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This study aims to make a unique contribution to the existing body of knowledge about rock strength and deformation parameters and crack stress thresholds through intelligent and statistical approaches applied to a database comprising various rock types (i.e., sedimentary, igneous, and metamorphic rocks). The database contains physical–mechanical and ultrasonic parameters. Six distinct machine learning (ML) algorithms— artificial neural network (ANN), random forest (RF), decision tree (DT), K-nearest neighbor (KNN), support vector regression (SVR), and bagging regressor (BR)— along with the conventional linear regression techniques, were employed to develop predictive models. These models estimate uniaxial compressive strength ( σ c ) and Tangent Young's modulus ( E t ) based on bulk density (ρ ) and P-wave ultrasonic velocity ( V p ). Furthermore, they predict crack stress thresholds (i.e., crack closure stress σ cc , crack initiation stress σ ci , and crack damage stress σ cd ) as a function of σ c , E t , ρ , V p , axial strain at failure ( ε 1 f ), and lateral strain at failure ( ε 3 f ). Various performance indices were utilized to evaluate and compare the performance of these models. The results indicated that the RF method outperformed other ML-based and linear regression-based approaches in predicting the output parameters. Additionally, the multiple parametric sensitivity analysis (MPSA) was carried out to determine the significance of input parameters in predicting the output variables. This analysis revealed that V p and ρ have the highest and lowest impact on predicting σ c and E t , respectively. On the other hand, σ c was identified as the most influential parameter in predicting σ ci and σ cd , while parameters ε 3 f and V p showed the least impact on the foregoing outputs, respectively. This is while ε 1 f and ρ were, respectively, found as the most important and least important factors in predicting σ cc . Finally, to facilitate easy access to the prediction results and enhance the practicality of the proposed RF model, a graphical user interface (GUI) was developed, which enables the practical application of the most performing developed prediction model. Highlights: A comprehensive database including different rock types was prepared to evaluate the rock strength parameters and crack stress thresholds. The used six robust machine learning algorithms effectively unveiled the latent complex nonlinear relationship between the parameters. The random forest algorithm outperformed the traditional regression and machine learning algorithms in predicting the output variables. P-wave velocity, uniaxial compressive strength, and axial strain at the failure point were identified as the most influential parameters in predicting outputs. The developed user-friendly graphical user interface brings the power of the random forest model to practitioners without the need for complex analyses and destructive laboratory tests. [ABSTRACT FROM AUTHOR]

Rock fatigue behaviour, including the fatigue threshold stress (FTS), post-peak instability and strength weakening/hardening during cyclic loading, is of paramount significance in terms of safety and stability assessment of underground openings. In this study, the evolution of the foregoing parameters for Gosford sandstone subjected to systematic cyclic loading, in the pre-peak and the post-peak regimes at different stress levels and under seven confinement levels ( σ 3 / UCS avg ) was evaluated comprehensively. The results showed that the FTS of rocks decreases exponentially from 97 to 80%, when σ 3 / UCS avg increases from 10 to 100%. The brittleness of rocks under monotonic and cyclic loading conditions increases with an increase in σ 3 / UCS avg when σ 3 / UCS avg ranging between 10 and 65% (known as the transition point). For higher confinements, however, the brittleness of rock transits from self-sustaining behaviour into ductile behaviour. The evolution of fatigue damage parameters for hardening tests showed that no critical damage happens within the specimens during cyclic loading; rather, they experience more compaction. This is while for weakening cyclic loading tests, continuous damage along with stiffness degradation was dominant. Furthermore, the variation of axial strain at failure point ( ε af ) shows that for lower confinement levels, the applied stress level does not affect the pre-peak irreversible deformation; its effect, however, becomes significant when confining pressure is high. For the specimens that did not fail in cycles, cyclic loading resulted in peak strength weakening or hardening depending on the applied stress level. The weakening effect was observed in higher confining pressures, which was mainly due to a higher amount of irreversible deformation accumulation in rocks in the pre-peak cyclic loading. An empirical model was proposed using classification and regression tree (CART) algorithm to estimate the peak strength variation of Gosford sandstone based on σ 3 / UCS avg and the applied stress level. Highlights: The effect of confining pressure and systematic cyclic loading history on the failure behaviour of rocks was investigated comprehensively. The lateral strain-controlled loading method and a modified triaxial testing procedure were used to measure rocks' failure behaviour. The evolution of fatigue threshold stress, rock brittleness, and peak strength with confining pressure and applied stress level was assessed. An empirical model was proposed to predict the peak strength variation using the classification and regression tree (CART) technique. [ABSTRACT FROM AUTHOR]

The post-peak behaviour of rocks subjected to cyclic loading is very significant to appraise the long-term stability of underground excavations. However, an appropriate testing methodology is required to control the damage induced by the cyclic loading during the failure process. In this study, the post-failure behaviour of Gosford sandstone subjected to the systematic cyclic loading at different stress levels was investigated using the double-criteria damage-controlled testing methodology, and the complete stress–strain relations were captured successfully. The results showed that there exists a fatigue threshold stress in the range of 86–87.5% of the average monotonic strength in which when the cyclic loading stress is below this threshold, no failure occurred for a large number of cycles and in turn, the peak strength improved up to 8%. Also, the variation of the energy dissipation ratio, rock stiffness and acoustic emission hits for hardening tests showed that cyclic loading in the pre-peak regime creates no critical damage in the specimen, and a quasi-elastic behaviour dominates the damage evolution. The post-failure instability of such tests was similar to those obtained for monotonic tests. On the other hand, by exceeding the fatigue threshold stress, the brittleness of the specimens increased with an increase in the applied stress level, and class II behaviour prevailed over total post-peak behaviour. A loose-dense-loose behaviour with different extents was also observed in the post-peak regime of all fatigue cyclic loading tests. This was manifested then as a secondary inverted S-shaped damage behaviour by the variation of the cumulative irreversible axial and cumulative irreversible lateral strains with the post-peak cycle number. Furthermore, it was confirmed that the damage per cycle in the post-peak regime decreases exponentially with an increase in the applied stress level. [ABSTRACT FROM AUTHOR]