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Equivalent deformation modulus of sandy pebble soil—Mathematical derivation and numerical simulation

1 School of Civil Engineering & Transportation, South China University of Technology, Guangzhou, Guangdong 510641, China
2 School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, M13 9PL, United Kingdom
3 Guangzhou University-Tamkang University Joint Research Centre for Engineering Structure Disaster Prevention and Control, Guangzhou University, Guangzhou, Guangdong 510006, China

Special Issues: Mathematical Methods in Civil Engineering

This study aims to investigate the mechanical properties of sandy pebble soil through theoretical deduction and finite element analysis. Based on the assumption of stress uniformity or strain uniformity, the analytical formulas for calculating the equivalent deformation modulus of pebble soil are derived through RVEs. To verify the accuracy of the formulas, a series of numerical experiments are conducted through ABAQUS. Results show that theoretical calculation values match numerical simulation results well and the analytical formulas are effective when the pebble content is 0–60%. For pebble content lower than 20%, the equivalent deformation modulus could be described by “Stress Uniformity Model”. When content is 20%–60%, pebble soil is a transition state from “Stress Uniformity” to “Strain Uniformity”, for which the constitutive model could be expressed as a modified transition formula. This research is helpful for further investigation of mechanical properties of pebble soil. The theories developed in this study can be used in determining shield excavation parameters, and predicting the ground settlement caused by shield excavation.
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Keywords sandy pebble soil; equivalent deformation modulus; constitutive equation; finite element simulation; representative volume element; stress uniformity; strain uniformity

Citation: Jizhi Huang, Guoyuan Xu, Yu Wang, Xiaowei Ouyang. Equivalent deformation modulus of sandy pebble soil—Mathematical derivation and numerical simulation. Mathematical Biosciences and Engineering, 2019, 16(4): 2756-2774. doi: 10.3934/mbe.2019137


  • 1. B. Y. Xue, Q. T. Yue, Y. D. Li, et al., Prediction for surface collapse deformation of shield construction based on LESSVM, Chin. J. Rock Mech. Eng., 32 (2013), 3666–3674.
  • 2. A. J. Markworth and J. H. Saunders, A model of structure optimization for a functionally graded material, Mater. Lett., 22 (1995), 103–107.
  • 3. J. D. Eshelby and R. E. Peierls, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. A, 241 (1957), 376–396.
  • 4. J. D. Eshelby and R. E. Peierls, The elastic field outside an ellipsoidal inclusion, Proc. R. Soc. A, 252 (1959), 561–569.
  • 5. X. Jin, Z. Wang, Q. Zhou, et al., On the solution of an elliptical inhomogeneity in plane elasticity by the Equivalent Inclusion Method, J. Elast., 114 (2014), 1–18.
  • 6. X. Jin, X. Zhang, P. Li, et al., On the displacement of a two-dimensional Eshelby inclusion of elliptic cylindrical, J. Appl. Mech., 84 (2017), 074501.
  • 7. G. Zuccaro, S. Trotta, S. Sessa, et al., Analytical solution of elastic fields induced by a 2D inclusion of arbitrary polygonal shape. Procedia Struct. Integr., 6 (2017), 236–243.
  • 8. M. Hu, G. Y. Xu and S. B. Hu, Study of equivalent elastic modulus of sand gravel soil with Eshelby tensor and Mori-Tanaka equivalent method, Rock Soil Mech., 34 (2013), 1437–1442+1448.
  • 9. H. Ma, M. Z. Gao, J. K. Zhang, et al., Theoretical model developed for equivalent elastic modulus estimation of cobblestone soil matrix. Rock Soil Mech., 32 (2011), 3642–3646.
  • 10. V. Buryachenko, Micromechanics of heterogeneous materials, Springer Science & Business Media, 2007.
  • 11. V. A. Buryachenko, On the thermo-elastostatics of heterogeneous materials: I. General integral equation, Acta Mech., 213 (2010), 359–374.
  • 12. M. Wang and N. Pan, Predictions of effective physical properties of complex multiphase materials, Mater. Sci. Eng. R. Rep., 63 (2008), 1–30.
  • 13. R. W. Zimmerman, Thermal conductivity of fluid-saturated rocks, J. Pet. Sci. Eng., 3 (1989), 219–227.
  • 14. M. Orrhede, R. Tolani and K. Salama, Elastic constants and thermal expansion of aluminum-SiC metal-matrix composites, Res. Nondestruct. Eval., 8 (1996), 23–37.
  • 15. V. A. Buryachenko and W. S. Kreher, Internal residual stresses in heterogeneous solids-A statistical theory for particulate composites, J. Mech. Phys. Solids, 43 (1995), 1105–1125.
  • 16. C. P. Wong and R. S. Bollampally, Thermal conductivity, elastic modulus, and coefficient of thermal expansion of polymer composites filled with ceramic particles for electronic packaging, J. Appl. Polym. Sci., 74 (1999), 3396–3403.
  • 17. M. R. Wang and N. Pan, Predictions of effective physical properties of complex multiphase materials, Mater. Sci. Eng. R. Rep., 63 (2008), 1–30.
  • 18. B. Paul, Prediction of elastic constants of multiphase materials. Trans. Metall. Soc. AIME, 218 (1960), 36-41.
  • 19. Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behavior of multiphase materials, J. Mech. Phys. Solids, 11 (1963), 127–140.
  • 20. Z. Hashin, Theory of mechanical behavior of heterogeneous media, Appl. Mech. Rev., 17 (1964), 1–9.
  • 21. J. Z. Huang and G. Y. Xu, Study on the Constitutive Model of Sandy Pebble Soil. In: Wu W., Yu HS. (eds) Proceedings of China-Europe Conference on Geotechnical Engineering. Springer Series in Geomechanics and Geoengineering. Springer, Cham (2018), 26–30.
  • 22. T. A. Ghezzehei and D. Or, Rheological properties of wet soils and clays under steady and oscillatory stresses, Soil Sci. Soc. Am. J., 65 (2001), 624–637.
  • 23. C. M. Bishop, M. Tang, R. M. Cannon, et al., Continuum modelling and representations of interfaces and their transitions in materials, Mater. Sci. Eng. A, 422 (2006), 102–114.
  • 24. W. G. Holtz and H. J. Gibbs, Triaxial shear tests on pervious gravelly soils, ASCE J. Soil Mech. Found. Div., 82 (1956), 1–22.
  • 25. K. Zhou, H. J. Hoh, X. Wang, et al., A review of recent works on inclusions. Mech. Mater., 60 (2013), 144–158.
  • 26. Z. Yuan, F. Li, F. Xue, et al., Analysis of The stress states and interface damage in a particle reinforced composite based on a micromodel using cohesive elements, Mater. Sci. Eng. A. Struct. Mater. Prop. Microstruct. Process., 589 (2014), 288−302.
  • 27. K. E. Koumi, L. Zhao, J. Leroux, et al., Contact analysis in the presence of an ellipsoidal inhomogeneity within a half space, Int. J. Solids Struct., 51 (2014), 1390–1402.
  • 28. L. Rodriguez-Tembleque, F. Buroni, R. Abascal, et al. Analysis of FRP composites under frictional contact conditions. Int. J. Solids Struct., 50 (2013), 3947–3959.
  • 29. J. J. Williams, J. Segurado, J. LLorca, et al., Three dimensional (3D) microstructure-based modeling of interfacial decohesion in particle reinforced metal matrix composites, Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process., 557 (2012), 113−118.
  • 30. Y. Su, Q. Ouyang, W. Zhang, et al., Composite structure modeling and mechanical behavior of particle reinforced metal matrix composites, Mater. Sci. Eng. A. Struct. Mater. Prop. Microstruct. Process., 597 (2014), 359–369.


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