 Column Length (m)
Settlement (m)
2 3 4 5 6 7
Es=30MPa-Column13 Es=40MPa-Column13 Es=60MPa-Column13 Es=80MPa-Column13 Es=100MPa-Column13 Es=30MPa-Column25 Es=40MPa-Column25 Es=60MPa-Column25 Es=80MPa-Column25 Es=100MPa-Column25
8 9 10
Fig. 13. Settlements of stone column 13 obtained from the analyzed models with various 4s.
Fig. 16. Lateral deformations of stone columns 13 and 25 for various values of Es.
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Load (kPa)
D=.5
Settlement (m)
D=.8 D=1 D=1.2 D=1.5
Fig. 17. Settlements of stone column 13 obtained from the analyzed models with various Ds.
Column Length (m)
Lateral Strain
D=.5 D=.8
3. Results of the 3D numerical analyses showed that increasing the internal friction angle of the stone column material results in increases in the resistance of the columns against failure and, consequently, the lateral deformations and settlements of the columns decrease. However, compared to the other variables studied in the current analyses, performance of GECs was found to be less sensitive to the internal friction angle of the stone column material. 4. Sensitivity of the load carrying capacity of the GECs to the variation of the elastic modulus of the stone column material was found to be small. This may be a result of a number of opposite effects that are caused by the change in the elastic modulus of the column. 5. Increasing stone column diameter decreases the effectiveness of the encasement due to the increase in the lateral deformations; however, an increase in the diameter while keeping the center to center spacing between the stone columns constant is equivalent to an increase in the overall Area Replacement Ratio of the stone column group. This has a more pronounced influence on the performance of the GEC group, and results in an improvement in the bearing capacity of the system.
D=1 D=1.2
References
D=1.5
Fig. 18. Lateral deformations of stone column 25 obtained from the analyzed models with various Ds.
5. Conclusions In this paper, the influence of various parameters on the performance of geosynthetic encased stone columns is studied through 3D numerical modeling. Based on the results obtained from this study, the following conclusions can be made: 1. Evaluation of the effects of the arrangement of encased columns in a group of columns on the overall performance of the groups indicated that, when settlements and lateral deformations of stone columns are concerned, it may be sufficient to encase only a selected set of the columns without losing a substantial percentage of the overall performance of the ground improvement system. The location of the selected columns depends on the foundation stiffness and loading distribution. 2. Increase in the stiffness of the geosynthetic encasement of stone columns leads to increases in the column stiffness, the hoop tension force mobilized in the encasement, and the lateral confinement provided to the column, leading to substantial enhancement in the performance of the GEC group.
Alexiew, D., Brokemper, D., Lothspeich, S., 2005. Geotextile Encased Columns (GEC): load capacity, geotextile selection and pre-design graphs. In: Proceedings of Geo-Frontiers 2005, Austin, Texas, United States, pp. 497e510. Ayadat, T., Hanna, A.M., 2005. Encapsulated stone columns as a soil improvement technique for collapsible soil. Ground Improvement 9 (4), 137e147. Bauer, G.E., Al-Joulani, N., 1994. Strengthening of marginal soils by confined stone columns. In: 7th International Cold Regions Engineering - A Global Perspective, Edmonton, Alberta Specialty Conference, pp. 97e117. Gniel, J., Bouazza, A., 2009. Improvement of soft soils using geogrid encased stone columns. Geotextiles and Geomembranes 27, 167e175. Kempfert, H.G., Raithel, M., 2002. Experiences on Dike Foundations and Land Fills on Very Soft Soils. International Symposium on Soft Soils Foundation Engineering, Mexico. Kempfert, H.G., Gebreselassie, B., 2006. Excavations and Foundations in Soft Soils. Springer Pub, pp. 474e481. Khabazian, M., Kaliakin, V.N., Meehan, C.L., 2010. 3D numerical analyses of geosynthetic encased stone columns. ASCE Conference Proceedings, 201e208. Lo, S.R., Zhang, R., Mak, J., 2010. Geosynthetic-encased stone columns in soft clay: a numerical study. Geotextiles and Geomembranes 28 (3), 292e302. Murugesan, S., Rajagopal, K., 2006. Geosynthetic-encased stone columns: numerical evaluation. Geotextiles and Geomembranes 24 (6), 349e358. Murugesan, S., Rajagopal, K., 2007. Model tests on geosynthetic-encased stone columns. Geosynthetics International 14 (6), 346e354. Murugesan, S., Rajagopal, K., 2010. Studies on the behavior of single and group geosynthetic encased stone columns. Journal of Geotechnical and Geoenvironmental Engineering 136 (1), 129e139. Raithel, M., 1999. Zum Trag- und Verformungsverhalten von geokunststoffummantelten Sandsäulen. Schriftenreihe Geotechnik, Universität Gesamthochschule Kassel, Heft 6, Kassel, Germany. Van Impe, W.F., 1989. Soil Improvement Techniques and Their Evolution. A.A. Balkema, Rotterdam, Netherlands. Wu, C.S., Hong, Y.S., 2008. The behavior of a laminated reinforced granular column. Geotextiles and Geomembranes 26 (4), 302e316.
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Geotextiles and Geomembranes journal homepage: www.elsevier.com/locate/geotexmem
3D numerical analyses of geosynthetic encased stone columns L. Keykhosropur*, A. Soroush, R. Imam Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran 15875-4413, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 May 2011 Received in revised form 26 May 2012 Accepted 21 July 2012 Available online 3 August 2012
Stone columns are commonly used as ground improvement elements since they act as reinforcing inclusions. However, due to the lack of sufficient lateral confinement for the columns, this technique is not applicable for the improvement of grounds that consist of very soft soils. In order to provide lateral confinement and increase the load bearing capacity of stone columns installed in very soft clay soils, they are usually encased with suitable geosynthetic materials, forming geosynthetic-encased columns (GECs). In this paper, a 3D numerical approach is used to study the effect of varying the encasement length of different columns of a group of GECs on the overall group behavior. These results are compared with those obtained from a group of fully encased columns, through comparison of the settlements and lateral deformations (bulging) of the columns. The analyses are calibrated through modeling the behavior of GECs used in a ground reclamation project in Hamburg, Germany. Parametric studies are also carried out to investigate the effects of factors such as stiffness of the geosynthetic encasement, column diameter, and modulus of elasticity and friction angle of the column material on the overall behavior of the GEC group. The results indicated that encasing only the outer columns of the stone column group is sufficient in providing an optimal design. It was also shown that increasing the stiffness of the encasement and the column diameter enhance the overall behavior of the GEC group through increasing the overall stiffness of the stone columns and the ratio of the soft soil replaced by the stone columns (i.e. the area replacement ratio), respectively. Moreover, it was observed that the performance of GECs is comparatively less sensitive to the internal friction angle of the column material, and that, in general, the modulus of elasticity of the column material has only a small effect on the group behavior. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Ground improvement Stone column Geosynthetic encased columns Finite element method 3D analysis
1. Introduction Stone columns are being increasingly used as a cost-effective and environmentally friendly method for improvement of weak soils such as clays, silts and silty sands. The main functions of the stone columns are: the increase in the soil bearing capacity, the reduction in the soil total settlement, and the increase in the soil drainage capacity. This method involves replacement of a portion of the soft or loose soil by vertical columns made of compacted aggregates, turning the in-situ soil into a composite material that exhibits higher shear strength and permeability, and lower compressibility. Stone columns are normally expected to derive their strength and stiffness primarily from the confining stresses provided by the surrounding soil. However, in very soft soils (cu < 15 kPa), the confining stresses developed may not be sufficient; and, although some additional confinement is expected to be
* Corresponding author. Tel.: þ98 21 64543009. E-mail addresses: [email protected] (L. Keykhosropur), Soroush@ aut.ac.ir (A. Soroush), [email protected] (R. Imam). 0266-1144/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.geotexmem.2012.07.005
mobilized due to the application of the structural loads, in weak soils, generation of the necessary confinement requires high radial deformations of the stone column, and this may lead to it’s failure. In order to provide the required lateral column confinement and enhance the bearing capacity in soft soils, the columns may be encased with high stiffness, creep-resistant geosynthetics, resulting in “Geosynthetic Encased Columns (GECs)”. The main advantage of GECs in comparison with ordinary stone columns is that the low confining stresses developed in the soft soil are compensated by the radial confinement provided by the encasement. The geosynthetic encasement also prevents the aggregates from laterally squeezing out of the columns in very soft soils. This results in a minimal loss of aggregates and quicker installation of the columns (Murugesan and Rajagopal, 2006). The idea of encasing stone columns was first proposed by Van Impe in 1985 (see also Van Impe, 1989). Bauer and Al-Joulani (1994) investigated the behavior of sleeved stone columns using uni-axial and tri-axial compression tests. Ayadat and Hanna (2005) studied the advantages of encasing stone columns in collapsible soils. Murugesan and Rajagopal (2006) compared the performance of ordinary and encased stone columns using numerical analyses.
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They later performed some laboratory tests on stone columns installed in a unit-cell tank and reported that the tensile modulus of the encasement has the most important role in the strength of the GECs (Murugesan and Rajagopal, 2007). Gniel and Bouazza (2009) evaluated experimentally and numerically the effects of encasement length on the behavior of GECs, based on the Unit-Cell concept. Wu and Hong (2008) investigated the axial stressestrain relations of embedded granular columns encapsulated with flexible reinforcement, using an analytical procedure based on the concept of cavity expansion. The results were validated by tri-axial testing of a reinforced sand specimen. Murugesan and Rajagopal (2010) carried out laboratory tests to compare the shear load capacity of stone columns with and without encasement by inducing lateral soil movements in a soft soil treated with stone columns. Lo et al. (2010) and Khabazian et al. (2010) also investigated the performance of GECs through numerical studies. This paper presents the results of 3D numerical analyses of different aspects of the performance of GECs using the finite element code ABAQUS. Calibration of the procedures used in the numerical analyses is carried out by modeling a ground reclamation project in Hamburg, Germany, reported by Kempfert and Raithel (2002). Effects of varying the encasement length of different columns of a group of GECs on the group performance are then examined. Parametric analyses are later carried out to evaluate the influence of different factors such as stiffness of the encasement, column diameter, and friction angle and elastic modulus of the stone column material, on the behavior of the GEC group. 2. Three dimensional numerical analyses The analysis procedure was calibrated by modeling a land reclamation project implemented as part of an area extension for the airplane dockyard at the Elbe River in Hamburg, Germany. In this project, the area extension was carried out by enclosing the polder with a 2.4 km long dike constructed on very soft sludge with undrained shear strength of 0.4 kPae10 kPa. A total of 60,000 geotextile encased columns with a diameter of 800 mm was used as part of the foundation for the dike. The project data including its plan, dike sections, and geometric and mechanical properties of the GECs are reported by Kempfert and Raithel (2002). In order to calibrate the analytical procedure used in the current study, Section VI of the dike, shown in Fig. 1, was modeled, and its measured settlements during construction were compared with the settlement results obtained from the current FEM analyses. The
subsoil conditions shown in Fig. 1 are those reported by Kempfert and Raithel (2002) for Section VI of the dike. Based on the actual project information, the 800 mm diameter stone columns were modeled with 2 m spacing in the middle of the dike section (total of 13 columns in each row) and 3 m spacing on each side (28 columns in each row), as shown in Fig. 1. The length of the columns is 11.2 m, which is the same as the thickness of the soft soil layer as reported by Kempfert and Raithel (2002). It should be noted that because of computational limitations, it was not possible to model the dike over its full length.; Instead, a representative 10 m of its length, which includes 5 rows of the encased stone columns along the dike length, were simulated as shown in Fig. 2. Due to similar limitations, the circular section of the stone columns was replaced by a square section with an equivalent circumference (0.63 m side length). Analyses of the behavior of the equivalent square section showed settlements and variations of stresses over column length very close to those of the actual circular section. Due to the large length of the dike, boundary conditions were selected such that no movement along the longitudinal axis of the dike (Y axis in Fig. 2) was allowed. The 9 m high dike was modeled using 6 layers with equal thickness. Due to the symmetry in geometry and loading conditions with respect to the YeZ plane, only half of the dyke section was modeled. Since the parameters provided by Kempfert and Raithel (2002) were those of the Mohr-Coulomb constitutive model, this model was used for simulating the behavior of the soft soil and stone column materials. These parameters are shown in Table 1. The dike was constructed during 9 months and, therefore, loading condition of the soft soil was considered to be undrained. The geotextile encasement was modeled as a linear elastic material using 3-node triangular membrane elements with a J ¼ 2000 kN/m stiffness. Values of the elastic modulus and thickness of the encasement were selected to satisfy the equation J ¼ E t. The finite element mesh for the foundation soil was constructed using 8-node linear brick elements for the stone columns and the soft soil. The dike was modeled using 6-node linear triangular prism elements. In the numerical model, due to the limitations in modeling the multilayer soil in contact with the stone columns by the software used, the various layers of the soil in the actual project were replaced by a single layer with mechanical properties equivalent to the average properties of the actual soil layers. A comparison between the measured maximum settlements reported by Kempfert and Raithel (2002) for the various construction stages and those obtained from the current numerical analyses is shown in Fig. 3. Although there is an 110.7 mm difference between the numerical results and the field measurements in
Fig. 1. Section VI of the dyke, (Kempfert and Raithel, 2002).
L. Keykhosropur et al. / Geotextiles and Geomembranes 35 (2012) 61e68
Fig. 2. The geometry and boundary conditions of the model.
the first stage of loading, the overall match for the subsequent loading stages is reasonable. 3. Flexible and concrete foundations supported by GECs In this section, effects of arrangements of encased columns in a group of stone columns installed under a flexible foundation are examined. Effects of encasing various portions of length of the stone columns installed under a concrete foundation on the behavior of the GEC group are also investigated. The settlement and lateral deformation of stone columns are used as criteria for comparison of behaviors of the various GEC configurations. 3.1. Effects of arrangement of encased columns installed under a flexible foundation Effects of configuration of GEC groups installed under a flexible foundation were first evaluated by analyzing 3 numerical models similar to the dike modeled in the previous section and with different arrangement of encased stone columns which are shown in Fig. 4. It should be noted that the encased stone columns in this figure are denoted by circles with thick borders. In order to simplify the problem description, stone column rows were numbered as shown in Fig. 4 and, considering symmetry of the system, only half of the columns in each row (21 columns) are presented. In the first model, only the columns located in the perimeter of each of the 5 stone column rows were encased. In the second model, the 23 middle columns of each of the 5 stone column rows were encased and in the third model a combination of the encased stone columns used in the first and second models was assumed. The geometric and material properties, the load conditions and the element types used in the finite element analyses of these three models were the same as those previously used in Section 2. Comparisons between the final settlements of the stone columns in row 1 (the middle row) of the three models analyzed are presented in Fig. 5. It is observed that stone columns of model 1, especially the middle columns, experienced much more settlements than the initial model, in which all the stone columns were encased. In the second model, in which the 23 middle columns of each row were encased, settlements of the non-encased side columns were more than their counterparts in the initial model.
63
However, final settlements of all of the stone columns were approximately equal or less than the maximum settlement obtained from the initial model. Finally, in the third model, the settlement of the stone columns has almost the same trend as the initial model, but a maximum difference of about 140 mm between the settlements of the two models is obtained. This maximum difference occurs in the areas of columns number 14 to 16. Maximum lateral deformation of the 6th, 11th and last columns of Row 1 of the analyzed models are shown in Fig. 6, in which the initial model was referred to as model number 4. As shown in this and the previous figures, maximum lateral deformations and stone column settlements of Model 3 and the initial model are very similar, indicating that there is only a small difference between the performances of the two models. Variations of final settlements of the 1st, 2nd, 6th, 11th and 19th columns of row 1 with the amount of geosynthetic consumption are shown in Fig. 7. The amount of geosynthetic consumption was calculated to be 5785.184 m2 for the initial model and 2483.712 m2, 3245.67 m2, 4431.168 m2 for models 1 to 3, respectively. It is obvious that in spite of the use of 23% less geosynthetic material in model No. 3 compared to the initial model, settlements of both models are almost the same. Considering the settlement and bulging results discussed before, it may be concluded that due to the greater height of the middle part of the dike section, the stone columns installed in this part should all be encased. However, due to the decrease in the height of the dike section on its sides, only the circumferential columns may need to be encased in these areas and, therefore, without losing a significant percentage of the load carrying capacity and performance of the GEC group, construction costs may be reduced by about 23% by selectively encasing the stone columns. 3.2. Effect of encasement length combinations for columns under a concrete foundation In order to study the effect of encasement length combinations on the behavior of a group of GECs installed under a concrete foundation, a group of 25 encased stone columns having 800 mm diameter and arranged in a 2 m c/c square pattern was analyzed. Thickness of the soft soil and length of the stone columns were assumed to be 10 m. A 500 kPa surcharge pressure was applied in 100 increments on the GEC group through a 1 m thick, linear elastic concrete foundation. The soft soil and the stone column material behaviors were simulated using the Modified Cam Clay and DruckerePrager Cap constitutive models respectively. The finite element mesh was developed using 8-node linear brick elements for the stone columns, the concrete foundation and the soft soil. The geosynthetic encasement was also modeled as a linear elastic material using 3-node triangular membrane elements. Material properties selected in the analyses were based on the material properties that Gniel and Bouazza (2009) used in their tests, and are presented in Table 2. According to Alexiew et al. (2005), the most common range of tensile stiffness J of the encasement is between 2000 kN/m and 4000 kN/m; therefore, a tensile stiffness of 3000 kN/m was used in the analyses. Thickness of the encasement was assumed to be 5 mm in all models.
Table 1 Material properties used in numerical models (Kempfert and Raithel, 2002). Material
Density, (kg/m3)
Internal friction angle, ( )
Dilation angle, ( )
Cohesion, (KPa)
Elastic modulus, (MPa)
Poisson’s ratio, (y)
Soft soil Stone column material Geotextile encasement
1500 1900 e
0 32.5 e
0 2.5 e
7 1 e
0.6 50 400
0.3 0.3 0.3
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Dike Height (m)
Settlement (mm)
Settlement results reported by (Kempfert and Raithel, 2002) Numerical results
Fig. 3. Comparison of maximum settlements for the calibration analyses.
The various stone columns are referred to using the column numbers shown in Fig. 8. In order to study the effect of encasement length combinations on the behavior of the modeled GEC group, a total of 20 numerical models with various encasement length combinations as shown in Table 3 were analyzed. Column number 13 is introduced as the “central column” in this table. Similarly, columns 7, 8, 9, 12, 14, 17, 18, 19 are referred to as the “Central Ring Columns” and columns 1, 2, 3, 4, 5, 6, 10, 11, 15, 16, 20, 21, 22, 23, 24, 25 are defined as the “circumferential ring columns”. In each of model descriptions presented in Table 3, not mentioned stone columns are assumed to be fully encased. Final settlement of column number 13 and final maximum lateral deformation of column number 25 obtained from the analyzed models are presented in Figs. 9 and 10, respectively. Based on the results shown in Figs. 9 and 10, it may be noticed that encasement of the central columns and the central ring columns have small effects on the behavior of the group; and, the increase in the settlement and bulging of the selected columns due to the removal of the encasement of these groups of columns from models No. 1 to 15 is negligible. However, encasement of the circumferential ring columns is so important in improving the performance of the group that removing the encasement of these columns results in an increase of up to 74.8% and 150% in the settlement and bulging of the selected columns, respectively, as compared to the initial model with all its columns encased. Based
on the results obtained from the current analyses, it can be concluded that in practical projects involving the use of GECs under relatively rigid foundations, it may be possible to encase only the outer columns, without losing a significant percentage of the foundation bearing capacity. 4. Factors affecting performance of GECs under a concrete foundation In order to examine the effects of various design parameters on the performance of GEC groups installed under a concrete foundation, analyses were carried out using a finite element model with the same geometric and material properties, load conditions and element types used in Section 3.2. Settlement of column number 13 and lateral deformation of column number 25 obtained from the analyses were selected as representatives of the group behavior. Effects of encasement stiffness, stone column material friction angle and stiffness, and stone column diameter were investigated. 4.1. Encasement stiffness For this study, the tensile stiffness J of the geosynthetic encasement was varied between 300 and 10000 kN/m Figs. 11 and 12 show the settlements of Column 13 and the lateral deformations of Column 25, respectively, as obtained from the analyses in each case. An increase in the stiffness of the geosynthetic results in the increase in its mobilized hoop tension force and lateral confining action, leading to a higher overall stiffness for the stone columns. Therefore, the lateral deformation and the resultant settlement of the GEC group decrease, such that with an increase in the encasement tensile stiffness J to 10000 kN/m, the amounts of settlement and lateral deformation of the aforementioned columns decrease by up to 62% and 79%, respectively, compared to the model with the un-encased (ordinary) columns. 4.2. Internal friction angle of the stone column material The geosynthetic encasement was modeled as a linear elastic material with J ¼ 2000 kN/m. The internal friction angle of the stone column material, 4s, was varied from 30 to 45 to evaluate its effect on the performance of the GEC group. It should be noted that since the stone column material was modeled using the
Fig. 4. Arrangement of encased stone columns in: a) Initial model, b) Model 1, c) Model 2, d) Model 3.
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65 1st column
Column Number
2nd column
Initial model Model No. (1)
Settlement (m)
Settlement (m)
6th column 11th column 19th column
Model No. (2) Model No. (3)
Geosynthetic Consumption (m2)
Fig. 5. Final settlements of row 1 of stone columns in the models analyzed.
Fig. 7. Settlement of different columns versus geosynthetic consumption.
DruckerePrager Cap model, 4s was converted to the parameter b used in this model, through the equation.
tanb ¼
6sin4 3 sin4
Settlement of column number 13 and lateral deformation of column number 25 obtained from the analyzed models are presented in Figs. 13 and 14, respectively. As expected, increasing the internal friction angle of the column material increases the strength of the column and decreases its potential for failure, leading to the decrease in the size of the zones in which the stone column material may fail. As a result, lateral deformation and settlement of the stone column decrease, resulting in the reduction in the hoop tension force induced in the encasement. The results shown also indicate that the effect of the increase in friction angle is more pronounced in the higher range of the applied loads when settlements are considered (Fig. 13); and, around the mid-height of the columns when lateral deformations are considered (Fig. 14). These are conditions in which higher stresses and strains develop, and greater potential for failure of the material exists. Such increase in the size of the yielding zone in the stone column material leads to a decrease in the settlement and lateral deformation of the column. Based on the results shown, an increase in 4s from 30 to 45 can result in up to 20% decrease in both settlement and lateral deformation of the stone columns considered. 4.3. Elastic modulus of the stone column material The geosynthetic encasement was modeled as a linear elastic material with J ¼ 2000 kN/m. Elastic modulus of the stone column material, Es, was varied from 30 MPa to 100 MPa, and its effect on the performance of the GEC group was investigated. Settlement of column number 13 and lateral deformation of columns number 13 and 25 obtained from the analyzed models are presented in Figs. 15 and 16. A decrease in Es results in a decrease in the portion of the load carried by the stone columns, compared to that carried by the Maximum lateral deformation of the 6th column
Maximum Lateral Deformation (m)
Maximum lateral deformation of the 11th column Maximum lateral deformation of the last column
surrounding soil; and, because of the decrease in the stone column stiffness compared to that of the encasement, it leads to an increase in the hoop tension force induced in the encasement. Settlement of stone columns may be considered to occur due to contributions from three components: the elastic compression of the column due to axial loading, the settlement caused by the downdrag force caused by the consolidation of the surrounding soil, and the settlement due to the lateral deformation of the stone column (Ayadat and Hanna, 2005). It should be mentioned that due to the loading method and analysis procedure the consolidation settlements were not considered in the analyses. If the load carried by the stone column remains unchanged, a decrease in Es is expected to result in an increase in the first and third of the aforementioned settlement components, while the effect of the second component is expected to be small as a result of the uniform settlement of the columns and the surrounding soil under the relatively rigid foundation. However, a decrease in Es also leads to a decrease in the load portion carried by the GEC group compared to its surrounding soil and a decrease in the stone column settlement. Therefore, as shown in Fig. 15, the overall increase in settlement due to decrease in Es for the case considered is small. On the other hand, Raithel (1999) indicates that application of an external vertical pressure (Ds) to a unit cell induces vertical reaction stresses in both the stone column (Dsv, c) and the soil (Dsv, s), the values of which depend on the ratios of the areas of the stone Table 2 Material properties used in the numerical models. Material properties
Soft soil
Stone column material
Geosynthetic
Concrete
Friction angle, ( ) Cohesion, (kPa) Saturated density, (kg/m3) Compression index, (Cc) Recompression index, (Cr) Elastic modulus, (MPa) Poisson ratio, (y) (M)a Preconsolidation pressure, (kPa) Initial void ratio (R)b (a)c
e e 1620
35 0 2020
e e e
e e e
0.8
0.011
e
e
0.09
0.003
e
e
e
60
1650
20000
0.35 0.7 50
0.3 e e
0.3 e e
0.3 e e
2 e e
0.595 0.4 0.05
e e e
e e e
Slope of critical-state line in p0 -q plane. Eccentricity of the cap yield surface in DruckerePrager Cap model. c Small number which is used to define a smooth transition surface between the DruckerePrager shear failure surface and the cap. a
Model Number Fig. 6. Maximum lateral deformations obtained from the analyzed models.
b
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Final Settlement (m)
66
Model No.
Fig. 8. Stone column numbers used in numerical modeling.
columns and the surrounding soil. Corresponding horizontal stresses (Dsh, c) and (Dsh, s) also develop due to the aforementioned vertical stresses. The change in the hoop tension force (DFr) due to the external pressure in an encasement having a radius (rgeo), can be converted to an equivalent horizontal stress (Dsh, geo) using the equation (Dsh, geo ¼ DFr/rgeo). Equilibrium of stresses in the horizontal direction leads to the following relationship between the aforementioned stresses and a horizontal stress difference (Dsh, diff) defined as:
Dsh;diff ¼ Dsh;c Dsh;s þ Dsh;geo
A decrease in Es relative to the encasement stiffness leads to an increase in the hoop tension force induced in the encasement and, consequently, the radial strain and lateral deformation of the GEC increase. But the horizontal stress difference (Dsh, diff) results in a horizontal deformation in the soft soil such that a corresponding additional earth pressure is mobilized in the soil which brings the horizontal stresses to equilibrium (Kempfert and Gebreselassie,
Final Lateral Deformation , (m)
Fig. 9. Comparison of final settlement results of stone column number 13 obtained from the analyses.
Model Noo.
Fig. 10. Final maximum lateral deformations of stone column number 25 obtained from the analyses.
2006). A decrease in Es leads to increases in both (Dsh, geo) and (Dsh, s), resulting in a decrease in the value of (Dsh, diff), and its associated bulging of the GEC. In the middle columns of a group such as in column 13 shown in Fig. 8, due to the higher confinement provided by the surrounding columns, the decrease in (Dsh, diff) has more effect on bulging than the increase in the hoop tension force and, therefore, the decrease in Es results in a very slight decrease in
Table 3 Encasement length combinations of the analyzed models. Model no.
Encasement length formation
Model no.
Encasement length formation
1
All columns encased 100%
11
2
Central column length 75% encased
12
3
Central column length 75% encased - Central ring columns lengths 75% encased
13
4
Central column length 50% encased
14
5
Central column length 50% encased - Central ring columns lengths 75% encased
15
6
Central column length 25% encased
16
7
Central column without encasement
17
8
Central column length 25% encased - Central ring columns lengths 75% encased
18
9
Central column without encasement - Central ring columns lengths 75% encased
19
10
Central column length 50% encased - Central ring columns lengths 50% encased
20
Central column length 25% encased - Central ring columns lengths 50% encased Central column length 75% encased - Central ring columns lengths 50% encased Central column without encasement- Central ring columns lengths 50% encased Central column length 25% encased - Central ring columns lengths 25% encased Central column and Central ring columns without encasement Central column and Central ring columns without encasement - circumferential ring columns lengths 90% encased Central column and Central ring columns without encasement - circumferential ring columns lengths 75% encased Central column and Central ring columns without encasement - circumferential ring columns lengths 50% encased Central column and Central ring columns without encasement - circumferential ring columns lengths 25% encased All columns without encasement
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Lateral Deformation (m)
Column Length (m)
Settlement (m)
Load (kPa)
67
J=10000kN/m J=6000kN/m J=3000kN/m J=1500kN/m J=300kN/m Ordinary stone column
Fig. 11. Settlements of stone column 13 obtained from models with various encasement stiffnesses.
Fig. 14. Lateral deformations of stone column 25 obtained from the analyses with various 4s.
Lateral Deformation (m) 0
0
100
200
Load (kPa) 300
400
Settlement (m)
Column Length (m)
ES=40MPa
0.2
ES=60MPa
0.3
ES=80MPa
0.4
ES=100MPa
0.5 0.6
Fig. 15. Settlements of stone column 13 for various values of Es.
Fig. 12. Lateral deformations of stone column 25 obtained from models with various encasement stiffnesses.
bulging of this column. On the other hand, in circumferential columns such as column 25, less confinement stresses are provided by the soft soil, and the situation is opposite such that a decrease in Es results in a slight increase in bulging of the stone columns. 4.4. Stone column diameter Unlike the laboratory tests carried out by Murugesan and Rajagopal (2006) and the numerical analyses performed by Murugesan and Rajagopal (2007) and Khabazian et al. (2010), in which the influence of the stone column diameter, Ds, on the behavior of GECs was examined by applying the load directly to the column, in the current study, the load was applied to the whole stone column group and the surrounding soil through a concrete foundation. In order to evaluate the effects of the stone column diameter on the performance of the GEC group, the value of Ds, was varied from 0.5 m to 1.5 m to, while the center to center spacing between the stone columns was kept constant. Therefore, the changes in Ds from 0.5 m to 1.5 m are equivalent to changes in the area replacement ratio from 0.049 to 0.441. The “Area Replacement Ratio” or ARR is defined as the ratio of the area of the ground surface that is
600
ES=30MPa
0.1
J=10000kN/m J=6000kN/m J=3000kN/m J=1500kN/m J=300kN/m Ordinary stone column
500
replaced by the stone columns to the original area of the ground surface prior to installation of the columns. It is noted that in this section, because GECs with different diameters were analyzed, lateral deformations were replaced by lateral strains of the stone columns as criteria for comparison of the lateral behavior. Settlements of column 13 and lateral strains of column 25 obtained from the analyzed models are presented in Figs. 17 and 18. As shown in these figures, increases in Ds from 0.5 m to 1.5 m lead to decreases in the settlement and lateral strain of the selected columns by 53.6% and 84%, respectively. It is noted that, in general, increase in the column diameter leads to increase in the total load carried by the columns and decrease in the lateral confinement provided by the encasement. However, while the increase in Ds has a negative effect on the performance of each single GEC due to the decrease in the effectiveness of its encasement, it leads to an increase in the ARR, which has a larger influence on the performance of the GEC and results in an improvement in the overall performance of the GEC group. Applying the load only on the stone columns, as assumed in the aforementioned studies, ignores the positive effect of the increase in the ARR on the overall performance.
0
0.01
0.02
Lateral Deformation (m) 0.03 0.04
0.05
0.06
0.07
0
Load (kPa)
1 Column Length (m)
Settlement (m)
2 3 4 5 6 7
Es=30MPa-Column13 Es=40MPa-Column13 Es=60MPa-Column13 Es=80MPa-Column13 Es=100MPa-Column13 Es=30MPa-Column25 Es=40MPa-Column25 Es=60MPa-Column25 Es=80MPa-Column25 Es=100MPa-Column25
8 9 10
Fig. 13. Settlements of stone column 13 obtained from the analyzed models with various 4s.
Fig. 16. Lateral deformations of stone columns 13 and 25 for various values of Es.
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Load (kPa)
D=.5
Settlement (m)
D=.8 D=1 D=1.2 D=1.5
Fig. 17. Settlements of stone column 13 obtained from the analyzed models with various Ds.
Column Length (m)
Lateral Strain
D=.5 D=.8
3. Results of the 3D numerical analyses showed that increasing the internal friction angle of the stone column material results in increases in the resistance of the columns against failure and, consequently, the lateral deformations and settlements of the columns decrease. However, compared to the other variables studied in the current analyses, performance of GECs was found to be less sensitive to the internal friction angle of the stone column material. 4. Sensitivity of the load carrying capacity of the GECs to the variation of the elastic modulus of the stone column material was found to be small. This may be a result of a number of opposite effects that are caused by the change in the elastic modulus of the column. 5. Increasing stone column diameter decreases the effectiveness of the encasement due to the increase in the lateral deformations; however, an increase in the diameter while keeping the center to center spacing between the stone columns constant is equivalent to an increase in the overall Area Replacement Ratio of the stone column group. This has a more pronounced influence on the performance of the GEC group, and results in an improvement in the bearing capacity of the system.
D=1 D=1.2
References
D=1.5
Fig. 18. Lateral deformations of stone column 25 obtained from the analyzed models with various Ds.
5. Conclusions In this paper, the influence of various parameters on the performance of geosynthetic encased stone columns is studied through 3D numerical modeling. Based on the results obtained from this study, the following conclusions can be made: 1. Evaluation of the effects of the arrangement of encased columns in a group of columns on the overall performance of the groups indicated that, when settlements and lateral deformations of stone columns are concerned, it may be sufficient to encase only a selected set of the columns without losing a substantial percentage of the overall performance of the ground improvement system. The location of the selected columns depends on the foundation stiffness and loading distribution. 2. Increase in the stiffness of the geosynthetic encasement of stone columns leads to increases in the column stiffness, the hoop tension force mobilized in the encasement, and the lateral confinement provided to the column, leading to substantial enhancement in the performance of the GEC group.
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