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Influence of Train Speed on Ground Surface Vibrations in Urban Rail Tunnels

This study utilizes finite element analysis on Tehran Metro Line 6 to demonstrate that increasing train speeds, particularly when two trains operate simultaneously at 90 km/h, significantly intensifies ground surface vibrations to levels (84 dB) that may disturb nearby residents.

Original authors: Sakineh Etemadi, Soheil Sharifi Boroujerdi, Hamid Reza Nejati, Seyed Amin Moosavi, Reza Nateghi, Kamran Goshtasbi, Masoud Abedini

Published 2026-07-27

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CC BY 4.0

Original authors: Sakineh Etemadi, Soheil Sharifi Boroujerdi, Hamid Reza Nejati, Seyed Amin Moosavi, Reza Nateghi, Kamran Goshtasbi, Masoud Abedini

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the ground beneath your feet not as a solid, unshakeable floor, but as a giant, invisible trampoline. When you jump, the fabric stretches and snaps back, sending ripples through the air and the structure. Now, imagine that trampoline is the Earth itself, and instead of a single jumper, you have a heavy, roaring train speeding through a tunnel deep underground. This is the world of ground-borne vibration. It's a branch of physics and engineering that studies how moving heavy objects shake the soil around them. When a train rolls over tracks, it doesn't just move forward; it pushes and pulls on the ground, creating waves of energy that travel upward. If these waves get too strong, they can rattle windows, disturb sleep, or even mess with delicate machines in nearby buildings. The big question scientists ask is: "How fast can a train go before the ground starts to complain?"

This paper dives into that exact question, focusing on the bustling city of Tehran, Iran. The researchers, a team of engineers from Tarbiat Modares University and others, wanted to see what happens when trains zoom through underground tunnels at different speeds. They didn't just guess; they built a giant, virtual computer model of the Tehran Metro's Line 6. Think of it like a high-tech video game simulation where they could control the speed of the trains and watch exactly how the ground above reacted. They tested three specific speeds: 40 km/h (a slow crawl), 60 km/h (a moderate pace), and 90 km/h (a fast sprint). They also looked at what happens when just one train is moving versus when two trains are zooming past each other at the same time.

The team discovered that speed definitely matters, but not in a perfectly straight line. As the trains sped up, the shaking got worse. At the slowest speed of 40 km/h, the ground stayed relatively calm, with vibration levels staying under a "normal" limit of 70 decibels (a unit used to measure how loud or intense the shaking feels). However, once the trains hit 60 km/h and especially 90 km/h, the ground started to rumble much harder. The most chaotic scenario happened when two trains were moving at the same time at the top speed of 90 km/h. In this "double trouble" case, the vibration levels spiked to a whopping 84 decibels.

The researchers found that this extreme shaking wasn't just because the trains were fast; it was also because the waves from the two trains were hitting the ground at the same time, stacking up on each other like waves in the ocean crashing together to form a giant tsunami. This "stacking" effect made the ground shake even more violently than a single train ever could. In fact, the simulation showed that at 90 km/h with two trains, the ground surface was moving at a peak speed of 3.1 mm/s, which is enough to cause real discomfort for people living nearby and could potentially disturb sensitive equipment.

Interestingly, the paper suggests that the ground doesn't just get louder forever as speed increases. The jump in shaking was most dramatic when going from 40 to 60 km/h. When they pushed the speed from 60 to 90 km/h, the shaking still got worse, but the increase was a bit more moderate. The authors suggest this might be because the soil itself acts like a shock absorber, soaking up some of the extra energy at very high speeds, preventing the vibration from exploding even further.

In the end, the study concludes that while slower trains are generally safe for the neighborhood, speeding up to 90 km/h, especially with two trains running at once, pushes the ground vibrations past the safety limits set by international standards. The ground, it seems, has a speed limit too, and for the residents above the Tehran Metro, that limit might be lower than the trains' top speed. The researchers used these computer simulations to show that without careful planning, the convenience of a fast subway could come at the cost of a very shaky, noisy neighborhood.

Technical Summary: Influence of Train Speed on Ground Surface Vibrations in Urban Rail Tunnels

Problem Statement
As underground rail networks expand and train speeds increase, train-induced ground-borne vibrations have become a significant environmental concern. These vibrations propagate from the wheel-rail interface through the track structure and subgrade to the surface, potentially disturbing residents and damaging sensitive equipment. While vertical dynamic loads are recognized as the primary driver of ground vibration, the specific relationship between train speed, multi-train interactions, and the resulting surface vibration levels in urban tunnel environments requires precise quantification. This study addresses the need to evaluate how varying train speeds and simultaneous train movements affect ground surface vibrations, using Tehran Metro Line 6 as a case study.

Methodology
The research employs a two-phase numerical approach utilizing Finite Element Analysis (FEM) to simulate the dynamic interaction between trains and the ground.

Dynamic Load Simulation (3D Model):
- A three-dimensional model was developed to simulate the wheel-track-subgrade system. The train wheel follows the S1002 profile, and the rail uses the UIC54E1 geometry.
- The train carriage and suspension systems were modeled as equivalent lumped masses and spring-damper elements connected via Multiple Point Constraints (MPC).
- Dynamic loads were calculated for three specific speeds: 40, 60, and 90 km/h. The simulation accounted for the wheel-rail contact using a penalty method with a friction coefficient of 0.3.
- The study determined that dynamic loads increase with speed, with maximum recorded loads of 147.7 kN (40 km/h), 178.9 kN (60 km/h), and 214.4 kN (90 km/h).
Ground Vibration Analysis (2D Model):
- A two-dimensional model of the Tehran Metro Line 6 tunnel (8.85 m outer diameter, 0.35 m thick concrete segments) was constructed.
- The surrounding soil was divided into saturated and unsaturated zones, modeled using the Mohr-Coulomb constitutive model.
- Rayleigh damping was applied to the soil and concrete structures to simulate energy dissipation. Coefficients were calculated based on the soil's first natural frequency (5 Hz) and the dominant frequency of the input dynamic load.
- Scenarios: Nine distinct scenarios were analyzed to cover various operational conditions: single-train and double-train configurations at speeds of 40, 60, and 90 km/h.
- Evaluation: Vibration velocity levels were measured at the ground surface directly above the tunnel. Results were converted to decibels (VdB) using the US Federal Transit Administration (FTA) reference velocity ( $10^{-6}$ mm/s) and compared against FTA regulatory thresholds (70 dB normal limit, 80 dB upper limit).

Key Contributions and Results
The study provides a quantitative assessment of how train speed and traffic density influence ground vibrations:

Speed-Vibration Correlation: There is a direct correlation between train speed and peak particle velocity (PPV). However, the increase is nonlinear; a more pronounced rise in vibration occurs between 40 and 60 km/h, while the increment from 60 to 90 km/h is comparatively moderate. The authors attribute this to soil damping and the dynamic response of the track-ground system mitigating further amplification at higher speeds.
Multi-Train Interaction: The simultaneous movement of two trains significantly amplifies ground vibrations compared to single-train scenarios due to the in-phase superposition of dynamic waves (constructive interference).
Scenario Outcomes:
- Scenario 1 (Single train, 40 km/h): Resulted in 66 dB, remaining below the 70 dB normal threshold.
- Scenario 6 (Two trains, 90 km/h): Produced the highest vibration levels, reaching 84 dB with a PPV of 3.1 mm/s. This exceeds the FTA upper limit of 80 dB.
- Scenario 5 (Two trains, 60 km/h): Exceeded the 80 dB threshold.
- Mixed-Speed Scenarios: Scenarios involving trains at different speeds (e.g., 60 and 90 km/h) resulted in lower vibration levels (e.g., 79 dB) compared to equal-speed scenarios, attributed to partial wave desynchronization reducing interference effects.

Significance and Claims
The paper claims that its findings offer critical insights for the environmental assessment of underground rail infrastructure in densely populated urban areas. The primary significance lies in demonstrating that while increasing train speed generally intensifies ground vibrations, the most critical factor for exceeding regulatory limits is the combination of high speed and simultaneous double-track operations.

The authors conclude that at 40 km/h, vibrations generally remain within acceptable limits. However, at higher speeds (60 and 90 km/h), particularly when two trains operate simultaneously, vibration levels can exceed permissible thresholds, posing a risk of disturbance to nearby residents and sensitive equipment. The study suggests that speed mismatches between trains may serve as a natural mitigation mechanism by reducing wave interference, whereas synchronized high-speed operations require careful engineering consideration to manage ground-borne vibrations.

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