Having carefully researched the B. Paul's strength theory and systematically demonstrated it by experiments through the analysis of the characteristics of the failure strength of rock-like materials under the general triaxial stress states, we put forward the idea of the three parameter's single hexagonal pyramidal failure surface suitable extensively to rock-like materials, which thought the effects of both the intermediate principal stress and the hydrostatic pressure at one time, and formed the correspondent criterion for rock-like materials.
In the underground winning and the open pit mining, such the problems as the steadiness and the fracturing failure of rock-masses under the general triaxial stress will all be met undoubtedly. To ensure the safety of mining, we must research the criterion for failure of rock-masses under the general triaxial stress states and determine under what triaxial stress states rock-masses may be fractured. So a great many of rock mechanics workers over the world have systematically researched the characteristics of the failure strength of rock-like materials under the general triaxial stress states and have put forward a variety of criteria for failure of rock like materials (1–5). By comprehensive analysis of these criteria for failure, we have discovered that these criteria for failure of rock- like materials either neglect the intermediate principal stress or the hydrostatic pressure, or are too complex to use, therefore, it's essential to go further into a criterion for failure of rock-like materials which thinks the effects of both the intermediate principal stress and the hydrostatic pressure at one time and has so simple mathematical expression that it's convenient in use.
In order to research the criterion for failure of rock-like materials, B. Paul (2) has put forward the idea of the three parameter's single hexagonal pyramidal failure surface suitable extensively to rock-like materials which thought the effects of both the intermediate principal stress and the hydrostatic pressure at one time by spreading the well known Tresca Yield Surface in the plasto-elasticity, and has point out that the failure loci on the cross section perpendicular to the hydrostatic axis in the same pyramidal failure surface have different sizes with the distance from the vertex and have all threefold symmetry. Figure 1 gives the general space-formation of the three parameter's single hexagonal pyramidal failure surface in the three-dimension principal stress space, and Figure 2 gives the failure loci on the vertical section through the hydrostatic axis of the failure surface and the failure loci on the cross section perpendicular to the hydrostatic axis of the failure surface.
Limestone and fine-grain sandstone and median-grain sandstone concerned in the experiment were all obtained from the region around Nanton Coal Mine in Chongqing and could be regarded as the macroscopic homogeneous isotropic materials, and its values of physical-mechanical coefficient are listed in Table 2.
By the measured failure strength of specimens under the general triaxial stress states.
