Mirenkov V. E., Evstigneev D. S. – Institute of Mining, the Siberian Branch of RAS, Novosibirsk, the Russian Federation. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
The problem on the plane weakened by a straightline final fracture, is widely used in different sciences due to
the analytical character of the solution. Analytical solution to the problem on a fracture is obtained for a weightless plane,
so a need arises to consider the factor of the dead rock weight influence on the solution. The phenomenological model
is proposed for deforming the rocks in the vicinity of crack. This model takes into account the own weight of rocks and
describes their action which does not coincide with the direction of compression stresses on the upper crack edge in the
upper half-plane; in the lower half-plane, these directions coincide. In-situ measurements of crack edge displacements
are used, and a dimensionless parameter characterizing the upper edge-to-lower edge displacement ratio for one and
the same crack point before deformation is introduced. The parameter is determined experimentally. To account for
additional information obtained from redetermination of boundary conditions implies to solve inverse problems in view of
impracticability of a classical solution.
Key words: crack; rock weight; inverse problems; displacements; stresses.
REFERENCES
1. Irwin C. R. The crack-extension force for a crack at free surface boundary. Report No. 5120. Naval Research Lab.
1958, pp. 613-627.
2. Bowie O. L., Neol D. M. Single edge cracks in rectangular tensile sheet, Transe. ASME. Ser. E. S. Appl. Mech. 1965,
vol. 32, no. 3, pp. 708–719.
3. Stallybrass A. M. P. A crack perpendicular to an elastic half-plane. Int. J. Enging. Sci., 1970, vol. 8, no. 5, pp. 351–362.
4. Hasebe N., Chen Y. An edge crack problem in a semi-infinite plane subjected to concentrated forces. Applied Math.
and Mech., 2001, vol. 22, no. 1, pp. 1279–1290.
5. Mirenkov V. E. Finite stress in fracture mechanics. Engineering Fracture Mechanics, 1994, vol. 48, no. 1, pp. 63–68.
6. Mikhlin S. G. [Regarding the stresses within rock over the coal bed]. Izvestiya Akademii naik SSSR. OTN – News of
the Academy of Sciences of the USSR. Department of Technical Sciences, 1942, no. 7–8, pp. 13–28. (In Russ.)