Tensile failure criterion for transversely isotropic rocks

A common problem encountered in rock engineering involves the specification of strength anisotropy in transversely isotropic rocks such as slate and schist. The strength anisotropy under compression has been relatively well established, whereas the formulation of the tensile strength anisotropy has received less attention due to the difficulty of experimental validation. In this paper, a recently developed 3-D tensile failure function for transversely isotropic rocks is further examined. The failure condition incorporates three strength parameters and employs a 2nd order tensor, whose principal directions are those of material fabric, to describe the spatial variation of the tensile strength. It is shown that both the single plane of weakness theory of tensile failure and Nova and Zaninetti's failure condition are two special cases of the 3-D criterion in the context of the spatial distribution of the tensile strength. A procedure for the identification of the strength parameters is outlined. The direct tensile tests on the transversely isotropic samples with various orientations are simulated by invoking the critical plane approach with the 3-D tensile failure function. The loading conditions considered in the simulation include uniaxial tension, triaxial tension, triaxial extension and true triaxial extension. The ultimate value of the axial tensile stress at failure and the associated orientation of the failure plane are discussed.