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Legendre polynomial-based stochastic micromechanical model for the unsaturated concrete repaired by EDM

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Abstract

A Legendre polynomial-based stochastic micromechanical framework is proposed to quantify the unbiased probabilistic behavior for the unsaturated concrete repaired by the electrochemical deposition method (EDM). By following the authors’ previous works, a deterministic micromechanical model with new multilevel homogenization scheme for the repaired unsaturated concrete is presented based on the material’s microstructures. With the stochastic descriptions for the microstructures of the repaired unsaturated concrete, the deterministic framework is extended to stochastic. The unbiased probabilistic behavior of the repaired concrete is reached by incorporating the Legendre polynomial approximations and the Monte Carlo simulations. The predictions herein are then compared with the available experimental data, existing models and the commonly used probability density functions, which indicate that the presented stochastic micromechanical framework is capable of characterizing the EDM healing process for unsaturated concrete considering the material’s random microstructure. Finally, the statistical effects of the deposition products and unsaturated pores are discussed.

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References

  1. Ferrante, F., Graham-Brady, L.: Stochastic simulation of non-Gaussian/non-stationary properties in a functionally graded plate. Comput. Methods Appl. Mech. Eng. 194, 1675–1692 (2005)

    Article  MATH  Google Scholar 

  2. Chen, Q., Zhu, H.H., Ju, J.W., Yan, Z.G., Jiang, Z.W., Chen, B., Wang, Y.Q., Fan, Z.H.: Stochastic micromechanical predictions for the probabilistic behavior of saturated concrete repaired by the electrochemical deposition method. Int. J. Damage Mech. (2019). https://doi.org/10.1177/1056789519860805

    Article  Google Scholar 

  3. Zhu, H.H., Chen, Q., Ju, J.W., Yan, Z.G., Guo, F., Wang, Y.Q., Jiang, Z.W., Zhou, S., Wu, B.: Maximum entropy based stochastic micromechanical model for a two-phase composite considering the inter-particle interaction effect. Acta Mech. 226(9), 3069–3084 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, Q., Zhu, H.H., Ju, J.W., Guo, F., Wang, L.B., Yan, Z.G., Deng, T., Zhou, S.: A stochastic micromechanical model for multiphase composite containing spherical inhomogeneities. Acta Mech. 226(6), 1861–1880 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Rahman, S., raborty, Chak: A stochastic micromechanical model for elastic properties of functionally graded materials. Mech. Mater. 39, 548–563 (2007)

    Article  Google Scholar 

  6. Chen, Q., Zhu, H.H., Ju, J.W., Jiang, Z.W., Yan, Z.G., Li, H.X.: Stochastic micromechanical predictions for the effective properties of concrete considering the interfacial transition zone effects. Int. J. Damage Mech 27(8), 1252–1271 (2018a)

    Article  Google Scholar 

  7. Chen, Q., Zhu, H.H., Ju, J.W., Yan, Z.G., Wang, C.H., Jiang, Z.W.: A stochastic micromechanical model for fiber-reinforced concrete using maximum entropy principle. Acta Mech. 229(7), 2719–2735 (2018b)

    Article  MathSciNet  Google Scholar 

  8. Jiang, Z.W., Yang, X.J., Yan, Z.G., Chen, Q., Zhu, H.H., Wang, C.H., Ju, J.W., Fang, Z.H., Li, H.X.: A stochastic micromechanical model for hybrid fiber-reinforced concrete. Cement Concr. Compos. 102, 39–54 (2019)

    Article  Google Scholar 

  9. Ostoja-Starzewski, M.: Material spatial randomness: from statistical to representative volume element. Probab. Eng. Mech. 21(2), 112–132 (2006)

    Article  Google Scholar 

  10. Otsuki, N., Hisada, M., Ryu, J.S., Banshoya, E.J.: Rehabilitation of concrete cracks by electrodeposition. Concr. Int. 21(3), 58–62 (1999)

    Google Scholar 

  11. Ryu, J.S., Otsuki, N.: Crack closure of reinforced concrete by electro deposition technique. Cem. Concr. Res. 32(1), 159–264 (2002)

    Article  Google Scholar 

  12. Mohankumar, G.: Concrete repair by electrodeposition. Indian Concr. J. 79(8), 57–60 (2005)

    Google Scholar 

  13. Chen, Q.: The stochastic micromechanical models of the multiphase materials and their applications for the concrete repaired by electrochemical deposition method. Ph.D. dissertation Tongji University (2014)

  14. Ryu, J.S.: New waterproofing technique for leaking concrete. J. Mater. Sci. Lett. 22, 1023–1025 (2003)

    Article  Google Scholar 

  15. Ryu, J.S., Otsuki, N.: Experimental study on repair of concrete structural members by electrochemical method. Scripta Mater. 52, 1123–1127 (2005)

    Article  Google Scholar 

  16. Zhu, H.H., Chen, Q., Yan, Z.G., Ju, J.W., Zhou, S.: Micromechanical model for saturated concrete repaired by electrochemical deposition method. Mater. Struct. 47, 1067–1082 (2014)

    Article  Google Scholar 

  17. Chen, Q., Zhu, H.H., Yan, Z.G., Deng, T., Zhou, S.: Micro-scale description of the saturated concrete repaired by electrochemical deposition method based on Mori–Tanaka method. J. Build. Struct. 36(1), 98–103 (2015)

    Google Scholar 

  18. Chen, Q., Zhu, H.H., Yan, Z.G., Ju, J.W., Deng, T., Zhou, S.: Micro-scale description of the saturated concrete repaired by electrochemical deposition method based on self-consistent method. Chin. J. Theor. Appl. Mech. 47(2), 367–371 (2015)

    Google Scholar 

  19. Chen, Q., Jiang, Z.W., Zhu, H.H., Ju, J.W., Yan, Z.G.: Micromechanical framework for saturated concrete repaired by the electrochemical deposition method with interfacial transition zone effects. Int. J. Damage Mech 26(2), 210–228 (2017)

    Article  Google Scholar 

  20. Yan, Z.G., Chen, Q., Zhu, H.H., Ju, J.W., Zhou, S., Jiang, Z.W.: A multiphase micromechanical model for unsaturated concrete repaired by electrochemical deposition method. Int. J. Solids Struct. 50(24), 3875–3885 (2013)

    Article  Google Scholar 

  21. Chen, Q., Jiang, Z.W., Yang, Z.H., Zhu, H.H., Ju, J.W., Yan, Z.G., Li, H.X.: The effective properties of saturated concrete healed by EDM with the ITZs. Comput. Concr. 21(1), 67–74 (2018)

    Google Scholar 

  22. Chen, Q., Jiang, Z.W., Zhu, H.H., Ju, J.W., Yan, Z.G., Li, H.X., Rabczuk, T.: A multiphase micromechanical model for unsaturated concrete repaired by electrochemical deposition method with the bonding effects. Int. J. Damage Mech. (2018). https://doi.org/10.1177/1056789518773633

    Article  Google Scholar 

  23. Chen, Q., Jiang, Z.W., Yang, Z.H., Zhu, H.H., Ju, J.W., Yan, Z.G., Wang, Y.Q.: Differential-scheme based micromechanical framework for saturated concrete repaired by the electrochemical deposition method. Mater. Struct. 49(12), 5183–5193 (2016)

    Article  Google Scholar 

  24. Chen, Q., Jiang, Z.W., Yang, Z.H., Zhu, H.H., Ju, J.W., Yan, Z.G., Wang, Y.Q.: Differential-scheme based micromechanical framework for unsaturated concrete repaired by the electrochemical deposition method. Acta Mech. 228(2), 415–431 (2017)

    Article  MathSciNet  Google Scholar 

  25. Chatterji, S.: An explanation for the unsaturated state of water stored concrete. Cement Concr. Compos. 26, 75–79 (2004)

    Article  Google Scholar 

  26. Persson, B.: Moisture in concrete subjected to different kinds of curing. Mater. Struct. 30, 533–544 (1997)

    Article  Google Scholar 

  27. Delmi, M.M.Y., Ait-Mokhtar, A., Amiri, O.: Modelling the coupled evolution of hydration and porosity of cement-based materials. Constr. Build. Mater. 20(7), 504–514 (2006)

    Article  Google Scholar 

  28. Yaman, I.O., Hearn, N., Aktan, H.M.: Active and non-active porosity in concrete part II: evaluation of existing models. Mater. Struct. 35(3), 110–116 (2002)

    Article  Google Scholar 

  29. Wang, H.L., Li, Q.B.: Prediction of elastic modulus and Poisson’s ratio for unsaturated concrete. Int. J. Solids Struct. 44, 1370–1379 (2007)

    Article  MATH  Google Scholar 

  30. Chen, Q., Mousavi, Nezhad M., Fisher, Q., Zhu, H.H.: Multi-scale approach for modeling the transversely isotropic elastic properties of shale considering multi-inclusions and interfacial transition zone. Int. J. Rock Mech. Min. Sci. 84, 95–104 (2016)

    Article  Google Scholar 

  31. Nezhad, M.M., Zhu, H.H., Ju, J.W., Chen, Q.: A simplified multiscale damage model for the transversely isotropic shale rocks under tensile loading. Int. J. Damage Mech. 25(5), 705–726 (2016)

    Article  Google Scholar 

  32. Chen, Q., Zhu, H.H., Yan, Z.G., Ju, J.W., Jiang, Z.W., Wang, Y.Q.: A multiphase micromechanical model for hybrid fiber reinforced concrete considering the aggregate and ITZ effects. Constr. Build. Mater. 114, 839–850 (2016)

    Article  Google Scholar 

  33. Ju, J., Zhang, X.: Micromechanics and effective transverse elastic moduli of composites with randomly located aligned circular fibers. Int. J. Solids Struct. 35, 941–960 (1998)

    Article  MATH  Google Scholar 

  34. Ju, J., Yanase, K.: Micromechanical effective elastic moduli of continuous fiber-reinforced composites with near-field fiber interactions. Acta Mech. 216, 87–103 (2011)

    Article  MATH  Google Scholar 

  35. Ju, J., Sun, L.: Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: micromechanics-based formulation. Int. J. Solids Struct. 38, 183–201 (2001)

    Article  MATH  Google Scholar 

  36. Sun, L., Ju, J.: Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part II: applications. Int. J. Solids Struct. 38, 203–225 (2001)

    Article  MATH  Google Scholar 

  37. Sun, L., Ju, J.: Elastoplastic modeling of metal matrix composites containing randomly located and oriented spheroidal particles. J. Appl. Mech. 71, 774–785 (2004)

    Article  MATH  Google Scholar 

  38. Zhu, H.H., Chen, Q.: An approach for predicting the effective properties of multiphase composite with high accuracy. Chin. J. Theor. Appl. Mech. 1, 41–47 (2017)

    Google Scholar 

  39. Ju, J., Sun, L.: A novel formulation for the exterior-point Eshelby’s tensor of an ellipsoidal inclusion. J. Appl. Mech. 66, 570–574 (1999)

    Article  Google Scholar 

  40. Ju, J., Yanase, K.: Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions. Acta Mech. 215, 135–153 (2010)

    Article  MATH  Google Scholar 

  41. Yanase, K., Ju, J.W.: Effective elastic moduli of spherical particle reinforced composites containing imperfect interfaces. Int. J. Damage Mech. 21, 97–127 (2012)

    Article  Google Scholar 

  42. Christensen, R.M., Lo, K.H.: Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330 (1979)

    Article  MATH  Google Scholar 

  43. Ju, J.W., Chen, T.M.: Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities. Acta Mech. 103, 103–121 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  44. Ju, J.W., Chen, T.M.: Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities. Acta Mech. 103, 123–144 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  45. Mura, T.: Micromechanics of Defects in Solids. Kluwer Academic, Dordrecht (1987)

    Book  MATH  Google Scholar 

  46. Berryman, J.G.: Long-wave propagation in composite elastic media II. Ellipsoidal inclusion. Acoust. Soc. Am. J. 68, 1820–1831 (1980)

    Article  MATH  Google Scholar 

  47. Smith, J.C.: Experimental values for the elastic constants of a particulate-filled glassy polymer. J. Res. Natl. Bureau Stand. 80A, 45–49 (1976)

    Article  Google Scholar 

  48. Li, H., Xu, C., Dong, B., Chen, Q., Gu, L., Yang, X., Wang, W.: Differences between their influences of TEA and TEA.HCl on the properties of cement paste. Constr. Build. Mater. (2020). https://doi.org/10.1016/j.conbuildmat.2019.117797

    Article  Google Scholar 

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Acknowledgements

This work was supported by National Key Research and Development Plan (2018YFC0705400). This work was also supported by the National Natural Science Foundation of China (51508404, 51478348, 51278360, 51308407, U1534207), the 1000 Talents Plan Short-Term Program by the Organization Department of the Central Committee of the CPC, the Funds of Fundamental Research Plan for the Central Universities.

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Chen, Q., Liu, X.Y., Zhu, H.H. et al. Legendre polynomial-based stochastic micromechanical model for the unsaturated concrete repaired by EDM. Arch Appl Mech 90, 1267–1283 (2020). https://doi.org/10.1007/s00419-020-01663-w

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  • DOI: https://doi.org/10.1007/s00419-020-01663-w

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