Track Stiffness Research Articles

An experimental analysis of dynamic deformation and settlement resistance in a novel prestressed railway subgrade

ABSTRACT The dynamic deformation characteristics of track-subgrade systems under moving train loads provide valuable insights for vibration and serviceability assessment of the track-subgrade. This study developed three 1:5 scale track-subgrade models incorporating the novel prestressed subgrade structure and conducted two series of dynamic tests to examine how the heavy-haul train axle loads and prestress levels affected the track-subgrade dynamic deformation. The primary frequency of the subgrade dynamic displacement was observed closely aligned with the input loading frequency of 2 Hz, indicating the validity of the test setup. The track-subgrade dynamic displacement decreased with increasing distance from the loading source, of which the elastic deformation near the subgrade shoulder attenuated by approximately 79% compared to that at the sleeper end. The elastic deformation at the monitoring points approximately linearly increased with the axle load at rates ranging from 0.0018 to 0.0029 mm/t. Conversely, increasing prestress reduced the track-subgrade elastic deformation with average rates of 22.8 and 1.63 μm/100 kPa at the sleeper end and subgrade shoulder, respectively. Furthermore, application of prestress enhanced the track stiffness, with the equivalent track stiffness rising by 16.3% and 17.7% when the prestress increased from 0 to 50 kPa and from 50 to 100 kPa, respectively. The study also showed that the prestressed reinforcement structures could significantly mitigate the cumulative track-subgrade settlement over 60%, comparing the prestressed subgrade with 50 kPa prestress to the unreinforced subgrade, which highlighted the superior deformation resistance of prestressed subgrades under the train loads.

Dynamic train-track interactions over track stiffness discontinuities in railway track transitions mitigated by resilient materials

Dynamic train-track interactions over track stiffness discontinuities in railway track transitions mitigated by resilient materials

Research on Magnetic Levitation Control Method under Elastic Track Conditions Based on Backstepping Method

The vehicle–guideway coupled self-excited vibration of maglev systems is a common control instability problem in maglev traffic while the train is suspended above flexible girders, and it seriously affects the suspension stability of maglev vehicles. In order to solve this problem, a nonlinear dynamic model of a single-point maglev system with elastic track is established in this paper, and a new and more stable adaptive backstepping control method combined with magnetic flux feedback is designed. In order to verify the control effect of the designed control method, a maglev vehicle–guideway coupled experimental platform with elastic track is built, and experimental verifications under rigid and elastic conditions are carried out. The results show that, compared with the state feedback controller based on the feedback linearization controller, the adaptive backstepping control law proposed in this paper can achieve stable suspension under extremely low track stiffness, and that it shows good stability and anti-interference abilities under elastic conditions. This work has an important meaning regarding its potential to benefit the advancement of commercial maglev lines, which may significantly enhance the stability of the maglev system and reduce the cost of guideway construction.

Intelligent identification of differential subgrade settlement of ballastless track system based on vehicle dynamic responses and 1D-CNN approach

The millimeter-scale deformation control standards of high-speed railways make the monitoring and identification of subgrade settlement a key technology, especially for ballastless track systems. Addressing the uncoordinated deformation between track and subgrade caused by high track stiffness, this paper proposes an intelligent identification method for subgrade settlement based on vehicle vibration signals and deep-learning technology. Firstly, a high-speed vehicle-ballastless track-subgrade coupled dynamics model considering the track-subgrade nonlinear contact state is utilized, to obtain various vibration responses of the vehicle subsystem due to differential subgrade settlement. After data preprocessing, a multi-channel one-dimensional convolutional neural network (1D-CNN) is established to extract features from the vehicle vertical acceleration dataset and output subgrade settlement status automatically. Finally, the robustness of the model is verified using Gaussian white noise. The research indicates that the vertical accelerations of the car body and bogie frame contain dynamic characteristics caused by medium-long wavelength settlements, while the vertical acceleration of the wheelset is more sensitive to short-wavelength settlements. It is feasible to identify the degree of subgrade settlement using car body, bogie frame and wheelset vertical accelerations as parameterized multi-source input of the 1D-CNN network. The three-channel input model significantly improves the identification accuracy and demonstrates the robustness against noise interference compared to the single-input and dual-input models. This method can effectively enhance the identification capability of ‘concealed’ subgrade settlements in high-speed railways, offering a scientific methodology for status maintenance of ballastless track lines.

Research on the influence of random stiffness of the rubber tie plate on the coupled vehicle-turnout system based on the probability density evolution method

Track supporting stiffness plays a crucial role in the running quality of a vehicle crossing through a turnout. This paper mainly focuses on the influence of random stiffness of the rubber tie plate on the vehicle-turnout coupling system. The relevant random field is constructed via the number theoretical method (NTM). The coupled vehicle-turnout model with flexible rails is built via the modal superposition method. The probability density function (PDF) is obtained via the probability density evolution method (PDEM). Cases of normal distributions with various mean values of stiffness are compared to contrast the relevant impact on the dynamic wheel–rail interaction. Research results indicate that an increase of the stiffness of the rubber tie plate can abate the transverse sway of the vehicle and low down the wheel number. The target stiffness should be taken as 35 kN/mm and corresponding normal distribution with a confidence interval of plus and minus 5 kN/mm can be accepted. The discrepancy between the mean value and the relevant PDF contour clarify the importance and necessity for analysis of randomness. Research results of this paper can serve as the theoretical fundament of the track stiffness homogenisation of a turnout in the future.

Field assessment of different tamping operations for newly constructed or renovated railway tracks

ABSTRACT The tamping process is crucial for correcting geometric irregularities on railway tracks, especially on newly constructed or renovated tracks that are more susceptible to accumulating defects. Recent studies have demonstrated that multiple insertions of tamping tines lead to greater ballast compaction and improved lateral resistance of the track. However, further evaluation is necessary to assess their impact on other important track parameters. This study evaluated single and multiple insertions to determine which would promote more effective maintenance for newly built or renovated track conditions, focusing on geometry correction, track structural behaviour, and potential ballast degradation. These tamping methods were tested in a heavy haul line, showing that multiple insertions improved geometric quality, increased lateral resistance, and enhanced vertical track stiffness without causing significant ballast degradation. Therefore, using multiple insertions is recommended for newly built or renovated tracks to enhance geometric quality and structural behaviour, providing a more effective maintenance solution.

Quantifying the impact of stiffness distributions on the dynamic behaviour of railway transition zones

Railway transition zones (RTZs) are regions where abrupt track stiffness changes occur that may lead to dynamic amplifications and subsequent track deterioration. The design challenges for these zones arise due to variations in material properties in both the depth (trackbed layers composed of different materials) and longitudinal directions of the track, as well as temporal variations in mechanical properties of materials due to several external factors over the operational period. This research aims to investigate the effects of these variations in material properties (i.e., of the resulting stiffness distributions in vertical and longitudinal directions) on the behaviour of RTZs, assess from this perspective the performance of a novel transition structure called the SHIELD, and establish a methodology for designing a robust solution to mitigate the dynamic amplifications in these zones. Results indicate that stiffness variations in both vertical and longitudinal directions significantly influence the dynamic behaviour of the RTZs. The study also suggests a permissible range of stiffness ratios to control the amplification of strain energy in the most critical components of RTZs, both in the initial state as well as during the operational phase (where material properties may vary over time). Moreover, the proposed methodology offers a valuable tool for the design and evaluation of RTZs and is applicable to various transition types and a broad spectrum of material properties.

Control of the maglev system with a low stiffness elastic track beam by pole assignment and a reduced order state observer

A maglev train system is an open loop unstable and strongly nonlinear system. Self-excited coupling vibration between the magnet and the track beam can occur even when the train is stationary. To avoid this, the track beam is generally designed with high stiffness, which directly increases the construction cost of the maglev line. In this research, a new control method for the maglev system with a low stiffness elastic track is proposed based on full state feedback theory and pole assignment theory. In the newly designed controller, track beam DOF is introduced into the control loop with the use of the reduced order state observer (ROSO) to make the control system have the ability to suppress track vibration actively, thus reducing the over dependence of the system stability on track properties. Effectiveness of the proposed control strategy is verified through experiments. Results show that it exhibits a better response compared to the traditional control method, with smaller fluctuations in levitation air gap and magnet acceleration. Furthermore, it can maintain system stability with relatively lower track stiffness, reducing the minimum requirements for track stiffness by 53.4% in the test.

Experimental Study on In-plane Stiffness of Track in a Turnout of the Railway in Vietnam

Aims: This study aims to determine the in-plane stiffness of the track in a turnout of the railway in Vietnam. Background: Track stiffness is a basic parameter of railway tracks that influences the bearing capacity of the track, the dynamic behavior of passing vehicles, the quality of track geometry, and the life of track components. Objective: The objective of this research is to determine the in-plane stiffness of the track based on substructure modulus, and rail pad stiffness at a track section in a turnout. Methods: Various tests which included the field tests of the substructure modulus, and rail pad stiffness tests in the laboratory were done. Substructure modulus was investigated at ten locations in the field. Rail pad stiffness was tested with five samples in the laboratory. In-plane stiffness of the track was calculated through substructure modulus and rail pad stiffness. The finite element method was used to evaluate the bearing capacity of bearings with different in-plane stiffness values. Results: Based on the results obtained, the substructure modulus was from 0.49 N/mm3 to 1.48 N/mm3. The rail pad stiffness is from 32.99 kN/mm to 34.92 kN/mm. These results are used to calculate the in-plane stiffness of the track. The in-plane stiffness of a track section in a turnout in Vietnam is from 25.18 kN/mm to 30.19 kN/mm. According to the finite element method, it is possible to determine the maximum value of forces transmission to the supports from 37.743 kN to 38.989 kN corresponding to the above stiffness values with the axle load of train 14 tons and rail P60. Conclusion: The stiffness of the supporting is proportional to the value of the force transmitted to the supporting. This study clearly showed that the substructure (soil and ballast) properties had the most impact on the total in-plane stiffness of the track. The results will be a tool for the track maintenance engineer to implement correct maintenance activities.

Influence of ballast heterogeneity on railway induced vibrations and identification of heterogeneous properties of a ballast layer

In the context of railway induced vibration, the excitation induced by a passing train can be separated into a quasi-static and a dynamic component. The quasi-static component is related to the weight of the train transmitted through the wheels to the track. The dynamic component is related to the dynamic train-track excitation resulting from the irregularities of the running surfaces or from the variation of the track stiffness. At sub-Rayleigh speed on a track with longitudinally invariant properties, quasi-static excitation has no significant influence on the far-field vibration. In this paper, a randomly-fluctuating heterogeneous continuum model of the ballast layer is considered. Mechanical properties are represented as 3D random fields. First, the influence of ballast heterogeneity on the vibration field induced by a moving load is studied. The results show that heterogeneity is responsible for the generation of waves propagating away from the track. Then an identification process of the heterogeneous model of the ballast is presented based on experimental measurements of train passages.

Wavelet-based neural network model for track stiffness signal detection

With the rapid development of the railway industry, railway safety has received increasing attention. However, traditional methods for signal detection are limited by high cost and energy requirements. Data-driven methods are becoming increasingly popular for railway signal detection. In this paper, we propose a wavelet-based network model for railway track stiffness signal detection by combining deep neural networks and wavelet transform. In the training phase, we propose a wavelet-based convolutional neural network. We use wavelet coefficients to enhance the input features to improve the convolutional neural network. In the detection phase, we combine the sliding window algorithm and the voting algorithm to detect anomalous signals. Extensive experiments on general metrics demonstrate the effectiveness of our proposed model. The classification performance still outperforms the general network by 30–50% in terms of accuracy, precision and F1 score, which is a huge improvement. In addition, we test the model classification performance under different wavelet functions to validate the superiority of neural networks using wavelets.

The Impact of Anisotropic Properties of the Rail Track Superstructure on the Parameters of Dynamic Settlement of Bridge Approaches

Numerous artificial structures, bridges, overpasses, tubes, channels, chutes are operated on railway networks. Artificial structures are considered to have a longer life cycle and thus will need during it overhaul and reconstruction with the use of modern technology. Currently, there is an increase in axial load and traffic speed, the makes even more relevant the solution of tasks referring to dynamic impact of trains on artificial structures and superstructure. See the features of construction and maintenance of rail track sections at the approaches to bridges, the respective problems merit special consideration.The research which results are presented in the article was dedicated to the impact of the anisotropy of the track superstructure on the parameters of the dynamic settlement of sections of transitional stiffness located at the approaches to bridges and built using bottomless box culverts.The research proposed to model the railway track within the transitional section as a set of flat elements of constant thickness, while each of them is regarded as a anisotropic plate supported by deformable foundation with its own deformability rates. By setting boundary conditions for individual fragments of the track structure and varying the anisotropy coefficients that determine the ratio of mechanical characteristics in different directions of anisotropy, it is possible to select necessary rail track stiffness rates for a section at bridge approaches, that paves the way to further research on structural features of designing and arrangement of those structures.

Vold–Kalman filter order tracking of axle box accelerations for track stiffness assessment

Intelligent data-driven monitoring procedures hold enormous potential for ensuring safe operation and optimal management of railway infrastructure in the face of increasing demands on cost and operations efficiency. Numerous studies have highlighted track stiffness as a main parameter influencing the evolution of degradation that drives maintenance processes. As such, the measurement of track stiffness is fundamental for characterizing the performance of the track in terms of deterioration rate and noise emission. In this work, we propose a rail stiffness assessment scheme relying on low-cost, on board monitoring sensors, namely axle-box accelerometers, that are mounted on in-service trains and enable frequent, real-time monitoring of the railway infrastructure network. A Vold–Kalman filter is proposed for decomposing the signal into periodic wheel and track related excitation–response pair functions. We demonstrate that these components are in turn correlated to operational conditions, such as wheel out-of-roundness and the rail type. We further illustrate the relationship between the track stiffness, the measured wheel-rail forces and the sleeper passage amplitude, which can ultimately serve as an indicator for predictive track maintenance and prediction of track durability.

Enhancing railway track stiffness and sustainability through flowable dredged soil backfill

This study investigates flowable dredged soil backfill using air-foam technology and simulates a bridge approach structure under high-speed train loads. A comparison between conventional cement-treated soil (CTB) and innovative flowable dredged soil backfill solutions reveals crucial findings: Resilient modulus tests highlight the significant impact of cement and air foam, favoring mixtures with over 210 kg/m3 cement content and less than 10% air-foam, resulting in a resilient modulus of 354 MPa. Finite Element Method (FEM) simulations show CTB compliance with k1/k2 standards for all track options and the effectiveness of lightweight soil, especially Silty Soil (SM), in preventing critical k1/k2 increases. The lightweight soil exhibits superior performance through FEM analysis, settling only 3 mm after 800,000 cyclic train loads compared to nearly 5 mm in conventional CTB systems. This confirms the feasibility of lightweight dredged soil backfill in strengthening weak bridge approach foundations, enhancing railway track infrastructure sustainability and performance.

Evaluating the dynamic behavior of railway-bridge transition zone: numerical and field measurements

Short-span bridges are one of the most frequent infrastructures along railway tracks where railway track stiffness suddenly changes. The sudden variation in the vertical stiffness of railway tracks increases dynamic loads and causes numerous defects in ballasted railroads. Therefore, improving the dynamic performance of railway tracks can be conducted by constructing countermeasures along the transition zone. In this regard, the approach slab is a practical technique used in railway-bridge transition zones. As the dimensional shape of the approach slab plays a significant role in the dynamic response of transition zones, this study evaluated the effects of its main geometric parameters. A three-dimensional model of the railway portal bridge, including the approach slab, was built using the finite element method and analyzed by imposing moving wheel loads as a series of acting force points along rail elements. The model was validated with field-obtained results acquired through a laser/camera-based measuring technique. Then, some sensitivity analyses were performed to find optimized geometric dimensions of approach slabs to improve the dynamic behavior of railway-bridge transition zones. Obtained results of the geometrical sensitivity analysis show that when the geometrically optimized approach slab is used along the railway-bridge transition zone, the displacements of rail and ballast are decreased by 24% and 18%, respectively.

Evaluating railway track stiffness using axle box accelerations: A digital twin approach

While various train-borne techniques have been developed for measuring railway track stiffness, differentiating stiffness at different track layers remains a challenge. This study proposes a digital twin framework for the vehicle–track interaction system, which enables track stiffness evaluations based on axle box accelerations (ABA). The digital twin consists of a physics-based model, a model library and data-driven models. Compared to existing techniques, the proposed method simultaneously evaluates the stiffness of the railpad, sleeper and ballast layers at a sleeper spacing resolution, while being robust to varying track conditions, such as track irregularities and vehicle speeds. This is accomplished by employing a localized frequency-domain ABA feature capable of distinguishing between the characteristics of different track layers. Furthermore, track stiffness is evaluated in near real-time. This is achieved using a model library derived from physics-based simulations of a range of track conditions. Two data-driven models that can quickly select or interpolate model instances contained in the library are developed. During operation, the data-driven models use the measured ABA features as input and then infer the stiffness for the different track layers. The proposed method is applied to evaluate the track stiffness of a downscale test rig in a case study. The track stiffness evaluated by the proposed method is compared with that obtained through hammer tests and with the observations of the track component conditions. These comparisons show that the proposed method can capture the stiffness variations due to periodically fastened clamps and substructure misalignments at different speeds. In addition, the proposed method is demonstrated to be superior to the commonly used hammer test method for evaluating track stiffness under loaded conditions.

Warping deformation of the track slab and their influence on the interlayer stiffness and vibration transmission characteristics of the unit ballastless track

The unit ballastless track partially segments the concrete track bed in the longitudinal direction, and relieves the concrete temperature stress by isolating the upper and lower layers. However, the layer isolation leads to the incompatible deformation of the upper and lower track structures under the effect of the temperature gradient. A large temperature gradient on the track slab will cause local contact between layers, the contact area between layers will then decrease, thus leading to “stiffness softening” between layers. When the vehicle passes, the contact area between layers will gradually increase, which, in turn, leads to “stiffness hardening”. The analysis results show that the greater the design stiffness between layers, the more significant the “stiffness softening” effect will be under the temperature gradient. When k0 = 400 × 106 (N·m−1)·m−2 and Tg = 90 °C·m−1, the interlayer stiffness decreases by 88%.The simulation analysis results of the wheel-drop impact test show that under a positive temperature gradient, the peak value of rail vibration acceleration increases, and the peak value of the track slab and base plate vibration acceleration decreases. The greater the stiffness designed between layers, the more obvious the influence will be. With the increase of the positive temperature gradient, the vibration acceleration of the rail and the track slab will be reduced in the 1–30 Hz and 40–100 Hz frequency domains. With the increase of the negative temperature gradient, the vibration acceleration of the rail in the 4–10 Hz, 20–50 Hz frequency domains, and the vibration acceleration of the track slab in the 70–200 Hz frequency domains will be increased. A large positive temperature gradient inhibits the transmission of high-frequency vibrations above 40 Hz to the substructure, while a negative temperature gradient inhibits the transmission of low-frequency vibrations within 30 Hz and 70–200 Hz to the substructure. A positive temperature gradient is beneficial to restrain the downward transmission of low-frequency vibration. When k0 = 200 × 106 (N·m−1)·m−2, the low-frequency vibration transmission loss of the track slab to the base plate is close to 0 dB without temperature gradient, but the positive temperature gradient increases the transmission loss by about 10 dB, the greater the temperature gradient, the higher the transmission loss of the track slab to the base plate under high stiffness.

Influence of railway wheel tread damage on wheel–rail impact loads and the durability of wheelsets

Dynamic wheel–rail contact forces induced by a severe form of wheel tread damage have been measured by a wheel impact load detector during full-scale field tests at different vehicle speeds. Based on laser scanning, the measured three-dimensional damage geometry is employed in simulations of dynamic vehicle–track interaction to calibrate and verify a simulation model. The relation between the magnitude of the impact load and various operational parameters, such as vehicle speed, lateral position of wheel–rail contact, track stiffness and position of impact within a sleeper bay, is investigated. The calibrated model is later employed in simulations featuring other forms of tread damage; their effects on impact load and subsequent fatigue impact on bearings, wheel webs and subsurface initiated rolling contact fatigue of the wheel tread are assessed. The results quantify the effects of wheel tread defects and are valuable in a shift towards condition-based maintenance of running gear, and for general assessment of the severity of different types of railway wheel tread damage.

Monitoring and Expertise of Sections with a Sudden Change in Railway Track Stiffness—Transition Zones of Bridges

The subject of the research is the investigation of the behavior of railway tracks in places with a significant change in the stiffness of the track. These parts can be designed from various structural elements and their materials, and this mainly results in a height change of the track level during its operation. These transition zones are monitored and expertly examined to detect undesirable deformations of the geometrical position of the track caused by the trains running. The transition zones are at the points where the fixed track transitions to the classic track bed, in our case it is their combination with bridge structures, especially at their supports. In Slovakia, under the conditions of the Railways of the Slovak Republic, the issue is topical within the framework of the modernization of trans-European railway corridors. The results of experimental measurements and their analysis will provide relevant data for subsequent research solutions for their new numerical modelling, which will ensure a smooth passage through these points of change without height fluctuations, vibrations, and shocks from the wheels of train sets.

Performance Evaluation of a Combined Transition System in Slab-Ballasted Railway Track Using a Vehicle-Track-Substructure Interaction Model

Abrupt stiffness variations along the railway track may increase the geometrical and mechanical defects of railway lines. The conjunction points of a railway track with concrete and ballast pavements, which are called slab-ballasted track transitions, are one of the main areas where vertical track stiffness changes sharply. Therefore, the potential benefits of a combined transition system along the slab-ballasted transition, made of an approach slab and additional rails, are studied in this paper. For this purpose, a vehicle-track-substructure interaction model, which included three main segments of the railway track (slab track, transition zone, and ballasted track) was programmed based on the finite element method. A test line with the mentioned combined transition system was built to measure the railway track responses through field study. Then, the three-dimensional (3D) numerical model was validated using the results obtained from the experimental tests. Afterwards, a number of parametric studies were performed to analyze the dynamic responses of the combined transition zone. The results indicated that this type of transition system promotes a smoother stiffness transition between the slab track segment and the ballasted track segment by making the transition in three gradual steps. The track displacements in the analyzed case-study gradually increased by about 22%, 28%, and 34% along the combined transition zone in the junction points of the slab and ballasted tracks.