A Macro-element for Modeling the Non-linear Interaction of Soil-shallow Foundation under Seismic Loading

Van Quan Huynh, Xuan Huy Nguyen, Trung Kien Nguyen


This paper presents a macro-element for simulating the seismic behavior of the soil- shallow foundation interaction. The overall behavior in the soil and at the interface is replaced by a macro-element located at the base of the superstructure. The element reproduces the irreversible elastoplastic soil behavior (material non-linearity) and the foundation uplift (geometric non-linearity) at the soil- foundation interface. This new macro-element model with three degrees-of-freedom describes the force-displacement behavior of the footing center. The single element is restrained by the system of equivalent springs and dashpots. The footing is considered as a rigid body. It is solved by a suitable Newmark time integration scheme and implemented in Matlab to simulate the nonlinear behavior of soil-shallow foundation interaction under seismic loading. A reduce scaled soil-foundation system has been tested on a shaking table at the University of Transport and Communications, Hanoi, Vietnam. Five series of earthquake motions were used with maximum acceleration increased from 0.5  to 2.5 . The comparison of numerical results obtained from the simulation and experimentations shows the satisfactory agreement of the model. The proposed macro-element can be used to predict the seismic behavior of a wider variety of configurations.


Macro-element; Soil–foundation Interaction; Non-linearity; Seismic Loading.


Nova, R., and L. Montrasio. “Settlements of Shallow Foundations on Sand.” Géotechnique 41, no. 2 (June 1991): 243–256. doi:10.1680/geot.1991.41.2.243.

Montrasio, L., and R. Nova. “Settlements of Shallow Foundations on Sand: Geometrical Effects.” Géotechnique 47, no. 1 (February 1997): 49–60. doi:10.1680/geot.1997.47.1.49.

Paolucci, R. “Simplified Evaluation of Earthquake-Induced Permanent Displacements of Shallow Foundations.” Journal of Earthquake Engineering 1, no. 3 (July 1997): 563–579. doi:10.1080/13632469708962378.

Cremer, C., A. Pecker, and L. Davenne. “Modeling of Nonlinear Dynamic Behavior of a Shallow Strip Foundation with Macro-Element.” Journal of Earthquake Engineering 6, no. 2 (April 2002): 175–211. doi:10.1080/13632460209350414.

Cremer, C., Alain Pecker, and Luc Davenne. “Cyclic Macro-Element for Soil-Structure Interaction: Material and Geometrical Non-Linearities.” International Journal for Numerical and Analytical Methods in Geomechanics 25, no. 13 (September 2001): 1257–1284. doi:10.1002/nag.175.

Chatzigogos, C.T., A. Pecker, and J. Salençon. “Macroelement Modeling of Shallow Foundations.” Soil Dynamics and Earthquake Engineering 29, no. 5 (May 2009): 765–781. doi:10.1016/j.soildyn.2008.08.009.

Grange, Stéphane, Panagiotis Kotronis, and Jacky Mazars. “A Macro-Element to Simulate 3D Soil–structure Interaction Considering Plasticity and Uplift.” International Journal of Solids and Structures 46, no. 20 (October 2009): 3651–3663. doi:10.1016/j.ijsolstr.2009.06.015.

Grange, Stéphane, Panagiotis Kotronis, and Jacky Mazars. “A Macro-Element to Simulate Dynamic Soil-Structure Interaction.” Engineering Structures 31, no. 12 (December 2009): 3034–3046. doi:10.1016/j.engstruct.2009.08.007.

Figini, R., R. Paolucci, and C.T. Chatzigogos. “A Macro-Element Model for Non-Linear Soil-Shallow Foundation-Structure Interaction Under Seismic Loads: Theoretical Development and Experimental Validation on Large Scale Tests.” Earthquake Engineering & Structural Dynamics 41, no. 3 (February 23, 2012): 475–493. doi:10.1002/eqe.1140.

Di Prisco, Claudio, and Federico Pisanò. “Seismic Response of Rigid Shallow Footings.” European Journal of Environmental and Civil Engineering 15, no. sup1 (January 2011): 185–221. doi:10.1080/19648189.2011.9695308.

Paolucci, Roberto, Masahiro Shirato, and M. Tolga Yilmaz. “Seismic Behaviour of Shallow Foundations: Shaking Table Experimentsvs Numerical Modelling.” Earthquake Engineering & Structural Dynamics 37, no. 4 (2008): 577–595. doi:10.1002/eqe.773.

Khebizi, Mourad, Hamza Guenfoud, and Mohamed Guenfoud. "Numerical modelling of soil-foundation interaction by a new non-linear macro-element." Geomechanics and Engineering 14, no. 4 (2018): 377-386.

Jin Z. “Numerical investigation of caisson foundations in sand under.” Ph.D. Thesis, Ecole Centrale de Nantes, France, (January 2019).

Barari, A., Ghaseminejad, V., & Ibsen, L. B. “A Macro-Element design method for shallow foundations accounting for SSI effects: characterizing response as failure envelopes.” Proceeding of the 2nd International Conference on Natural Hazards & Infrastructure, (June 2019).

Paroissien, Eric, Frédéric Lachaud, Lucas F.M. da Silva, and Salah Seddiki. “A Comparison Between Macro-Element and Finite Element Solutions for the Stress Analysis of Functionally Graded Single-Lap Joints.” Composite Structures 215 (May 2019): 331–350. doi:10.1016/j.compstruct.2019.02.070.

Gorini, Davide Noè, and Luigi Callisto. “A Macro-Element Approach to Analyse Bridge Abutments Accounting for the Dynamic Behaviour of the Superstructure.” Géotechnique (November 18, 2019): 1–9. doi:10.1680/jgeot.19.ti.012.

Gazetas G. “Foundation Vibrations, Foundation Engineering Handbook, Second Edition” (November 2013).

Huynh V.Q., Nguyen X.H., Nguyen T.K. “Modeling the nonlinear soil-footing geometric in seismic analysis of structures” Transport and Communications Science Journal 66, (October 2018), 3-11.

Full Text: PDF

DOI: 10.28991/cej-2020-03091503


  • There are currently no refbacks.

Copyright (c) 2020 Van Quan Huynh, Xuan Huy Nguyen, Trung Kien Nguyen

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.