مطالعه عددی تأثیر ژئوگرید بر پایداری جانبی دینامیکی و سرعت بحرانی افقی خطوط راه‌آهن بالاستی پرسرعت در بستر نرم

The rapid expansion of high-speed rail networks has intensified the need to understand the dynamic behavior of the track–soil system, particularly when trains operate near the critical speed on soft ground. While geogrids are widely employed to reinforce ballasted tracks, their influence on the critical speed phenomenon under high-speed moving loads has remained insufficiently addressed, especially regarding the optimal placement depth and the role of soil–geogrid interaction quality in soft subgrade conditions. This study presents a three-dimensional numerical investigation into the effect of geogrid reinforcement on the critical speed of ballasted high-speed railway tracks founded on soft soils. A detailed finite element model was developed using the MIDAS/GTS/NX software. The model incorporated nonlinear soil behavior through the small-strain hardening soil (HSsmall) constitutive model, capable of capturing stiffness degradation and hysteretic damping at small strain levels. The numerical model was thoroughly validated against well-documented field measurements from the Ledsgard site, demonstrating good agreement for train speeds below, near, and above the critical speed. A comprehensive parametric study was conducted, examining the effects of train type (Velaro and HEMU-430X, differing in bogie arrangement and axle spacing), number of wagons, axle load (representing passenger occupancy), geogrid stiffness (modulus of elasticity ranging from 120 to 4000 MPa), placement position within the track profile (five locations from the ballast–subballast interface down to the subballast–subgrade interface), and the soil–geogrid interaction strength reduction factor (R, ranging from 0.2 to 1.0). Both vertical and horizontal critical speeds were evaluated based on the peak dynamic displacement responses of the rail at various train velocities. The results reveal that train geometry plays a significant role in dynamic response; the Velaro train with its specific bogie spacing and higher axle load generated larger vertical displacements than the HEMU-430X. However, increasing the number of wagons (train length) did not noticeably alter the critical speed value. In contrast, increasing axle load led to a reduction in the vertical critical speed (from 324 km/h to 288 km/h) owing to the nonlinear stress-softening of the ballast and subgrade layers. Regarding geogrid reinforcement, the findings demonstrate that geogrids, due to their tensile nature and negligible bending stiffness, do not significantly affect the vertical critical speed. Under all conditions—varying stiffness, placement, and interaction quality—the vertical rail response curves remained essentially unchanged. Conversely, geogrids proved highly effective in controlling lateral displacements and enhancing the horizontal critical speed. The lateral confinement and mechanical interlock provided by the geogrid reduced horizontal rail displacements by an average of 39% relative to the unreinforced case (averaged over speeds above the horizontal critical speed) for the stiffest geogrid, effectively increasing the horizontal critical speed. The optimal geogrid placement was found to be highly dependent on subgrade stiffness. In contrast to conventional recommendations for competent subgrades, where placement at the ballast–subballast interface is considered optimal, for the soft-subgrade conditions investigated here (shear wave velocity < 175 m/s), positioning the geogrid (E=1000 MPa; R=0.8) 20 cm below the ballast–subballast interface within the subballast layer provided the best overall performance among the geogrid locations examined. This configuration reduced horizontal displacements by an average of 39% relative to the unreinforced case and yielded a horizontal critical speed of 144 km/h, the highest value obtained among all geogrid locations tested. Parametric analyses further showed that this critical speed could increase to 180 km/h with increased geogrid stiffness and stronger soil–geogrid interaction. A strong soil–geogrid interface (R close to 1.0) is essential to mobilize the full confining potential of the geogrid; even a stiff geogrid performed poorly when the interface bond was weak. The relationship between R and lateral displacement reduction was nonlinear, with the greatest improvements observed when R increased from 0.4 to 0.6. In summary, this research clarifies that geogrid reinforcement primarily benefits the lateral stability and horizontal critical speed of high-speed ballasted tracks on soft ground, without altering the vertical critical speed. The study provides practical guidance for the optimal placement of a single geogrid layer in weak subgrades and underscores the critical importance of achieving high-quality interlock between the geogrid and the surrounding granular material. These insights contribute to safer and more efficient design of reinforced ballasted tracks for high-speed rail networks.