Search

The instability of the pillar was discussed based on the potential energy principle and the cusp catastrophe theory, and a simplified mechanical model of the pillar was established considering the mining effect. The necessary-sufficient conditions, the jump value of displacement of pillar and the released energy expressions were deduced. The results show that the instability of the pillar is related to the properties of the rock, the external force and the relative stiffness of the elastic area to the plastic area. The instability of system is like to occur with the enlarging of the softening area or the decreasing of E/λ. The calculation done shows that the estimated results correspond to practical experience.

A detailed analysis of mode II stress intensity factors(SIFs) for the double edge cracked Brazilian disk subjected to different diametral compression is presented using a weight function method. The model II SIFs at crack tips can be obtained by simply calculating an integral of the product of mode II weight function and the shear stress on the prospective crack faces of uncracked disk loaded by a diametral compression. A semi-analytical formula for the calculation of normalized mode II SIF, fII, is derived for different crack lengths (from 0.1 to 0.7) and inclination angles (from 10° to 75°) with respect to loading direction. Comparison between the obtained results and finite element method solutions shows that the weight function method is of high precision. Combined with the authors’ previous work on mode I fracture analysis, the new specimen geometry can be used to study fracture through any combination of mode I and mode II loading by a simple alignment of the crack relative to the diameter of compression loading, and to obtain pure mode II crack extension. Another advantage of this specimen geometry is that it is available directly from rock core and is also easy to fabricate.

A new specimen geometry—the double edge-cracked Brazilian disk and a relevant fracture analysis by weight function method are proposed for the investigation of rock fracture caused by compression-shear loading. Not only can the mixed mode fracture with any ratio of KI/KII be achieved, but also the pure mode II crack extension can be obtained. The combined mode fracture analysis for this geometry shows that diametral compression in the farfield can induce a compression-shear stress state in the singular stress field ahead of crack tips. Experimental investigations conducted on marble specimens show that the pure mode II crack extension can be obtained when the dimensionless crack length a>0.7 and the inclined crack angle 5°⩽ϕ⩽40°. Normalized mode I and mode II stress intensity factors decrease from −0.45 and 2.47 at ϕ=5° to −1.65 and 1.52 at ϕ=40°, respectively. The strains at three points of specimen are also measured in order to investigate the influence of stress singularity on initial crack extension. The results show that the principal orientations of strain at three points are very stable in the loading process. The derived formulae are quite explicit, and the specimen geometry is easy to fabricate and convenient to achieve the pure mode II crack extension. Therefore, it can hopefully be used to obtain mode II fracture toughness of rock.