The pendulum-type wave phenomenon is a unique mechanical phenomenon in deep rock mass. It propagates at low frequencies and low speeds in the rock mass, and can cause deep rock engineering disasters such as rockbursts. For determining the low-frequency characteristics of a pendulum-type wave, the frequency response of the pendulum-type wave in block-rock mass with bimodulus characteristics is studied under a half-sine impact load. The dynamic pendulum-type wave model in a block–rock mass is used to determine the low frequency characteristics of the wave. The improved central difference method is applied, and the influence of the modulus ratio on frequency response is analyzed. Furthermore, the natural frequency of the system is inverted, through the frequency response of the block, and its correctness is verified. The results show that a decrease in the modulus ratio causes an obvious increase in the number of frequency response peaks of the block. The amplitude of the frequency response peaks decreases and the position of peaks moves to a low frequency range. The low-frequency characteristics of the pendulum-type wave in the block–rock mass with bimodulus characteristics are more obvious. The natural frequency of the system can be inverted by the fact that it corresponds to the peak frequencies of the frequency response. This approach provides a new method for the determination and measurement of the natural frequency of nonlinear systems.

Natural rock materials, containing micro-cracks and pore defects, significantly alter their mechanical behavior. This study investigated fracture interactions of red sandstone containing double close-round holes (diameter: 10 mm; bridge angle: 30°, 45°, 60°, 90°) using acoustic emission (AE) monitoring and the discrete element simulations method (DEM), which was a novel methodology for revealing dynamic failure mechanisms. The uniaxial compression tests showed that hole geometry critically controlled failure modes: specimens with 0° bridge exhibited elastic–brittle failure with intense AE energy releases and large fractures, while 45° arrangements displayed elastic–plastic behaviors with stable AE signal responses until collapse. The quantitative AE analysis revealed that the fracture-type coefficient k had a distinct temporal clustering characteristic, demonstrating the spatiotemporal synchronization of tensile and shear crack initiation and propagation. Furthermore, numerical simulations identified a critical stress redistribution phenomenon, that axial compressive force chains concentrated along the loading axis, forming continuous longitudinal compression zones, while radial tensile dispersion dominated hole peripheries. Crucially, specimens with 45° and 90° bridges induced prominently symmetric tensile fractures (85° to horizontal direction) and shear-dominated failure near junctions. These findings can advance damage prediction in discontinuous geological media and offer direct insights for optimizing excavation sequences and support design in cavern engineering.