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• 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]