INTRODUCTION the parameters of the stone column such


Fast growing population and the facilities needed for human being resulted in the utilization of resources around the world. Where moment from one place to other place becomes difficult due to some geological conditions. One of the fastest on ground travelling facilities are the railway trains which operates with different efficiency, to utilize the full efficiency (speed) of the train a stable track with good bearing capacity of ground is required thus the regions where the soil don’t possess this property (good bearing capacity) different ground improvement techniques are used to improve the soil conditions for proper utilization. These ground improvement techniques vary with respect to the ground condition. Reinforcing of soil by densification or replacement are the basic principle of these improvement techniques. By adding cementitious material, either permeation in granular soil or mixing in all types of soil results in ground improvement. Upon subjected to surcharge load the vertical drains decreases the amount of time soil takes to settle and strengthen.

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Literature review was carried out to know about different ground improvement techniques. On comparing the different improvement techniques for reinforcing the ground (stone columns) vibro replacement method was found very useful because of its less expense, good environmental impacts, improvement in permeability and bearing capacity of soil. This method is implementing very successfully for loose soil to improve its bearing capacity all over the world.

Different installation method of stone column and its influencing factor has been studied and discussed in detail. The improvement of the loose soil and the strength of stone column depend upon the parameters of the stone column such as the area replacement ratio, length of casing, diameter of column, spacing between the column.

After learning the software Abaqus a 2D asymmetrical numerical analysis of stone column model for a railway embankment was carried out and the results were compared with the other observed results in the literature. 


Soft soils are widespread all over the world and the places of them are in important cities. There are two main problems encountered when undertaking civil constructions in soft soil deposits, excessive settlement and low shear strength. Due to large void ratio and inherent compressibility of such clays, consolidation and displacements can be noticeable under construction loads and continue long time after implementation of the structure. Low shear strength is particularly hazardous when constructing large embankment on soft clay base, facilitating potential circular or sliding failure planes. Hence, the need to ground improvement schemes is very necessary. Following are the different ground improvement techniques observed around the world.




A ground improvement technique which improves soft, high moisture clays, peats and other weak soils mixing them with dry cementitious binder to create soilcrete. A high-speed drill deep down into the soil, a drill rod with radial mixing paddles near the bottom of the drill string to construct a soilcrete column. (Kirsch and Bell, 2012)


Such a ground improvement technique that mostly densifies the fill lands or materials by using a heavy drop-down weight.  The heavy weight is dropped repeatedly on ground surface which transmit vibration below the surface resulted in improvement of soil to some depth. Where the drop location and the spacing in determined by the ground conditions, loading and geometry.(Kirsch and Bell, 2012)


Energy is transferred to ground loose soil by rapid impact force, which results in the soil densification by rearranging. The location of force is specified before by a gridding pattern whereas the spacing of grid is determined but the ground condition, foundation loading, and geometry.  The soil is then improved in density, friction angle and stiffness.(Kirsch and Bell, 2012)


Aqueous solutions are injected into soil of collapsible and desiccated clay and railroad subgrade mud pockets for treatment. The injection unit having injection pipes which deeps down into the ground and solution of water, lime slurry and cement slurry is injected to reduce shrinkage. This technique is used to treat existing railways, roadways and buildings.(Kirsch and Bell, 2012)


In this technique a bottom-feed mandrel with top mounted vibrator is inserted into the soil and the soil is densified along the circumference of opening. Later concrete or ground is then pumped through the shaft and the mandrel is moved up and down to form expanded base. The shaft is then brought out to settle down the cement or grout.(Kirsch and Bell, 2012)


The assembly consist of a hanged vibrator on a crane. The vibrator is inserted into the ground with the help of water jets under its own weight. The vibrator densifies the loose soil with its vibration. Due to densification volume of soil reduced which is compensated by clean sand backfills typically.(Kirsch and Bell, 2012)


A powerful drill advances a mixing tool as binder slurry is pumped through the connecting drill steel, mixing the soil to the target depth. Additional mixing of the soil is completed as the tool is withdrawn to the surface. Mass wet soil mixing, or mass stabilization, is performed with a horizontal axis rotary mixing tool at the end of a track hoe arm. (Kirsch and Bell, 2012)


Densifying of the granular soil first by vibrator as advancing a bottom feed, down-hole vibratory probe into the ground. Concrete is pumped, and the vibrator is raised and lowered within the bearing depth and an expendable base is formed. In the end the assembly is raised to the surface and concrete is filled into the void to form an expendable top. (Kirsch and Bell, 2012)


Aggregate pier location is initially drilled by boring machine and will remain open. Another assembly of vibrator is inserted with the help of a standard crane in the pre-drilled hole. New crush stone or recycled concrete is filled into the hole through bottom-feed system and the vibrator compact the filling and densify the granular soil around the hole. (Kirsch and Bell, 2012)


This technique densifies and reinforces all soil. Stone columns are constructed by either wet top-feed method or dry bottom-feed method. In both process aim is to densify the soil by aggregate column. The stone columns increase the permeability of soil results in fast dissipation of excess pore water pressure.(Kirsch and Bell, 2012)


Stone column is one of the ground improvement technic widely used all over the world; its excessive use is due to fast installation, cost effective, more efficient, environmental friendly and easy installation. Mostly it is in practice for railway tracks, airports, harbor and other large-scale projects due to its easier, fast and cheap construction. Construction of stone columns results in transfer of loads to deeper and stronger depth of the ground results in improved bearing capacity of loose soil controlling the excessive settlement, dissipating excessive pore water pressure and accelerating primary consolidation process.

The application of Vibro compaction was reported, first time in Berlin in year 1937. The main aim reported was to densify loose sand deposit under a building in Berlin by penetrating poker to the ground. (Slocombe et al., 2004)

From last three decades this method of ground improvement is widely in practice for compaction of cohesion-less soils and reinforcing of soft soil by granular columns. The method has shown to be an effective and reliable technique for ground improvement, especially where high sensitivity of settlement is not critical. It was proved to be a very effective alternative of the past traditional deep pile foundation methods which are costly and time consuming as well (Douglas and Schaefer, 2015).


Stone columns are installed by two main techniques which are as follows, wet top feed method and dry feed method where the dry feed method can also be subdivided into dry top fed method and dry bottom feed method.

1.      Vibro-Replacement (Wet, Top Feed Method)

2.      Vibro-Displacement (Dry, Feed Method)

a.      Vibro-Displacement (Dry, top Feed Method)

b.      Vibro-Displacement (Dry, Bottom Feed Method)



Wet top feed method is one of the common method of stone column installation, in this method water is injected into the ground through the head of a vibrator bid mounted on the edge of drilling rig. The water pressure helps the penetration of vibrator (Raju et al., 2004). The required penetration is achieved with the help of vibrator and high pressure of water jet. When vibrator reaches the required depth of ground then crush/stone is fed from the top by a shovel to form stone column. The process mainly acts as replacement of some soil by water pressure and rest is displaced and compressed by the action of vibrator. Up to 30m of depth this method is applicable to treat soil (Raju et al., 2004). Below image shows the installation process.


Dry top method is also used for improving soil, this method consists of a machine supporting the top feed vibrator assembly. Vibrator is penetrated in the ground up to a required depth with the help of vibration and a downward force acted by machine which is holding the vibrator (Raju et al., 2004). After reaching the required depth stone is fed by a shovel from top which is compressed along the hole bottom and surrounding by the vibrator assembly. This method is well suited for loose soil because it does not use water in the whole processes  (Raju et al., 2004). Below figure represents the installation process. 


In this method a custom machine supports the bottom feed vibrator assembly. The vibrator is penetrated to a required depth with the help of vibration and downward force of machine (Raju et al., 2004). After reaching the required depth stone is fed through a bin from top of the machine which reaches directly to the vibrator bid without having a contact with surrounding soil. The process includes compression and displacement of soil to form the stone column. As this method don’t use water thus it is effectively used in congested areas and location of limited access. It can treat soil up to depth of 20m (Raju et al., 2004).


 Different installation method of stone columns.

Figure: Wet top feed method of stone column. (Mokhtari and Kalantari, 2012)

Figure: Drop top feed method of stone column. (Mokhtari and Kalantari, 2012)

Figure: Dry bottom feed method of stone column. (Mokhtari and Kalantari, 2012)


As stone column is introduced in loose soil to reduce the settlement and strengthen it where the stone column and the surrounding soil works together to share the stresses introduced by the acting load on ground. The response of bearing capacity of both column and soil together is influenced by material properties of both these materials. To solve this type of complex problem theoretically a certain level of idealization is required which can formed by the unit cell idealization method. In most existing research theories stone and clay were considered as perfect elastic or elastic-plastic materials (Barksdale and Bachus, 1983).   Therefore, design of stone column required knowledge of parameters such as area replacement ratio, depth ratio, spacing, permeability, stiffness, stress concentration factor, friction angle and improvement factor (Watts et al., 2000).

Typical design procedure of stone columns can be summarized as follows.

·         Predict the ultimate bearing capacity of stone column using internal friction angle and shear strength of undrained soil.

·         To determine the diameter of stone column and the allowable spacing between them.


The installation of stone columns pattern can be of different type, triangular, squared and hexagonal. The installation pattern depends on area replacement method, loading capacity, workability and cost of installation. Following installation patterns have different influence on the area of column in the unit cell approach (SHAHRAKI and WITT, 2015).


The triangular, squared or hexagonal pattern installation of stone columns have different influence area in a soil as a unit cell. Unit cell can be defined as a cylinder with an influential zone in the soil having diameter (de) enclosing surrounding soil and one stone column. In unit cell approach the influenced area as from triangular, squared or hexagonal pattern is converted to an equivalent circular influence area with a diameter of (de) as indicated before (Barksdale and Bachus, 1983).

Unit cell idealization of square and equilateral triangular pattern of stone Column proposed by (Barksdale and Bachus, 1983).


Area replacement ratio s is the ratio of the granular pile (stone column) area (Ac) over the whole area of the equivalent cylindrical unit cell whereas (As) is the area of soil. The amount of soil replaced by a stone column has an important effect upon the performance of weak soils. Increasing the area ratio of the column improves the overall strength of loose soil reinforced by stone column. As from various observation and experimentation it was recommended that area replacement ratio of 0.25 or greater is required for significant improvement in bearing capacity (Muir Wood et al., 2000).

s = Ac / (Ac + As)              

Ac = Area of stone column             As = Area of soil

Area ratio can be expressed in terms of diameter and spacing of the stone column.

s = ( / 4) * (d / S)2   for triangular pattern

s = ( / 2?3) * (d / S)2   for square pattern


Increase in length of the stone column results in the increase in permeability as well as the dissipation of excessive pore water pressure of soil in very short period. Stone column having a depth ratio of ? = 0.1 takes about 10,000 days for excess pore water pressure ?u, dissipation whereas stone column having depth ratio ? = 1.0 takes 15 days for dissipation of excess pore water pressure ?u (Ng and Tan, 2014).


 Figure: Illustration of the pore water pressure dissipation w.r.t depth ratio.


The embankment or foundation construct over the reinforced ground by stone column, important concentration of stress occur in the soil and the stone column as well. The stress in the surrounding less stiff soil decreases due to inclusion of stone column which bears the major portion of stress (Greenwood, 1900). As same vertical settlement occurs for the soil and stone column, stress concentration in stone column occurs because it is stiffer than the surrounding soil/ground.

Consider conditions for unit cell concept for which it is valid, load applied to a group of stone column have either square, triangular or hexagonal pattern where the vertical stress distribution can be expressed as the stress within a unit cell, can be expresses by stress concentration factor SCF (Fattah et al., 2013).

   SCF = ?c / ?s

The stress concentration magnitude influences on relative stiffness of stone column and soil for which avg. stress (?) and individual ?c , ?s over a unit cell can be expressed as.

? = ?cs + ?s(1- s)

?c = (SCF. ?) / (1 + (SCF -1) s) = ?c?

?s = (?) / (1 + (SCF -1) s) = ?s?

Priebe’s design curves for stress concentration ratio (Priebe, 1998)



The settlement performance of a floating stone column examination is quite difficult. The parametric study carried to examine the key influencing parameters of the settlement improvement factors for floating stone columns which are as follows. The parameters include area replacement ratio (), the effective friction angle of the column material (c’), the loading intensity (q), the modulus ratio (m), and the post installation earth pressure (k), (Ng and Tan, 2014).

Area replacement ratio (), friction angle of the column material (c’), the loading intensity (q) and the post-installation earth pressure (k) are the most influential parameters in the design of floating stone columns whereas the modular ration effect was found negligible.

As from parametric study (Ng and Tan, 2014), proposed a new design equation for floating stone column reinforced grounds where the settlement improvement factor n, can be predicted as from the correction factors.

n = no 1 – (C + C + Cq + Ck)

no = 9.432 +1.49 +1.06

Figure: Correction factors C , C , Cq and Ck for Improvement factor


Stone column never fails as end bearing capacity element and settlement of load area leads to bulging of stone column whereas the volume remains constant over the whole length stone column (Priebe, 1998). Soil improvement achieved in such conditions reinforced by stone column is evaluated based on assumption that the column materials shear from the beginning whereas the surrounding soil reacts elastically. Further, it is also assumed that the surrounding soil expand already during the installation of stone column to such extent that its initial resistance corresponds to the liquid state, coefficient of earth pressure amounts K=1, (Priebe, 1995). Such evaluation result is expressed by means of basic improvement factor no as.

no = 1 + (Ac/A) (1/2 + f (Vs, Ac/A)) / (Kac f (Vs, Ac/A)) -1

f (Vs, Ac/A) = (1-Vs) (1-Ac/A) / (1-2Vs + Ac/A)

Kac = tan2 (45 – c/2)

Adopting, for the native soil, a Poisson’s ratio of Vs = 1/3 which is adequate for the state of final settlement in most cases, leads to the simple expression.

no = 1 + (Ac/A) (5 – Ac/A) / (4Kac (1- Ac/A)) -1

The below figure illustrates the well-known (Priebe, 1998), design chart with reciprocal area ratio A/Ac with chosen friction angle (35′ to 45′) for poison ratio 1/2 and 1/3.

Ac= Area of stone column      A= Area of unit cell


(Priebe, 1998) Design curves for improvement factor with passion ration 0.5 and 0.3


Geosynthetic encasement avoids the bulging failure or penetration of column in soft clay. For the scaled modelling of the model undrained condition was assumed for the soft clay with linear elastic perfectly plastic Mohr-Coulomb and drained condition was assumed for the stone column using Mohr-Coulomb. For all cases encasement were modelled on their tensile stiffness value. The scale modeling of the stone column and the clay was carried out with Clay thickness of 2m and width 2m and the floating stone column of diameter D and length 1.5m was inserted with geosynthetic casing with length L.






Figure: (Dutta et al., n.d.) Simulation model of stone column


The failure pattern of stone column can be observed in the below figure with respect to encasement length keeping the encasement stiffness constant. The bulging starts just below the lading plate in un incased column where it shifts to the end of encasement in the encased columns. Later, the bulging of column tends to decrease after length of 4D, which may be due to transfer of load to surrounding soil.


Figure: (Dutta et al., n.d.) Failure, without and with encasement (J=200KN/m) by varying length.


Below figure shows the displacement contour of the un encased column and the 4D length incased column in the horizontal and vertical displacement can be observed for J=200KN/m. The stone column without encasement shows more horizontal displacement. 







Figure:  (Dutta et al., n.d.) Displacement contour for un encased and 4D length encased stone column.


 Improvement was observed in pressure settlement on increasing the encasement length with constant stiffness whereas further improvement tends to decrease after L=4D. On increasing the stiffness with constant length of column and encasement improvement of pressure settlement was observed and again the improvement is less obvious after J=400KN/m. After some time the improvement is not obvious (Dutta et al., n.d.).Fig: Varying encasement length at J=200KN/m      Fig: Varying Stiffness at (L=1.5 m & H=1.5m)



A 2D Symmetrical model was developed where the parameters of the stone column and the surrounding soil were taken from the literature review.  The diameter of the stone column is assumed as 0.75m at a depth of 6m as a floating column. The cross-sectional area of the surrounding for analysis is taken as 20m by 20m. Load are also applied in five different steps, starting from the gravity load to the additional load. Boundary Condition of the geometry is defined as follows.

Bottom –  Fixed Support.

Right and Left – Roller Support.

Soil to Column – For interaction no support condition is defined.

Below figure shows the geometry of the simulated 2D symmetrical model of the floating stone column, soil to column interaction ratio and friction between them are also assigned.


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