Shallow Buried Periodic In-Filled Pipe Barriers for Efficient Ambient Vibration Mitigation: A Comprehensive Study


The rapid urbanization and the development of modern transportation systems have advanced quality of life of the people worldwide. However, this progress has not been without a downside. One significant concern that has arisen in the wake of this development is the issue of ambient vibration and noise. These nuisances are particularly problematic in areas sensitive to vibrations, such as densely populated residential zones, laboratories housing precise instruments, hospitals, and historic buildings. One of the challenges in addressing this issue lies in the characteristics of these vibrations. They tend to have low frequencies and long wavelengths, making them distinct from other forms of vibrations, such as those caused by machinery, wind, or traffic noise. For example, the primary frequency range of ground-borne vibrations induced by metro trains typically falls within the range of 30 to 80 Hz, with wavelengths spanning several meters. A significant portion of the energy associated with these vibrations is carried by Rayleigh waves that propagate along the surface of elastic half-spaces. As a result, controlling surface waves becomes a central concern in mitigating ambient vibrations. Various methods for vibration mitigation can be categorized based on their point of action: at the vibration source, along the transmission path, or at the receiver. In comparison to addressing the source and receiver, methods and technologies that disrupt the wave transmission path offer advantages in terms of implementation and cost-effectiveness. They do not require disrupting traffic, roads, or tracks, making them suitable for both new and existing buildings, regardless of the location.

Recently, novel types of wave barriers have emerged, such as periodic in-filled trenches, periodic pile barriers, periodic in-filled pipe pile barriers, and periodic pillared barriers. These barriers have shown significant wave attenuation within the attenuation zones (AZs). While this progress was promising, several challenges must be addressed such as the number of AZs is limited, with narrow bandwidth, which can restrict the range of vibration mitigation also the size of periodic wave barriers is often impractically large, especially when Bragg scattering is the main working mechanism and the construction of large-scale periodic wave barriers may be challenging and costly. Therefore, building upon the lessons learned from acoustic and optical systems, a new concept has emerged: metasurfaces. Metasurfaces offered a novel approach to designing periodic wave barriers. These planar metamaterials are characterized by their subwavelength thickness and flat surface. They have been demonstrated to effectively interact with propagating waves and have shown promise in mitigating Rayleigh waves. Furthermore, researchers have investigated the feasibility of using natural metasurfaces, such as forests, to achieve strong surface wave attenuation and recent efforts have focused on enhancing the wave attenuation performance of metasurfaces, leveraging new working mechanisms, including inertial amplification, nonlinearity, and negative stiffness. Inspired by these developments, and in a new study published in the Journal Engineering Structures by PhD candidate Anchen Ni and Professor Zhifei Shi from the Beijing Jiaotong University in collaboration with Professor Qingjuan Meng from the Tangshan University and Professor C.W. Lim from the City University of Hong Kong   proposed a novel solution: shallow buried periodic in-filled pipe barriers, or metasurface barriers, designed to mitigate Rayleigh waves. These barriers, characterized by their subwavelength characteristics and flat surfaces, offer potential solutions to the three major challenges faced by traditional wave barriers.

The research team provided an in-depth description of the research methodology and analysis, focusing on complex dispersion and transmission characteristics. Numerical analysis, conducted using Comsol Multiphysics, plays a central role in understanding the vibration mitigation performance of wave barriers in actual site conditions. The dispersion analysis takes into account various design parameters, such as the lattice constant, depth of buried pipes, and the size and thickness of the pipes. The complex dispersion analysis provided insights into the dynamic properties of these barriers, including their ability to attenuate surface waves. The authors conducted complex dispersion analysis and identified surface wave attenuation zones (SWAZs). These are frequency ranges within which surface waves can be effectively attenuated. Complex dispersion analysis provided a more comprehensive understanding of SWAZs, including the identification of complex wave modes and the interaction between resonators and propagating waves. They also discussed the performance of shallow buried periodic in-filled pipe barriers, exploring various design parameters, gradient layouts, and material damping. Their analysis aimed to optimize the design of these barriers to ensure effective surface wave attenuation.

One key parameter under investigation is the width of the barriers, often represented by the number of rows of pipes. The authors findings indicate a significant wave attenuation within SWAZ, with a marked increase in the number of pipe rows. Their results suggest that, for a row number exceeding 15, the vibration reduction reaches a desirable level. This aspect highlights the cost-effectiveness and practicality of periodic in-filled pipe barriers. They also explored the influence of working location, distinguishing between active and passive isolation scenarios. The barriers are found to be effective in both cases, with a slight advantage in terms of vibration reduction in active isolation settings. This finding underscores the versatility of these barriers for various applications.

Additionally, the study considered the potential for gradient layout, enabling the adaptation of barriers to site-specific conditions. This gradient layout optimization shows promise in enhancing the barriers’ performance in different scenarios. Moreover, the influence of material damping is analyzed, indicating that barriers are more effective in the presence of realistic material damping.

The researchers conducted experiments involving the construction of a scale model simulating subway-induced ground vibrations, and the installation of shallow buried periodic in-filled pipe barriers at varying configurations. The experimental results confirmed the substantial vibration reduction achieved by these barriers, consistently within the main frequency range of subway-induced vibrations. Notably, the shallow buried periodic in-filled pipe barriers outperform traditional in-filled trenches, highlighting their superiority in terms of both performance and cost-effectiveness.

In conclusion, the comprehensive study by Professor Zhifei Shi and colleagues focused on the innovative use of shallow buried periodic in-filled pipe barriers, or metasurface barriers, for ambient vibration mitigation. They present opportunities for enhanced ambient vibration control, ultimately improving urban living conditions. The practicality and cost-effectiveness of shallow buried periodic in-filled pipe barriers, combined with their superior performance, make them a promising innovation with far-reaching potential in the field of engineering and urban development.

Shallow Buried Periodic In-Filled Pipe Barriers for Efficient Ambient Vibration Mitigation: A Comprehensive Study - Advances in Engineering
Fig.1 Periodic in-filled pipe barrier for ambient vibration mitigation.
Shallow Buried Periodic In-Filled Pipe Barriers for Efficient Ambient Vibration Mitigation: A Comprehensive Study - Advances in Engineering
Fig.2 Dynamic characteristics of periodic in-filled pipe barrier. (a) Dispersion relation; (b) experimental amplitude reduction spectra; (c) mode shapes.
Shallow Buried Periodic In-Filled Pipe Barriers for Efficient Ambient Vibration Mitigation: A Comprehensive Study - Advances in Engineering
Fig.3 Application to Beijing subway line 13. (a) Measuring equipments; (b) vertical acceleration data of train-induced ground vibrations; and (c) corresponding Fourier spectra.

About the author

Anchen Ni is currently a PhD candidate in Civil Engineering at Beijing Jiaotong University. He received the master’s degree in Civil Engineering from Beijing Jiaotong University in 2021. He won the BJTU Outstanding Master Graduates in 2021.

His research interests include: metamaterials; vibration & noise control; and numerical methods.

About the author

Zhifei Shi is a Full Professor of the Department of Civil and Environmental Engineering at Beijing Jiaotong University. He received the Ph.D. degree from Harbin Engineering University, Harbin, China, in 1992. He was a Post-Doctoral Fellow with the Harbin Institute of Technology, Harbin, from 1992 to 1994. He joined the Beijing Jiaotong University, Beijing, China, in 1994. He visited The HongKong Polytechnic University, University of Illinois at Urbana-Champaign and University of Houston in 1997, 2005 and 2009, respectively.

His research interests include: earthquake engineering, ambient vibration control, periodic structures, smart materials and structures, structural analysis, functionally graded or laminated composites, fracture and fatigue of engineering materials, variational principles and numerical methods. He has been listed in the World’s Top 2% Scientists announced by Stanford University Since 2020.

More information about professor Shi can be found at the webpage: or

About the author

Qingjuan Meng is a Full professor of the Department of Civil engineering at Tangshan University. She received the Ph.D. degree from Beijing jiaotong University, Beijing, China, in 2019. She has published 20 international journal papers. Her research interests include: periodic structures/metamaterials and soil dynamics.

About the author

CW Lim currently is a fellow of ASME, ASCE, EMI and HKIE. Professor Lim received a B.Eng. from UTM (Malaysia), M.Eng. and PhD from NUS and NTU, respectively.  He was a post-doctoral research fellow at UQ (Australua) and HKU.  He is currently the subject editor for JSV and AMM, joint-editor for JoMMS, Managing Editor (Asia-Pacific) for JVET, Assoc Editor for IJBC, etc.  He has published one very well-selling title entitled “Symplectic Elasticity”, more than 380 international journal papers and have more than 15,000 citations.  His paper has recorded over 1,200 citations since first published in JMPS in 2015.  Recently Professor Lim was awarded the prestigious 2020 JN Reddy Medal as a recognition “for significant and original contributions to vibration of plates and shells, smart piezoelectric structures, nanomechanics, and symplectic elasticity”.  He delivered a plenary lecture and chair another plenary lecture at WCCM-APACM 2022 where an estimate of over 3,000 participants attended the congress.


Anchen Ni, Zhifei Shi, Qingjuan Meng, C.W. Lim, A novel buried periodic in-filled pipe barrier for Rayleigh wave attenuation: Numerical simulation, experiment and applications, Engineering Structures, Volume 297, 2023, 116971.

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