Many experimental results have demonstrated the apparent discrepancy of a rock material between its flexural tensile strength measured using various bending methods and its tensile strength measured using direct tension method or Brazil disc (BD) method. To understand the physical mechanism for such discrepancy, numerical simulation using the realistic failure process analysis (RFPA) is carried out in this work to simulate the tensile failure of heterogeneous rocks. Direct tension and semi-circular bend (SCB) tests are simulated using RFPA for rock materials with different levels of inhomogeneity, which is characterized by the homogeneity index of the Weibull distribution used in RFPA. The numerical results show that the discrepancy in the tensile strength values is caused by the inhomogeneity of the rock material. Furthermore, non-local failure criterion is adopted to calculate the characteristic length of the rock materials used in the simulation. It is shown that below a certain value of the homogeneity index, both the characteristic length and discrepancy between two types of tensile strengths of rock decrease with increase of the homogeneity index up to a critical value, at which the discrepancy disappears and the rock material is essentially homogeneous.
