A great number of failure criteria have been proposed over the last 30 years or so to characterize the ultimate strength of intact rock specimens submitted to laboratory tests. After reviewing some features of rock failure for tensile and compressive stress states, the authors propose a multiaxial failure criterion that makes use of the Mises-Schleicher paraboloid surface and of the Nadai-Drucker-Prager conical surface. The proposed formulation differs from most existing ones in the way it describes ultimate strength of rock at low and relatively high mean stresses. The adequacy of the proposed MSDP criterion is demonstrated by using results on various types of rock taken from the literature. Finally, some features of the criterion are discussed.


In the early stages of the investigation on the strength of rocks, failure criteria have been introduced to characterize the limiting loading conditions that the material can sustain. Because such a limiting state has become so important in the usual design methods for engineering rock mechanics, a great deal of effort, both from the theoretical and experimental point of view, has been devoted to studying the behavior of rock material loaded to failure. It should be mentioned, however, that although the vast majority of failure criteria for rocks have been expressed in terms of stress state, some others have been written as a function of cumulated strain (e.g., Li, 1990; Sakurai et al., 1993), or a combination of stress and strain (e.g., Gates, 1988). Also, in many existing criteria, the effect of the intermediate principal stress s2 is neglected so that only s1 and s3 are included in the formulation. This is the case for many popular expressions including the frictional Coulomb-Navier criterion (e.g., Vutukuri et al., 1974) or its more recent versions (e.g., Kwasniewski, 1987), as well as the well-known empirical criteria of Bieniawski (1974), Hoek and Brown (1980), and Johnston (1985). Many other failure criteria have been developed in recent years. The reader is referred to state-of-the-art presentations for more details (e.g., Jaeger and Cook, 1979; Franklin and Dusseault, 1989; Lade, 1993; Andreev, 1995). In this paper, the authors present a multiaxial failure criterion expressed through a combination of two quadric functions. At low mean stress, the MSDP criterion is reduced to the Mises-Schleicher paraboloid surface, while at higher mean stress it becomes a conical surface similar to the Drucker and Prager (1952) criterion.


A rock specimen submitted to external forces will deform and eventually fail due to several different mechanisms. At low deviatoric stress, most rocks show an elastic response followed by, at higher stress, an inelastic behavior characterized by irreversible strains upon unloading. Numerous factors may affect the failure strength of a rock specimen in the laboratory, including its size and shape, loading rate, environmental conditions (humidity, temperature, etc.), orientation of the stresses, porosity, density and homogeneity of the material (e.g., Vutukuri et al., 1974; Franklin and Dusseault, 1989; Fuenkajorn and Daemen, 1992; Lade, 1993).

This content is only available via PDF.
You can access this article if you purchase or spend a download.