Consolidation of Stone-Columned Soils
Research Scholar
and
Professor
Department of Civil Engineering
Indian Institute of Technology
Kharagpur, India.
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Consolidation of Stone-Columned Soils
Research Scholar and Professor |
SYNOPSIS
The stone column accelerates the settlement in weak soil by means of its higher draining properties and increases the stiffness of the subgrade. Saturated soil with plenty of loose fine suspended particles in the pore water, the fine particles get partly adhered to the soil mass and the rest flow with the seepage, resulting in a change of permeability.
Colloidal and hydrodynamic forces are responsible for the release of fines. Hydrodynamic forces cause the particles to exhibit different motion such as rolling, sliding, and lift. The colloidal forces also cause the fine particles to be released. The fine particles present in the flowing fluid may be captured depending upon the concentration of fine particles in the moving fluid.
The rate of change of the mass of the soil medium is suitably incorporated in the Biot’s type of formulation. The medium is assumed to be elastic. The finite element method has been adopted for the solution of the problem.
The material for the stone column should be chosen in such a way that there would be smooth surface of pore to facilitate the release of the captured particles. When the capture tendency of the surrounding soil is at higher range, the degree of consolidation is high.
Parametric studies have been conducted to ascertain the influence of various parameters involved in the formulation. Results are compared and presented in tabular and graphical form.
Keywords: Clogging, consolidation, deformation, drainage, elastic properties, finite element method, Galerkin weighted residual method, foundation, permeability, pore water pressure.
INTRODUCTION
The prediction of weak-soil response under large load concerns civil engineers in designing the structure and its foundation in regions of soft soil. Weak-soil poses the problem of large settlement in the long period of time. To accelerate the settlement of weak soil, stone columns are often provided with appropriate spacing under the foundation system. Conventional stone column is essentially a method of soil reinforcement in which soft cohesive soil is replaced by compacted stone or crushed rock in pre-bored vertical holes to form columns or piles within the soil. The stone column serves two basic functions, namely, (1) it provides strength reinforcement to the soil and (2) it acts as a vertical drain to allow the subsoil consolidation to occur quickly under any given loading. Greater stiffness of the stone column compared to that of the surrounding soil causes a large portion of the vertical load to be transferred to the column. The entire soil below a foundation, therefore, acts as a reinforced soil with higher load carrying capacity than the virgin soil. The pore pressure dissipation by radial flow accelerates the consolidation of the subsoil.
Many works [Baron (1948), Booker (1974), Booker et al. (1979)] have been carried out for prediction of settlement of saturated weak soil medium. It has been established [Balaam and Poulos (1978) Pande et al. (1994)] that stone column provision stabilizes the weak soil. The stone columns accelerate the settlement in weak soil by means of its higher draining properties and increased stiffness of the sub-grade. Normally a soil medium is saturated with turbid water in the sense that there are fine suspended particles in the pore water and loose fine particles get adhered to the soil mass and fill in the void spaces, resulting in prolong period of drainage [Gruesbeck and Collins (1982)].
Many investigators [Booker (1974), Booker et al. (1979)] have carried out the consolidation analysis with the permeability remaining constant and zero time rate of change of the mass of medium. In this paper, a time rate of change of the mass of soil medium has been considered in the formulation of the problem. The change of permeability of the medium has been considered with a suitable type of model. The finite element method has been adopted for solution of the problem.
FORMULATION OF PROBLEM
Considering the equilibrium of the differential element, shown in Fig. 1, Biot (1941) has established a differential equilibrium equation. The symbol for normal stress is s and shear stress is t with appropriate subscripts to denote the directions. To incorporate the effect of particle release and capture process, let the release rate per unit volume of soil be denoted by rr , where rr = rate of mass release of fine particles per unit volume (in kg/m3/sec). The capture rate is denoted by rc , where rc = rate of mass capture of fine particles (in kg/m3/sec).
Figure 1. Elemental description and sign convention
If the body force per unit volume of the soil in the y-direction is wy, and the depth along the z direction is b, elemental equilibrium in the y-direction can be written as
 |
(1) |
where vy is the velocity of moving fluid in the y-direction.
The term (rr - rc)yvy arises due to the net release of mass of the fine particles. Since the net released particles in the y direction will move along with the fluid with the same velocity as that of the fluid, the rate of change of momentum of the released particles is (rr - rc)yvy. According to Newton’s third law, the force on the soil mass is in the opposite direction to that on fine particles.
Similarly considering equilibrium in the x-direction, one can obtain
 |
(2) |
For deriving the continuity equation, let the volumetric strain be denoted by k. The volume of the differential element is Dx Dy b. Therefore the rate of change of volume is given by
 |
Therefore the rate of change of volumetric strain is given by
 |
(3) |
Using Darcy’s law and making corrections for particle movement, the velocity in the y-direction can be written as
 |
(4) |
and similarly the velocity in the x-direction is given by
 |
(5) |
where (rr – rc)yvyand (rr – rc)xvx are the additional pressure gradients due to net release of particles in the y and x-directions respectively, gx the unit weight of water and p is the pore water pressure.
Differentiating Eq. (4) with respect to y we have
 |
(6) |
Similarly differentiating Eq. (5) with respect to x, one can get
 |
(7) |
Substituting Eq. (6) and (7) into Eq. (3) and rearranging, it results in
 |
(8) |
Eqn. (8) is similar in form to that derived by Biot (1941) but with different coefficients.
Using Galerkin’s weighted residual method to the continuity Eq. (8) carries out a finite element formulation of the problem. Eqn. (8) is multiplied with virtual pore pressure p* and integrated over area, which gives rise to
 |
(9) |
Applying Zienkiewicz-Green theorem, Eq. (9) can be rewritten as
 |
(10) |
in which S is the total boundary, dl is the differential line element on the boundary and vn is the seepage velocity normal to the boundary, which is given by
 |
(11) |
in which 
and 
are the unit vectors in the x and y-directions, respectively.
Finite element discretisation is introduced in Eq. (10) and the displacement vector, {d} is assumed to vary over the finite element mesh according to
 |
(12) |
where [N] is the displacement shape function matrix, and {a} is the nodal displacements vector.
Similarly the pore water pressure vector {p} is assumed to vary in the mesh according to
 |
(13) |
where [
] is the pore pressure shape function matrix, and {q} is the nodal pore water pressure vector.
Virtual pore pressure is assumed to vary in the mesh according to the same shape functions as the pore pressure and is given by
 |
(14) |
where {q*} is the nodal virtual pore pressure vector.
The strain vector is related through
 |
(15) |
and the gradient of pore pressure is given by
 |
(16) |
where [E] is obtained by differentiating []. A vector {m} is defined as
 |
(17) |
such that
 |
(18) |
in which {s} is the total stress vector and {s' } is the effective stress vector, and the volumetric strain, k is given by
 |
(19) |
Substituting eqns. (11) to (19) into Eq. (10) one can obtain
 |
(20) |
where [k] is the permeability matrix given by
 |
(20a) |
Writing
 |
(20b) |
 |
(20c) |
Eq. 20c and Eq. (20) can be written as
 |
(21) |
Integrating Eq. (21) between the time t and t + Dt, one can obtain
 |
(22) |
In performing the above integration, the following approximation has been made
 |
(22a) |
where {q1} = {q(t)} and {q2} = {q(t+Dt)}
An approximate integration method becomes implicit or explicit depending upon the value of q. If the value of q is ½ then the integration method is an explicit method. Coefficient q defines the way that {q} varies during the time interval. For example q = ½ represent a linear variation and trapezoidal integration rule. We have adopted the value of q as 1, which is an implicit method of integration and vn is integrated. Eqn. (22) becomes
 |
(23) |
where vn2 = vn(t + Dt).
Galerkin’s weighted residual method is now applied to the equilibrium equations. Multiplying Eq. (1) by the virtual vertical displacement, v, and Eq. (2) by the virtual horizontal displacement, h, and integrating over the area one can get
 |
(24) |
But eqns. (4) and (5) can be rewritten as
  |
(25) |
Substitution of Eq. (25) into Eq. (24) results in
 |
(26) |
Applying Zienkiewicz-Green theorem to Eq. (26) can be rewritten as
 |
(27) (28) |
where nx, ny and nz are direction cosines of the normal to the surface and h, v are virtual displacements of the elements in the x and y directions of the element.
Since h and v are virtual displacements of the element, one can write
|
| (29) |
where tx = nxsx + nytxy and ty = nxtxy + nysy and noting the compressive positive sign which is opposite to the outward normal. These are called tractions.
Writing
 |
 |
(30) |
From Eq. (15)
 and  .
|
Therefore Eq. (30) reduces to
 |
(31) |
The incremental form of Eq. (31) can be written as
 |
(32) |
Since the body force vector w is constant, its increment will be vanishing. Therefore, Eq. (32) reduces to
 |
(33) |
Note that 
where 
, 
, and 
.
Therefore, Eq. (33) reduces to
 |
(34) |
The second term of Eq. (34) contains a boundary integral. Only those boundary nodes, having no prescribed pore pressure boundary conditions are included in the above boundary integral term. Writing
,
,
, and 
.
Eqs. (34) and (23) can be combined as
 |
(34a) |
A finite element program has been developed to solve the above Eq.(34a). A frontal solution method has been incorporated in the solution process.
RATE OF RELEASE, RATE OF CAPTURE
Rate of Release
The release of fines from a pore surface is the first step in the phenomenon of migration of fines in the porous medium. In general two major types of forces are responsible for the release of fines; colloidal and hydrodynamic.
Hydrodynamic forces act in different directions, which cause the particles to exhibit different motion such as rolling, sliding and lift. Gruesbeck and Collins (1982) have conducted experiments and found that the rate of release of fine particles varies directly as how much the flow velocity is more than the critical flow velocity. The experiment was conducted on the system of glass bead-sand pack. It was found that the critical flow velocity, above which there is release of fines, lies in the range from 0.01 to 0.1m/s. But in the present system of weak soil and stone column, the flow velocity is far less than the mentioned range. However, there is always a tendency of release of fines due to flow of fluid in the soil system.
The colloidal forces also cause the fine particles to be released. Khilar et al. (1990) have found that the rate of release of fines due to colloidal force varies directly as the concentration of fine particles present on the surface over which the flow is taking place. The use of the capture and release has been considered for cases of filter studies. The updating of permeability due to capture of particles has been considered independently to the stress level at which the capture and release form an independent equation and is solved simultaneously along with the other flow equation. Therefore in the present work the equations presented by these authors have been used with the release coefficient varying directly as velocity of flow as follows
 |
(35) |
where X is the concentration of particles that remain adhered to the solid surface at any time t expressed in amount (mass) per unit pore volume [i.e. kg/m3 ] and a is the release coefficient. Solving the Eq. (35) one can obtain
 |
(36a) |
But at t = 0, X = X0, therefore c = 0. Hence
 |
(36b) |
Since the release coefficient a varies directly as velocity during consolidation one can write
 |
(37) |
The coefficient a1 depends on the type of soil. A soil having more fine particles, loosely adhered to the pore surface will have high a1 value. The diffusivity of the fines and thickness of the boundary layer of flow also governs the value of a1. In the present numerical study, the value of a1 is taken to lie in the range from 10-1 to 104. The lower range 10-1 has been taken for analysis since below this value, a1 has negligible effect on the soil behaviour. The higher range chosen was 104 because above this value the behavior of the soil will deviate from the consolidation characteristics. The soil has been chosen to be high eroding when the value of a1>101 and low eroding when a1< 101.
Rate of Capture
The fine particles present in the flowing fluid, are considered to be captured depending upon the concentration of fine particles in the moving fluid. When the concentration goes beyond a limit, the condition for capture arises, otherwise the particle goes on moving along with the flowing fluid. The condition for capture has been studied in detail by Khilar et al.(1985). However there is a tendency of capture when the flowing fluid has suspended fine particles. The rate of capture is proportional to the concentration of fines in the permeating fluid. The rate of capture can be expressed as
|
(37) |
where 
[in kg/m3] is the concentration of fine particles that remain adhered to the pore surface and C [in kg/m3] is the unit concentration of fines in the moving fluid. Solution of Eq. (37) can be written as
 |
(38a) |
In the present analysis it was assumed that initially C0 = 0. The release process increases the value of C0 with time. That means the C0 value is updated with time. The value of b varies directly as the velocity as suggested by Khilar (1981). Therefore
 |
(38b) |
The value of b1 depends on the type of soil. It depends on number of collectors per unit volume, diameter of the collector i.e. the pore constrictions size. The range for b1 assumed is 10-1 - 104. The lower range of the value of b1 is taken as 10-1 because values less than the lower range have no effect on the soil consolidation. Values of b1 above the higher range are impractical as the product of the number of collectors and diameter of the collectors cannot be more than the higher range.
At each time step the value of a is calculated depending upon the velocity of the flow by Eq. (36b) substituting the value of a into Eq. (36a) the value of a is re-calculated. The value of particle concentration in the permeating fluid is updated by means of the fact that the amount of particles released is suspended in the flowing fluid. The amount of particles released from the pore surfaces causes the porosity to change. The amount of suspended particles thus calculated is used in eqns. (37) and (38) to update the values of capture rate and concentration of the suspended fine particles in the flowing fluid due to capture. The amount of fine particles captured also changes the permeability of the soil medium. To formulate the porosity change, let the change in the amount of concentration of fine particles on the pore surfaces be denoted as ‘ds’, porosity be denoted as ‘n’, and change in porosity is denoted by ‘dn’. Then
 |
(39) |
where rs is the mass density of soil.
Therefore the permeability is expressed as
 |
(40) |
The permeability of the soil is assumed to change according to the model
 |
(41) |
The above formula is given in standard textbooks where n is the updated porosity calculated from Eq. (40) and
 |
(42) |
in which kv is the shape factor, h is the viscosity of the permeating fluid and S is the specific surface area. In the present problem the value of k1 remains constant due to the fact that the process of the release or capture changes the value of viscosity of the flowing fluid as well as the specific surface area, such that the value of the product remains constant, the shape factor is constant for a particular soil body, hence the value of k1 remains constant.
EXAMPLE, CALCULATION AND VERIFICATION
The soil-foundation system studied in the present work and descretisation of the system are shown in Fig. 2. The footing is taken to be impermeable. The effect of the stone column on the improvement of the ground has been considered and the effect of the footing size is not been taken into consideration. Footing is flexible type and loading condition is shown in Fig. 3.
Figure 2. Soil-foundation system with a view to using basic elements
Figure 3. The step loading for analysis
The system considered for the present analysis is shown in Fig. 4. The reasons for such a consideration can be outlined as follows:
For the same volume of a conventional stone column, the new type of the stone column that is considered can increase the strength of the soil mass. For example taking the radius of conventional stone column to be r, the area becomes pr2.
If the present type of stone column is used with an inner radius r and the outer
radius 
, one can achieve the same area with an increased consolidating area.
The consolidation of a large circular loaded area can be achieved with less cost than the conventional method.
Analysis of the problem becomes general, in the sense that a conventional stone column situation can be achieved through a consideration of inner radius equals to zero.
In the analysis carried out, the strain and pore pressure is assumed to vary linearly across the element. As the strain is assumed to vary linearly, a linear strain triangle, having six displacement nodes and three pore pressure nodes, is used as the basic element. The soil mass (clay) under consideration is cylindrical in shape having a radius of 40 m and depth of 8 m.
The considered values of kx, ky, E, n, g of the soil mass are:
kx = horizontal permeability = 1.0x10-8 m/s; ky = vertical permeability = kx; E = Young's modulus = 3 MPa; n = Poisson's ratio = 0.25; g = effective unit weight = 10 kN/m3.
The values of kx, ky, E, n, g of the stone column are:
kx = horizontal permeability = 4.9x10-4 m/s; ky = vertical permeability = kx; E = Young's modulus = 1.89X105 kPa; n = Poisson's ratio = 0.3; g = effective unit weight = 12 kN/m3.
The parameters for calculation of change of permeability are given below.
The time factor used in presenting results is defined as T = cT t / h2, in which cT = K / gw (1 + 2n) = an equivalent coefficient of consolidation, where K = modified bulk modulus of soil mass = (permeability) ´ [(e/(1+e)], gw = unit weight of water, e, l and m are respectively the void ratio and Lame's parameters of the soil mass. The degree of consolidation is defined as the absolute value of 100(u-u0)/(u∞-u0) in which u0 is initial settlement and u∞ is ultimate settlement of the footing.
Figure 4. Stone Columns: Conventional and Proposed
Figure 5. Convergence of finite element formulation
The results obtained in the present analysis have been found to compare closely with those obtained by Booker (1974). The variation of time factor (T) versus degree of consolidation has been plotted for a system with soil clay-only and varying the number of elements (Fig. 5). It has been found that the result converges confirming the applicability of the programs used. The time integration of Eq. (22) is carried out using discretisation with 40 elements and is shown in Fig. 6 for the selection of time step. Selection of the time step may affect the stability of the numerical solution. But it has been shown that if q ³ 0.5 (Eq. 22a) in the time integration, it gives an unconditional stability [Desai and Christian (1977)]. Stable solutions are obtained in the present work with q = 1, and the time steps used are shown in Table 1. The time steps are selected in such a way that equal numbers of points are distributed in each cycle of the semi log scale. Moreover the influence of further smaller values of Dt on the footing behaviour was found to be negligible as shown in Fig. 6. The analysis is carried out for inclusion of stone column at various position and size, one of which is shown in Fig. 7. The stone column shown is assumed to be cylindrical in shape with outer diameter of 2m and inner diameter of 1m. Other arrangements, for which the analysis has been carried out, are given in Table 2.
Figure 6. Effect of time steps on consolidation analysis
Figure 7. Soil-foundation system with stone column (shown shaded)
The variation of pore pressure with depth for various ratios of a1 of stone column and clay is shown in Fig. 8. The time factor at which the pore pressure variation is taken is 0.015. This is the time factor at which much of the pore pressure gets dissipated and thus the remaining pore pressure variation is compared because the residual water pressure governs the efficiency of the stone columns. The pore pressure is less and the rate of pore pressure decrease with depth is high when a1 of the stone column is much more than that of the clay. When the ratio is less the pore pressure is high and the rate of pore pressure decrease with depth is also less. This is because near the higher range of a1 for the stone column than clay there will be faster dissipation of pore pressure as the stone column allows for the faster dissipation of pore pressure. But when the a1 of the stone column is less than that of the clay the pore pressure decrease does not change with change of a1 value of the stone column. Curves for variation of pore pressure, when the release coefficient of clay is varied are given in Fig. 9. Comparing Figs. 8 and 9, it is observed that the effect of variation of release coefficient is not as much as that of the stone column. The permeability decrease of low permeable surrounding soil does not affect the pore pressure decrease of the whole system. This is because the permeability of the clay is already very low and it is the higher permeability of the stone column that contributes to the pore pressure dissipation. Therefore the permeability decrease of low permeable surrounding soil that is clay does not affect the pore pressure decrease of the medium to a considerable magnitude. The degree of consolidation curves, for different release coefficients of clay is given in Fig. 11. Again, the degree of consolidation curves does not differ much. Release coefficients of the surrounding soil have practically no effect on the consolidation process of the whole system.
Figure 8. Residual pore pressure variation with change of a1 of stone column
(b1 of clay is 1.0 and that of stone column is 0.1)
Figure 9. Residual pore pressure variation for change of a1 of clay
(b1 of clay is 1.0 and that of stone column is 0.1)
Figure 10. Degree of consolidation with variation of a1 of stone column
(b1 of clay is 1.0 and that of stone column is 0.1)
Figure 11. Degree of consolidation for variation of a1 of clay
(b1 of clay is 1.0 and that of stone column is 0.1)
Figure 12. Residual pore pressure for variation of b1 for stone column
(a1 of clay is 1 and that of stone column is 1)
The pore pressure variation curves, for different capture coefficients of the stone column, are given in Fig. 12. In normal situation, the capture tendency of the stone column is low. During the consolidation process, the stone particle surface gets covered up with wet finer particles with adsorbed water. This may increase the attractive force on the particle and in the process the capture rate of the stone column increases and even exceeds that of the surrounding clay. The stone column material having higher capture tendency than that of clay will not decrease the pore pressure at faster rate. This is because the higher capture rate will not allow the water to escape through the stone column at a faster rate. But when the capture coefficient of the stone column is much high than that of clay for example 1000 times that of the clay the value of rc in Eq. (25) and Eq. (26) is higher than rr giving (rr – rc) a negative value so that the pressure gradient becomes high, physically it means that the inertial effect is so high that the pressure decreases due to the inertial effect of the captured particles. The pore pressure variation curves, for different capture coefficients of the clay, are given in Fig. 13. The capture tendency of the surrounding soil has a peculiar effect on the pore pressure of the permeating fluid because of the effect of inertia of the surrounding soil is of greater importance. As the capture tendency increases the pore pressure also decreases at a faster rate as can be seen in Fig.13 consolidates the soil at a faster rate. The steep gradient of the curve of the higher capture coefficient value suggests that the pore pressure decreases at a faster rate. Therefore the consolidation curve is shifted downward. When a1 of the stone column is higher there will be both release and capture, and the value of rr is higher than rc, therefore the rate of consolidation is high. But after a while, when the release is sufficient, the capture rate also increases and the rate of consolidation becomes approximately the same for any value of release rate, which is observed by the coincidence of different curves at higher time factor. The degree of consolidation curves, for different capture coefficients of the stone column, is given in Fig. 14. The capture of fine particles will decrease the consolidation due to the decrease in the permeability of stone column. The inertial effect of the captured particles in the stone column is less than the effect of the decrease in permeability of the stone column due to capture. The degree of consolidation curves, for different capture coefficients of the clay, is given in Fig. 15. When the capture tendency of the surrounding soil is at the higher range, the degree of consolidation is high. This is explained as the capture of fine particles in the surrounding soil which gives rise to an inertia effect on the surrounding soil. The inertial effect of the captured particles in the stone column is more than the effect of decrease in the permeability of the system, rendering the consolidation of the whole system to be more.
Figure 13. Residual pore pressure for variation of b1 of clay
(a1 of clay is 1 and that of stone column is 1)
Figure 14. Degree of consolidation for variation of b1 of the stone column
Figure 15. Degree of consolidation for variation of b1 of clay
The curves of degree of consolidation, for various stone columns arrangement is given in Figs.16 through 24, for various conditions. For studying the effect of the size of the stone column on the behavior of particle transport a of stone column was kept at 100, and a of the clay was taken as 10. b of the stone column was kept at 0.1, and a of the clay was taken as 10. The pattern of the curves for other values of parameters does not change. From Fig. 16, it is observed that the soil with stone column having inner diameter of 0.5m and outer diameter of 1m, without capture or release, will require stone column approximately of inner diameter of 0.5m and outer diameter of 1.5m, for achieving same degree of consolidation. Similarly Fig.17 shows that the soil with stone column having inner diameter of 1m and outer diameter of 1.5m, without capture or release, will require stone column approximately of inner diameter of 1m and outer diameter of 2.5m, for achieving the same degree of consolidation. In Figs.18 to 20, similar curves are presented with varying inner diameter. The curves between inner diameters versus outer diameter to achieve the same degree of consolidation are given in Figs. 21 through 23, for various properties of soil and stone column. Fig. 21 shows that as the inner diameter is increased the outer diameter required to achieve the same degree of consolidation also increases. But, when the inner diameter reaches the value near 2.0m, the outer diameter to achieve the same degree of consolidation increases without bound, which means that when the inner diameter of the stone column approaches the middle of the foundation the outer diameter goes beyond the foundation corner and thus the desired consolidation of the foundation can not be achieved with higher outer diameter. This pattern is observed for various values of release coefficient and capture coefficient. From Fig. 21, it can be concluded that as the release rate of the stone column is increased, the outer diameter requirement decreases, because the rate of consolidation increases for higher release rates. From Fig. 22, it is observed that the release rate of the clay i.e. the surrounding soil has practically no effect on the outer diameter requirement. The requirement of higher outer diameter is observed for a higher capture rate of the stone column is observed in Fig. 23. This is because the higher capture rate of the stone column decreases the rate of consolidation. The requirement of lower outer diameter is observed for higher capture rate of the surrounding soil clay as is observed in Fig. 24. This is because the higher capture rate of the clay increases the rate of consolidation due to inertial effect.
Figure 16. Degree of consolidation vs log(time factor) for various outer diameter
(with inner diameter of .5 m.)
Figure 17. Degree of consolidation vs log(time factor) for various outer diameter
(with inner diameter of .5 m.)
Figure 18. Degree of consolidation for different
diameter with inner diameter 1.0
It has been observed (Fig. 16) that the soil with stone column having inner diameter of 0.5m and outer diameter of 1m, without captures or release, will require a stone column approximately of inner diameter of 0.5m and outer diameter of 1.5m, for achieving same degree of consolidation. Similarly it has been observed (Fig. 17) that the soil with stone column having inner diameter of 1m and outer diameter of 1.5m, without capture or release, will require stone column approximately of inner diameter of 1m and outer diameter of 2.5m, for achieving the same degree of consolidation. Again, as the inner diameter is increased the outer diameter required achieving the same degree of consolidation also increases (Fig. 21). But, when the inner diameter reaches the value near 2.0m, the outer diameter to achieve the same degree of consolidation increases without bound. Thus the stone column should be placed in such a way that it remains well within the foundation under which the stone column is provided. This pattern is observed for various values of release coefficient and capture coefficient.
CONCLUSION
The pore pressure is seen to be decreasing and the rate of pore pressure-decrease with depth is high when a1 of the stone column is much more than that of the clay. When the ratio is less the pore pressure is high and rate of pore pressure decrease with depth is also less. This is because near the higher range of a1 for the stone column than clay, there will be faster dissipation of pore pressure as the stone column opens up the means for dissipation of pore pressure. But when a1 of the stone column is less than that of clay, the pore pressure decrease does not change with change of the a1 value of the stone column. The stone column material having higher release tendency consolidates the soil at a faster rate. Therefore the material for the stone column should be chosen in such a way that there would be a smooth surface of pore to facilitate the release of the captured particles. This can be achieved by providing pebbles with smooth surface. The stone column material having higher capture tendency than that of the clay will not decrease the pore pressure at a faster rate. This is because the higher capture rate will not allow the water to escape through the stone column at a faster rate. The capture of fine particles will decrease the consolidation due to a decrease in the permeability of the stone column. Hence the stone column material having surface with higher adhering capacity should be avoided. Inertial effect of the captured particles in the stone column is less than the effect of decrease in permeability of the stone column due to capture. When the capture tendency of the surrounding soil is at higher range, the degree of consolidation is high. The inertia effect due to the capture of particles in the surrounding soil, clay is more. It has been observed that as the release rate of the stone column is increased; the outer diameter requirement decreases because the rate of consolidation increases for higher release rate. For the present type of stone column it is observed that the stone column should be placed in such a way that it remains within the foundation under which the stone column is provided.
REFERENCES
Table 1a. Analysis with total of 5 steps
| ||||
| Increment No. |
No. of steps. | < t (days) | Total time (days) | Time factor (T) |
| ||||
| 1 | 1 | .115 | .115 | .0015 |
| 2 | 2 | 11.455 | 11.46 | .15 |
| 3 | 2 | 1145.83 | 1157.3 | 15 |
| ||||
Table 1b
| ||||
| Increment No. |
No. of Steps. |
< t (days) |
Total time (days) |
Time factor (T) |
| ||||
| 1 | 1 | .115 | .115 | .0015 |
| 2 | 2 | 2.195 | 2.31 | .03 |
| 3 | 4 | 1155.09 | 1157.4 | 15 |
| ||||
Table 1c.
| ||||
| Increment No. |
No. of Steps. |
< t (days) |
Total time (days) |
Time factor (T) |
| ||||
| 1 | 1 | .115 | .115 | .0015 |
| 2 | 5 | 4.514 | 4.629 | .06 |
| 3 | 7 | 1152.771 | 1157.4 | 15 |
| ||||
Table 2.
| |
| Inner diameter (d1) (metre) |
Outer diameter (d2) (metre) |
| |
| 0.5 | 1.5 |
| 0.5 | 2.0 |
| 0.5 | 2.5 |
| 1.0 | 1.5 |
| 1.0 | 2.0 |
| 1.0 | 2.5 |
| 1.5 | 2.0 |
| 1.5 | 2.5 |
| 1.5 | 3.0 |
| 1.5 | 3.5 |
| 2.0 | 2.5 |
| 2.0 | 3.0 |
| 2.0 | 3.5 |
| 2.5 | 3.0 |
| 2.5 | 3.5 |
| 2.5 | 4.0 |
| |
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