Multiple interacting curvilinear crack problems: a method of solution and numerical results

A. M. Linkov, S. G. Mogilevskaya, J. A.L. Napier

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations


The importance of accounting for multiple cracks and the blocky structure of rock is emphasized, and a method to solve plane problems for such structures is developed. The method makes use of (i) hypersingular equations to deal with discontinuities combined with (ii) complex variables to facilitate evaluation of singular and hypersingular integrals. New approximations for the accurate representation of displacement discontinuities are suggested; they include linear combination of common and conjugated polynomials for ordinary elements together with a special form of asymptotic function for crack tip elements. This results in simple analytical recurrence formulae for the 'crucial' (singular and hypersingular) integrals over arbitrary curvilinear elements (both ordinary and tip). The remaining non-singular integrals over elements are efficiently evaluated by common methods. Moreover, in the important particular cases of a straight element and a circular arc element they are also evaluated in a simple analytical form. All the significant details of the method are presented. A computer program, worked out on this basis, provides an opportunity to deal with blocky systems, defined by multiple straight and curvilinear cracks as well as a basis for the simulation of propagating curvilinear cracks. Examples illustrating the efficiency of the method are given.

Original languageEnglish (US)
Pages (from-to)218.e1-218.e12
Number of pages1
JournalInternational journal of rock mechanics and mining sciences & geomechanics abstracts
Issue number3-4
StatePublished - Apr 1 1997
Externally publishedYes
EventProceedings of the 1997 36th US Rock Mechanics ISRM International Symposium - New York, NY, USA
Duration: Jun 29 1997Jul 2 1997

Bibliographical note

Publisher Copyright:
© 1997


  • approximation
  • blocky structure
  • complex variables
  • crack
  • hypersingular equations
  • quadratures


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