Field and Analytical Investigation of a 3D Dynamic Train-Track Interaction Model at Critical Speeds
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The Pennsylvania State University The Graduate School Department of Civil and Environmental Engineering FIELD AND ANALYTICAL INVESTIGATION OF A 3D DYNAMIC TRAIN-TRACK INTERACTION MODEL AT CRITICAL SPEEDS A Dissertation in Civil Engineering by Yin Gao 2016 Yin Gao Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2016 ii The dissertation of Yin Gao was reviewed and approved* by the following: Hai Huang Associate Professor of Rail Transportation Engineering Dissertation Adviser Co-chair of Committee Shelley Marie Stoffels Professor of Civil Engineering Co-chair of Committee Tong Qiu Associate Professor of Civil and Environmental Engineering Jamal Rostami Associate Professor of Energy and Mineral Engineering Patrick Fox Professor of Civil and Environmental Engineering Department Head of Civil and Environmental Engineering *Signatures are on file in the Graduate School iii ABSTRACT Railroad transportation, especially high-speed passenger rail, has been developing at sensational speed, creating the needs to evaluate the track safety and predict the potential hazards for railroad operation. As train speed increases, the responses of the train and track substructure present larger dynamic behavior, which raises problems in passenger comfort, operational safety and track structures. With the boom of modeling and computing techniques, numerical simulation becomes a more feasible, safe and effective tool to identify the problems in railroad engineering. In this dissertation, a self-developed three-dimensional train-track interaction model is formulated, validated and implemented to predict the potential risks and explore the mechanisms of rail track problems. The developed 3D dynamic track-subgrade interaction model includes a train model, 2D discrete support track model and 3D computation-efficient finite element (FE) soil subgrade model. The rail beam is modeled as a Euler-Bernoulli Beam. The 2D track model discretizes the tie and ballast as rigid bodies with designated spacing. The discretely supported system enables the track model to take the track longitudinal variations into consideration. The subgrade model is simulated by finite element method with quadrilateral elements. Since the subgrade of a tangent track is considered as homogeneous in the moving direction, the formulation of the subgrade is derived in a computing-efficient way by expanding the longitudinal direction in the frequency domain. Therefore, the computing time is significantly reduced. The entire model is a self-developed program, which is coded in MATLAB. Field data collected in x, y, z directions were used to validate the accuracy of the dynamic track-subgrade interaction model. Testing sites were located on Amtrak’s highest speed (240 km/hr) line near Kingston, Rhode Island, on the Northeast Corridor in United States. Track deflections and the ground wave motion measured in the field were compared with those predicted by the 3D dynamic track-subgrade interaction model. Some applications of the 3D dynamic track-subgrade interaction model are included in this dissertation, as follow. Critical speed study: Amtrak requires more frequent maintenance for the North East Corridor (NEC) at Kingston, Rhode Island (known as the Great Swamp area). It was suspected that a condition, known as critical speed, might exist at this particular location. The conventional definition of critical speed of a railroad system is the speed at which vibrations propagate within iv the track structure and subgrade at a speed close to the Rayleigh wave velocity of the subgrade soil. As trains travel at speeds approaching the critical speed, all track components are expected to present significantly increased vibrations. However, no historical data indicated such dramatic increment in track responses at the “Great Swamp” area. Therefore, the 3D dynamic track-subgrade interaction model was used to evaluate the track performance under the current range of operation speeds and predicted the track responses at train speeds higher than the track speed limits. According to the results and analysis, the critical speed effect at the Kingston site could not be comprehensively explained by the conventional definition of the critical speed. Therefore, a two- level explanation is used to address the phenomenon at this site. Hanging tie detection: the hanging tie condition is that in which voids have developed beneath the ties, causing tie-ballast gaps. The existence of the tie-ballast gaps can result in larger peak accelerations at the unsupported or poorly supported ties. This will increase the dynamic contact force between tie and ballast, and then further deteriorate the track structure. However, currently the railroad industry has difficulties in identifying hanging ties in the field since the problem is buried beneath the track. Therefore, the previously developed model was used to propose a fast, nondestructive screening method to identify the hanging tie problem. The method utilized a dynamic track model to characterize the track's “Moving Deflection Spectrum (MDS)” under different tie-supporting scenarios. The MDSs of tracks without a hanging tie problem have a clear peak at the “Tie Spacing Frequency.” However, tracks have a hanging tie problem if the MDSs present a significantly increased peak in the low frequency region (the frequency below the “Tie Spacing Frequency”). The modeling results were further validated by the field investigations conducted on three metro lines in Boston and St. Louis. Accelerometers were mounted on a high- rail vehicle to measure the acceleration of the moving wheels. The MDSs were then calculated to predict the potential locations of hanging ties. The locations of hanging ties predicted by the model matched the field observations. Tie movements characterization: modeling techniques were used to predict the movements of railroad ties under moving train passage in this study. The ballast and other track substructures performances are largely dependent on the tie-ballast contact. Therefore, characterizing the tie movements could potentially bring new concepts to the conventional laboratory tests and practical maintenance for railroad engineering. In order to obtain the tie movements numerically, two steps were made by combining a commercial vehicle dynamics model with a track model established in the commercial software ABAQUS. The modeling results showed that the motion of ties not only v contains translational movements, but also rotations. The field tests to validate this finding were conducted on an Amtrak high-speed passenger line and a freight railroad short line. The measuring units were mounted on ties to record the accelerations and the changes in Euler angles of the ties in three orthogonal directions. The measurements of tie displacements and rotations in the field tests had good agreement with the modeling results. Moreover, field tests indicated that the tie- ballast gaps may cause higher accelerations and angular velocities of ties. Then the effect of tie rotation was investigated by discrete element modeling. The modeling results showed that the acceleration of individual ballast particles and ballast contact forces could have significant increase when the tie rotation is considered. Overall, the 3D train-track interaction model is capable of simulating the railroad tracks of various conditions by integrating the discrete supports and 3D subgrade model. The model can be a reliable and effective tool for railroad industry. The versatility of the model makes it have great potential for future research and references. vi TABLE OF CONTENTS ABSTRACT ............................................................................................................................. iii TABLE OF CONTENTS ......................................................................................................... vi LIST OF FIGURES ................................................................................................................. x LIST OF TABLES ................................................................................................................... xv ACKNOWLEDGEMENTS ..................................................................................................... xvi Chapter 1 RESEARCH INTRODUCTION, MOTIVATION, OBJECTIVES AND METHODOLOGY ........................................................................................................... 1 Introduction and Motivation ............................................................................................ 1 Objectives......................................................................................................................... 2 Scope and Methodology ................................................................................................... 3 Expected Contribution ..................................................................................................... 4 Engineering Significance ................................................................................................. 4 Chapter 2 BACKGROUND AND LITERATURE REVIEW ................................................. 6 A Brief Introduction to Railway Engineering .................................................................. 6 Railway Vehicle ............................................................................................................... 11 Vehicle Modeling ............................................................................................................