Dynamic similarity framework and governing criteria for saturated rock masses under combined static and dynamic loading

In deep underground engineering environments, the strong interaction between pore water and the rock skeleton constitutes the fundamental mechanical mechanism behind dynamic disasters such as rockbursts and water inrush. This study systematically develops a dynamic similarity criterion system applicable to saturated porous media under combined static and dynamic loading. Through rigorous dimensional analysis, four key dimensionless parameters are proposed: Cauchy number (CA), Euler number (EU), Darcy number (DA), and Biot number (BI), each characterizing solid inertia, fluid impact, nonlinear seepage, and coupling diffusivity, respectively. These parameters form a coupled system of similarity equations, revealing the paradox of similarity constraints in physical model design. The framework is further validated by applying it to experimental data, enabling analysis of how geometric scaling and loading intensity influence coupling responses. Specifically, results show that under dynamic loading, the CA value increased by over four orders of magnitude while the EU value dropped by seven orders, signifying a critical shift from a pressure-driven to an inertia-dominated regime. Furthermore, the analysis reveals that both the DA and BI values increase linearly with the geometric similarity ratio, fundamentally altering the hydraulic response and suppressing pore pressure build-up in downscaled models. This work provides critical theoretical guidance and a quantitative basis for improving hazard simulation and experimental model design in deep engineering applications.