Purpose and Methodology The level of development in a nation’s transportation infrastructure can serve as a dependable indicator for predicting its future economic growth. Constructing tunnels establishes an alternative route that bypasses congested areas, hence improving traffic efficiency. The number of generated modes is affected by the tunnel system’s vibrational frequencies. Therefore, enhancing tunnel design through precise calibration of eigenfrequencies via mass and stiffness distribution is essential to prevent resonance and retain structural integrity, safety, and functionality. This study presents a computational modelling tool for the modal analysis of tunnels that include railway sub-track systems, employing finite element methods. It focuses on a horseshoe-shaped tunnel encircling a rock formation. This computational model aims to identify variations in modal properties, specifically natural frequencies and corresponding mode shapes, that are influenced by various factors affecting the system’s modal features. A thorough parametric study was undertaken to evaluate performance through model validation against previous research, assessment of mesh efficiency and convergence, and analysis of Mass Participation Factors (MPFs), which denote the fraction of the total mass of the tunnel-soil-train system that contributes to a specific mode of vibration. Additionally, frequency shift analysis measures the extent of frequency variation, while Modal Assurance Criterion (MAC) analysis assesses alterations in mode shape; both are crucial for validating finite element method (FEM) results and bolstering confidence in interpretations. Outcomes This inquiry primarily examines the dominant response of a railroad tunnel by analyzing various modal characteristics, including the rock grade surrounding the tunnel and the presence of train lines within the system. The FEM modal analysis of the horseshoe-shaped railway tunnel provides rigorous, scientifically valuable insights into its dynamic characteristics by delivering quantitative metrics, such as precise natural frequencies, calculated frequency shifts, mode classification, MPF, and MAC comparisons, exceeding simple qualitative observations. Understanding the essential modes and their mass participation enables researchers to determine the requisite strength and stiffness of the tunnel lining to withstand dynamic stresses. The cumulative mass participation factor (MPF) of this research indicates that the tunnel and railway sub-track system accounts for 90% of the total mass in the initial 15 modes. The natural frequency is elevated in intricate torsional mode configurations. The Modal Assurance Criterion (MAC) is a statistical tool used in modern finite element method (FEM) tunnel analysis to evaluate various modal analysis outcomes, thereby measuring the consistency between two mode shape vectors and enhancing confidence in their interpretation. It produces a result ranging from 0 (indicating no correlation) to 1 (indicating perfect correlation). A more substantial structure, such as a tunnel containing a train track, requires a greater force to achieve acceleration compared to a tunnel without such a track, leading to diminished natural frequencies for the former due to its increased mass. The track system, particularly the rails and fasteners, enhances the rigidity of the tunnel, especially along the longitudinal axis. Nevertheless, the additional mass and structural integrity of the tunnel with the track typically result in diminished natural frequencies relative to a tunnel devoid of a track. The tunnel system exhibits reduced mass and stiffness without the track, resulting in increased natural frequencies. Higher-grade rocks exhibit a greater modulus of elasticity compared to surrounding rocks, indicating increased stiffness and enhancing the tunnel system’s resistance to deformation. This, then, results in increased natural frequencies. The decreasing modulus of elasticity in lower-grade rocks signifies diminished stiffness, leading to increased flexibility and lowered natural frequencies. Grade I rock exhibits a superior modulus of elasticity relative to grade V surrounding rocks, resulting in enhanced stiffness, higher natural frequencies, and diminished displacements. The stiffness of the soil influences the deformation distribution within the tunnel, potentially altering the mode shapes, especially for higher modes. Limitation/implication The present study focuses on the modal analysis of a tunnel with a railroad track structure. Tunnel and railroad specialists can leverage this investigation to enhance the structural efficiency and functionality of the railroad tracks within the tunnel. Moreover, it may serve as a basis for subsequent assessments of dynamics and fatigue, considering the numerous dynamic loads that impact the tunnel.

Modal Analysis of Tunnel and Track Vibrations in Rock Environments Via Computational Modelling

期刊论文
发表日期：

2025年8月22日

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Akash Kumar,
K. Nallasivam

摘要

Purpose and Methodology

The level of development in a nation’s transportation infrastructure can serve as a dependable indicator for predicting its future economic growth. Constructing tunnels establishes an alternative route that bypasses congested areas, hence improving traffic efficiency. The number of generated modes is affected by the tunnel system’s vibrational frequencies. Therefore, enhancing tunnel design through precise calibration of eigenfrequencies via mass and stiffness distribution is essential to prevent resonance and retain structural integrity, safety, and functionality. This study presents a computational modelling tool for the modal analysis of tunnels that include railway sub-track systems, employing finite element methods. It focuses on a horseshoe-shaped tunnel encircling a rock formation. This computational model aims to identify variations in modal properties, specifically natural frequencies and corresponding mode shapes, that are influenced by various factors affecting the system’s modal features. A thorough parametric study was undertaken to evaluate performance through model validation against previous research, assessment of mesh efficiency and convergence, and analysis of Mass Participation Factors (MPFs), which denote the fraction of the total mass of the tunnel-soil-train system that contributes to a specific mode of vibration. Additionally, frequency shift analysis measures the extent of frequency variation, while Modal Assurance Criterion (MAC) analysis assesses alterations in mode shape; both are crucial for validating finite element method (FEM) results and bolstering confidence in interpretations.

Outcomes

This inquiry primarily examines the dominant response of a railroad tunnel by analyzing various modal characteristics, including the rock grade surrounding the tunnel and the presence of train lines within the system. The FEM modal analysis of the horseshoe-shaped railway tunnel provides rigorous, scientifically valuable insights into its dynamic characteristics by delivering quantitative metrics, such as precise natural frequencies, calculated frequency shifts, mode classification, MPF, and MAC comparisons, exceeding simple qualitative observations. Understanding the essential modes and their mass participation enables researchers to determine the requisite strength and stiffness of the tunnel lining to withstand dynamic stresses. The cumulative mass participation factor (MPF) of this research indicates that the tunnel and railway sub-track system accounts for 90% of the total mass in the initial 15 modes. The natural frequency is elevated in intricate torsional mode configurations. The Modal Assurance Criterion (MAC) is a statistical tool used in modern finite element method (FEM) tunnel analysis to evaluate various modal analysis outcomes, thereby measuring the consistency between two mode shape vectors and enhancing confidence in their interpretation. It produces a result ranging from 0 (indicating no correlation) to 1 (indicating perfect correlation). A more substantial structure, such as a tunnel containing a train track, requires a greater force to achieve acceleration compared to a tunnel without such a track, leading to diminished natural frequencies for the former due to its increased mass. The track system, particularly the rails and fasteners, enhances the rigidity of the tunnel, especially along the longitudinal axis. Nevertheless, the additional mass and structural integrity of the tunnel with the track typically result in diminished natural frequencies relative to a tunnel devoid of a track. The tunnel system exhibits reduced mass and stiffness without the track, resulting in increased natural frequencies. Higher-grade rocks exhibit a greater modulus of elasticity compared to surrounding rocks, indicating increased stiffness and enhancing the tunnel system’s resistance to deformation. This, then, results in increased natural frequencies. The decreasing modulus of elasticity in lower-grade rocks signifies diminished stiffness, leading to increased flexibility and lowered natural frequencies. Grade I rock exhibits a superior modulus of elasticity relative to grade V surrounding rocks, resulting in enhanced stiffness, higher natural frequencies, and diminished displacements. The stiffness of the soil influences the deformation distribution within the tunnel, potentially altering the mode shapes, especially for higher modes.

Limitation/implication

The present study focuses on the modal analysis of a tunnel with a railroad track structure. Tunnel and railroad specialists can leverage this investigation to enhance the structural efficiency and functionality of the railroad tracks within the tunnel. Moreover, it may serve as a basis for subsequent assessments of dynamics and fatigue, considering the numerous dynamic loads that impact the tunnel.