The two chevron notched specimen geometries for rock Mode I fracture toughness measurement, CB and SR, recommended by the ISRM have several disadvantages, such as very low loads required to initiate failure, complicated loading fixtures, difficult to be developed for rock mixed mode fracture testing, relatively large amounts of intact rock core needed for the test and complex specimen preparation for the SR geometry. The cracked chevron notched Brazilian disc (CCNBD) and the cracked straight through Brazilian disc (CSTBD) specimen geometries overcome these problems and they are believed to be ideal geometries for rock fracture investigations. The general case for the cracked Brazilian disc fracture problem is when the specimen is loaded diametrically with the crack inclined at an angle to the loading direction. Different combinations of Mode I and Mode II fracture intensities can be obtained simply by changing this angle and the loading fixture still remains as simple as for a normal Brazilian test. A special superimposition technique is developed to theoretically solve the stress intensity factor (SW) values for the CSTBD fracture problem with the help of dislocation and complex stress function methods. This evaluation can generate accurate SIF results for the problem with any crack length a(a/R) = 0.05-0.95, while the mixed mode SIF solution for a>0.60 has not been reached by previous researchers. The relative theoretical SW solution for the corresponding CCNBD fracture problem (single or mixed fracture modes) is obtained by using Bluhm's slice model proposed for general crack problems. Numerical calibrations for Mode I fracture problems of the CSTBD and the CCNBD specimens have been conducted by using 194 different specimen geometries and the results prove the correctness of the theoretical evaluations. The valid CCNBD geometrical range for a valid rock Mode I fracture toughness test is numerically investigated and then experimentally validated based on 40 different CCNBD geometries by using 42 different rocks. Experimental studies on the minimum specimen size requirement for a valid CCNBD rock Mode I fracture toughness test are also carried out and the approximate critical criteria is given. The great advantages of using the CCNBD specimens for rock fracture toughness measurement have been investigated and the documentation for recommending the CCNBD specimen geometry to the ISRM as the third suggested method for rock Mode I fracture toughness test is presented. The rock Mode I fracture toughness values are then related to rock conventional properties for the purpose of prediction. Rock cutting mechanics is analyzed by probabilistic fracture mechanics and Weibull's distribution model is found to better express the characteristics of rock cutting performance parameters. Some initial predictions for these parameters based on this mode are then presented.