Behavior of Geosynthetic-Encased Stone Columns in Soft Clay : Numerical and Analytical Evaluations

The type of improvement technique that will be applied to a soil beneath an embankment depends on the nature of the problematic soil existing at the site. Soft soils beneath embankments typically present high compressibilities and low shear strengths. In some cases, geosynthetic-encased stone columns (GECs) have shown advantages over other solutions to improve embankment behavior. The aim of this study is to investigate the performance of GECs by means of numerical and analytical methods. Finite Element Analyses were conducted to evaluate the behavior of ordinary and geosyntheticencased stone columns underneath an embankment. Parametric studies were then conducted to investigate the influence of geosynthetic stiffness, column spacing, friction angle of column material and Stress Concentration Ratio (SCR) on the performance of the columns. The results obtained have shown that there are several parameters that are of paramount importance in improving the performance of GECs, such as geosynthetics stiffness, column spacing and thickness of soft soil layer.


Introduction
In some cases, soil properties are not appropriate for supporting structures such as buildings, embankments, dams and bridges.This leads to the need for a proper method that can be effective to improve the performance of the geotechnical structure.The use of stone columns is a popular solution that has been considered when dealing with soft soils.Stone columns not only reduce settlements but also behave like vertical drains and accelerate the consolidation process (Han & Ye, 2001).
Since the performance of ordinary stone columns is highly dependent on the lateral confinement provided by surrounding soil, when it comes to very soft soils (S u < 15 kPa) the application of this solution may not be feasible.This problem can be solved by increasing lateral confinement to the column material by using geosynthetic encasement.In this context, Geosynthetic Encased Columns (GECs) have been applied successfully in several engineering works (Raithel & Kempfert, 2002;Alexiew et al., 2005;Araujo et al., 2009;De Mello et al., 2008;Alexiew & Raithel, 2015;Schnaid et al., 2017).
Considering previous studies that have provided valuable information on the performance of GECs, further studies are still needed for a better understanding of the key parameters in designing GECs.Besides experimental and analytical solutions, numerical analysis can be used as a powerful tool to investigate the performance of GECs (e.g.Khabbazian et al., 2010;Kaliakin et al., 2012;Keykhos-ropur et al., 2012;Alkhorshid et al., 2014;Yoo, 2015;Mohapatra et al., 2017).
Since most of the analytical solutions have considered unit cell idealization in their procedure, this concept and axisymmetric analyses have been adopted to assess the influence of geosynthetic encasement on the behavior of stone columns (EBGEO, 2011;Elsawy, 2013;Almeida et al., 2013;Hosseinpour et al., 2014;Alkhorshid, 2017).
The analytical solution presented by Barron (1948) was focused on the behavior of the foundation system reinforced by vertical drains, discussing the dissipation of excess pore water pressure and the rate of consolidation settlement.This solution was a basis for later studies on the foundation reinforced by conventional and encased stone columns (Wang, 2009;Castro & Sagaseta, 2011;Santos, 2011) considering the time-settlement behavior under consolidation process.On the other hand, some other studies (Raithel & Kempfert, 2000;Pulko et al., 2011;Zhang & Zhao, 2014) were also developed to evaluate the behavior of encased stone columns and the surrounding soil which did not consider time-dependent settlement of the foundation.
In this study, the Finite Element Method (FEM) was used to investigate the effect of encasement on the column beneath an embankment.The FEM predictions were then compared with those from three analytical methods..1.1. Raithel & Kempfert (2000) method Raithel & Kempfert (2000) proposed an analytical method (hereafter referred to by the code R&K) for the design of encased stone column foundations which is adopted by the German Standard EBGEO (2011).This method was firstly proposed by Raithel (1999) and assumes identical settlements for both stone column and surrounding soil and aims to predict the behavior of a single column and the surrounding soil as a whole (unit cell, Fig. 1) under long-term drained condition when maximum value of radius variation and settlements are obtained.As illustrated in Fig. 1b, the load on the unit cell is shared by the column (Ds v,c ) and surrounding soil (Ds v,s ).In this method, the ring (geotextile) tensile force can be calculated by:

2
where J is the geotextile tensile stiffness, Dr geo and r geo are geotextile casing radius variation and initial casing radius, respectively.The settlement at the top of column can be determined by: where r c , Dr c and h are column radius, column radius variation and column length, respectively.This method uses the load redistribution factor (E) which represents the stress concentration on the top of the column.As shown in Eq. 2, the settlement of the column is a function of the column radius variation (Dr c ) which is dependent on the applied stress shared by the surrounding soil (s v,B ) that can be calculated by the following equation: where, s 0 , E and a c are vertical stress on the unit cell, load redistribution factor and area replacement ratio, respectively.The area replacement ratio can be determined by: where, A c and A E are column and unit cell area, respectively.On the other hand, the settlement of the surrounding soil is also a function of s v,B and consequently dependent on E. Thus, by equalizing the settlement of the column and the surrounding soil (S c = S B ), E can be found by some iteration process.When E is determined, the column radius variation can be calculated.

Pulko et al. (2011) method
The method proposed by Pulko et al. (2011), (hereafter referred to by the code PEA) is an extension of the elastic analysis proposed by Balaam & Booker (1985) and Raithel & Kempfert (2000) and considers elastoplastic behavior of the column material considering confined column yielding based on the dilatancy theory presented by Rowe (1962).In this method the vertical deformations at the top of the column and the surrounding soil are also assumed to be equal.The shear stress along the column/soil interface is neglected.Furthermore, the soil is considered to remain elastic and the column is supposed to behave as a perfectly elastoplastic material satisfying the Mohr-Coulomb failure criterion.Additional information on the method is presented by Pulko et al. (2011).

Zhang & Zhao (2014) method
Zhang & Zhao ( 2014) developed an analytical method (code Z&Z) for the design of conventional and geotextile encased stone columns.The method adopts the unit cell idealization and considers the column as an elastic material.The column is divided from top to bottom into i (i = 1, 2,..., n) sections.For each section there is a unique settlement and radius variation.The total settlement is the sum of the settlements obtained in each section.Comparing to Raithel & Kempfert (2000), this method takes into account the shear stress between the soil and the column considering settlement inequality at the top of the column and of the surrounding soil.More details on the method are presented by Zhang & Zhao (2014).

Hardening Soil (HS) model
The Hardening Soil (HS) model (available in PLA-XIS 2D) is a development on Mohr-Coulomb model, created by linking non-linear elastic and elastoplastic models, also known as hyperbolic elastoplastic model.HS is able to model the double stiffening performance of soil, which is not influenced by the compressive yield or shear failure.This model can simulate the stress dependency of soil stiffness but does not take into account soil secondary compression and stress relaxation.Additional information about this model is presented by Schanz et al. (1999).

Axisymmetric model
The behavior of GECs and soft clay unit cell under axisymmetric conditions (Fig. 2) was modeled using PLA-XIS 2D (Brinkgreve & Vermeer, 2014).The column was entirely buried in the surrounding soil with its tip resting on a rigid layer at the bottom.The soft clay was modelled by the HS model (Gäb & Schweiger, 2008) and the embankment and the column were modelled using Mohr-Coulomb model assuming typical values of properties of these materials.The properties of the soft clay, stone column and embankment are shown in Table 1.
The geosynthetic material was modelled as a linear elastic material (the same assumption was adopted in all three analytical methods).The boundary conditions of the unit cell (Fig. 2

Comparisons Between Predictions by Fem and Analytical Methods
Comparisons between results from the four cited methods (Finite element, R&K, PEA and Z&Z) were carried out for the analysis of an embankment reinforced with GECs distributed in a square pattern.In the validation model, the radius of the columns within the unit cell, r c, was equal to 0.4 m (typical for GECs, Alexiew et al., 2005) Zhang & Zhao (2014) pointed out that in case of large deformations, the method Z&Z may not provide appropri-ate results.In order to minimize this issue, in the present study the calculation procedure was changed so that the column was assumed to be as a whole, not in sections.For i = 1, the maximum value of radius variation (Dr c,max z = 0) and then the vertical strain of the column (e zc ) were determined.Then, the e zc was multiplied by the entire length of the column (l c ).For small level of deformation this procedure may not provide appropriate results.
As shown in Fig. 3a and Table 2, the settlements estimated by R&K and Z&Z are in good agreement with those of FEM.The maximum values of radius variation under different embankment heights estimated by R&K (Fig. 3b and Table 3) show good agreement with those of FEM.On the other hand, PEA and Z&Z led to underestimation and overestimation of the radius, respectively.The maximum values of radius variation from Z&Z, up to an embankment height of 3 m, are closer to those of FEM.For PEA, the re- sults present significant differences for any height of embankment.Figure 3c presents settlement at the top of the column for different values of diameter ratio, N, where it can be seen that the results from R&K and Z&Z also compare better with FEM predictions than PEA.

Parametric Study
The effects of geosynthetic encasement, column radius of influence, unit cell heights and friction angle of the stone column material (j c ) on the behavior of the column were investigated by a parametric study comparing FEM with analytical methods.The parameters used in parametric study are given in Table 4.

Settlement and radius variation of GECs
Geosynthetic encasement provides a confinement around the column that reduces radius variation (Dr c ).   from FEM (just for encased column), the overall deviations of R&K predictions are considerably less than those of PEA and Z&Z.The minimum and maximum deviations of R&K were equal to 1.5% (for J = 1000 kN/m) and 24% (for J = 4000 kN/m), respectively.On the other hand, PEA and Z&Z presented higher values of maximum deviations reaching 38% (for J = 500 kN/m) and 36% (for J = 4000 kN/m), respectively.The average deviation of Z&Z (23.8%) was less than that of PEA (33.8%).Another parameter that affects radius variation value is the diameter ratio (N).By increasing N for the same value of r c , the area replacement ratio (a) decreases and the maximum value of radius variation increases.As shown in Fig. 4b, the geosynthetic tensile stiffness significantly influences column radius variation.
Figure 4c shows column radius variation versus embankment height for different values of N and J = 2000 kN/m.The results also show the significant influence of N on column radius variation.In Fig. 4d the maximum value of radius variation is plotted against different embankment heights for different column soil friction angles.Radius variation increases as soil friction angles decreases.As shown in Fig. 3 and also in Figs.4c-d, predicted values of settlement and maximum radius variation are significantly influenced by the embankment height.By increasing the vertical stress at the top of the unit cell, the settlements and column radius variations increase markedly.However, using lower values of N improves the performance of the column.Alternatively, increasing the value of the friction angle of the column, reduces deformations of the column.stiffness.Predicted values of tensile force indicate that, as tensile stiffness of geosynthetic increases, radius variation reduces at any depth along the column.In addition, increments of J values do not influence significantly the depth of the maximum value of radius variation.Several studies have shown this depth varies between 1.5 to 3 column diameters (Ali et al., 2012;Hong et al., 2016;Alkhorshid, 2017).Comparing the results of both numerical and analytical studies indicate that R&K, from depth ratio of almost 5 and beyond underestimated the results while PEA presented better estimates.It is important to consider that R&K provides more accurate predictions of the maximum tensile force.Finally, it is possible to observe that the curves have completely different trends and this is because of the better accuracy of the Finite Element Method, whereas the analytical methods have to adopt some simplifying assumptions.Similar variations in tensile forces along the column length were also observed in other studies (Gniel & Bouazza, 2009;Pulko et al., 2011;Almeida et al., 2013).
The results, presented in Fig. 6a, clearly indicate the importance of the unit cell height on the column behavior.The geosynthetic tensile stiffness is also important in the reduction of column settlements.In Fig. 6b, the vertical settlement at the top of the column due to an embankment height of 10 m is plotted versus different values of J.The results indicate that at any value of J, the minimum settlement is obtained for higher friction angle.The lowest values of settlement are obtained for j c = 45°.

Influence of geosynthetic stiffness on Stress Concentration Ratio (SCR)
The stress concentration ratio (SCR) is defined as the ratio between the vertical stress supported by the column (q c ) and that supported by surrounding soil (q s ), (SCR = q c /q s ).SCR basically depends on the geosynthetic tensile stiffness, physical properties of soil, column materials and distance between adjacent columns, that may be arranged in triangular, square or hexagonal patterns.As shown in Figs.7 and 8, the greater the geosynthetic stiffness, the higher additional confinement along the column length which results in supporting larger shares of vertical stress.This means that for higher values of J, geosynthetic encasement produces greater values of SCR, depending on tensile stiffness.Figure 7 shows the effective stress distributions as cross marks.When it comes to the conventional column, these cross marks in the surrounding soil are visibly greater than those for the encased column, which means that a higher share of vertical stress goes to surrounding soil.The SCRs predicted by means of FEM and analytical analyses show that R&K results take a different trend for higher values of J, whereas PEA and Z&Z results are closer to those of FEM (Fig. 9a).There is almost a unique agreement between PEA and Z&Z on SCR.
The influence of N values is shown in Fig. 9b.As it can be seen, higher N values lead to lower SCR values and also the difference between SCRs for higher values of J is greater.As shown in Fig. 9c, the friction angle of column (j c ) can affect SCR, because higher values of j c make the column capable of sustaining higher vertical stresses.

Influence of geosynthetic stiffness on maximum tensile force
As cited in this study, vertical stress on top of the unit cell causes settlement and radius variation of the column.The radius variation causes a ring tensile stress in the geosynthetic encasement.Tensile force is a function of geo-

Figure 2 -
Figure 2 -Axisymmetric unit cell model and boundary condition.
, radius of the influence area of the column r e = 1.4 m, diameter ratio (N = r e /r c ) equal to 3.5, area replacement ratio (a = r c 2 / r e 2 ) equal to 8.16%, column length (l c ) and unit cell height (H s ) both equal to 10 m, height of embankment (H emb ) equal to 10 m, and geosynthetic tensile stiffness (J) equal to 2000 kN/m (EBGEO, 2011).

Figure 3 -
Figure 3 -Settlement behavior of GECs under embankment loading: (a) vertical settlement of the column from FE and analytical methods; (b) variation of column radius; (c) vertical settlement of column for different values of N.
Figure 4a and Table 5 show the maximum value of radius variation versus geosynthetic tensile stiffness for the same properties and characteristics adopted in the comparison between FEM and predictions from analytical methods.Comparing the results from analytical methods with those Soils and Rocks, São Paulo, 41(3): 333-343, September-December, 2018.337 Behavior of Geosynthetic-Encased Stone Columns in Soft Clay: Numerical and Analytical Evaluations

Figure 4 -
Figure 4 -Radius variation: (a) Maximum value of radius variation versus geosynthetic stiffness by different methods (FEM, R&K, PEA, and Z&Z); (b) maximum value of radius variation versus geosynthetic stiffness using FEM for different values of N; (c) maximum value of radius variation versus different embankment heights using FEM with different values of N and (d) maximum value of radius variation versus different embankment heights using different values of friction angle of the column.

Figure
Figure 5a-c show tensile force versus depth ratio (h = depth/r c ) for different values of geosynthetic tensile

Figure 6 -
Figure 6 -Vertical settlement at the top of the column: (a) vertical settlement versus embankment heights (b) vertical settlement versus geosynthetic stiffness.

Table 1 -
Material parameters in FE model.

Table 2 -
Settlement at the top of the column considering different methods (m).

Table 3 -
Maximum value of radius variation of the column (Dr c,max ) considering different methods (mm).

Table 4 -
Parameters used in the parametric studies.