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On Rock Failure Under True Triaxial Conditions

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**John Rudnicki**

Northwestern University

United States

*Abstract:*

The role of the intermediate principal stress in rock failure has been a subject of continuing debate since the pioneering work of Mogi with true triaxial tests in which all three principal stresses are different. In recent years an increase in data from such tests, some at constant Lode angle and/or constant mean stress, has provided additional fodder for discussion. The variety of failure conditions that have been proposed are phrased mostly in terms of the principal stresses themselves or their principal invariants. There are, however, advantages of simplicity and transparency for formulations in terms of the mean normal stress, the Mises equivalent stress (2nd invariant of the deviatoric stress), and a Lode angle defined here so that it is zero for a stress state of deviatoric pure shear . Such a form has obvious advantages for tests in which the mean stress and/or Lode angle are constant but also can provide insight into conventional tests in which the intermediate and least principal stresses, , are fixed while is increased to failure. An example is the following, a generalized form of the Matsuoka – Nakai/Lade – Duncan condition, employed previously by Haimson and Rudnicki for the prediction of fault angle:

where . is determined by the mean stress dependence in deviatoric pure shear ( ). controls the shape of the failure surface in deviatoric planes: For the shape is circular, as for a Drucker-Prager material; for , the shape is triangular, as for a Rankine material. Dependence of on allows changes of shape of the failure surface with mean stress. A constant value of can be chosen so that the predictions describe typical results of conventional true triaxial tests: the observed failure stress ( ) for fixed values of the least compressive stress ( ) increases and then decreases as the intermediate principal stress ( ) increases from to .