Multiple Time Parameter Superposition Based on Separation of Measure Theory Study on Similar Design Problems

The self-contradiction of time similarity ratios in geomechanical model tests under superimposed multiple time parameters hinders experimental accuracy. This study investigates the root causes of such variability: (1) divergent derivation outcomes from distinct control parameters, (2) empirical formulas exhibiting dimensional nonhomogeneity, and (3) the superiority of a unit time similarity ratio in liquefaction and creep modeling. A novel similarity ratio calculation scheme is proposed by integrating the separation of magnitudes theory and aberration-compensated design theory. The centrifugal shaking table model test for earthquake–rainfall coupling is employed to demonstrate the method. By decomposing the system into subsystems (soil, seismic, and rainfall) and applying distortion compensation, conflicting time scales (e.g., seismic duration versus rainfall duration) are unified. Results show that the corrected similarity ratio resolves parameter contradictions while maintaining prototype consistency. This work establishes a theoretical framework for selecting time similarity ratios in multi-parameter geomechanical tests, addressing a critical gap in existing methodologies. Innovations include the systematic application of magnitude separation and distortion compensation to overlapping time scales, validated through a complex coupling scenario.