An Expanded Wing Crack Model for Fracture and Mechanical Behavior of Sandstone Under Triaxial Compression

A new model is developed to predict the mechanical behavior of brittle sandstone under triaxial compression. The proposed model aims to determine the normalized critical crack length (<i>L</i>_{<i>c</i><i>r</i>}), through which the failure strength (<i>σ</i>_<i>f</i>) of sandstone can be estimated based on fracture mechanics applied to secondary cracks emanating from pre-existing flaws, while considering the interaction of neighboring cracks. In this study, the wing crack model developed by Ashby and Hallam (1986) was adopted to account for the total stress intensity at the crack tip (<i>K</i>_<i>I</i>) as the summation of the stress intensity due to crack initiation and crack interaction. The proposed model is developed by first deriving the <i>L</i>_{<i>c</i><i>r</i>} and then setting the crack length equal to the <i>L</i>_{<i>c</i><i>r</i>}. Next, the total stress intensity is set equal to the rock fracture toughness in the original equation of <i>K</i>_<i>I</i>, resulting in an estimate of the <i>σ</i>_<i>f</i>. Finally, to evaluate the performance of the proposed model on predicting <i>σ</i>_<i>f</i>, theoretical results are compared with laboratory data obtained on sandstone formations collected from Wyoming and the published literature. Moreover, the <i>σ</i>_<i>f</i> predicted by our proposed model is compared with those predicted from other failure criteria from the literature. The comparison shows that the proposed model better predicts the rock failure strength under triaxial compression, based on the lowest RMSE and MAD values of 36.95 and 30.93, respectively.