Investigation of three-dimensional dynamic response and work area depth in heavy-haul railway subgrade based on a theoretical model

Extending the Biot porosity theory, a three-dimensional (3D) dynamic theoretical model coupled with a tracksleeper-ballast-unsaturated subgrade was developed. A double Fourier transform was used to derive a semianalytic solution for the 3D dynamic response of the unsaturated subgrade of the heavy-haul railway in the frequency domain. The spatial distribution law of the dynamic stress in the unsaturated subgrade was revealed. A calculation model for the working area depth (WAD) of a heavy-haul railway subgrade, considering the train axle load, subgrade saturation, and thickness of the ballast layer, was presented based on the theoretical calculation findings. The results illustrate that the attenuation laws of normal stress sigma x, sigma y and sigma z are essentially the same, and the attenuation rate gradually lowers as depth rises. In contrast to normal stress, shear stress tau zx increases initially before decreasing as depth increases. The train speed has far less impact on the dynamic response of the heavy-haul railway subgrade than the axle load, thickness of the ballast layer, and subgrade saturation. In particular, train speed has little impact on the normal stress sigma z and shear stress tau zx. The train axle load, ballast layer thickness, and subgrade saturation are all directly related to the WAD of the heavy-haul railway subgrade. The larger the thickness of the ballast layer and subgrade saturation, the smaller the WAD of the heavy-haul railway subgrade. The WAD of a heavy-haul railway subgrade increases with train axle load.