Filled joints significantly influence the dynamic response of rock masses, exhibiting coupled nonlinear compression-hardening and viscous deformation. However, the combined effects of these mechanisms on wave propagation remain unclear. This study develops a theoretical model based on a nonlinear viscoelastic formulation, in which a compression-hardening spring (governed by the Bandis–Barton model, with its initial compressive stiffness and maximum allowable closure) is connected in series with a viscous dashpot. Using the displacement discontinuity method and the method of characteristics, we analyze the transmission of compressive stress waves across a filled joint. The results show that the transmission coefficient increases with incident wave amplitude but decreases with frequency, whereas reflection exhibits the opposite trends. The initial compressive stiffness has a minimal impact on transmission but induces a nonlinear decrease in reflection. Increasing the maximum allowable closure slightly reduces transmission but sharply increases reflection, whereas higher viscous stiffness enhances transmission and slightly suppresses reflection. Energy attenuation grows rapidly with amplitude before stabilizing. The initial compressive stiffness is most influential at low amplitudes, the maximum allowable closure is most significant at moderate amplitudes, and viscous effects remain consistent across all amplitudes. Increases in frequency lead to a nonlinear decrease in attenuation, with the initial compressive stiffness and maximum allowable closure dominating at high frequencies, and viscous effects prevailing at low frequencies. This work systematically reveals the coupled roles of nonlinear compression-hardening and viscosity in wave propagation across filled joints, providing theoretical support for dynamic hazard mitigation and geophysical exploration.

To address the challenge of quantitatively coupling fire smoke evolution and occupant evacuation in the underground powerhouses of large-scale pumped-storage power stations, full-scale three-dimensional numerical models were developed using PyroSim for fire dynamics and Pathfinder for egress behavior. A multi-factor coupled ASET–RSET safety margin matrix was constructed, integrating fire heat release rate (HRR), sprinkler intervention, egress passage blockage, and occupant load. The results show that visibility continuously dropping below 10 m at a characteristic hazardous height of 4.5 m serves as the governing criterion determining the available safe egress time (ASET). Under a 10 MW fire without sprinklers, the ASET is 343.0 s, whereas activating the sprinkler system effectively suppresses smoke and reduces temperatures, extending the ASET to 380.9 s. With both exits unobstructed, the required safe egress time (RSET) for the baseline 130 occupants is 303 s and increases marginally to only 304 s as the crowd scales to 250 occupants, thereby maintaining a positive safety margin under all scenarios. Conversely, the blockage of a single-sided passage induces a pronounced bottleneck shift. Specifically, blockage of the main access tunnel exhibits acute sensitivity to crowd enlargement: the RSET surges to 441.8 s for 250 occupants, resulting in a severe safety margin deficit that cannot be fully rectified even with sprinkler intervention. Accordingly, two distinct risk boundaries—management-sensitive and structure-constrained regimes—are identified. An optimal egress routing scheme characterized by “hierarchical zoning, lateral priority, and nearest-ascending egress” is proposed, accompanied by a two-dimensional cooperative prevention and control strategy: “source control to delay ASET and capacity expansion to reduce RSET.” This work provides quantitative support for performance-based fire safety design and emergency management in deep-buried underground powerhouses.