A semi-analytical elastic stress-displacement solution for notched circular openings in rocks

Exadaktylos, GE; Liolios, PA; Stavropoulou, MC

dc.contributor.author	Exadaktylos, GE	en
dc.contributor.author	Liolios, PA	en
dc.contributor.author	Stavropoulou, MC	en
dc.date.accessioned	2014-03-01T01:18:33Z
dc.date.available	2014-03-01T01:18:33Z
dc.date.issued	2003	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15085
dc.subject	Boreholes	en
dc.subject	Breakouts	en
dc.subject	Complex variables	en
dc.subject	Conformal mapping	en
dc.subject	Notches	en
dc.subject	Plane elasticity	en
dc.subject.classification	Mechanics	en
dc.subject.other	Brittle fracture	en
dc.subject.other	Elasticity	en
dc.subject.other	Failure (mechanical)	en
dc.subject.other	Mapping	en
dc.subject.other	Strain	en
dc.subject.other	Notched circular opening	en
dc.subject.other	Rocks	en
dc.subject.other	borehole	en
dc.subject.other	displacement	en
dc.subject.other	rock mechanics	en
dc.subject.other	stress	en
dc.title	A semi-analytical elastic stress-displacement solution for notched circular openings in rocks	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0020-7683(02)00646-7	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0020-7683(02)00646-7	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	A semi-analytical plane elasticity solution of the circular hole with diametrically opposite notches in a homogeneous and isotropic geomaterial is presented. This solution is based on: (i) the evaluation of the conformal mapping function of a hole of prescribed shape by an appropriate numerical scheme and (ii) the closed-form solutions of the Kolosov-Muskhelishvili complex potentials. For the particular case of circular notches - which resemble to the circular cavity breakout in rocks - it is demonstrated that numerical results pertaining to boundary stresses and displacements predicted by the finite differences model FLAC2D, as well as previous analytical results referring to the stress-concentration-factor, are in agreement with analytical results. It is also illustrated that the solution may be easily applied to non-rounded diametrically opposite notch geometries, such as ""dog-eared"" breakouts by properly selecting the respective conformal mapping function via the methodology presented herein. By employing a stress-mean-value brittle failure criterion that takes into account the stress-gradient effect in the vicinity of the curved surfaces in rock as well as the present semi-analytical solution, it is found that a notched hole, e.g. borehole or tunnel breakout, may exhibit stable propagation. The practical significance of the proposed solution lies in the fact that it can be used as a quick-solver for back-analysis of borehole breakout images obtained in situ via a televiewer for the estimation of the orientation and magnitude of in situ stresses and of strain-stress measurements in laboratory tests. © 2002 Elsevier Science Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Solids and Structures	en
dc.identifier.doi	10.1016/S0020-7683(02)00646-7	en
dc.identifier.isi	ISI:000181264500006	en
dc.identifier.volume	40	en
dc.identifier.issue	5	en
dc.identifier.spage	1165	en
dc.identifier.epage	1187	en