The Conundrum of the Crack Initiation Stress of Rock Type Material – I. The Trapezoid Rule Method

In part I of this study, the great practical importance of the onset of stable crack growth was outlined, since several researchers have supported that it can serve as a more realistic estimation of the in-situ spalling strength of the rock mass, in comparison with the more frequently used uniaxial compressive strength. Moreover, a short review was also provided regarding the empirical techniques that have been proposed in the last six decades for the prediction of the crack initiation stress. The main criticism of each method was also mentioned. Subsequently, a new method was proposed, based on the Trapezoid Rule, an elementary calculus approximation technique. The latter technique possesses a strong and robust physical explanation, easy application, and complete objectiveness. The Trapezoid Rule method was applied to ten rock specimens, eight marbles and two vesicular basalts, that were subjected to uniaxial compressive tests. The results of the newly suggested method were compared to those obtained using the established methods of the existing literature. Ultimately, it displayed exceptionally close results with all other methods for the ten specimens, thus indicating that it can accurately and consistently predict the crack initiation stress for the two rock types.