Mode I fractures with distributed bridges. Scaling and monitoring

Traces of Mode I fractures in rocks (cracks in rock samples, hydraulic fractures, magmatic dikes, Mis-Ocean Ridges) are usually not straight; they exhibit interruptions and overlappings [1]. These are 2D features belonging to a particular cross-sectional view. In 3D interruptions and overlappings represent local bridges connecting the opposite sides of the fracture and distributed all over it. These bridges constrict the fracture opening and reduce the values of the stress intensity factor. The dimensions, the number and the geometry of the bridges depend upon the rock structure (at the scale microscopic with respect to the fracture length). Therefore, understanding the effect of bridges on the stress intensity factor can shed light on the rock microstructure. The combined effect of uniformly distributed bridges is accounted for by the introduction of constriction length [1]. As a result, under the given stress the stress intensity factor depends on both the fracture length and the ratio of fracture length to the constriction length.

Fracture propagation is controlled by fracture toughness, which is usually determined by measuring/estimating the fracture length, and the load at which fracture propagates. For this the conventional models neglecting the effect of bridges are employed. This shows a scale effect, the increase of fracture toughness with fracture length [2-5]. We used the model of constricted fracture propagation and found that for each scale there exists a constriction length such that scale effect of fracture toughness disappears and the fracture toughness remains constant.

Determination of constriction length allows more realistic monitoring of fracture growth and provides insight into the rock structure. It will also allow developing a more realistic scaling of fracture growth in strain rock burst and thermal spallation.

Acknowledgement. The authors acknowledge financial support from of the Australian Research Council through project DP250103594.

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