A new analytical solution is presented to study soft soil improvement, both reduction of settlement and consolidation time, by means of encased stone columns. The proposed solution pretends to be a simple and useful tool for design. Therefore, only a unit cell, i.e. an end-bearing column and its surrounding soil, is modelled in axial symmetry under a rigid and constant load. Soil is assumed as elastic but plastic strains are considered in the column using the Mohr-Coulomb yield criterion and a non-associated flow rule, with a constant dilatancy angle. An elasto-plastic behaviour is also considered for the encasement by means of a limit tensile strength. The solution is presented in a closed form and is directly usable in a spreadsheet. Parametric studies of the settlement reduction, stress concentration and consolidation time show the efficiency of encasing the columns, which is mainly ruled by the encasement stiffness compared to that of the soil. Column encasement is equally useful for common area replacement ratios but columns of smaller diameters are better confined. Besides, the applied load should be limited to prevent the encasement from reaching its tensile strength. A simplified formulation of the solution is developed assuming drained condition. The results agree well with numerical analyses

This paper describes the results of numerical simulations investigating the installation effects of stone columns in a natural soft clay. The geometry of the problem is simplified to axial symmetry, considering the installation of one column only. Stone column installation is modelled as an undrained expansion of a cylindrical cavity. The excess pore pressures generated in this process are subsequently assumed to dissipate towards the permeable column. The process is simulated using a finite element code that allows for large displacements. The properties of the soft clay correspond to Bothkennar clay, modelled using S-CLAY1 and S-CLAY1S, which are Cam clay–type models that account for anisotropy and destructuration. Stone column installation alters the surrounding soil. The expansion of the cavity generates excess pore pressures, increases the horizontal stresses of the soil, and most importantly modifies the soil structure. The numerical simulations performed allow quantitative assessment of the post-installation value of the lateral earth pressure coefficient and the changes in soil structure caused by column installation. These effects and their influence on stone column design are discussed.

This paper presents a set of systematic 2D and 3D finite element analyses that study the performance of groups of encased stone columns beneath a rigid footing. Those numerical analyses show that, if the area replacement ratio, i.e. area of the columns over area of the footing, and the ratio of encasement stiffness to column diameter are kept constant, the column arrangement (both number of columns and column position) has a small influence on the settlement reduction achieved with the treatment. For high encasement stiffnesses, placing the column near the footing edges may be slightly more beneficial reducing the settlement; on the contrary, the maximum hoop force at the encasement is notably higher. Based on the minor influence of column arrangement, this paper proposes a new simplified approach to study groups of encased stone columns, which involves converting all the columns of the group beneath the footing in just one central column with an equivalent area and encasement stiffness. This simplified model is used to conclude that, for settlement reduction and fully encased columns in a homogeneous soil, there is a column critical length of around two or three times the footing width. The critical length of the encasement for partially encased columns is slightly lower than that of the fully encased columns

This paper reviews the main modeling techniques for stone columns, both ordinary stone columns and geosynthetic-encased stone columns. The paper tries to encompass the more recent advances and recommendations in the topic. Regarding the geometrical model, the main options are the “unit cell”, longitudinal gravel trenches in plane strain conditions, cylindrical rings of gravel in axial symmetry conditions, equivalent homogeneous soil with improved properties and three-dimensional models, either a full three-dimensional model or just a three-dimensional row or slice of columns. Some guidelines for obtaining these simplified geometrical models are provided and the particular case of groups of columns under footings is also analyzed. For the latter case, there is a column critical length that is around twice the footing width for non-encased columns in a homogeneous soft soil. In the literature, the column critical length is sometimes given as a function of the column length, which leads to some disparities in its value. Here it is shown that the column critical length mainly depends on the footing dimensions. Some other features related with column modeling are also briefly presented, such as the influence of column installation. Finally, some guidance and recommendations are provided on parameter selection for the study of stone columns.