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Evaluation of Strength and Failure of Brittle Rock Containing Initial Cracks under Lithospheric Conditions

Li X., Qi C., Shao Z., Ma C.

Acta Geophysica

2018

Vol. 66, no. 2

141--152

Natural brittle rock contains numerous randomly distributed microcracks. Crack initiation, growth, and coalescence play a predominant role in evaluation for the strength and failure of brittle rocks. A new analytical method is proposed to predict the strength and failure of brittle rocks containing initial microcracks. The formulation of this method is based on an improved wing crack model and a suggested micro-macro relation. In this improved wing crack model, the parameter of crack angle is especially introduced as a variable, and the analytical stress-crack relation considering crack angle effect is obtained. Coupling the proposed stresscrack relation and the suggested micro-macro relation describing the relation between crack growth and axial strain, the stress-strain constitutive relation is obtained to predict the rock strength and failure. Considering different initial microcrack sizes, friction coefficients and confining pressures, effects of crack angle on tensile wedge force acting on initial crack interface are studied, and effects of crack angle on stress-strain constitutive relation of rocks are also analyzed. The strength and crack initiation stress under different crack angles are discussed, and the value of most disadvantaged angle triggering crack initiation and rock failure is founded. The analytical results are similar to the published study results. Rationality of this proposed analytical method is verified.

Interaction of surface and internal cracks in railhead

Dhanasekar M., Han J., Qin Q. H.

Computer Assisted Mechanics and Engineering Sciences

2007

Vol. 14, No. 1

79-89

This paper presents a two-dimensional model for the analysis of interaction between surface and internal cracks in the railheads subjected to wheel loading. The shape of the railhead, the surface crack and the internal crack are modelled as curved cracks defined by the theory of continuous distribution of dislocation in an infinite body. From the boundary conditions along these cracks, a system of singular integral equations is deduced. Influence functions in these singular integral equations are first expanded into the Cauchy kernel multiplying normal functions and later are reduced to a system of linear equations and solved numerically. Stress intensity factors (SIFs) of the surface crack tip are calculated from the numerical solution of distribution function along these cracks directly, eliminating need for any indirect integral method. The method does not require meshing and hence idealisation of the shapes of the cracks, thereby improving accuracy and reducing pre- and post processing efforts. Interaction between the internal crack and the surface crack is examined in detail through several examples.