Prediction of rock failure mechanism in 3D high stress field using empirical and linear regression methods

In this paper, the effect of the intermediate principal stress on the failure of different rocks and the accuracy of several 3D criteria in estimating failure of the true tri-axial tests results was investigated. Then, applying linear and nonlinear regression, a new 3D criterion was proposed that the criterion can successfully predict failure behavior of deep rocks with accuracy higher than other existing criteria.Failure criteria are relations between the strength properties of rock and applied stresses and used to describe the behavior and failure of rocks. This function is determined based on analytical and empirical methods. Some researchers neglect the effect of intermediate principal stress σ2 in the failure mechanism of rocks (2D failure criteria). However, there are experimental documents showing that the intermediate principal stress affects the failure behavior for at least some of the rocks (3D failure criteria. The intermediate principal stress has considerable effect on failure mechanism of very deep underground rock masses (such as hydraulic fracturing, wellbore and reservoir stability, underground storage in petroleum engineering). In this paper, the effect of the intermediate principal stress on the failure of five different rock types in 175 true tri-axial tests was studied. Also, the accuracy of several 3D criteria (such as Von Mises, Drucker-Prager and Pan & Hudson) in estimating failure of the tests results was investigated. Applying nonlinear regression, a new 3D criterion was proposed based on the true tri-axial tests results. Maximum, minimum, and intermediate principal stresses, along with uniaxial compressive strength and internal friction angle are used in the new criterion. In order to validation of the proposed criteria for other rocks, results of the true tri-axial tests for 190 specimens of seven different rock types were studied.The results of studies showed that the effect of intermediate principal stress is more significant in competent rocks than weak rocks and Pan & Hudson criterion gives the most accuracy with an MRAE equal to 0.24. Von Mises and Drucker-Prager criteria gave the next best results by MRAE respectively equal to 0.28 and 0.44. Also, RSQ and MRAE of the proposed criterion for all type of rocks are equal to 0.94 and 0.06 respectively that the criterion can successfully predict failure behavior of deep rocks with accuracy higher than other existing criteria.