Probabilistic Fracture Energy Assessment of Natural Fibre Reinforced Concrete by Two Parameter Weibull Distribution

  • Authors

    • Neha P Asrani
    • Murali G
    • Arthika J
    • Karthikeyan. K
    • Haridharan. M.K
    2018-07-20
    https://doi.org/10.14419/ijet.v7i3.12.16116
  • Fracture energy, Weibull Distribution, Reliability, Shape parameter, Scale parameter, Natural fibre.

  • Abstract

    Fracture energy is the post-crack energy absorption ability of the material that represents the energy absorbed by the structure at the time of failure. Its analysis has gained importance and hence requires a powerfulmethod for its development. A two parameter Weibull distribution proves to be an efficient tool in analysing the scattered experimental test results. In this paper, the specific fracture energy of plain concrete and concrete reinforced with natural fibres of hemp, wheat straw and elephant grass are statistically analysed by two parameter Weibull distribution by using graphical method. For determining Weibull parameters, 21 equations have been used and the best equation is taken for the reliability analysis. A Weibull reliability curve is plotted, which shows the specific fracture energy at each reliability level. This curve enables an engineer to choose the fracture energy of a particular mix based on its reliability requirement and safety limit. Therefore, reliability curves are a pioneer in statistical analysis as they eliminate the time-consuming and costly experimental process. This method can be applied in areas with similar uncertainties.

     

     

  • References

    1. [1] P.-S. Laplace, EssaiPhilosophique Sur Les Probabilités, Courcier, Paris, 1814.

      [2] A. Hazen, Storage to be provided in impounding reservoirs for municipal water supply, Trans. Am. Soc. Civil Eng. 77 (1914) 1547–1550.

      [3] California Department of Public Works, Flow in California streams, Calif., Dep. Public Works, Div. Eng. Irrig., Bull. 5 (1923).

      [4] California Department of Public Works, Flow in California streams, Calif., Dep. Public Works, Div. Eng. Irrig., Bull. 5 (1923).

      [5] W. Weibull, A statistical theory of strength of materials, Ing. Vet. Ak. Handl. (Stockholm) 151 (1939).

      [6] L.R. Beard, Statistical analysis in hydrology, Trans. Am. Soc. Civil Eng. 108 (1943) 1110–1160.

      [7] A. Benard, E.C. Bos-Levenbach, The plotting of observations on probability paper, Statistica 7 (1953) 163–173.

      [8] G. Blom, Statistical Estimates and Transformed Beta-variables, J. Wiley and Sons, 1958.

      [9] J.W. Tukey, The future of data analysis, Ann. Math. Stat. 33 (1) (1962) 21–24.

      [10] I.I. Gringorten, A plotting rule for extreme probability paper, J. Geophys. Res. 68 (1963) 813–814.

      [11] J. Filliben, The probability plot correlation coefficient test for normality, Technometrics 17 (1975) 111–117.

      [12] A.F. Jenkinson, The Analysis of Meteorological and Other Geophysical Extremes, Meteorological Office, UK, 1977, Technical Note No. 58.

      [13] C. Cunnane, Unbiased plotting positions—a review, J. Hydrol. 37 (1978) 205–222.

      [14] K. Adamowski, Plotting formula for flood frequency, J. Am. Water Resour. Assoc. 17 (2) (1981) 197–202.

      [15] R.M. Hirsch, Estimating probabilities of reservoir storage for the upper Delaware River basin, in: Open File Report 81–478, U.S. Geological Survey, Reston, VA, 1981.

      [16] A. Khalili, K. Kromp, Statistical properties of Weibull estimators, J. Mater. Sci. 26 (24) (1991) 6741–6752.

      [17] R. Ross, Graphical methods for plotting and evaluating Weibull distributed data, in: Proc. 4th Int. Conf. Properties Applicat. Dialectric Maters., June 3–8th 1994, Brisbane, Australia, 1994, pp. 250–253.

      [18] J. Gong, A new probability index for estimating Weibull modulus for ceramics with the least-square method, J. Mater. Sci. Lett. 19 (2000) 827–829.

      [19] S. Nohut, C. Lu, L. Gorjan, Optimal linear regression estimator in the fitting of Weibull strength distribution, J. Test. Eval. 42 (6) (2014) 1396–1407.

      [20] R. Bedi, R. Chandra. Fatigue-life distributions and failure probability for glass-fiber reinforced polymeric composites. Composites Science and Technology 69 (2009) 1381–1387. doi:10.1016/j.compscitech.2008.09.016

      [21] H. Li, M. Zhang, J. Ou, Flexural fatigue performance of concrete containing nano-particles for pavement, Int. J. Fatigue 29 (7) (2007) 1292–1301. http://dx.doi.org/10.1016/j.ijfatigue.2006.10.004.

      [22] S. Raif, A. Irfan, Statistical analysis of bending fatigue life data using Weibull distribution in glass-fiber reinforced polyester composites, Mater. Des. 29 (6) (2008) 1170–1181. http://dx.doi.org/10.1016/j.matdes.2007.05.005.

      [23] L. Wang, H. Wang, J. Jia, Impact resistance of steel-fibre-reinforced lightweight-aggregate concrete, Mag. Concr. Res. 67(2009) 539–547, http://dx.doi.org/10.1680/macr.2007.00128.

      [24] S. Goel, S.P. Singh, P. Singh, Fatigue analysis of plain and fiber-reinforced self consolidating concrete, ACI Mater. J. 109 (2012) 573–582. http://dx.doi.org/10.14359/51684089.

      [25] Y Ding, D Lia, Y Zhang, C Azevedo. Experimental investigation on the composite effect of steel rebars and macro fibers on the impact behavior of high performance self-compacting concrete. Construction and Building Materials 136 (2017) 495–505. http://dx.doi.org/10.1016/j.conbuildmat.2017.01.073

      [26] Yeon, K.S., Choi, Y.S., Kim, K.K., and Yeon, J.H., “Flexural fatigue life analysis of unsaturated polyester-methyl methacrylate polymer concrete,†Construction and Building Materials, Vol. 140, pp. 336–343 (2017). doi: 10.1016/j.conbuildmat.2017.02.116

      [27] Merta, I., and Tschegg. E.K., “Fracture energy of natural fibre reinforced concrete,†Construction and Building Materials, Vol. 40, pp. 991–997 (2013). doi: 10.1016/j.conbuildmat.2012.11.060

      [28] Weibull, W., A statistical theory of the strength of materials, Series 151, General stabenslitografiskaanstaltsförlag, Stockholm, (1939).

      [29] Ali, M.A.E.M., Soliman, A.M., and Nehdi, M.L., “Hybrid-fiber reinforced engineered cementitious composite under tensile and impact loading,†Materials Design, Vol. 117, pp. 139–149 (2017). doi: 10.1016/j.matdes.2016.12.047

      [30] Murali, G., Monika Vincy, T., Suraj, K., Ramkumar, V.R., and Karthikeyan, K., “Assessment of Impact Strength of Fibre Reinforced Concrete by Two Parameter Weibull Distribution,†ARPN Journal of Engineering and Applied Sciences, Vol. 12(5), pp. 1440-1445 (2017).

      [31] Murali, G., Muthulakshmi, T., NycilinKarunya, N., Iswarya, R., Hannah Jennifer, G. and Karthikeyan, K., “Impact Response and Strength Reliability of Green High Performance Fibre Reinforced Concrete Subjected to Freeze-Thaw Cycles in NaCl Solution,†Materials Science Medziagotyra, Vol. 23(4), pp. 384-388 (2017).

      [32] Murali, G., Santhi, A.S. and Mohan Ganesh, G., “Impact resistance and strength reliability of Fiber-reinforced concrete in bending under drop weight impact load,†International Journal of Technology, Vol. 5(2), pp. 111-120 (2014).

      [33] Murali, G., Santhi, A.S., and Mohan Ganesh, G., “Impact resistance and strength reliability of fiber reinforced concrete using two parameter Weibull distribution,†ARPN Journal of Engineering and Applied Sciences, Vol. 9(4), pp. 554-559 (2014).

      [34] Sakin, R., and Irfan, A.Y., “Statistical analysis of bending fatigue life data using Weibull distribution in glass-fiber reinforced polyester composites,†Materials and Design, Vol. 29, pp. 1170–1181 (2008). doi: 10.1016/j.matdes.2007.05.005

      [35] Sriram, V., Sirisha, K., Keerthi, P.R., Murali, G., Haridharan, M.K., Karthikeyan, K., “A New Method to Estimate Weibull Parameter for the Fatigue Life of Self Compacting Fibre Reinforced Concrete Beams,†International Journal of Civil Engineering Technology, Vol. 8(7), pp. 326–331 (2017).

      [36] G. Murali, T. Indhumathi, K. Karthikeyan and V.R. Ramkumar. Analysis of flexural fatigue failure of concrete made with 100% coarse recycled and natural aggregates. Computers and Concrete, Vol. 21, No. 3 (2018) 291-298.

      [37] Jianqiang, Wei, and Christian, Meyer, “ Degradation rate of natural fibre in cement composites exposed to various accelerated aging environmental conditions,†Corrosion Science, 88, pp.118-132 (2014).

      [38] Yongfu, Xu, “The fractal evolution of particle fragmentation under different fracture energy,†Powder Technology, Vol. 323, pp. 337-345 (2018).

      [39] Karahan, O., Ozbay, E., Atis, C.D., Lachemi, M., and Hossain, K.M.A., “Effects of Milled Cut Steel Fibers on the Properties of Concrete,†KSCE. J. Civil. Eng, Vol. 20(7), pp. 2783-2789 (2016). doi: 10.1007/s12205-016-0577-3.

      [40] Kin-tak, Lau, “Properties of natural fibre composites for structural engineering applications,†Composites Part B: Engineering, Vol. 136, pp. 222-233 (2018).

  • Downloads

  • How to Cite

    P Asrani, N., G, M., J, A., K, K., & M.K, H. (2018). Probabilistic Fracture Energy Assessment of Natural Fibre Reinforced Concrete by Two Parameter Weibull Distribution. International Journal of Engineering & Technology, 7(3.12), 407-410. https://doi.org/10.14419/ijet.v7i3.12.16116

    Received date: 2018-07-23

    Accepted date: 2018-07-23

    Published date: 2018-07-20