An analytical probability distribution for the factor of safety in underground rock mechanics

Nomikos, PP; Sofianos, AI

dc.contributor.author	Nomikos, PP	en
dc.contributor.author	Sofianos, AI	en
dc.date.accessioned	2014-03-01T01:35:06Z
dc.date.available	2014-03-01T01:35:06Z
dc.date.issued	2011	en
dc.identifier.issn	1365-1609	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20970
dc.subject	Density function	en
dc.subject	Factor of safety	en
dc.subject	Pillar stability	en
dc.subject	Probability of failure	en
dc.subject	Suspended roofs	en
dc.subject	Underground rock mechanics	en
dc.subject.classification	Engineering, Geological	en
dc.subject.classification	Mining & Mineral Processing	en
dc.subject.other	Density functions	en
dc.subject.other	Factor of safety	en
dc.subject.other	Pillar stability	en
dc.subject.other	Probability of failure	en
dc.subject.other	Suspended roofs	en
dc.subject.other	Underground rock mechanics	en
dc.subject.other	Distribution functions	en
dc.subject.other	Probability density function	en
dc.subject.other	Probability distributions	en
dc.subject.other	Random variables	en
dc.subject.other	Rock mechanics	en
dc.subject.other	Rocks	en
dc.subject.other	Roofs	en
dc.subject.other	Structural design	en
dc.subject.other	Safety factor	en
dc.subject.other	failure analysis	en
dc.subject.other	pillar	en
dc.subject.other	probability density function	en
dc.subject.other	rock mechanics	en
dc.subject.other	roof	en
dc.subject.other	safety	en
dc.subject.other	subterranean environment	en
dc.title	An analytical probability distribution for the factor of safety in underground rock mechanics	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijrmms.2011.02.015	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijrmms.2011.02.015	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	In many underground rock mechanics cases, the factor of safety may be defined as the ratio of the capacity, of the rock or its support elements, to the pertinent demand. By representing the capacity and the demand as uniform random variables, an analytic solution is obtained for the probability distribution of the factor of safety and its probability density and cumulative distribution functions. Closed form solutions for the calculation of the mean value, the standard deviation and the minimum and maximum values of the factor of safety, are thus provided. Four relative positions are possible for the demand and capacity density functions, according to their limits. Closed form solutions are provided for the probability of failure for the identified relative positions. Application of the developed analytical solutions for the probabilistic analysis of two cases of underground roofs and four cases of room pillars follows straight forward. This methodology proves also useful for the utilization of field observations or for the extrapolation of any specific design. It allows, finally, for the parametric evaluation of the effect of specific design variables to the distribution of the safety factor. (C) 2011 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Rock Mechanics and Mining Sciences	en
dc.identifier.doi	10.1016/j.ijrmms.2011.02.015	en
dc.identifier.isi	ISI:000290783300008	en
dc.identifier.volume	48	en
dc.identifier.issue	4	en
dc.identifier.spage	597	en
dc.identifier.epage	605	en