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The cracked chevron notched semi-circular bend (CCNSCB) method has been utilized in split Hopkinson pressure bar (SHPB) tests to measure the rock dynamic mode I fracture toughness. However, the measuring principle has never been thoroughly evaluated. In this study, a three-dimensional discrete element method has been employed to numerically investigate the dynamic fracture mechanism of CCNSCB specimens in SHPB testing considering different loading rates and supporting spans. Our results show that, even if the dynamic force balance can be efficiently satisfied, the conventional quasi-static analysis can still be questionable. For specimens with smaller supporting spans, the developing crack fronts are rather curved during the loading process, and the critical crack length is highly dependent on the loading rates. While for specimens with a large supporting span, the crack profiles are less affected and the critical crack fronts are finely confined within the chevron ligament with few undesirable damages. Thus, the CCNSCB method with a larger supporting span appear to be sound in the SHPB tests for measuring dynamic mode I fracture toughness of rocks. [ABSTRACT FROM AUTHOR]

• An oblique impact method using inclined cylinder specimens is employed in a split Hopkinson pressure bar (SHPB) apparatus modified with an axial pressure chamber to achieve the compression-shear loading in a combined static-dynamic mode. • Numerical simulations using both the finite element method and the discrete element method are conducted to assess the validity of this compression-shear specimen and to establish a new data processing method. • Experimental results highlight the combined effects of the loading rate and the axial confinement on the failure strength, fracturing mode and deformation characteristics of sandstone. The compression-shear behavior and failure mechanism of rocks under combined static-dynamic loading are of essential importance for mechanical characterization and construction safety in deep underground engineering applications. An inclined cylinder specimen is designed using a split Hopkinson pressure bar (SHPB) apparatus modified with an axial pressure chamber for laboratory studies. Specific issues on the validity of this compression-shear specimen that were not addressed previously have been numerically assessed involving the dynamic equilibrium of force and moment, stress uniformity, and interfacial friction effects. Experiments are conducted at different loading rates ranging from 500 to 4000 GPa/s and under axial pressures of 7, 21, 35, 49, and 63 MPa. Experimental results verify the dynamic equilibrium of inclined specimens in the axially constrained SHPB tests using pulse shaping techniques, which validates the data processing method newly proposed. Both the dynamic strength and total strength linearly increase with the loading rate. With the increasing pre-load ratio (ratio of the axial confining load to the unconfined compression strength of the tested material), the dynamic strength decreases, while the total strength increases and then keeps constant, where the turning point of the pre-load ratio approximates 0.7. High-speed photographs at a high loading rate illustrate that the increasing confinement can result in less shear but more tensile cracks. Particularly at a high confining condition, the inclined specimen fails by a feather-like shear fracture band where tensile secondary cracks extensively develop. The equivalent stress-strain relationships indicate the reinforcing effect of the confinement on the deformation and energy dissipation. Image, graphical abstract [ABSTRACT FROM AUTHOR]

• Rate-dependent cracking behaviors of single-flawed rock specimen under dynamic loading are numerically observed via DEM simulation. • Tensile wing cracks dominate specimen failure under low strain rate, while anti-wing cracks and shear cracks are prevalent under high strain rate. • Different initiation locations of tensile wing cracks are explained by stress filed visualization and theoretical analysis. • The initiation angles of tensile wing cracks are predicted via GMTS criteria, and the length of FPZ increases with increasing strain rate. This paper numerically investigated the rate-dependent progressive cracking behaviours of single-flawed rock specimens in split Hopkinson pressure bar (SHPB) tests. First, a 3D numerical SHPB system is established based on the discrete element method (DEM). By comparing with our laboratory experiments, micro-parameters of the DEM model are calibrated, which guarantees the reliability of the numerical simulations results. Via slice-cutting view, the inner and surface progressive cracking processes are explicitly revealed and compared, which compensates some defects in laboratory tests. Our numerical simulation results show that the progressive cracking behaviours of the single-flawed rock specimens exhibit evident rate dependence. Under low strain rates, tensile wing cracks dominate the entire cracking process, and only a few shear cracks appear during the post-peak stage. In contrast, under high strain rates, tensile wing racks are significantly suppressed, while anti-wing cracks and shear cracks are fully developed, leading to the final X-shaped failure modes. In addition, progressive cracking behaviours of the single-flawed rock specimens with different flaw inclination angles are assessed. Via stress field visualization and theoretical analysis, the different initiation locations of tensile wing cracks are explained. Furthermore, based on the generalized maximal tangential stress (GMTS) criteria, the fracture initiation angles of tensile wing cracks are predicted. The results show that the fracture initiation angles and the fracture process zone (FPZ) are significantly affected by the strain rate. The length of FPZ under dynamic loads is evidently longer than that under static loads, and the length of FPZ generally increases with an increasing strain rate, exhibiting evident rate dependence. [ABSTRACT FROM AUTHOR]

• Numerical modeling was performed to study dynamic mixed mode I/II fracture behavior of rocks. • Different mixed mode loading conditions and various loading rates were considered. • Dynamic mixed mode fracture of the specimens was mainly induced by tensile damages at the micro scale. • Mixed mode fracture resistance of rocks showed loading rate dependence. • A semi-analytical criterion could predict well the dynamic mixed mode fracture of rocks. Research on rock fracture behavior is usually limited to static mixed mode I/II fracture and static or dynamic mode I fracture. In this study, the notched semi-circular bend (NSCB) specimens with different notch inclination angles were introduced into the split Hopkinson pressure bar (SHPB) system to numerically investigate dynamic mixed mode I/II fracture behavior of cracked rocks. First, the feasibility and reliability of our discrete-element-method-based numerical system to model dynamic fracture behavior of rock were validated; then, the effects of different mixed mode loading conditions and various loading rates on the mixed mode fracture of NSCB specimens were studied. The dynamic mixed mode fracture of the specimens was found to be mainly induced by tensile damages at the micro scale. The results also showed the loading rate dependence of the mixed mode fracture resistance. Moreover, for the same increment of the loading rate, the dynamic mode I fracture toughness increases more than the dynamic mode II fracture toughness. Subsequently, the fracture resistance and fracture initiation angles observed in the modeling were compared with the theoretical predictions based on some brittle fracture criteria. It was demonstrated that a semi-analytical criterion could reproduce well the dynamic mixed mode fracture behavior of rocks. [ABSTRACT FROM AUTHOR]