The Effect of Aspect Ratio on the Shape Factors of Rectangular Footings on Sandy Soil

Öz

The dimensional of the footing is crucial parameter affecting the ultimate bearing capacity and failure surface geometry. However, the recommendations found in the literature often conflict with one another. Therefore, in this study, rigorous parametric three-dimensional finite element analyses using PLAXIS 3D with the Hardening Soil (HS) model were conducted to examine the unit weight component of the shape factors (Sγ), the pressure-settlement responses and the failure mechanisms of rectangular footings with an aspect ratio (L/B), defined as the ratio of the length (L) to the width (B) of the footing, ranging from 1 to 10. These analyses were performed four relative densities (Dr) of the sandy soil ranging from 10% to 80%. The results revealed that Sγ values increased with the L/B ratio, peaking at L/B=1.5, followed by a decline as the L/B ratio continued to increase. An increase in the internal friction angle of the soil led to higher Sγ values. This behavior contradicts some earlier studies and is attributed to the three-dimensional interaction of the failure surface, failure surface geometry and displaced soil volume. Furthermore, non-linear regression analysis was performed to produce novel equations to predict Sγ for rectangular footings and unit weight component of the bearing capacity factor (Nγ) for strip footings in sandy soil, demonstrating strong agreement with FE results.

Anahtar Kelimeler

• Shape factor
• aspect ratio
• shallow footing
• finite element analysis
• PLAXIS 3D

Kaynakça

1. Terzaghi, K., Theoretical Soil Mechanics, 1st ed., New York, USA. Wiley, 1943.
2. Prandtl, L. Über Die Harte Plastischer Körper, Nachrichten Von Der Könighlichen Gesellschaftder Wissenschaften Zur Göttingen, Mathematisch-Physikalischen Klasse, 1, 15-20, 1920.
3. Reissner, H., Zum Erddruckproblem, 1st International Congress for Applied Mechanics. Delft, The Netherlands, 1924.
4. Meyerhof, G. G., Some Recent Research on the Bearing Capacity of Foundations. Canadian Geotechnical Journal, 1(1), 16-26, 1963.
5. Hansen, J. B., A Revised and Extended Formula for Bearing Capacity. Danish Geotechnical Institute, 28, 5–11, 1970.
6. Vesic, A. S., Analysis of Ultimate Loads of Shallow Foundations. Journal of the Soil Mechanics and Foundations Division, 99(1), 45-73, 1973.
7. Michalowski, R., An Estimate of the Influence of Soil Weight on Bearing Capacity Using Limit Analysis. Soils and Foundations, 37(4), 57-64, 1997.
8. Soubra, A. H., Upper-Bound Solutions for Bearing Capacity of Foundations. Journal of Geotechnical and Geoenvironmental Engineering, 125(1), 59-68, 1999.

9. Zhu, D., The Least Upper-Bound Solutions for Bearing Capacity Factor Nγ. Soils and Foundations, 40(1), 123-129, 2000.
10. Hjiaj, M., Lyamin, A.V., Sloan, S.W., Numerical Limit Analysis Solutions for the Bearing Capacity Factor Nγ. International Journal of Solids and Structures, 42(5-6), 1681-1704, 2005.
11. Martin C. M., Exact Bearing Capacity Calculations Using the Method of Characteristics, 11th International Conference of the International Association for Computer Methods and Advances in Geomechanics, Turin, Italy, 2005.
12. Kumar, J., Kouzer, K. M., Effect of Footing Roughness on Bearing Capacity Factor Nγ. Journal of Geotechnical and Geoenvironmental Engineering, 133(5), 502-511, 2007.
13. Lyamin, A.V., Salgado, R., Sloan, S.W., Prezzi, M., Two-and Three-Dimensional Bearing Capacity of Footings in Sand. Géotechnique, 57(8), 647-662, 2007.
14. Jahanandish, M., Veiskarami, M., Ghahramani, A., Effect of Stress Level on the Bearing Capacity Factor, Nγ, by the ZEL Method. KSCE Journal of Civil Engineering, 14, 709-723, 2010.
15. Kumar, J., Khatri, V. N., Bearing Capacity Factors of Circular Foundations for a General C–Φ Soil Using Lower Bound Finite Elements Limit Analysis. International Journal for Numerical and Analytical Methods in Geomechanics, 35(3), 393-405, 2011.
16. TBEC. Turkey Building Earthquake Code. Ministry of Environment and Urbanization of Türkiye. 2018.
17. Hansen, J. B., Simpel Beregning af Fundamenters Bæreevne. Ingeniøren, 22(1) 95-100, 1955.
18. Hansen, J. B., A General Formula for Bearing Capacity, Bulletin No. 11, Danish Geotechnical Institute, Copenhagen, Denmark, 1961.
19. De Beer, E. E., Experimental Determination of the Shape Factors and the Bearing Capacity Factors of Sand. Géotechnique, 20(4), 387-411, 1970.
20. Perau, E. W., Bearing Capacity of Shallow Foundations. Soils and Foundations, 37(4), 77-83, 1997.
21. Okamura, M., Mihara, A., Takemura, J., Kuwano, J., Effects of Footing Size and Aspect Ratio on the Bearing Capacity of Sand Subjected to Eccentric Loading. Soils and Foundations, 42(4), 43-56, 2002.
22. Janabi, F. H., Raja, R. A., Sakleshpur, V. A., Prezzi, M., Salgado, R., Experimental Study of Shape and Depth Factors and Deformations of Footings in Sand. Journal of Geotechnical and Geoenvironmental Engineering, 149(2), 04022128, 2023.
23. Khezri, A., Moradi, M., Mir Mohammad Hosseini, S. M., Park, H., Lee, D., Effect of Footing Shape on the Rocking Behavior of Shallow Foundations. Buildings, 14(3), 573, 2024.
24. Michalowski, R. L., Upper-Bound Load Estimates on Square and Rectangular Footings. Géotechnique, 51(9), 787-798, 2001.
25. Zhu, M., Michalowski, R. L., Shape Factors for Limit Loads on Square and Rectangular Footings. Journal of Geotechnical and Geoenvironmental Engineering, 131(2), 223-231, 2005.
26. Puzakov, V., Drescher, A., Michalowski, R. L., Shape Factor Sγ for Shallow Footings. Geomechanics and Engineering, 1(2), 113-120, 2009.
27. Antão, A. N., da Silva, M. V., Guerra, N., Delgado, R., An Upper Bound-Based Solution for the Shape Factors of Bearing Capacity of Footings Under Drained Conditions Using a Parallelized Mixed F.E. Formulation With Quadratic Velocity Fields. Computers and Geotechnics, 41, 23-35, 103-120, 2012.
28. Shafiqul Islam, M., Rokonuzzaman, M., Sakai, T., Shape Effect of Square and Circular Footing Under Vertical Loading: Experimental and Numerical Studies. International Journal of Geomechanics, 17(9), 06017014, 2017.
29. Mohapatra, D., 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.
30. Mohapatra, D., Kumar, J., Bearing Capacity of Embedded Foundations Using Quasi-Kinematic Limit Analysis. Computers and Geotechnics, 117, 103275, 2020.
31. Osman, A. S., Upper Bound Solutions for the Shape Factors of Smooth Rectangular Footings on Frictional Materials. Computers and Geotechnics, 115, 103177, 2019.
32. Eurocode 7. Geotechnical Design – Part 1: General Rules, EN 1997-1:2004. 2004.
33. Golder, H. Q., Fellenius, W., Kogler, F., Meischeider, H., Krey, H., Prandtl, L., The Ultimate Bearing Pressure of Rectangular Footings. Journal of the Institution of Civil Engineers, 17(2), 161-174, 1941.
34. FHWA. Geotechnical Engineering Circular No. 6 Shallow Foundations. FHWA-SA-02–054. United States. Federal Highway Administration. Office of Bridge Technology, Washington, DC, USA. 2002.
35. AASHTO. LRFD Bridge Design Specifications. American Association of State Highway and Transportation Officials, Washington, DC, USA. 2020.
36. CFEM. Canadian Foundation Engineering Manual, 5th Ed., The Canadian Geotechnical Society, Canada. 2023.
37. GEO. Foundation Design and Construction. GEO Publication No. 1/2006. The Government of the Hong Kong Special Administrative Region, Hong Kong. 2006.
38. Yünkül, K., Usluoğulları, Ö. F., Gürbüz, A., Numerical Analysis of Geocell Reinforced Square Shallow Horizontal Plate Anchor. Geotechnical and Geological Engineering, 39(4), 3081-3099, 2021.
39. Hakro, M. R., Kumar, A., Ali, M., Habib, A. F., de Azevedo, A. R., Fediuk, R., Sabri, M. M. S., Salmi, A., Awad, Y. A.., Numerical Analysis of Shallow Foundations with Varying Loading and Soil Conditions. Buildings, 12(5), 693, 2022.
40. Alnmr, A., Alsirawan, R., Numerical Study of the Effect of the Shape and Area of Shallow Foundations on The Bearing Capacity of Sandy Soils. Acta Polytechnica Hungarica, 21(1), 103-120, 2024.
41. Demirdöğen, S., Gürbüz, A., Yünkül, 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.
42. Örnek, M., Laman, M., Demir, A., Yıldız, A., Numerical Analysis of Circular Footings on Natural Clay Stabilized with a Granular Fill. Acta Geotechnica Slovenica, 9(1), 61-75, 2012.
43. Demir, A., Yıldız, A., Laman, M., Örnek, M., Experimental and Numerical Analyses of Circular Footing on Geogrid-Reinforced Granular Fill Underlain by Soft Clay. Acta Geotechnica, 9, 711-723, 2014.
44. Mansouri, M., Imani, M., Fahimifar, A., Ultimate Bearing Capacity of Rock Masses Under Square and Rectangular Footings. Computers and Geotechnics, 111, 1-9, 2019.
45. Malik, Z. B., Alshameri, B., Jamil, S. M., Umar, D., Experimental and Numerical Modeling of Bearing Capacity of Foundations on Soft Clay Stabilized with Granular Material. International Journal of Geosynthetics and Ground Engineering, 7, 1-17, 2021.
46. Gupta, S., Mital, A., A comparative study of bearing capacity of shallow footing under different loading conditions. Geomechanics and Geoengineering, 17(4), 1338-1349, 2022.
47. Cerato, A. B., Lutenegger, A. J., Scale Effects of Shallow Foundation Bearing Capacity on Granular Material. Journal of Geotechnical and Geoenvironmental Engineering, 133(10), 1192-1202, 2007.
48. Demirdöğen, S., Gürbüz, A., Yünkül, K., Performance of Eccentrically Loaded Strip Footings on Geocell-Reinforced Soil. Geotextiles and Geomembranes, 52(4), 421-434, 2024.
49. Jaky, J., The Coefficient of Earth Pressure at Rest. Journal of the Society of Hungarian Architects and Engineers, 7, 355–358, 1944.
50. Al-Defae, A. H., Caucis, K., Knappett, J. A., Aftershocks and the Whole-Life Seismic Performance of Granular Slopes. Géotechnique, 63(14), 1230-1244, 2013.
51. Das, B. M., Shallow Foundations, 3rd ed., Boca Raton, USA. CRC press, 2017.
52. Arı, A., Mısır, G., Three-Dimensional Numerical Analysis of Geocell Reinforced Shell Foundations. Geotextiles and Geomembranes, 49(4), 963-975, 2021.
53. Kaya, Z., Erol, A., Comparison of Bearing Capacities of Undisturbed Organic Soils by Empirical Relations and 2D Finite Element Analysis. Arabian Journal of Geosciences, 14(19), 1975, 2021.
54. Barari, A., Zhou, J., Bo Ibsen, L., Nazem, M., Nielsen, K., A Theoretical and Practical Framework Based on Plasticity Theory for the Drained Behavior of Single and Multiple Shallow Footings. International Journal for Numerical and Analytical Methods in Geomechanics, 47(16), 2872-2898, 2023.
55. Budhu, M., Soil Mechanics and Foundations, 3rd ed., New York, USA. John Wiley and Sons, 2010.
56. Coduto, D. P., Foundation Design: Principles and Practices, 2nd ed., USA. Pearson Education Limited, 2014.
57. Bowles, J. E., Foundation Analysis and Design, 5th ed., New York, USA. McGraw-Hill Book Company, 1996.
58. Fang, H. Y., Foundation Engineering Handbook, New York, USA. Springer Science and Business Media, 2013.
59. Baban, T. M., Shallow Foundations: Discussions and Problem Solving, 1st ed., United Kingdom. John Wiley and Sons. 2016.
60. Meigh, A. C., Nixon, I. K., Comparison of In Situ Tests for Granular Soils, 5th International Conference on Soil Mechanics and Foundation Engineering, Paris, France, 499-508, 1961.
61. Rodin, S., Experiences with Penetrometers, with Particular Reference to the Standard Penetration Test, 5th International Conference on Soil Mechanics and Foundation Engineering, Paris, France, 517-521, 1961.
62. Thorburn, S., Tentative Correction Chart for the Standard Penetration Test in Non-Cohesive Soils. Civil Engineering and Public Works Review, 58(683), 752-3, 1963.
63. Aiban, S. A., Znidarčić, D., Centrifugal Modeling of Bearing Capacity of Shallow Foundations on Sands. Journal of Geotechnical Engineering, 121(10), 704-712, 1995.
64. Adams, M. T., Collin, J. G., Large Model Spread Footing Load Tests on Geosynthetic Reinforced Soil Foundations. Journal of Geotechnical and Geoenvironmental Engineering, 123(1), 66-72, 1997.
65. Mestat, P., Berthelon, J. Finite Element Modeling of Shallow Foundation Tests at the Labenne Site. Bull. Lab. Ponts Chaussees, 234, 37-67, 2001.
66. Siddiquee, M. S. A., Tatsuoka, F., Tanaka, T., Tani, K., Yoshida, K., Morimoto, T., Model Tests and FEM Simulation of Some Factors Affecting the Bearing Capacity of a Footing on Sand. Soils and Foundations, 41(2), 53-76, 2001.
67. Mosallanezhad, M., Hataf, N., Ghahramani, A., Experimental Study of Bearing Capacity of Granular Soils, Reinforced with Innovative Grid-Anchor System. Geotechnical and Geological Engineering, 26, 299-312, 2008.
68. Ziccarelli, M., Valore, C., Muscolino, S. R., Fioravante, V., Centrifuge Tests on Strip Footings on Sand with a Weak Layer. Geotechnical Research, 4(1), 47-64, 2017.
69. Kyparissis, A., Lopes, M. P., Bearing Capacity of Reinforced Soil under a Strip Footing: Centrifuge Tests. 11th International Conference on Geosynthetics, Seoul, Korea, 2018.
70. Shadmand, A., Ghazavi, M., Ganjian, N., Scale Effects of Footings on Geocell Reinforced Sand Using Large-Scale Tests. Civil Engineering Journal, 4(3), 497-508, 2018.
71. Wang, J. Q., Zhang, L. L., Xue, J. F., Tang, Y., Load-Settlement Response of Shallow Square Footings on Geogrid-Reinforced Sand Under Cyclic Loading. Geotextiles and Geomembranes, 46(5), 586-596, 2018.
72. Bharti, G., Shukla, B. K., Srinivasan, V., Bansal, V., Experimental Study on Eccentrically Loaded Rectangular Footing on Sand for Embedded Condition to Enhance Serviceability of Structures. Materials Today: Proceedings, 61, 517-522, 2022.
73. Latha, G. M., Venkateswarlu, H., Krishna, A., Geocell Anchor Cage for Enhanced Load Support in Soil Structures. Construction and Building Materials, 425, 135998, 2024.
74. Hamed, E., Demiröz, A., Optimization of Geotechnical Characteristics of Clayey Soils Using Fly Ash and Granulated Blast Furnace Slag-Based Geopolymer. Construction and Building Materials, 441, 137488, 2024.
75. Yünkül, K., Karaçor, F., Gürbüz, A., Budak, T. Ö., Prediction of the Undrained Shear Strength of Remolded Soil with Non-Linear Regression, Fuzzy Logic, and Artificial Neural Network. Journal of Mountain Science, 21(9), 3108-3122, 2024.
76. Meyerhof, G. G., Influence of Roughness of Base and Ground-Water Conditions on the Ultimate Bearing Capacity of Foundations. Géotechnique, 5(3), 227–242, 1955.
77. Cascone, E., Biondi, G., Casablanca, O., Groundwater Effect on Bearing Capacity of Shallow Strip Footings. Computers and Geotechnics, 139, 104417, 2021.
78. Park, D., Kim, I., Kim, G., Lee, J., Groundwater Effect Factors for the Load-Carrying Behavior of Footings from Hydraulic Chamber Load Tests. Geotechnical Testing Journal, 40(3), 440-451, 2017.