Abstract: In view of the size effect in the process of rock tensile strength testing, we designed three groups of grey sandstone split tests with different diameters (50 mm, 75 mm and 100 mm) and a group of three-point bending tests. Based on the theory of cumulative failure probability of generalized weakest chain, we investigated into the mutual conversion of the measured tensile strength of grey sandstone splitting tensile strength under geometrically similar and non-geometrically similar conditions. Results show that: 1) When the diameter of disc sample increased from 50 mm to 100 mm, the corresponding average value of split tensile strength gradually decreased in a steep first and then gentle trend. The average tensile strength measured by the three-point bending method is about 1.18-1.4 times of the average split tensile strength. 2) The statistical model of grey sandstone established by the size-effect statistical method can obtain the splitting tensile strength of grey sandstone of different sizes under the premise of a given failure probability. Furthermore, we calculated the equivalent strength coefficient under split loading mode by the approximate integration method, and obtained the calculation formula of equivalent strength coefficient. In association with the calculation method of equivalent strength coefficient under the three-point bending loading mode, the conversion of tensile strength measured by Brazilian splitting and three-point bending loading is realized.

Key words: :grey sandstone, tensile strength, size effect, loading mode, Brazilian splitting, three-point bending, statistical model