Parametric study on the lateral deformation of the granular column using recycled materialsAbstract
This research article presents the results of lateral displacement behaviour of granular columns filled with stiff and flexible recycled materials reinforced in soft soil. In this investigation, finite element analysis was carried out to analyse the lateral displacement response with depth of granular column reinforced into soil stratum. Design parameters of granular columns have been varied including centre to centre spacing varied from 2 m to 4 m and the ratio of depth of columns to depth of soil stratum varied from 0.5 to 1.0. Homogenous soil stratum of 11 m square section has been analysed by varying lateral displacement with depth of columns and variation of principle effective stress with lateral displacement of granular columns. The outcomes reveal that with the increase in depth of granular column, lateral deformation decreases and principle effective stress increases. Similarly, lateral deformation increases for spacing to diameter ratio from 3 to 4 and for spacing to diameter ratio of 2, the zone of high concentrations has been observed due to disproportionate lateral interface among closely spaced columns, resulting in increased lateral deformation and compromised stability. These findings emphasize the critical importance of improving geometrical parameters in the design of granular columns incorporating recycled materials to enhance structural integrity and performance in geotechnical applications.
Keywords:
Liquefaction; Granular column; Finite element method; Recycled materials; Effective stress; Lateral deformation
1. Introduction
Generally, in most countries, reduction in the settlement of infrastructure for long term and enabling economically design of foundation with adequate bearing capacity are prerequisites for infrastructure development. Excessive settlement from soft clay foundation could result in undrained soil failure in the absence of actual improvement in ground (Basack et al., 2018). Loss of shear strength in saturated soils as a result of excessive pore pressure generation associated with liquefaction leads to lateral displacement under seismic conditions. Many grounds improvement technique, such as compression, hardening, vertical drains, deep soil mixing and granular column (granular pile) might lessen the risk of liquefaction and the ensuing ground deformation (Lu et al., 2019). The vertical displacement with varying geometrical cases and consolidation effect has been shown in Pradhan & Tiwari (2024). Due to inadequate lateral confining pressures, granular columns were unable to support their load capacity in exceptionally weak soft clay, supplied from the nearby soils and might not even be sufficient to form the columns while they were being installed under a severe circumstance. Srijan & Gupta (2023) demonstrates by experiment that the soil stratum's bearing capacity rises with the use of vertical and horizontal reinforcement layers. Numerous academics have examined the soil stratum and compatibility of granular columns thus far. Tan et al. (2021) simulated stone column integrity failure and high-risk locations during installation and injection, respectively, taking into account complex geological circumstances (interlayers). Remadna et al. (2020) demonstrates how accounting for the installation effect can lessen the deformation of the surrounding soil and the columns by raising the soil's lateral earth pressure coefficient. Rainfall induced slope failures have become more common in tropical regions due to increasing extreme rainfall events driven by climate change (Rangarajan et al., 2024).
Based on the previously mentioned research, it was evident from the ground model and all formalized approach stare the behavior of the granular columns in the composite soil was significantly analyzed. After examining the various studies mentioned above, it became evident that the behavior of granular columns in composite ground is extensively analyzed by field models and all analytical approaches. Despite the many benefits of using granular columns to prevent liquefaction, debris used as a filler material has a significant impact on the settlement profile. This analysis covered the granular column filler material that was the subject of several research. The appropriate use of stone aggregate derived from construction and industrial waste was taken into account in order to forecast the results. The present investigation employs parametric study across a broad range of parameters, revealing that the expected model effectively utilized to forecast the impacts of varying factors on the composite ground's settlement response and load carrying capacity. The degree of granular pile (GP) penetration into soil is included in the projected model. GP deformation moduli are mainly thought to be constant with depth. To forecast the expected site's settlement response, stratification of the soil layer is also taken into account. In this study, the reinforced soil model was designed to analyze the lateral displacement profile of the granular columns using finite element analysis. The group of nine granular columns varied geometrically with their centre to centre spacing (s) and depth of penetration of columns (L). The influence of principle effective stress (σ' 1) varied with the lateral displacement (Ux ) was also studied.
2. Materials
For numerical analysis, the primary material includes soft clay stratum and various recycled aggregates include marble, granite, sandstone, limestone, crushed brick, glass, and lightweight expanded clay aggregates (LECA) characterized by its own set of geotechnical properties such as modulus of elasticity and Poisson’s ratio. These materials play a crucial role in accurately predicting the settlement of composite ground.
2.1 Soft clay
The soft clay considered for the analysis represents a natural weak soil layer that typically requires improvement. It is characterized by low shear strength and high compressibility (CH). The properties assigned to soft clay includes γdry = 16.63 kN/m3. It was hypothesized that the Es of soft clay followed a reverse relation with mv for a specific pressure range (100-200 kPa). Table 1 shows the properties of considered soil.
2.2 Recycled materials
The granular column with grain size 10 mm to 20 mm was filled with substitute materials like broken brick, marble, granite, limestone, glass, sandstone, recycled concrete aggregate (RCA), and lightweight expanded clay aggregate (LECA). The excess of waste materials continues to be a problem for society because of the large amount of construction and demolition (C&D) waste stone aggregates, concrete, plastics and other materials that are produced each year all over the world. Table 2 shows the recycled material properties used in the analysis.
3. Numerical formulation
The Mohr-Coulomb failure criterion has been considered for soil behavior to evaluate displacement characteristics under given loading conditions. The linear elastic material model has been used for recycled materials signifies their relative stiffness. A general condition has been employed in which the homogenous soft clay was reinforced with a group of 9 granular columns. Filler aggregates between 10 mm to 20 mm were considered in recycled form including higher stiffness to lower stiffness. Higher stiffness materials (Egp > 70 GPa) include limestone, granite and marble, medium stiffness material (45 < Egp < 70 GPa) include sandstone and recycled concrete aggregates (RCA) whereas lower stiffness material (Egp < 45 GPa) include brick, glass and LECA. Figure 1 shows the mesh of the 3D model. Figure 2 shows the sectional shape of the ground condition considered for the analysis part having group of 9 granular columns with diameter (d) of the columns and the centre to centre spacing (s) has been varied as shown in the plan. Figure 3 shows the section of the granular columns with their length (L) reinforced into the soil deposit up to the stiff base (Hs ). A soft clay stratum of 11 m square sectional shape has been analysed with finite element technique in PLAXIS 3D. The diameter (d) of the granular columns were kept constant during the analysis and assigned to 1 m where the depth (L) of the columns increased from 7.5 m to 15.0 m. For no slippage condition in the column and soil interaction, the hard stratum (Hs ) was assumed at 15 m for the observation.
3.1 Boundary conditions
The boundary conditions employed for the analysis such that displacement was permitted at peripheral edges of the section of soil while radial displacement was constrained. Now, for the lowest section of reinforced soil, the displacement in radial and peripheral edges were not permitted.
3.2 Parametric study
The geometry of granular columns varied in their spacing from 2 m to 4 m i.e., s/d = 2, s/d = 3 and 4. The diameter of 1 m has been assigned to the columns with variation in depth from 7.5 m to 15.0 m i.e., L/H = 0.5 to L/H = 1.0 up to hard stratum. A direct load of 100 kPa intensity has been applied to the columns in order to obtain the lateral displacement profile of the model. The lateral displacement (Ux ) of the reinforced soil medium has been varied with spacing (s/d = 2,3 and 4) and depth of columns (L/H = 0.5 to L/H = 1.0).
The model has been designed in the geotechnical software PLAXIS 3D which was used to simulate the model. For comparison of parametric values with lateral displacement of granular columns with different recycled materials, the analysis taken place of for wide range of parameters. The surcharge of 100 kN/ m2 has been applied to the granular columns with the prescribed displacement of 100 mm. Experiments are used to analyse the crucial mesh in order to accurately determine the corresponding designs. The situation where a uniform surcharge was applied to the granular columns and a soil layer was inserted at a suitable depth. Up to the hard layer, homogeneous ground conditions were taken into account. The design study was predicted on the soil's (μs ) and pile's (μgp ) Poisson’s ratios as well as their respective young's moduli (Egp and Es ) and it was intended for the Poisson ratio to be constant up to the layer. Table 3 lists the granular pile (GP) parameters that were taken into consideration during design.
4. Result and discussion
4.1 Variation of lateral displacement of granular columns with depth (L/H = 0.5 to L/H = 1.0) for different values of spacing (s/d = 2, 3 and 4)
It was observed that with the increase in the depth of granular columns, the value of lateral displacement reduces to a certain extent. For L/H = 0.5, the maximum lateral displacement profile was observed between 0.5 m to 2.5 m while for L/H = 1.0, the maximum lateral displacement profile was observed between 7 m to 15 m. Similarly, the centre to centre spacing from 2 m to 4 m was assigned to the model to observe the variation of spacing with the lateral displacement. In the analysis, high stress zone was developed for 2 m and 3 m spaced granular columns which leads to increase in the lateral displacement profile for the closely spaced columns. The optimum spacing of granular columns depends upon the sectional shape of the soil stratum and here, more prominent results were observed for 4 m spacing i.e., s/d = 4. The marble, limestone and granite show maximum reduction due to higher elastic modules while lightweight expanded clay aggregate, glass and brick shows minimum reduction due to lower values of elastic modules in the lateral displacement profiles of granular columns. The sandstone and recycled concrete aggregate show preferable results to minimize the lateral displacement profile to a certain extent.
Figure 4 shows the variation of lateral displacement for L/H = 0.5 and s/d = 2 granular columns made with recycled aggregates. Here, at 1 m depth of granular columns, the maximum variation of lateral displacement was observed for all materials. The maximum and minimum lateral displacement was observed for light weight expanded clay aggregates and marble i.e., 1.44 mm and 1.00 mm respectively. For other materials including limestone, brick, sandstone, recycled concrete aggregates, glass and granite, the values of lateral displacements were 1.03, 1.22, 1.15, 1.16, 1.22 and 1.09 mm respectively. At the upper section of column groups, the variation of lateral displacement was maximum as compared to lower depths due to punching.
Figure 5 shows variation of lateral displacement profile for L/H = 1.0 and s/d = 2. At 9 m depth, the maximum lateral displacement variation has been observed for all the materials. The maximum and minimum Ux were observed for LECA and marble i.e., 0.93 mm and 0.30 mm respectively. Similarly, for other materials including limestone, sandstone, granite, glass and brick, the Ux reported as 0.35, 0.49, 0.42, 0.62 and 0.84 mm respectively. Here, in the lower section of column groups, the variation of Ux profile was maximum compared to upper section. The increase in the concentration of stresses and generation of high stress zone at full depth of columns causes an increase in the peak of lateral displacement at lower section.
Figure 6 shows the variation of lateral displacement for L/H = 0.5 and s/d = 3 granular columns made with recycled aggregates. Here, at 0.5 m depth of granular columns, the maximum variation of lateral displacement was observed for all materials. The maximum and minimum lateral displacement was observed for light weight expanded clay aggregates and marble i.e., 0.8 mm and 0.23 mm respectively. For other materials including limestone, brick, sandstone, recycled concrete aggregates, glass and granite, the values of lateral displacements were 0.26, 0.67, 0.39, 0.42, 0.46 and 0.32 mm respectively. These outcomes show the influence of material stiffness, where marble, limestone and granite reduce Ux and other materials allow more deformation.
Figure 7 shows variation of lateral displacement profile for L/H = 1.0 and s/d = 3. At 9 m depth, the maximum lateral displacement variation has been observed for LECA and at 13 m depth, maximum lateral displacement variation observed for all other materials. The maximum and minimum Ux were observed for LECA and marble i.e., 0.62 mm and 0.27 mm respectively. Similarly, for other materials including limestone, sandstone, granite, glass and brick, the Ux reported as 0.53, 0.51, 0.52, 0.64 and 0.59 mm respectively. Here, the increase in depth of the column from 7.5 m to 15 m reduces the Ux to a certain extent. The values of Ux are highly influenced by material stiffness, spacing and depth of column, such that material with high value of modulus of elasticity shows less Ux and with increased in the s/d ratio from 2 to 3, the confinement of surrounding materials get reduced, leading to increase in Ux in a particular interval.
Figure 8 shows the variation of lateral displacement for L/H = 0.5 and s/d = 4. Here, at 1 m depth of granular columns, the maximum variation of lateral displacement was observed for all materials. The maximum and minimum lateral displacement was observed for light weight expanded clay aggregates and marble i.e., 0.33 mm and 0.12 mm respectively. For other materials including limestone, brick, sandstone, recycled concrete aggregates, glass and granite, the values of lateral displacements were 0.13, 0.29, 0.18, 0.19, 0.2 and 0.15 mm respectively. The depth of column group for 7.5 m engaging less with the deeper, stiffer soil layers, leading to more movement near the surface where the soil offers less confinement.
Figure 9 shows variation of lateral displacement profile for L/H = 1.0 and s/d = 4. At 5 m depth, the maximum lateral displacement variation has been observed for all the materials. The maximum and minimum Ux were observed for LECA and marble i.e., 0.69 mm and 0.6 mm respectively. Similarly, for other materials including limestone, sandstone, granite, glass, recycled concrete aggregate and brick, the Ux reported as 0.642, 0.669, 0.602, 0.68, 0.644 and 0.683 mm respectively. Here, with increase in the depth of column group, resistance from the surrounding materials increases which leads to larger accumulation of lateral displacement as varying stiffness of materials influencing the deformation.
4.2 Variation of principle effective stress with the lateral displacement for different recycled aggregates as filler in granular columns
Moreover, to examine the influence of relative stiffness of the materials, the principle effective stress of the columns was also varied with lateral displacement for all the materials with variation in the spacing, i.e., s/d = 2, 3 and 4. Here, with increase in the depth of penetration of columns in the soil, the principle effective stress increases. The lateral displacement profile of the soil medium surges with the increase in the principle effective stress due to nonlinear behaviour of the soil. It was observed that nearby soil and granular columns undergo nonlinear stress-strain behaviour which results in the increment of lateral displacement with effective stress. The higher values of soil compression were also responsible for the increasement of the effective stress of the soil with increase in the lateral displacement of the soil.
Figure 10 shows variation of principle effective stress (σ' 1) with lateral displacement Ux for brick material. The spacing between the granular columns also varied from 2 to 4 m i.e., s/d = 2, 3 and 4. It was noted that with increase in the spacing between the columns, the lateral displacement Ux increases for s/d = 2 to s/d =4. However, the results were similar for s/d =2 and s/d = 3. The principle effective stress in brick material reaches up to 1350 kPa for lateral displacement of 76 mm corresponds to s/d = 2. For s/d = 3, the principle effective stress reaches up to 1162 kPa for Ux of 65 mm. Similarly, the principle effective stress for s/d = 4 reaches up to 871 kPa for lateral displacement of 141 mm. Due to high stress zone in the columns, the consideration of spacing was not showing significant results.
Figure 11 shows variation of principle effective stress (σ' 1) with lateral displacement Ux for recycled concrete aggregate (RCA). The spacing between the granular columns also varied from 2 to 4 m i.e., s/d = 2, 3 and 4. Here, the spacing s/d =3 and s/d =4 were more prominent than s/d = 2. The principle effective stress in recycled concrete aggregate reaches up to 1517 kPa for lateral displacement of 77 mm corresponds to s/d = 2. For s/d = 3, the principle effective stress reaches up to 1469 kPa for Ux of 69 mm. Similarly, the principle effective stress for s/d = 4 reaches up to 1253 kPa for lateral displacement of 124 mm.
Variation of principle effective stress with lateral displacement for recycled concrete aggregate (RCA).
Figure 12 shows variation of principle effective stress (σ' 1) with lateral displacement Ux for sandstone material. The spacing between the granular columns also varied from 2 to 4 m i.e., s/d = 2, 3 and 4. It was noted that with increase in the spacing between the columns, the lateral displacement Ux increases for s/d = 3 to s/d = 4. The principle effective stress in sandstone material reaches up to 1900 kPa for lateral displacement of 77 mm corresponds to s/d = 2. For s/d = 3, the principle effective stress reaches up to 1723 kPa for Ux of 72 mm. Similarly, the principle effective stress for s/d = 4 reaches up to 1665 kPa for lateral displacement of 111 mm. Here also, due to nonlinear behaviour and high stress zone in the columns, the consideration of spacing was not showing significant results for s/d = 2.
Figure 13 shows variation of principle effective stress (σ' 1) with lateral displacement Ux for granite material. The spacing between the granular columns varied from 2 to 4 m i.e., s/d = 2, 3 and 4. Similarly, here also the considerable results were observed for s/d =3 to s/d = 4. The principle effective stress in granite material reaches up to 2721 kPa for lateral displacement of 79 mm corresponds to s/d = 2. For s/d = 3, the principle effective stress reaches up to 2473 kPa for Ux of 77 mm. Similarly, the principle effective stress for s/d = 4 reaches up to 2577 kPa for lateral displacement of 83 mm.
Figure 14 shows variation of principle effective stress (σ' 1) with lateral displacement Ux for limestone material. The spacing between the granular columns also varied from 2 to 4 m i.e., s/d = 2, 3 and 4. Here, almost similar results were observed for the spacing s/d = 2, s/d = 3 and s/d = 4. The principle effective stress in brick material reaches up to 3816 kPa for lateral displacement of 79 mm corresponds to s/d = 2. For s/d = 3, the principle effective stress reaches up to 3472 kPa for Ux of 82 mm. Similarly, the principle effective stress for s/d = 4 reaches up to 3627 kPa for lateral displacement of 62 mm.
5. Conclusion
A numerical investigation has been conducted using finite element techniques to evaluate the lateral deformation profile of the granular columns using stiff and flexible materials as a filler. Simultaneously, principle effective stress has been varied with lateral deformation in order to observe the behaviour of columns in terms of stress generation. The geometrical parameters were also varied with lateral deformation of granular columns including variation in spacing from 2 m to 4 m (s/d =2 to 4) and variation in depth of granular columns form 7.5 m to 1.0 m (L/H = 0.5 to 1.0). On the basis of the outcomes prevails; the following conclusion has been drawn:
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The marble has maximum resistance to the lateral displacement among all the materials due to its higher young modulus of elasticity whereas LECA has shown minimum resistance to lateral displacement;
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The marble, limestone, granite and sandstone showed satisfactory performance in granular column construction due to their higher stiffness making them suitable for enhancing the lateral stability in various geotechnical applications;
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With increase in the depth of granular columns in the soil stratum, the lateral deformation decreases and principle effective stress increases in significant amount;
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The principle effective stress increases with increase in the lateral deformation of granular columns. The peak of the lateral displacement increases with an increase in the spacing between the granular columns;
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At s/d = 2, the zone of high stress concentration has been generated causes increases in the lateral deformation;
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Similarly, the principle effective stress is minimum for brick and maximum for marble when varied with lateral deformation.
List of symbols and abbreviations
c/c Center to center
cu Cohesion
d Diameter of the pile
de Unit cell diameter
r Radial distance from z-axis /Coordinate of axi-symmetry
s spacing
u Displacement in r direction
w Water absorption
w Displacement in z direction
z Axis of symmetry
Egp Modulus of elasticity of granular pile
Es Modulus of elasticity of soil
Fn Load bearing capacity
C&D Construction and Demolition
CH Clay of high compressibility
EC Embodied Carbon
G Specific gravity
GP Granular Pile
H Thickness of soil layer
L Length of the pile
LECA lightweight expanded clay aggregates
LL Liquid limit
OMC Optimum moisture content
Pr Perceive Settlement ratio
PI Plasticity Index
RCA recycled concrete aggregate
Ux Lateral displacement
UDL Uniformly Distributed Load
γbulk Bulk density
γdry Dry density
µgp Poisson’s ratio of granular pile
µs Poisson’s ratio of soil
σ Stress
σ'1 Principle effective stress
σgp Stress in granular pile
σs Stress in surrounded soil
σz Intensity of uniformly distributed load
Φ Angle of internal friction
Acknowledgements
For encouragement of this study, the author would like to thank the Malaviya National Institute of Technology.
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Discussion open until May 31, 2026.
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Data availability
All data produced or examined in the course of the current study are included in this article.
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Declaration of use of generative artificial intelligence
This work was prepared without the assistance of any generative artificial intelligence (GenAI) tools or services. All aspects of the manuscript were developed solely by the authors, who take full responsibility for the content of this publication.
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Edited by
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Editor:
Renato P. Cunha https://orcid.org/0000-0002-2264-9711
Data availability
All data produced or examined in the course of the current study are included in this article.
Publication Dates
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Publication in this collection
17 Nov 2025 -
Date of issue
2026
History
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Received
01 Feb 2025 -
Accepted
20 May 2025
