Influence of Aspect Ratio on the Performance of Geocell-Reinforced Footings in Sandy Soils

Abstract

The aspect ratio of the shallow footing is a key parameter affecting the bearing capacity performances. However, the recommendations of previous studies exhibit notable inconsistencies among themselves for the unreinforced condition, and no numerical study in the literature has investigated the effect of aspect ratio under geocell-reinforced condition. This pioneer study investigates the influence of footing aspect ratio and soil relative density on the ultimate bearing capacity, shape factor, improvement factor, and failure mechanism of unreinforced and geocell-reinforced footings resting on sandy soils. A total of 36 rigorous three-dimensional finite element analyses were performed and validated against physical model tests. The analyses considered footings with aspect ratios ranging from 1 to 10 placed on loose and dense sands. The results showed that geocell reinforcement substantially improves footing performance by increasing bearing pressures, ultimate bearing capacities, stiffness of the footing pressure versus footing settlement ratio curves and shape factor values. Improvement factors were observed to lie between 1.12 and 2.56, with square footings showing the maximum improvement, and the magnitude of improvement increasing as the relative density increased. Furthermore, for unreinforced footings, the maximum shape factor occurred at aspect ratio of 2, whereas in geocell-reinforced conditions, the peak shifted to aspect ratio of 1. The shape factor values also increased with increasing relative density. Moreover, it was observed that the aspect ratio influences both the failure surface geometry and reinforcement mechanism of geocell.

Keywords

• Geocell
• Geosynthetic
• Aspect ratio
• Shape factor
• Finite element analysis

Kumlu Zeminler Üzerine Yerleştirilmiş Geocell ile Güçlendirilmiş Temellerin Performansına En Boy Oranının Etkisi

Abstract

Bu çalışmada, temelin en-boy oranının ve zemin rölatif sıkılığının, kum zeminler üzerine yerleştirilen hem güçlendirilmemiş hem de geocell ile güçlendirilmiş temellerin nihai taşıma gücü, şekil faktörü, iyileştirme faktörü ve yenilme mekanizması üzerindeki etkisini araştırmaktadır. Bu kapsamda, fiziksel model deneyleriyle doğrulanan toplam 36 adet kapsamlı üç boyutlu sonlu elemanlar analizi gerçekleştirilmiştir. Analizler, en-boy oranı 1 ile 10 arasında değişen temeller ile gevşek ve sıkı kum koşulları için değerlendirilmiştir. Elde edilen sonuçlar, geocell donatısının temel gerilmelerini, nihai taşıma kapasitelerini, gerilme-deplasman oranı eğrilerinin rijitliğini ve şekil faktörü değerlerini artırarak temel performansını önemli ölçüde iyileştirdiğini göstermiştir. İyileşme faktörlerinin 1.12 ile 2.56 arasında değiştiği, en yüksek iyileşmenin kare temellerde elde edildiği ve rölatif sıkılığın artışı ile birlikte iyileşme faktörü değerlerinin artış gösterdiği gözlemlenmiştir. Ayrıca, güçlendirilmemiş temellerde maksimum şekil faktörünün en-boy oranının 2’ye eşit olduğu durumda görülürken, geocell ile güçlendirilme sonucunda bu pik değer en-boy oranı 1’e kaymıştır. Yapılan çalışmadan elde edilen bulgular, sığ temelin en-boy oranının ve zeminin rölatif sıkılığın geocell ile güçlendirilmiş temellerin performansı üzerindeki önemli etkisini vurgulayarak, pratik uygulamalarda temel geometrisi ve donatı tasarımının optimize edilmesi için değerli rehberlik sağlamaktadır.

Keywords

• geocell
• geosentetik
• temelin en-boy oranı
• şekil faktörü
• PLAXIS 3D

References

1. Prandtl, L., “Über die harte plastischer körper, nachrichten von der könighlichen gesellschaftder wissenschaften zur göttingen”, Mathematisch-Physikalischen Klasse, 1:15-20, (1920).
2. Reissner, H., “Zum Erddruckproblem”, Proceedings of the 1st International Congress for Applied Mechanics, Delft, The Netherlands (1924).
3. Fellenius, W., “Mechanics of Soils” Statika Gruntov, Gosstrollzdat, (1926).
4. Terzaghi, K., “Theoretical Soil Mechanics”, 1st ed., Wiley, New York, USA, (1943).
5. Hansen, J.B., “A General formula for bearing capacity” Bulletin No. 11, Danish Geotechnical Institute, Copenhagen, Denmark (1961).
6. Meyerhof, G.G., “Some recent research on the bearing capacity of foundations”, Canadian Geotechnical Journal, 1(1): 16-26, (1963). DOI: https://doi.org/10.1139/t63-003.
7. De Beer, E.E., “Experimental determination of the shape factors and the bearing capacity factors of sand”, Geotechnique, 20(4): 387-411, (1970). DOI: https://doi.org/10.1680/geot.1970.20.4.387.
8. Perau, E.W., “Bearing capacity of shallow foundations”, Soils and Foundations, 37(4): 77-83, (1997). DOI: https://doi.org/10.3208/sandf.37.4_77.

9. Zhu, M., and Michalowski R.L., “Shape factors for limit loads on square and rectangular footings”, Journal of Geotechnical and Geoenvironmental Engineering, 131(2): 223-231, (2005). DOI: https://doi.org/10.1061/(ASCE)1090-0241(2005)131:2(223).
10. Lyamin, A.V., Salgado, R., Sloan, S.W., and Prezzi, M., “Two-and three-dimensional bearing capacity of footings in sand”, Géotechnique, 57(8): 647-662, (2007). DOI: https://doi.org/10.1680/geot.2007.57.8.647.
11. Puzakov, V., Drescher, A., and Michalowski R.L., “Shape factor Sγ for shallow footings”, Geomechanics and Engineering, 1(2): 113-120, (2009). DOI: https://doi.org/10.12989/gae.2009.1.2.113.
12. Antao A.N., da Silva M.V., Guerra, N., and Delgado R., “An upper bound-based solution for the shape factors of bearing capacity of footings under drained conditions using a parallelized mixed fe formulation with quadratic velocity fields”, Computers and Geotechnics, 41: 23-35, (2012). DOI: https://doi.org/10.1016/j.compgeo.2011.11.003.
13. Mohapatra, D., and Kumar, J., “Collapse loads for rectangular foundations by three‐dimensional upper bound limit analysis using radial point interpolation method”, International Journal for Numerical and Analytical Methods in Geomechanics, 43(2): 641-660, (2019). DOI: https://doi.org/10.1002/nag.2885.
14. Yunkul, K., Gurbuz, A., and Demirdogen, S., “The effect of aspect ratio on the shape factors of rectangular footings on sandy soil”, Turkish Journal of Civil Engineering, 37(1): 35-63, (2026). DOI: https://doi.org/10.18400/tjce.1637258.
15. Michalowski, R.L., “Upper-bound load estimates on square and rectangular footings”, Géotechnique, 51(9): 787-798, (2001). DOI: https://doi.org/10.1680/geot.2001.51.9.787.
16. Shafiqul Islam, M., Rokonuzzaman, M., and Sakai, T., “Shape effect of square and circular footing under vertical loading: experimental and numerical studies”, International Journal of Geomechanics, 17(9): 06017014, (2017). DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000965.
17. Osman, A.S., “Upper bound solutions for the shape factors of smooth rectangular footings on frictional materials”, Computers and Geotechnics, 115, 103177, (2019). DOI: https://doi.org/10.1016/j.compgeo.2019.103177.
18. Pantelidis, L., Assefa, E., and Sachpazis, C.I., “The effect of footing shape on the bearing capacity of shallow foundations: A review”, Archives of Computational Methods in Engineering, 32(3): 1597-1617, (2025). DOI: https://doi.org/10.1007/s11831-024-10184-6.
19. Pancar, E.B., and Akpınar, M.V., “Comparison of effects of using geosynthetics and lime stabilization to increase bearing capacity of unpaved road subgrade”, Advances in Materials Science and Engineering, 2016(1), 7129356, (2016). DOI: https://doi.org/10.1155/2016/7129356.
20. Isik, A., and Gurbuz, A., “Pullout behavior of geocell reinforcement in cohesionless soils”, Geotextiles and Geomembranes, 48(1): 71-81, (2020). DOI: https://doi.org/10.1016/j.geotexmem.2019.103506.
21. Arslan, A., Gumus, M., and Unal, E., “Effect of support conditions on the performance of B70 sleeper overlying reinforced ballast and sub-ballast layer: Experimental and analytical investigation”, Transportation Geotechnics, 37: 100847. (2022). DOI: https://doi.org/10.1016/j.trgeo.2022.100847.
22. Yunkul, K., and Gurbuz, A., “Uplift behavior of shallow horizontal plate anchors reinforced with geocells in cohesionless soil”, European Journal of Environmental and Civil Engineering, 26(4): 1243-1266, (2022). DOI: https://doi.org/10.1080/19648189.2019.1707123.
23. Isik, A, Anil, O., and Gurbuz, A., “Proposed novel bond-slip model for geocell reinforcement under pull-out loading condition”, Géotechnique, 73(11): 961-973, (2023). DOI: https://doi.org/10.1680/jgeot.21.00120.
24. Latha, G.M., Venkateswarlu H., and Krishna, A., “Geocell Anchor Cage for enhanced load support in soil structures”, Construction and Building Materials, 425: 135998, (2024). DOI: https://doi.org/10.1016/j.conbuildmat.2024.135998.
25. Dash, S.K., Krishnaswamy, N.R., and Rajagopal K., “Bearing capacity of strip footings supported on geocell-reinforced sand”, Geotextiles and Geomembranes, 19(4): 235-256, (2001). DOI: https://doi.org/10.1016/S0266-1144(01)00006-1.
26. Dash, S.K., “Influence of relative density of soil on performance of geocell-reinforced sand foundations”, Journal of Materials in Civil Engineering, 22(5): 533-538, (2010). DOI: https://doi.org/10.1061/(ASCE)MT.1943-5533.0000040.
27. Gurbuz, A., and Mertol, H.C., “Interaction between assembled 3D honeycomb cells produced from high density polyethylene and a cohesionless soil”, Journal of Reinforced Plastics and Composites, 31(12): 828-836, (2012). DOI: https://doi.org/10.1177/0731684412447529.
28. Shadmand, A., Ghazavi, M., and Ganjian, N., “Scale effects of footings on geocell reinforced sand using large-scale tests”, Civil Engineering Journal, 4(3): 497-508, (2018). DOI: http://dx.doi.org/10.28991/cej-0309110.
29. Fazeli Dehkordi, P., Ghazavi, M., and Karim, U.F.A., “Bearing capacity-relative density behavior of circular footings resting on geocell-reinforced sand”, European Journal of Environmental and Civil Engineering, 26(11): 5088-5112, (2022). DOI: https://doi.org/10.1080/19648189.2021.1884901.
30. Banerjee, S., Manna, B., and Shahu, J.T., “Experimental investigation of the geometry of geocell on the performance of flexible pavement under repeated loading”, Geotextiles and Geomembranes, 52(4): 654-670, (2024). DOI: https://doi.org/10.1016/j.geotexmem.2024.03.007.
31. Demirdogen, S., Gurbuz, A. and Yunkul, K., “3D-printed geocells in footing systems: A comprehensive physical and numerical studies on scaling and performance under centric and eccentric loading scenarios”, Transportation Geotechnics, 45: 101214, (2024). DOI: https://doi.org/10.1016/j.trgeo.2024.101214.
32. Demirdogen, S., Gurbuz, A., and Yunkul, K., “Performance of eccentrically loaded strip footings on geocell-reinforced soil”, Geotextiles and Geomembranes, 52(4): 421-434, (2024). DOI: https://doi.org/10.1016/j.geotexmem.2023.12.007.
33. Demirdogen, S., Gurbuz, A., and Yunkul, K., “Parameters affecting performance of fully instrumented model testing of strip footings on geocell-reinforced soils”, Geotextiles and Geomembranes, 52(6): 1191-1206 (2024). DOI: https://doi.org/10.1016/j.geotexmem.2024.08.002.
34. Evirgen, B., Kara, H.O., Ucun, M.S., Gultekin, A.A., Tos, M., and Ozturk V., “The effect of the geometrical properties of geocell reinforcements between a two-layered road structure under overload conditions”, Case Studies in Construction Materials, 20: e02793, (2024). DOI: https://doi.org/10.1016/j.cscm.2023.e02793.
35. Demirdogen, S., and Gurbuz, A., “Load-induced strain analysis in geocell reinforced footing systems”, Geotextiles and Geomembranes, 53(5): 1156-1167, (2025). DOI: https://doi.org/10.1016/j.geotexmem.2025.05.002.
36. Gurbuz, A., Demirdogen, S., Yunkul, K., and Karatas, F., “Interference effect of geocell-reinforced shallow strip foundations on sandy soil”, Journal of Materials in Civil Engineering, 37(7): 04025200, (2025). DOI: https://doi.org/10.1061/JMCEE7.MTENG-18828.
37. Gurbuz A., Yunkul K., Demirdogen S. and Kalkan, H., “Performance assessment of 3D-printed scaled geocell-reinforced sandy soils under varying footing sizes”, Transportation Geotechnics, 56: 101751, (2026). DOI: https://doi.org/10.1016/j.trgeo.2025.101751.
38. Ari, A., and Misir, G., “Three-dimensional numerical analysis of geocell reinforced shell foundations”, Geotextiles and Geomembranes, 49(4): 963-975, (2021). DOI: https://doi.org/10.1016/j.geotexmem.2021.01.006.
39. Banerjee, S., Manna, B., and Shahu, J.T., “Behaviour of geocell reinforcement in a multi-layered flexible pavement under repeated loading”, International Journal of Geosynthetics and Ground Engineering, 10(3): 34, (2024). DOI: https://doi.org/10.1007/s40891-024-00541-7.
40. Kumar, A., Gupta, A., Choudhary, A.K., and Choudhary, A.K., “Influence of geometrical parameters of geocell reinforcement on the load carrying capacity of footing”, Arabian Journal for Science and Engineering, 49(10): 13539-13557, (2024). DOI: https://doi.org/10.1007/s13369-024-08706-2.
41. Gurbuz, A., Karatas, F., Yunkul, K., and Demirdogen, S., “Numerical modelling of geocell-reinforced interfering strip footings on cohesionless soil”, Proceedings of the 22th International Istanbul Scientific Research Congress on Life, Engineering, Architecture and Mathematical Sciences, İstanbul, Türkiye, 518-530 (2025).
42. Zhao Y., Lu Z., Liu J., Hu C. T., Tang C. X., Yan T. Z., Li J., Wang H. and Yao H. L. “Compaction-induced prestressing effect of geocell reinforcement”, Geosynthetics International, 1-19, (2025). DOI: https://doi.org/10.1680/jgein.24.00082.
43. Hegde, A., “Geocell reinforced foundation beds-past findings, present trends and future prospects: a state-of-the-art review”, Construction and Building Materials, 154: 658-674, (2017). DOI: https://doi.org/10.1016/j.conbuildmat.2017.07.230.
44. Yunkul K. and Gurbuz A., “Use of geocells and working mechanism”, Proceedings of the 1st International Symposium on Innovative Approaches in Scientific Studies, Antalya, Türkiye, 354-360, (2018).
45. Banerjee, S., Manna, B., and Shahu, J.T., “Geocell as a promising reinforcement technique for road pavement: a state of the art”, Indian Geotechnical Journal, 54(4): 1644-1665, (2024). DOI: https://doi.org/10.1007/s40098-023-00818-0.
46. Fazeli Dehkordi, P., Ghazavi, M., and Karim, U.F.A., Valinezhad Torghabeh, N., “Interacting footings on geo-reinforced soils: A state-of-the-art review”, Arabian Journal for Science and Engineering, 49(1): 1-25, (2024). DOI: https://doi.org/10.1007/s13369-023-07979-3.
47. Zhang, L., Zhao, M., Shi, C., and Zhao, H., “Bearing capacity of geocell reinforcement in embankment engineering”, Geotextiles and Geomembranes, 28(5): 475-482, (2010). DOI: https://doi.org/10.1016/j.geotexmem.2009.12.011.
48. Koerner, R.M., Designing with Geosynthetics, 6th edition, Xlibris Corporation, (2012).
49. Sitharam, T.G., and Hegde, A., “Design and construction of geocell foundation to support the embankment on settled red mud”, Geotextiles and Geomembranes, 41: 55-63, (2013). DOI: https://doi.org/10.1016/j.geotexmem.2013.08.005.
50. Demirdogen, S., Gurbuz, A., and Yunkul., “A new semi-empirical bearing capacity calculation method for geocell reinforcement in foundations”, Transportation Geotechnics, 49: 101442, (2024). DOI: https://doi.org/10.1016/j.trgeo.2024.101442.
51. Avesani Neto, J.O., Bueno, B.D.S., and Futai, M.M., “A bearing capacity calculation method for soil reinforced with a geocell”, Geosynthetics International, 20(3): 129-142, (2013). DOI: https://doi.org/10.1680/gein.13.00007.
52. Arvin, M.R., Shiau, J., and Irannezhad Parizi, M., “A semi-empirical method for studying load-settlement behavior of geocell-reinforced footings”, Geotechnical and Geological Engineering, 41(2): 1115-1135, (2023). DOI: https://doi.org/10.1007/s10706-022-02326-z.
53. Iai, S., “Similitude for shaking table tests on soil-structure-fluid model in 1g gravitational field”, Soils and Foundations, 29(1): 105-118, (1989). DOI: https://doi.org/10.3208/sandf1972.29.105.
54. Hegde, A., and Sitharam, T.G., “3-Dimensional numerical modelling of geocell reinforced sand beds”, Geotextiles and Geomembranes, 43(2): 171-181, (2015). DOI: https://doi.org/10.1016/j.geotexmem.2014.11.009.
55. Obrzud, R.F., “On the use of the Hardening Soil Small Strain model in geotechnical practice”, Numerics in Geotechnics and Structures, 16: 1-17 (2010).
56. Ornek, M., Laman, M., Demir, A., Yildiz, A., “Numerical analysis of circular footings on natural clay stabilized with a granular fill”, Acta Geotechnica Slovenica, 9(1): 61-75, (2012).
57. Kahyaoglu, M.R., and Sahin, M., “Model studies on polymer strip reinforced soil retaining walls”, Geomechanics and Engineering, 25(5): 357–371, (2021). DOI: https://doi.org/10.12989/gae.2021.25.5.357.
58. Yunkul, K., and Gurbuz, A., “Numerical simulation of polymeric strap material reinforced walls under seismic excitation”, Transportation Research Record, 2678(10): 1181-1204, (2024). DOI: https://doi.org/10.1177/036119812412364.
59. Yunkul, K., Usluogullari, O.F., and Gurbuz, A., “Numerical analysis of geocell reinforced square shallow horizontal plate anchor”, Geotechnical and Geological Engineering, 39(4): 3081-3099, (2021). DOI: https://doi.org/10.1007/s10706-021-01679-1.
60. Hegde A., and Sitharam T. G., “Joint strength and wall deformation characteristics of a single-cell geocell subjected to uniaxial compression”, International Journal of Geomechanics, 15(5): 04014080, (2015). DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000433.
61. Jaky, J., “The coefficient of earth pressure at rest”, Journal of the Society of Hungarian Architects and Engineers, 7: 355–358, (1944).
62. Portakal, G.G., Yeşiltepe, O., and Ornek, M., “Investigation of the effects of foundation geometry and dimensions on bearing capacity in soils reinforced with geocells”, Journal of the Institute of Science and Technology, 13(4): 2730-2742, (2023). DOI: https://doi.org/10.21597/jist.1314170.
63. Abu-Farsakh, M., Chen, Q., and Sharma, R., “An experimental evaluation of the behavior of footings on geosynthetic-reinforced sand”, Soils and Foundations, 53(2): 335-348, (2013). DOI: https://doi.org/10.1016/j.sandf.2013.01.001.
64. Saha Roy, S., and Deb, K., “Bearing capacity of rectangular footings on multilayer geosynthetic-reinforced granular fill over soft soil”, International Journal of Geomechanics, 17(9): 04017069, (2017). DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000959.
65. Saha Roy, S., and Deb, K., “Effects of aspect ratio of footings on bearing capacity for geogrid-reinforced sand over soft soil”, Geosynthetics International, 24(4): 362-382, (2017). DOI: https://doi.org/10.1680/jgein.17.00008.
66. Saha Roy, S., and Deb, K., “Effect of aspect ratio of footings on settlement response of geosynthetic-reinforced granular fill-soft soil system”, European Journal of Environmental and Civil Engineering, 26(1): 216-238, (2022). DOI: https://doi.org/10.1080/19648189.2019.1655484.
67. EN 1997-1, “Eurocode 7”, Geotechnical Design – Part 1: General Rules, (2004).