Calculation method of wheel-rail interaction forces for subway integrated ballast bed during station entry and exit focusing on frequency range of interest in environmental vibration

To accurately predict and control environmental vibrations induced by the subway during station entry and exit, in this paper, an efficient method suitable for the acceleration and deceleration processes of subway station entry and exit for calculating wheel-rail interaction forces throughout the entire process was developed. Based on the moving time-domain Green's function method, a calculation model for wheel-rail interaction forces under the working condition of subway running at a constant speed was established. The calculation results were compared and verified with those from the frequency-domain wheel-rail force calculation method. By considering the influence of track parameter excitation, equivalent roughness samples of parameter excitation were established. Through the solution methods of moving roughness and Green's function, the time history of wheel-rail forces under variable speed operation conditions was obtained, and the spectral characteristics were analyzed. Research results show that within the frequency range of 3 - 600 Hz, the wheel-rail force spectra obtained by the two methods are basically consistent; the fluctuation range of dynamic wheel-rail forces is approximately 50 - 90 kN; the fluctuation amplitude reaches 20 kN compared with the axle load. Parameter excitation generates significant peaks at sleeper-passing frequencies (27.8, 55.6 Hz, etc.), and the equivalent roughness curve exhibits a mid-span cosine distribution. The proposed method can quickly and efficiently solve the non-stationary medium-high frequency wheel-rail interaction forces throughout the entire process of subway station entry and exit within the frequency range of primary interest for environmental vibration. In terms of computational performance, the traditional challenges of constructing excessively long track models and solving wheel-rail forces with large-scale degree-of-freedom matrices are efficiently avoided. Regarding model accuracy, the method incorporates the parameter excitation characteristics induced by the track and the nonlinear wheel-rail contact, making the model more aligned with actual engineering conditions. This approach provides reliable input for accurately predicting the environmental vibrations caused by subways entering and exiting the stations, offering references for vibration reduction design and environmental assessment in integrated construction projects.