Confidence interval in Kirsch equations

  • Authors

    • Morteza Khodabin Karaj Branch, Islamic Azad University
    • Vahid Hosseinitoudeshki Zanjan Branch,~Islamic Azad University
    2014-09-05
    https://doi.org/10.14419/ijamr.v3i4.3281

  • Rocks at depth are affected by stresses resulting from the weight of the overlying strata and tectonic stresses. When a tunnel is excavated in this rock, the stress field is locally disordered and radial, tangential and shear stresses are induced in the rock around the tunnel. Knowledge of the magnitudes and directions of these induced stresses is essential. Since the measuring of specific gravity and depth are inevitably affected by environmental noise, we consider a random version of P2 in Kirsch equations. By doing this, we define random version of the Kirsch equations. Then we introduce an algorithm to calculate confidence intervals for the Kirsch parameters. Finally we use Alborz tunnel characteristics for creating these confidence intervals as a case study. The results show that the proposed amounts of radial, tangential and shear stresses lie in desired range.

    Keywords: Kirsch equations; Confidence interval; confidence level; Alborz tunnel; normal distribution.

  • References

    1. Alavi M. Tectonostratigraphic synthesis and structural style of the Alborz mountain system in northern Iran J Geodyn 1994; 21: 1-33.
    2. Brady BHG, Brown ET. Rock Mechanics for Underground Mining, 1st edn Allen and Unwin, London 2004.
    3. Casella G, and Berger R. Statistical Inference, 2rd ed, R. R. Donnelley and Sons Co, Craw-fordsville 2001.
    4. Goodman RE. Introduction to Rock Mechanics. Wiley, New York 1989; 478 pp.
    5. Jaeger C. Rock Mechanics and Engineering, Cambridge University Press 1979; 523 pp.
    6. Kirsch G. Die theorie der elastizitat und die bedurfnisse der festigkeitslehre. Veit Ver Deut Ing 1898; 42: 797-807.
    7. Singh B, Goel RK. Rock Mass Classification, A Practical Approach in Civil Engineering. Elsevier, Amsterdam 1999; 265 pp.
    8. Yassaghi A, Salari-Rad H, Kanani-Moghadam H. Geomechanical evaluations of Karaj tuffs for rock tunneling in Tehran-Shomal Freeway, Iran Engineering Geology 2005; 77: 83-98.

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  • How to Cite

    Khodabin, M., & Hosseinitoudeshki, V. (2014). Confidence interval in Kirsch equations. International Journal of Applied Mathematical Research, 3(4), 375-379. https://doi.org/10.14419/ijamr.v3i4.3281