CHAPTER 2 LITERATURE REVIEW

Transcription

1 7 CHAPTER 2 LITERATURE REVIEW 2.1 INTRODUCTION Stone column consists of crushed coarse aggregates of various sizes filled in a cylindrical form in the ground. The crushed aggregates in the definite proportion are filled into the soil at regular intervals throughout the area of the land where the soil bearing capacity is to be improved. This is done either by using vibratory probes which are forced into the ground, the aggregates are then allowed to take the place of the displaced soil or by ramming the aggregates placed in a prebored hole by hammer. The treated compacted soil is capable of sustaining higher bearing pressure for the same settlement as the untreated soil and undergoes smaller settlement for the same bearing pressure. The void ratio and compressibility of the treated soil is decreased and the shearing resistance of soil is increased. The reduction in void ratio achieved depends on the grain shape, soil composition and force of vibration. As a vertical drain, it speeds up the consolidation process, which depends on spacing between the columns and their arrangement. But the stone columns are not applicable to thick deposits of peat or highly organic silts or clay (Alexiew et al 2005, Raithel et al 2005). There is a lack of lateral resistance offered by the surrounding soil resulting in poor load carrying capacity of the column. Further, due to the soft nature of surrounding soil, there may be intermixing of stone and soft soil. To overcome these problems, stone columns can be encapsulated by geogrid/ geocomposite, which improves the efficiency of the stone column with

2 8 respect to strength as well as compressibility. This is a recent advancement to enhance the load carrying capacity of stone column and is practiced on a very limited scale. 2.2 STONE COLUMN Stone columns were in existence in the early 1830s (IRC 1995, Nayak 1983) and they have been rediscovered only in the recent past. Research is going on in this area continuously to improve the existing design methods and improve the performance of stone columns. It is a technique for improving both cohesive clay and silty sands. Potential applications include stabilising the foundation soils to support embankments, approach fills, supporting retaining structures (including Reinforced Earth), landslide stabilisation and reducing liquefaction potential of clean sands. Also, stone columns under proper conditions can greatly decrease the time required for primary consolidation. Stone column made with uncemented stone/granite chips, derives its load capacity mainly through the passive resistance mobilised along the shaft of the column. The stone column resists the vertical load by lateral bulging. When stone columns are used for stabilising large areas, they increase the unit weight by replacement, drain rapidly the excess pore water pressures generated, act as strong and stiff elements and carry higher shear stresses. Further the stone columns prevent sudden building up of high pore pressure under dynamic loading, thus mitigating liquefaction potential of the stabilised bed and damage to the structures. Soil whose undrained shear strength ranges from 7 to 50 kpa or loose sandy soils including silty or clayey sands represent a potential class of soils requiring improvement by stone columns.

3 9 The main advantage of the stone column is its ability to adjust itself to the applied load and redistribute the applied load when stress is concentrated on it. This is due to the increase in deformation associated with bulging when the critical vertical stress level is exceeded. This response is different from load sharing response of a pile in soft clay wherein the pile can offer the resistance mainly by bearing, hence pile of longer length than stone column is required. A further advantage of the stone column in soft clay is that irrespective of the type of foundation, there is no drag force on the stone column and therefore in areas where pile foundations are subjected to drag force the stone column would score over piles. The stone column acts more or less like a sand drain. The assumption that the discharge capacity of sand drains is adequate to allow the flow of water that is being squeezed out of the clay stratum may not be valid for small diameter drains in highly compressible clays. The band drains have evident advantages, however when shallow depths have to be treated and sand drains are used, and the discharge capacity becomes critical for efficient functioning of sand drains. The stone column being more permeable overcomes all these problems. 2.3 GEOGRID/GEOTEXTILE ENCASED STONE COLUMN Ground improvement using vibro-stone columns has not been particularly successful in very soft clay deposits such as peat and organic clay. This is largely because of the insufficient lateral support that the surrounding soil can provide to the granular columns. These soils are generally considered the poorest in-situ materials because of their very high compressibility and exceedingly low strength. Engineers and contractors face considerable difficulties and challenges when dealing with these soils. Considerable benefit can be achieved by reinforcing the columns with geogrids, particularly in very soft clays. This approach has been implemented

4 10 on a trial basis in full-scale application for a high-speed railway embankment over a landfill site in the Netherlands (Nods 2002). It was reported that this approach has increased the load bearing capacity and post construction settlements reduced considerably. Geotextile encased columns (GEC) consist of inserting continuous, seamless, high-strength geotextile tubes into soft soil with a mandrel and filling the tube with sand (or fine gravel) to form a column with a high bearing capacity. The method can be used for supporting new roadway embankments and large pavement areas on soft peat material. Advantages of this system over stone columns include: (i) the column is confined in such a way that it does not intrude into the soft soil; (ii) a consistent diameter is maintained by the geotextile tube; and (iii) improved shear capacity to the column is provided by the tensile strength of the geotextile material and increased confinement of the sand or gravel. The geotextile also functions as a filter and prevents (separator) the intrusion of fines (and long-term loss of soil) while allowing water to drain through. This significantly improves drainage and accelerates consolidation. Consolidation rates in the order of 80 to 90 percent have been reported within three months. The technique allows for rapid installation of the columns with minimum noise. Although this technique has not been reported as having been used for seismic applications, such as stone columns and sand piles, it has potential for liquefaction mitigation too. 2.4 CLASSICAL THEORIES ON STONE COLUMN Several theories concerning the analysis and behavior of granular piles have been proposed by various researchers over the past 3 decades. Greenwood (1970) was one of the first few who developed a design method for stone columns assuming conditions as prevailing in a triaxial test. The

5 11 idea behind this technique is that when load is applied from a spread footing it tends to concentrate on the column, as it is the stronger element of the composite foundation soil. The column dilates and applies lateral stress to the surrounding clay, which is resisted by the passive pressure. Thus there is a triaxial stress system within the column. Under triaxial stress with equal allround restraining pressure, the maximum bearing capacity of a column will increase when the ratio of the principal stresses is also a maximum depending upon the angle of friction of the column material. Under widespread loads, lateral passive restraint for the columns away from the edge of the loaded area is much higher due to the equal allround influence of the applied load. Generally the contribution of applied load to restraining pressure is much larger than that due to soil strength and density, and the total carrying capacity of the column increases until the limiting factor becomes either local shear in the clay due to contact stress with individual backfill particles or the resistance to penetration of the column as an end bearing pile. An important difference between stone columns and conventional piles is the facility of the former to provide accelerated dissipation of excess pore pressures in the foundation soils due to load. Unlike a RCC pile, which is rigid, a granular pile shows bulging failure mode in soft clays. Figure 2.1 shows deformed shape of the granular pile in model tests (after Hughes and Withers 1974) and Figure 2.2 shows the deformed shape of the insitu column after installation (after Hughes et al 1975) and the deformed shapes are more or less similar to each other.

6 12 Figure 2.1 Deformation of the laboratory model stone column of 38mm diameter (Hughes and Withers 1974) Figure 2.2 Measured shape and deflections of a stone column (Hughes et al 1975)

7 13 The various design approaches available for stone column could be grouped in the following categories. Passive pressure or plastic failure approach Greenwood (1970), Hughes and Withers (1974) General shear failure approach Madhav and Vitkar (1978) Elastic equilibrium approach Baumann and Bauer (1974) Cavity expansion approach Datye and Nagaraju (1981) Unit cell approach Empirical approach Priebe (1976, 2005), Poorooshasb and Meyerhof (1997) Greenwood (1970) and Thornburn (1975) Yield Design approach Bouassida and Hadhri (1995) and Bouassida et al (1995) Finite difference approach Madhav and Van Impe (1992) Passive Pressure or Plastic Failure Approach In the passive pressure or plastic failure approach (Greenwood, 1970) the load applied through a strip footing on a granular pile tends to share the load as described in the earlier para. The ultimate bearing capacity of a single granular pile (Greenwood, 1970) for a two dimensional plastic failure case, is as follows q ult = P p = z k p + 2 c u k p (2.1) where, q ult is the ultimate load bearing capacity of the granular pile, is the bulk density of clay, z is the total depth of the limit of bulge of the pile, k p coefficient of passive earth pressure and c u is the undrained shear strength. The total depth of bulge is the critical length of the pile and it is found to be 2 times the pile diameter as reported by Greenwood (1970). However the critical length is found to be 4 times the pile diameter, in case of

8 14 bulging failure mode in clay (Hughes and Withers 1974). Generally the effect of surcharge load, q to the restraining pressure is much larger than the strength of the surrounding soil and its density. Thus the load carrying capacity of the granular pile increases until the local shear failure in clay or the end bearing failure whichever occurs earlier. Thus the enhanced capacity of stone column due to surcharge pressure is as follows. q ult = zk p + 2c u k p + q k p (2.2) where, q is the surcharge load. Hughes et al (1975) state that the ultimate column load depends on the friction angle of the gravel used to form the column, the size of the column formed and the restraint of the clay on the uncemented gravel. The calculation of column strength was based on the lowest value of measured passive restraint rl, which would be expected to occur over the critical length of column. The expression for the total limiting radial stress rl is 4c ' u rl r0 0 (2.3) where r0 is the initial radial effective stress, c is the cohesion of the soil and u 0 the initial excess pore-pressure. If the stone in the column approaches shear failure with an angle of internal friction of the limiting axial stress v in the column is given by 1 sin ' ' (4 0 v c ) 1 sin ' (2.4) if u 0 = 0 ; drainage into the columns makes this possible. The value of rl or c should be the minimum that would be expected over the critical length of the column. If it is assumed that vertical shear stress developed along the side of the column is equal to the average shear strength of the soil when end

9 15 bearing failure is about to occur, the critical length can be evaluated by equating the boundary forces on the column, i.e. column load equals the sum of shaft friction resistance and end bearing force as shown in equation (2.5). p _ c A s N c ca c (2.5) where p is the ultimate column load, N is the appropriate bearing capacity factor (taken normally as 9 for a long column), A s is the surface area of the side of the column of diameter D ( DL c ), L is the critical column length, A is the column cross-sectional area ( D 2 /4), c and c are the average shaft cohesion and the cohesion at the bottom of the critical length respectively. Hence L c can be determined by trial of values of soil properties. The critical column length is the shortest column, which can carry the ultimate load regardless of settlement General Shear Failure Approach Madhav and Vitkar (1978) demonstrated the plane strain version of a granular pile as a granular trench and postulated the failure mechanism. The bearing capacity of a footing on a soil stabilised with a granular trench is determined using the upper bound theorem. A work equation is formed by equating the external rate of work done due to applied load, soil weight and soil surcharge, to the internal energy dissipated in the plastically deformed region, for which coulombs yield criterion is applied. The bearing capacity of a footing on a soil stabilised with stone columns is determined using the upper bound theorem. A general shear failure mechanism is considered along with Coulombs criterion for the yielding of soils. Figure 2.3 shows an assumed failure mechanism for the soil system with a granular trench of width A both for A/B 1 and 1. The width of the strip load is B. Equating the work done

10 16 by external load q ult to the energies dissipated by cohesion, and work done on account of soil weight and surcharge, the following relation is arrived at q ult = c 2 N c + ( 2 B/2)N +D f 2 N q (2.6) where, N c = (c 1 /c 2 ) N c1 + N c2 and N = ( 1 / 2 ) N 1 + N 2. N c1, N c2, N 1, N 2 and N q are the dimensionless bearing capacity factors that depend on the properties of trench and soil materials and the ratio A/B. c 2, 2 and c 1, 1 are cohesion and unit weight of soil and trench materials respectively, and D f is depth of foundation. Equation (2.6) is similar to Terzaghis bearing capacity equation for homogeneous soil. Figure 2.3 General shear failure mechanism (Madhav and Vitkar 1978) To obtain the minimum value of the ultimate bearing capacity of the strip footing, i.e., the best upper bound, q ult / = 0 and q ult / = 0. The bearing factors N c, N and N q have been evaluated separately. Equation (2.6) must be modified by incorporating shape factors for the three bearing capacity factors as suggested by Vesic (1972) for an axisymmetric condition.

11 Elastic Equilibrium Approach Baumann and Bauer (1974) studied the performance of foundations on stabilised soils by the conventional equilibrium approach. The calculation of the bearing capacity of the stone columns in cohesive soil is based on the concept of composite soil made up of clay and stones, in which the load of the structure above ground is concentrated on the stone columns. The bearing capacity will depend on the strength parameters of the compacted material, column diameter and the lateral deformation properties of the cohesive soil. The total settlement or the total compression of the loaded treated soil layer consists of the immediate settlement, 1, for which no volume change of the columns is assumed, and the consolidation settlement, 2. A rigid foundation will exert an average load intensity p o on the underlying material. Part of the imposed load will be carried by the column and the other part by the unimproved soil, such that p 0 A p A p A (2.7) c c s s where p o is the average load intensity, A is the footing area per compaction column, p c is the bearing stress on compaction column, A c is the area of compaction column, A s is the area of the untreated soil (A-A c ) and p s is the bearing stress on untreated soil. The settlement of the column, c, and the settlement of the untreated soils, s, has to be equal for a rigid foundation. Based on the condition of compatible deformation the stress ratio between the column and soil is established as in equation (2.8). p p c s E E E E s c s c K K c s ln ln a r 0 a r 0 (2.8)

12 18 where E c and E s are the moduli of stone column material and soil respectively, K c and K s are the earth pressure coefficients respectively, r 0 is the radius of the column and a = A. The earth pressure coefficients K c and K s have very little influence on the p c /p s ratio and can be assumed with confidence. The moduli of deformation E c and E s have to be determined from field or laboratory investigations. The consolidation settlement, 2 is different as the vertical compression which will occur under a sustained load and which is associated with a decrease of voids of the soil. The amount of consolidation settlement is calculated by H z 2 E (2.9) 0 in which E and are the drained modulus of deformation and the increase in vertical stress at any depth z below the foundation respectively. H is the thickness of the compressible soil layer. If a compressible stratum is very thick, or contains several layers, having different E values, the compression of each of the sub layers is computed and then added. E is related to the coefficient of volume compressibility, m v, by E 1 m v (2.10) The distribution of vertical within the compacted zone has to be estimated by using a Boussinesq or Newmark (1942) stress distribution. The total settlement two settlement components 1 and 2. within the compacted zone is the sum of the

13 Cavity Expansion Approach Theory of expansion of cavities in a homogenous, infinite, isotropic soil mass by a uniformly distributed internal pressure is considered analogous to the bulging of a single granular pile in a soil medium when it is subjected to a sustained vertical load on its top. Due to the internal pressure, the initial radius of the cavity increases resulting in an increase in the plastic zone around the cavity. The soil beyond this plastic zone remains in the elastic state of equilibrium. To arrive at the lateral limit stress, the soil in the plastic zone is assumed to behave as compressible plastic solid defined by Mohr- Coulomb shear strength parameters c and, and average volumetric strain, v. The soil in the elastic zone is assumed to behave as a linearly deformable isotropic solid defined by modulus of deformation E s and Poissons ratio,. It is further assumed that prior to the load application the entire soil mass has an isotropic effective stress m and the body forces within the plastic zone are negligible when considered with existing and newly applied stresses. Based on the above assumptions, the cavity expansion theory (Vesic, 1972) can be applied to arrive at the vertical yield stress according to the following equations, 3 = cf c +qf q ; 1 = 3 N where N = 1 1 sin sin. However, determination of the design values of cavity expansion factors are subject to several uncertainties because of the strong influence of construction methods on those factors (Datye, 1982) Unit Cell Approach Priebe (1976) considered the behavior of a single granular column and its surrounding tributary soil as a unit cell (Figure 2.4). A unit cell is an area A consisting of a single column with the cross section A c and the attributable surrounding soil. It is assumed that the column is incompressible and the state of stresses in the soft soil is isotropic (k 0 =1) where, k 0 = earth

14 20 pressure coefficient at rest, hence radial stress r = q s. It is shown that under these circumstances the stress concentration ratio, n = (q c /q s ) which is the ratio between the stress on column q c and stress on soil q s increases with area ratio A c /A. The improvement of soil achieved by the existence of stone columns is evaluated on the assumption that the column material shears from the beginning whilst the surrounding soil reacts elastically. Furthermore, the soil is assumed to be displaced already during the column installation to such an extent that its initial resistance corresponds to the liquid state, i.e. the coefficient of earth pressure amounts to K = 1. The result of the evaluation is expressed as the basic improvement factor, n 0 and is as defined in equation (2.11) for the Poissons ratio s = 1/3. Figure 2.4 Unit cell idealisation of a stone column

15 21 Reciprocal Area Ratio A/A c Figure 2.5 Design chart for basic improvement factor (Priebe 1976) n 0 1 Ac 5 Ac A 1 (2.11) A 4K 1 A A ac C The relation between the improvement factor n 0, the reciprocal area ratio A/A c and the friction angle of the backfill c is shown in Figure 2.5. Priebe (2005) extended his study for floating columns thus eliminating the assumption that the column is resting on a rigid layer. Two approaches have been suggested assuming that the balancing of stress takes place solely either in the upper treated zone or in the lower untreated zone. Based on the exclusive application on highway projects in South East Asia on very soft soils, it is reported, that even soils with an undrained shear strength as low as 5kN/m 2 can be treated and improved by vibro replacement stone columns. Poorooshasb and Meyerhof (1997) considered that stone column and soil combination acts as a thick cylinder, and each column derives its load bearing capacity from the lateral stresses developed at the column/soil interface.

16 22 Figure 2.6 Thick cylinder under internal pressure p and constrained from movement at its outer radius (Poorooshasb and Meyerhof 1997) A rigid frictionless piston forces the upper surface of the cylinder downwards and in doing so causes the hole to reduce its diameter. The stone column, because of its tendency to deform laterally, exerts certain stresses on the interior wall of the cylinder and causes the hole to expand. Each column derives its load bearing capacity (of the order of kN) from the ambient (lateral) stresses developed at the column/soil interface. The factors of influence are, the radius of the column a, the radius of influence of each cell b, (Figure 2.6), the physical properties of the native weak soil (its modulus of deformation E s and Poissons ratio ) and the deformation characteristics of the compacted granular column material. The deformation of the granular material is usually represented by two ratios ( / 1 and V/ 1 ) where is the ratio of the major principal stress to the minor principal stress, 1 is the axial strain of the column and V is the volumetric of the granular medium, having a negative value for a dilating (expanding) material. The two relations represent the stress deformation characteristics of a stone column,

17 (2.12) where 1 v= (2.13) is the major principal stress (the load intensity carried by the column), 3 is the minor principal stress, 1 is the axial strain (the vertical strain experienced by the column and the surrounding soils ), 3 is the lateral strain and v is the volumetric strain of the stone column respectively. the relation In the linear case, for equal settlement of the soil and the column 1 / E c p / Es must hold. The performance ratio (PR) is defined as the ratio of the settlement of the treated ground (ground with stone column inclusions) to that of the untreated ground under identical surcharges. The relation between the performance ratio and the settlement ratio is given by Performance ratio = (settlement ratio) 1 or PR = 1/ (2.14) The settlement ratio is given by equation (2.15). q / / E L c 1 A r E E c s 1 (2.15) where, A r is the area ratio since it represents the area of the cross section of the column to the area of the cross section of the influence cell (i.e. A r = a 2 /b 2 ) and q is the intensity of the uniformly distributed load carried by the a 1 ( b a ) p rigid mat plus the self weight of the mat given by, q 2, b where p is the intensity of load shared by the soil within the unit cell. It was concluded that the factors that most severely effect the performance of a stone column are the spacing, (or the area ratio) and the degree of compaction of the material in the columns, which, in turn, control their strength, stiffness and dilation properties.

18 Yield Design Approach Bouassida and Hadhri (1995) determined the extreme load on the soils reinforced by columns by making use of the Yield Design theory. Single column behaviour is studied for both plain strain and axisymmetric cases. Columns are considered as perfectly drained material. For soft soil, drained and undrained behaviours are considered. In the plain strain analysis, quasiexact solutions have been established for the undrained condition. Acceptable bounds of the extreme loads have also been established for the drained case. Under the axisymmetric analysis, bounds of the extreme loads have also been established for the undrained case. The influence of gravity has also been studied and it is found to increase the extreme load value in the plane strain analysis when the column has a high friction angle. Bouassida et al (1995) investigated the bearing capacity of a foundation resting on a soil reinforced by a group of columns. In this study, lower bound of the bearing capacity is determined within the framework of the yield design theory. The three-dimensional nature is taken into account and applied to a wide range of geometries. A parametric study on the improvement of the bearing capacity as a function of the proportion of the reinforcement and on the strength characteristics is studied. A complete analytical solution is given for the strength of a composite cell subjected to a triaxial loading, which provides an insight into the reinforcement mechanism Finite Difference Approach Madhav and Van Impe (1992) proposed a model for the analysis of the granular layer covering the stone column reinforced soil. The response of the system is shown to depend on the relative stiffness of the gravel bed. The load transferred to the stone column varies significantly with the stiffness of the gravel bed relative to the column and the soil. The design criterion proposed ensures that the gravel bed deforms uniformly.

19 25 If the granular pad is rigid, the uniform settlement,, and the ratio, m r, of the load on the stone column are = (b/a) 2 /{K R +(b/a) 2-1} (2.16) m r = K R /{K R +(b/a) 2-1} (2.17) where a is the radius of the stone column and b is the radius of the unit cell. K R = K c /K s, K c and K s are the coefficient of subgrade reactions of the stone column and soil respectively. The loads carried by the stone columns are evaluated from the equation 2.17 and are presented in Figure 2.7 for various c ( c = K c a 2 /G f H f, G f is the shear modulus of the granular bed material and H f is the thickness of the granular bed). Lower values of the parameter c imply a stiffer gravel bed and lead to higher loads to be transferred to the stone columns. The percentage of load (m) carried by the stone column decreases with increasing values of c. The influence of the gravel bed is more if the stone columns are spaced closer. Figure 2.7 Load on stone column (Madhav and Van Impe 1992)

20 STUDIES ON CONSOLIDATION BEHAVIOR OF STONE COLUMN Settlement response of soft soil reinforced by compacted sand column was studied by Juran and Guermazi (1987). This paper presents the results of a laboratory study that was conducted to investigate the effect of several parameters, including the loading process and the loading rate, the replacement factor, the group effect, and the partial consolidation of the soft soil due to the radial drainage through the column in a soil-column system. It was concluded that the consolidation and partial drainage of the soil during loading have an important effect on the load-transfer mechanism. The rate of generation and dissipation of the excess pore-water pressures depends primarily upon the replacement factor and the ratio of the loading rate to the soil permeability. The influence on the values of stress concentration ratio (n) and settlement ratio ( ), depends essentially on the replacement factor (A r ). In cases of relatively high values of A r, the group effect prevents the plastic yielding of the column and of the soft soil and consequently, significantly decreases the settlement. In case of relatively small value of A r, effective mobilisation of the group effect requires larger radial strains of the column. Therefore, it is mobilised only when the column reaches a state of plastic yielding, restraining the lateral expansion. Poorooshasb and Meyerhof (1997) examined the consolidation settlement of raft foundation due to radial drainage by considering the factors such as column spacing, deformation and dilation properties of the column and mechanical properties of the weak soil in which the columns are installed. An equation to determine the settlement of group of stone columns based on elastic theory was proposed including the variation of pore water pressure and contact pressure at various stages of loading based on the unit cell concept. It was reported that the load transferred to the stone column was three times the

21 27 value of maximum load carried by the raft for a stone column spacing of two times the diameter. The load on the stone column increased with increase in spacing of stone column. The consolidation of the foundation due to radial drainage towards the column is examined by taking into account column spacing, the deformation and dilation properties of the columns as well as the mechanical properties of weak soil in which the columns are installed. If 1 denotes the settlement of the raft per unit height of the stone column, then the volume of water leaving (draining towards the column) in a cylinder of unit height and concentric radius r, with the stone column is (b 2 -r 2 ) (Figure 2.8). From this settlement the velocity of flow is evaluated as b 2 / r 2 r and using this equation in conjunction with Darcy Law the governing equation is obtained and solved. Figure 2.8 Thick cylinder idealisation (Poorooshasb and Meyerhof 1997)

22 28 It may be noted that Barron equation does not make any reference to the load carried by the column or its stress deformation (in particular its dilatation) properties. Hence, Poorooshasb and Meyerhof (1997) modified the Barrons equation to account for the factors listed above. The performance ratio of stone column is represented for various densities of stone column by the modified Barrons equation which is as given below. PR = PR (1-exp -2T/f(N) (2.18) where PR is the performance ratio at any time, t and PR is the Performance ratio constant depending on area ratio, A r and the modular ratio of the column and clay (Poorooshasb and Meyerhof 1997). T is the Time factor and f(n) = N 2 /(N 2-1)*ln (N)- (3*N 2-1)/(4*N 2 ), N = a/b, the diameter ratio. Figure 2.9 Effect of compaction of stones on time factor (Poorooshasb and Meyerhof 1997) The Figure 2.9 shows the effect of compaction of stones on the time factor, T. They concluded that the performance ratio obtained by the elastic theory and by the modified Barrons equation exhibited excellent agreement. Han and Ye (2001) proposed a simplified equation for consolidation rate of stone column reinforced foundations taking into account

23 29 the effect of stiffness difference between the stone column and the surrounding soil which was ignored by Barron (1947). Barrons equation is based on the assumption that the reduction of soil volume is equal to the discharge of water from the soil which is given as a partial differential equation for axisymmetric flow (Figure 2.10) in equation (2.19). _ u t u u u cr c 2 v 2 (2.19) r r r z where c r = coefficient of consolidation in the radial direction; c v = coefficient of consolidation in the vertical direction; u = excess pore water pressure at a certain location (r, z) in soil; u = average excess pore water pressure at a depth z in soil; r, z = cylindrical coordinates and t = time. Figure 2.10 Definition of terms for modeling (Han and Ye 2001)

24 30 Considering that the consolidation characteristics of a stone column reinforced foundation are different from those of fine-grained soils with drain wells, the following assumptions were made. (i) stone columns are freedraining at any time and each stone column has a circular influence zone, (ii) the surrounding soil is fully saturated, and water is incompressible, (iii) stone columns and the surrounding soil only deform vertically and have the equal strain at any depth and (iv) the load is applied instantaneously through a rigid foundation and maintained constant during the consolidation period. Based on the above assumptions including equal strain condition the equation (2.19) is modified as c ' 1 r r u r 2 u 2 r ' c v 2 u 2 z _ u t (2.20) where c r =( k r / w )[m vc (1-a s )+m vs a s ]/[m vs m vc (1-a s )], a modified coefficient of consolidation in the radial direction; and c r =( k r / w )[m vc (1-a s )+m vs a s ]/[m v,s m v,c (1-a s )], a modified coefficient of consolidation in the vertical direction. The stress concentration ratio, n s, can also be defined as the ratio of the total vertical stress on the columns to that on the soil at certain time t. The steady vertical stresses within the stone column and the surrounding soil cs and ss, respectively, can be rewritten as m E cs vs c n s (2.21) ss mvc Es where E c and E s are the elastic moduli of the stone column and the surrounding soil, respectively; c and s are the Poisson ratios of the stone column and the surrounding soil, respectively; and is a Poisson ratio factor.

25 31 The modified coefficients of consolidation are expressed using the stress concentration ratio n s as in equation ' 1 1 ' 1 c r cr ns ; c c 1 n ; 2 v v s N 1 N 2 1 (2.22) where N = a diameter ratio (a/b). The new solutions demonstrated the stress transfer and the dissipation of excess pore water pressures due to drainage and vertical stress reduction in the process of consolidation. Comparison between the results from this simplified method and the numerical study by Balaam and Booker (1981) exhibited reasonable agreement, especially when the stress concentration ratio is within a typical range (26). Han and Ye (2002) continued their research work to bring out the effect of smear and well resistance on consolidation rate and derived a factor known as modified coefficient of consolidation. Solution to get the average degree of consolidation incorporates a well resistance factor, which takes care of the smear effect. A parametric investigation revealed that the factors influencing the rate of consolidation are the diameter ratio of influence zone to stone column, permeability of stone column, stress concentration ratio, the size of smeared zone, permeability of smeared zone and thickness of soft soil. Fessi and Bouassida (2005) investigated the settlement estimation of soils reinforced by stone columns using a poroelastic model. A unit cell model is used and analysed. An analytical poroelastic solution was derived that provides, in addition to the degree of radial consolidation and excess pore water pressure dissipation, the evolution with time of the reinforced soil settlement. The latter is predicted by introducing the concept of equivalent membrane assuming a uniform excess pore water pressure in the soft clay. The radial water flow towards the column will be controlled through this

26 32 equivalent membrane. The Barrons radial consolidation theory is also adopted that provides the determination of the permeability of this equivalent membrane. The solution to the poroelastic problem reduces to that of an elastic problem of a composite cell subjected to a uniform displacement at the top surface and an isotropic state of stress within the soft clay, corresponding to the excess pore pressure in the clay. 2.6 EXPERIMENTAL STUDIES ON STONE COLUMN From full scale field tests, Munkfakh et al (1983) showed the effectiveness of the vibroreplacement stone columns in improvement of the stability of the embankment that modeled the actual design of a wharf structure. The test program consisted of installation of stone columns, the construction of a reinforced earth embankment on the stone column stabilised soil and on untreated insitu soil, and monitoring the behavior of treated and untreated foundation soils for a specific consolidation period using proper instrumentation system. At the end of consolidation period, the stability of both the embankments was analysed. The findings of this field study confirmed that the stone columns improve the stability of embankment constructed on soft cohesive soil and slope cut made in this soil. It effectively reduced total settlements, horizontal displacements, and accelerated consolidation. The time for 100 percent primary consolidation of the stone column treated area was equivalent to that of 25 percent consolidation of the clay stratum outside the stone column area. Mitchell and Huber (1985) studied the performance of stone columns installed to a depth of 15m in soft estuarine deposit to support a wastewater treatment plant. Vibro-replacement stone columns were installed to support distributed foundation stresses up to 145 kpa. The basic design requirement was a loading of 265 kn stone column with a settlement of less than 6 mm under that load in a test on a single column within a group.

27 33 Column spacing ranged from a 1.2 m x 1.5 m pattern under the most heavily loaded areas, to a 2.1 m x 2.1 m pattern under lightly loaded areas. Twentyeight single column load tests were done during the installation of the 6,500 stone columns to evaluate load-settlement behavior. Laboratory tests were also conducted to provide soil property data needed for finite element analysis for the predictions of both the load test behavior and settlements of the completed structures. Predicted load test settlements were somewhat greater than those recorded during the load tests, but agreement was generally good. The installation of stone columns led to a reduction in settlements to about 30-40% of the values to be expected on unimproved ground. The settlement of a large uniformly loaded area of improved ground was predicted to be about ten times that measured in a load test on a single column within the area. Measured settlements varied from 25-60mm for a soft sediment thickness of m. A settlement of about 64 mm was predicted by the finite element analysis. Bergado and Lam (1987) conducted full-scale field load tests on soft Bangkok clay stabilised with granular piles of different densities and mixtures of soft gravel and sand. A total of 13 granular piles of 0.30m diameter and 8.0m long each at spacing of 1.2m installed in a triangular pattern were tested. The piles were categorized into five groups. Groups 1, 2 and 3 with 3 sand piles in each group were compacted at 20, 15 and 10 hammer blows per layer respectively. Group 4 was piles made of gravel mixed with sand in the proportion of 1:30 by volume and group 5 was made of gravel alone. Both the groups consisted of two piles and each was compacted at 15 blows per layer using the same hammer energy. The ultimate capacity of each granular pile was determined from load test results and found that the pile that was compacted at 20 blows/layer showed the higher capacity. The group 5 granular piles yielded the highest ultimate capacity. From the study it was found that gravel was the most efficient

28 34 granular column material having higher friction angle at lower compaction energy and the maximum bulging occurred between 10 and 30cm below the ground surface. Madhav and Thiruselvam (1988) studied the effect of method of installation on the behaviour of granular pile reinforced soil. The behaviour of a large group represented by a single unit consisting of a granular pile surrounded by the soil is studied in the laboratory in a CBR mould. Cased and uncased bore holes, amount of compactive energy, number of lifts, spacing of granular piles are the factors studied. The load carrying capacity of granular piles is more and their settlement is less in case of cased than uncased installation. Similarly the larger the compactive energy, the more the number of lifts, and the closer is the spacing, the better is the response of the granular piles. Narasimha Rao et al (1992) conducted experimental studies on single column and continued the work (Rao et al 1997) on group of columns comprising 2, 3 and 4 columns in soft clay to study the influence of moisture content of the soft clay and the effect of slenderness ratio (L/d) of the stone column. The results showed that the presence of stone columns increases the support capacity of the soft clay by 2 to 3 times. The other conclusions drawn are as follows: Consistency index plays an important role in load carrying capacity of the stone column, since the load carrying capacity of stone column depends on the extent of bulging of column. It was found that the increase in consistency index increases the capacity under the imposed load, and the stone column bulges satisfactorily in a soil with consistency index of 0.5. The L/d ratio is an important parameter for the mobilisation of skin friction. The overall length of the column, diameter of the

29 35 column and bulging control the skin friction. The ideal L/d ratio of stone columns for the consistencies tested is in the range between 5 and 10. The end bearing values are more in short columns particularly in column with L/d = 2.5; however the contribution due to end bearing is less with L/d and is negligible for longer columns (i.e. higher slenderness ratio). The optimum L/d is 5 to 7, beyond this critical length there is no significant increase in the load carrying capacity. The size of the bearing area has significant effect on the load carrying capacity of stone columns with lower L/d ratios. At higher values of L/d of 7 to 9 the increase in bearing area has no influence on capacity. Also the contribution from the end bearing on limiting axial stress is very little compared to that due to skin friction. Group effect in stone column foundations was studied by Wood et al (2000). In this study, model tests were conducted to know the mechanism of response for beds of clay reinforced with stone columns subjected to surface footing loads. The columns were constructed using sand by a replacement technique and were of floating type. A constant rate of loading of 0.061mm/min was adopted to ensure a drained condition. An exhumation technique was adopted to discover the deformed shapes of the model stone columns with a view to deduce the way by which the columns transfer loads to the surrounding clay. Tests have also been conducted to explore the effect of varying diameter, length and spacing of the model stone column on load transfer mechanism. Miniature pressure transducers have been used to reveal the distribution of contact pressure between columns and clay at various stages during the loading of the footings. From the test on column groups it

30 36 was reported that the columns at mid-radius of the footing are typically the most heavily loaded columns. When a column is loaded and not prevented from expanding radially by adjacent columns of the group, the mean stress increases in the column, and it bulges laterally. If a column is subjected to high stress ratios with little lateral restraint, and hence little opportunity for increase in mean stress, then a diagonal shear plane may form through the column. If a column is sufficiently short for significant load to be transmitted to the base of the column then it will penetrate the underlying clay. Mckelvey et al (2004) conducted tests on floating stone columns in transparent material with clay like properties and in kaolin clay. Tests in kaolin clay were conducted to investigate the load deformation characteristics of reinforced soil. Transparent material is used to have a visual examination of deforming granular columns during loading with circular, strip and pad foundations. Uniformly graded fine sand was used to form granular columns in both test series. The results showed that the presence of columns significantly improved the load carrying capacity of soft clay. However the columns longer than 6 times their diameter did not indicate further increase in capacity. Studies also showed that bulging was significant in long columns (L/d > 6) and punching was predominant in shorter columns. The columns bulged in the unrestrained directions, hence the centre columns bulged uniformly, whereas edge columns bulged away from the neighbouring columns. At lower loads, long columns (L/d=10) showed a stress concentration ratio of 4, but short columns (L/d<6) showed a stress concentration ratio of 2. At higher loads the stress concentration ratio appeared to reach a constant value of approximately 3.

31 37 Large triaxial samples of kaolin clay (100mm diameter and 200mm height) were reinforced with vertical columns of sand by Black et al (2007). Tests were carried out on single columns and three column groups. It was found that the samples reinforced with an isolated, fully penetrating column with area ratio 10% showed strength increase of 33% over that of samples with no columns. Group of columns with same area replacement ratio made no particular difference in the load carrying capacity. 2.7 NUMERICAL STUDIES ON STONE COLUMN Mitchell and Huber (1982) conducted an axisymmetric finite element analysis of the stone column system using an axisymmetric computer program developed by Duncan (1970). The undrained test results were used to define soil strength and deformation parameters for the short-term load test; whereas, the drained test results were used to estimate long-term settlements. Non-linear, stress dependent material properties can be used in the analysis. To account for the presence of other individual columns, cylindrical rings of elements containing stone column material properties were included in the finite element model. Using the finite element method, vibro-stone columns formed to support a large waste water treatment plant founded on 15m soft estuarine deposit was modeled and analysed. The predicted settlements were closely in agreement with the settlements measured from the field load tests and the computed stress concentration ratio from the analysis was between 2 and 3. Further it was stated that the modulus of stone column material has limited effect on the calculated settlement values, which indicates that the accurate determination of its stiffness value is not very much necessary for establishing structural settlements. Lee and Pande (1998) proposed a numerical model to analyse elastic as well as elastoplastic behavior of stone column reinforced foundations. The stone columns are assumed to be dispersed within the insitu

32 38 soil and a homogenisation technique is invoked to establish equivalent material properties for insitu soil and soil column composite. In this approach, both the clay and the stone column are assumed to behave elasto-plastically and a separate yield function for each constituent material is considered. The insitu soil is represented by the modified cam clay model, and the stone column is modeled by the Mohr-Coulomb criterion. The proposed model is implemented in an axi-symmetric finite element code and numerical prediction is made for the behaviour of model rigid circular footings resting on stone-column reinforced foundations. This prediction is validated through a test on stone column reinforced foundations where the stone columns of 17.5mm diameter are arranged in a square array (5x5 columns) and are installed by the replacement method having 30% of volume ratio. In the proposed procedure, equilibrium as well as kinematic conditions implied in the homogenisation procedure are satisfied for both elastic as well as elastoplastic stress states. The prescribed settlement versus vertical stress curve shows that the numerical prediction is in good agreement with the vertical stress measured underneath the rigid footing. Schweiger and Pande (1986) performed numerical analysis for settlement and failure loads of rafts resting on stone columns reinforced soft clay assuming equal strain condition. A constitutive model is presented for an equivalent material consisting of soil and columns which includes critical state model for clay and Mohr-Coulomb criterion for gravel. The proposed model is incorporated in a FE code. The problem of a circular footing is solved by employing this method by varying the spacing of columns and dilatancy angle of the column material. Flexible and rigid foundations are considered. Stresses in column are significantly high for the flexible raft, the maximum being at the top or slightly below the surface. Maximum plastic strains are observed at the top for a dilatant column under a flexible

33 39 foundation whereas the strains are small for the columns under the rigid foundation. Hird et al (1992) developed a methodology for representing vertical drains in plane strain finite element analyses of embankments on soft ground. Criteria for matching the effect of single drain in axisymmetric and plain strain analyses were developed. Matching is achieved by adjusting the geometry (drain spacing) and/or the permeability of the soil. For modeling the effect of vertical drains in plane strain analyses, the matching is done for the time taken for a given degree of consolidation to be achieved by horizontal drainage under plain strain and axisymmetric conditions. The proposed matching procedure has been validated for drains installed in uniform soil with linear compressibility characteristics. The average degree of consolidation obtained from both geometry-matched and permeabilitymatched models are in good agreement with the theoretical results of Hansbo (1981). Kirsch and Sondermann (2003) carried out a numerical analysis on the ground improvement by stone columns. Ground improvement improves the performance of soil not only by the reduction of the total settlement under load but also by speeding up the process of settlement. To simulate these consolidation effects with finite element procedures it is necessary to follow the concept of effective stresses. Hence the structural deformation has to be coupled with the field of the pore water pressures. In the following equation system, having both displacements u and pore water pressures p as nodal degrees of freedom, the stiffness-matrix K, the matrix of permeability H and a coupling matrix Q are given by, (2.23)

34 40 By the numerical solution of this system of differential equations the direct coupling of structural and fluid mechanics is achieved. For the necessary integration over time the implicit backward Euler method is used. Comparisons with conventional design methods are used to check their usefulness for the analysis of column groups and the interaction of soil, columns and footing. The quality of the method proposed, was brought out with some examples of numerical analyses both of in-situ measurements and laboratory model tests. The validation with in-situ measurement and laboratory model tests provide reasons for developing more accurate numerical simulation techniques. Huang et al (2001) conducted laboratory tests to study the interaction between granular column and surrounding soil. Four types of conventional and modified triaxial tests were performed on gravel-clay specimens under constant confining pressure to get the relationship between the two materials; so that they can describe the interaction between the reinforcement and surrounding soil. The results show that the radial stress, r of reinforcement is significantly larger than the cell pressure while the clay is weakened a little. According to the numerical analysis, this phenomenon is caused by the dilatancy of gravel. As a result, the gravel column weakens the clay while the clay strengthens the gravel. But for the composite specimen, the strength was increased. The results also show that it is necessary for surrounding soil to provide enough confining pressure for the granular reinforcements so as to increase the strength of the composite ground with gravel columns. Based on Duncan-Chang Model, a simple method called Non-perfect Elastic Model was presented to analyse numerically the stress and strain reaction of specimens with circular symmetry due to axial loading. From the study Huang et al (2001) concluded that along with the radius from core to outer face, the radial and circumferential stresses of

35 41 column are constant and significantly higher than cell pressure, while the radial stress of soil declines from that high value to cell pressure; that of foundation soil, which is also minimum principle stress, is much lower than cell pressure in the interface. It can be also said that soil strengthens the gravel column by weakening itself a little. But for the composite specimen, the strength increases. The lower the cell pressure, the more is the strengthening of column and weakening of foundation soil. The surrounding soil should be strong enough to provide sufficient confining pressure for the granular reinforcements so as to increase the strength of the composite ground. Ambily and Gandhi (2007) carried out experimental and finite element analyses to study the effect of shear strength of soil, angle of internal friction of stones, and spacing between the stone columns on the behavior of stone column stabilised bed. Experiments were carried out by loading the column area alone as well as the entire unit cell area to study the limiting axial stress on the stone column and stiffness of the stabilised ground respectively. It was concluded that when column area alone is loaded, failure is by bulging with maximum bulging at a depth of about 0.5 times the diameter of stone column. The axial capacity of column decreases and settlement increases upto a s/d (spacing/diameter) of 3, beyond which the change is negligible. The ratio of limiting axial stress on column to corresponding shear strength of surrounding clay is found to be constant for any given s/d and the angle of internal friction of stones and it is independent of the shear strength of the surrounding clay. Guetif et al (2007) simulated the installation of stone column in soft clay by adopting a composite cell model. The simulation using Plaxis software demonstrates a significant improvement of the characteristics of soft clay subjected to vibrocompacted column installation. The process of

36 42 installation, consolidates the soft clay and improves the modulus of soil surrounding the column. It was further reported that, immediately after column installation, high excess pore pressures are developed in the surrounding soft clay with unchanged effective mean stress. However, in the drained column material the effective mean stress increases to about four times with respect to that predicted in soft clay. After a period of 11 months, during which the primary consolidation in the soft clay has taken place after the stone column installation, a quasi-total dissipation of excess pore water pressures with significant increase of the effective mean stress is caused by the increase of effective radial stress. 2.8 THEORETICAL STUDIES ON ENCASED STONE COLUMN Alexiew et al (2005) reported that Geosynthetic Encased Columns (GECs) include a high-modulus, creep resistant geotextile encasement called Ringtrac that confines the compacted sand or gravel column thereby providing constructability and bearing capacity even in extremely soft soil. The specific characteristics of the GEC system as reported are as follows: 1. The primary function is the radial confining reinforcement of the bearing column. 2. The secondary functions are separation, filtration and drainage. 3. The system is not completely settlement-free. 4. The GEC is typically an end-bearing element transferring the loads to a firm underlying stratum. 5. The GECs are water-permeable; they practically do not influence the flow of groundwater streams, which has its ecological advantages. 6. The GECs also may perform as high-capacity vertical drains, although it is not their primary function.

37 43 The GECs are significantly stiffer than the surrounding soil, the pressure acting on the adjacent soil is lowered resulting in an overall reduction of the total settlement. The design procedure (Raithel et al 2005) is based on the unit cell concept shown in Figure The average vertical stress from the overlying embankment acts over the hexagonal area of influence of a single column unit area (A E ). This stress is equivalent to the higher stress imposed on the column ( v,c ) acting over the area of the column (A c ) plus the lower vertical stress ( v,s ) acting over the area of the adjacent soil (A E - A c ). The difference in vertical stresses acting over the column due to concentration and the adjacent soil creates a corresponding difference in a ring tensile force in the geotextile. This confining tensile force in the encasement provides the missing component for the state of equilibrium. As shown in Figure 2.11, there is an additional horizontal stress in the column h,c (index h = horizontal) due to the additional vertical stress v,c (index v = vertical) over the column head. In view of the equilibrium between the additional surface loading and the corresponding vertical stresses on the column v,c and the soft soil h,s, it can be stated:. A E = v,c. A C + v,c. (A E - A C ) (2.24) The vertical stresses due to the loading and the different soil weights produce horizontal stresses ( v,0,c and v,0,s are the initial vertical stresses in the column and the soil if the excavation method is used, K 0,s* must be substituted by K 0,s ): h,c = v,c. K a,c + v,0,c. K a,c (2.25) h,s = v,s. K 0,s + v,0,s. K 0,s * (2.26) The geotextile casing (radius r geo ) has linear-elastic behaviour (stiffness J), whereby the ring tensile force FR can be transformed into a horizontal stress h,geo, which is assigned to the geotextile:

38 44 F R = J. r geo /r geo and h,geo = F R /r geo (2.27) By the use of the separate horizontal stresses a differential horizontal stress can be defined, which represents the partial mobilisation of the passive earth pressure in the surrounding soft soil: h,diff = h,c ( h,s + h,geo ) (2.28) Figure 2.11 Calculation model for encased stone column (Raithel et al 2005) The stress difference results in an expansion of the column. The horizontal deformation r c and the settlement of the soft soil s s are calculated according to Ghionna and Jamiolkowski (1981). Assuming equal settlements of column s c and soft soil s s, the following calculation equation 2.29 can be derived (oedometric modulus E oed,s, Poisson ratio s). This equation can be solved by iterative procedure. The oedometric modulus E oed,s of the soil should be introduced stress dependent. It was concluded that the entire reinforced GEC system is strongly strain - dependent, and the behavior of GECs is "softer" in relation to traditional piles. It is an interactive, ductile, self-regulating system.