Non-local failure theory and two-parameter tensile strength model for semi-circular bending tests of granitic rocks

Several indirect tension tests have been proposed and widely used to quantify rock tensile strength due to difficulties associated with experimentation in direct tension tests. However, discrepancies exist between rock tensile strengths obtained from the direct tension tests and those from indirect tension tests. The non-local theory has been used to reconcile such differences. However, the physical meaning of the characteristic material length δ in the non-local theory is still unclear. We investigate the physical meaning of the characteristic length δ by testing three typical granitic rocks featuring different grain sizes. An indirect tension method - semi-circular bending (SCB) test is applied to obtain the flexural tensile strength for these rocks. The specimens are perfectly split into two quadrants by a main crack through the center of the specimen. The flexural tensile strengths of three rocks generally decrease with the span distance. From flexural tensile strengths under different testing conditions, the optimized values of the characteristic material length δ and the rock intrinsic tensile strength are determined for these three rocks. It is found the tensile strengths of three rocks predicted by the non-local theory match well with those obtained from independent experiments using the Brazilian disc method. The non-local failure theory is used to explain the observation that the flexural tensile strength of three rocks decreases with the span distance. Moreover, the material characteristic length δ correlates well with the rock grain size, and the physical meaning of material characteristic length can be considered as the scaled average grain size of rocks. Based on the successful application of the non-local theory, a two-parameter tensile strength model for rocks is proposed.