An analytical solution of direction evolution of crack growth during progressive failure in brittle rocks

Abstract Microcrack growth during progressive compressive failure in brittle rocks strongly influences the safety of deep underground engineering. The external shear stress τ xy on brittle rocks greatly affects microcrack growth and progressive failure. However, the theoretical mechanism of the growth direction evolution of the newly generated wing crack during progressive failure has rarely been studied. A novel analytical method is proposed to evaluate the shear stress effect on the progressive compressive failure and microcrack growth direction in brittle rocks. This model consists of the wing crack growth model under the principal compressive stresses, the direction correlation of the general stress, the principal stress and the initial microcrack inclination, and the relationship between the wing crack length and strain. The shear stress effect on the relationship between y ‐direction stress and wing crack growth and the relationship between y ‐direction stress and y ‐direction strain are analyzed. The shear stress effect on the wing crack growth direction during the progressive compressive failure is determined. The initial crack angle effect on the y ‐direction peak stress and the wing crack growth direction during the progressive compressive failure considering shear stress is also discussed. A crucial conclusion is that the direction of wing crack growth has a U‐shaped variation with the growth of the wing crack. The rationality of the analytical results is verified by an experiment and from numerical results. The study results provide theoretical support for the evaluation of the safety and stability of surrounding rocks in deep underground engineering.