Estimating rock strength parameters across varied failure criteria: Application of spreadsheet and R-based orthogonal regression to triaxial test data

Triaxial tests, a staple in rock engineering, are labor-intensive, sample-demanding, and costly, making their optimization highly advantageous. These tests are essential for characterizing rock strength, and by adopting a failure criterion, they allow for the derivation of criterion parameters through regression, facilitating their integration into modeling programs. In this study, we introduce the application of an underutilized statistical technique—orthogonal regression— well-suited for analyzing triaxial test data. Additionally, we present an innovation in this technique by minimizing the Euclidean distance while incorporating orthogonality between vectors as a constraint, for the case of orthogonal linear regression. Also, we consider the Modified Least Squares method. We exemplify this approach by developing the necessary equations to apply the Mohr-Coulomb, Murrell, Hoek-Brown, and Úcar criteria, and implement these equations in both spreadsheet calculations and R scripts. Finally, we demonstrate the technique's application using five datasets of varied lithologies from specialized literature, showcasing its versatility and effectiveness.