**Simulation of Dynamic Train Loads Using Fourier Series in Single- and Twin-Track Tunnels**

**Article Details**

**Authors**

**Dariush Mohammadi, Ehsan Azad, Kourosh Shahriyar, Hossein Salarirad**

**Place of Publication**

**Third Regional Conference and 12th National Conference on Tunnelling in Iran**

**Publication Year**

**November 29, 2017**

**Article Summary**

This article investigates the **dynamic behavior of urban tunnels under train-induced loading**, an issue that plays a critical role in safety during both the construction and operational stages. Train movement through a tunnel generates **dynamic loads with frequencies ranging from 2 to 22 Hz** in the surrounding soil, which can affect adjacent structures. To provide a practical approach, this study uses **Fourier series** to transform the applied wheel loads of the train from the time domain into the frequency domain. Using **PLAXIS 2D**, the dynamic behavior of **single- and twin-track tunnels** along **Tehran Metro Line 7** was then analyzed.

The results show that, in **single-track tunnels**, the passage of either one train or two trains simultaneously does not cause a significant difference in the **displacement, velocity, or acceleration of the ground surface**. However, in **twin-track tunnels**, the velocity and acceleration values increase significantly, while the displacement decreases. It was also found that **vibration attenuation is greater in twin-track tunnels than in single-track tunnels**, which is an important consideration in assessing the environmental effects of vibrations.

In conclusion, the study shows that **twin-track tunnels generate greater vibrations than single-track tunnels when two trains pass simultaneously**, particularly in terms of the **vibration velocity and acceleration at the ground surface**. These findings highlight the importance of selecting the appropriate tunnel configuration, evaluating **geotechnical conditions**, and conducting detailed **dynamic analyses** during the design and operational stages of urban tunnels. They can also provide valuable support for **engineering decision-making in similar projects**.