Ballast Stiffness Research Articles

Ballast stiffness estimation based on measurements during dynamic track stabilization

Ballast compaction with the Dynamic Track Stabilizer (DTS) is known to improve the lateral track resistance by increasing the stiffness of the ballast. This paper presents two approaches for estimating the strain dependent ballast shear modulus G based on measurements during dynamic track stabilization. One approach uses the Hardin equation with its enhancement for coarse-grained soils to estimate the small strain shear modulus for a given grain size distribution curve. Since different shear strains are induced on an observed sleeper (with fixed location) by a bypassing DTS, the measurement of ballast shear strains with accelerometers on the top and the bottom edge of the ballast layer yield shear modulus degradation curves G/Gmax. It is shown for data from a regular maintenance operation, that these shear modulus degradation curves are in accordance with previous research. For the second approach, a SDOF model for the track-ballast interaction under harmonic loading (caused by the dynamic track stabilizer) is developed. Influence lines are used to estimate the mass, the mass moment of inertia and the geometry of an equivalent machine foundation (with spring and dashpot coefficients according to the Hall analog). An optimization algorithm is used to fit the model response to the measured data from field tests with the DTS. The resulting shear moduli show plausible values for loose and compacted ballast conditions, which proves the potential of the presented method as a basis for a future system for Intelligent Compaction (IC) with the DTS.

Correlation Analysis of Railway Track Alignment and Ballast Stiffness: Comparing Frequency-Based and Machine Learning Algorithms

Correlation Analysis of Railway Track Alignment and Ballast Stiffness: Comparing Frequency-Based and Machine Learning Algorithms

Investigating the effect of ballast contamination in vertical and shear interlocking stiffness: Experimental and numerical study

The maintenance of railway tracks faces a significant challenge due to ballast contamination. This issue arises from the inevitable ingress of fine particles into the track structure through various means, such as fine sands, coal infiltration, aggregate breakage, and substructure pumping. Climate change exacerbates these conditions, leading to increased external debris contamination and the accelerated degradation of ballast aggregates. This contamination has major consequences, impacting track quality in terms of drainage capacity and dynamic behavior. As a response to this, the study focuses on assessing ballast contamination from sand infiltration, specifically evaluating vertical and shear interlocking stiffness through a dedicated experimental setup for ballast behavior analysis. Using materials from an actual track, contamination levels from clean to 30 % were simulated, and an empirical formulation of contaminated ballast stiffness was derived based on laboratory tests. Moreover, numerical sensitivity analyses were conducted to explore the impacts of ballast contamination on the dynamic behavior of track components. The findings indicate a significant increase in dynamic track responses up to a 30 % contamination level, based on gravimetric measurements, leading to substantial increases in maximum absolute accelerations of sleeper and ballast layer as well as exerted forces on the ballast layer by about 28 %, 21 %, and 46 %, respectively.

The Influence of an Unsupported Sleeper on the Vertical Bearing Characteristics of Heavy-Haul Railway Ballast.

In order to study the influence of an unsupported sleeper on the vertical bearing characteristics of heavy-haul railway ballast, a three-dimensional discrete element model (DEM) was established for a ballasted track, by removing ballast particles that come into contact with the bottom of the sleeper from the model to simulate the unsupported sleeper. Vertical bearing characteristics for ballast on different types of unsupported sleepers were studied. The results showed that an unsupported sleeper could reduce the bearing area of the ballast below the sleeper and reduce the number of ballast particles that were in contact. It could also lead to an increase in the maximum contact force between the particles, accelerating the deterioration of the particles (thus affecting the overall performance of the ballast) and reducing the vertical stiffness of the ballast. As the unsupported length and width increased, vertical stiffness gradually decreased. The vertical ballast stiffness for an unsupported sleeper was then used in a dynamic coupled vehicle/track model, and the effect of the unsupported sleeper on wheel/rail interaction was analyzed. Results showed that increasing the unsupported length and width leads to a decrease in the supporting force on the unsupported sleeper and to an increase in the supporting force on the adjacent sleepers.

Track‐Bridge Interaction: Influence of Transition Zone on the Stability of Continuous Welded Rail

AbstractRealization of high‐speed rail track demands continuous welded rail (CWR) to be laid on bridges without providing special expansion joints. In India, the existing rail bridges must be evaluated for their suitability for upgradation to CWR. CWR Inherently develops axial stress on account of the surrounding temperature changes. CWR in track‐bridge transition zone is subjected to additional stress and displacements as a result of track‐bridge interaction (TBI). Longitudinal thermal loading is a major source of rail stress and substructure forces due to TBI. Also, TBI results in accumulation of large compressive stress in transition zone. Further, the tamping effect in the transition zone by passing vehicles due to sudden change in vertical stiffness weakens the transition zone ballast. CWR is a slender steel element prone to buckling under large compressive stress. A numerical model is developed for track bridge interaction phenomenon in SAP2000 considering the aspect of CWR track buckling. In this study, the developed model is utilized to perform nonlinear buckling analysis to assess the influence of change in ballast stiffness on CWR stability in transition zone. Also, the influence of missing ballast contact raising from ballast subsidence locally in the transition zone was investigated. A single span simply supported steel bridge is considered. Longitudinal thermal loading is considered in this study. CWR supported on the ballasted track is considered. Material Nonlinearity associated with ballast is considered. Maintenance of CWR track is found to play a key role in track stability as the loose ballast or missing of ballast underneath the rail sleeper is to introduce discontinuity in CWR track support and reduces the critical buckling temperatures of the track considerably. Overall, this study contributes to the understanding of track‐bridge interaction and the stability of CWR in the transition zone.

Estimation of the dynamic stiffness of railway ballast over a wide frequency range using the discrete element method

Ballast is an integral part of railways, serving as a load transfer medium between the rails and the subgrade. In analytical modeling of track dynamics, ballast is idealized as a spring with constant stiffness at all excitation frequencies, which is a reasonable assumption for studying track dynamics at low frequencies up to 100 Hz. For modeling railway noise, the frequency dependency of ballast stiffness and damping at high frequencies is of utmost importance. Since ballast is a granular material whose properties depend on the packing, density and size distribution of the particles, the discrete element method is a promising tool for determining the frequency-dependent ballast stiffness. In the current work, a novel approach is presented to determine the frequency dependency of dynamic stiffness of the ballast used by the Swiss Federal Railways, using Discrete Element Method (DEM). First, a characterization of the Hertzian contact parameters required for modeling the ballast is performed. The effectiveness of the discrete element method for modeling the dynamic behavior of the ballast is evaluated by comparing the results obtained from our calculations with experimental results obtained under two different boundary conditions. The evaluated dynamic stiffness varies significantly with the frequency of excitation, especially above 100 Hz. The validated DEM model is then used to determine the effects of preloads on the dynamic stiffness.

Stiffness contributions of ballast in the context of dynamic analysis of short span railway bridges

Railway bridges are subjected to intensive dynamic loading. In structural calculations, the resulting response is estimated by dynamic calculations. As the basis of these calculations, the system's natural frequencies are to be numerically determined. Various studies have shown that a discrepancy between these measured natural frequencies and the numerical determination often occurs for short-frame bridges. In common practice, the ballast is assumed to be non-contributing to the global structural stiffness. In some cases, rheological models are developed to consider possible ballast stiffnesses based on small-scale model tests. The resulting spring-damper models are based on empirical values and are not directly related to the material behaviour of ballast.This paper discusses the ballast stiffness at the material level using relationships known from soil dynamics. The research shows that the material properties of the ballast can be determined in terms of stress and shear strain dependence. An equivalent ballast stiffness can be determined and considered in dynamic calculations for a known stress state and corresponding superstructure accelerations. The paper presents an approach for determining vertical and horizontal ballast stiffness according to shear strains and superstructure accelerations.This developed approach is validated by experimental tests using a small-scale bending beam and accompanying numerical calculations.Furthermore, a parameter study shows that the stiffness of the ballast does not contribute significantly to the global bending stiffness. Thus, the first bending natural frequency is hardly influenced by the ballast track.

Effect of rock strength on the degradation of ballast equipped with under sleeper pad

Railway ballast aggregates are the components that are dramatically influenced by train passage and lead to track degradation. The current study is conducted to determine the effects of ballast Uniaxial Compressive Strength (UCS) values of ballast parent intact rock core specimens and Under Sleeper Pad Bedding Modulus (USP-BM) on ballast abrasion and degradation and settlement through an extensive laboratory program. For this purpose, At the onset, to investigate the physical and mechanical characteristics of two ballast types, rock core specimens derived from parent intact rocks of Shahriar (S) and Kouhin (K) quarries were classified by implementing a series of standard laboratory tests and UCS test on prepared rock cores. Subsequently, the rock cores were categorized based on UCS values as hard rock core (159 MPa) and considerably hard rock core (285 MPa). Consequently, by adjusting the ballast grading curve according to the Australian TfNSW heavy rail network, various laboratory tests were carried out, an indication of the amount of fine-grained material with a sieve diameter of finer than 75 µm, clay lumps, bulk specific gravity, bulk density, Los Angeles abrasion, Micro-Deval abrasion, water absorption, and flakiness index. In the following, 18 laboratory experiments of the ballast box test were conducted in the absence and presence of soft and stiff USPs with USP-BM of 0.13 and 0.3 N/mm3 under 200,000 loading cycles. Finally, the results of ballast box tests were extracted in the index forms of settlement, estimation of correlation equation of ballast settlement, ballast breakage index (BBI), ballast damping ratio (DR), and ballast stiffness. Results of analysis demonstrate that by changing the USP type from stiff into soft for S ballast quarry type, the values of settlement, BBI and stiffness have declined by 16.6%, 7.9%, and 34.6%, respectively, while DR has increased by 114.66%. On the other hand, these reported percentages have changed due to the increased UCS value of Ballast parent intact rock core specimens in the K ballast quarry type. In the long run, the results delineate that the soft USP is most effective in controlling the ballast stiffness and settlement when focusing on the ballast rock cores' values of UCS.

Influence of the nonlinear behaviour of ballast on the dynamics of simply supported railway bridges

In this work, the vertical motion of a simply supported railway bridge which is subjected to the circulation of high speed trains was studied. A system consisting of two-layer beam was considered to model the dynamics of the bridge structure. The upper beam represents the rails with the sleepers and the lower beam the bridge deck. These two beams are coupled through distributed nonlinear springs that model the ballast action. The characteristics of these elements were identified from experimental measurements performed on real rail track. Considering the circulation of high speed train at given velocity, the influence of the nonlinear stiffness of the ballasted track on the response of the bridge system was analyzed. This was achieved by using the Galerkin method and the Runge-Kutta scheme to solve numerically the nonlinear partial differential equations governing the motion of the two beams. It was found that the nonlinear behaviour of the ballast affects notably the dynamics of the bridge, especially when the ballast stiffness is low. The proposed modelling enables to get more understanding regarding the vertical dynamics of ballasted track bridge in high speed line.

Fast and robust identification of railway track stiffness from simple field measurement

We propose to combine a physics-based finite element (FE) track model and a data-driven Gaussian process regression (GPR) model to directly infer railpad and ballast stiffness from measured frequency response functions (FRF) by field hammer tests. Conventionally, only the rail resonance and full track resonance are used as the FRF features to identify track stiffness. In this paper, eleven features, including sleeper resonances, from a single FRF curve are selected as the predictors of the GPR. To deal with incomplete measurements and uncertainties in the FRF features, we train multiple candidate GPR models with different features, kernels and training sets. Predictions by the candidate models are fused using a weighted Product of Experts method that automatically filters out unreliable predictions. We compare the performance of the proposed method with a model updating method using the particle swam optimization (PSO) on two synthesis datasets in a wide range of scenarios. The results show that the enriched features and the proposed fusion strategy can effectively reduce prediction errors. In the worst-case scenario with only three features and 5% injected noise, the average prediction errors for the railpad and ballast stiffness are approximately 12% and 6%, outperforming the PSO by about 6% and 3%, respectively. Moreover, the method enables fast predictions for large datasets. The predictions for 400 samples takes only approximately 10 s compared with 40 min using the PSO. Finally, a field application example shows that the proposed method is capable of extracting the stiffness values using a simple setup, i.e., with only one accelerometer and one impact location.

Time-domain Markov chain Monte Carlo–based Bayesian damage detection of ballasted tracks using nonlinear ballast stiffness model

This article reports the development of a methodology for detecting ballast damage under a sleeper based on measured sleeper vibration following the Bayesian statistical system identification framework. To ensure the methodology is applicable under large amplitude vibration of the sleeper (e.g. under trainload), the nonlinear stress–strain behavior of railway ballast is considered. This, on one hand, significantly reduces the problem of modeling error, but, on the other hand, increases the number of uncertain model parameters. The uncertainty associated with the identified model parameters of the rail–sleeper–ballast system may be very high. To overcome this difficulty, the Markov chain Monte Carlo–based Bayesian model updating is adopted in the proposed methodology for the approximation of the posterior probability density function of uncertain model parameters. Owing to the nonlinear behavior of the system, the model updating is performed in the time domain instead of the modal domain. The applicability of the proposed damage detection methodology was first verified numerically using simulated impact hammer test data in two damaged cases perturbed with Gaussian white noise. Second, impact hammer tests of in situ sleepers in the full-scale in-door ballasted track test panel were carried out to collect data for the experimental verification of the proposed methodology. Artificial ballast damage was simulated under the target concrete sleeper by replacing normal-sized ballast particles (∼60 mm) by small-sized ballast particles (∼15 mm). The proposed methodology successfully identified the location and severity of ballast damage under the sleeper. From the calculated posterior marginal probability density functions of model parameters, one can quantify the uncertainties associated with the damage detection results. The proposed methodology is an essential step in the development of a long-term railway track health monitoring system utilizing train-induced vibration.

Qualitative Prediction Model for Dynamic Behavior of Ballasted Tracks

Theoretical, experimental, analytical, and statistical evaluations were performed to predict and assess the dynamic behavior of a ballasted track, such as the track support stiffness, track impact factor, or dynamic wheel–rail forces. Field measurements were then performed to evaluate the dynamic behavior of the ballasted track and its components. A qualitative prediction model was then developed to predict and assess track performance as a function of dynamic wheel-rail force and variation in track support stiffness. The developed two-degree-of-freedom dynamic track model can define the rail pad and ballast stiffness ranges based on designed and measured values. Using the proposed model, qualitative analysis results are presented as a discrete space of various track responses and parameters, rather than as single values. The proposed model was then validated using field measurements, which demonstrated that the proposed model predicted the vertical rail displacement and rail bending stress within approximately 2–5% of the obtained field measurements. Overall, the developed qualitative prediction model allows the dynamic response of in-service ballasted tracks to be estimated as a function of the rail pad and ballast stiffness using only a simple field measurement.

Effect of deconstructed tire under sleeper pad on railway ballast degradation under cyclic loading

In this paper, the effect of different thicknesses of Deconstructed Tires Under Sleeper Pads (DT-USP) and different Unconfined Compressive Strength (UCS) values of mother rocks of ballast aggregates were studied in the degradation of railway ballast. For this purpose, in the first step, both static and dynamic bedding modulus of DT-USP's were extracted in the laboratory according to DIN standard requirements. In continuation, the physical and mechanical properties of the three different ballast types taken from Shahriar, Anjilavand, and Kouhin quarries in Iran were obtained via a series of standard lab tests. The UCS of core specimens taken from the mother rocks of the mentioned queries were ranked as low (159 MPa), medium (216 MPA), and high (285 MPa) respectively. Finally, 36 ballast box test experiments with and without the presence of DT-USPs in three thicknesses of 7, 11, and 13 mm were carried out and their results were compared up to 200,000 loading cycles to investigate the cyclic behavior of ballast samples. Experiment results were elicited in the form of settlement, Hardin breakage index (Br), ballast stiffness, and ballast Damping Ratio (DR). The results demonstrate for ballast of Shahriar quarry by increasing of the DT-USP's thickness from 7 to 13 mm, settlement, Br, and stiffness have decreased by 38.4%, 6.9%, and 80.5% respectively and DR has increased by 199.2% while these reported percentages, i.e. settlement, Br, and Stiffness have decreased and DR has increased after strengthening the ballast mother rock in the cases of Anjilavand and Kouhin quarries. On the other side, based on the achieved results for all three categories of ballast strengths, the DT-USP with 11 mm thickness has shown the most suitable performance.

Uncertainty analysis of track degradation at railway turnouts aided by a multi-body simulation software

Railway turnouts are elements exposed to an accelerated track degradation when compared to plain line track. The particular and complex wheel/rail contact characteristics in railway turnouts make the contact forces acting on the wheel/rail interface particularly high. As a consequence of the train/track interaction force magnitude, track degradation is more accelerated here, having a big impact on the general costs used for track maintenance. The contact phenomenon has a stochastic nature due to the great number of variables involved in the interaction problem. Moreover, the uncertainty levels associated with each of the aforementioned variables require in-depth stochastic analyses that reflect the real variability of the parameters which characterize the dynamic interaction and consequently the degradation problem at railway turnouts. The scope of this work is to perform a probabilistic assessment of a railway switch and crossing, aided by the multi-body simulation software, GENSYS. The critical track components with a major impact on track degradation are identified by means of a sensitivity assessment based on the elementary effects method while the uncertainty is assessed by using the Monte Carlo simulation method. The proposed methodology used to evaluate the probabilistic problem is a suitable approach to identify the railpad stiffness, the mass of the bogie, the damping value of the primary suspension and the ballast stiffness, being the critical parameters with the highest impact in the uncertainty analysis of track degradation at turnouts.

Investigating the Effect of Some Train and Track Parameters on Contact-impact Forces in the Vicinity of a Rail Breakage

Broken rails or welds are the main causes of derailment in railway networks. Therefore, a wheel-rail interaction model, which precisely estimates contact-impact forces in the presence of broken rails, can have a significant effect on derailment risk reduction. This paper attempts to present contact-impact forces in the vicinity of broken rails by employing a detailed 3D finite element model. The model is verified using a field test carried out on a ballasted railway track. Effects of train speed, gap length, axle load and railpad and ballast characteristics are studied on rail-wheel contact forces as well as on railpad and ballast forces. Results suggest that increasing the train speed from 60 km/h to 110 km/h would increase dynamic impact force from 2.46 to 4.11. It is also observed that increasing axle load results in an increase in the wheel-rail impact forces and in railpad and ballast forces, while leading to a reduced dynamic impact factor. Furthermore, investigating the effect of the track parameters demonstrates that ballast stiffness is the most important characteristic of the track, which has a reverse effect on dynamic impact forces. Moreover, unloading length increase and consequently derailment risk increase is highly sensitive to increasing train speed.

Stiffness and strength of structural layers from cohesionless material

The deformation modulus and permissible stress are two independent parameters that depict the carrying capacity of foundations, including earthworks and ballast layer. Nevertheless, while designing the track superstructure or controlling its state, they are considered separate to each other, even though they are terms of the same measure. The scientific problem is due to the practical necessity of unified building rules and standards. The carrying capacity of earthworks and foundations is regulated with standards based both on deformation and on stress criteria, which are not related to each other. This plays particularly important role for railway ballast layer, as an intermediate between the solids and soil. The objective of the present research is to estimate the relationship between deformation modulus and the strength of ballast layer. An overview of modern approaches according to the relation between the stiffness, deformation modulus, elasticity and strength of soils and crushed stone is done. The strength of ballast layer is considered depending on the experimental test: the direct shear test, compressive strength in the uniaxial or biaxial stress state. Load transfer model in crushed stone is proposed. The load transfer angle and cone of loading distribution are determined based on the load transfer and compressive strength models. The relation between deformation modulus and strength is derived from two simple laboratory experiments with cohesionless ballast material. The experiment tests have shown that the ballast stiffness as well as its strength are influenced with the support stress. The measurement of elastic and residual settlements for the different support stress values enables to determine the relation. It can be potentially used for the development of methods for the ballast compaction control, unification of construction norms. The research result should be considered as an approach for unification of two different ways to reflect the carrying capacity of ballast layer.

Dynamic Deflection of a Railroad Sleeper from the Coupled Measurements of Acceleration and Strain.

Dynamic deflection of a railroad sleeper works as an indicator of ballast stiffness, reflecting the health conditions of a ballast track. However, difficulty exists in measuring dynamic deflection of a railroad sleeper by conventional deflection transducers such as a linear variable differential transformer (LVDT) or a potentiometer. This is because a fixed reference point is unattainable due to ground vibrations during train passage. In this paper, a patented signal processing technique for evaluation of pseudo-deflection is presented to recover dynamic deflection of a railroad sleeper using a coupled measurement of acceleration and strain at the concrete sleeper. The presented technique combines high-frequency deflections calculated from double integration of acceleration and low-frequency deflections determined from strains. Validity of the combined deflections was shown by the deflections measured with a camera target on a concrete sleeper, captured by a high-resolution DSLR camera with superb video capturing features and processed by computer vision techniques, such as Canny edge detection and Blob analysis.

Development of condition‐based tamping process in railway engineering

AbstractBallast, rails and sleepers form a quasi‐elastic track system. When the deformations exceed the elastic limit of the system and the track is no longer lying in its correct position, precautions have to be taken. During a technical track examination several parameters are measured. Should the operational tolerance values of these parameters be exceeded, track maintenance needs to be conducted. Track maintenance includes levelling, lifting, lining and tamping of the track, which is performed by a tamping machine, where the tamping tines penetrate the ballast and compact it beneath the sleeper. For the purpose of this research project, a tamping machine was equipped with a number of strategically positioned sensors in order to perform the in‐situ measurements required to describe the interaction of the tamping tines with the ballast and its compaction beneath the sleeper. With a special emphasis on the energy transferred into the ballast and alteration of ballast stiffness during compaction, conclusions concerning efficiency of the tamping process in different ballast conditions are made and presented.

Bayesian ballast damage detection utilizing a modified evolutionary algorithm

This paper reports the development of a theoretically rigorous method for permanent way engineers to assess the condition of railway ballast under a concrete sleeper with the potential to be extended to a smart system for long-term health monitoring of railway ballast. Owing to the uncertainties induced by the problems of modeling error and measurement noise, the Bayesian approach was followed in the development. After the selection of the most plausible model class for describing the damage status of the rail-sleeper-ballast system, Bayesian model updating is adopted to calculate the posterior PDF of the ballast stiffness at various regions under the sleeper. An obvious drop in ballast stiffness at a region under the sleeper is an evidence of ballast damage. In model updating, the model that can minimize the discrepancy between the measured and model-predicted modal parameters can be considered as the most probable model for calculating the posterior PDF under the Bayesian framework. To address the problems of non-uniqueness and local minima in the model updating process, a two-stage hybrid optimization method was developed. The modified evolutionary algorithm was developed in the first stage to identify the important regions in the parameter space and resulting in a set of initial trials for deterministic optimization to locate all most probable models in the second stage. The proposed methodology was numerically and experimentally verified. Using the identified model, a series of comprehensive numerical case studies was carried out to investigate the effects of data quantity and quality on the results of ballast damage detection. Difficulties to be overcome before the proposed method can be extended to a long-term ballast monitoring system are discussed in the conclusion.

Railway ballast damage detection by Markov chain Monte Carlo-based Bayesian method

This article reports the development of a Bayesian method for assessing the damage status of railway ballast under a concrete sleeper based on vibration data of the in situ sleeper. One of the important contributions of the proposed method is to describe the variation of stiffness distribution of ballast using Lagrange polynomial, for which the order of the polynomial is decided by the Bayesian approach. The probability of various orders of polynomial conditional on a given set of measured vibration data is calculated. The order of polynomial with the highest probability is selected as the most plausible order and used for updating the ballast stiffness distribution. Due to the uncertain nature of railway ballast, the corresponding model updating problem is usually unidentifiable. To ensure the applicability of the proposed method even in unidentifiable cases, a computational efficient Markov chain Monte Carlo–based Bayesian method was employed in the proposed method for generating a set of samples in the important region of parameter space to approximate the posterior (updated) probability density function of ballast stiffness. The proposed ballast damage detection method was verified with roving hammer test data from a segment of full-scale ballasted track. The experimental verification results positively show the potential of the proposed method in ballast damage detection.