Soil-Stone Column Interaction

The performance of floating stone columns (FSCs) has been recently adopted to improve thick soft clay deposits, but their behavior is not yet fully understood. To provide a comprehensive understanding, field load tests were conducted with varying area replacement ratios and length-to-diameter ratios (L/D) at Misono-cho, Suzuka City, Mie Prefecture, Japan. Bulging failure modes were observed using strain gauges, and stress sharing between the stone columns and the surrounding soil was monitored using earth pressure cells. The PLAXIS 3D FEM program was used to conduct finite-element computations on 10-noded tetrahedral elements. The FEM model was calibrated and adjusted to account for the installation effects of FSCs and aligns closely with the outcomes of the field test. The settlement improvement factor for FSCs was found to be slightly higher in the long term compared to the short-term condition. Moreover, the settlement improvement factor increases with the applied stress and over time. The ultimate bearing capacity of FSCs depends on the additional confinement provided by adjacent columns. An improved model and design charts were proposed to estimate the ultimate bearing capacity and settlement of FSC-improved ground, showing lower relative error compared to other published results. Finally, a design procedure was anticipated to assist geotechnical engineers in designing FSCs constructed in soft clay.

Stone columns are an efficient ground improvement technique for treating problematic soils. The confidence in the prediction accuracy of bearing capacity remains unsatisfactory. This paper aims to investigate the bearing capacity of single stone column using three-dimensional numerical analysis. Failure modes were observed and the effect of key parameters such as column's friction angle, undrained shear strength of surrounding soil and modular ratio were investigated. Numerical results showed bulging and a combination of bulging and punching are two dominant failure modes for the single stone column. Ultimate bearing capacity is mainly influenced by the column's friction angle and the undrained shear strength of the surrounding soil. Based on the results, a new prediction method is developed and compared reasonably well with the existing analytical solution and the field measurements.

This study used a finite element analysis approach employing Plaxis 3D to analyze the stress concentration ratio, a critical parameter in geotechnical engineering, to examine stresses operating on stone columns and soft soils. This study also looked at the effect of the stiffness ratio between the stone column and the neighboring soil. With the same length and three different diameters, 0.8 m, 1.0 m, and 1.2 m, or three area replacement ratios ranging from 7% to 16%, respectively, floating and end-bearing stone columns were used. The influence of soft soil undrained cohesion, cu ranging from 6 kPa to 40 kPa, was also considered in the current study. The stiffness ratio for columns to adjacent soil, end bearing or floating stone column, and area ratio all have a significant impression on the performance of the stone column in treating soft soil and stress transmission mechanisms in the enhanced soil body, according to parametric studies. The average stress concentration ratio in soil...

Stone columns are one of the common types of ground improvement methods that applied to reduce the settlement and increase the stability of structures. This paper focuses on the non-uniform diameters of the stone column and aimed at providing some practical insights into the design by reducing the constructing material of the stone column with increasing the bearing capacity of the soft soil. In this study, two dimensional (2D) Finite Element analyses through PLAXIS 2D were performed to investigate the bearing capacity of uniform and non-uniform stone columns in soft soil. A Mohr-Coulomb constitutive soil model was adopted in the numerical analyses. The non-uniform stone columns modelling by creating two different diameters and lengths. The upper diameter d 1 was always larger than the lower half diameter d 2 with investigated ratio d 2 : d 1 of 1:2, 1:4 and 1:5. The columns were 10 m long but varied in diameter length with nine different length ratios (l 1 : l 2). By comparing between uniform and non-uniform shapes, one can determine the optimum column's design. The highest bearing capacity obtained by the non-uniform stone column was one with the d 2 :d 1 ratio equals to 1:5. The most economical shape for the stone column (the least volumes used to construct stone columns) was achieved at a ratio of d 2 :d 1 = 1:2 and a length ratio of l 1 :l 2 = 3:7.

Mumbai marine clay is problematic in nature for substructures and it needs to be strengthening before making it available for any construction activity. Out of many available geotechnical solutions, stone columns are quite handy in significantly improving the bearing capacity of marine clay, which also supplements by dissipating excess pore water pressure and reducing the settlements of clay beds under external loads. For the investigation on behavior of stone columns, marine clay was collected from the Uran site near Mumbai, India. Slurry consolidated clay beds were prepared and gravity loading mechanism was adopted to consolidate the clay beds in the laboratory. Laboratory tests were performed to ascertain the uniformity and repeatability of the clay beds by slurry consolidation. Augers of 50, 75 and 100 mm diameter were used to bore the holes in the clay bed and aggregates were used for stone column preparation by replacement method. The static displacement controlled tests were performed on the stone column reinforced clay bed. In the present study, the loading is applied on stone column alone, as it leads to the ultimate axial capacity of stone column improved ground. Clay bed reinforced with stone column exhibits improved load-settlement response, compared to unreinforced clay beds. The improvement was very significant at higher settlements. The failure load of reinforced clay bed is around 6 times more than the unreinforced clay bed. In order to further understand the behaviour of stone column reinforced ground, numerical modeling of stone column reinforced clay bed is conducted using FLAC 3D. Using the validated numerical model of the stone column, the effect of variation of the diameter of stone column on its performance was studied. From the numerical analysis and physical tests conducted in laboratory, it is observed that the stone columns with smaller diameter when subjected to vertical loading carried higher bearing pressures when compared to that of the larger diameter stone columns, which may be due to the greater confining and larger bulge formed at a depth of 2-3 times the diameter of stone columns.

This paper presents two set of 2D finite element analyses that study on the settlement ratio of floating stone column for small and large column groups. The settlements of floating stone columns are difficult to be predicted especially for large column groups. Unit cell model was used in this study for large column group assuming infinite column grid. The influence of key parameters such as column length, area replacement ratio, loading intensity and post installation lateral earth pressure on the settlement ratio were investigated. Based on the results, a simplified solution was proposed to calculate the settlement ratio for floating stone columns. On the other hand, the settlement performance of floating stone column in small group was examined for different area replacement ratio and column length. Design chart developed from this study was validated by a case study where a reasonable agreement was obtained.

This study investigates the effectiveness of encapsulated polypropylene (PP) column in enhancing the undrained shear strength of kaolin (soft clay). The usage of PP in treating problematic soil is a more sustainable and cost-effective alternative compared to other materials. The installation of granular column can be done by using vibro-replacement method. Several geotechnical tests to determine the properties of materials were conducted. The shear strength of treated kaolin sample was examined by using Unconfined Compression Test (UCT). There are seven (7) batches of soil sample in total which included a control sample, three (3) batches of 14 mm and three (3) batches of 20 mm diameter PP column. Different diameters of PP column were examined with 60 mm, 80 mm and 100 mm height, respectively with soil sample of 50 mm in diameter and 100 mm in height. The shear strength improvement of kaolin is 33.82%, 46.51%, and 49.88% when implanted with a PP column with a 7.84 area replacement ratio and 0.6, 0.8 and 1.0 penetration ratio. The soft soil treated using 16.00 area replacement ratio with 0.6, 0.8 and 1.0 penetration ratio has a shear strength increment of 25.22%, 33.39% and 37.59% respectively. In short, the shear strength improvement of the kaolin clay depends on the parameter of the PP column used to reinforce the sample.

Background: In weak clay soil, a proper ground improvement technique using a stone column can be limited by the absence of sufficient lateral confining pressure. Stone columns should be strengthened to provide the minimum required lateral confining pressure. Objective: The aim of this study is to find out the significant improvement of the composite stone columns compared to the conventional stone columns by comparing the bearing capacity enhancement and the treated soil stiffness for both models. Composite stone columns with a solid concrete part at the top-head not only enhance the bearing capacity of the stone columns but also decrease the bulging failure and increase the surrounding soil stiffness. Methods: The 2D finite element analyses were carried out to simulate an experimental study conducted by Ambily and Gandhi on conventional stone columns. ABAQUS software program with the Mohr-Coulomb criterion for soft clay soil and stones was used in the simulation. First, a prelimina...

Soft Clay is often known to be a problematic soils in construction because of its low strength and high compressibility characteristic. Before construction begins, ground improvement needs to be done to improve the soil bearing capacity so that the superstructure can be placed on top of it and reduce settlement and consolidation. In this study, the soft clay is going to be reinforced with crushed brick column which is part of construction waste produced during construction stage to achieve sustainable construction. This study was aimed to investigate the effectiveness of single and group crushed brick column in improving the shear strength by using laboratory scale model. Kaolin is being used as soil sample while crushed brick as the reinforced column. Few laboratory tests are conducted to determine the properties of kaolin clay and crushed brick. Unconfined Compression Test (UCT) also used to test the shear strength of the reinforced kaolin samples The improvement of shear strength of single crushed brick column with area replacement ratio of 4.00% (10mm column diameter) are 3.34%, 4.60% and 1.07% at sample penetration ratio, Hc/Hs of 0.6, 0.8 and 1.0 respectively while for area replacement of 10.24% (16 mm column diameter) are 7.56%, %, 16.37% and 4.97% at the same penetration ratio.. The result shows that the improvement shear strength for height penetration ratio of 1.0 is 13.33% which was the highest, while 0.6 and 0.8 are 12.31% and 9.79% respectively for group crushed brick columns with diameter 10mm. The improvement of shear strength is highest for height penetration ratio of 1.0 with 16.10% improvement which was slightly higher than 0.6 and 0.8 which were 13.49% and 11.35% respectively in sample reinforced with grouped columns with diameter 16mm. It can be concluded that the shear strength of soft clay could be improved by installation of single and group crushed brick column.

Ground improvement via stone column has gained popularity around the globe as an effective ground improvement technique to improve the load bearing capacity of soft soils. End-bearing stone columns are commonly used but occasionally floating stone columns are adopted as it has been proven to achieve the necessary load carry capacity and serviceability requirements. However, stone column parameters are often estimated without much basis for simulation and design purpose due to lack of practical research and real-life case studies in this area. Hence, in order to develop fundamental understanding on the load-settlement responses of the floating stone columns in soft clays, detailed back-analysis was performed in this paper. Throughout the back-analysis, all the numerical models were validated by comparing the analysis results with the field measurements. This study highlights (i) the existence of some critical interpreted parameters, namely soil cohesion, c', friction angle, ' and dilation angle, ' as well as (ii) soil-structure interaction mechanism that influences the load-settlement responses of the floating stone columns. The successful characterization of the stone column materials and the modeling technique of stone columns in finite element analyses have shown great potential in assessing the real-life performance of floating stone columns in soft clays.

Numerous approaches exist for the prediction of the settlement improvement offered by the vibro-replacement technique in weak or marginal soil deposits. The majority of the settlement prediction methods are based on the unit cell assumption, with a small number based on plane strain or homogenization techniques. In this paper, a comprehensive review and assessment of the more popular settlement prediction methods is carried out with a view to establishing which method(s) is/are in best agreement with finite element predictions from a series of PLAXIS 2D axisymmetric analyses on an end-bearing column. The Hardening Soil Model in PLAXIS 2D has been used to model the behaviour of both the granular column material and the treated soft clay soil. This study has shown that purely elastic settlement prediction methods overestimate the settlement improvement for large modular ratios while the methods based on elastic-plastic theory are in better agreement with finite element predictions at higher modular ratios. In addition, a parameter sensitivity study has been carried out to establish the influence of a range of different design parameters on predictions obtained using a selection of elastic-plastic methods.

The Stone-column is a useful method for increasing the bearing capacity and reducing settlement of foundation soil. The prediction of accurate ultimate bearing capacity of stone columns is very important in soil improvement techniques.Bulging failure mechanism usually controls the failure mechanism. In this paper, an imaginaryretaining wall is used such that it stretches vertically from the stone column edge. A simple analytical method is introduced for estimation of the ultimate bearing capacity of the stone column using Coulomb lateral earth pressure theory.Presentedmethodneeds conventional Mohr-coloumb shear strength parameters of the stone column material and the native soil for estimation the ultimate bearing capacity of stone column. The validity of the developed method has been verified using finite element method and test data. Parametric studies have been carried out and effects of contributing parameters such as stone column diameter, column spacing, and theinternal fricti...

A series of model footing load tests were carried out on floating stone columns reinforced clay bed to understand the load deformation behavior. All the experiments were carried out on stone columns in groups to understand the group effects and interactions. The parameters varied in this experimental investigation were length and spacing of the stone column without changing the undrained shear strength of the clay. The undrained strength of clay bed was kept constant as 5kPa in all the tests. In this paper the results obtained from experimental investigations were analysed in terms of load carrying capacity, deformation behaviour of stone column and the interaction amongst the stone columns. It was observed that the bearing capacity of the stone column reinforced clay bed can withstand a load more than 4 times that of the soft clay bed alone. The optimum length and spacing of the stone column were obtained from experimental results and strong interaction has been observed for too small spacing of stone column.

Numerous approaches exist for the prediction of the settlement improvement offered by the vibro-replacement technique in weak or marginal soil deposits. The majority of the settlement prediction methods are based on the unit cell assumption, with a small number based on plane strain or homogenization techniques. In this paper, a comprehensive review and assessment of the more popular settlement prediction methods is carried out with a view to establishing which method(s) is/are in best agreement with finite element predictions from a series of PLAXIS 2D axisymmetric analyses on an end-bearing column. The Hardening Soil Model in PLAXIS 2D has been used to model the behaviour of both the granular column material and the treated soft clay soil. This study has shown that purely elastic settlement prediction methods overestimate the settlement improvement for large modular ratios while the methods based on elastic-plastic theory are in better agreement with finite element predictions at higher modular ratios. In addition, a parameter sensitivity study has been carried out to establish the influence of a range of different design parameters on predictions obtained using a selection of elastic-plastic methods.

A series of model footing load tests were carried out on floating stone columns reinforced clay bed to understand the load deformation behavior. All the experiments were carried out on stone columns in groups to understand the group effects and interactions. The parameters varied in this experimental investigation were length and spacing of the stone column without changing the undrained shear strength of the clay. The undrained strength of clay bed was kept constant as 5kPa in all the tests. In this paper the results obtained from experimental investigations were analysed in terms of load carrying capacity, deformation behaviour of stone column and the interaction amongst the stone columns. It was observed that the bearing capacity of the stone column reinforced clay bed can withstand a load more than 4 times that of the soft clay bed alone. The optimum length and spacing of the stone column were obtained from experimental results and strong interaction has been observed for too small spacing of stone column.

The emphasis of current work is on assessing the settlement improvement ratio, which is described as the ratio between the settled soils treated with a stone column and the settlement of the non-treated soil (Sr = Streated/Suntreated). The research was conducted using a 300 mm diameter and 300 mm high stone-column container testing model. On 14 modeled stone columns made only from crush stones and using various backfill content, model tests including static axial compression tests were performed. The substance used in the stone backfill column had been changed by sand or lime or cement percentages. The shear strength prepared by the containers varied between 5.5 kPa and 13.5 kPa. Results show that the settlement ratio values, Sr achieved with crush stone, crushed stone +50% sand, crushed stone +5% dry lime, crushed stones +10% dry lime, crushed stone +2.5% cement +5.0% crushed stone +5.0% cement, respectively, was 0.23, 0.12, 0.16, 0.15 and 0.09. In other words, there is a drop in the settlement from 77% to 91%.

Numerous approaches exist for the prediction of the settlement improvement offered by the vibro-replacement technique in weak or marginal soil deposits. The majority of the settlement prediction methods are based on the unit cell assumption, with a small number based on plane strain or homogenization techniques. In this paper, a comprehensive review and assessment of the more popular settlement prediction methods is carried out with a view to establishing which method(s) is/are in best agreement with finite element predictions from a series of PLAXIS 2D axisymmetric analyses on an end-bearing column. The Hardening Soil Model in PLAXIS 2D has been used to model the behaviour of both the granular column material and the treated soft clay soil. This study has shown that purely elastic settlement prediction methods overestimate the settlement improvement for large modular ratios while the methods based on elastic-plastic theory are in better agreement with finite element predictions at higher modular ratios. In addition, a parameter sensitivity study has been carried out to establish the influence of a range of different design parameters on predictions obtained using a selection of elastic-plastic methods.

Arching is characterized by a stress distribution where the load is transferred from softer to stiffer regions of a structure forming a stable configuration. Since it is a stable arrangement, arching is not a typical limit state problem. However, it can be formulated in a manner that allows using the static theorem of limit analysis to assess the likelihood of arching. Radial stress fields within piles of sand are constructed to search for stress distributions that promote arching. Governing equations are derived for radial stress distributions with regions varying from the yielding stress state to the elastic stress state. The stress fields with an elastic core promote arching, whereas the field where all material is in the active limit state does not support arching. However, if a passive limit state is induced in a sand heap, arching over the central part of the pile base becomes a distinct feature of the fully plastic stress field. Considerations are limited here to wedge-shaped sand heaps, though many of the conclusions are applicable to conical (axi-symmetrical) sand piles.

The current rate of development in the construction industry has given rise to higher demands for land. In pursuit of satisfying the needs of property developers, engineers have resorted to new ground improvement technologies to eventually implement construction on lands which were previously regarded as unfeasible or uneconomical for this purpose. This study therefore aimed at investigating the potential use of singular stone columns in improving a soft wet clay of South African origin. Bench scale tests were conducted to evaluate the effect of the moisture content of the base soil and the column diameter. The results indicated a clear improvement in the vertical applied stress as well as in the settlement of the clay, when subjected to a compressive load. These findings were ultimately used to generate information regarding the stress concentration ratio and the settlement reduction ratio.

Stone columns have proved to be the most suited technique for improving the bearing capacity of weak or soft soils. Being cost effective and environmental friendly, stone columns are used worldwide for supporting flexible structures such as embankments, oil storage tanks etc. which can tolerate some settlements. However, when the stone columns in very soft soils are loaded; stone columns undergo excessive settlement due to low lateral confinement provided by the soft soil, leading to the failure of the structure. The excessive settlements may be avoided or at least reduced to a great extent, when the columns are encased with a suitable geosynthetics. In the present study, the effect of reinforcement on bearing capacity of composite soil has been investigated by conducting laboratory plate bearing tests on model floating and end-bearing single stone columns of 30 mm diameter and 300 mm length. The columns were reinforced by providing geosynthetic encasement over varying column length...

A number of methods are introduced to estimate the ultimate bearing capacity of weak clayey soils stabilized with stone piles. Most of these methods are based on a plane strain failure mechanism. The present study introduces a theoretical method for estimating the maximum load that can be carried by soft clayey soils reinforced with a stone pile. This method is based on establishing the theoretical failure planes assuming that the surrounding soil would fail under a passive earth pressure condition due to the bulging of the stone pile. These failure planes are established based on the Terzaghi's (1943) method, and the stresses along these planes are analyzed to finally obtain the load the column can carry. To verify the results of the present study, a comparison is made with previous well known studies.

Two analytical closed-form elastic-rigid-plastic solution methods to predict the rigid foundation behaviour on stone-column reinforced soil are compared, both of which takes into account the stone material yield within the host soil according to stress-dilatancy theory. These are the mechanistic methods developed by the author (2004, 2005) [that presently incorporates the dilatancy angle as per Schanz and Vermeer (1996)] and that developed by Pulko and Majes (2006), that takes into account the column yield as per Rowe dilatancy theory. Since optimal design of stone column necessitates optimum stress concentration on column, which is generally composed of dense gravel with/or without sand, the vertical stress on granular column is often close to its peak strength and the material dilates. To arrive at closed-form analytic solution to this complex soil-stone column interaction problem, some common assumptions like axi-symmetric soil-stone column 'unit-cell', elastic host soil and rigid-plastic Mohr-Coulomb stone column material are combined with equilibrium and kinematic conditions. The results reflect the beneficial effect of dilatancy within the optimal range or techno-economic domain of area-ratio. The settlement predictions are compared with other analytical methods available in literature as well as with measured settlement reduction of stone-column reinforced ground at different subsoil conditions around the globe reported in literature.

The stone columns improve the performance of foundations on soft and loose soil due to the ability of composite ground to sustain increased structural loads under reduced settlements. The interaction between the two basic elements: the ambient subsoil and installed column, present a complexity of behaviour, both in terms of applied stresses and resulting strains. Moreover, as the same is provided in-group in a regular array beneath foundations, the performance of an individual column is likely to be influenced by the presence of neighbouring columns. The present paper addresses this very issue. Analysis of reported field hydro-test data of large diameter oil storage tanks in soft ground in reference to some existing theories led to the development of the stone-column ‘group efficiency factor’. In order that such factor is of general use, it was felt necessary to examine the applicability of the factor to different sizes of groups under varied subsoil conditions. With this in view, some model test results reported in literature of single and group of columns have been analysed and in the process an explicit relationship regarding the stone-column ‘group-effect’ could be established.

The stone columns improve the performance of foundations on soft and loose soil due to the ability of composite ground to sustain increased structural loads under reduced settlements. The interaction between the two basic elements: the ambient subsoil and installed column, present a complexity of behaviour, both in terms of applied stresses and resulting strains. Moreover, as the same is provided in-group in a regular array beneath foundations, the performance of an individual column is likely to be influenced by the presence of neighbouring columns. The present paper addresses this very issue. Analysis of reported field hydro-test data of large diameter oil storage tanks in soft ground in reference to some existing theories led to the development of the stone-column 'group efficiency factor'. In order that such factor is of general use, it was felt necessary to examine the applicability of the factor to different sizes of groups under varied subsoil conditions. With this in view, some model test results reported in literature of single and group of columns have been analysed and in the process an explicit relationship regarding the stone-column 'group-effect' could be established.

–In finite element analysis, mesh size is a critical issue. It closely relates to the accuracy, computing time and efforts required for meshing of finite element models, which determines their complexity level. This paper presents study of the effects of mesh size on accuracy of numerical analysis results. Based on these results the guidelines for choosing the appropriate mesh strategy in finite element modelling are provided. The static and buckling analysis is carried out to know the effects of mesh sizes by using Femap and NX-Nastran. The model under study is of a structure made up of steel plate. Index Terms— Finite element analysis, mesh size, static analysis, buckling analysis. I. INTRODUCTION In finite element analysis (FEA), the accuracy of the FEA results and required computing time are determined by the finite element size (mesh density). According to FEA theory, the FE models with fine mesh (small element size) yields highly accurate results but may take longer computing time. On the other hand, those FE models with coarse mesh (large element size) may lead to less accurate results but smaller computing time. Also, small element size will increase the FE model's complexity which is only used when high accuracy is required. Large element size, however, will reduce the FE model's size and is extensively used in simplified models in order to provide a quick and rough estimation of designs. Due to its importance, in generating FEA models, the foremost problem is to choose appropriate elements size so that the created models will yield accurate FEA results while save as much computing time as possible. The objective of this paper is to present guidelines for choosing optimal element size for different types of finite element analyses. In order to achieve that goal, in this study, a series of static, and buckling analyses were performed on a structure model made up of plates to reveal the effects of the element size on the accuracy of the FEA results. The solver NX-Nastran and Femap pre and post-possessor, used for modeling and analyses involved in this work.

A series of model footing load tests were carried out on floating stone columns reinforced clay bed to understand the load deformation behavior. All the experiments were carried out on stone columns in groups to understand the group effects and interactions. The parameters varied in this experimental investigation were length and spacing of the stone column without changing the undrained shear strength of the clay. The undrained strength of clay bed was kept constant as 5kPa in all the tests. In this paper the results obtained from experimental investigations were analysed in terms of load carrying capacity, deformation behaviour of stone column and the interaction amongst the stone columns. It was observed that the bearing capacity of the stone column reinforced clay bed can withstand a load more than 4 times that of the soft clay bed alone. The optimum length and spacing of the stone column were obtained from experimental results and strong interaction has been observed for too small spacing of stone column.

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Numerous analytical approaches exist for the prediction of the settlement improvement offered by the installation of granular columns in weak or marginal soil deposits. In this paper, an appraisal of some of the more popular settlement prediction methods applicable to vibro-replacement design is carried out. The settlement improvement factors calculated using the different design methods are compared with both the 'bottom feed' and 'top feed' data from a previously published database of settlement improvement factors for stone columns in soft clays and silts. The calculated improvement factors are plotted as a function of the main variables in vibro-replacement design, namely the area-replacement ratio (a measure of the amount of insitu soil replaced with stone), and the modular ratio, which relates the stiffness of the column to that of the in-situ soil. In addition, finite element analyses have been carried out using PLAXIS 2D for comparison with both the field data and the design method predictions. Load settlement behaviour (primary settlement) has been analysed using the Hardening Soil Model to model the behaviour of both the column material and the treated soil. The majority of the design methods appear to predict similar settlement improvement factors. Purely elastic methods overestimate the settlement improvement factor for large modular ratios while it appears that better matches between finite element and analytical predictions are found at higher modular ratios, as the analytical methods assume a significant bulging mechanism which is more prevalent in soft soils.

Numerous approaches exist for the prediction of the settlement improvement offered by the vibroreplacement technique in weak or marginal soil deposits. The majority of the settlement prediction methods are based on the unit cell assumption, with a small number based on plane strain or homogenisation techniques. In this paper, a comprehensive review and assessment of the more popular settlement prediction methods is carried out with a view to establishing which method(s) is/are in best agreement with finite element predictions from a series of PLAXIS 2D axisymmetric analyses on an end-bearing column. The Hardening Soil Model in PLAXIS 2D has been used to model the behaviour of both the granular column material and the treated soft clay soil. This study has shown that purely elastic settlement prediction methods overestimate the settlement improvement for large modular ratios, while the methods based on elastic-plastic theory are in better agreement with finite element predictions at higher modular ratios. In addition, a parameter sensitivity study has been carried out to establish the influence of a range of different design parameters on predictions obtained using a selection of elastic-plastic methods.

This study investigated the behaviour of single rammed stone columns. Prior to this assessment, the load – settlement and bulging responses of the columns were evaluated by conducting laboratory tests using a specially designed bench scale tank. The latter was a mild steel cylindrical tank which represented unit cells reinforced with single stone columns. The testing technique enabled the evaluation of the influence of variation of column diameter on stone column deformation responses and also provided data that was compared with the numerical results. In the numerical analysis, Mohr-Coulomb and modified Drucker-Prager models were used in the idealization of the behaviour of the column and soil materials respectively. Results revealed that the bigger the column diameter, the higher the loading capacity of the columns. Increasing the column diameter,D by 1.5, 2 and 3 times its initial size generally led to improved load carrying capacity by approximately 2, 4 and 10 times the initial strength respectively. The radial expansion of the columns was prominent in their upper parts with the highest value being experienced at a depth of about 0.5D from the ground surface.

Reinforcement of ground by granular “pinning” are becoming increasingly popular and has been identified as an effective means of ground improvement technique. The composite mass has been found to carry higher loads at reduced settlements than virgin ground. The strain propagation along the cylindrical unit of soil encapsulating a stone column at the center being envisaged to be non-linear, full scale instrumented columns were load tested at two sites for multistoried buildings founded on stone column reinforced ground in Kolkata. The installation procedure followed rammed stone column technique. Four numbers of strain recorders were embedded within the test column along its axis at suitable depths to measure the shortening of the column under increasing stress levels. The load displacement data along-with the segmental strains, diametrical strain (2dh/d), column bulge (dh), proportion of axial-strain (dvz/dv), axial strain (dv/dz) are all plotted against normalized depths (z/H) for increasing stress levels. The stress-strain response believed to be site-specific and problem-geometry oriented, some interesting features of the response could be identified.

An effort has been made in the present investigation to explain the complex mechanism of soil-stone column interaction in the light of arching action of soils, which is–"one of the most universal phenomena encountered in soils both in the field and in the laboratory" as noted by Terzaghi (1943). Regardless of the plastic-versus-elastic state, simple force equilibrium at the column-soil boundary has been analyzed to explain the improvement in terms of the stress orientation angle- the natural free-standing, self-supported "thrust ring action" that follow the equation of a catenary-the shape taken by a chain held at the ends. The vertical, horizontal and shear stresses have been quantified in terms of the material properties of the in-situ soil and the installed column. The capacity of the stone column has been obtained using arching theory and findings are compared with some available results in published literature.

The study presents a mechanistic model backed by a detailed analysis of dilating granular column in soil-stone column interaction in ground improvement technology. For an optimal design of stone column, an optimum stress concentration on the column is required and the column material used being generally dense gravel with/ or without sand, the vertical stress on the stone column is often close to its peak strength and the granular material dilates. The effect of this dilatancy is investigated by incorporating a dilatancy factor in the proposed model. The results reflect the beneficial effect of dilatancy within the optimal range or economically feasible domain of area ratio. The settlement predictions are compared with Van Impe & Madhav’s (1992) model of dilating stone-column along-with measured settlement reduction of stone-column reinforced ground at different subsoil conditions reported in literature. The significance of inclusion of such refinement in the ‘unit-cell’ model to explain the reported settlement reduction of treated ground is highlighted.

Despite the widespread use of stone columns, present design methods are largely based on empirical data and / or simplified concepts of the action of columns. Nevertheless, this method has emerged as a powerful and effective means of ground improvement technique. The field application of the technology has developed much faster than the design methodology because the mechanism of interaction of load sharing between the two basic elements- the installed column and the native soil is complex, both in terms of induced stresses and resulting strains. As such, the soil-stone column interaction in field situations calls for a rational understanding, since the output behavior is influenced by the interdependence of the external stress level, the material properties of host soil and backfilled column, the column dimensions, construction procedure and its installation array. The present investigation analyzes some full-scale load test results in available literature (Prakash et al, 2005) on rammed stone columns installed in a wide range of alluvials ranging from loose to medium dense sands / silty sands and clayey silt / silty clays with and without fill over them. The back analysis is in the light of theoretical concepts and mechanistic models developed by the author (Saha, 2007). The extensive load tests and penetration tests prior to and after construction of columns and the extent of improvement achieved have been critically examined in the light of theoretical concepts encompassing the relevant design parameters, and some interesting findings are reported.

Analysis of consolidation of fine grained soils by drain-wells by Barron (1947) is a classical example of the underlying mathematics governing the radial flow through the installed well, usually consisting of sand as a backfill material. Till today, the most frequently and extensively used method to account for accelerating radial consolidation is due to his pioneering work. However, Barron equation accounts for the factors affecting the water dissipation through the drain-well, without navigating into the strength factor that the sand ‘well’ or ‘column’ incorporates to the virgin ground due to its inherent higher rigidity. The present analytical study ventures into this very issue of radial drainage vis-à-vis load-settlement behavior of the reinforced ground. The consolidation and simultaneous strength increase of the composite system has been investigated in predicting the performance of soil-stone column cylindrical ‘unit’ loaded by a rigid raft (equal vertical strain) at upper boundary.

The stone columns improve the performance of foundations on soft and / or loose soil by reducing settlements and increasing the load carrying capacity of the composite ground. The interaction between the two basic elements within the idealized ‘unit-cell’-comprising of the ambient subsoil cylinder encapsulating an installed granular column present a complexity of behavior under varying external stress levels both in terms of load transfer and the resulting strains. Moreover, since the same is provided in-group in a regular array beneath foundations, the performance of an individual column is likely to be influenced by the presence of neighboring columns. The overall output behavior of the composite foundation system is governed by the induced strains at the level of external load application as well as the soil-stone column material properties and unit-cell geometry. The present paper addresses this very issue. Series of full-scale load test data of tank foundation in soft ground has been analyzed with reference to some existing theories and the ‘group-effect’ of the complex mechanism brought out and discussed. Finally, a simple analytical method has been put forth, which incorporates the so-called group-effect and determines the ‘group interaction factor’ in soil-stone column interaction.

The present paper deals with genetic algorithms (GA) to find out the minimum Factor of Safety (FOS) of a virgin slope vis-à-vis stone column reinforced slope and highlights some potent points that emerged during the search process. GA-a new generation and nontraditional search and optimization procedure is fast becoming popular for its increased versatility in handling complex engineering problems, since it does not require problem specific knowledge for carrying out the search. It is a tool guided by stochastic principles instead of gradients and hence one has the liberty to start with a wide range of values (or a ‘population’ of points) for the decision variables to process the value convergence of the objective function to near optimal solution at a very rapid rate. The output is found to be independent of the value of the initial vector. The slope stability analysis is carried out on the computer using GA as a function optimizer in slope analysis. The present paper is a sequel to author’s previous study (2001, 2003a, 2003b) wherein the raw data of a virgin slope example cited by Spencer (1967) is used as input, and the output was obtained by integrating GA with Bishop's simplified method of slices (1960) for virgin slope and Author’s (2001) method for stone-column reinforced slope. The search process, besides unfolding increase in FOS of stone-column reinforced slope over virgin slope against failure on a cylindrical slip surface, unleashed some other powerful features that are described in the paper.

Ground improvement by installation of stone columns has emerged as a powerful and effective means of ground improvement technique. The field application of the technology has developed faster than the design methodology because the mechanism of interaction between the two basic elements- the installed column and the native soil is complex, both in terms of induced stresses and resulting strains. The output behaviour of the ‘unit-cell’ comprising of the column and soil is influenced by the interdependence of the external stress level, the material properties of host soil and backfilled column and its dimensions, the construction procedure and its installation array. An effort has been made in the present paper to predict the upper and lower bounds in application of this technology for optimal cost effectiveness in terms of the area ratio of unit-cell and height-diameter ratio of column for a given set of material properties. For validation of the model, the results are compared with some field tests reported in literature, and the salient interesting findings are discussed

A mathematical model of a unit cell of a ‘granular-pinned’ slope had been analyzed (Saha 2001) to predict the increased resistance of potential sliding mass of the ‘pinned’ slope due to higher shear strength and free-draining characteristics of the ‘granular-pin’ or column. The present investigation illustrates the effectiveness of a new generation optimization procedure, the genetic algorithms (GA), to find out the minimum Factor of Safety of virgin slope vis-à-vis reinforced slope. GA does not require problem specific knowledge for carrying out the search since it is a tool guided by stochastic principles instead of gradients. The objective function to be optimized in the two cases has been taken as the factor of safety expression of Bishop's simplified method (1960) for virgin slope
and Saha’s (2001) expression for reinforced slope. A specific stretch of vulnerable ‘Bhagirathi-Hooghly’ river bank (-the southern part of River Ganges- the major hydrodynamic system that formed the world's largest delta) has been chosen for the analysis. The study compares the results of prediction of failure susceptibility of river bank by directed grid-search in literature (Parua, 1992) with the present random search analysis. It emerged from the study that marked improvement in stability of such slopes could be achieved by granular-pinning that results in changing the potential virgin failure surface. Both gradual drawdown (GD) and instantaneous drawdown (ID) analysis exhibited marked improvement; though improvement in ID case, that is likely to govern in tidal deltaic zones, is about thrice than that obtained in GD case.

An in depth study of the load-settlement behavior of stone column treated ground has been made encompassing all the relevant parameters governing design and performance including material properties of the in-situ soil and backfilled stone column, the external vertical stress level and geometry of column installation under different sets of assumptions and boundary conditions. The predictions based on the proposed method are compared with existing theories and ultimate column capacities reported in literature. The stress concentration on column and settlement reduction of composite ground developed by the proposed model has been presented, and results compared with other approaches available in literature. Finally, back analysis of published full scale load test results on ultimate column capacities available in literature has been done by the proposed model, and significant findings presented.