The Effect of Triaxial Stress Systems on the Strength of Rocks at Atmospheric Temperatures

Abstract

Summary The experimental work described in this paper was carried out in order to discover more about the laws governing the effect of the stress system on brittle fracture, with particular reference to rocks. Consideration of the implications of Griffith's theory of brittle fracture when an arbitrary, uniform plane stress system is applied (Murrell 1964a, b) enabled a number of fracture criteria to be postulated for triaxial stress conditions which required experimental investigation. An apparatus has been built which enables cylindrical rock specimens to be subjected to various combinations of principal stress (tension with compression, triaxial compression with the intermediate principal stress equal either to the major or the minor principal stress) with or without a controlled pore pressure, and at the same time enables the axial and diametral strains to be measured. Confining pressures of up to 4kb can be applied, with pore pressures up to 2kb. A new method of measuring the tensile strength of very brittle materials is described. Experiments were carried out on an isotropic sandstone. It is shown that with one principal stress tensile fracture occurs at a critical value of the tensile stress (=K′) within the range of hydrostatic stresses which were studied. When none of the principal stresses is tensile fracture occurs when the shear stress (τ) on the fracture surface reaches a value which depends on the normal stress (σ) according to the law where λ (4K′)½ and n 0.61. Where pore pressures are applied ‘effective stresses’ must be used in the equation (that is, s must be replaced by σ′=σ+p, where p is the pore pressure). The intermediate principal stress has a slight but measurable effect on the fracture criterion. After fracture the load supported by the rock falls to a value which can be supported by friction between the fracture surfaces. It is found that Amonton's law of friction is not obeyed, and instead the shear stress () due to friction and the normal stress () follow a law where μo 2 and n 0.9. Again ‘effective stresses’ must be used in the equation when pore pressures are applied. Pore water lowers slightly the parameters λ and μo by some form of chemical action. When the shear stress required to cause fracture becomes equal to or less than that required to overcome sliding friction, fracture is no longer possible and there is a transition to ductile behaviour. This occurs at a confining pressure of ∼ 17 000 Lb/in2 (1.17 kb) in the case of the sandstone used in the experiments. Interesting fractures occur sometimes, after the confining pressure is removed, in specimens which have been plastically deformed.