Prova de Dinâmica

Considere a barra de seção transversal retangular Cisalhamento Um material de construção está submetido a um esforço de cisalhamento quando sofre a ação de uma força cortante V A tensão de cisalhamento é a razão entre a carga cisalhante ou força cortante e a área cisalhada Deformação no cisalhamento Supondo uma seção transversal quadrado sob a ação de forças de cisalhamento O ponto C deslocase para C e o ponto D para D 𝛾 gama 𝜏 68 Lei de Hooke 𝜏 tensão de cisalhamento pa G módulo de elasticidade transversal Pa 𝛾 ângulo de distorção rad 𝜏máx 𝜎x 𝜎y 22 𝜏xy2 𝜏máx 50 10 22 402 𝜏máx 50mpa 𝜎méd 𝜎x 𝜎y 2 50 10 2 20mpa Orientação 𝜃c tg 2𝜃c 𝜎x 𝜎y 2𝜏xy 50 10 240 𝜃c 184 𝜎y 10mpa 𝜎x 50 𝜏xy 40mpa 𝜏máx 50mpa 𝜎méd 20mpa 𝜏máx 𝜏x 70mpa 𝜏máx p 50mpa 𝜎min 𝜎y 30mpa 2𝜃p 53 𝜏xy 40 08082025 Dinâmica Estado uniaxial de tensão e deformação Lei de Hooke Estado duplo de tensão e deformação círculo de MoLar Estado Geral de tensões estado triplo Círculo de MoLar Critérios de resistência Material dúctil e material frágil Estabilidade de estruturas colunas ou pilares Estrutura espacial Bibliografia Beer Johnson Resistência dos Materiais Mibbeler Resistência dos Materiais Popov Resistência dos Materiais Popov mecânica dos sólidos Tensão normal de tração Aplicando se uma carga força P em uma barra na condição estática ela se deforma até que haja equilíbrio entre a carga externa aplicada e as forças internas resistentes Pi L comprimento inicial da barra A área da seção transversal E módulo de elasticidade S alongamento P carga externa aplicada Fazendo um corte imaginário na seção mn teremos uma distribuição uniforme e contínua das forças internas Dividindo a seção transversal por unidade de área e chamando de tensão σ a somatória dessas forças pela unidade de área teremos σ PA σ sigma ΔLL delta ε epsilon Roz mé 0296 MPa Gmáx σ Gméo K 0358 0296 0653 MPa Gmin σ Gméo P 0358 0296 0062 MPa G1 0200 MPa G1 0011 MPa G y 0258MPa σ 0653 MPa 3045 A área da seção transversal Ao área da seção oblíqua P carga axial aplicada f força normal perpendicular ao plano inclinado V força de cisalhamento paralela ao plano inclinado θ ângulo de inclinação do plano em relação a seção transversal σ tensão normal a força oblíqua τ tensão e cisalhamento na força oblíqua f Pcosθ V Psenθ A Pcosθ σ FAo Pcosθ Acosθ PA cos²θ a τ VAo Psenθ Acosθ PA senθ cosθ b Da equação a a tensão normal σ é máxima para θ 0 cos0 1 seção perpendicular ao eixo da barra portanto máxima ao eixo x Para θ 0 σmáx PA Para θ 90 a tensão normal será zero Estado uniaxial duplo e triplo de tensões Estado de tensão em um ponto material é o conjunto de todas as tensões ocorrendo nos planos passando pelo corpo Estado Uniaxial ou linear Estado plano Estado triplo 05092025 A barra mostrada está submetida a uma força P 6fON e as dimensões dadas nas figura sendo o diametro d 30mm Determinar A Tensão Normal e de cisalhamento em um elemento H b Os planos principais op e oc e as tensões principais óx e óy Fazendo um recorte em H Para o estado plano determinar a Os planos principais orientação Óp b As tensões principais Óx e Óy c A tensão de cisalhamento máxima T máx e sua orientação tO c Óx 50 mPa ót 10mPa Óxy 40mPa a tg 20p 26xy 240 20p 5313 ç 8p 265 Ómáx Óx Óy Óx ty cos 20p Óxy sem 20p 2 2 r Óx 50 10 50 10 cos 5313 40 sem 5313 2 2 Óx 70 mPa Ómin Óy Óx Óy Óx Óy cos 20p 0 xy sem 20p 2 2 Óy 50 10 50 10 cos 5313 40 sem 5313 20 2 Óy 30mPa Óx Óy Óx Óy as tensões são invariantes A review on railway track buckling prediction methods Dan Agustin a Qing Wu a Chayut Ngamkhanong bc a Centre for Railway Engineering Central Queensland University Rockhampton Australia b Advanced Railway Infrastructure Innovation and Systems Engineering ARIISE Research Unit Department of Civil Engineering Faculty of Engineering Chulalongkorn University Bangkok Thailand c GreenTech Nexus Research Center for Sustainable Construction Innovation Faculty of Engineering Chulalongkorn University Bangkok Thailand A R T I C L E I N F O Keywords Buckling Railway Dynamics Maintenance Safety A B S T R A C T Railway track buckling has long been a significant challenge in railway track engineering Various methods have been developed to predict andor prevent this phenomenon with the aim of enhancing safety efficiency and sustainability of railway operations This review discusses several relevant aspects including the theoretical foundations in understanding railway track buckling behaviour techniques for measuring and evaluating critical track parameters and maintenance strategies aimed at optimising the structural stability of the track Despite the progress in these approaches in the prediction and prevention of track buckling challenges remain due to the complex dynamics involved in this phenomenon field tests can be dangerous and impractical to scale analytical or numerical methods have assumptions and can be computationally inefficient An emerging trend in railway track buckling prediction is the integration of machine learning ML and artificial intelligence AI in acceler ating predictions of buckling risks Addressing these challenges can enhance the predictive capabilities of advanced track buckling prediction methods improving railway safety and efficiency 1 Introduction Track buckling presents a significant safety challenge in the rail in dustry Such phenomenon can lead to serious operational disruptions for entire rail networks Railway track buckling occurs as a sudden lateral displacement of railway tracks due to excessive longitudinal compres sive forces which may come from different sources such as thermal expansion external dynamic mechanical loads or suboptimal track stability Understanding these root causes is crucial for the prevention of this failure phenomenon Extensive research and efforts have been focused on the maintenance of the track structure primarily on under standing the dynamic response of railway tracks under the influence of various static and dynamic conditions This better understanding of track system behaviour leads to the development of models that quan tify measure and evaluate track system parameters This knowledge assists in creating and implementing informed maintenance and pre vention strategies against track buckling Due to the abrupt nature of track buckling its progression can prove to be difficult to stop once it starts Despite efforts to understand the track buckling phenomenon strategies in managing track stability are mostly preventive dealing with inspections or routine servicing of tracks to ensure good system condition These maintenance procedures can be disruptive to railway operations and be costly to perform Furthermore some of these actions may be unnecessary for tracks still in good condition Therefore evolving maintenance strategies from pre ventive to predictive is essential to optimise the management of track stability particularly in preventing track buckling During extreme heat train operators often impose speed restrictions to reduce the risk of track buckling These restrictions are typically part of heat action plans acti vated when rail temperatures approach critical thresholds While essential for safety speed restrictions can lead to delays and operational disruptions impacting both passenger and freight services In regions like Australia the significance of track buckling is heightened by envi ronmental and operational challenges Numerous derailment incidents in recent years according to the 678910 demonstrate the prevalence and severity of this issue highlighting not only the financial impact but also the risks to safety According to the Office of the National Rail Safety Regulator 79 derailment incidents remain a critical concern with 42 runniunciteng line derailments for freight trains recorded in 20222023 equating to a rate of 049 per million kilometers of track coupled with two serious and five minor injuries from these derailments Moreover the financial implications of these incidents are Corresponding author Email address qwucqueduau Q Wu Contents lists available at ScienceDirect Construction and Building Materials journal homepage wwwelseviercomlocateconbuildmat httpsdoiorg101016jconbuildmat2025140295 Received 3 December 2024 Received in revised form 22 January 2025 Accepted 3 February 2025 Construction and Building Materials 466 2025 140295 Available online 8 February 2025 09500618 2025 The Authors Published by Elsevier Ltd This is an open access article under the CC BY license httpcreativecommonsorglicensesby40 significant The broader annual economic burden of railway safety in cidents in Australia including derailments was estimated to be approximately 3601 million during the period 20072015 98 The ONRSR guidelines also recommend a precautionary approach to miti gate such risks adopting a Value of Statistical Life VoSL estimate of 57 million based on the research by the Office of Impact Analysis in 2024 78 This estimate is critical for duty holders conducting costbenefit analyses or risk assessments to evaluate the economic and safety implications of safety measures By integrating such safety con siderations and financial analyses into infrastructure decisions railway operators can better address the challenges posed by track buckling and minimise the associated risks In this paper a review of the current state of track buckling research is presented with its structure outlined in Fig 1 The primary objective of this review is to provide a deeper understanding of railway track buckling by consolidating and analysing advancements in the field The first part highlights the theoretical foundations of track buckling focusing on mechanisms driving this phenomenon This includes buck ling due to thermal expansion under extreme temperatures and the compounded effects of vehicle movement on track stability The second part examines the evolution of track models used for buckling assess ments exploring how railway engineers measure quantify and evaluate critical track parameters influencing track buckling The third part de tails the critical track system parameters identified in recent studies emphasising their role in both predicting and preventing buckling Lastly the fourth part discusses the application of advanced computa tional techniques particularly machine learning in improving the ac curacy and efficiency of buckling prediction By addressing these aspects this review aims to identify and highlight the gaps in existing research for further development of robust track buckling prediction methods and contribute to the design of safer and more reliable railway systems To achieve these objectives this review addresses several key ques tions What are the primary mechanisms driving railway track buckling and how do they vary under different operational and environmental conditions A followup to this is identifying the critical track parame ters that exert the greatest influence on buckling risk and how can they be optimized to enhance track stability Moreover how have track buckling evaluation models evolved over time and what are their cur rent limitations in representing realworld track behaviours Finally how are advanced computational methods such as machine learning currently being applied in railway engineering and how can they be further extended to enhance buckling prediction accuracy and support proactive maintenance strategies for track stability evaluation By framing the review around these questions the paper aims to provide actionable insights and guide future research efforts in improving track stability and resilience This review is framed within the context of understanding the development of track buckling prediction methods By examining the literature the review aims to highlight the transition from theoretical foundations to practical applications in track stability management and current trends such as the use of AI and machine learning for buckling prediction Methods and findings from previous studies are analysed to assess their potential for predicting track buckling and to identify areas for improvement in current approaches This review underscores the importance of integrating advanced research into maintenance practices and highlights the necessity for continuous innovation in predictive maintenance strategies to ensure the reliability and safety of railway networks and systems 2 Track buckling mechanism Track buckling is characterised by the sudden misalignment of tracks primarily due to high temperatures suboptimal track stability and the influence of vehicle dynamics 43464585 This phenomenon occurs when high compressive forces in the longitudinal direction of the rails induce movement in the lateral direction where resistance to movement is generally lower compared to the longitudinal and vertical directions This is mostly prevalent in continuous welded rails CWR in which the use of continuous rails inhibits rail expansion leading to the accumu lation of compressive forces A basic diagram of the buckling phenom enon is shown in Fig 2 showing track lateral buckling mode configurations for CWR The different buckling modes typically resemble a sine wave and are heavily influenced by the shape of the initial misalignments present in the track Tangent tracks generally buckle in a symmetric mode forming three halfwaves while curved tracks tend to buckle in the symmetric mode with one halfwave 4645 In the postbuckling configuration rails outside the buckling zone exhibit only longitudinal displacements for tangent tracks or radial movements for curved tracks These dis placements allow the rails to extend and pull into the buckled zone providing the additional rail length necessary for the buckle to form P αEAΔT 1 An expression of the compressive forces as a function of temperature is expressed in Eq 1 Here P denotes the compressive force α is the coefficient of thermal expansion of the rail material E is the Youngs modulus A is the rails crosssectional area and ΔT is the change in the rails temperature with respect to the rails stressfree or neutral tem perature It is important to note that Eq 1 provides a simplified repre sentation of the compression experienced by rails due to temperature In practice the compressive force decreases along the length of the rails particularly near the buckled zone as the large lateral displacements allow for rail extension which in turn releases some of the compressive load 45 The extent of lateral deflection during buckling can render a section of the track unfit for vehicle passage at recommended speeds necessi tating emergency measures such as speed reduction or temporary track Fig 1 Review Structure D Agustin et al Construction and Building Materials 466 2025 140295 2 closure to perform corrective maintenance measures These reactive actions are highly disruptive and often leave entire track sections out of service resulting in costs significantly higher than those of routine maintenance and inspections Implementing preventive measures can help avoid such corrective actions and provide a more costeffective approach to managing track stability The buckling behaviour of railway tracks is primarily influenced by compressive forces within the rails which arise due to thermal expan sion or mechanical loads from passing vehicles Under ideal conditions a wellconstrained track system should resist both longitudinal and lateral movements of the rails caused by these forces However when the compressive forces exceed the tracks structural resistance including its lateral resistance lateral deflections occur Lateral resistance is a critical factor in countering these compressive forces and lateral de flections maintaining track stability when it is insufficient the track becomes more susceptible to buckling This phenomenon can be un derstood by examining the relationship between track temperature and lateral displacement as shown in Fig 3a and b As the temperature rises to a critical level lateral displacement increases progressively until the track reaches an unstable equilibrium state marked by ΔTMax and is also known as the bifurcation point At this critical temperature the track may suddenly buckle into a new lateral position as indicated by the dashed arrowed line Any further increase in temperature beyond ΔTMax will result in inevitable and further lateral deflection The dotted line represents the uncertain buckling region corre sponding to the temperature range within which the track is at risk of snapthrough buckling and is defined as the temperature range between ΔTMax and ΔTmin Within this range any additional energy input into the track whether from abrupt temperature increases or mechanical loads can trigger an uncontrollable and sudden increase in lateral displace ment Fig 3b shows an example of this scenario in which the track experiences a premature buckle prior to reaching the critical tempera ture Fig 3c illustrates the related axial load distribution of the rails after buckling has occurred After reaching the maximum critical temperature or load the axial force sharply decreases but stabilises at the minimum critical axial force required for buckling Fig 3 illustrates the buckling response curves for a standard track where the difference between the minimum and maximum critical temperatures is significant offering a safety margin prior to buckling However the temperature range defining the unstable region as shown in Fig 4a is significantly influ enced by track conditions such as weakened ballast resistance poor alignment or material nonlinearities These factors can lower the crit ical temperature resulting in a narrower unstable region for buckling In a worstcase scenario as illustrated in Fig 4b the buckling response curve for a weakened track show that ΔTMax and ΔTmin effectively converge This results in a single critical temperature beyond which lateral deflection increases progressively and uncontrollably while the rail axial force decreases gradually It should be noted that the buckling temperature for snapthrough buckling is usually higher than that for progressive buckling Addi tionally it is interesting to point out that during the prebuckling stage the track may gradually experience significant lateral displacement as the temperature increases This can clearly induce track misalignment which may escalate into more severe buckling phenomena Further more it is difficult to detect the critical temperature for progressive buckling In this case monitoring the rail compressive force can be beneficial as the critical temperature can be interpreted from the point where the compressive force reaches its maximum and then begins to progressively reduce as the lateral deflection continuously increases Describing track buckling using this relationship has been used extensively as the foundation of most studies of this failure phenome non helping in the establishment of different buckling theories Kerr 43 introduced the concept of the unstable region in the track where there are large lateral displacements and the adjacent region referred Fig 2 Lateral Track Buckling Modes as adapted from Kish et al 45 Fig 3 Buckling Response Curves illustrating snapthrough behavior a Snapthrough buckling upon reaching the critical temperature b Premature snapthrough buckling before the critical temperature c Temperature change vs rail axial force adapted from 45 and 111 D Agustin et al Construction and Building Materials 466 2025 140295 3 to as the adjoining zone where deformations are only axial The dis tribution of the rail axial force along the track is illustrated in Fig 5 This concept is supported by his track beam model wherein analytical formulations are used to define the buckling phenomenon The model is simple enough to provide a method to conceptualise buckling but it does not account for other track parameters such as rotational stiffness provided by the pad fasteners and only assumed buckling shapes for the unstable region limiting its practical applicability Kerrs work focused mainly on obtaining temperaturebased lateral displacement curves corresponding to the elastic response of the track like the one shown in Fig 3a and Fig 4a Kerr concluded that while lateral misalignment in the track has little influence on the safe tem perature which is the temperature range below ΔTmin it can still affect the buckling temperature or ΔTMax Kish and Samavedams research 1979 1985 expanded on Kerrs research by incorporating track geometry imperfections and other typical track parameters of American railway tracks into Kerrs track beam model This improved the evaluation of track buckling by the help of Fourier series to consider the nonlinearity of the tracks lateral resistance which has been assumed constant in Kerrs analysis In these studies the track parameters included in the buckling analysis has been expanded greatly accounting for rail material properties track cur vature ballast strength sleeperballast friction torsional and longitu dinal track resistance Subsequent works by both Kish and Samavedam 46 have included the influence of dynamic train loads into their buckling theory which adds to the accuracy of buckling evaluations for preventive and predictive safety considerations These models analyse the added effect of vehicle load variations on track stability analysing how these dynamic forces interact with the track structure and contribute to the risk of track buckling In particular these studies have shown how train movement induces shifts in the track structure resulting in a reduction of lateral stability and amplifying the likelihood of buckling Understanding the mechanisms behind track buckling is crucial for its accurate prediction and prevention Although the representation in Figs 3 and 4 simplifies buckling as a relationship between lateral deflection and temperature the actual phenomenon is far more com plex involving a wide array of track system variables and dynamic in teractions These interactions stem from environmental systemic and dynamic sources making it challenging to measure quantify and evaluate buckling risks effectively Recognising how various track sys tem variables such as rail temperature ballast condition sleeper prop erties and other track parameters affect track buckling is particularly important This knowledge equips railway engineers with the ability to identify critical thresholds develop strategies to anticipate potential buckling failures and ensure safe and efficient railway operations 3 Track models used for buckling assessments To address the complexities involved in the evaluation of buckling risks track models have been developed to represent tracks and capture as much information about the system as possible These models enable railway engineers to assess buckling risks thus predicting and pre venting any safety concerns while considering critical track system variables This helps in the implementation of targeted interventions to address issues found in the track To preface this section a simple track structure is presented in Fig 6 The simplest way to analyse track buckling is to consider the rails as a pair of statically equivalent beams resting on elastic foundations as shown in Fig 6 Most research in open literature have proposed models that are mostly numerical in nature and can be categorised into beam on elastic foundation BOEF models or beam on discrete supports BODS models as shown in the figure This abstraction allows researchers to isolate and examine the behaviour of the railsleeper system under various conditions while still accounting for the essential role of the supporting layers On the other hand other studies emphasise the importance of the ballast and underlying structure particularly in relation to their effects on track lateral resistance These investigations Fig 4 Buckling Response Curves for Buckling a Lateral Deflection vs Temperature Change for a weakened track b Progressive buckling for weak tracks and c Temperature Change vs Rail Axial Force as adapted from Kish et al 45 and Wongkaew et al 111 Fig 5 Reduction of rail axial force along the track as adapted from Kerr 43 Fig 6 Simple numerical models to describe rails as adapted from Esmaeili and Noghabi 22 D Agustin et al Construction and Building Materials 466 2025 140295 4 delve deeper into how the properties and conditions of the ballast and subballast influence the tracks ability to resist lateral forces which is crucial for maintaining track stability and alignment under extreme loads 31 Buckling analytical models Analytically tracks can be evaluated using complex differential equations to assess track buckling behaviour This approach primarily characterises buckling behaviour through the influence of temperature as shown in Figs 3 and 4 and discussed in previous sections In this simplified and idealised representation the temperature distribution along the rail is assumed to be homogeneous and can be expressed with the formula in Eq 2 σCR Eα TN TCR 2 Here σCR represents the critical longitudinal stress which depends on the boundary conditions of the rail column E is the Youngs modulus and α is the coefficient of thermal expansion of the rail and is typically known through design specifications TCR and TN are the critical Euler temperature and neutral temperature where the rail stress is at 0 respectively This formulation can be extended to relate the temperature to the critical buckling load through the application of Eulers buckling load equation σCR PCR A π2EI KL2 3 where PCR represents the critical buckling load the longitudinal forces acting on the rails A is the crosssectional area of the rail I is the second moment of area of the rails crosssection K is the effective length factor that depends on the boundary conditions of the rail column and L is the unsupported length of the rail under consideration This equation helps illustrate the fundamental principles of buckling theory which can be effectively applied to gain a deeper understanding of more complex systems in railway track In railway tracks the support conditions depend on several factors including the fastening system sleeper types and other track components It is important to note that Eqs 2 and 3 can be used to derive the same formulation as Eq 1 P αEAΔT demonstrating consistency among these idealized equations While Eqs 2 and 3 are highly idealized they provide an overview of how temper ature primarily influences buckling However to gain a deeper under standing of the complexity of buckling behaviour in railway tracks it is essential to study the more intricate relationships among various factors Accordingly these relationships are further examined and more com plex equations are introduced to account for additional critical vari ables such as lateral resistance thermal and mechanical stresses in the rails Some analytical models such as those developed by Samavedam 85 take a simplified approach by considering the rails as statically equivalent pair of EulerBernoulli beams sitting on an elastic foundation This enables the formulation of models and equations that assume ho mogeneity in rail properties providing equations that define the lateral deflection w of the buckled zone as a function of the rails longitudinal position xfor straight tracks Eq 4 or the rails angle of curvature θ for curved tracks Eq 5 as shown below EI d4w dx4 P τ0 d2w dx2 Fwx P d2w0 dx2 4 EI R4 d4w dθ4 P τ0 R2 d2w dθ2 Fwθ P R d2w0 dθ2 5 where the additional variables τ0 is the torsional stiffness of the track and R is the tracks curvature radius while w0 is the initial misalignment distribution The terms Fwx and Fwθ are the lateral distribution functions for tangent and curved tracks respectively This notation in dicates that the lateral resistance is dependent on the lateral displace ments relative to the position along the rail These equations mainly allow for the consideration of the nonlinear nature of the lateral resis tance of the track allowing for a more accurate representation of the tracks buckling behaviour Boggs 14 and Beliveau et al 13 expanded upon the approaches of Kish and Samavedam by including foundation stiffness and considering rail beam vibration frequencies to determine critical buckling loads They added a distributed layer of Winkler springs to mimic the foun dation of rail section in which for rail beams of length L the following relationship was proposed to link the natural frequency of the rails ωn to the critical compressive load of the rails P ωn 1 m EI nπ L 4 P nπ L 2 K 12 n 1 2 3 6 In this equation EI is the bending stiffness m is the mass per unit length and K is the Winkler foundation stiffness When K 0 the condition corresponds to the Euler buckling load applicable when the CWR can be considered equivalent to a EulerBernoulli beam However higher modes where shear deformations become significant require considering a Timoshenko beam instead To address this two infinite Timoshenko beams with rectangular cross sections are used to model the head and foot of rails connected by finite beams representing the web 113 This model includes translational and rotational components and accounts for shear deformation of the head and foot of the rail Compared to the Euler beam model this model showed better agree ment with experimental results particularly within the dominant fre quency range of 505000 Hz These additional insights are crucial for calculating critical buckling loads of the rails thus helping in predicting buckling risks Yang and Bradford 117 investigated the postbuckling behaviour of axially loaded infinite columns which they considered as rails on a track sitting on nonlinear foundations exhibiting softening effects like the lateral resistance shown in Fig 7 Their study used a semianalytical solution via a perturbation technique using the governing differential equation for buckling configuration shown below and a numerical technique based on a single shooting procedure to show localisation of thermal buckling EIυ AEαTυ dFdυ 0 7 Here F is the lateral resistance of the ballast while υ is the defor mation of the track Their results indicated that the postbuckling configuration transitions from a lengthwise periodic mode at initial loading stages to an isolated sinusoidal mode in later stages which aligns with practical observations of localised track buckling This is further supported by their subsequent study 118 wherein effects of geometric imperfections were added into their analytical model A set of more detailed differential equations were presented and used to show symmetric and antisymmetric post buckling configurations using the principle of stationary total potential Fig 7 Relationship between applied load and lateral deflection of track as adapted from Yang and Bradford 117 D Agustin et al Construction and Building Materials 466 2025 140295 5 More recently Kostovasilis 48 introduced a comprehensive analytical model that considers both tangent and curved rail tracks where vertical and lateral deflections are coupled an added innovation from previous analytical track model studies In this model an elastic foundation was used to represent the sleeper pads while the sleeper and ballast were modelled through layers of masses and springs Addition ally the sleepers were treated as flexible beams rather than rigid bodies This model provides generalisability as it can account for translational and rotational degrees of freedom analytically In a related but different approach a sandwich column model as illustrated in Fig 8 was developed by Zhu and Attard 126 to represent the railsleeper structure and analytically evaluate railway track buck ling behaviour Unlike the classic beamonelasticfoundation models this approach departs by formulating the structure as a sandwich col umn which allows for a different analytical treatment of the railsleeper interaction This model incorporates hyperelastic relationships for thermally induced stresses and finite strain in the track Thei findings suggest that fasteners with high rotational stiffness significantly enhance lateral stability However the model does not account for the influence of ballast lateral resistance as the study focused on the nonlinear localised buckling of the rails mainly due to the railfastener interaction Additionally they proposed a critical track length for studying the localised buckling behaviour for both symmetric and antisymmetric tracks which helps in generalising their method Another approach investigated the railway track buckling of dual gauge tracks 88 In this analytical model the total potential energy method was used to express buckling behaviour of the track using Eq 8 Mainly the critical temperature is determined by referencing Eq 1 using it to derive the temperature from the compressive force outlined in Eq 8 V 1 2 L 0 EIwʹʹdx L 0 wFxdx 1 2 L 0 P wʹ w0ʹ2 w0 2 dx 8 In this equation the first term represents the bending potential of the track the second term corresponds to the energy associated with ballast resistance and the third term accounts for the work done by the compressive forces The variable V denotes the total potential energy and wʹʹ is the second derivative of the lateral displacement The remaining variables follow the notation used in the previously listed equations The unique structural nature of dual gauge tracks is most evident in the first term where the bending potential is modified to account for the additional third rail A key assumption in their formu lation however is the simplification of the three railsleeper structure into an equivalent beam These analytical models collectively enhance the ability to evaluate buckling behaviour in railway tracks by providing mathematical equa tions that can be used to calculate track parameters with high precision offering insights crucial for maintaining track stability and safety under various conditions primarily under extreme temperatures However these analytical buckling studies often overlooked the combined effects of other track system components especially considering the lateral ballast resistance as they usually only considered the track structure above the ballast the rails sleepers and fasteners This inclination to derive equations mainly defining the rails and sleeper interactions and simplifying the foundation is evident in the track buckling studies presented which can affect the accuracy of buckling predictions on the total risk assessment of this complex and dynamic phenomenon 32 Numerical buckling models While analytical models offer a generalised approach for assessing buckling risks by evaluating rail stress and conducting static track analysis they are limited by simplifying assumptions such as linear material behaviour uniform track geometry and consistent lateral resistance These idealisations make them less accurate in representing realworld complexities including material nonlinearities localised imperfections and dynamic interactions from transient forces or passing trains Analytical models are also less suited for largescale systems as their static nature and limited parameter scope cannot fully capture the variability and interactions present in extensive track networks While they remain valuable for initial assessments due to their computational efficiency their limitations can be addressed by integrating hybrid ap proaches or incorporating empirical data to enhance predictive accuracy To introduce more realistic representations of track systems most research in open literature have proposed models that are mostly nu merical in nature and considers several key components the rails the sleepers the fastening system that secures the rails to the sleepers the ballast and the subballast which acts as foundational supports to the rail sleeper and fastener systems as shown in Fig 9 In the studies discussed in the following sections this basic ballasted track model is often used though with variations tailored to specific research objectives These models are primarily used for track dynamic analysis and the consid eration of more complex structural characteristics However some of the succeeding models have included the horizontal and lateral char acteristics of railway tracks to concentrate of lateral track stability and thus buckling 321 Unit cell model One of the first numerical models introduced to evaluate rail buck ling is the proposed unit cell model 12 shown in Fig 10 A repeated pattern of unit cells is made to construct a 200meter railway track section using ABAQUS to generate response curves and buckled shapes similar to the one shown in Figs 3a or 4a The novelty in this structural model is the discretisation of the rails fastening and sleepers facili tating the assessment of the tracks buckling response with respect to the individual properties of these track components for each unit cell With this numerical model buckling temperatures can be calculated which was shown to be overestimated if simpler 2D models which only consider the horizontal plane are used This numerical model has shown the capability to estimate track buckling temperatures more accurately helping in the prediction of the failure phenomenon While this model mainly considers the rails and sleepers and simplifies the foundation into elastic elements it has paved the way for more comprehensive models that not only account for a wider range of track system parameters and variables but also incorporate the nonlinearities in their values and properties moving beyond the assumption of constant characteristics This unit cell model is further expanded by including spring elements representing fasteners 56 and ballast 57 A 3D finite element model is implemented to study the static buckling of a 200meter track using geometrically nonlinear beam elements considering sleepers as linear EulerBernoulli beams Additionally material nonlinearity was intro duced in the springs representing the ballast behaving nonlinearly as the track started to buckle and experience large lateral deformations The 3D FEM model resulted in lower buckling loads compared to pre vious 2D models due to the inclusion of torsional and vertical de formations In these studies perfect elastic behaviour of the ballast springs is assumed with vertical ballast resistance modelled using linear springs Additionally the flexibility of the padfastener system which connects the rail to the sleepers is incorporated into the analysis A Fig 8 Analytical Sandwich Column Model as illustrated by Zhu and Attard 126 D Agustin et al Construction and Building Materials 466 2025 140295 6 comprehensive parametric study revealed that both the flexural rigidity of the crossties sleepers and the stiffness of the padfastener system have a significant impact on the buckling behaviour of the track Lim et al 55 in a subsequent study applied the concept of infinite boundary elements to address variabilities in ballast resistance and track irregularities A 50meterlong rail model with longitudinal beam ele ments added at each end demonstrated that buckling response curves obtained with this reducedlength model were as accurate as those from the fulllength model in their previous studies This approach allowed for extensive analysis of various ballast stiffness and track irregularities showing that stiffer ballast increases buckling temperatures while mis alignments decrease safe temperatures Further improvements to Baos unit cell model were made to account for infinite rails and ballastless tracks extending the analysis to longer track sections 107120 This adjustment reduced the number of pa rameters compared to conventional ballasted tracks The modified model effectively predicted buckling shapes and behaviours showing that certain buckling modes were more sensitive to variations in longi tudinal forces which contributed to track buckling under these conditions 322 Rail stress evaluation methods As with the previously discussed analytical models numerical ana lyses have been proposed to link rail vibration to axial load For instance using basic beamonelastic or discrete support models as illustrated in Fig 6 Thompson and Vincent 9796 examined the dynamic behaviour of rail tracks to predict vibrations In their work they introduced vari ations to the model by representing the rails as a continuous Timoshenko beam with 1 continuous support and 2 periodic support Addition ally a third model was proposed where the rail was replaced by an infinitely extended 3D FEM mesh based on periodic structure theory as depicted in Fig 11 These models allowed for the accurate evaluation and prediction of the rails dynamic stress response and thus track buckling Results also indicated that despite the rail mesh model being more complex and accounting for more factors the second model with periodic supports provided a better prediction of track vibrations and thus longitudinal compression of the rails This improved accuracy is likely due to the models closer representation of the periodic nature of the sleepers A more recent implementation linking rail vibrations to axial load Fig 9 Basic track system model with rails sleepers fastening ballast and subgrade Fig 10 Schematic of Unit Cell proposed by Bao 12 Fig 11 Thompson and Vincents 3D Rail Mesh Model 9796 D Agustin et al Construction and Building Materials 466 2025 140295 7 was presented by Urakawa et al 101 Their study focused on the effect of fasteners stiffness on the dynamic frequencies of rails using a 3D FE analysis that accounted for irregularities such as variations in sleeper spacing rail head wear and temperature dependency of the track They introduced a method for evaluating the axial force in CWR using natural frequency measurements and comparing them with actual measure ments onsite Although this method offers a straightforward approach its accuracy is compromised by variations in track conditions They identified factors affecting measurement accuracy and proposed an error correction method based on track FEM to improve precision Experi mental validation confirmed the improved accuracy of this method for measuring axial force in CWR It is important to note that rail axial loading and vibrations are not solely due to passing trains or thermal loading Extreme axial loading can also occur under seismic conditions significantly impacting track stability 22 They examined the FEM for analysing both superstructure and substructure components of the track and using shaking table tests for validation of their proposed model Their seismic track model marks a significant advancement over the widely used Beam on Elastic Foun dation BOEF and Beam on Discrete Supports BODS models as it in troduces additional track components Instead of relying solely on elastic or discrete supports their model accounts for the ballast sub ballast and subgrade layers providing a more comprehensive analysis of track behaviour under seismic conditions The development and application of these numerical models signif icantly enhance the ability to predict buckling behaviour in railway tracks offering insights that are crucial for maintaining track stability and safety under diverse operational conditions These models not only account for a wider range of track system parameters and variables but also incorporate variability in their values and properties Furthermore they emphasise the importance of considering structural and material nonlinearity localised imperfections such as reduced ballast resistance or misaligned rails and geometric irregularities Dynamic effects including transient forces generated by passing trains are also inte grated providing a more realistic representation of realworld condi tions However some issues persist as some numerical models sacrifice accuracy for more computational efficiency This can reduce the overall reliability of the numerical model as assumptions in the nature of the track system can be simplified for faster evaluations Regardless of this numerical models still offer higher scalability and configurability over analytical models providing a more comprehensive prediction of rail buckling enabling more effective predictive and preventative measures with regards to buckling to ensure the longterm integrity and safety of railway infrastructure 4 Parametric track buckling predictions The analytical and numerical models discussed in the previous sec tion only outlines an overview of the proposed methods in literature on how to quantify measure and analyse the track system parameters that contribute to the buckling phenomenon They are tools that help railway engineers assess buckling risks However understanding the factors that contribute to track buckling is essential for developing comprehensive prediction and prevention strategies Various parameters influence the buckling behaviour of railway tracks each playing a critical role in determining the stability of the track system These parameters include thermal forces track geometry material properties lateral ballast resistance and dynamic loads By examining these key factors a comprehensive understanding of the conditions that lead to track buckling can be obtained and help in identifying the critical thresholds that must be managed to ensure the safety and reliability of railway operations 41 Influence of rail temperature As previously established the compressive forces in rails are pri marily driven by temperature increases as defined by Eq 1 P αEAΔT and as shown in Fig 2 Studies in literature previously pre sented have emphasised determining the critical temperature range where the buckling regime is uncertain In the rail community the reference temperature point at which the rail is stressfree in the lon gitudinal direction is called the rail neutral temperature This parameter is usually used to evaluate buckling risk instead of the direct measure ment of rail stress or loads With this methods are developed to 1 measure temperature changes in tracks and associate them with the compressive forces within the rails 2 design rails to optimise the margin between these critical temperatures and the rails stressfree temperature and 3 ensure that the allowable temperature increase does not exceed safe or allowable limits 411 Temperature measurements and projections Extreme temperature variation in rails is an important aspect in investigating track sections that are prone to buckling However measuring and monitoring temperature increases in railway tracks is a complex task primarily due to two challenges 1 determining where to measure and 2 ensuring accurate readings over long rail segments Rail temperature can vary significantly along the track and localised mea surements may not reflect temperature gradients over an extended section of the track Measuring temperatures at selected locations risks underestimating the thermal effects across larger rail sections making such measurements less reliable for predicting potential buckling events Traditionally temperature sensors have been used to measure rail temperatures Thermocouples and linear variable differential trans formers LVDT have been used in a study commissioned by the Rail Safety and Standards Board in UK 112 to study the accuracy of such methods led to the conclusion that while measurements can be accurate compounding errors when scaled can be problematic when applied for buckling predictions Other methods to assess rail temperature are usually performed by measuring the strain experienced by the rail and then calculating the temperature using the equation for thermal expansion Techniques such as strain gauges 12758 ultrasonicbased methods 2032 or vibrationbased approaches 72108 have also shown effectiveness of deriving track rail temperatures using axial stress or strain However these approaches face challenges particularly related to the nonhomogeneity of the track system Moreover many methods require long observation periods under favourable weather conditions where both tension and compression of the rails are captured within the same measurement period to ensure accurate results In addition to direct measurements the rail community often relies on empirical models to estimate rail temperature by correlating air temperature and weather conditions These models incorporate factors such as ambient temperature solar radiation wind speed and rail sur face properties Examples of these empirical methods include the one established by Wittingham 110 and Hunt 31 where the rail tem perature is estimated to follow the equations shown in Table 1 Although these formulas provide broad estimates they may overlook localized heating effects particularly in sections exposed to intense sunlight In such cases rail coatings such as painting rails white are sometimes applied to reflect solar radiation and reduce rail temperature 64105 However while coatings can mitigate surface heating their effectiveness varies with environmental factors and may not fully Table 1 Rail temperature estimation methods Author Equations Parameters Wittingham Trail 1228Tair 97 0322A 0768Tair 262 0986Tair 075W 75 normal conditions at noon at noon with wind A is the altitude of the sun W is the wind speed Hunt Trail 15Tair Tair 17 for sunny days for cloudy days D Agustin et al Construction and Building Materials 466 2025 140295 8 address the thermal stresses that contribute to buckling risks Moreover these empirical models still rely on measured data both for initial formulation and ongoing validation making accurate field measure ments essential One way to measure these variations is using thermal imaging techniques which helps in finding thermal variations especially from shading effects 16102 With the help of Global Positioning Systems GPS this technique can offer valuable data for forecasting problem areas and recommend mitigation strategies such as tree plantings to provide shade on railway tracks In a subsequent study 17 the authors improved on these measurement techniques where the GPSenabled weather model was used to simulate the energy balance of the railway tracks improving projections of rail temperature distributions Testing their model on both a constructed test track and a live mainline track they demonstrate significant forecasting capabilities that enhance rail temperature management and help prevent weatherrelated delays On a related note implementing systems to measure and monitor rail tem peratures using thermal imaging and GPS can be a complex and resourceintensive task Therefore alternative rail stress monitoring systems can offer a more efficient and costeffective approach for obtaining rail temperature data Mandal and Lees 62 recommended the use of commercially available rail stress monitoring systems particularly rail creep measurement methods to provide insights into track behaviour and stress conditions aiding in the management of track stability However while these systems are effective for measuring rail stress in targeted problem areas their widespread implementation across large networks can still be prohibitively expensive Identifying problem areas with significant rail temperature varia tions presents a challenge While previous studies have generally approached rail stress measurements due to temperature specific track structural and geographical features can have a noticeable impact on rail temperatures and consequently buckling risk For instance shadows cast by geographical features or railway structures can lead to localized temperature differences along the track as shown in Fig 12 A great example is that of tunnel transition zones 59125 highlighting the difference in cyclic thermal loading of the different track sections exposed to sunlight These temperature variations due to differing exposure to sunlight contribute to the increased rail temperature vari ations leading to failure phenomenon such as rail creep or track buckling Weatherrelated concerns particularly rising temperatures affect the temperature variations in railway tracks and are a critical factor in preventing track buckling Projections 87 indicate that increased temperatures will likely lead to increased buckling failures due to increasing global temperature trends This conclusion was reached by performing Monte Carlo simulations using temperature projections and available buckling data Other projections were made which included more information and integrated more details of railway track behaviours In one study 69 higher operation and maintenance costs are projected along with increased risks of buckling These costs can be estimated using buckling models such as CWRSAFE 86 and CWERRI 24 which integrate climate projections highresolution GPS data and asset valuation information Another is by conducting a Petri net modelling approach 18 to assess track stability and operational per formance By incorporating weather influences in track asset manage ment valuable guidance on maintenance policies during heatwaves were implemented These projections highlight the need to update railway design and construction standards to accommodate future temperature increases and prevent potential buckling failures 412 Using parametric models Directly measuring and monitoring rail temperatures provides the advantage of obtaining precise data for predicting buckling risks However this approach is not feasible for extensive rail networks as it can become prohibitively expensive even when using commercially available lowercost rail monitoring systems Parametric buckling pre dictions that focus on rail temperature can utilize modelling techniques to achieve comparable accuracy in assessing buckling risks These include the analytical and numerical models previously discussed which focus on measuring and evaluating the critical temperatures at which railway tracks may buckle In this section additional parametric buckling models are explored to showcase their practical applications emphasizing the advantages of using modelling techniques to predict buckling temperatures A notable example of a parametric buckling model focused on tem perature was developed by Carvalho et al 15 and Pucillo 80 They focused on developing 3D numerical track models to conduct thermal buckling predictions Carvalho et al developed a 3D model using ANSYS and used nonlinear stabilisation techniques using the NewtonRaphson method while Pucillo created a parametric finite element model FEM of railway tracks designed to simulate the tracks sensitivity to varia tions in rail temperature and other key parameters Both findings highlighted that track misalignments and curvature significantly in crease susceptibility to thermal buckling This is important as in curved tracks the rails may undergo radial shifts due to temperature increases also known as radial breathing during the prebuckled state of railway tracks 434585 This slow but periodic movement introduces a pro gressive misalignment further weakening track stability The impact becomes particularly critical on sharp curves where reduced lateral resistance and increasing misalignments combine to heighten the risk of buckling Their models underscore the importance of considering additional factors such as misalignments and track curvature alongside temperature when predicting buckling risks Building on this subsequent studies by Pucillo 8182 investigate the impact of more realistic track conditions by incorporating defects of various shapes and sizes on critical buckling temperatures in CWR tracks Using FEM these studies simulate the effect of these defects showing that both plastically introduced defects and stressfree condi tions lead to conservative estimates of thermal buckling risks The presence of multiple defects as shown in Fig 13 further reduces the Fig 12 Effects of temperature on tunnel transition rails as illustrated by Luo et al 59 Fig 13 Pucillos 81 control chart in detecting track defects D Agustin et al Construction and Building Materials 466 2025 140295 9 safety factor against thermal buckling The study concludes with an evaluation criterion that considers the effects of multiple alignment defects on critical buckling temperatures in CWR tracks providing a more comprehensive understanding of thermal buckling risks and enhancing predictive capabilities More recent studies focusing on temperature for assessing and pre dicting track buckling includes Kabo and Ekberg 41 where a networkwide analysis of track buckling risk was conducted identifying specific weak points along the track This hinges on the nonhomoge neous nature of the track structures lateral resistance and initial mis alignments highlighting the increased risk of thermal buckling at these locations A numerical model was developed to predict thermal buckling using the concept of an equivalent temperature to account for the variability in track parameters These studies present methodologies to utilise temperature which is an external uncontrollable factor often considered a primary driver of buckling events to analyse and predict track buckling By gaining a deeper understanding of this variable researchers and engineers can conduct more comprehensive and accurate assessments of buckling risks This improved insight allows for the development of targeted strategies to mitigate the influence of temperature thereby enhancing the overall reliability and safety of railway tracks With proper rail temperature management and monitoring the capability to predict and manage thermal buckling can be optimised to ensure maintaining the integrity of railway infrastructure particularly under varying opera tional and environmental conditions 42 Influence of track structure Another key factor influencing track stability is the tracks buckling resistance which plays a crucial role in reducing lateral deflections caused by compressive forces train movements or other external fac tors As shown previously in Figs 3 and 4 lateral deflection of the track has a close relationship with rail temperatures and track buckling Buckling resistance is mostly assessed through lateral resistance as it serves as a primary parameter in determining the tracks stability under compressive forces Studies 47 1990 86 on the effect of the peak lateral resistance as the primary parameter in investigating the effect of lateral resistance on the tracks buckling strength has been significant in track buckling research presenting observations on how higher peak lateral resistance can lead to increases in maximum buckling tempera tures helping widen the margin from spontaneous buckling For example Fig 14 shows different idealisations of how the lateral resistance relates to lateral displacement of the track Assuming a con stant lateral resistance simplifies analysis but provides a less represen tative depiction of track stability In contrast incorporating nonlinear lateral resistance offers a more realistic and accurate representation of track behaviour accounting for the complex interactions and material properties of the track system Studies such as those previously discussed and presented has shown that as the peak lateral resistance increases the upper and lower buckling temperatures also increase On the other hand the limiting lateral resistance gives a proportional change to the lower buckling temperature Both are established as important as both affects the determination of the allowable margin of safety in rail tem peratures This lateral resistance curve can be obtained through methods such as the Single Tie Push Test STPT or the Track Panel Test While the prior analysis has largely focused on lateral resistance as a key determinant of track stability this single parameter alone is insuf ficient for a complete understanding of track buckling behaviour Recent technological advancements in railway systems have introduced prac tical tools for measuring a broader range of track parameters offering more comprehensive methods to evaluate buckling resistance Zadeh et al 121 proposed a comprehensive method that combines geometric features of the track with the condition of its components to better quantify buckling resistance Their study introduced the Track Strength Index TSI a unified metric that assesses buckling resistance at a system level which integrates critical factors such as misalignment amplitude track curvature lateral resistance torsional resistance and longitudinal resistance Sensitivity analyses using CWRRisk software identified these parameters as key contributors to buckling resistance The integration of metrics like the TSI complements existing studies on lateral resistance by addressing the limitations of focusing solely on a single parameter Buckling resistance is influenced by a range of factors many of which stem from the nonlinear properties of the track structure These nonlinearities arise from the material behaviour of the ballast and fasteners as well as external conditions such as temperature gradients that modify the systems loading environment These factors can have a significant impact on lateral strength which makes the studying of the relationships between these factors and how it affects track lateral resistance an important aspect of the track buckling theory 421 Sleepers Innovations in optimising the sleeper component of the track play a crucial role in enhancing the lateral resistance of railway tracks a key factor in predicting and preventing track buckling Various studies have focused on different sleeper configurations and materials evaluating their impact on track stability under increasing temperature conditions It is important to highlight that different types of sleepers offer varying levels of resistance to track buckling based on their density and size The interaction between the sleeper and the ballast is also a crucial factor as the contact area and frictional surface influence the tracks overall stability A study conducted by De Ioro et al 19 provides further insight into the distribution of resistance generated across the sleepers For loosetamped ballast conditions and an unloaded track it was found that a monoblock sleepers lateral resistance contribution was distributed with approximately 50 from the crib 25 from the base and 25 from the shoulder Similarly the longitudinal resistance was divided with around 60 coming from the crib 30 from the base and 10 from the shoulder While these results highlight the role of traditional monoblock sleepers in resisting lateral forces subsequent research has demonstrated that structural innovations and alternative sleeper designs can further enhance lateral resistance as discussed in the following paragraphs This underscores the importance of optimizing the sleeperballast interface to improve overall track stability The distri bution of these resistances is illustrated in Fig 15 One way to optimise the sleeper component is to modify the struc tural design of how the sleeper is placed onto the railway track For example adding under sleeper pads USP has been found to increase the lateral resistance of tracks 83 These USPs can increase the friction in these components helping in minimising lateral movement especially under increased trafficinduced loads This has been supported by lateral resistance field tests using discrete cut panel pull tests in which it is found that USPs add significant lateral resistance performance Addi tionally the study has even recommended the use of different materials Fig 14 Idealised relationships between lateral resistance and displacement of track 47 1990 86 D Agustin et al Construction and Building Materials 466 2025 140295 10 for the pads particularly softer ones to maximise this benefit Similarly using stiffeners under steel sleepers has been shown to significantly in crease lateral resistance 123 This was shown by both laboratory and field investigations using Single Tie Push Test STPT and Multiple Tie Push Test MTPT methods which showed increases in lateral resistance by approximately 140 This enhancement addresses the issue of lack of lateral resistance in CWR on curved tracks where radial forces decompose longitudinal forces into tangential and radial components leading to potential defects such as track buckling and transversal shifting Another modification to the sleeper structural design is by using a different approach to fastening the sleeper Esmaeili et al 21 in troduces nailed sleepers a technique using steeldriven nails to enhance the lateral resistance of concrete sleepers in ballasted railway tracks They developed a 3D numerical model of a single sleeper bal lasted track using ABAQUS and validated with Single Tie Push Test STPT results Sensitivity analyses were conducted on nail parameters such as length diameter location and the subgrades elasticity modulus The optimal dimensions and locations for the nails were determined and structural impacts on concrete sleepers were assessed based on Australian standards Their field tests showed that using nails increased lateral resistance by over double the baseline compared to standard sleepers Lee et al 50 focus on developing a new girdersleeper fastener with adequate lateral resistance to prevent track buckling in CWR tracks on opendeck steel plate girder railway bridges Using FEM and parametric studies conducted in ABAQUS and LONG STAB they investigate the lateral resistance requirements of the fastener Their analyses examine the effects of peak lateral resistance curve radius girder length and lateral displacement of the girder Based on the results they propose a peak lateral resistance criterion for the girdersleeper fastener determining the minimum requirements needed to ensure stability and prevent buckling on CWR tracks Aside from modifications in the individual sleeper structure itself the tracks lateral resistance can also be optimised by changing the sleeper system and how it is configured in the track For example interspersed railway tracks have been shown to reduce the risk of track buckling 4277 In interspersed railway tracks degraded timber sleepers are replaced with concrete sleepers Using 3D FEM and eigen value analysis as shown in Fig 16 the effects of this configuration are examined including fully concrete tracks and tracks with onethird onehalf and onefourth of the sleepers replaced The results indicate that the interspersed approach may reduce the likelihood of track buckling by increasing critical buckling temperatures Notably this is the first study to explore the buckling behaviour of interspersed railway tracks offering valuable guidance for life cycle design and construction strategies Although this study provided a clear understanding of the impact of replacing timber sleepers with concrete it overestimated the buckling temperature due to the limitations of using a linear analysis solver In a subsequent study 75 a 3D FEM using LSDYNA to inves tigate the nonlinear buckling behaviour of interspersed railway tracks their research addresses the issue of inconsistencies in stiffness due to the different materials in the sleepers This research highlights the impact of boundary conditions on buckling behaviour and its buckling shapes and provides insights into improving the inspection and main tenance of the lateral stiffness of interspersed tracks in areas prone to extreme temperatures These findings can be used to predict buckling temperatures and inspect the conditions of interspersed railway tracks informing life cycle design maintenance and construction strategies for transitioning from timber to concrete sleepers While sleeper type is primarily associated with influencing a tracks lateral resistance some studies have also examined its effects on longi tudinal resistance Alizadeh et al 54 investigated the influence of sleeper type on track longitudinal resistance and stiffness highlighting its role in mitigating risks such as rail breakage misalignments and buckling Their research focused on the longitudinal behaviour of the track emphasizing the contribution of the sleeper and ballast system in transmitting longitudinal loads experienced by the rails This is partic ularly significant as it incorporates the longitudinal resistance contri bution of sleepers in addition to their lateral effects Using a finite element model implemented in ABAQUS they compared the longitu dinal resistance of steel sleepers with that of wooden and concrete sleepers Their findings indicated that steel sleepers provide acceptable levels of longitudinal resistance while requiring less ballast attributed to their unique geometric properties Similarly studies have been conducted to investigate the effect of the shape of sleepers into the lateral resistance of the track For example studies by Miri et al 67 and Mansouri et al 63 has explored the optimal sleeper shape to mitigate track buckling They performed push and pull tests to see whether conventional winged or frictional sleepers provide better lateral resistance Their results show that winged and frictional sleepers provide comparably increased lateral resistance over the use of conventional sleeper shapes Another sleeper system config uration study is done by Aela et al 3 where the lateral resistance of Yshaped steel sleepers in ballasted railway tracks is examined high lighting their impact on lateral track stability and track buckling They validate the effectiveness of Yshaped sleepers in enhancing lateral resistance using the Single Tie Push Test STPT This was made possible by using the discrete element method DEM to analyse the contribution of ballast components and the effect of shoulder ballast width on lateral resistance The results indicate that Yshaped sleepers provide more lateral resistance compared to monoblock sleepers with DEM simula tions showing that sufficient lateral resistance can be achieved even with less shoulder width compared to standard Further innovations in sleeper design are reflected in using ladder sleepers to enhance track stability 35363860 which was first proposed by Moses and McClung in 1967 68 This configuration is particularly wellsuited for highspeed railway tracks as they reduce ground vibrations from nego tiating trains Like other sleeperfocused studies ladder sleepers un derwent STPTs to assess their lateral track stability contributions Together these studies demonstrate how innovative sleeper designs including winged frictional Yshaped and ladder sleepers along with optimized ballast configurations contribute significantly to enhancing lateral resistance and mitigating the risk of track buckling particularly under challenging operational conditions The discussed research explores the effectiveness of replacing Fig 15 Sleeper contribution to lateral resistance by contact surfaces with ballast 19 Fig 16 Example of interspersed sleepers as adapted from Ngamkhanong et al 77 D Agustin et al Construction and Building Materials 466 2025 140295 11 traditional timber sleepers with concrete ones the use of steeldriven nails to improve lateral resistance and the development of specialised fasteners and sleeper pads These advancements not only contribute to better maintenance and inspection protocols but also provide valuable insights into the lifecycle design and construction strategies for modern railway systems The collective findings from these studies underline the importance of adopting innovative sleeper technologies to mitigate the risks associated with track buckling particularly in regions prone to extreme weather conditions and heavy traffic loads 422 Ballast The management of ballast conditions is crucial for improving the lateral resistance of railway tracks and mitigating the risks associated with track buckling under extreme temperature changes Recent studies have explored various aspects of ballast management including the effects of ballast material shape size distribution ballast fouling shoulder width superelevation and reinforcement techniques 37 These investigations provide valuable insights into improving the in spection maintenance and overall stability of railway tracks particu larly in regions prone to high temperatures and heavy traffic loads The following summaries present key findings from recent research on ballast management and its impact on track buckling prevention The appropriate selection of ballast aggregate material plays a crucial role in maintaining the integrity of the ballast structure as it directly affects ballast breakage and influences track lateral resistance Steel slag ballast has been proposed as an alternative to traditional limestone ballast due to its ability to provide higher lateral resistance 23 Ballast shape plays a crucial role in determining the lateral resis tance of railway tracks 91100 Ballast with a rounded shape tends to move more easily under load which leads to lower lateral resistance This is because the smoother rounded surfaces of the ballast particles provide less friction and interlocking between the ballast While the fresh ballast typically has an irregular shape with sharp edges which allows for better interlocking between particles This increased inter locking creates a more stable track bed improving lateral resistance and reducing the risk of track shifting or buckling Over time however ballast becomes worn and rounded due to repeated loading and envi ronmental factors decreasing its effectiveness Therefore periodic ballast renewal with proper compaction can significantly enhance lateral resistance improving track stability However it is important to note that maintenance activities such as ballast tamping can temporarily reduce lateral resistance This reduction occurs because tamping loosens and homogenizes the ballast bed diminishing its interlocking capability and overall stability To address this issue dynamic track stabilization is essential following ballast tamping This process ensures adequate ballast compaction restoring lateral resistance and enhancing track stability As mentioned in the previous section lateral resistance is further influenced by the track profile and the dimensions of the ballast layer including its depth shoulder width and height slope angle crib ballast and curvature 438586 Studies have identified the ballast bed and crib ballast as the primary contributors to lateral resistance Ballast depth plays a crucial role with an optimal depth of 300 mm determined through field and numerical studies 12444 The enclosure of the sleeper within shoulder ballast further enhances lateral resistance by increasing the ballasts weight and dimensions 39 2019a 2019b Additionally crib ballast height is a key factor contributing 3750 of total lateral resistance through friction with the sleeper sides 49 Beyond lateral stability proper crib ballast height also supports longi tudinal stability by maintaining sleeper spacing and helps mitigate the risk of ballast flight which is particularly important for highspeed rail operations Other studies focusing on the ballast implement numerical modelling techniques such as Discrete Element Method DEM 12444 Finite Element Method FEM 12240 and using experimental tests like the Single Tie Push Test STPT for validation to investigate the effects of various ballast conditions on the tracks lateral resistance One such study focused on analysing the effects of temperature changes and fouling conditions of the ballast using coupled 3D DEMFEM imple mented in BLOKS3D and LSDYNA 7376 It is noted that ballast fouling resulting from breakage tends to become more rounded and smaller making it easier to move under load Their research highlights that railway track buckling caused by extreme heat results in significant asset loss particularly in the ballast in railway systems By integrating lateral resistance data from previous Single Sleeper Push Test STPT simulations into a lateral spring model they investigate the effects of ballast degradation and rail misalignment on buckling temperatures The findings indicate that ballast fouling significantly increases the likelihood of track buckling as can be seen in Fig 17 even when localised at the bottom of the ballast layer More critically the allowable temperature can be reduced by up to half with completely fouled ballast These insights can be used to predict buckling temperatures and inspect ballast conditions particularly during summer This unprecedented study also highlights the buckling phenomena of interspersed railway tracks from their previous studies presented in the previous section 42 7775 providing valuable information to enhance the inspection and maintenance of ballast conditions in response to extreme heat Another implementation of a numerical modelling technique is proposed to investigate the effects of shoulder width and track super elevation on the lateral resistance of unloaded sleepers 2 Their find ings reveal that lateral resistance increases significantly with superelevation compared to an uncanted sleeper which mostly origi nates from the shoulder ballast Additionally widening the ballast shoulder leads to an increase in lateral resistance regardless of the su perelevation These results underscore the importance of maintaining the ballast shoulder particularly in superelevated track sections to enhance lateral stability The results from this study can be applied to a full curved railway track model where cant is essential for maintaining stability to investigate the buckling behaviour Xu et al 115 focused on the lateral resistance of a ballast bed and its significant impact on the lateral stability of ballasted railway tracks They emphasise the importance of precise evaluation of lateral ballast resistance for predicting rail buckling potential Differential ballast settlement can cause sleepers to separate from the ballast resulting in unsupported sleepers suspended from the rail This separation creates a gap with zero frictional force reducing the lateral ballast resistance On the other hand sleepers near unsupported sleepers bear extra Fig 17 Ballast Fouling condition of track ballast can affect track lateral stability Image adapted from 73 D Agustin et al Construction and Building Materials 466 2025 140295 12 weight becoming oversupported which affects their lateral ballast resistance contribution In a subsequent study Xu et al 116 introduce a dynamic method using 19 scaled models to rapidly and continuously measure lateral ballast resistance in a laboratory setting This method addresses the limitations of traditional singlesleeper pullout or push tests SSPTs which are labourintensive and require individual sleeper evaluations The new approach facilitates nondestructive investigations of lateral ballast resistance particularly for assessing buckling risks due to earthquakes allowing for more rapid and extensive surveys necessary for early restoration of train operations postearthquake While these studies have demonstrated the influence of ballast con ditions and material nonlinearities on the tracks lateral resistance the interaction between ballast and sleepers plays a crucial role in providing this resistance Both components need to be optimized to ensure adequate protection against track buckling 43 Dynamic loads Understanding the impact of dynamic loads on railway track buck ling is crucial for developing effective prediction and prevention stra tegies Dynamic loads such as those generated by passing trains introduce additional forces and vibrations that can exacerbate the risk of buckling This section examines various studies that have focused on the effects of dynamic loads on track buckling and the methodologies used to predict and manage these impacts 431 Traininduced dynamic loads The dynamic buckling theory proposed by Kish et al 1990 first introduced the inclusion of dynamic train loads in evaluating the track buckling behaviour in addition to the thermal and structural variables This theory highlighted that train movement induces specific mecha nisms contributing to track instability For instance the uplift caused by train movement in the vertical plane of the track reduces lateral resis tance as shown in Fig 18 Additionally lateral forces generated by train motion can result in lateral track misalignments further amplifying buckling risks Longitudinal forces such as those caused by traction during acceleration or braking contribute to increased compressive forces within the rail which further lowers the critical buckling strength of the track Moreover vibrations generated by train movement can degrade ballast strength over time leading to a reduction in the lateral resistance provided by the ballast and as discussed in previous sections These dynamic forces interact with thermal forces compounding the influence of each other on the tracks stability and since then more research has been conducted to include train loads into track buckling evaluation and assessment For example to prevent track buckling in how weather a rational speed reduction scheme can be proposed 119 This scheme presented by Yi et al is based on a probabilistic method for evaluating the buckling risk of CWR tracks It considers permissible reduced speed levels accepted degrees of buckling probability practical management of rail temperature variations and the effects of maintenance work on track conditions Fig 19 shows a diagram of the speed reduction approach providing both a linear stepped approach and smoothed approach in determining train speeds under predicted buckling failure The comprehensive approach aims to improve the effectiveness of speed reduction strategies in preventing track buckling ensuring train safety against buckling in hot weather and both high and normal speed railways While a speed reduction scheme is a direct and practical approach to prevent buckling in hot weather it is mostly preventive rather than predictive Numerical modelling techniques can also be used to achieve track buckling prediction focusing on the influence of dynamic loads Miri et al 66 has developed a multibody traintrack model which includes a detailed 3D FE model of the track to simulate traintrack in teractions Their finite element model includes the track structure rails sleepers ballast and fastenersand considers material properties geometrical constraints and boundary conditions These simulations focus on the effect of train loads on the rails increasing the likelihood for misalignments and defects leading to buckling Machan et al 61 uti lised an eigenvaluebased simplified approach within the FEM to analyse railway track buckling incorporating the dynamic effects of passing trains Eigenvalue analysis determines critical buckling modes and loads while a parametric study examines the effects of unconstrained length lateral resistance and rail sections on buckling behaviour The results provide critical insights into track stability under various loading scenarios enhancing the understanding of buckling phenomena and informing improvements in track design maintenance and safety Another numerical modelling approach was presented by Taghipour et al 93 who investigated the effects of tensile and compressive longitudinal forces on rail sleeper and ballast layers under vertical moving loads using FEM in MATLAB using a model as shown in Fig 20 Fig 18 Uplift due to train movements causing reduced lateral resistance as adapted from Kish et al 1990 Fig 19 Speed reduction schemes to prevent track buckling as proposed by Yi et al 119 D Agustin et al Construction and Building Materials 466 2025 140295 13 Sensitivity analyses for varying longitudinal forces and train speeds were performed to study dynamic responses such as displacement ve locity and acceleration of railway track components Using the Wilson theta numerical integration method they concluded that increases in train speed significantly increases rail displacement inducing more axial load to the rails These studies collectively advance the understanding of dynamic loads due to train movement on track buckling offering methodologies and insights crucial for enhancing railway safety and operational reli ability By integrating these dynamic effects approaches can be devel oped to provide a comprehensive framework for predicting and mitigating track buckling risks Despite significant advances in under standing the effects of dynamic train loads on track buckling several research gaps remain particularly in the context of sharp curved tracks When trains approach such curves at high speeds overbalanced speed lateral forces acting on the rails increase particularly pushing the outer rail This can not only raise the risk of derailment but also contribute to lateral track shift which in turn heightens the risk of track buckling Furthermore other train induced effects such as aerodynamic forces generated by highspeed trains and forces on inclined tracks are more prominently studied in the context of train dynamics such as stability ride comfort and operational safety rather than track dynamics While these factors are occasionally considered in other railway engineering analyses their contribution to track buckling is understood to be less significant compared to the welldocumented effects of thermal forces and dynamic train loads Current research primarily emphasizes the role of thermal expansion and traininduced forces in influencing track sta bility with less attention given to aerodynamic forces in the context of track buckling Existing studies tend to focus primarily on longitudinal forces and their effects on lateral and vertical track dynamics however there is a need for more comprehensive investigations into the combined effects of lateral longitudinal and vertical forces especially on curved tracks 432 Seismic effects In addition to traininduced dynamic loads seismic forces represent another critical influence on track stability particularly in regions prone to earthquakes Unlike traininduced forces seismic forces act on the track system generating a combination of longitudinal lateral and vertical accelerations These accelerations can disrupt the structural integrity of the track system not only reducing lateral resistance but also inducing track geometry irregularities such as misalignments and ver tical displacements 54 Such irregularities coupled with ballast degradation and redistribution caused by seismic shaking further amplify the risk of track buckling and instability Esmaeili and Noghabi 22 developed an FEM model that in corporates the superstructure rails and sleepers and substructure ballast subballast and subgrade of ballasted tracks to evaluate their seismic response Their study demonstrated that seismic excitations significantly influence the effective length of the track during seismic events validated through shaking table tests Similarly Wang et al 106 employed DEM to investigate the effects of peak ground acceler ations PGAs on ballast resistance finding that higher PGAs correspond proportionally to greater reductions in lateral resistance due to decreased ballast compaction and diminished contact between the sleeper and ballast exacerbating the risk of track instability Experimental studies have further corroborated the seismic vulner ability of ballasted tracks Wang et al 104 conducted shaking table tests on continuous welded rail CWR tracks on bridges and found that seismic loads weaken ballast integrity leading to changes in longitudi nal resistance due to cyclic loading effects The tests revealed that simplified elasticplastic assumptions underestimate displacement re sponses particularly at higher seismic intensities Nakamura et al 71 evaluated the aseismic performance of ballasted tracks using fullscale shaking table tests concluding that lateral resistance decreases signifi cantly with increased PGA leading to amplified lateral displacements Subsequent studies by Nakamura et al 70 and Ishikawa et al 33 explored the dynamic behaviour of ballasted tracks under seismic con ditions emphasizing the cumulative strain characteristics of ballast and proposing countermeasures such as grouted layers to enhance seismic resilience Seismic effects in transition zones where embankments connect to bridge sections present additional challenges due to the combined in fluence of seismic inertia forces and hanging sleepers Takahashi et al 94 demonstrated through scaled laboratory tests that rail buckling potential is underestimated when these combined effects are not considered They proposed countermeasures such as antibuckling plates and ballast retaining walls to address these vulnerabilities Similarly bridge structures supporting railway tracks are also critically affected by seismic forces Wei et al 109 analysed the dynamic sta bility of trains moving over bridges due to seismic vulnerabilities of the track structure finding that vertical ground motions significantly in fluence the trainrailbridge systems stability These studies collectively underscore the complex and multifaceted impact of seismic forces on railway track systems While seismic effects are more prominently studied in the context of ballasted tracks due to their impact on ballast degradation they also critically affect bridge systems where dynamic interactions between train rail and bridge components exacerbate instability risks However key factors such as ground motion frequency duration and the distance of the epicenter from the railway track have not been adequately considered in existing studies Addressing these challenges requires further integration of seismic considerations into predictive models and the development of countermeasures tailored to both track and bridge systems to enhance resilience under seismic conditions 5 Prediction of buckling risk using machine learning and artificial intelligence Studies discussed in previous sections have highlighted de velopments in understanding traintrack dynamics in the context of track buckling Despite advancements in accurately representing com plex track models and using track system parameters to assess and predict buckling issues of scalability data availability and computa tional efficiency persist While these studies have deepened the under standing of track buckling current limitations hinder the prompt Fig 20 Additional axial loads due to traintrack dynamic interactions as adapted from Taghipour et al 93 D Agustin et al Construction and Building Materials 466 2025 140295 14 evaluation and prediction of railway track buckling However modern computational methods offer new opportunities for innovation in track management and maintenance Machine Learning ML techniques offer a potential strategy enabling preventive maintenance by identifying and mitigating poten tial issues before they become critical ML methods facilitate predictive maintenance forecasting future problems based on current and histor ical data and prescriptive maintenance providing recommendations to avoid or delay failures using artificial intelligence AI technology As presented in a study by Tang et al 95 the use of ML and AI in railway engineering has been increasing in recent years As shown in Fig 21 Maintenance and Inspection subdomain of research includes a significant portion of published literature on the use of ML and AI in railway systems This domain focuses on assessing the deterioration and operating status of complex mechanical and electrical systems within railway infrastructure Various AI applications address diverse prob lems including defect detection fault detection and diagnosis defect prediction failure prediction maintenance planning and autonomous maintenance These technologies are critical for predicting and pre venting railway track buckling ensuring safe and reliable train operations For defect detection most are enabled through visionbased moni toring approaches 1 Ferrari et al 26 utilised natural language processing NLP applications to identify defects within railway signal ling requirements documents Studies on trackrelated defect detection have concentrated on fastening systems track geometry and rail con ditions Trinh et al 99 and Xia et al 114 employed Adaboostbased approaches to train classifiers for identifying defective anchors and broken fasteners respectively Feng et al 25 and Wang et al 103 used Latent Dirichlet Allocation and deep neural networks DNNs to detect fastener defects Support Vector Machines SVMs and Fully Convolutional Neural Networks FCNN were leveraged by Gibert et al 27 for detecting fastening defects and Li et al 53 for rail crack monitoring using acoustic emission wave classification Object detection using images has also been explored by Guo et al 28 to perform realtime railway track inspection to detect acute track component changes or defects In defect prediction researchers focused on trackrelated elements analysing track geometry deterioration and rail defects with some studies incorporating rolling stock aspects Ritika and Rao 84 used the Inceptionv3 network by Szegedy et al 92 to predict vegetation overgrowth and rail defects Various AI techniques were applied including Artificial Neural Networks ANN for track deterioration by Lee et al 51 SVM for track geometry defects by Hu and Liu 30 and Decision Trees DTs for track geometry and railwheel wear conditions 5289 Sharma et al 89 also employed the Markov Chain and Ber noulli Process to enhance maintenance decisionmaking while Li et al 52 combined DT and SVM to predict failure alarms due to hot bearings These defect detection and prediction studies highlight the capabil ities of AI and ML in supporting buckling research However challenges remain regarding data availability and quality which are crucial for developing reliable AI models By integrating AIML with datadriven strategies railways can enhance predictive maintenance improving track safety and operational efficiency Most studies that focus on track buckling prediction using ML and AI implements a probabilistic approach to buckling risk evaluation For example Bae et al 11 presented a datadriven probabilistic buckling analysis scheme for CWR tracks using regression and the advanced firstorder secondmoment method to derive equations calculating the buckling probabilities These data used to arrive at these equations are mostly based on previously established analytical models that define the relationships among the different track parameters used in their study Here probabilities are calculated as a function of temperature increase from limit state equations as shown and simplified in Fig 22 showing a comparison of buckling probability curves for tracks with varying track parameters denoting its strength or stability The effectiveness of this approach is compared with existing methods such as CWERRI 24 and CWR Buckle 86 highlighting its potential for more accurate and less conservative predictions of track buckling The highlight of this study is the ability to consider multiple track parameters and condense their contribution to buckling probability into at most two equations allow ing for a detailed assessment of buckling risks Track parameters in this study include but not limited to track resistance misalignment track curvature and train speed On the other hand using datasets derived from numerical models is also something that has been explored to develop ML algorithms to predict buckling Ngamkhanong and Kaewunruen 74 has presented the use of artificial neural networks ANN to conduct buckling risk assessments in ballasted railway tracks due to extreme temperatures Here they established predictive models using data from their FEM simulation results providing higher accuracy in the representation of track conditions The neural network model demonstrated high accu racy in estimating buckling temperatures aiding in the detection of track buckling during summer A similar approach was further devel oped by Wongkaew et al 111 which developed an ML approach to predict buckling failure modes in ballasted railway tracks using comprehensive track system parameters in addition to mainly using temperatures Using simulation data from advanced numerical studies the study processed and analysed this data with sophisticated ML al gorithms XGBoost was identified as the most effective model and the approach demonstrated proficiency in identifying early signs of buck ling facilitating timely interventions and improving railway safety The proposed model has been successfully implemented for actual buckling detection in Thailand Based on data from previous actual incidents it has proven to be reliable in practice Other approaches in sourcing the training data are also possible it is not only limited to analytical or numerical modelling of the railway tracks Hong et al 29 developed an ML model to predict rail temper atures by incorporating weather and solar effects The model achieved high prediction accuracy using techniques and ML algorithms such as XGBoost SVM random forest polynomial regression and ANN The Fig 21 Use of AI and ML in railway engineering percentage of papers published as shown by Tang et al 95 D Agustin et al Construction and Building Materials 466 2025 140295 15 study also introduced the Train Speed Limit Alarm Map TSLAM to help impose speed restrictions based on predicted rail temperature de viations enhancing track safety and train timeliness Jerripothula et al 34 proposed a datadriven approach to detecting track misalignments a significant cause of railway derailments The Track Misalignment Detection TMD dataset was introduced and the study leveraged feature extraction and transfer learning TL for binary image classifi cation Experiments demonstrated that TL models selected based on the proposed evaluation criterion outperformed other models during testing Similarly Minguell and Pandit 65 explored new datadriven techniques for identifying railway track faults using YOLOv5 Faster RCNN and EfficientDet The models were trained and tested on a dataset of images containing different railway track elements showing high precision in detecting nondefective elements and varying recall rates for defective elements Stodczyk et al 90 used fuzzy sets to predict minimum buckling temperatures for railway tracks addressing the limitations of conventional rail buckling models due to uncertain track properties The fuzzy sets model trained with buckling data derived from experimental and field tests demonstrated low prediction error and rapid calculation times The flexibility of this methodology suggests potential applications beyond track buckling including vari ables like track geometry and vehicle dynamics However the level of accuracy of using this model is only as high as the quality of track buckling data available and used While these approaches are fundamentally datadriven they do not rely exclusively on the calculation of traditional track parameters to make their predictions Instead they leverage alternative data sources such as environmental factors like temperature or imagery of the track to assess buckling risks This represents a significant advancement from earlier methods that primarily depended on track parameters alone for predicting buckling behaviour By incorporating diverse data points these techniques broaden the scope of buckling risk assessment enabling the use of nontraditional metrics to predict track stability This development not only enhances the accuracy of predictions but also facilitates more flexible and adaptive monitoring strategies allowing for the timely identification of potential buckling events based on a wider array of indicators ML and AI play a pivotal role in predicting buckling risks and other defects in railway systems By employing various AI techniques re searchers can detect predict and manage defects ensuring the safety and reliability of railway operations These advancements contribute to improved maintenance planning autonomous inspection and dynamic scheduling of maintenance activities ultimately enhancing the resil ience and efficiency of railway infrastructure 6 Discussion and identified research gaps Understanding railway track buckling has long been a critical chal lenge in railway engineering essential for ensuring safety efficiency and sustainability in railway operations This review of existing litera ture explores various approaches undertaken by railway researchers and engineers to minimise track buckling risks The findings discussed in this section directly address the research objectives outlined in the introduction Specifically this review evalu ates the mechanisms driving track buckling examines the evolution and limitations of modelling approaches identifies critical track parameters such as lateral resistance and material properties and explores the po tential of advanced computational methods like machine learning for improving prediction accuracy These insights provide a foundation for identifying key research gaps and proposing future directions for enhancing track stability a Recognising Track Buckling Parameters Fundamental to the theory of buckling is the identification and understanding of various parame ters involved in track buckling These include rail temperature lateral resistance track geometry material properties and material deterioration all of which influence the stability of the track Among these material nonlinearities such as ballast weakening plastic deformation in rails and changes in stiffness and lateral alignment play a critical role in influencing track stability By further reducing lateral resistance and altering critical temperature thresholds these nonlinearities increase the susceptibility of the track to buckling The models discussed in this review try to integrate these parameters accounting for their variability and nonlinear behaviour to provide a more comprehensive and realistic representation of track stability under diverse conditions b Risk Assessment and Management Implementing strategies to assess and manage track buckling risks is crucial This involves optimising buckling safety margins ensuring the structural integrity of the track and conducting regular maintenance to mitigate risks Tech niques such as track inspections stress testing and the use of buckling prediction models are commonly employed Focusing on the recognised track buckling factors can further guide both track design and maintenance strategies to address reduced track stability For instance designing tracks to maximise resistance to lateral movement can be achieved by selecting optimal rail and sleeper fastening systems determining appropriate sleeper type and spacing and employing effective ballast designs Additionally maintenance schedules can be optimised to maintain safe rail temperatures ensuring that critical rail temperatures remain within acceptable limits Regular ballast maintenance monitoring rail alignment and Fig 22 Buckling probabilities as a function of temperature Graph adapted from Bae et al 11 D Agustin et al Construction and Building Materials 466 2025 140295 16 implementing stress relief procedures are essential practices to mitigate the risk of buckling By integrating these design and main tenance measures railways can effectively address the primary fac tors contributing to track buckling and enhance overall track stability c Advances in Modelling Significant progress has been made in the development of models that can well represent realworld condi tions These models simulate the behaviour of tracks under various loads and environmental conditions providing insights into poten tial buckling scenarios Utilisations of FEM and other computational techniques have been instrumental in this area However emerging approaches like DEM and coupled DEMFEM techniques are proving even more effective particularly for simulating granular materials like ballast This is due to the granular nature of ballast which consists of discrete particles interacting through contact forces While these methods offer greater accuracy in simulating complex interactions they come with high computational cost and memory consumption especially for largescale tracks DEM simulations require detailed particlescale information leading to significant resource consumption while FEM models may oversimplify material properties or boundary conditions Coupled DEMFEM techniques inherit the challenges of both making them highly resource intensive Additionally these models rely on precise input data such as material properties and lateral resistance which may not always be available introducing uncertainties Validation remains another challenge as largescale experiments are costly and small scale tests often fail to replicate realworld complexities However as computer technology evolves the availability of highspec ma chines with enhanced processing power and more efficient algo rithms could make these techniques more practical for largescale use d Computational Methods The potential of advanced computational methods for optimising track buckling prediction and prevention is substantial ML algorithms and datadriven approaches are increas ingly being used to analyse complex datasets identify patterns and predict buckling risks with high accuracy These methods enable more proactive maintenance and better decisionmaking Despite these advantages challenges remain in implementing these methods at scale Accurate predictions depend on the availability of high quality diverse datasets and the integration of realtime data from distributed monitoring systems requires significant infrastructure investment Moreover the complexity of ML algorithms can make their outputs less interpretable necessitating collaboration between domain experts and data scientists to ensure practical and actionable insights However despite the vast amount of research and literature avail able significant gaps still exist in fully understanding and mitigating track buckling These gaps are particularly evident in the context of the combined impacts of static track structures and train dynamics on track buckling failure The identified gaps include a Implications of External Dynamic Loads There is a limited under standing of how external dynamic forces including those generated by train movement and seismic activity interact with static track structures to influence buckling For example the impact of longi tudinal forces within long track sections remains underexplored as most models focus on relatively short tracks with simplifying as sumptions about boundary conditions These models often impose fixed boundaries to approximate the behavior of longer tracks which may not fully capture the distribution and propagation of longitu dinal forces over extended distances Dynamic train loads in longi tudinal lateral and vertical directions significantly affect track stability yet their interaction with static track structures is not fully understood Additionally seismic forces are often treated separately in current research rather than being integrated into comprehensive buckling prediction frameworks The transient and residual effects of seismic events such as weakened lateral resistance and residual displacements remain underdeveloped areas of study highlighting the need for holistic approaches that incorporate multiple dynamic loading scenarios into buckling analysis b Efficient 3D Modelling There is a need for more efficient modelling and simulation methods that can accommodate extensive 3D track dynamics while incorporating a wider range of track parameters and their corresponding properties including variability and nonlinear behaviour Current models often lack the capability to simulate largescale track systems with such detailed considerations limiting their applicability in realworld scenarios These models often simplify material properties track alignment boundary conditions and variability in lateral resistance to reduce computational costs which compromises their realism Inclusion of these parameters is essential for accurately capturing track behaviour and ensuring reliable and comprehensive evaluation results To enhance their applicability future models must incorporate advanced numerical techniques and multiphysics simulations capable of capturing the nonlinear and dynamic behaviour of track systems Additionally scalable methods are needed to account for variations in environ mental and operational conditions along extended rail corridors c Buckling risk map Integrating numerical results with corresponding realtime track conditions in areas prone to buckling along with forecasting temperature data provides a more comprehensive pre diction of potential buckling risk at specific locations This integra tion enhances the predictive capability of buckling risk maps and supports more informed decisionmaking for railway operators By incorporating realtime measurements of track conditions such as rail temperature sleeperballast contact conditions track alignment and ballast degradation alongside historical weather data and tem perature forecasts risk maps can dynamically predict the likelihood of track buckling To implement this approach realtime monitoring of railway tracks in areas prone to buckling is essential This moni toring system would provide continuous updates on track conditions and integrate them with numerical models and temperature forecasts to dynamically assess buckling risks However existing approaches lack seamless integration of these datasets and challenges remain in developing systems capable of processing and analysing such real time inputs at scale Further advancements in predictive analytics and sensor technology are essential to enhance the utility and reli ability of buckling risk maps for operational decisionmaking Addressing these gaps is crucial for improving the accuracy of track buckling predictions With the help of modern computational methods currently being used in railway engineering these challenges are sur mountable To overcome these challenges future research should focus on hybrid approaches that integrate numerical simulations with real time monitoring systems and datadriven methods For instance coupling multiphysics models with machine learning algorithms can enable dynamic predictions that account for evolving track conditions Realtime monitoring data such as temperature fluctuations and lateral displacement measurements can enhance predictive models providing railway operators with actionable insights for proactive maintenance Additionally advances in highperformance computing and algorithm optimization will make largescale 3D modelling more practical allowing for realtime risk assessments of entire rail networks In summary the advancement of railway engineering particularly concerning track buckling hinges on the synthesis of complex and innovative track modelling and the creative utilisation of ML techniques Focusing on these two crucial aspects lays the groundwork for reducing the risk of future railway accidents ensuring safer and more reliable railway systems for the future By addressing these research gaps the railway industry can significantly enhance its ability to predict and mitigate track buckling Improved modelling and monitoring techniques will not only reduce operational disruptions but also ensure safer and D Agustin et al Construction and Building Materials 466 2025 140295 17 more resilient railway systems The integration of advanced computa tional methods into maintenance practices will support targeted in terventions optimize resource allocation and ultimately reduce costs associated with buckling incidents 7 Conclusion Railway track buckling remains a critical challenge in railway en gineering posing risks to safety efficiency and sustainability of railway operations This review highlights the importance of understanding key variables including rail temperature lateral resistance and track structure and their role in influencing track stability Various methods have been developed to predict and prevent this phenomenon including theoretical foundations techniques for measuring critical track param eters and maintenance strategies aimed at optimising track stability However significant challenges persist due to the complex dynamics of track buckling and limitations in current modelling approaches Field tests can be dangerous and impractical to scale while analytical or numerical methods can be computationally inefficient Advances in FEM and other computational techniques have signifi cantly contributed to simulating realworld conditions and providing insights into potential buckling scenarios However gaps remain in comprehensively understanding and mitigating track buckling partic ularly regarding the combined impacts of static track structures and train dynamics further increasing the complexity of track stability analysis There is a need for more efficient 3D modelling and simulation methods to accommodate extensive track dynamics accurately Addressing these gaps is crucial for improving the accuracy of track buckling predictions A key takeaway is the potential of modern computational methods such as the application of ML and AI in accelerating buckling risk pre dictions These modern computational methods and technologies offer promising solutions to the identified gaps in current research by facili tating the analysis of complex datasets identifying patterns and pre dicting buckling risks with high accuracy enabling more proactive maintenance and better decisionmaking which are crucial for enhancing railway safety and efficiency To fully leverage these tech nologies research must focus on integrating them with traditional models bridging the gap between static and dynamic factors and developing efficient 3D modelling frameworks capable of accommoda ting largescale track systems Overall integrating advanced computational methods such as ML AI and big data analytics into railway engineering can provide deeper insights and more reliable predictions ultimately enhancing the resil ience and reliability of railway track systems By overcoming current challenges these innovative approaches can significantly improve rail way safety and operational efficiency CRediT authorship contribution statement Ngamkhanong Chayut Writing review editing Methodology Conceptualization Agustin Dan Writing review editing Writing original draft Methodology Formal analysis Data curation Conceptu alization Wu Qing Writing review editing Supervision Method ology Conceptualization Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article Acknowledgements Dan Agustin is the recipient of Australian Research Council Stipend Scholarship and Central Queensland University International Excellence Award Qing Wu is the recipient of an Australian Research Council Discovery Early Career Award project number DE210100273 funded by the Australian Government Data availability Data will be made available on request References 1 P Aela J Cai G Jing HL Chi Visionbased monitoring of railway superstructure a review Constr Build Mater 442 2024 137385 httpsdoi org101016jconbuildmat2024137385 2 P Aela L Zong W Powrie G Jing Influence of ballast shoulder width and track superelevation on the lateral resistance of a monoblock sleeper using discrete element method Transp Geotech 42 2023 101040 httpsdoiorg101016j 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