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FIELD AND ANALYTICAL INVESTIGATION OF A 3D DYNAMIC TRAIN-TRACK INTERACTION MODEL AT CRITICAL SPEEDS
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 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 twolevel 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 highrail 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 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 tieballast 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.
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 ………………………………………………………………………………………………. 13
Railway Track …………………………………………………………………………………………………… 17
Rails ………………………………………………………………………………………………………….. 18
Rail Pad and Tie Plate …………………………………………………………………………………. 18
Rail Tie ……………………………………………………………………………………………………… 19
Ballast ……………………………………………………………………………………………………….. 19
Track Modeling …………………………………………………………………………………………………. 19
Two-Dimensional Track Models ………………………………………………………………….. 20
Three-Dimensional Track Models…………………………………………………………………. 23
2.5-Dimensional Track Models …………………………………………………………………….. 26
Train-Track Interaction Modeling ………………………………………………………………………… 27Wheel-Rail Contact and Track Irregularities ………………………………………………….. 27Train-Track Interaction Model ………………………………………………………………………28
Ground Vibration Due to Moving Loads ………………………………………………………………. 29
Introduction ……………………………………………………………………………………………….. 29
Critical Speed Effect …………………………………………………………………………………… 32
Summary ………………………………………………………………………………………………………….. 35
Chapter 3 MODEL FORMULATION AND FIELD VALIDATION OF A THREEDIMENSIONAL DYNAMIC TRAIN-TRACK INTERACTION MODEL ………………. 38
Overview ………………………………………………………………………………………………………….. 38
Introduction ………………………………………………………………………………………………………. 38
3D Dynamic Train-Track Interaction Model …………………………………………………………. 41
Train Model ……………………………………………………………………………………………….. 43
Track Structure Formulation ………………………………………………………………………… 44
The Green’s Function for Subgrade ………………………………………………………………. 46
Train-Track-Soil Coupling …………………………………………………………………………… 50
Field Validation …………………………………………………………………………………………………. 51
Instrumentation Plan …………………………………………………………………………………… 52
Model Parameter Characterization ………………………………………………………………… 53
Traffic Information ……………………………………………………………………………………… 58
The Acceleration Data at Kingston Calibrated by Multi-depth Deflectometers
(MDDs) …………………………………………………………………………………………………….. 60
Model Prediction ……………………………………………………………………………………………….. 67
Lac La Biche Field Verification …………………………………………………………………………… 72
Conclusions ………………………………………………………………………………………………………. 76
Chapter 4 HIGH SPEED RAILWAY TRACK DYNAMIC BEHAVIOR NEAR
CRITICAL SPEED ……………………………………………………………………………………………. 77
Overview ………………………………………………………………………………………………………….. 77
Introduction ………………………………………………………………………………………………………. 78
Site Investigation ……………………………………………………………………………………………….. 80Amtrak Northeast Corridor (NEC) Study Area ……………………………………………….. 81Ground Penetrating Radar (GPR) and Light Detection and Ranging (Lidar) ……….83
Seismic Wave Velocity Testing (SWVT) ………………………………………………………. 84
Laboratory Tests …………………………………………………………………………………………. 85
Field Measurements and Speed Effect Characterization ………………………………………….. 86
Field Measurement ……………………………………………………………………………………… 86
Speed Effect Characterization ………………………………………………………………………. 89
3D Dynamic Track-Subgrade Interaction Model Prediction ……………………………………. 92
Model Inputs and Site Characterization …………………………………………………………. 93
The Maximum Vertical Displacement of Rail ………………………………………………… 95
Ground Surface Wave Motion ……………………………………………………………………… 97
Compressive Stress Contour in Ballast and Subgrade ……………………………………… 99
Discussion of Critical Speed at Kingston Test Site ………………………………………….. 100
Conclusions ………………………………………………………………………………………………………. 102
Chapter 5 HANGING TIE STUDY USING THE “MOVING DEFLECTION
SPECTRUM” ……………………………………………………………………………………………………. 104
Overview ………………………………………………………………………………………………………….. 104
Introduction ………………………………………………………………………………………………………. 105
Numerical Modeling ………………………………………………………………………………………….. 107
Characterization of the “Moving Deflection Spectrum (MDS)” ………………………………. 108
Field Investigations and Discussions ……………………………………………………………………. 111
Conclusions ………………………………………………………………………………………………………. 116
Chapter 6 CHARACTERIZATION OF THE MOVEMENTS OF RAILROAD TIES
UNDER TRAIN PASSAGE ON STRAIGHT LINES ……………………………………………. 118
Overview ………………………………………………………………………………………………………….. 118
Introduction ………………………………………………………………………………………………………. 118
Train-Track Interaction Modeling ………………………………………………………………………… 120
Vehicle Dynamics Model …………………………………………………………………………….. 120
Track Model ………………………………………………………………………………………………. 121
Modeling Results………………………………………………………………………………………… 122
Field Investigation and Analysis …………………………………………………………………………..124
Field Instrumentation and Site Characterization ……………………………………………… 124
The Kingston Site ……………………………………………………………………………………….. 126
The Hollidaysburg Site ………………………………………………………………………………… 128
Effect of Tie Rotation on Ballast Performance by Discrete Element Modeling (DEM)
…………………………………………………………………………………………………………………. 132
Conclusions and Future Work ……………………………………………………………………………… 135
Chapter 7 CONCLUSIONS AND RECOMMENDATIONS ………………………………………….. 137
Conclusions ………………………………………………………………………………………………………. 137
Recommendations ……………………………………………………………………………………………… 139
References ……………………………………………………………………………………………………………….. 140
Appendix A Train Passage Log at Kingston ………………………………………………………………… 147
Appendix B Field Equipment at Kingston …………………………………………………………………… 149
Appendix C DCP Analysis at Kingston ………………………………………………………………………. 159
Appendix D Accelerometer Specifications ………………………………………………………………….. 170
Chapter 1
RESEARCH INTRODUCTION, MOTIVATION, OBJECTIVES AND METHODOLOGY
Introduction and Motivation
Passenger transport becomes a significant portion of rail transport as the train speed increases. Due to its environmentally friendly technologies and time saving in short-distance travel, high speed rail (HSR) has been proven to be a powerful technological advance in the transportation industry. Over ten thousand miles of HSR rail have been built in the world. Without exception, as many other countries, United States also has a long-term goal of the HSR program. However, one of the most critical problems of the HSR development in United States is to evaluate and then upgrade the current railway lines for high-speed trains. Unlike some other countries build new railway lines for HSR, United States is prone to upgrading existing railway tracks for most HSR lines for economical reason. But, increasing speed brings many challenges to a conventional railway system, which include rail system control, passenger safety and comfort, noise and vibration hazards. Among those challenges, ground-borne vibration induced by HSR is the focus in this research. Those vibrations could bring potential problems of operational safety by accelerating the deterioration of the conventional railway tracks and affect passenger comfort. However, it is a complex problem to measure the effect of vibrations on vehicle, track and human comfort. Therefore, a comprehensive and effective modeling method integrating the entire railway structures will be an appropriate tool to investigate the railway performance.
According to previous research, high speed trains on soft ground could induce a significant increase in vibration level when trains move at critical speeds. The critical speed is that at which resonance occurs when the speed of a moving train is close to or above the speed of the Rayleigh wave of subgrade soil. Many high speed lines1-5 have been suspected to have the critical speed effect. In the United States, Amtrak requires more frequent maintenance for the North East Corridor (NEC) at Kingston, Rhode Island (known as the Great Swamp area), and so identified the need for investigating the site. It was suspected that the critical speed effect might exist at this particular location as well. However, it is expensive and perilous to run a train at critical speed to test the vibration of the subgrade soil. Therefore, it would be applicable and effective to develop and
validate a 3D dynamic train-track interaction model, and then use it to predict the track and ground vibrations and substructure performance under trains moving at critical speeds. The dynamic traintrack interaction model should be a complex system with train, track and soil subgrade. The model needs to have the capabilities to simulate any track profiles, different train speeds and wave propagation generated by HSR.
Field validation is an important step that is made to validate the developed numerical model which inherently has many assumptions and simplifications. Once it is validated, the model can be implemented with confidence to solve specific problems under certain conditions. For this reason, the validation of the model was conducted at the Kingston site. The following tasks were planned: 1) comprehensive field investigation of the problem site, including both laboratory testing and onsite characterization; 2) development of an instrumentation plan designed to quantitatively evaluate track vibration and its change under different train speeds; 3) validation of the 3D dynamic traintrack interaction model to study the track performance and critical speed phenomenon.
The validated model has the versatility to solve many problems in an effective and efficient way. The model can be appropriately modified and coupled with other benchmarked programs to extend the capabilities of the current model. If the right assumptions are made, the modified model can still have its own ability and take full advantages of other programs at the same time. Then, it will be an efficient and effective way to solve some specific problems. Hanging tie detection and characterization of tie movements are two examples discussed in this dissertation. The commonality of these two cases is that currently there are no effective tools or inspection techniques that can explore the mechanism and predict potential hazards of both issues. The developed model is then modified and coupled with other numerical programs to solve the problems. Therefore, the developed model is not just a method to settle the specific problems in this dissertation, but also has great potential to be extended to solve many other railway problems.
Objectives
The overarching goal of this dissertation is to formulate and validate an effective and comprehensive train-track interaction model to investigate the mechanism of various railway problems. The interaction of railway system becomes more and more essential as the heavy axle load and high speed trains develop rapidly. The dissertation combines a comprehensive literature review (Chapter 2) with a series of manuscripts to fulfill the following specific objectives:
- Formulate a 3D dynamic train-track interaction model. Make sure it is capable of predicting the performance of vehicle, track, and subgrade; (Chapter 3)
- Validate the developed model by conducting field tests on the rail deflection and ground wave motion on selected railway lines; (Chapter 3)
- Use the model to investigate the critical speed effect at the Kingston site and predict the track performance that could not be measured directly; (Chapter 4)
- Use the model to propose a fast, nondestructive screening method to identify the hanging tie problem; (Chapter 5)
- Combine the model and other commercial programs to characterize the tie movements under repeated train loading. (Chapter 6)
Scope and Methodology
In this dissertation, a semi-analytical model was formulated which is capable of simulating the wheel-rail contact scenario, movements of tie, discrete support condition of the track and soil subgrade response to moving trains. The wheel forces were coupled with the rail using Hertzian contact theory. The ties were discretized along the longitudinal direction with specific tie spacing. The ties were modeled as constant masses interacting with rail and ballast by springs and dampers. In addition, the subgrade was modeled as 3D finite element method with plane-stress quadrilateral finite elements, which makes the calculation time-saving but needs to assume the subgrade as a homogeneous domain in the longitudinal direction. The entire model is self-coded in MATLAB.
For the field validation, a 3 3 array of piezoelectric, triaxial accelerometers were temporarily installed along the track and right-of-way with a general longitudinal spacing of 25 tie spaces (15 m) and a general lateral spacing of 7.5 m. The Dynamic Cone Penetrometer Test (DCP) was conducted to construct the cross-sectional data input for the dynamic track model. In addition, traffic information, such as vehicle speed and train types, was also collected during the field validation tests. The acceleration data was calibrated by Multi-depth Deflectometer (MDD) and then double integrated to get the rail deflections.
For the hanging tie detection, the track’s “Moving Deflection Spectrums (MDS)” under different tie-supporting scenarios were investigated and characterized by the dynamic track model. The track model included a moving dynamic load and a track with discrete supports. For describing the tie movements under repeated train loading, a vehicle dynamics model coupled with a threedimensional finite element track model was used.
Expected Contribution
The ultimate contributions of this dissertation to the railroad community will be:
- An effective and reliable modeling methodology to predict track performance in terms of rail deflection, ground surface wave motion and vertical compressive stress in cross sections at different train speeds, train loadings and many other conditions.
- Applications by using the model to substantially improve the current method of maintenance, which is high-cost and time-consuming.
Engineering Significance
Significance of the dissertation research can be communicated best in terms of the need for the aforementioned contributions. The developed model is able to simulate the track performance and explore the mechanism of track problems in an efficient and effective way. The following explanations address the significance of this dissertation in addressing the limitations of current analysis approaches.
Ø A 3D dynamic train-track interaction model at critical speeds
The conventional definition of critical speed of a railroad system is the speed at which vibrations propagate within the track structure and subgrade at a speed close to the Rayleigh wave velocity of the subgrade soil. One of crucial issues of increasing speed is that high speed trains on soft ground where Rayleigh waves travel slower can generate a significant increase in vibration level when train speeds approach the critical speed of the system. In another word, when a train operates at its critical speed, it could cause high-level of track vibration, excessive rail deflection and even derailment. It has been considered as an important factor of operational safety when highspeed rails run on soft subgrade. A track section on the North East Corridor (NEC) at Kingston, Rhode Island (known as the Great Swamp area) was suspected that the critical speed effect might exist at this particular location because Amtrak requires more frequent maintenance for this site. The modeling and field study indicated that the critical speed effect does not match the conventional criteria and could be defined in two levels for the Kingston site: 1) the speed causing significant increase in the cross section stress intensity, at which more frequent ballast maintenance becomes a concern; 2) the speed causing significant increase in rail deflection, at which derailment becomes a concern.
Ø Study of the mechanism and detection of the hanging tie problem
A hanging tie is a form of railroad track distress that occurs when voids have developed beneath the ties due to uneven ballast settlement and improper maintenance practices. It will lead to an increase in dynamic impact loading on the top of the ballast and therefore further deteriorate the track structure. The study proposed a fast, nondestructive screening method to identify the hanging tie problem by using the self-developed model. The method utilized the dynamic track model to characterize the track’s “Moving Deflection Spectrum (MDS)” under different tiesupporting scenarios. The field experiments were also conducted to validate findings from numerical modeling. The finding of this research is significant because hanging tie problem requires a long maintenance period and high cost at current state. The quick identification method could improve the maintenance efficiency in railroad industry and provide a safer rail service.
Ø Characterization of the movements of railroad ties
The ballast performance, degradation, breakage and deformation largely depends on the tie-ballast contact condition. Previous research on ties or ballast assumes that the movements of a railroad tie under the repeated train loading are along the vertical direction. A unidirectional actuator which was used for these laboratory tests was perpendicular to the ballast surface. The setup results in tie-ballast contact forces being applied in the vertical direction. However, field instrumentations installed at Kingston indicated that the tie movements in real world were not only translational but also rotational. Therefore, an accurate description of the tie-ballast contact interaction is an essential and imperative study and has the potential to improve the laboratory research and practical maintenance.
FIELD AND ANALYTICAL INVESTIGATION OF A 3D DYNAMIC TRAIN-TRACK INTERACTION MODEL AT CRITICAL SPEEDS
