Rock materials contain cracks, and under certain conditions, these cracks will extend, branch and coalesce, which have received the most attention recently. In this paper, an attempt is made to set up a fracture criterion for the special case as cracks are situated along a straight line. Under compression, cracks close and the crack surface friction can resist crack surface sliding. A set of complex stress functions and the solution of stress intensity factors have been presented in the author's previous publication and will be applied in this paper. A fracture criterion for the case of collinear cracks under compression is developed, which is expressed in terms of principal stresses. For the case of materials without pre-existing cracks, this new fracture criterion becomes the well known Coulomb-Mohr failure criterion.

1. Introduction

Fracture or Failure criterion describes the limiting loading conditions that materials can sustain. Because such a limiting state has become so important in the usual design methods for engineering rock mechanics, a great deal of effort, both from the theoretical and experimental point of view, has been devoted to studying the behaviour of rock materials loaded to failure, and many fracture or failure criteria have been developed (Bieniawski, 1974; Hoek and Brown, 1980; Johnston, 1985; Gates, 1988; Li, 1990; Fuenkajorn and Daemen, 1992; Zhu, 1999).

Most brittle materials in nature contain preexisting cracks or flaws, such as underground rock mass and concrete, and they usually are subjected to compressive loads. Therefore, in the study of rock material fracture criterion, the following three aspects have to be considered:

  1. the interaction between cracks, because cracks affect each other, and under certain conditions, they extend, branch and coalesce, which have received the most attention (Nemat-Nasser and Horii, 1982; Steif, 1984; Ashby and Hallam, 1986; Li and Nordlund, 1993; Germanovich et al., 1994; Baud et al. 1996; Rice et al., 2001; Sih, 2002). However, no exactly analytical solution is available today for multiple cracks under compression;

  2. crack surface friction, because under compression, cracks close and friction exists between the crack surfaces. The friction can resist crack surface sliding and thus it significantly affects crack tip stress intensity factor (Zhu et al. 2006; Zhu 2009); and

  3. confining stress, because material strength increases as confining stress increases (Zhu et al. 1996; 1997; 2006; 2008; Zhu, 1999; 2009).

The general fracture criteria for mode II crack can be written as KII KIIC However, such fracture criterion is difficult to apply because KIIC is difficult to measure, and the measurement results are usually scattered in a large range. In order to avoid such difficulties in measuring rock fracture toughness, the general fracture criterion will be transformed into a new form expressed in terms of principal stresses, without KII and KIIC involved.

In this paper, a new fracture criterion is developed for specimens containing two collinear cracks under compression, and also for specimens containing a single crack, the corresponding fracture criterion is obtained which is the same as the criterion of two collinear cracks.

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