Sustainable Railway Infrastructure: Modernization Strategies for Integrating 1520 mm and 1435 mm Gauge Systems

Abstract

This article examines the modernization of railway systems with a focus on sustainable infrastructure development, aligning with the European Commission’s strategy for integrating 1520 mm gauge railways into the European 1435 mm gauge network. A key challenge lies in addressing the technical aspects of the railway infrastructure that are not explicitly detailed in the European strategy but have evolved through the parallel historical development of two distinct railway engineering systems. An analysis of calculation methodologies highlights that the primary difference in determining technical parameters for 1435 mm and 1520 mm tracks stems from the selection of the primary classifier based on functional purpose and strength requirements. Furthermore, the existing concept of mechanical system motion presents limitations in harmonizing the technical aspects of railway systems with different track gauges. To bridge this gap, two potential solutions are proposed. The first suggests expanding the conventional mechanical system motion framework by incorporating principles from the theory of relativity, while the second explores the application of elastic wave propagation theory as a novel conceptual model for railway system dynamics. The choice of modernization strategy will play a crucial role in ensuring long-term sustainability of the railway infrastructure, requiring a balanced approach that accounts for the operational intensity, infrastructure wear, and specific technical requirements of track elements in different railway gauge systems.

1. Introduction

Is it possible to integrate railway systems with 1520 mm and 1435 mm gauges without a comprehensive strategy, or does such an approach inevitably lead to a technological and logistical dead end? This question becomes particularly relevant in the context of railway system modernization aligned with the European Commission’s strategy [1], which plays a strategic role in developing trade, transit potential, and competitiveness; improving transport and logistics infrastructure; expanding railway corridors and the network of intermodal terminals; and enhancing control systems, security, and international cooperation.

According to the European Commission strategy, a plan has been developed for implementing a 1435 mm gauge railway network, which will be operated alongside the existing 1520 mm gauge network, based on the following principles:

• “The 1435 mm gauge system would focus on higher-speed transportation (international passenger, IC, and container/platform wagon freight), with the 1520 mm system catering for lower-speed transport (local and regional passenger traffic and heavy bulk).
• The development of a 1435 mm backbone network in the two countries would be implemented in a phased manner, from West to East, with the largest urban agglomerations eventually connected to the new 1435 mm corridors to support future economic development.
• For each line, the required configuration is defined (1435 mm only, 1520 mm only, or both). This is based on a number of factors including:
  • Cost and combined network-wide operational aspects (1435 mm and 1520 mm systems).
  • Time for project development and implementation.
  • Ensuring the capacity of the current 1520 mm gauge system during the implementation and operation of the new lines.”

The European Commission strategy applies an advanced planning methodology that takes into account the existing data limitations and uncertainties inherent to the current situation. Although the European Commission strategy considers the economic and infrastructure aspects of integration, the successful implementation of the project largely depends on the technical compatibility of railway infrastructure systems. Unfortunately, the tendency to write scientific articles is focused on the discussion of tactical decisions in engineering tasks, rather than strategic decisions. However, the article focuses on the technical strategy of integrating 1520 mm and 1435 mm gauges. Therefore, this article examines the feasibility of implementing this strategy from an engineering perspective.

The challenge lies in considering technical aspects that are not reflected in statistical data, but rather are the result of the parallel historical development of two distinct railway engineering systems: 1435 mm and 1520 mm.

The fundamental differences between these engineering systems stem from the selected railway classification frameworks, the conceptual approaches used to evaluate track performance, and the modeling methodologies that were applied during the development of each system.

Thus, the goal of this study is to justify the need to consider not only the efficiency of modernizing railway engineering systems but also the historical development of their concepts, while integrating modern technical requirements.

The main question addressed in this study is as follows:

Should railway infrastructure be developed through the introduction of new engineering concepts, or should existing technologies be adapted to new conditions?

To comprehensively present the current state of railway engineering development, this article is structured as follows:

Section 2 examines the technical aspects defined by the European Commission strategy and presents a comparative analysis of the key approaches to the development of railway track engineering systems with 1435 mm and 1520 mm gauges. Section 3 discusses the challenges and solutions that define the technical aspects of railway tracks. This section sets out an approach to modernizing the description of the physical interaction processes between the track and rolling stock. Two potential solutions are proposed. The first suggests expanding the conventional mechanical system motion framework by incorporating principles from the theory of relativity, while the second explores the application of elastic wave propagation theory as a novel conceptual model for railway system dynamics. Section 4 presents a discussion on the feasibility of implementing the European Commission strategy. Section 5 provides the conclusions and recommendations based on the conducted research.

2. Materials and Methods

2.1. Technical Aspects Formed in the «Strategy for the EU Integration of the Ukrainian and Moldovan Rail Systems»

• The European Commission strategy characterizes the analysis of the existing 1520 mm railway track system through the lens of the 1435 mm railway network as follows:

Section 4.1.1.3 «The Ukrainian network mainly comprises Rail R65 and R50 types. Standard rail length ranges between 12.5 m and 25 m, with joints and two joint bars or fishplates bolted through the web of the rail. Rail type R50 is not compliant with TEN-T requirements regarding axle load. With 51.50 kg/m weight, it is used on some mainline sections with 200 m length, but mainly on siding areas and marshalling yards. Rail type R65 complies with the TEN-T axle load standards.».

Section 4.1.1.4 «Main issues in relation to poor track condition can be classified as follows:

• Inadequate and/or absence of drainage leading to flooding.
• Track components in poor condition, with geometry in good condition (alignment and level defects).
• The profile of tracks not maintained (rail’s corrugations, rail head’s surface defects with cracks, intrusion, shelling, etc.).
• Sleepers (old and second hand) and/or not well adjusted (squareness of the ties). Heterogeneity in track support (e.g., use of mixed wooden and concrete sleepers on a given section) can also affect track condition and lead to speed restrictions.
• Ballast polluted and/or missed.
• Elastic fastening missing, and crampon not adequate for modern tracks.
• Absence of uniform track gauge.
• Joints low and in poor condition.
• Rail with excessive wear and/or important side wear, becoming worn down.
• Weak rails and sleepers.
• Turnouts in poor condition.
• Rail life span is conditioned by the overall tonnage catered for by the different lines and determined by established rules.»

Section 4.4 Maintenance

• «Significant deterioration of rail infrastructure affects provision of high-quality and safe freight and passenger transportation services. The situation leads to numerous speed restrictions and lower average speed of transportation of cargo and passengers»;
• «Speed restrictions mainly apply to regional lines; however, it is estimated that about 50% of the network is operated with a limitation in the order of 60 km/h».

Section 4.9 SWOT analysis:

c.

Strengths: (i) the existing rail infrastructure provides sufficient capacity and coverage. (ii) With investments into modern interlocking systems, track protection, traffic management and communication, level crossings, and limited alignment corrections, an operational speed of 200 km/h on certain parts of the network are possible. (iii) With the high axle loads of 25 t and a longer train development length of approximately 1000 m, the capacities for heavy bulk transport are comparatively high;

d.

Weaknesses: (i) low technological level of the rail system. With the introduction of modern interlocking and traffic management systems (ERTMSs), the performance and therefore the competitiveness of the rail system can be significantly improved. (ii) Different track gauge than in the neighboring EU countries. The rail system is currently not compatible with the EU rail system;

e.

Opportunities: as part of the future revised TEN-T regulation there will be opportunities for enhanced coordination in the medium and long-term development of the lines.

Section 5.1.1 Technical and operational integration of the Ukrainian and Moldovan rail systems into the EU, including the ERTMS: one of the key elements to achieve integration is ensuring rail interoperability. In that regard, compliance with the technical specification for interoperability (TSI) is essential.

Section 5.2.10 Opening up the rail markets to up-to-date technologies is essential for future development and the EU integration of both systems. In addition to safety and security improvements, the use of new technologies will increase the capacity of the system and its operational flexibility.

2.

The main changes in the reconstruction of 1520 mm gauge railway systems are characterized in study [1] by the following concepts:

Section 6.1.1 Investments that allow for the continuous and effective operation of the 1520 mm system will be crucial. This could include, for example, the modernization of damaged and outdated infrastructure, but also investments at border-crossing areas to improve their effective throughput capacity. Nevertheless, bearing in mind the expected integration with the EU and the planned transition to 1435 mm track gauge, it is recommended that when investing in the 1520 mm network, such investments already consider a future potential transformation into the 1435 mm gauge system by, for example, using polyvalent sleepers able to accommodate both gauges. This approach has been applied successfully in similar situations (e.g., Spain), with the difference in the cost of such sleepers being insignificant.

Section 6.1.4 presented options for the reconstruction of railway infrastructure systems, from which four options were selected, shown in Figure 1, Figure 2, Figure 3 and Figure 4. In Section 6.1.5, a cost assessment of these options was conducted, demonstrating the reconstruction of the following elements of the railway track system:

• «Track substructure.
• Drainage-main line.
• Track superstructure.
• Turnouts.
• Level crossings.
• Sidings.
• Supply and installation of fencing (for high speed only).
• Small bridges.
• Signalling-ETCS-interlocking-telecommunications.
• Overhead Catenary System (OCS).
• Power supply.»

Figure 1. Option 3: 1520 mm single-track upgrading; 1520 mm to 1435 mm single-track transformation [1].

Figure 1. Option 3: 1520 mm single-track upgrading; 1520 mm to 1435 mm single-track transformation [1].

Figure 2. Option 4: 1520 mm to 1435 mm double-track transformation [1].

Figure 2. Option 4: 1520 mm to 1435 mm double-track transformation [1].

Figure 3. Option 7: 1520 mm double-track upgrading; 1435 mm single-track parallel new construction [1].

Figure 3. Option 7: 1520 mm double-track upgrading; 1435 mm single-track parallel new construction [1].

Figure 4. Option: 1520 mm single-track to 1435 mm transformation [1].

Figure 4. Option: 1520 mm single-track to 1435 mm transformation [1].

Section 6.2 defined the defined the network functionalities:

• «1435 mm network functionalities:
  • Passenger International;
  • Passenger National;
  • Freight Fast.
• 1520 mm network functionalities:
  • Passenger Local/Regional;
  • Passenger Night trains;
  • Freight Slow/heavy.»

Section 6.7 «Parameters that are not subject to a specific options analysis in this study For certain parameters, there is no need to develop an options analysis as they are either already defined by policy requirements (e.g., TSI), or they should be developed to be compatible to the existing network (interoperability). For other parameters, the options analysis should be developed in the Feasibility Studies for each corridor.»

Section 6.7.1 «Axle load and structure gauge. The axle load is considered a “Hard” parameter in the TSI and thus, its minimum value is defined there, depending on the traffic category of each rail line.

For rail lines with a track gauge of 1520 mm, the minimum axle load is 22.5 t for dedicated passenger lines and 25 t for freight or mix traffic lines. In both cases, as a minimum the structure gauge S defined in the TSI should be applied.

Regarding the future 1435 mm lines, most of them will be envisaged for mixed traffic. Consequently, recommendation is to develop them with an axle load of 22.5 t and structure gauge GB or GC, depending on the envisaged traffic category. If in the future some 1435 mm rail lines are planned to be developed for passenger use only, the axle load and structure gauge requirements should be assessed in a Feasibility Study, depending on the traffic category.»

Thus, the aforementioned technical aspects will be further used for a comparative analysis of the key approaches to the formation of technical aspects of railway track engineering systems with 1435 mm and 1520 mm gauges, their modern implementation, and interchangeability. Additionally, the nuances of the possible expansion of the accumulated operational experience of both systems are discussed, taking into account the modernization of concepts regarding the physical nature of the interaction processes between the track and rolling stock by supplementing existing concepts with the principles of elastic wave theory.

2.2. Technical Aspects of Railway Track Classification

To solve most techno-economic challenges in transport process management, a classification system for railway lines and sections is required.

In many countries, the concept of “railway track classification” is not established as an independent regulatory standard; however, the use of track classes, categories, or groups serves as a foundational element in shaping the regulatory framework for railway infrastructure management. This classification is crucial for standardizing design and operational practices, as well as for ensuring consistent safety and maintenance requirements.

Railway classification varies across countries based on several key parameters.

Table 1. Railway track classifiers.

Country	Axle Load	Max Axle Load	Freight Traffic Density	Theoretical Transport Volume	Max Speed	Freight/Passenger Train Speeds	Structure Gauge	Usable Length of Platform/Train Length
Germany		x	x		x
France				x
USA			x		x
Canada			x			x
European Union (TSI INF)	x				x		x	x

presents the main characteristics used in international practice for infrastructure evaluations.

For 1435 mm gauge railways, different countries employ single-, dual-, and triple-parameter classification systems [2,3,4,5] (see Table 1). In the context of 1520 mm gauge railways, two classification systems have historically evolved [6]. The first of these systems is centered on design standards, the purpose of which is to regulate geometric alignment, track profiles, and substructure specifications. The second system is centered on operational criteria, the purpose of which is to define the structure of the track and its maintenance requirements.

As shown in Table 1, the TSI INF (Technical Specifications for Interoperability relating to the “Infrastructure” subsystem of the EU rail system) proposes a classification system based on four key classifiers.

The classification of railways in different countries has evolved due to historical development and functional differences in the railway infrastructure. The fundamental criteria, validated through decades of railway operation, that influence classification choices include the track strength [7,8,9,10,11,12], stability [13,14,15,16,17,18], and safety [19,20,21,22,23,24].

Engineering and Structural Considerations

Currently, the selection of track structure characteristics is carried out according to regulatory documents. However, it is important to note that initial classification criteria were based on track strength calculations.

Track strength calculations aimed to answer whether certain structural elements could be used within the track system by establishing stress criteria in specific locations. These stress values were determined based on extensive experiments and operational experience.

Key Findings from Comparative Methodology Analysis

• Researchers studying both 1435 mm and 1520 mm gauge track systems based their track strength calculations on the prevailing knowledge of physics and mathematics of their time. These calculations were grounded in several well-established principles: the differential equation of rail bending, treating the rail as a beam on a continuous elastic foundation under a vertical static load; dynamic process modeling using Gaussian probability distributions to account for the influence of multiple independent factors; and the inclusion of horizontal forces [25,26], drawing on the foundational work of Timoshenko [27].
• Mixed passenger and freight traffic—including both empty and heavily loaded trains—is a defining feature of the 1520 mm railway system, with operational safety for this diverse flow as its primary objective. As a result, a dynamic factor analysis emphasized the evaluation of force variations (dynamic loads). The calculated values for key forces—such as (i) the maximum equivalent load for stress calculations in rails, (ii) the maximum equivalent load for deflection calculations of rails, stresses, and forces in the sub-rail foundation elements, and (iii) the dynamic force exerted by the rail on its support—account for multiple influencing factors, including the structural design of rolling stock bogies, train speed, the presence of isolated and continuous wheel irregularities, and the characteristics of track geometry deviations.
• For 1435 mm railways, the narrower range of axle loads and emphasis on track maintenance cost optimization led to a focus on the Dynamic Amplification Factor (DAF), which measures the track condition based on track–vehicle interaction dynamics without specifying which aspect of the impact is considered.

Accounting for Thermal Forces in Stability Calculations

The track stability assessment methodology, particularly concerning thermal forces (track stress caused by temperature fluctuations), revealed a common dependence between rail elongation and temperature variations [28,29,30]. However, differences in track strength calculation methodologies for different gauge widths resulted in distinct applications of this dependency.

Uniformity of Track Elevation Calculation Methodology

The method for calculating rail elevation in curved track sections is consistent across different track gauges, as it is based on universal physical principles. This approach considers factors such as unbalanced acceleration, train speed, and curve radius and applies a unified formula to determine the required rail elevation.

Similarly, derailment risk assessment principles remain consistent for both 1435 mm and 1520 mm gauge tracks [31,32].

Engineering Approaches in Track Design and Unification Challenges

Historical railway engineering developments show that both 1435 mm and 1520 mm gauge railway infrastructure systems were built using similar principles available at the time.

The primary difference between track parameter calculation methodologies for 1435 mm and 1520 mm tracks arose from the choice of the main classification factor, which was based on the functional purpose of the tracks and structural strength requirements.

Efforts to standardize railway requirements have been made through international standards such as TSI INF. However, differences in the operational conditions, infrastructure, and economic models make it impractical to create a universal classification or to transfer design solutions directly from one gauge system to another.

3. Results

3.1. Challenges in Defining the Technical Aspects of Railway Tracks

When calculating railway tracks, three key challenges arise: (1) the uncertainty of the interaction mass, (2) the heterogeneity of the track structure, and (3) the need to account for dynamic loads in different planes. Below, we examine how these challenges relate to traditional mechanical concepts.

To begin with, let us consider the challenges in the conceptual description of mechanical systems.

Firstly, historically, there have been two stages in the development of mechanical system descriptions:

• Analysis of uniform rectilinear motion using Newton’s laws, where
  • The nature of motion was determined by Newton’s First Law, stating that inertial reference frames record rectilinearity and uniformity of motion in the absence of interactions or when the resultant force equals zero.
  • The parameters of mechanical motion were formulated by Newton’s Second Law, defining the relationship among (i) the resultant force applied to the body, (ii) the rate of velocity change in the direction of the applied force, and (iii) the mass involved in the interaction.
  • Newton’s Third Law established equilibrium in mechanical systems by considering forces/reactions from each interacting body.
• Analysis of accelerated/decelerated rectilinear and rotational motion, where
  • The nature of motion was defined by introducing non-inertial reference frames.
  • The parameters of mechanical motion were formulated using D’Alembert-Lagrange’s principle and its further developments [33,34,35,36].
  • To create a balanced closed system, “fictitious” forces were introduced, such as inertial forces, centrifugal force, and Coriolis force [37,38,39,40,41,42,43].

Railway track calculations, as part of mechanical systems, fully utilize these principles [44,45,46,47,48,49,50]. However, railway tracks have three inconvenient properties:

• Their dimensions exceed the local interaction zones with rolling stock, meaning that the interaction mass is unknown.
• Their structure is heterogeneous both in length and depth, necessitating the introduction of stiffness characteristics in all computational planes, at various levels, and along the track length. This significantly affects the velocity variation of track and rolling stock components during the interaction.
• For railway tracks to be considered a balanced system, the interaction of active and passive forces in different planes must be accounted for. This complicates calculations as it becomes difficult to determine the exact resultant force impact.

In all dynamic track calculations, three unknown parameters remain, making it necessary to conduct experiments to identify interaction patterns between rolling stock and rails.

Secondly, all railway track calculations rely on a geometric assessment of the localized force distribution, independent of time. The concept of a “time step” is used, which determines the position of structural track and rolling stock components for force distribution under given interaction conditions. It is assumed that all forces and reactions are applied simultaneously [50,51,52,53,54,55,56,57].

This approach requires probabilistic consideration of the possible simultaneous impacts of various forces, with a specific correlation of force magnitudes, obtained through experimental studies that determine “equivalent” or “reduced” interaction masses

Thirdly, rolling stock movement on railway tracks is characterized by complex oscillations, caused by the following: (i) changes in the movement regime along track sections, (ii) heterogeneities in the track structure, alignment, and profile, (iii) design features of rolling stock, and (iv) atmospheric and climatic conditions.

These physical aspects of the track–rolling stock interaction must be considered in geometric descriptions by analyzing non-uniform curvilinear motion.

A key feature of this motion’s geometric description is the distinction between “normal” and “tangential” interaction components. This distinction is entirely artificial, introduced to describe observed motion trends in curves, and does not reflect the underlying physical processes occurring during curvilinear motion.

In rectilinear motion, the force direction fully determines the velocity change direction of a body/system after impact.

However, oscillations caused by curvilinear motion exhibit different origins and force application locations. The determination of force magnitudes requires solving separate problems, each with distinct reference frames.

For instance, the “fictitious” centrifugal force can be incorporated into calculations in various forms, including as the Newtonian centrifugal force, D’Alembert’s centrifugal force, or as the normal component of the transport inertia force within the equations of relative motion.

The lack of understanding of fictitious forces requires extensive experimental research to determine the conditions under which they occur and their effects. For this purpose, research centers have been established to conduct a series of experiments on railways to evaluate the effect of fictitious forces on the stability of trains on curves.

However, developing experimental methodologies is essential, as they must account for the causes of the studied effects. Any methodology is based on a specific concept, which is missing for these forces. This is why fictitious forces have been introduced based on observed effects rather than on their physical origins.

Thus, the existing regulatory framework for both 1435 mm and 1520 mm track systems was developed through extensive experimental and operational experience.

Consequently, under the current calculation concept, transferring requirements from one system to another is impossible without large-scale experimental studies. Attempts to transfer TSI INF standards to 1520 mm railway tracks have shown that without large-scale experiments, adapting these standards requires substantial modifications [2].

If such conditions had been met, a unified calculation system for railway maintenance would likely already be in place—capable of simulating the real behavior of track sections under actual rolling stock operations, while accounting for long-term climatic influences specific to each location. To achieve this, calculation models must incorporate time-dependent geometric changes resulting from track–rolling stock interactions, variations in stiffness over time, and track geometry monitoring data that enable modeling under different train configurations, speeds, and load conditions.

Thus, overcoming the challenges in defining railway track technical aspects requires a new calculation concept for modeling the railway track and rolling stock interaction. The most promising concept today is the theory of elastic waves.

Since this study is part of a broader research direction, some aspects of elastic wave theory application for railway track modeling and monitoring have already been addressed in studies [58,59,60,61]. This article will focus on demonstrating the potential of this theory for determining the technical aspects of railway tracks, applicable to both 1435 mm and 1520 mm gauges, based on the known properties of waves.

As mentioned earlier, the main limitations of the existing concept are related to the following:

• The lack of time-dependent modeling of mechanical system motion.
• The lack of understanding of force origins in curvilinear motion modeling.
• The inability to model stiffness processes.

The following sections will address these issues in detail.

3.2. Overcoming Challenges in Defining the Technical Aspects of Railway Tracks

3.2.1. Considering Time in the Modeling of Mechanical System Motion

Time is one of the seven fundamental physical quantities, forming the basis for understanding the process of recording what is referred to as “change.”

The concepts of “statics” and “dynamics” are inherently relative and are interpreted in each context based on two key factors: the time scale over which changes are observed and the capabilities of the measuring instruments used by the observer.

Any change is considered “static” if, during the measurement period, the measuring instruments do not detect a transition from one fixed state to another due to external influences. Thus, the concept of statics and dynamics depends not only on the physical process itself but also on the method of its observation and measurement. If different states are recorded, the change is considered “dynamic.”

In the natural sciences, changes are typically described through scalar quantities, which represent specific states, and vectors, which characterize the transitions between these states.

Mathematical descriptions of “change” can be constructed without directly incorporating time in vector representations. This approach is widely used but is limited by the difficulty of deriving analytical dependencies, leading to the broad application of numerical methods. Furthermore, various vector formulations exist depending on their functional use in modeling.

Without incorporating time, the description of natural phenomena using vectors becomes incomplete. Therefore, modern physics increasingly considers processes not in a three-dimensional spatial system but in a four-dimensional space–time framework. This approach accounts for both the geometric properties of a system and its evolution over time, which is particularly important for analyzing dynamic processes.

The consideration of time in mechanical systems is especially crucial when analyzing the propagation of elastic waves, as their dynamics are directly linked to changes in energy over time.

In elastic wave theory, there are two primary types of waves: longitudinal and transverse waves. All other types of waves are specific cases that arise under particular propagation conditions.

Although waves have a well-defined propagation speed, this parameter is often neglected in practical problem-solving. This characteristic is widely used in structural monitoring (e.g., non-destructive testing), yet it is rarely included in mathematical models. However, the fact that waves inherently propagate at a specific speed makes them highly suitable for use as vectors. As is well known, waves serve as carriers of energy, making them physical vectors of energy transmission through space and time. Due to the fundamental properties of waves, it is always possible to determine the following:

• The direction in which the wave will propagate.
• The speed at which it moves.
• The way in which its amplitude will change as it propagates.

Elastic wave propagation is a natural phenomenon, which, according to the theory of relativity, remains invariant in any reference frame. This property allows elastic waves to be used to describe the motion of mechanical systems, complementing classical concepts of interactions. Therefore, incorporating elastic waves into the description of mechanical system motion offers an expanded interpretation of Newton’s laws.

For example, Newton’s first law can be reinterpreted through the lens of elastic wave theory as follows: any change in momentum P(t) results in a change in the state of a mechanical system, and conversely, altering the system’s state requires an impulse. While classical mechanics focuses on the motion of objects, it does not explain how an impulse propagates through a medium—this gap is addressed by elastic wave theory, which describes motion as a time-dependent process of energy transmission.

Newton’s second law can be extended by incorporating the time-dependent nature of its fundamental components, including the momentum P(t), force F(t), interacting mass m(t), and velocity u(t), thereby providing a more dynamic and realistic representation of mechanical interactions over time.

At any given moment t over a time period T, these components are related as follows: P(t) = F(t)T = m(t)u(t).

This allows changes in the system to be considered not only in terms of applied forces but also in terms of the distribution of energy across all points within the system over time. Thus, the second law of Newton gains an additional interpretation through energy distribution processes in space and time.

Impulse propagation in a system is based on the wave property of forming sequences of incidence–transmission–refraction when encountering barriers, such as at the transition between different structural elements or the presence of defects. This property of waves demonstrates the law of energy conservation, allowing for the superposition of impulses at any location while accounting for changes in the impulse magnitude over time.

Additionally, the superposition of waves within a mechanical system, such as incident and reflected waves, provides a complete understanding of dissipation processes. This further supports the law of energy conservation and formalizes thermodynamic laws by specifying energy magnitudes, types, and transformation directions.

Moreover, the superposition of refracted waves (the interaction of waves as they transition between different media) provides a complete description of system inertia, including all components of the second law of Newton (momentum, velocity, displacement) during motion in response to an applied impulse.

The third law of Newton, in its original form, explains interactions between bodies that were not previously in contact. However, it struggles to explain reaction forces in systems that were already in contact within the existing mechanical system motion framework.

The phenomenon of incidence–transmission–refraction in wave propagation is fully described by the laws of energy, momentum, and angular momentum conservation [58,59]. This principle explains energy transmission within a system, eliminating the need for fictitious forces that were historically introduced to balance mechanical equations.

This effect is evident in the propagation of elastic waves through a multi-element rotating structure, where waves reflect at the boundaries between elements, transmit into adjacent media, and undergo amplitude changes depending on the material properties at the contact interfaces.

This insight allows previously unexplained effects to be understood without introducing fictitious forces (such as centrifugal force or Coriolis force). By employing elastic wave theory with time-dependent effects, the need for fictitious forces disappears, and interactions within a system can be naturally described.

As mentioned earlier, the traditional mechanical motion model considered time only in terms of discrete steps (“time steps”). In this framework, time was treated logically, based on observed amplitude–phase relationships obtained through experiments.

For example, after numerous experiments, sensor characteristics were established for measuring deflections and stresses in track structures under the impact of rolling stock. These studies relied on an amplitude–frequency analysis. Although recorded oscillograms of passing trains appeared visually different in length at different speeds, this aspect was not considered relevant in traditional data processing.

A similar approach is used in geometric wave representation, where logical time is applied, and amplitude–frequency characteristics are evaluated based on wavelength.

However, the fact that humans can recognize speech or music regardless of location indicates that sound waves propagate identically across different points. This suggests that impulse propagation should be analyzed not only along wave propagation directions (spatial dimensions) but also at each local point, incorporating time-dependent factors.

By integrating time into elastic wave theory, the description of wave processes from impulse impacts becomes more precise, incorporating superposition effects and the ability to analyze vibration amplitudes at any spatial location.

The specified capability enables an expanded description of many dynamic processes. For example, the following sections illustrate how modeling can be extended for fracture mechanics processes and phenomena, such as shock waves. Both processes are associated with considering amplitude variations at specific locations.

For a comprehensive study of fracture mechanics in explosions, it is necessary to analyze the propagation of elastic and electromagnetic waves while accounting for the structural composition of the medium. This is because interactions between surfaces in mechanical systems involve complex energy transfer processes similar to the propagation of elastic waves. For instance, considering an explosive wave, the explosion impulse can be represented as a function consisting of two parts. The first part is a steeply rising segment, where the impulse magnitude increases rapidly over a short period, representing the rate of impulse change over time. The second part is a decaying curve, which lasts significantly longer than the first part, while the rate of impulse variation is considerably lower. The intensity characteristics of both parts have a crucial impact on the destructive effect and the alteration of material properties, defining zones of irreversible changes.

For elastic waves, this is determined by the relationship between the rate of explosion impulse change and the propagation speed of this impulse in the materials affected by the explosion. The boundaries of irreversible changes due to elastic wave impact will be present if the following condition is met: the rate of explosion impulse change is greater than the propagation speed of the elastic wave in the medium.

Thus, irreversible processes under an elastic wave influence are primarily determined by the first part of the explosion impulse. However, when considering all aspects of fracture mechanics, the general criterion for defining the boundary of irreversible changes under an impulse impact is as follows: the energy directed toward the realization of the explosion amplitude is greater than the energy required to maintain bonds within the medium.

Shock wave phenomena can be more intuitively understood through aircraft motion.

The impulse intensity function resulting from an aircraft’s passage at each point along its trajectory is determined by both the aircraft’s geometry and its velocity. Since an aircraft has a specific configuration at a constant speed, every cross-section along its path will experience the same impulse intensity over time, meaning that the process of the aircraft passing through a given section remains consistent. However, variations in impulse characteristics depend on the aircraft’s speed. As the speed increases, the time required to traverse a given section decreases. Therefore, on one hand, increasing the speed shortens the duration of passage or effectively reduces the aircraft’s perceived length, while on the other hand, it alters the characteristics of the impulse effect. Consequently, modeling an aircraft’s flight involves analyzing the superposition of waves over time, generated by the aircraft’s impulse at each trajectory point, considering both the aircraft’s velocity and wave propagation in the medium.

Regarding the application of elastic wave theory with time considerations in the “rolling stock–railway track” system, this approach provides two key advantages.

First, it enables modeling based on real impulse sources, such as wheel–rail contacts, while accounting for their location and duration of action. Second, it allows for the use of experimental recording tools that consider the parameters of these impulses. This approach facilitates the adaptation of theoretical studies to experimental data while accounting for different data update rates. This is because theoretical modeling updates data based on wave propagation speeds, whereas experimental data updates depend on sensor characteristics and their inertia. However, analyzing experimental data obtained in this manner enables a comprehensive assessment of the impact of all components within the “rolling stock–railway track” system, ensuring a well-informed interpretation of recorded data.

This approach not only improves the diagnostic accuracy but also enables the refinement of existing mathematical models based on real-world data. Incorporating time into elastic wave theory allows for the recording of the amplitude–frequency characteristics of the system while also enabling an inverse analysis—determining the impulse source based on its response.

Table 2. Comparison of classical mechanics and elastic wave theory.

Criterion	Classical Mechanics	Elastic Wave Theory
Main Object of Analysis	Rigid and elastic bodies in space	Wave propagation in a medium
Role of Time	Describes object motion but does not account for energy propagation over time	Time is a key parameter that determines energy propagation
Momentum Transfer	Momentum is transferred only upon contact	Momentum is transferred through the medium as wave processes
Interaction Description	Uses forces (Newtonian and fictitious) to explain motion	Interaction is described through wave reflection, refraction, and superposition
Fictitious Forces	Introduced to explain motion in non-inertial systems (centrifugal force, Coriolis force)	Not required, as interaction dynamics are explained by wave propagation
Energy Conservation	Considered as the sum of potential and kinetic energy	Energy is transmitted through elastic waves, allowing for dissipation and inertia effects
Dynamic System Analysis	Describes object motion under applied forces	Describes momentum and energy changes over time and space
Application in Calculations	Used for analyzing strength, stability of structures, and motion of bodies	Used in defectoscopy, vibration modeling, and dynamic process simulations
Application in Railway Mechanics	Calculates track strength, stability, and dynamic loads on tracks	Enables real-time analysis of track and rolling stock behavior

presents a comparative analysis based on elastic wave theory, drawing on data from sources [58,59,60,61].

3.2.2. The Nature of Rotational Forces in the Modeling of Curvilinear Motion

It is well known that a perpendicular force or distributed load applied to the surface of an object induces normal stresses in the section under the applied impulse, and calculating these stresses has never posed a difficulty. Issues arise, however, when the force is applied outside the considered section. In such cases, concepts such as the moment of force, tangential stresses, and tangential forces come into play. This force application can cause rotation, and in engineering terminology, there are various names for this effect, including torque, rotational moment, twisting moment, and bending moment.

The existing concept of mechanical motion accepts this effect as a given and does not focus on the nature of its emergence. However, the propagation of elastic waves in space and time fully explains this process.

It is commonly known that

• The point of force application, perpendicular to its axis, divides any space into two zones: compression and tension.
• Pure longitudinal waves always propagate in the direction of the applied force.
• Pure transverse waves always propagate perpendicular to the direction of the applied force.
• In all other directions, both longitudinal and transverse waves propagate.
• Thus, the point of force application divides the surrounding space into two regions:

  a.

  Radially converging towards the force application point.

  b.

  Radially diverging from it.

• Within the force field:

  a.

  Any point along the radial direction aligned with the force experiences either compression or tension, depending on its position relative to the force application point.

  b.

  Any point along the radial direction perpendicular to the force experiences pure shear stress in the force direction, regardless of its position relative to the force application point.

  c.

  Any point along other radial directions, except for those perfectly aligned or perpendicular to the force, experiences rotation:

  i.

  Clockwise rotation if the point is to the left of the force direction.

  ii.

  Counterclockwise rotation if the point is to the right of the force direction.

The force axis and the perpendicular direction can be considered time axes, since the propagation speeds of longitudinal and transverse waves are known. Thus, the ellipsoidal surfaces with semi-axes in equal time intervals demonstrate identical phases of medium/particle oscillation under force action in time and space.

Since elastic waves are spherical by nature, the amplitude of oscillations decays inversely proportional to the distance from the source. Therefore, every point in the radial space experiences the same impulse effect in terms of duration and nature but with a time shift and a decreasing impact depending on its location relative to the force application point.

Previously, we examined the incidence–reflection–refraction wave chain phenomenon as the basis for force formation within a system. Next, we will analyze the nature of rotational force emergence using a specific example.

Example: The Effect of a Tangential Force on a Disk

Let us consider the effect of a tangential force on a disk, illustrated in Figure 5.

To do so, we will use the explanation of a single force F applied at point O, as described earlier. For simplicity, we assume a disk centered at O₁, where both points O and O₁ lie on the same straight line. We analyze the case where the disk is fixed such that it can only rotate about its center O₁.

When the force F is applied at point O, the straight line OO₁ divides space into the following:

• A region radially converging toward the force application point.
• A region radially diverging away from it.

At all times, there exists a pair of vectors (converging and diverging) lying in the same plane and positioned at the same angle to force F.

As an example, Figure 5 illustrates two such diagonal vectors, 1 and 1′.

Since the process occurs within the same body, the wave propagation speed is identical.

Therefore, these vectors will simultaneously reach the body boundaries at points A and B, where the incidence–reflection–refraction wave chain phenomenon occurs.

In this case, we do not analyze wave motion outside the disk, so we limit our scope to the emergence of reflection waves 2 and 2′. It is well known that reflection waves are oriented at the same angle to the normal as the incident waves. Hence, the wave characteristics of these vectors are identical, but their directions differ. When they simultaneously reach points C and D, the process continues.

This process will occur for various pairs of vectors within the disk plane. Since the vectors tend to rotate in the same direction, their effect can be interpreted as a force moment. Additionally, there will be diametrically opposite vectors, which means that the action of force F can be represented using the conventional force-pair approach.

3.2.3. Modeling of Stiffness Processes

In classical mechanics, the stiffness of an object is defined by its elasticity and resistance to external loads. However, in dynamic systems, stiffness is determined not only by static characteristics but also by energy transmission processes within the material, which is especially important for the propagation of elastic waves. In this context, stiffness can be considered through the dynamic characteristics of the medium and the conditions of its contact with other objects.

It is well known that an object’s stiffness depends not only on the characteristics of the applied impulse but also on three fundamental factors: the material’s physical and mechanical properties, the object’s geometric features, and the conditions of its interaction with surrounding elements—typically expressed as boundary conditions in computational models.

Previously in this article, the phenomenon of the incidence–reflection–refraction chain was discussed. Below, we examine how the conditions for stiffness formation are considered through this wave propagation phenomenon over time.

The consideration of the physical and mechanical properties of materials in stiffness formation has been extensively studied from the perspective of elastic wave propagation in time.

In classical mechanics, stiffness is determined based on the static parameters of the material. However, in dynamic systems, wave propagation plays a key role in stiffness formation since the wave velocity is directly related to the material properties.

The speed of wave propagation in any medium is determined by three fundamental properties: the material’s density, its elastic modulus, and Poisson’s ratio.

Therefore, the question of wave propagation in space and time does not pose significant difficulties in terms of theoretical modeling.

In addition, materials exhibit specific critical angles related to the behavior of longitudinal and transverse waves, as defined by Snell’s law. The first critical angle marks the minimum incidence angle at which a longitudinal wave ceases to penetrate the second medium, generating head waves. The second critical angle corresponds to the threshold at which the refracted transverse wave no longer enters the second medium, leading to the formation of Rayleigh surface waves. The third critical angle defines the minimum incidence angle for a transverse wave at which no reflected longitudinal wave is produced.

These angles are crucial in calculating structural stiffness, as they determine how waves transmit energy within a material. For example, if the incident wave angle exceeds the second critical angle, Rayleigh surface waves are generated in the material, significantly affecting local structural stiffness.

Thus, the incidence–reflection–refraction chain phenomenon accounts for the individuality of each material and provides the broadest explanation of how force interactions propagate within objects.

The consideration of the geometric characteristics of an object is well-researched and thoroughly described in the scientific literature.

When waves reach the boundaries of objects, impact, reflection, and refraction processes occur. These wave interactions, over time, determine the distribution of stresses within the object, influencing its response to external loads.

However, stiffness is determined not only by the internal properties of an object but also by how it interacts with other structural elements. In real-world conditions, all mechanical systems interact with one another, making the consideration of contact properties critically important.

Contact Stiffness Considerations

The description of contact conditions has been the subject of extensive research, with contact stiffness defined by a combination of factors: the material properties of the interacting objects, their geometric configurations, and the geometry of the contact surfaces.

For example, it is well known that the direction of wave reflection changes when bodies with different densities come into contact. This phenomenon is closely related to the concept of acoustic impedance, which is defined as the product of a medium’s density and the speed of sound propagation within it. At the same time, the speed of sound itself depends not only on the material’s density but also on its elastic properties, creating either a hard or soft acoustic medium.

Although contact stiffness is fundamentally determined by the material properties and geometry of the objects involved, in practice, it is also influenced by additional factors such as the contact pressure, friction, and surface characteristics of the materials. In elasticity theory, these influences are accounted for by modeling impulse variations across both time and space.

Stiffness as a Function of Elastic Waves

Examining stiffness through the lens of elastic waves allows for the connection of the static and dynamic characteristics of a system.

Traditional calculations typically separate stiffness into static and dynamic components; however, wave-based methods enable its representation as a continuous time-dependent function. By accounting for various impulse characteristics through wave superposition, stiffness can be accurately modeled under a wide range of conditions. This approach is especially valuable in engineering applications such as analyzing vibrational loads on rails and evaluating the dynamic response of bridge structures, ultimately contributing to improved travel comfort and greater environmental sustainability [62,63].

Unlike traditional methods, which consider only static stiffness, wave-based modeling allows for a time-dependent analysis of structural behavior.

This significantly improves the accuracy of calculations and enhances the prediction of potential structural failures.

4. Discussion

This section analyzes the feasibility of harmonizing the technical requirements of railway systems with track gauges of 1520 mm and 1435 mm within the framework of the European Commission’s concept. It also examines the technical viability of the European Commission’s proposals [1] for integrating post-Soviet railways with a 1520 mm gauge into the European railway system with a 1435 mm gauge. The analysis aims to identify potential challenges and possible solutions.

4.1. Background Analysis

In previous sections, it was demonstrated that the experience gained through numerous experiments and railway track operations has been instrumental in establishing technical assessment criteria for tracks with gauges of 1435 mm and 1520 mm.

As shown in Table 1, various countries have extensive experience in classifying railway tracks based on different parameters for the 1435 mm gauge. This facilitates the harmonization of technical aspects under alternative parameters. However, such experience is entirely lacking for the 1520 mm gauge railway track, as, during the formation of classification criteria, this railway system belonged to a single country. Following the dissolution into separate nations, the classification approach remained unchanged. Consequently, there is a complete absence of unified classification experience that incorporates both design and maintenance aspects, as observed for the 1435 mm gauge.

Therefore, the direct transfer of methodologies from the 1435 mm system to the 1520 mm system is impossible. To ensure reliability, additional experiments are required to establish appropriate classification criteria.

From this perspective, the existing concept requires adaptation and further research to harmonize the technical aspects of the two railway infrastructure systems with different track gauges. This process is both time- and resource-intensive.

To reduce time and resource expenditure, two conceptual modifications are possible. Based on the analysis of challenges and their solutions in defining the technical aspects of railway tracks, the following conceptual approaches for mechanical system motion are proposed.

4.2. Considerations for Technical Aspects of Railway Tracks

For evaluating the technical aspects of railway tracks, it is essential to consider the principles of mechanics that form the basis for stability and strength calculations. Historically, the concept of mechanical system motion was developed based on identifying the correlation between critical technical states of a mechanical system and its operating conditions. In other words, the feasibility of the mechanical system functioning under specific operational conditions was examined by defining the critical state as a limiting factor for its operation. To achieve this, the motion process of the mechanical system itself needed to be analyzed. Therefore, the process observed in experiments was described.

In traditional approaches to mechanical system calculations, the primary focus was on geometric changes in structures and strength assessments. This justified the use of idealized models that ignored dynamic factors such as wave processes and external influences. In most cases, the decisive factor in choosing a mechanical system option was the economic feasibility of its manufacturing, construction, and operation.

A key challenge in modern operational conditions lies in understanding and managing the interrelationship among three critical technical aspects: the functional purpose of the railway track, the maintenance and servicing system, and the structural characteristics of the track elements and construction.

Under this approach, the primary selection criterion is the functional safety of the railway track, both from the user’s perspective and in terms of environmental impact.

Thus, contemporary advancements in human understanding necessitate consideration not only of the movement process of the mechanical system under load but also of the natural phenomena accompanying this process. Consequently, it is essential to account for the rate of changes in the stress–strain state of the mechanical system itself and the speed of natural phenomena within it.

As is known, there is a fundamental contradiction from this perspective that prevents the application of the currently accepted concept of mechanical system motion:

• The classical law of velocity addition has a limited scope of application.

This limitation arises because, on the one hand, discussing velocity without specifying a reference system is meaningless within the existing concept of mechanical system motion. On the other hand, the invariance of elastic and electromagnetic wave velocity in media with certain characteristics is an established fact and is supported by the general principles of relativity theory.

4.3. Possible Solutions for Harmonizing Technical Aspects of 1435 mm and 1520 mm Railways

Based on the above considerations, there are two possible solutions to the problem of harmonizing the technical aspects of railway tracks with 1435 mm and 1520 mm gauges.

The first option involves introducing dependency coefficients for various parameters into the existing concept of mechanical system motion by accounting for the following:

-

The property of waves to decrease in amplitude proportionally to their length.

-

The interaction time between wheels and rails at different train speeds.

-

The relationships of mass, time, and length in accordance with the theory of relativity.

The second option involves applying the theory of elastic wave propagation in space and time as the concept of mechanical system motion [58,59,60,61].

Thus, each option provides a solution to the problem but with opposite potential capabilities in describing the analytical dependence between influencing factors and the results of changes.

Table 3. Comparison of proposed options.

Criterion	Option 1: Coefficients	Option 2: Elastic Waves
Method Basis	Introduction of coefficients to adjust calculations	Complete rethinking of the model based on wave processes
Ease of Implementation	Easier, as it adjusts existing calculations	Requires a new methodology and experiments
Required Data	Depends on empirical coefficients	Operates with the physical characteristics of the medium
Accuracy	Limited by the correctness of the coefficients	Potentially more accurate, as it accounts for the dynamics of the path

presents a comparative analysis based on elastic wave theory, drawing on data from sources [26,58,59,60,61].

The use of coefficients (Option 1) allows for adapting the existing concept; however, it remains dependent on empirical data, which reduces the accuracy of forecasts. At the same time, transitioning to a model based on elastic waves (Option 2) requires significant computational resources but potentially provides a more accurate description of the dynamics of the railway track.

4.4. Technical Feasibility Analysis of Integrating the 1520 mm Railway Network into the 1435 mm European System: Challenges and Critical Factors

Below is an analysis of the technical feasibility of the proposals introduced by the European Commission [1] for integrating the post-Soviet railway network with a track gauge of 1520 mm into the European railway system with a track gauge of 1435 mm.

The characteristics of the railway system with a 1520 mm gauge, presented in Sections 4.1.1.3, 4.1.1.4, 4.4, 4.9, 5.1.1, and 5.2.10, demonstrate a lack of understanding of the discrepancies between the technical aspects and the classification of requirements for railway infrastructure systems with gauges of 1435 mm and 1520 mm.

It has previously been shown that the primary difference between the calculation methods for determining the technical parameters of railway tracks with gauges of 1435 mm and 1520 mm is due to the functional purpose of the tracks.

For instance, in the railway system with a 1520 mm gauge, there are no established correlations between the force, the load-bearing area, stresses, or deformation modulus of granular materials and their thickness. There is also no classification of fastenings operating under specific force and stiffness characteristics. Moreover, there are no limitations on the magnitude of force impacts from rolling stock on the track, neither in classification nor in experimental studies.

At the same time, for example, on the railways of Ukraine, a system of the multiple reuse of rail and sleeper grid elements is employed. On sections with lower traffic intensity, so-called “old stock materials” are used—materials that have reached their usage limits according to established criteria for more intensive operating conditions. Furthermore, in an effort to accommodate the maximum amount of freight, railway systems with a 1520 mm gauge consider the impact of repeated maximum dynamic forces. However, while stress limitations are considered, displacement restrictions are not. Therefore, the elasticity modulus of the track in the vertical plane was previously unrestricted.

For clarity,

Table 4. Track structure characteristics and module values (MPa).

Track Structure Type	Module Values (MPa)
	Average	Maximum	Minimum
P651(6)214403(HBZ)4SCH5	24	46	9
P65(6)1600(HBZ)SCH	25	48	9.5
P65(6)1840(HBZ)SCH	26	50	10
P65(6)2000(HBZ)SCH	26.8	52	12
P50(6)1440(IA,IB)SCH	22	40	8
P50(6)1600(IA,IB)SCH	22.5	42	8.5
P50(6)1840(IA,IB)SCH	23	44	9
P50(6)2000(IA,IB)SCH	24	48	9.5

¹—Type of rails; ²—the wear value (in mm) is shown in parentheses; ³—sleeper spacing, pcs/km; ⁴—designation of reinforced concrete sleepers with KB fastening; ⁵—designation of crushed stone ballast.

presents the stiffness characteristics of the track. The research was conducted between 1998 and 2001 by staff members of the “Track and Track Facilities” department and the track testing laboratory of DIIT [64]. The track stiffness was measured using a modular railcar. Table 4 demonstrates the moduli of elasticity of the sub-rail foundation in the vertical direction (MPa) under axial loads of 22–25 kN and train speeds of up to 140 km/h for passenger trains and 90 km/h for freight trains under summer conditions.

As seen in Table 2, the average values of actual elasticity modules are far from the modern requirements. The variation between the minimum and maximum values ranges from 4.3 to 5 times. Therefore, considering subpoints (ii) and (iii) in Section 4.9 as a strong aspect is illogical, as this assessment is made from the perspective of meeting the criteria used in the railway system with a track gauge of 1435 mm. A railway section with such subgrade characteristics cannot be certified without a complete reconstruction, while in [1] the proposed reconstruction options, the highest costs for upgrading the substructure amount to a maximum of 5%; see Figure 6.

Thus, replacing the upper part of the subgrade and the superstructure of the track, as indicated in Section 6.1.1, will not yield operational benefits even in the medium term when using such a foundation under the influence of rolling stock moving on one track at 200 km/h and on the other with axle loads of 25 tons.

Furthermore, the main problem lies in the fact that the intensity of use of the railway system with a 1520 mm track gauge has historically been much higher than that of the 1435 mm gauge. As of today, the restoration measures proposed based on the experience of rehabilitating worn-out but non-aging track structures are unsuitable. Therefore, it is necessary to consider the current state of railway infrastructure systems with a 1520 mm gauge, which differs from that of railway tracks with a 1435 mm gauge.

Moreover, the gradual reconstruction options presented in Section 6.1.4 imply the operation of rolling stock with different functional purposes in the same direction on an unprepared foundation. In other words, using two tracks of different gauges, where rolling stock moves simultaneously as on single-track lines, ensures the possibility of trains running in the same direction.

Neither the methodology for calculating the impact of temperature changes considers the influence of longitudinal forces from rolling stock on track stability, nor does any railway system impose restrictions based on this criterion. Therefore, assuming that the effect of longitudinal forces can be neglected in cases where longitudinal displacements originate from two sources with different amplitude–frequency characteristics is inadequate, even on a prepared foundation. This is even more critical for a trackbed that has been in operation for over 100 years and was built according to the requirements in place at the time of construction.

Considering all the above, the following conclusions can be drawn:

• The implementation of the European Commission’s concept requires an adaptation of the methodology, as the 1435 mm and 1520 mm systems have historically been developed independently, and their operational characteristics differ significantly. Without accounting for these differences, it is impossible to ensure the safety and durability of the railway infrastructure.
• A direct transfer of technical requirements is impossible due to the absence of unified assessment criteria for 1520 mm tracks.
• For successful harmonization, either the gradual introduction of corrective coefficients or the development of a fundamentally new model based on wave processes is required.

5. Conclusions

The study has shown that the successful integration of 1520 mm and 1435 mm railway systems requires not only the adaptation of regulatory frameworks but also a rethinking of the methodology for calculating strength, stability, and safety. The article analyzes existing challenges and proposes alternative approaches to addressing them.

When modernizing the railway infrastructure, it is crucial to consider not only the efficiency of new solutions but also the evolution of existing engineering systems, as well as contemporary operational requirements.

The work emphasizes the importance of considering technical aspects in the creation of a unified classification of railway infrastructure systems. This requires the harmonization of existing operational and design regulatory frameworks, which are based on different methodologies for calculating strength, stability, and safety.

The analysis presented in this study on the harmonization possibilities of technical aspects of railway infrastructure systems with different track gauges has shown that existing methods are insufficient. To overcome the identified difficulties, it is necessary either to adapt current concepts to new factors or to apply a new paradigm based on the wave modeling methods of railway systems. Both approaches offer different solutions to the problem, requiring further research and experimentation.

The proposed paradigm for railway system modernization is based on modern scientific concepts and takes into account dynamic processes in the “track–rolling stock” system. Unlike traditional methods, the new approach considers the propagation of loads over time, taking into account the interaction of elastic waves.

This paradigm relies on the concept of elastic wave propagation over time, which allows for the consideration of dynamic characteristics of the track and rolling stock, such as the vibration amplitude, load variation speed, and stress distribution effects. Unlike traditional methods, this approach describes not only static parameters but also the influence of time-dependent factors on track stability.

The conceptual implementation of railway system modernization depends on the chosen strategy. Emphasizing the introduction of new concepts requires significant investment in research and testing but ensures maximum accuracy in calculations and improved operational reliability. At the same time, expanding existing technologies reduces costs and the adaptation time but limits the implementation of fundamentally new approaches to load and track stability management. The final choice of strategy should consider the intensity of railway operations, the state of infrastructure, and the specifics of track design in each railway system.

Therefore, the successful modernization of railway infrastructure systems requires a comprehensive approach that integrates theoretical analysis, experimental data, and a strategically selected method of adaptation. In this context, the author intends to further develop models of dynamic interactions between the track and rolling stock based on the principles of elastic wave theory.