Vertical and Lateral Displacement Response of Foundation to Earthquake Loading

Document Type: Original Article


1 Civil Engineering Department, College of Engineering, University of Baghdad, Iraq

2 Ministry of Higher Education and Scientific Research, Department of Reconstruction and Projects, Baghdad, Iraq

3 Building and Construction Engineering Department, University of Technology, Baghdad, Iraq


Risks are confronting the foundations of buildings and structures when exposed to earthquakes which leads to high displacements that may cause the failure of the structures. This research elaborates numerically the effect of the earthquake on the vertical and lateral displacement of footing resting on the soil. The thickness of the footing and depth of soil layer below the footing was taken as (0.5, 1.0, and 2.0 m) and (10, 20 and 40m), respectively. The stiffness ratio of soil to footing was also elaborated at 0.68, 0.8, 1.0, and 1.7. The results showed an increase in the verticle displacement of footing as the duration of the earthquake increases. The increase of soil layer thickness below the footing leads to a reduction in the vertical and lateral displacement. While an increase in the thickness of the footing leads to a decrease in the lateral displacement of the footing meanwhile no effect was noticed in the vertical displacement. It was noticed that the time lag between the maximum vertical displacement and the highest value of the earthquake loading is about 0.27 s. It was found that as the distance between the footing and the source of earthquake load increases, the effect of damping on the earthquake load increases while the lateral displacement decreases. The results revealed that an increase in the stiffness ratio leads to a decrease in the vertical displacement and a reduction in the response of the lateral displacement till reaching the value of stiffness ration of unity.


1.     Ishihara, K. and Koga, Y., "Case studies of liquefaction in the 1964 niigata earthquake", Soils and Foundations,  Vol. 21, No. 3, (1981), 35-52. doi:10.3208/sandf1972.21.3_35
2.     Moura, A., Neto, S. and de Aguiar, M., "A comparative study of vibration frequency estimates of the surface foundations of wind turbines built on the sand dunes of the ceará coast",  (2008).
3.     Das, B.M. and Luo, Z., "Principles of soil dynamics, Cengage Learning,  (2016).
4.     Richart, F.E., "Foundation vibrations", Transactions of the American Society of Civil Engineers,  Vol. 127, No. 1, (1962), 863-897.
5.     Jefferies, M. and Been, K., "Soil liquefaction: A critical state approach, CRC press,  (2015).
6.     Roy, D., "Design of shallow and deep foundations for earthquakes", J. Geotech. Earthq. Eng,  (2013), 1-8.
7.     Tiznado, J.C. and Paillao, D., "Analysis of the seismic bearing capacity of shallow foundations",  (2014).
8.     Maeda, Y., Irie, T. and Yokota, Y., "Bearing capacity formula for shallow foundations during earthquake", in 13th world conference on earthquake engineering. Vancouver, BC. 1-6.
9.     Gajan, S., Kutter, B.L., Phalen, J.D., Hutchinson, T.C. and Martin, G.R., "Centrifuge modeling of load-deformation behavior of rocking shallow foundations", Soil Dynamics and Earthquake Engineering,  Vol. 25, No. 7-10, (2005), 773-783. doi:10.1016/j.soildyn.2004.11.019
10.   Chakraborty, D. and Kumar, J., "Seismic bearing capacity of shallow embedded foundations on a sloping ground surface", International Journal of Geomechanics,  Vol. 15, No. 1, (2015), 04014035. doi:10.1061/(ASCE)GM.1943-5622.0000403
11.   Pender, M., "Earthquake inertia effects on shallow foundation bearing strength", Géotechnique,  Vol. 68, No. 7, (2018), 640-645. doi:10.1680/jgeot.17.T.006
12.   Fattah, M.Y., Al-Mosawi, M.J. and Al-Ameri, A.F., "Dynamic response of saturated soil-foundation system acted upon by vibration", Journal of Earthquake Engineering,  Vol. 21, No. 7, (2017), 1158-1188. doi:10.1080/13632469.2016.1210060
13.   Namdar, A., "Liquefaction zone and differential settlement of cohesionless soil subjected to dynamic loading", Electronic Journal of Geotechnical Engineering,  Vol. 21, (2016), 593-605.
14.   Fattah, M.Y., Al-Mosawi, M.J. and Al-Americ, A.F., "Stresses and pore water pressure induced by machine foundation on saturated sand", Ocean Engineering,  Vol. 146, (2017), 268-281. doi:10.1016/j.oceaneng.2017.09.055
15.   Moghaddas Tafreshi, S., Darabi, J. and Dawson, A., "Cyclic loading response of footing on multi-layered rubber-soil mixtures", Geomechanics and Engineering,  Vol. 14, No. 2, (2020). doi:10.12989/gae.2018.14.2.115
16.   Namdar, A., Dong, Y. and Liu, Y., "Timber beam seismic design–a numerical simulation", Frattura ed Integrità Strutturale,  Vol. 13, No. 47, (2019), 451-458. doi:10.3221/IGF-ESIS.47.35
17.    Daghigh, Y., "Numerical simulation of dynamic behaviour of an earthdam during seismic loading",  (1993).