International Journal of Civil, Structural, Environmental and Infrastructure Engineering Research and Development (IJCSEIERD) ISSN 2249-6866 Vol.2, Issue 2 June 2012 10-16 © TJPRC Pvt. Ltd.,

NUMERICAL ANALYSIS OF SLOPE REINFORCED

WITH STONE COLUMN

1PATEL PARESH & 2VASANWALA SANDIP

1P.G. Student, S.V. National Institute of Technology, Surat, Gujarat, India. 2Associate Professor, S.V. National Institute of Technology, Surat, Gujarat, India.

ABSTRACT

Slope failures in tropical countries are common particularly during rainy seasons. Retaining wall,

vegetation, and pile etc. are the common methods adopted for the natural slope stabilization. Stone

column can also be used for stabilization of natural clayey slope. A finite-element model was employed

to carry out a parametric study on a number of governing factors such as slope angle, optimum location

of single & multiple rows of stone column, friction angle of stone column, diameter of stone column.

The influence of these factors on factor of safety are compared and discussed in this study.

KEYWORDS: Slope, Stabilization, Stone column.

INTRODUCTION

Factor affecting the slope instability are soil properties, pore water pressure, slope geometry,

earthquake, and vibration. Various methods are available for the slope stabilization. Among techniques

which increase resisting forces and basically act externally on the soils or rocks sliding are geometrical

methods (USDA, 1994), hydraulic improvement, surface and subsurface drainage (USDA, 1994),

structural barriers such as rigid walls and piles (Hassiotis et al., 1997; Ausilio et al., 2001), physical and

mechanical improvement (Komak Panah, 1994), reinforcement with geosynthetics (Zornberg, 2002;

Kousik Deb et al., 2007), soil nailing (Turner and Jensen, 2005; Sugawara, 2006), etc.

Stone columns (Barksdale & Bachus, 1983; Cheung, 1998; Kousik Deb et al., 2007; Ambily, 2007)

are another method for slope stabilization. Such columns have been used since 1950 normally for

cohesive soil improvement. It is a hole with circular section which is filled by gravel, rubble etc., and is

an effective method to increase the shear strength on the slip surface of clayey slopes. The most

important cases for utilizing stone columns (Barksdale & Bachus, 1983) are: (a) Improving slopes

stability of both embankment and natural slopes, (b) Increasing the bearing capacity of shallow

foundations constructed on soft soils, (c) Reducing total and differential settlements, (d) Decreasing the

liquefaction potential of sandy soils. The performance of stone columns for reinforced and improved soil

is easier and cheaper than other methods such as geotextile, grouting, and compaction (Barksdale &

Bachus, 1983). The diameter of stone column usually varies between 0.3 to 1.2 m and their intervals

between 1.5 to 3 m. Stone columns are normally constructed in multiple rows, depending on the soil

condition.

Many research articles had been published since the publication of the first method of analysis by

Fellenius (Fellenius, 1936) that were either related to slope stability or involved slope stability analysis

Numerical Analysis of Slope Reinforced with Stone Column 11

subjects. Among the available analysis methods; limit equilibrium methods of slices, boundary element

methods (Jiang, 1990) finite element methods (Matsui and San, 1992), and neural network methods

(Jaritngam et al., 2001), limit equilibrium methods of slices are the most commonly used methods among

others since simplicity and ease of use are the main advantages.

Based on two-dimensional analysis of slopes, for 3-D analysis, a 3-D stone column must be changed

to 2-D. “Figure 1” shows a sample of grouped stone column arrangement. With respect to this figure, one

row of successively stone columns with center to center spacing of S is replaced with an equivalent

column strip. The volumes of stone column materials are identical in both two and three dimensional

conditions. On the basis of equality of volumes, equivalent strip width for each row of the stone columns

is obtained from (Barksdale & Bachus, 1983; Cheung, 1998):

SR2π

(1)

Where R is radius of 3-D stone columns, and S is distance between centres of stone columns in each row.

Figure 1 : Plan of grouped stone columns (Barksdale & Bachus, 1983)

FINITE ELEMENT METHOD

The finite element method can be used to study the stability of slopes using a failure definition

similar to that in the limit equilibrium method (such as the finite element strength reduction method).

Many methods for slope stability analysis using finite elements have been proposed during the last two

decades. Among those methods, gravity increase method (Swan and Seo, 1999) and strength reduction

method (Matsui and San, 1992) are considered the most widely used methods. In the gravity increase

method, gravity forces are increased gradually until the slope fails then the factor of safety is defined as

the ratio between the gravitational acceleration at failure and the actual gravitational acceleration. In the

strength reduction method, soil strength parameters are reduced until the slope becomes unstable,

therefore, the factor of safety is defined as the ratio between the initial strength parameter and the critical

strength parameter. Therefore, strength reduction method has exactly the same definition as the limit

equilibrium methods (Griffiths and Lane, 1999). The gravity increase method is used to study the

Patel Paresh & Vasanwala Sandip  12

stability of embankments during construction since it gives more reliable results while the strength

reduction method is used to study the stability of existing slopes.

The Mohr-Coulomb model, used in the analysis, needs six parameters as inputs; ϕ, friction angle; c,

cohesion; ψ, dilation angle; E, deformation modulus (Young’s modulus); υ, Poisson’s ratio; and γ, unit

weight. For slope stability analysis, ψ = 0 was adopted assuming a non-associated flow rule, based on the

results by Griffiths and Lane, 1999. Young’s modulus and Poisson’s ratio are of insignificant importance

in slope stability analysis using strength reduction method, due to the nature and mathematical

formulation of the method (Matsui and San, 1992).

In this paper PLAXIS, finite element software was used to determine the static safety factor of

slopes reinforced with single & multi-rows of stone columns. Triangular elements with 15 nodes were

used to construct the meshes in 2D analysis assuming plane strain conditions. “Figure 2” shows a slope

reinforced by a row of stone columns which in this figure X is horizontal distance of column strip from

top most of the slope. With the presence of column on the slope face, the shear strength on the slip

surface is mobilized.

Figure 2 : Geometry of reinforced slope

One and two rows of stone columns are used to reinforce the slope and then parametric studies have

been performed to achieve the best location of the column in slope face and to determine the effects of

contributing parameters such as geotechnical properties of stone column materials, geometrical

specifications of the slope, diameter of the stone columns.

Geometry of the study slope is shown in the “Figure 2”. Several analyses were performed using

finite element methods. “Tables 1” & “Table 2” show soil and stone column material properties used for

analysis and further parametric studies.

Numerical Analysis of Slope Reinforced with Stone Column 13

Table 1 : Geotechnical properties of clayey soil

Friction angle

ϕc (degree)

Cohesion

Cc (kN/m2) Unit weight γc (kN/m3)

Modulus of elasticity

Ec (kN/m²)

Poisson’s ratio

υs

10 15 17 5000 0.35

Table 2 : Geometrical and geotechnical properties of stone column

Diameter

of Column

D (m)

Friction angle

ϕs (degree)

Cohesion

Cs

(kN/m2)

Unit weight γs (kN/m3)

Modulus of elasticity

Es (kN/m²)

Poisson’s ratio

υs

0.80, 0.90, 1.00

35, 40, 45 0 20 50000 0.30

PARAMETRIC STUDIES

Parametric study is being carried out considering the stone column position, diameter & friction

angle of stone column material and slope angle by PLAXIS.

Effect of Location of Stone column on Factor of Safety

In this section, one and two rows of stone columns are used to reinforce the slope and parametric

studies have been performed to determine the effect of location of stone column on safety factor by

moving the location of a row of columns along the slope. The greatest safety factor achieved for the

single row of stone column (Figure 1) is at a distance of 0.25 times the slope length (i.e. X = 0.25L) and

that for the two row of stone column (Figure 2) is at 0.25 & 0.50 times the slope length (i.e. X = 0.25L,

0.50L). The same trend has been observed in all analyses. In addition, this factor decreases by moving

the column from the slope crest toward the slope toe.

Figure 3 : Effective location of single row of stone column (D = 0.8 m, β = 45˚)

Patel Paresh & Vasanwala Sandip  14

Figure 4 : Effective location of two rows of stone column (D = 1 m, β = 45˚)

Effect of Column Diameter on Factor of Safety

The relation between diameter of column, friction angle of column & safety factor is depicted in the

Figure 6 for single row of column located at 0.25L from the crest. It can be seen that considerable

amount of increase in factor of safety is achieved for larger diameter of stone column.

Figure 6 : Effect column diameter with single row stone column

(X = 0.25L, β = 35˚)

Effect of Angle of Internal Friction of Stone column on Factor of Safety

The effect of friction angle of column material on the factor of safety is shown in the Figure 7,

considering the different value of column diameter with single row of stone column at distance 0.25L

from the crest of the slope. The safety factor of 1m diameter reinforced slope is about 1.10 times the

unreinforced slope. Similar results are observed for other diameter of stone columns.

Numerical Analysis of Slope Reinforced with Stone Column 15

Figure 7 : Effect of angle of internal friction of column material

(X = 0.25L, β = 25˚)

Effect of Slope Angle on Factor of Safety

Figure 8 depicts the effect of slope angle on safety factor. A considerable increase in safety factor is

observed for gentle slope. About 1.80 times FOS increases if slope angle decrease from 45° to 25°. And

1.47 times FOS increase for slope varying from 45̊ to 35̊.

Figure 8 : Effect of slope angle on factor safety ( D = 1m, X = 0.25L, ϕs=45̊ )

CONCLUSIONS

The analysis of slope reinforced with the stone column was done considering the different

parameters such as friction angle of column material, diameter of column, location of column and slope

angle. The following conclusions may be drawn from the above analytical results.

The effective location of a single row of stone column is at a distance of 0.25L and that for two

rows of stone column is 0.25L & 0.50L from the crest.

Both, angle of internal friction & diameter of column having a significant effect on stabilization

of slope.

For a gentle slope, higher factor of safety is achieved than of steeper slope.

Patel Paresh & Vasanwala Sandip  16

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