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Abstract

A new theory of spacing of extension fracture in flattened, or compressed layered rocks, provides a basis for predicting some fracture patterns, and the theory is confirmed by model studies.

Fracture spacing may be controlled by elastic stress concentrations. In compressed layered rocks the initial uniform stress field may become unstable and periodic stress concentrations may develop. This instability is caused by differences in mechanical properties of the layered sequence, causing incremental interfacial stresses as deformation continues. A critical stress is required to initiate the instability. If critical stress exceeds the rock strength, then fracture occurs according to older theory, but loads of equal magnitude can cause elastic instability in bodies of other shapes.

By using strain energy methods a quantitative theory is developed. Work done in lengthening a stiff layer is computed and equated to the elastic strain energy of deformation. This energy is computed for the change in shape associated with the necking of the stiff layer and is then combined with the deformation energy computed for the loading on the restraining medium. When external work and strain energy (as computed above) are equal, the necked shape is favored over the straight form, which is the earliest stable shape in the deformation.

Various combinations of interfacial forces are used to obtain a measure of the effect of friction and welding at layer interfaces. Fracture spacing computed for these cases agrees well with experimental values. This theory may be applied in devising patterns of rock bolting, and perhaps in setting charges in advancing rock faces in rapid excavations.

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