Document Type : Research Paper

**Authors**

Department of Civil Engineering, University of Shahrood, Shahrood, Iran

**Abstract**

One of the conventional methods for temporary support of tunnels is to use steel sets with shotcrete. The nature of a temporary support system demands a quick installation of its structures. As a result, the spacing between steel sets is not a fixed amount and it can be considered as a random variable. Hence, in the reliability analysis of these types of structures, the selection of an appropriate probability distribution function of spacing of steel sets is essential. In the present paper, the distances between steel sets are collected from an under-construction tunnel and the collected data is used to suggest a proper Probability Distribution Function (PDF) for the spacing of steel sets. The tunnel has two different excavation sections. In this regard, different distribution functions were investigated and three common tests of goodness of fit were used for evaluation of each function for each excavation section. Results from all three methods indicate that the Wakeby distribution function can be suggested as the proper PDF for spacing between the steel sets. It is also noted that, although the probability distribution function for two different tunnel sections is the same, the parameters of PDF for the individual sections are different from each other.

**Keywords**

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[14] Milford, R. (1987). Annual maximum wind speeds from parent distribution functions. Journal of wind Engineering and Industrial Aerodynamics, 25, pp. 163-178.

[15] Ghamishon, R., & Malekian,A. (2011). Determination of the most suitable statistical distribution functions for regional floods (Case study of southwest Kerman Province). Proceedings of Sixth National Watershed Sciences and Engineering Conference and forth national congress on soil erosion and sediment, Tarbiat-Modares University.

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[17] Cochran, W.G. (1952). The χ^2 test of goodness of fit. Institute of Mathematical Statistics, Vol 23, No. 3, pp. 315-345. http://www.jstor.org/stable/2236678

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[19] Darbandi, S., Mahmudi, S., & Ebrahimi, S., & Shoeybi-Nobarian, M. R. (2012). Introduction and application of Anderson-Darling in river engineering of East Azerbaijan Province. Fifth National Conference on Watersheds and management of soil and water resources.

December 2015

Pages 187-203