Numerical Methods in Civil Engineering

Numerical Methods in Civil Engineering

3D Finite Element Study of Inclined Soil-Cement Columns Adjacent to Shallow Foundations on Slopes

Document Type : Research

Authors
1 Assistant Professor, Department of Civil Engineering, Fasa University, Fasa, Iran
2 Assistant Professor, Faculty of Civil Engineering, K.N. Toosi University of Technology, Tehran, Iran
3 M.Sc. Graduate, Department of Civil Engineering, Fasa University, Fasa, Iran
Abstract
The construction of shallow foundations adjacent to slopes is a complex geotechnical problem due to stress redistribution, reduced confinement, and development of plastic zones, which collectively reduce bearing capacity and slope stability. Ground improvement methods such as soil–cement columns installed by deep mixing or jet grouting have been widely adopted; however, most previous studies have focused on vertical columns, while the effects of inclined column installation on the coupled soil–foundation–slope system remain insufficiently investigated. This study evaluates the influence of soil–cement column inclination on the bearing capacity of a shallow foundation and the stability of an adjacent slope using three-dimensional numerical modeling in PLAXIS 3D. The nonlinear behavior of soil is simulated using the Hardening Soil model, and columns are modeled using embedded beam elements. Model validation is performed against available experimental data, showing good agreement in load–settlement response and failure mechanisms. A parametric analysis is conducted considering column inclination and spacing between columns. Results indicate that vertical columns maximize bearing capacity by improving load transfer to deeper soil layers, whereas inclined columns with an angle of approximately 45° provide the greatest improvement in slope stability by intersecting potential slip surfaces more effectively. Furthermore, as the column inclination angle relative to the vertical axis decreases, the bending moment in the foundation increases, highlighting the need for combined geotechnical and structural design considerations. An optimal configuration is proposed for balanced performance in bearing capacity and slope stability.
Keywords
Subjects

[1] Cheuk, J. C. Y., Lai, A. W. L., Cheung, C. K. W., Man, V. K. W., & So, A. K. O. (2013). The use of jet grouting to enhance stability of bermed excavation. Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering, Paris, pp. 1255–1258.
[2] Huang, C. C. (2019). Effects of restraining conditions on the bearing capacity of footings near slopes. Soils and Foundations, 59(1), 1–12.
[3] Coldwell, E., Khosravi, M., Zaregarizi, S., Perkins, S., & Montgomery, J. (2020). Stability analysis of an embankment supported by spatially variable soil-cement columns. Geo-Congress 2020, ASCE, pp. 507–515.
[4] Severino, A., Wahrhaftig, A. D. M., Tiutkin, O., Gubashova, V., & Neduzha, L. (2022). Effective jet-grouting application for improving the state of deformation of landmarks. Buildings, 12(3), 368.
[5] Phutthananon, C., Jongpradist, P., Wonglert, A., Kandavorawong, K., Sanboonsiri, S., & Jamsawang, P. (2023). Field and 3D numerical investigations of the performances of stiffened deep cement mixing column-supported embankments built on soft soil. Arabian Journal for Science and Engineering, 48(4), 5139–5169.
[6] Mehdizadeh, M. J., Dehghan Khalili, H., & Raisianzadeh, J. (2024). Investigation of effectiveness of deep mixing method on seismic response of liquefiable soils using 3D numerical simulation. Numerical Methods in Civil Engineering, 8(4), 79–91.
[7] Ramezani, B., Dehghan Khalili, H., Moradi, P., & Pourbagheri, A. (2025). Seismic resilience with deep soil mixing: numerical and experimental insights into liquefaction mitigation. Geotechnical and Geological Engineering, 43(2), 71.
[8] Vahedi, M., Dehghan Khalili, H., Arvin, M. R., & Borazjani, S. (2022). Laboratory investigation of the effect of soil-cement columns on the bearing capacity of foundations adjacent to soil slopes. Proceedings of the 9th National Conference on Sustainable Development in Civil Engineering, Tehran.
[9] Borazjani, S. (2021). Numerical investigation of the effect of deep mixing columns on the behavior of foundations on slopes. MSc Thesis, Fasa University, Iran.
[10] Schanz, T., Vermeer, P. A., & Bonnier, P. G. (1999). The hardening soil model: Formulation and verification. In Beyond 2000 in computational geotechnics (pp. 281-296). Amsterdam.
[11] Acharyya, R., & Dey, A. (2021). Assessment of bearing capacity and failure mechanism of single and interfering strip footings on sloping ground. International Journal of Geotechnical Engineering, 15(7), 822–833.
[12] Lee, H. R., Park, H. J., & Kim, D. S. (2018). Bearing capacity of shallow footings in simulated lunar environments using centrifuge tests. Journal of Geotechnical and Geoenvironmental Engineering, 144(7), 04018042.
[13] Mansouri, M., Imani, M., & Fahimifar, A. (2019). Ultimate bearing capacity of rock masses under square and rectangular footings. Computers and Geotechnics, 111, 1-9.
[14] Sadek, M., & Shahrour, I. (2004). A three dimensional embedded beam element for reinforced geomaterials. International journal for numerical and analytical methods in geomechanics, 28(9), 931-946.
[15] Al-abboodi, I., & Sabbagh, T. T. (2019). Numerical modelling of passively loaded pile groups. Geotechnical and Geological Engineering, 37(4), 2747-2761.
[16] Granitzer, A. N., Hosseini, S., Bui, T. A., Felić, H., & Tschuchnigg, F. (2026). Enhanced embedded pile formulation for spatial soil‐structure interaction. geotechnik, 49(2), 132-145.
Volume 10, Issue 4
Spring 2026
Pages 30-43

  • Receive Date 22 June 2026
  • Revise Date 28 July 2026
  • Accept Date 09 August 2026