Many studies have been done for the fracture of excavation in geological engineering and rock mechanics. For a small crack in arock, fracture mechanics can be applied. Microscopic study has been made(Yokobori, 1954) in mechanical engineering. But the direction of a crack growth is not always made clear yet in the case of rock. Griffith(1921) and, Erdogan. F. and Sih G. C.(1971) postulated that the a crack would open up in the plane normal to the direction of maximum tangential stress, and the direction of Maximum decreasing rate of total potential energy (Anderson, C.P. 1971). Recently, Sih(1973) has proposed strain energy density theory. By the way, rock masses has complicated mechanical properties, that is, the strength is different for tension, compresion and these combined stress. Fracture behavior in such a materials have not been studied perfectly in the past.

Then a new fracture criterion is proposed for these materials in this paper. The fracture factor F defined in this paper based on the theoretical considerations can explain well the experimental results carried out under compression loading with using PMMA and plaster speciments. These materials were used as an imitation model of rock and weak rock.


As an underground excavation subjected to deadweight of rock masses, it is necessary to make clear the crack initiation and Propagation behavior around the excavation under compression load. Then, in order to obtain fundamental informations, crack extension from an inclined crack is studied at first.

The crack propagation under compressive Load

At first, as shown in Fig.l the stress state near a crack in an infinite plate subjected to an uniaxial compression is considered.

(Figure in full paper)

In Fig. 1, β is the crack angle and p is a compression stress applied. The stress components p, and p„ in the Y and X direction are written as p, = p cos2 β, p„ = p sins β.cos β (1) Stress component p, act normal to a crack to close it. Therefore, p, is not effective to propagate the crack and p„ is a shearing stress. For β = 90° or β =0°, p„=0, then the crack doesn't propagate. On the other hand, for β=45°, p,, takes the maximum value. Hence stress field near a crack tip is expressed as where a is a half length of the crack. As the first term has a singularity depend. on r-1/2 for r→0, we can neglect the effect of the second term for a smaller r (tensile stress can not be neglected). Then the effective stress to grouth a crack at the crack tip can be expressed by MODE II term only approximately.

The stresses near a crack tip and a slit were analyzed in the case of MODE II by FEM (A.T. Yokobori…1980). In this paper, the principal stresses are calculated in the similar way. For MODE II load, the stress field near a crack tip can be expressed as

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