Dynamic Triaxial Testing and Constitutive Modeling of Goaf Ground Soil Under High-Speed Railway Cyclic Loading

Coal-mining-induced goaf areas are widely distributed in China and pose potential risks to high-speed railways. Repeated train-induced cyclic loading may further disturb the already weakened ground and aggravate deformation of the subgrade. A study on the goaf ground soil along the Taijiao High-Speed Railway utilized a GDS dynamic triaxial apparatus and controlled variable method to examine how waveforms, cyclic stress ratios (CSRs), effective confining pressures, vibration frequencies and cycles affect soil dynamics. The results show that cumulative plastic strain and residual pore pressure ratio generally tended to stabilize after rapid early development; however, both responses increased markedly within the 2–3 Hz frequency range. Among the investigated variables, the cyclic stress ratio (CSR) exerted the most significant influence and showed an exponential relationship with cumulative plastic strain and residual pore pressure ratio, whereas effective confining pressure produced a nearly linear decreasing trend. A dynamic stress–strain backbone curve was constructed, and by introducing the influence of vibration cycles into the H-D framework, the modified model achieved better agreement with the experimental backbone curves than the conventional H-D model. Furthermore, ABAQUS simulations further demonstrated that train speed and subgrade form significantly influence the distribution of dynamic stress and vertical displacement in goaf ground, with a more severe response in the cutting section. The optimized constitutive model and numerical results provide theoretical support for foundation design, long-term stability assessment and settlement prediction of high-speed railways constructed over goaf ground.