Behavior of Geotextile-Encased Single Stone Column in Soft Soils

Arabian Journal for Science and Engineering https://doi.org/10.1007/s13369-019-04299-3 RESEARCH ARTICLE - CIVIL ENGINEERING Behavior of Geotextile‑Encased Single Stone Column in Soft Soils Rowad Esameldin Farah1 · Zalihe Nalbantoglu1 Received: 30 July 2019 / Accepted: 23 December 2019 © King Fahd University of Petroleum & Minerals 2020 Abstract Stone columns have become a widely used method of increasing bearing capacity of soft soils. This study investigates floating stone columns with and without encasement in soft soils. Although the stone columns in single-layered soil have been studied extensively, stone columns constructed in a base of varying soil layers are not fully understood. In the present study, the behavior of both single-layered soft soil and layered soil consisting of loose sand overlaying the soft soil was investigated by using small-scale laboratory pilot tests. The bearing capacity of soft soil was improved in all cases of stone column application. The contribution of stone columns on the bearing capacity of soft soil was presented by the term bearing improvement ratio (BIR). With a non-encased stone column in single-layered soft soil, the BIR was about 3.3-fold and with geotextile encasement in the same soil, the improvement ratio increased to 3.4-fold. For a non-encased stone column in layered soils, the BIR was about 2.0-fold and with geotextile enhancement in the same soil, this improvement ratio increased to 4.0-fold. The inclusion of geotextiles resulted in improved bearing capacity by distributing the induced stresses over larger areas. The maximum bulging of non-encased stone column in single-layered soft soil was observed at the depth of 1.5 times the original diameter of the stone column from the top, whereas for encased stone column in single-layered soft soil, the maximum bulging was transferred to a depth of 3.0 times the original diameter of the stone column. Keywords Stone column · Column bulging · Floating column · Layered soil · Soft soil · Geotextile 1 Introduction Structures constructed on soft soils experience problems such as total and differential settlements, liquefaction, and, over the long term, instability and poor durability [1–3]. Among a variety of methods used for ground improvement, stone column application is a method widely used to improve soil conditions [4–9]. Stone columns gain their bearing capacity from their confinement by the surrounding soils. However, stone columns in very soft soils experience excessive bulging due to very low lateral confinement by the surrounding soils. Confinement provided by such soils may not be adequate to develop the required bearing capacity of the stone columns [2, 10]. * Rowad Esameldin Farah [email protected] Zalihe Nalbantoglu [email protected] 1 Department of Civil Engineering, Eastern Mediterranean University, Via Mersin 10, Famagusta, North Cyprus, Turkey Improvement in the bearing capacity of the stone column can be achieved by the encasement of stone columns by using geotextiles [11]. The increase in the confinement of the stone column prevents the squeezing of the stone column materials into the surrounding soils, reduces the lateral bulging and transfers the loads to deeper layers and thus results in an increase in the bearing capacity of the stone column [12, 13]. The higher the confinement provided by the geotextile, the greater the increase in the bearing capacity of the stone column. For the improvement of soft soils where the hard stratum lies at deeper layers, the choice of floating stone columns may be one of the best options [6]. The literature review indicated that most of the studies on the performance of stone columns focus on end-bearing stone columns [14–16]. There has been very limited research performed on the bearing capacity of floating stone columns [14–16]. Hence, in the present study, small-scale laboratory model tests were performed to evaluate the effectiveness of floating stone columns with and without geotextile encasement. Studies in the literature [2, 3, 5] investigated the performance of stone columns in the settlement and bearing 13 Vol.:(0123456789) Arabian Journal for Science and Engineering capacity of soft single-layered soils. There has been very limited research conducted on the behavior of stone columns in layered soils [9, 17–19]. However, in reality, footings are usually set in multi-layered soils and understanding the behavior of stone columns in layered soils is very important for civil engineers [17–21]. In the literature, the condition of layered soils was generally considered to be a soft soil overlaying a very soft soil, each of varying thicknesses [9, 18, 19]. Some studies considered the performance of stone columns in layered soils consisting of soft soils overlaying a relatively stronger silty soil [9, 18]. After an extensive literature review, it has been observed that the performance of stone columns in loose sand overlaying a soft soil has not been considered. Therefore, in the present study, the performance of stone columns in layered soil consisting of loose sand overlaying a soft soil was studied in a small-scale laboratory model test tank with the single stone column at the center and the layered soil surrounding it. Hasan and Samadhiya [22] stated that the single granular pile behavior with unit cell concept simulates the field behavior for an interior pile when large number of piles is simultaneously loaded. Hughes and Withers [4] were among the first researchers to analyze the complex behavior of stone columns. They developed the unit cell concept to predict the capacity of the stone columns, where the capacity of a group of stone columns is equal to the sum of the capacity of the individual columns in the group. In the literature, the existing design techniques for settlement control related to large group of stone column configurations are analyzed based on the performance of an isolated stone column under unit cell concept [3, 20, 23]. The unit cell model involves a single stone column and an equivalent circular influence zone [3]. This approach was found to provide a good correlation with actual observed field behavior for infinite groups [3, 20]. In the present study, bearing capacity of stone columnimproved ground was designed based on the simplified geometrical unit cell model approach by considering one single stone column at the center of the tank and the soft soil surrounding it. Stone columns can increase the bearing capacity of soft soils. Bearing capacity of stone columns is a function of column arrangement, stone column encasement, length to diameter ratio, column spacing, etc. Various researchers performed a series of laboratory tests to evaluate the performance of stone columns on bearing capacity of soft soils [2–6]. In the present study, the effect of geotextile encasement on the performance of stone columns in single-layered and layered soils was investigated. To obtain the degree of improvement achieved, the results were plotted as bearing improvement ratio and denoted as qr/qu where qr is the vertical stress of reinforced soil at a given 13 settlement and qu is the vertical stress of unreinforced soil at the same settlement. The bearing capacity and settlement behavior of a single stone column is significantly influenced by the method of applying the vertical load over the stone column [3, 20]. Applying the load through a rigid foundation over an area greater than the stone column diameter increases the vertical and lateral stress in the surrounding soft soil [3, 20]. The larger bearing area together with the additional support of the stone column results in less bulging and greater ultimate load capacity of the stone column [20]. Barksdale and Bachus [20] stated that by applying the load on the soil–stone column composite, the bearing capacity of the composite increases to more than the bearing capacity of the stone column alone. In this study, in order to evaluate the effectiveness of stone columns in soft soil improvement, the worst condition was tried to be simulated in the vertical load application so that the bearing capacity of the stone column alone could be evaluated. Therefore, in the study, a footing diameter of 5 cm was used as the same diameter of the stone column and the vertical load was applied just over the area of the stone column. The main objective of this research was to evaluate the effectiveness of a single stone column in layered soils on which limited research findings existed in the literature [9, 17–19]. The majority of the laboratory-scale testing carried out on stone columns referred only to initial compression and primary consolidation settlement [22–26] with no distinction between initial compression, primary consolidation settlement, and creep [27]. Within the scope of the present study, in order to compare the obtained results with the existing findings in the literature, only the initial compression of the single stone column was measured and the effectiveness of the stone column in single-layered and layered soil was discussed. 2 Modelling Considerations In laboratory conditions, it is quite expensive and time-consuming to test full-scale stone column-reinforced soft soils. For these reasons, experiments performed in laboratory are usually limited to observation of the behavior of small models which simulate the actual foundations at a predefined ratio [28]. The main difficulty in laboratory tests is the scaling effect. Allersma [29] stated that four types of physical models can be identified according to the scale of the model. These types are the full-scale field tests, small-scale physical field tests, small-scale physical laboratory tests (1 g), and small-scale centrifuge tests. According to Altaee and Fellenius [28], the chief condition for agreement between the small-scale model and the prototype is that the initial soil states of both must be at equal proximity to the steady-state Arabian Journal for Science and Engineering line. Then, when stresses are normalized to the initial mean stress, the small-scale model will, in all respects, behave similarly to the prototype [28]. Altaee and Fellenius [28] indicated that the soil in the small-scale model can be no looser than the maximum void ratio of the soil in the prototype and it must not be denser than a value that corresponds to a prototype soil at the minimum void ratio. Debnath and Dey [12] defined a similitude ratio as the ratio of any linear dimension of the prototype to the equivalent dimension of the small-scale model. Debnath and Dey [12] stated that typically the prototype stone columns have a diameter (dp) ranging from 0.6 m to 1.0 m and the column length to diameter ratio (l/dp) varies between 5 and 20 [30]. Muir Wood et al. [31] specified that the particle size of the aggregates (ds) used in the prototype stone columns range from 25 mm to 50 mm and the dp/ds ratio varies between 12 and 40. Within the scope of this study, the small-scale laboratory model tests were not performed with any particular prototype in mind; rather, the tests were completed as a generic study. The diameter and the length of the stone column in the model test setup were designed along the lines exemplified by Debnath and Dey [12]. As well, the particle sizes of the column aggregates were designed as previously demonstrated by Muir Wood et al. [31]. More details related to the model design of this study are given in Sect. 3. 3 Experimental Investigation 3.1 Materials Used 3.1.1 Soft Soil For the model test, soft soil, sand, crushed stone aggregates, and geotextiles were used as materials. Table 1 introduces some of the properties of the materials used in this study. The soft soil has been excavated from a depth of approximately 1 m from the ground surface in Famagusta, North Cyprus. All the physical and index property tests on the soft soil were performed according to the American Society for Testing and Materials (ASTM) standards. The physical and compressibility characteristics of the soft soil are shown in Table 1. Test results indicated that the soil did not contain any organic matter. According to the Unified Soil Classification System (USCS), the soil was classified as silt with high plasticity (MH). To create soil samples at different consistencies according to the relationship between consistency and unconfined compressive strength (UCS), as suggested by Das [39], test specimens were compacted at standard Proctor compaction energy with varied water content and UCS tests were performed on these specimens. Test results indicated that the Table 1 Physical properties of the materials used in the study Properties Index properties of soft soil Fraction of clay size (< 2 μm)a (%) Fraction of silt size (2–74 μm) a (%) In situ bulk density, ρbb (g/cm3) In situ moisture contentb (%) Specific gravityc, (Gs) Liquid limitd, LL (%) Plastic limitd, PL (%) Plasticity indexd, PI Compression index, Cc Rebound index, Cr Activityd Soil classificatione Properties of Bedis sand Specific gravityc Maximum dry densityf, ρd(max) (g/cm3) Minimum dry densityf, ρd(min) (g/cm3) Internal friction angle, ϕ° at loose state (°) Uniformity coefficient (Cu)g Coefficient of curvature (Cc)g Mean diameter, D50 (mm) Soil classificatione Properties of the crushed stone aggregates Specific gravityc Maximum dry densityf, ρd(max) (g/cm3) Minimum dry densityf, ρd(Min) (g/cm3) Internal friction angle, ϕ° (at 70% relative density) (°) Bulk density (at 70% relative density), (g/cm3) Uniformity coefficient (Cu)g Coefficient of curvature (Cc)g Mean diameter, D50 (mm) Soil classificatione a Values 48.0 52.0 1.77 30.0 2.65 58.0 30.0 28.0 0.20 0.21 0.58 MH 2.65 1.55 1.46 31.0 1.29 1.06 0.22 SP 2.48 1.61 1.49 46.0 1.57 1.67 0.99 3.00 SP According to ASTM D 422-98 [32] b According to ASTM D 2937-17 [33] c According to ASTM D 854-06 [34] d According to ASTM D 4318 [35] e According to ASTM D 2487-00 (Unified Soil Classification System) [36] f According to Impact method [37] g According to ASTM D 2487-06 [38] soil sample compacted at 33% water content resulted in a UCS value of 33 kPa. According to Das [39], soil at this UCS value is determined to be soft. The bulk density of the soil at the same water content (33%) was found to be 1.81 g/cm3. In order to achieve the same soil consistency throughout the tests, all the soil specimens were compacted to this density and water content for the study. 13 Arabian Journal for Science and Engineering 3.1.2 Sand The sand used in the study was taken from Bedis Beach in Famagusta, North Cyprus. The properties of the Bedis sand are presented in Table 1. According to the Unified Soil Classification System, the Bedis sand was classified as poorly graded sand (SP). in granular piles is maintained at 400 kN/m, whereas in laboratory model tests, the tensile strength of geosynthetics material was within the range of 1.5–20 kN/m [2, 40–42]. In this study, the geotextile material had a tensile strength of 7 kN/m. The properties of the non-woven geotextile used in this study are presented in Table 2. 3.2 Experiment Setup 3.1.3 Crushed Stone Aggregate 3.2.1 Model Design The crushed stone aggregate used in the construction of the stone columns had sizes ranging between 1 mm and 5 mm. The properties of the crushed stone aggregate are shown in Table 1. The particle size distribution of the crushed stone aggregates, soft soil, and sand are given in Fig. 1. 3.1.4 Geotextile Non-woven geotextile was utilized to encase and increase the confinement of material in the stone column. In practice, the tensile strength of geosynthetics materials utilized Fig. 1 Particle size distribution of soft soil, sand and crushed stone aggregates used in the study As aforementioned, in the present study, the diameter (d) and the length (l) of the stone column in the model tests were designed along similar lines as Debnath and Dey [12] utilized. The diameter (d) and the length (l) of the stone column in the model test were 5 cm and 50 cm, respectively. Therefore, the l/d ratio was 10, placing it in the 5–20 range as suggested by Debnath and Dey [12]. The particle size of the stone column aggregates (ds) used in the study ranged between 1 mm and 5 mm, and the mean particle size diameter (D50) was 3 mm resulting in d/D50 ratio of 17 which 100 90 80 Passing (%) 70 60 50 40 30 20 Soft soil Crushed stone aggregates 10 0 0.000 Table 2 Properties of the nonwoven geotextile [43–49] 13 Sand 0.001 0.010 0.100 1.000 Particle Size (mm) 10.000 100.000 Test Standard Value Unit Weight Thickness (2 kPa) Tensile strength (longitudinal transverse) Break extension (longitudinal-cross) Static puncture Dynamic puncture Water permeability, VH50 Visible pore size, O90 EN ISO 9864 EN ISO 9863-1 EN ISO 10319 EN ISO 10319 EN ISO 12236 EN ISO 13433 EN ISO 11058 EN ISO 12956 500 2.7 7 min. 60 2040 10.04 0.034 0.070 gr/m2 mm kN/m % N mm l/s * m2 mm Arabian Journal for Science and Engineering was in the 12–40 range suggested by Muir Wood et al. [31]. The selected dimensions of the model test in this study fit the suggested similitude ratio of Debnath and Dey [12] and Muir Wood et al. [31]. In the model test, the layered soil consists of loose sand overlaying soft soil. Altaee and Fellenius [28] stated that physical modelling in sand depends mainly on the initial mean effective stress and the initial void ratio of the prototype soil. Since there was no specific prototype in mind and the maximum void ratio of loose sand used in this study was known, the maximum void ratio of the loose sand was assumed to be the initial void ratio in the model test. The physical laboratory model tests performed here were just a pilot test and were intended to be purely illustrative. Full understanding of the stone column in soft soils can only be possible through full-scale tests on prototypes and that is beyond the scope of the present study. In previous studies, some researchers [50, 51] stated that the failure wedge in a foundation bed spreads to within two to two and half times the footing width from its center. Meyerhof and Sastry [52] noted that the failure zone under rigid piles reached to a depth two times its diameter. Barksdale and Bachus [20] noted that bulging depth of the stone column was about two to three times the stone column’s diameter. Considering these previous findings, a circular steel test tank of 40 cm diameter and 80 cm deep was used in the present study. In order to avoid interference between the chamber wall and the failure wedge, a circular steel plate of 5 cm diameter was used for loading. The distance of the chamber walls from the center of the footing was about 20 cm. Finally, the load-settlement tests were performed sequentially with first the single-layered soft soil then the layered soil. The load-settlement behavior of the natural (non-reinforced) soft soil bed was tested in the model test tank, and then, the load-settlement behavior of stone column-reinforced soft bed with and without geotextile was examined. 3.2.3 Preparation of Single‑Layered Soft Soil in the Test Tank In the study, the single-layered soft soil bed was placed in the test tank at 33% water content and 1.81 g/cm3 bulk unit weight. Before placing the soft soil in the test tank, lubricating oil was applied on the walls of the test tank and a nylon sheet was placed in order to ease the removal of the soil sample after testing. A sand bed of 5 cm thickness was placed in the bottom of the test tank for drainage purpose. To achieve identical soil samples in all tests, the required amount of soft soil to fill the test tank was calculated and divided into seven equal layers of 10 cm thickness and placed in the test tank. After placing the soft soil in the test tank, a circular plate with the same diameter of the test tank was placed on top of the soft soil bed surface. To simulate the situation in the field, a surcharge pressure of 9.05 kPa was applied to the circular plate as in situ overburden pressure to consolidate the soft soil in the test tank. Two dial gauges with an accuracy of 0.002 mm were attached to the circular plate to measure the settlement. The measurement of the settlement was continued until 0.04 mm/day was reached. The consolidation of the soft soil was completed in 5 days. 3.2.4 Preparation of Layered Soil in the Test Tank 3.2.2 Test Setup and Procedure The depth of the single-layered soft soil bed in the test tank was 70 cm. Further explanation of the soft soil preparation in the test tank is given in Sect. 3.2.3. Floating stone columns with l = 50 cm were used in the study. The diameter of the stone column was selected to be 5 cm in all tests. A 5-cm-diameter steel auger was utilized to drill the 5-cmcircular hole for the construction of the single stone column in the test tank. A steel rod of 2 cm diameter was used for the compaction of the stone column material to reach the required density. The load was applied via a 5-cm-diameter circular steel plate with 38 mm thickness. Two linear variable differential transformers (LVDT) were used to measure the settlement of the loading plate. For testing the layered soil in the model test tank, 35 cm of soft soil was placed in the tank and then 35 cm of loose sand was spread on top of it. Further explanation of this soil preparation is given in Sect. 3.2.4. The same steps as used for the single-layered soft soil bed preparation were then followed. For the preparation of layered soil, the same procedure was followed as for the single-layered soft soil. The thickness of the soft soil and the loose sand were each 35 cm. After placement and complete consolidation of the soft soil layer, the sand layer was spread over it. For the placement density of the sand layer, the minimum index density of 1.46 g/cm3 was utilized as shown in Table 1. Tables 3 and 4 show the details of the stone columns constructed in the single-layered soft soil and layered soils in the test tank. Table 3 Details of the stone columns constructed in the single-layered soft soil Sample no Thickness of soft soil (cm) Stone column diameter (cm) Stone column length (cm) Geotextile used 1 2 3 70 70 70 – 5 5 – 50 50 No No Yes 13 Arabian Journal for Science and Engineering Table 4 Details of the stone columns constructed in the layered soil Sample no Thickness of layered soils (cm) Layers formation 1 70 A (Top) + B (Bottom) 2 70 A (Top) + B (Bottom) 3 70 A (Top) + B (Bottom) A = Sand (35 cm in thickness) B = Soft soil (35 cm in thickness) 3.2.5 Construction of the Single Stone Column After the placement of the soft soil bed in the test tank, a cylindrical hole of 5 cm in diameter was made at the center of the bed using a 5-cm-diameter steel auger. The internal and external surfaces of a hollow steel pipe were coated with oil to prevent friction between the pipe and the surrounding soil. The pipe was vertically set into the hole to aid the placement of the crushed stone aggregate. The upright position of the pipe was carefully checked with a level. The selected relative density of the crushed stone aggregate was 1.57 g/cm 3 which corresponded to 70% relative density (dense state). The weight of crushed stone aggregate to be placed in the hole was calculated according to the chosen relative density (1.57 g/cm3) and the volume of the hole. To form the floating stone column, the calculated amount of crushed stone aggregate was divided into five equal batches. Each batch was poured into the hole and lightly compacted using a 2-cm-diameter tamping rod until reaching the required height of 50 cm. The light compaction was performed to avoid lateral deformation during the construction of the stone column. The tamping rod was dropped 25 times from a height of 10 cm. For encasement of the stone column with geotextile, the required area of geotextile was calculated and cut according to the volume of the hole plus 2 cm. The geotextile was formed into a cylindrical shape with the two edges overlapping by 2 cm. Then, the fabric of the areas of overlap was bonded together with epoxy which was allowed to set-up for 24 h. For the encased stone columns, a tubular steel pipe with a 4 cm outer diameter was used for vertical insertion of the geotextile into the bored hole. The same series of procedure and conditions were applied in layered as were applied in single-layered soils. After the preparation of the soil and column specimens in the test tank, the vertical load was applied over the area of the stone column at a constant rate of 1.2 mm/min up to 30 mm vertical settlement of the footing. The loading period was kept short to simulate undrained conditions during construction. Figure 2 presents the schematic diagram of the single floating stone column in the singlelayered and layered soils used in this study, respectively. 13 Stone column diameter (cm) Stone column length (cm) Geotextile used – 5 5 – 50 50 No No Yes After completion of each test, the crushed stone aggregate in the stone column was carefully scooped out and then a cement paste was poured into the hole to maintain the shape of bulging formed during loading. After hardening of the cement paste, the surrounding soil was removed carefully and then the deformed shape of the stone column was extracted. The diameter of the bulged shape of the stone column was measured. 4 Results and Discussion 4.1 Bulging Failure of Stone Columns Figure 3 shows the picture of the stone columns with and without geotextile encasement in layered soil after loading. In the present study, in the case of stone column in layered soil, the bulging failure of the stone column after loading could not be investigated due to the lack of lateral confinement provided by the loose sand surrounding the stone column. Under the applied loading, the stone column materials spread out unevenly toward the loose sand and did not show typical bulging failure. For this reason, the deformed shapes of the stone column from the hardened cement paste in layered soil could not be obtained. This behavior of the stone column in loose sand can be seen in Fig. 3a. Muir Wood et al. [31] stated four modes of deformation of stone columns: bulging, shearing, punching, and bending. Single stone columns tend to bulge or punch, depending on column length, whereas groups of stone columns exhibit bulging, punching, shearing, and bending [31]. As Nazariafshar et al. [13] stated in single stone column application, the stresses due to loading around the single stone column are uniform because the stone column is located at the center of the loading plate. However, in group of stone columns since the columns are not located at the center of the loading plate, the induced stresses around the stone columns are not uniform and the deformations generated are the combinations of bulging and lateral deflection (bending) in the group of stone columns [13]. Bulging failure usually occurs based on whether the base of the stone column is floating in soft soil or resting on a hard layer. In a long stone column Arabian Journal for Science and Engineering Fig. 2 The schematic diagram for single floating stone column in; a single-layered soft soil; b layered soil with a length to diameter ratio over 5, failure occurs due to bulging [20, 42, 53–56]. In a floating stone column, with a length to diameter ratio less than 3 (a short stone column), the ultimate vertical stress is determined by the punching failure [13, 57]. General shear failure occurs in short stone columns that rest on hard layers [20, 58]. Some researchers [13, 22, 59] stated that bulging modes of deformation was the governing failure mechanism in all non-encased and encased single stone column applications. In the present study, the length to diameter ratio of the encased and non-encased stone columns was 10 which was greater than 5 and according to some researchers [20, 42, 53–56], the bearing capacity of the encased and non-encased stone columns was controlled by bulging failure. This statement was in line with the measured deformed shapes of the stone columns shown in Fig. 4. Figure 4 shows the non-dimensional bulging profile for non-encased and encased floating stone columns in singlelayered soft soil. In the figure, bulging was expressed as a percentage of the diameter of the stone column (Db − D0)/D0 (%), where Db is the bulging diameter of stone column and D0 is the original diameter of the stone column. The profile showed the variation of the non-dimensionalized bulging with normalized depth (Z/D0), where Z is the total length of the stone column. According to McKelvey et al. [1], the axial load transfer from the foundation to the stone column was higher near the top part of the stone column, whereas, in the lower part, the stone column carried little loads or no load transfer. In the present study, for the non-encased floating stone column, the maximum bulging was found to occur at a depth of 1.5 times the original diameter of the stone column from the top of the stone column (7.5 cm), whereas for encased floating stone column, the maximum bulging was found to occur at a depth of 3.0 times the original diameter of the stone column from the top (15.0 cm). The maximum bulging for non-encased and encased floating stone columns were 16.5% and 11.4%, respectively. It became clear that when the stone column was encased in geotextile, the maximum bulging depth increased, whereas the maximum bulging diameter was reduced by about 30% compared to the non-encased floating stone column. Due to the additional confinement of the stone column provided by the geotextile, excessive bulging into the surrounding soft soil was prevented and the applied axial load was transferred to deeper layers, resulting in higher bearing capacity of the encased stone column. The total length of the non-encased floating stone column experiencing bulging was found to be within the depth of 0.0–17.5 cm (3.5D0) of the stone column, whereas, in the encased floating stone column, the total length of bulging was within the depth of 2.5 cm to 27.5 cm (0.5D0–5.5D0) of the stone column. Tables 5 presented the bulging failure for non-encased and encased floating stone columns. The comparison of 13 Arabian Journal for Science and Engineering these findings indicated that the obtained results of the present study were in close agreement with the existing findings [12, 22, 60]. 4.2 Vertical Stress‑Settlement Behavior In the small-scale laboratory model tests reported in the literature, different settlement values were considered in the determination of the ultimate vertical stress of the stone column. Some researchers [22, 26] considered the ultimate vertical stress corresponding to 30 mm settlement. Malarvizhi and Ilamparuthi [61] considered the ultimate vertical stress at the settlement value corresponding to 10% of the diameter of the stone column, whereas Debnath and Dey [12] and Deb et al. [60] determined the ultimate vertical stress corresponded to a settlement of 20% of the diameter of the footing. A comprehensive literature review has shown that there is no specific standard on this. Hughes and Withers [4] stated that the ultimate bearing capacity of the stone column was reached at a vertical displacement of 58% of the stone column diameter, whereas Al-Mosawe et al. [62] found that the ultimate bearing capacity of the stone column was obtained at a vertical displacement of 60% of the diameter of the stone column. In the present study, in order to reach the clear ultimate load in the load-settlement curves of each stone column application, the loading of the stone column was continued until 30 mm settlement which was corresponding to 60% of the diameter of the stone column and the vertical stress corresponding to this settlement value was considered to be the ultimate vertical stress of the stone column. (a) (b) Fig. 3 Stone columns in layered soil after loading; a without encasement; b with encasement Lateral bulging, (Db-D0)/D0) (%) 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 Encased floating stone column 9 10 13 1 0 Depth of stone column /Original diameter of stone column, Z/D0 Fig. 4 Variation of the nondimensionalized bulging profile with normalized depth for nonencased and encased floating stone columns in single-layered soft soil Non-encased floating stone column Arabian Journal for Science and Engineering Table 5 Bulging failure for non-encased and encased floating stone columns Stone column Bulging depth and diameter Present study Hasan and Samadhiya [22] Deb et al. [60] Debnath and Dey [12] Non-encased floating stone column Max bulging depth 5.0 cm from the surface (1.0 * dstone) 5.82 cm (1.16 * dstone) 15 cm from the surface (3 * dstone) 5.57 cm (1.114 * dstone) (1–1.6) * dstone 1.20 * dstone – – 1.24 * dstone – – – 2.84 * dstone – – 1.08 * dstone Max bulging diameter Encased floating stone column Max bulging depth Max bulging diameter Fig. 5 Vertical stress of stone columns in single-layered soft soil with and without encasement Vertical Stress (kPa) 0 100 200 300 400 500 600 700 800 900 0 5 Settlement (mm) 10 15 20 25 30 Single-layered soft soil 35 40 Non-encased floating stone column Encased floating stone column column Figure 5 shows the vertical stress-settlement curves of stone columns in single-layered soft soil with and without encasement. The ultimate vertical stress value of the non-encased floating stone column was about 650.4 kPa at 30 mm settlement. The encased floating stone column gave higher vertical stress value than the non-encased floating stone column after attaining 24 mm settlement. The vertical stress value of this soil at 24 mm settlement was 640.0 kPa; this value increased further and reached 692.5 kPa at 30 mm settlement. This behavior of the encased stone column could be explained due to the radial elongation of the geotextile under increasing loading [2]. As the geotextile expanded further toward the surrounding soil, more interaction between the geotextile and the surrounding soil was achieved and this resulted in higher ultimate vertical stress of the encased stone column. Figure 6 illustrates the vertical stress of the stone columns in layered soil, loose sand overlaying the soft soil with and without column encasement. It was observed that the inclusion of non-encased and encased floating stone columns in soft layered soil enhanced the ultimate vertical stress. The ultimate vertical stress value of the non-encased floating stone column was about 90.9 kPa at 30 mm settlement. The same behavior of stress gain was obtained for the layered soils as was obtained in the singlelayered soft soil. The encased floating stone column produced a higher vertical stress value than the non-encased floating stone column after reaching 16 mm settlement. The vertical stress value of this soil at 16 mm settlement was 189 kPa and then, due to the further expansion of the geotextile, this value increased and reached to 367.5 kPa at 30 mm settlement. 13 Arabian Journal for Science and Engineering Fig. 6 Vertical stress of stone columns in layered soil with and without encasement Vertical Stress (kPa) 0 50 100 150 200 250 300 350 400 450 500 0 Natural layered soil Non-encased floating stone column 5 Encased floating stone column Settlement (mm) 10 15 20 25 30 35 The shape of the curves obtained in Fig. 6 for the nonencased and encased floating stone columns in layered soil were very similar to the one obtained in Fig. 5 for the single-layered soft soil. However, comparison of the values of the ultimate vertical stresses in single-layered and layered soils indicated that there was a significant reduction in the ultimate vertical stress values obtained for the layered soil. That result could be explained by the presence of loose sand overlaying the soft soil. Very little confinement provided by the surrounding loose sand caused a reduction in the bearing capacity of the layered soil, whereas in single-layered soil, higher confinement of the surrounding soft soil caused an increase in the ultimate vertical stress values of the stone column. Table 6 Comparison of the predicted and measured ultimate vertical stress values of nonencased floating stone column in single-layered soft soil Table 6 shows the comparison of the ultimate vertical stress of non-encased floating stone column in single-layered soft soil with the existing derived formulas in the literature. As it can be seen from Table 6, the findings of Hughes and Withers [4] and Christouls et al. [56] were in good agreement with the present study. For the layered soil condition, since the same layered soil condition (loose sand overlying soft soil) was not studied in the literature, no comparison of the findings was given for this case. 4.3 Bearing Improvement Ratio of Stone Column To evaluate the efficiency of stone columns on the bearing capacity of soft soils, the bearing improvement ratio (BIR) Derived formula Reference Predicted value (kPa) Measured value (kPa) 1+sin 𝜙�s Hughes and Withers [4] 607.0 650.4 Mitchell [63] Christouls et al. [56] 413.0 660.0 1−sin 𝜙s� (𝜎r� + 4Cu ) = qult CuNp = qult 𝜋D×L×Cu As = qult ϕs = Internal friction angle of stone column 𝜎r′ = Effective radial stress Cu = Undrained shear strength qult = Ultimate vertical stress of stone column Np = Bearing capacity factor D = Stone column diameter L = Stone column length As = Stone column area 13 Arabian Journal for Science and Engineering Fig. 7 BIR of stone columns in single-layered soft soil with and without encasement 0 10 20 30 s/D (%) 40 50 60 70 0 Bearing Improvement ratio, BIR (qr/qu) Encased floating stone column 0.5 Non-encased floating stone column 1 1.5 2 2.5 3 3.5 4 Table 7 The bearing improvement ratio of stone columns in case of single-layered and layered soils with and without encasement Stone column Single-layered soil Non-encased floating stone column Encased floating stone column Layered soil Non-encased floating stone column Encased floating stone column BIR (corresponding to 30 mm settlement) 3.29 3.42 2.05 4.04 was presented. The BIR represents the ratio of vertical stress of reinforced soil at a given settlement to vertical stress of unreinforced soil at the same settlement (qr/qu). Figure 7 illustrates the BIR of stone columns in singlelayered soft soil with and without encasement. In the figure, the corresponding settlement values (s) to bearing improvement ratio were normalized by footing diameter (D) and the values were given as s/D in percentages. Table 7 gives the calculated BIRs corresponding to 30 mm settlement. From the values in Table 7, the BIR of encased floating stone columns was slightly higher than the non-encased floating stone column. Figure 8 shows the BIR versus the normalized settlement curves of stone columns in layered soil with and without encasement. The BIR values corresponding to 30 mm settlement for non-encased and encased floating stone columns are also given in Table 7. From the table, it can be seen that in both cases of soil layering conditions, the BIR values increased with geotextile encasement of the stone columns. Compared with the BIR value of the non-encased floating stone column in single-layered soft soil, the BIR value of the encased floating stone column in single-layered soft soil increased by 1.04-fold. The BIR value of the non-encased floating stone column in layered soil was much lower than the BIR value of the encased floating stone column in layered soil. With geotextile enhancement, the BIR value of the encased floating stone column in layered soil increased by 1.97 times the BIR value of the non-encased floating stone column in layered soil. The smaller value of the BIR in non-encased floating stone column in layered soil was due to the presence of loose sand surrounding the stone column. The BIR value of the non-encased floating stone column in single-layered soft soil was approximately 1.60 times higher than the BIR value of the non-encased floating stone column in layered soil. This is due to the insufficient lateral confinement provided by the loose sand which caused reduction in the BIR value of the non-encased floating stone column in layered soil. These findings indicate the effectiveness of geotextile in the improvement of bearing capacity of the stone columns. The inclusion of geotextile in the stone column increased the bearing capacity of both single-layered and layered soils and resulted in higher BIR values compared to the BIR values of the non-encased floating stone columns. 5 Conclusions Based on the small-scale laboratory pilot test results, the following conclusions were drawn from this study: 13 Arabian Journal for Science and Engineering Fig. 8 BIR of stone columns in layered soil with and without encasement s/D (%) 0 10 20 30 40 50 60 70 Bearing Improvement ratio, BIR (qr/qu) 0 Non-encased floating stone column 0.5 1 Encased floating stone column 1.5 2 2.5 3 3.5 4 4.5 • The bearing capacity of soft soils has been improved in all cases of stone column application. The non-encased stone column increased the bearing capacity of singlelayered soft soil by at most 3.3 times. With geotextile encasement, the bearing capacity of single-layered soft soil increased by 3.4 times, whereas, for the non-encased stone column, the increase in the bearing capacity of layered soil was found to be 2.0 times and with geotextile encasement, the bearing capacity of layered soil increased by 4.0 times. • In single-layered soft soil, the maximum bulging for non-encased and encased stone columns were 16.5% and 11.4% of the original diameter of stone column, respectively. As compared to non-encased stone column, about a 30% reduction in the maximum bulging diameter can be achieved with the provision of an encased stone column. • The inclusion of geotextile encasement with stone columns resulted in further improvement of soft soils by distributing the induced stress over larger areas. 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