Chronological and Mathematical Development of True Triaxial Failure Criteria of Brittle Rocks

Earlier researchers such as von Kármán, Mohr, Coulomb and Griffith did not contemplate the strengthening of materials due to intermediate principal stress σ2. Böker and Handin et al. showed the strengthening effect of σ2 in marble, and in limestone, dolomite and glass, respectively. Murrell extended the Griffith’s criteria to its three-dimensional form residing in octahedral plane, and even included the uniaxial tensile strength of material. Afterwards, Nadai, Drucker and Prager, Bresler and Pister, and Wiebols and Cook and more included all the principal stresses in their respective criteria. In 1971, Mogi put the dubiety to rest by testing dolomite and trachyte in a high capacity true triaxial testing machine. Then, many researchers such as Lade and Duncan, Michelis, Takahashi and Koide, Smart, Haimson and Chang, Alexeev et al., Tiwari and Rao, He et al. and several others developed their own true triaxial testing machines and conducted their own experiments. This paper discusses this chronological and mathematical development of brittle failure criteria which describes the true stress state existing at the depths. Simultaneously comparative assessment is made to segregate the conditional nature of the failure criteria. These developments are pertinent to know how the underground brittle failure such as strainburst is perceived today.