A rational function is proposed as a failure criterion for isotropic, dry and intact rocks to be used in both tensile and compressive regions. The criterion is capable of predicting the triaxial behavior of rock under low confinements satisfying the exact values of uniaxial tensile and compressive strengths. The capability of the rational criterion is assessed by applying brittle-ductile transition and downward concavity boundary conditions into the criterion introducing λ and γ parameters. The sensitivity of the criterion response is analyzed by varying under variation of λ and γ parameters. It has been shown that the Hoek's rule of thumb for brittleductile transition could be used for all types of rocks in low confinements and the proper boundary between low and high confinements is obtained. It was also experimental that the acceptable envelope could be obtained for low confinements using a dataset including only two triaxial tests together with uniaxial tensile and compressive strengths. Also, the parameters and concavity of the crite
Empirical rock failure criteria are expressed as an equation in terms of some parameters. The parameters of a failure criterion are dependent on rock type and its engineering properties . The parameters are predicted by applying laboratory tests and the criterion should satisfy the certain boundary conditions such as tensile strength, uniaxial compressive strength, concavity requirement and brittle-ductile transition (BDT) properly predicting failure conditions . Jaeger and Cook  indicated that a different type of behavior is shown by some rocks in high confinements, notably carbonates and some sediments, which was first studied in detail in the work of von Karman  on Carrara marble. For this type of rock, in confining pressures of up to about 50 MPa, brittle fracture was occurred with an increase of strength and a small increase in permanent set, but the behavior of rock for σ3 = 68.5 MPa was completely different, since the material could undergo strains of over 7 percent with no loss of strength. This is generally known as ductile behavior. The conclusion is that there is a rather ill-defined value of the confining pressure at which there is a transition from typical brittle behavior to fully ductile behavior. This is called the BDT. At higher confining pressures, 165 and 326 MPa, σ1 increases steadily with increasing strain after the yield point has been passed (work-hardening). Similar and more detailed results have been obtained by Heard  for Solenhofen limestone. It is well recognized that the behavior of most rocks changes from brittle to ductile at some elevated confining pressure, defined by Byerlee  as the BDT pressure. Not only does the shape of the stress-strain curve change at this pressure, but the mechanism of deformation also changes in the transition zone . Therefore, it cannot be expected that a strength criterion developed for application in the brittle range, should be equally applicable in the ductile range . Hence, some researchers tried to obtain the transition between brittle into ductile regions.