Modeling of Train-Induced Environmental Vibrations from Railway Traffic: A State-of-the-Art Review
The expansion of urban and intercity rail networks—exemplified by China's 162,000 km of railway operating mileage and 48,000 km of high-speed lines by the end of 2024—has intensified concerns over train-induced environmental vibrations. Although typically of low amplitude, these vibrations can cause long-term structural deterioration, interfere with precision instruments, and disrupt human comfort. Documented cases include the 1000-year-old Probhutaratna Pagoda in Beijing, located 130 m from a major railway, which exhibited signs of vibration-induced degradation despite measured levels remaining within regulatory thresholds; the 632-year-old Bell Tower in Xi'an, where two overlapping metro lines produced cumulative vibration effects on ancient timber; and Peking University laboratories, where Metro Line 4 vibrations caused visible image distortion in electron microscopes. The complex dynamic interactions among train, track, infrastructure, soils, and buildings render vibration prediction a formidable challenge. This paper provides a comprehensive review of state-of-the-art modeling methods for train-induced vibrations from surface and underground railway traffic. It begins by addressing wave propagation in natural soils, followed by an in-depth examination of analytical, numerical, and empirical approaches for predicting ground and building vibrations. The review identifies unresolved issues and outlines areas requiring further investigation, including the need for efficient prediction models to assess vibrations and design mitigation measures.