KSCE Journal of Civil Engineering

, Volume 23, Issue 9, pp 3764–3776 | Cite as

Analyzing the Deformation of Multilayered Saturated Sandy Soils under Large Building Foundation

  • Chun Li
  • Zhanguo XiuEmail author
  • Yingchun Ji
  • Feili Wang
  • A. H. C. Chan
Geotechnical Engineering


The generalized plasticity theory has been subject of much research in geomechanics. The Pastor-Zienkiewicz model and its modified versions are among these. For large foundations resting on multilayered soils the actual loading is often non-linear. In this study we developed a new mathematical model which can apply non-linear loading using the subfield of planar mesh method. A sensitivity study was first performed to evaluate the contribution of deformation from various model parameters. It is found that the plastic modulus parameters only have marginal contributions. An engineering case study was used to valid the proposed model and it is evident from measured stresses that the loading of the foundation is non-linear. The deformations calculated by the proposed model agreed well with the monitored deformations. It is also found that the maximum deformation point is not necessarily in the centre of foundation and it does not coincide with the maximum loading point either. The distance between the maximum deformation point and the maximum loading point can be as far as 15.59 m for the bottom layer soil from this case. This research proves the necessity of using non-linear loading to calculate the foundation deformations for large foundations with multilayered saturated soils.


large building foundation Pastor-Zienkiewicz model sensitivity analysis foundation deformation multilayered soils 


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  1. Akhaveissy, A. H. (2011). “Analysis of tunnel and super structures for excavation.” Scientia Iranica, Vol. 18, No. 1, pp. 1–8, DOI: Scholar
  2. Akhaveissy, A. H., Desai, C. S., Sadrnejad, S. A, and Shakib, H. (2009). “Implementation and comparison of a generalized plasticity and disturbed state concept for the load-deformation behavior of foundations.” Scientia Iranica, Transaction A: Civil Engineering, Vol. 16, No. 3, pp. 189–198.Google Scholar
  3. Bezvolev, S. G. (2002). “Method of accounting for the deformability of an inhomogeneous elastoplastic bed in analyzing foundation slabs.” Soil Mechanics and Foundation Engineering, Vol. 39, No. 2, pp. 162–170, DOI: Scholar
  4. Boussinesq, J. (1878). “Équilibre d'élasticité d'un sol isotrope sans pesanteur, supportant différents poids.” Comptes Rendus de l'Académie des Sciences, Paris, Vol. 86, pp. 1260–1263.zbMATHGoogle Scholar
  5. China National Standards (2011). Code for design of building foundation, GB 50007-2011, Ministry of Housing and Urban-Rural Development of the People's Republic of China, Beijing, China.Google Scholar
  6. Denis, A., Elachachi, S. M., and Niandou, H. (2011). “Effects of longitudinal variability of soil on a continuous spread footing.” Engineering Geology, Vol. 122, Nos. 3–4, pp. 179–190, DOI: Scholar
  7. Diaz, E. and Tomás, R. (2016). “A simple method to predict elastic settlements in foundations resting on two soils of differing deformability.” European Journal of Environmental and Civil Engineering, Vol. 20, No. 3, pp. 263–281, DOI: Scholar
  8. Farzaneh, O., and Iraji, A. (2016). “Two-Phase Model for nonlinear dynamic simulation of reinforced soil walls based on a modified Pastor-Zienkiewicz-Chan model for granular soil.” Journal of Engineering Mechanics, Vol. 142, No. 6, pp. 1–17, DOI: Scholar
  9. Gazetas, G. (1980). “Static and dynamic displacements of foundations on heterogeneous multilayered soils.” Géotechnique, Vol. 30, No. 2, pp. 159–177, DOI: Scholar
  10. Iraji, A., Farzaneh, O., and Hosseininia, E. S. (2014). “A modification to dense sand dynamic simulation capability of Pastor-Zienkiewicz-Chan model.” Acta Geotechnica, Vol. 9, No. 2, pp. 343–353, DOI: Scholar
  11. Kumari, S. and Sawant, V. A. (2013). “Use of infinite elements in simulating liquefaction phenomenon using coupled approach.” Coupled Systems Mechanics, Vol. 2, No. 4, pp. 375–387, DOI: Scholar
  12. Li, C. (2009). Research on subsidence of building foundation with layered sandy subgrade, PhD Thesis, Northeastern University, Shenyang, China.Google Scholar
  13. Li, H. E., He, Y. J., Fan, G. Y, Li, T. C., and Pastor, M. (2011). “Recent developments of generalized plasticity model for saturated and unsaturated soils.” Water Science and Engineering, Vol. 4, No. 3, pp. 329–344, DOI: Scholar
  14. Li, H. E., Li, Z., Fan, G Y, Xu, H. E, and He, Y J. (2016). “Pastor-Zienkiewicz based constitutive model and determination method of its state parameters.” Rock and Soil Mechanics, Vol. 37, No. 6, pp. 1623–1632, DOI: Scholar
  15. Ling, H. I. and Liu, H. (2003). “Pressure-level dependency and densification behavior of sand through generalized plasticitymodel.” Journal of Engineering Mechanics, Vol. 129, No. 8, pp. 851–860, DOI: Scholar
  16. Ling, H. I. and Yang, S. (2006). “Unified sand model based on the critical state and generalized plasticity.” Journal of Engineering Mechanics, Vol. 132, No. 12, pp. 1380–1391, DOI: Scholar
  17. Liu, H. and Ling, H. I. (2002). “A sand model based on generalized plasticity.” Proc. 15 th Engineering Mechanics Conference, ASCE, Columbia University, New York, USA.Google Scholar
  18. Liu, H. and Song, E. (2005). “Seismic response of large underground structures in liquefiable soils subjected to horizontal and vertical earthquake excitations.” Computers and Geotechnics, Vol. 32, No. 4, pp. 223–244, DOI: Scholar
  19. Mroz, Z. and Zienkiewicz, O. C. (1984). “Uniform formulation of constitutive equations for clays and sand.” Mechanics of Engineering Materials, Desai C. S., Gallagher R. H. (eds.), Chapter 22, Wiley, New York, pp. 415–459.Google Scholar
  20. Onopa, I. A., Skopintseva, E. V, and Dokhnyanskii, M. P. (1983). “Settlement of buildings on heterogeneous bases.” Soil Mechanics and Foundation Engineering, Vol. 20, No. 6, pp. 227–230, DOI: Scholar
  21. Pastor, M. (1986). “A generalized plasticity, hierarchical model for sand under monotonic and cyclic loading.” Proc. 2nd Int. Symp. on Numerical Models in Geomechanics, Ghent, pp. 131–150.Google Scholar
  22. Pastor, M., Zienkiewicz, O. C., and Chan, A. H. C. (1990). “General plasticity and the modelling of soil behavior.” International Journal for Numerical & Analytical Methods in Geomechanics, Vol. 14, No. 3, pp. 151–190, DOI: Scholar
  23. Pastor, M., Zienkiewicz, O. C., and Leung, K. H. (1985). “Simple model for transient soil loading in earthquake analysis. II: Non-associative models for sands.” International Journal for Numerical & Analytical Methods in Geomechanics, Vol. 9, No. 5, pp. 477–498, DOI: Scholar
  24. Pradhan, T. B. S., Tatsuoka, F., and Sato, Y. (1989). “Experimental stress-dilatancy relations of sand subjected to cyclic loading.” Soils and Foundations, Vol. 29, No. 1, pp. 45–64, DOI: Scholar
  25. Tonni, L., Cola, S., and Pastor, M. (2006) “A generalized plasticity approach for describing the behavior of silty soils forming the Venetian lagoon basin.” Proc. 6th European Conference on Numer Meth in Geotech Eng., London, pp. 93–99, DOI: Scholar
  26. Zienkiewicz, O. C., Leung, K. H., and Pastor, M. (1985). “Simple model for transient soil loading in earthquake analysis. I: Basic model and its application.” International Journal for Numerical & Analytical Methods in Geomechanics, Vol. 9, No. 5, pp. 453–476, DOI: Scholar
  27. Zienkiewicz, O. C. and Mroz, Z. (1984). “Generalized plasticity formulation and applications to geomechanics.” Mechanics of Engineering Materials, Vol. 44, No. 3, pp. 655–680.Google Scholar

Copyright information

© Korean Society of Civil Engineers 2019

Authors and Affiliations

  • Chun Li
    • 1
  • Zhanguo Xiu
    • 1
    Email author
  • Yingchun Ji
    • 2
  • Feili Wang
    • 1
  • A. H. C. Chan
    • 3
  1. 1.School of Resource and Civil EngineeringNortheastern UniversityShenyangChina
  2. 2.School of the Built EnvironmentUniversity of SalfordSalfordUK
  3. 3.School of Engineering and Information TechnologyFederation University of AustraliaBallaratAustralia

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