Journal of Engineering Geology

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Introduction
The design engineers usually follow a specific decision-making process for optimal selection of the type of required foundation and its design. In this state, in case the surface foundation is not appropriate for the project conditions, before making any decisions about the use of deep foundations, the proper methods for optimization of the liquefied soil should be evaluated in order to compare the advantages and disadvantages of each of them with those of deep foundation, in terms of efficiency, implementation problems, costs, and finally to select the best choice. One of the best methods of soil improvement is the use of stone columns. The rationale behind the use of stone columns is the high shear strength of materials and the provision of lateral grip by surrounding soil. Therefore, the stone column can receive the load from the structure, and transfer it to the resistant layers. In the soils with low shear resistance, the lateral constraint crated by the surrounding soils is not enough for preventing the sideway buckling of the column under which is subjected to the loads. Thus, special measures should be considered for the use of stone columns in these soils. One of these methods is the use of reinforcement shelves such as geogrid and geotextile. Investigating the previous studies, the lack of evaluation of the design parameters such as the settlement ratio of the soil improved by the reinforced stone column to the geogrid, and provision of design graphs in this regard, has been revealed. Therefore, by extension of the studies conducted by Chub Basti et al. in 2011, the design graphs were provided in this regard.
Material and methods
The PLAXIS V8 Software was used for modelling the soft soil improved by the stone column. For increasing the precision of the results, the 15-knot element was used in the current study. The fine mesh was used in the models made for the analysis of the problem. For simulation of the improved soft soil with the stone column in a single cell, the modelling was implemented in a two-dimensional environment in axial symmetry conditions. In the current study, it was assumed the rigid foundation is on the improved bed. Thus, for analysis of the simulated model, a vertical strain up to 2% of the soft soil height has been applied on the ground. Also, for simulation of the soil behavior, an appropriate model of soil and parameters proportional to the materials should be allocated to the construct geometry. The non-linear stress-strain of the soil in different levels of the problem can be simulated. The number of model parameters increases with the level of problem rupture. For precise simulation, we need the proper parameters of the materials. For modeling of soft soils and stone columns, elastic-plastic model with Mohr-Coulomb rupture criterion was used. In the current study, it was assumed the soft bed is located on a very hard layer of soil. Therefore, the vertical deformation was prevented on this horizontal boundary. Also, the horizontal deformation in two vertical edges was prevented and only deformation in vertical direction was allowed. The soft bed close to saturation was considered without the determined free water level. For models with stone columns, the element of interface between the stone column and soft soil, has been used. The reason behind using this element is that the stone column rupture is of shear form and due to this, a significant shear stress is created on the common surface between the stone column and soft soil. The percentage of the replacement area is defined as the ratio of the total area of the stone columns to the total area of the non-improved area. In the current study, the percentage of the replacement area is utilized between 10 to 30%, which is used in implementation. Also, the diameter of the stone columns is from 0.6 to 1.2, in the analyses.
Results and discussion
The results of the numerical study were compared with the existing theoretical relationships provided by Poorooshasb and Meyerhof (1997), and Pulko et al. (2011). Figure 1 shows the comparison of the replacement percentage (RP) and settlement ratio (SR) in the non-reinforced state in the current study as well as theoretical relationships proposed by the previous researchers. Based on this figure, there is a difference between the results of the current study and those of Poorooshasb and Meyerhof (1997), and Pulko et al (2011). Poorooshasb and Meyerhof (1997) calculated the settlement ratio in their proposed material with the assumption of linear elasticity of the materials without consideration for plastic settlement. Therefore, the settlement of the improved soft soil with stone column, calculated by Poorooshasb and Meyerhof, would not show the real amount. However, Pulko et al. (2011), with consideration for the elastoplastic behavior of the materials, the lateral expansion of the stone column, and the primary stress of the soil around the column, provided more realistic results that correspond closely with the present study. Also, for designing the stone column, the results of its reinforcement have been also provided in the graph presented in Figure 2. Thus, by the use of these graphs, the ratio of settlement reduction can be obtained for each distance between columns and with different percentages of alternatives../files/site1/files/124/2jalili%DA%86%DA%A9%DB%8C%D8%AF%D9%87.pdf

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Introduction
Bearing capacity is very important in geotechnical engineering, which depends on factors such as footing shape, stress distribution under footing and failure mechanism of soil. Construction of the footing near a slope affects the behavior of footing and reduces the bearing capacity. Also, construction of structures on soft soil usually involves problems such as excessive settlement, deformation and stability problems. In order to increase the bearing capacity, especially in soft soils, one method is adding stone columns to soils. In this method 15 to 35 percent of unsuitable soil volume is replaced with appropriate material. In this research, the bearing capacity and settlement of a strip footing on a clayey slope reinforced with stone columns is investigated. For this purpose, a series of small-scale model tests was performed on the slope reinforced with both types of ordinary and vertical encased stone columns. The effects of length of stone column and location of stone column on the behavior of footing was studied and the optimum length of column and best location for column were determined. Also, some tests were performed on the effect of group stone columns on the footing and the efficiency of columns was investigated.
Material and methods
In order to determine properties of clay soil, stone column and encasement material, some preliminary standard tests were performed. The stone column material was selected with aggregate size ranging from 2-10 mm considering the scale effect. The performance of stone column depends on the lateral confinement provided from the surrounding soil and this lateral confinement represents undrained shear strength of the soil. In very soft soils (cu<15 kPa), the lateral confinement is not adequate and the stone column cannot perform well in carrying the required bearing capacity. For this reason, a series of undrained shear strength standard tests were carried out on clay samples with different water contents. According to these tests, the amount of water content of clay related to cu-15kPa was equal to 25%; while the natural water content of the clay was 4%. Therefore, the additional amount of water was weighted and added to clay. The apparatus of this research was consisted of two main parts including a test box and a hydraulic loading system. The test box dimensions should be such that for all states of the tests, the stress in the soil applied from the loading would be almost zero at all boundaries of the box. Thus, a box was built to accommodate the clay slope with 150 cm×120 cm×30 cm dimensions. The test box was built using steel material and steel belts were welded around it to prevent the deformation at high loads. The front side of the box was made from two pieces of tempered glass and a 10 cm×10 cm grid was drawn on them, for making the slope during construction and observation of deformations during the loading easier. The model strip footing dimensions were 29 cm length, 10cm width and 4cm height and it was made from steel to have no deformation during the loading. The displacement of the footing was measured using two dial gauges with accuracy of 0.01 mm.
The clay was filled in the test box in 5 cm thick layers and compacted with a special 6.8 kg weight tamper. All model stone columns were constructed using the replacement method. In this method, a 10 cm diameter open ended steel pipe was inserted into the soil and the clay within the pipe was excavated. Then the stone column material charged into the hole in 5 cm layers and each layer was compacted using a 2.7 kg special circular steel tamper with 10 blows. The 5cm compactions were repeated until the construction of ordinary stone column was completed. For construction of vertical encased stone columns, the cylindrical encasement mesh should be constructed first. Then, after excavating the hole, the prepared encasement mesh was placed inside the hole and the aggregates were charged into the hole in 5 cm layers and compacted.
Results and discussion
The loading method used in all tests was a stress control method. Bearing capacity values were determined from pressure-displacement diagrams using tangent method. All test results show that when any type of stone columns was added to slope, the bearing capacity of adjacent footing was increased. Vertical encasing of stone columns leads to a further improvement in the behavior of the footing. Influence of length of ordinary stone columns on the behavior of strip footing near clayey slope, was studied for four different lengths. Results show that, the optimum length of stone columns giving the maximum performance is about 4 times their diameter. Also, the location of column for both ordinary and vertical encased stone columns was studied using a series of laboratory tests and results show that the best location for the stone column is right beneath the footing. Also, group stone column tests resulted that for both ordinary and vertical encased types of stone columns, the group of two columns had a better efficiency than the group of three columns.
Conclusion
In this investigation, some model tests with 1/10 model scale on a strip footing near a clayey slope reinforced with stone columns were performed and the effects of different parameters such as stone column length and location were studied. Based on results from experiments on different states of stone columns, the following concluding remarks may be mentioned:
- The maximum encasement influence was observed when the encased stone column is placed under the footing.
- The optimum length of ordinary stone columns which are placed beneath the strip footing gives the maximum performance more than 4 times to their diameter.
-Bulging failure mode governs when the stone column is placed under the footing. When stone column is not beneath the footing, the failure mode was lateral deformation.
- Comparing the different locations of stone columns in the slope shows that for both ordinary and vertical encased stone columns, the best location having the most influence on the strip footing is under the footing and with increasing the spacing between column and footing, the bearing capacity is reduced.
./files/site1/files/132/7Extended_Abstracts.pdf

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Introduction
Stone column installation method is one of the popular methods of ground improvement. One of the common uses of stone columns is to increase slope stability. Several studies have been performed to examine the behavior of stone columns under vertical loads. However, limited research, mostly focused on numerical investigations, has been performed to evaluate the shear strength of soil reinforced with stone column. The study presented herein is an experimental program, aimed to explore the shear strength of loose sand bed reinforced with stone column. Direct shear tests were carried out on specimens of sand bed material, stone column material and sand bed reinforced with stone column, using a direct shear device with in-plane dimensions of 305*305 mm² and height of 152.4 mm. Experiments were performed under normal stresses of 35, 55 and 75 kPa . In this study, 4 different area replacement ratios (8.4, 12, 16.4 and 25%), and 3 different stone column arrangements (single, square and triangular) were considered for investigation. The obtained results from this study showed that stone column arrangement had an impact on improving the shear strength of stone columns. The most increase in shear strength and stiffness values was observed for square arrangement of stone columns and the least increase was for single stone columns. This study also compares the equivalent shear strength values and equivalent shear strength parameters (internal friction angle and cohesion) measured during experiments with those predicted by analytical relationships. Results show that shear strength values and shear strength parameters measured from experiments are higher than those obtained from analytical relationships. Accordingly, a corrective coefficient was calculated for each column arrangement to represent the correlation between experimental and analytical results.
Material Properties of Loose Bed and Stone Column
Fine-grained sand with particle size ranging from 0.425 to 1.18 mm was used to prepare loose sand bed, and crushed gravel with particle size ranging from 2 to 8 mm was used as stone column material. The sand material used as bed material had a unit weight of 16 kN/m³ and a relative density of 32.5%, and the stone material used in stone columns had a unit weight of 16.5 kN/m³ and a relative density of 80%. The required standard tests were performed to obtain the mechanical parameters of bed material and stone column material. As the diameters of model scale stone columns were smaller than the diameters of stone columns installed in the field, the particle dimensions of stone column material were reduced by an appropriate scale factor to allow an accurate simulation of stone columns behavior.
Testing Procedure
In this study, large direct shear device with in-plane dimensions of 305*305 mm² and height of 152.4 mm was used to evaluate the shear strength and equivalent shear strength parameters of loose sand bed reinforced with stone column. Experiments were performed under normal stresses of 35, 55 and 75 kPa.
Two class C load cells with capacity of 2 ton were used to measure and record vertical forces and the developed shear forces during the experiments, and a Linear Variable Differential Transformer (LVDT) was used to measure horizontal displacement. All achieved data from the experiments including data on vertical forces, shear forces and horizontal displacements were collected and recorded using a data logger, and an especial software was used to transfer data between the computer and the direct shear device. All specimens were sheared under a horizontal displacement rate of 1 mm/min.
Testing Program
Experiments were performed on single stone columns and group stone columns arranged in square and triangular patterns. The selected area replacement ratios were 8.4, 12, 16.4, and 25% for single stone columns, and 8.4, 12 and 16.4% for square and triangular stone column arrangements. To eliminate boundary effects, the distance between stone columns and the inner walls of the shear box was kept as high as 42.5 mm. In total, 12 direct shear tests were carried out, including 2 tests on loose sand bed material and stone column material, and 10 tests on stone columns with different arrangements. From the tests performed on group stone columns, 4 tests were performed on single stone columns, 3 tests on stone columns with square arrangement and 3 tests on stone columns with triangular arrangement. Hollow pipes with wall thickness of 2 mm and inner diameters equal to stone column diameters were used to construct stone columns. To prepare the specimens, first, the hollow pipes were installed in the shear box according to the desired arrangement. Then, bed material with unit weight of 16.5 kN/m³ was placed and compacted in the box in 5 layers, each 3 cm thick. Stone material was uniformly compacted to construct stone columns with uniform unit weight. The compaction energy was 67 kJ/m³ in all tests.
Results and discussion
In this paper, the behavior of stone columns under shear loading was experimentally investigated in large direct shear device by performing tests with different area replacement ratios (8.4, 12, 16.4, and 25%), different stone column installation arrangements (single, square and triangular), and different normal stresses (55, 75 and 100 kPa). The key findings of this study are as follows:
1. Shear strength increases with increase of area replacement ratio due to the higher strength of combined soil-stone column system, and due to the increase of stone column area effective in shear plane. The amount of shear strength increase with area replacement ratio is low for ratios lower than 15%. However, this amount is higher for area replacement ratios higher than 15%.
2. For stone columns with equal area replacement ratios, higher shear strength was mobilized in stone columns with square and triangular installation arrangements compared to single stone columns. Among the installation patterns investigated in this study, stone columns with square arrangement experienced the highest increase in shear strength value, while single stone columns experienced the lowest. One of the reasons of shear strength increase in square and triangular patterns is the increase of confining pressure applied by stone columns to the soil between them. Another reason is the increase the total lateral surface by changing the column arrangement from single column to square and triangular patterns. This increased lateral surface increases the lateral force imposed on the stone columns, resulting in higher shear strength mobilization of stone material.
3. The slope increase of shear strength-horizontal displacement curves shows that soil-stone column system has higher stiffness than loose sand bed, and this stiffness varies with area replacement ratio and installation pattern. The maximum stiffness values refer to stone columns installed in square pattern and the minimum values refer to single stone columns. In general, stone column installation pattern has an effective role in increasing stiffness.
4. Results show that shear strength parameters increase in soil reinforced with stone column. The maximum increase in internal friction angle refers to stone columns with square pattern and the minimum increase refers to single stone columns.
5. The equivalent shear strength values measured from experiments are higher than those obtained from analytical relationships. Accordingly, it is conservative to use analytical relationships to calculate shear strength parameters. It is worthy to mention that these relationships assume that the value of stress concentration ratio is equal to 1. Results from this study indicate that the value of stress concentration ratio should be accurately calculated and used in the relationships.
6. As discrepancy was observed between values measured from experiments and those obtained from analytical relationships, corrective coefficients were calculated to modify analytical relationships. These coefficients were computed and presented based on stone column installation pattern, area replacement ratio and the applied normal stress values../files/site1/files/133/2Extended_Abstracts.pdf 

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Introduction
Stone column installation method is one of the popular methods of ground improvement. Several studies have been performed to investigate the behavior of stone columns under vertical loads. However, limited research, mostly focused on numerical investigations, has been performed to evaluate the shear strength of soil reinforced with stone column. The stress concentration ratio (n) is one of the important parameters that uses in soil improvement by stone column method. Stress concentration ratio is the ratio of the stress carried by stone column to that carried by the surrounding soil. In this paper, the results of a laboratory study were used to examine the changes in the stress concentration ratio when normal and shear stress applied. Direct shear tests were carried out on specimens of sand bed material, stone column material and sand bed reinforced with stone column, using a direct shear device with in-plane dimensions of 305*305 mm and height of 152.4 mm. Experiments were performed under normal stresses of 55, 77 and 100 kPa. In this study, three different area replacement ratios (8.4%, 12%, 16.4%), and three different stone column arrangements (single, square and triangular) were considered for investigation. Loose sand and crushed gravel were used to make the bed and stone columns, respectively. In this study, the equivalent shear strength and equivalent shear parameters measured from experiments were also compared with those predicted by analytical relationships at stress concentration value of 1 and stress concentration value obtained from experiments.
Material Properties
Fine-grained sand with particle size ranging from 0.425 to 1.18 mm was used to prepare loose sand bed, and crushed gravel with particle size ranging from 2 to 8 mm was used as stone column material. The sand material used as bed material had a unit weight of 16 kN/m³ and a relative density of 32.5%, and the crushed stone material used in stone columns had a unit weight of 16.5 kN/m³ and a relative density of 80%. The required standard tests were performed to obtain the mechanical parameters of bed material and stone column material. As the diameters of model scale stone columns were smaller than the diameters of stone columns installed in the field, the particle dimensions of stone column material were reduced by an appropriate scale factor to allow an accurate simulation of stone columns behavior.
Testing Procedure
In this study, large direct shear device was used to evaluate the shear strength and equivalent shear strength parameters of loose sand bed reinforced with stone column. Experiments were performed under normal stresses of 55, 75 and 100 kPa. Two class C load cells with capacity of 2 tons were used to measure and record vertical forces and the developed shear forces during the experiments, and a Linear Variable Differential Transformer (LVDT) was used to measure horizontal displacement. The main objectives of this study was to calculate the stress concentration ratio of stone columns in different arrangement. Stress concentration ratio is the ratio of the stress carried by stone column to that carried by the surrounding soil, and can be calculated using Equation 1. For this purpose, the direct shear device was modified. Two miniature load cells with capacity of 5 kN were employed. The load cells were mounted on the rigid loading plate with dimensions of 305*305 mm² and thickness of 30 mm, as shown in Figure 1, All achieved data from the experiments including data on vertical forces, shear forces and horizontal displacements were collected and recorded using a data logger, and an especial software was used to transfer data between the computer and the direct shear device. All specimens were sheared under a horizontal displacement rate of 1 mm/min.
Experiments were performed on single stone columns and group stone columns arranged in square and triangular patterns. The selected area replacement ratios were 8.4, 12 and 16.4% for single, square and triangular stone column arrangements. To eliminate boundary effects, the distance between stone columns and the inner walls of the shear box was kept as high as 42.5 mm. In total, 11 direct shear tests were carried out, including two tests on loose sand bed material and stone column material, and 9 tests on stone columns with different arrangements. From the tests performed on group stone columns, 3 tests were performed on single stone columns, 3 tests on stone columns with square arrangement and 3 tests on stone columns with triangular arrangement. Hollow pipes with wall thickness of 2 mm and inner diameters equal to stone column diameters were used to construct stone columns. To prepare the specimens, first, the hollow pipes were installed in the shear box according to the desired arrangement. Then, bed material with unit weight of 16.5 kN/m³ was placed and compacted in the box in 5 layers, each 3 cm thick. Stone material was uniformly compacted to construct stone columns with uniform unit weight.
Results and discussion

1. The SCR value increases for settlement up to 3 mm and then decreases with increasing the horizontal displacement and then approaches almost a constant value. Results also show that stress concentration ratio decreases with increase of stone column diameter. Results show that the value of stress concentration ratio in square pattern is higher than that in single and triangular pattern. Moreover, results show that stress concentration ratio decreases with increase of normal stress.
2. The value of the internal friction angle in (peak) state, for loose bed increases from 33 to 40 degrees in square arrangement and in the corresponding state of displacement of 10 % from 30 degrees in a loose bed increase to 32 degrees, for loose sand reinforced with stone column. Shear strength increases with the increase of modified area ratio in all stone column installation patterns in both the peak and the corresponding state of the horizontal displacement of 10%.
3. For stone columns with the same modified area ratio, the installation pattern has an effective role in defining the shear strength. Group stone columns mobilize higher shear strength compared to single stone columns. Among the installation patterns investigated in this study, stone columns with square arrangement experienced the highest increase in shear strength value while single stone columns experienced the lowest.
4. The equivalent shear strength values measured from experiments are higher than those obtained from analytical relationships. Accordingly, it is conservative to use analytical relationships to calculate shear strength parameters. It is worth explaining that these relationships assume that the value of stress concentration ratio is equal to 1. Results from this study show that the value of stress concentration ratio should be accurately calculated and used in the relationships.
5. Comparison between shear strength parameters obtained from experiments and those predicted by analytical relationships shows that in single stone columns, the value of stress concentration ratio should be 3 to 4.5, and in square and triangular patterns, this value should be 6 to 7 and in triangular patterns 4.5 to 5, respectively, to achieve good agreement between experimental and analytical results in peak condition. In horizontal displacement 10% the value of stress concentration ratio should be 2.5 to 3, in single, square and triangular patterns, to achieve good agreement between experimental and analytical results../files/site1/files/151/2.pdf