Assessing the Dynamic Behavior of Step Footing Placed on the Surface of Sandy Soil
Abstract
Numerous factors, including soil type, moisture content, foundation type, and excitation intensity, have impacted how soil responds to excitation forces. An accumulation of underlining soil deformation caused by the machine's vibration may exceed the limit. An experimental investigation was conducted to evaluate the effect of machine-induced vibrations on four prototype footings positioned at the soil's surface. Among the four footing models, three were designed with stepped areas, while one had a uniform rectangular section. The stepped footings were constructed with varying bottom-to-top area ratios (A/A) of 1.0, 1.2, 1.5, and 2. Three operating frequencies (10, 40, and 70 Hz) were applied to each of the four footings. The soil used was sand with a medium relative density of 50%. Dynamic response data include vertical amplitudes (displacement, velocity, and acceleration), settlement, and pressures at various depths. Despite different in magnitudes, it was found that the stepped footings significantly reduced the machine-foundation system's pressure, settlement, and amplitude movements. For instance, the stepped footing with area ratio of (A2/A1=2.0) displayed the lowest dynamic response. The pressure decreased by an average of 14.5% when the area ration changes from (A2/A1=1.0) (A2/A1=2.0), while the total settlement, amplitude displacement and acceleration were reduced by about 30%, 42% and 54%, respectively. Further, compared to a uniform footing, stepped footing is more cost-effective with high-performance.
References
- S. J. Mabawala, Behavior of machine foundations subjected to vertical dynamic loading, PhD Thesis, University of Pretoria, Pretoria, 2015.
- A. S. Abdulrasool, M. Y. Fattah and N. M. Salim, Displacements and stresses induced by vibrations of machine foundation on clay soil of different degrees of saturation,Case Studies in Construction Materials,Vol. 17, e01327, 2022. https://doi.org/10.1016/j.cscm.2022.e01327
- M. H. Hussein, M. A. Al-Obaydi and A. J. Zedan, Effect of soaking on the behavior of gypseous soil subjected to vibration load, AIP Conf. Proc. 3105, 050051, 2024. https://doi.org/10.1063/5.0212237
- A. A. Ahmed, M. Y. Fattah and M. K. Mohsen, Effect of frame foundation geometry on the dynamic response of high-speed turbo machine foundations, Heliyon, Vol. 11, e41050, 2025. https://doi.org/10.1016/j.heliyon.2024.e41050
- M. Y. Fattah, M. J. Al-Mosawi and A. F. Al-Ameri, Dynamic response of saturated soil - foundation system Acted upon by vibration, Journal of Earthquake Engineering,Vol. 2, Issue 7, pp. 11581188, 2016. https://doi.org/10.1080/13632469.2016.1210060
- N. K. Alhasso and Q. N., Settlement analysis of machine foundation under reciprocating load using FEM, Al-Rafidain Engineering Journal (AREJ), Vol. 26, Issue 1, pp. 37-43, 2021. https://doi.org/10.33899/rengj.2020.128010.1057
- ASTM: American Society of Testing and Materials, Standard Test Method for Specific Gravity. ASTM D 854, West Conshohocken, Pennsylvania, USA, 2010.
- K. G. Bhatia, Foundation for industrial machines: Handbook for practicing engineering, ISBN: 8190603205, 97881906 03201, 1st Edition, CRC Press, New Dlhi, 2009.
- K. W. Abdul Kaream, M. Y. Fattah and S. M. Zeyad, Response of different machine foundation shapes resting on dry sand to dynamic loading, Tikret Journal of Engineering Sciences. Vol. 27, pp.29-39, 2020. https://doi.org/10.25130/tjes.27.2.04
- M. Y. Fattah, M. J. Al-Mosawi and A. F. Al-Ameri, Stresses and pore water pressure induced by machine foundation on saturated sand, Ocean Engineering, Vol. 146, pp. 268-281, 2017. https://doi.org/10.1016/j.oceaneng.2017.09.055
- W. B. Joyner, and A. T. F. Chen, Calculation of nonlinear ground response in earthquakes, Bulletin of the Seismological Society of America, Vol. 65, Issue 5, p. 1315-1336, 1975. https://doi.org/10.1785/BSSA0650051315
- G. Gazetas, Analysis of machine foundation vibrations: State of art, Dynamic and earthquake engineering, Vol. 2, Issue 1, pp. 2-42, 1983. https://doi.org/10.1016/0261-7277(83)90025-6
- P. Dunaj and A. Archenti, Modeling the dynamic interaction between machine tools and their foundations, Precision Engineering Vol. 89, pp. 451472, 2020. https://doi.org/10.1016/j.precisioneng.2024.07.009
- M. Y. Fattah, A. A. Al-Azal and H. T. Al-Badri, "Design chart for machine foundation, Journal of Engineering, Vol.3, No.4, pp. 1940-1961, 2007. https://doi.org/10.31026/j.eng.2007.04.07
- H. Van Koten and P. C. J Hoogenboom, Vibrations of machine foundations and surrounding soil, Delft University of, Delft the Netherlands, HERON, Vol. 57, No. 1, pp. 29-54, 2012.
- M. A. Hussein, A. J. Zedan and M. A. Al-Obaydi, Assessing the vibration response of foundation embedment in gypseous soil, Journal of the Mechanical Behavior of Materials, Vol. 31, pp. 739747, 2022. https://doi.org/10.1515/jmbm-2022-0212
- K. W. Abdul Kaream, M. Y. Fattah and Z. S. Khaled, Effect of mode of vibration on response of machine foundation on sand, IOP Conference Series: Materials Science and Engineering, Vol. 737, 012089, 2020. https://doi:10.1088/1757-899X/737/1/012089
- S. Surapreddi and P. Ghosh, Impact of footing shape on dynamic properties and vibration transmission characteristics of machine foundation, International Journal of Geosynthtics and Ground Engineering, Vol. 8, Issue 1, 2022. https://doi.org/10.1007/s40891-021-00347-x
- P. Pathak and S. S. Sanghai, Analysis of reciprocating engine by varying speed and depth, International Journal for Science and Advance Research in Technology (IJSART), Vol. 3, Issue 3, pp. 497-500, 2017.




