PRELIMINARY STUDY OF SHAPING THE RAILWAY TRACK GEOMETRY IN TERMS OF THEIR MAINTENANCE COSTS AND CAPACITY

In Poland, due to the increase in investments made by railways in recent years, and thus the increase in the replacement value of transport infrastructure, the need for expenditure on infrastructure maintenance will increase in the next 30 years, or the development of the developed transport network will degrade. As part of the overall discipline of resource management, subdiscipline has emerged infrastructure asset management. As part of the management of railway transport infrastructure, the demand for cheaper maintenance costs will grow. The cost reduction of infrastructure maintenance is possible through meticulous assessment of its condition, rational selection of locations and scope of repairs at the assumed risk level, as well as at the stage of preparation of new construction or modernization projects taking into account aspects of later maintenance. For some time, we have been observing the accumulation of knowledge (methods, programs, procedures) in the country and abroad enabling optimization of infrastructure condition assessment and programming of its maintenance. The implementation of these solutions may result in a more rational use of funds for infrastructure maintenance and not disturb its smooth functioning in operation. The article discusses aspects that should be considered in the design process of railway infrastructure. Particular attention was paid to the durability of steel components of the railway superstructure, maintenance costs as well as aspects related to the capacity of the track node. An example of dependence of selected values of radial arcs depending on their durability and maintenance costs was presented. It was proposed to change the track layout at the Warszawa Srodmiescie passenger stop planned for reconstruction. Calculations of kinematic parameters for various configurations of railway turnouts were performed. Also, calculations of the capacity for the existing track system solution as well as the proposed track system after reconstruction of the analysed Warszawa Srodmiescie railway station were also carried out.


Introduction
In Poland, due to the increase in investments made by railways in recent years, and thus the increase in the replacement value of transport infrastructure, the need for expenditure on infrastructure maintenance will increase in the next 30 years, or the development of the developed transport network will degrade. As part of the overall discipline of resource management, subdiscipline has emerged -infrastructure asset management. It is a set of rules, methods and tools necessary for rational management of assets put into infrastructure (Heller 2016). It includes railroad infrastructure management. As part of the management of railway transport infrastructure, the demand for cheaper maintenance costs will grow. The cost reduction of infrastructure maintenance is possible through meticulous assessment of its condition, rational selection of locations and scope of repairs at the assumed risk level, as well as at the stage of preparation of new construction or modernization projects taking into account aspects of later maintenance. This requires, among others taking and disseminating following methods: − use of tools supporting design, − optimization of structural solutions for railway infrastructure elements, − recognition of the technical condition of the infrastructure, − dissemination of theoretical applications that allow an objective determination of the technical wear of the infrastructure, − technical condition forecasting and repair planning (including computer decision support), − ensuring the quality and durability of infrastructure repairs, − economical and reliable determination of repair costs, − ordering repair works in time, − certification of materials and works performed. For some time, we have been observing the accumulation of knowledge (methods, programs, procedures) in the country and abroad enabling optimization of infrastructure condition assessment and programming of its maintenance , (Jacyna and Wasiak 2015). The implementation of these solutions may result in a more rational use of funds for infrastructure maintenance and not disturb its smooth functioning in operation.
An important element in the proper functioning of the elements of railway transport infrastructure in large urban centres and agglomerations is the optimization (minimization) of its maintenance costs, as well as striving to maximize its capacity. The best example of the load on the railway infrastructure is the Warsaw Railway Junction (WRJ), including the diametrical line. The Warsaw Railway Junction is one of the most important elements of railway infrastructure, both in Poland and in Europe. It plays an important role in long-distance (domestic and international) and local communication -both in passenger and freight transport. Its special location because at the intersection of International Transport Corridors makes it strategic. Combined with the service of a very densely inhabited area of the Warsaw agglomeration, it creates very large, diverse and intersecting transport flows, requiring proper and efficient traffic organization on individual railway lines converging at the node. Preparation of appropriate interchange and transhipment infrastructure is also important, as conceptual and construction works are carried out by the PKP PLK Infrastructure Manager. The importance of WRJ in this diametrical line is evidenced by the fact that in 2017, according to the UTK report (UTK 2019), as many as 3 stations and one passenger stop lying on the diametrical line were in the group of 10 most loaded stations in Poland. In 2017, the Warszawa Srodmiescie stop served 29,4 million passengers, which means 477 trains a day. It becomes common to evaluate structures (including transport structures) by analysing the cost of their entire 'life cycle', e.g. rail roads (Marx and Fry 2010) shown in Figure 1. It can be considered as mapping the 'life cycle' for infrastructure in general. Attention should be paid to high maintenance costs (understood as ongoing efficiency and periodic recovery of used infrastructure). The costs of ongoing efficiency assurance and restoration of used infrastructure within 30 years can reach a level of 50-60 percent of the original value, which means that expenditure on infrastructure maintenance should be annually 1,6-2,0 percent of the infrastructure replacement value (it is estimated that the reconstruction of road infrastructure in the European Union amounts to over 8 billion EUR), while the actual expenditure in these countries has never exceeded 1 percent. This results in a progressive decapitalization of road infrastructure (it is even worse with railways) (EFR 2014). Also, in the aspect of modernization and reconstruction of railway junctions and station or line track infrastructure facilities, it is worth considering the possibilities of reducing maintenance costs as well as increasing the capacity of its capacity. The aim of the article is to analyse how to shape the railway track geometry in terms of their maintenance costs and capacity.

Literature review
The most important value for railway traffic is its safe and secure, efficient should be carried out in order to detect irregularities in a timely manner and be able to repair them instead of leading to tragedy -e.g. by modernization (Sharma et al. 2017). However, the repair option will depend on the amount of resources needed to carry it out (Liden and Joborn 2016). It should be noted that not only in railway transport, safety plays a very important role -it is the same, among others in air One of the methods to delay repair is the introduction of train speed limits on individual sections of railway lines (Sobota et al. 2018). This is a temporary measure to raise funds for a specific repair. This results in longer train travel times and an increase in the dissatisfaction of passengers or customers in the freight transport process (Bartoś and Gołębiowski 2019). This can be limited by, among others by using vehicles with better starting characteristics. When planning repairs, the appropriate thermal regime should also be taken into account (Izvolt et al. 2018). When considering the problems of shaping the railway network, energy aspects should also be taken into account -both from the point of view of supplying energy to vehicles (Szeląg and Patoka 2014), and from the point of view of supplying the equipment necessary to secure traffic (Feng et al. 2017). The problem of early detection of objects (obstacles) located in the track area is also important (Sacchi and Regazzoni 2000). Based on the above considerations, the following conclusion can be drawn when designing the shape of railway transport infrastructure, account should be taken of its maintenance costs, capacity and other aspects. In the scientific literature, it is difficult to find positions that would take up such topics related to railway infrastructure in the aspect of its maintenance. However, we can find selected scientific positions that relate to selected elements of the railway infrastructure -including the geometry of the railway line, open line capacity or the durability of the railroad structure. Optimization tools for railway line geometry elements including transition curves are also presented (Zboiński and Woźnica 2015).
The considerations are theoretical. However, they can also be one of the elements in minimizing the costs of maintaining rail infrastructure in railway arches.
Another case of consideration when designing track geometrical systems for durability is publication (Bałuch 1983). The authors present here aspects related to the essence of design due to durability, including anticipated changes in operation as well as the impact of these changes on durability. An important element discussed in this publication is the selection of radii and bevels for railway turnouts, taking into account the durability of the railway surface. These are important issues because these elements of the railway pavement in operation are exposed to rapid wear and affect the capacity of the station system or railway route. train capacity and deceleration. The influence of diversified railway structure on railway capacity is presented. In the article (Rychlewski 2009) the impact of modernization of railway lines on their capacity was assessed, aspects of collision of track systems and the concept of reconstruction of turnout roads were taken into account.

Analyses -case studies 3.1. General assumptions
Designing new or modernizing existing railway infrastructure once took place in a "classic" way, i.e. it represented traditional principles of designing both linear and point facilities. Design documentation in the form of analytical calculations and a set of drawings were made using the AutoCAD program or earlier also manually. Design support programs that appeared a few years ago, aim to improve designing (support designing), and not to replace the designer completely. Therefore, the designer is constantly re-quired to have knowledge of the art and design principles that are extremely important in the profession of designer. There are many application solutions that are used in professional design. In addition to knowledge of design principles and the use of design-supporting tools, it should also be necessary to consider aspects of the subsequent maintenance of these objects as well as their functionality. Both aspects the maintenance system and the functionality of the used solutions can affect lower operating costs as well as greater capacity of the route or station track node. Optimization analysis can be carried out with a selection of max radius of arches or appropriate selection of the type of turnout to suit the needs of the movement.

Analysis due to the durability of rail elements
The value of radii of arches or slants of railway turnouts is important for their durability, especially when a significant part of the traffic takes place on a lateral direction, this is the case, among others, at railway stations or technical and holding stations serving the railway undertakings' fleet in terms of maintenance. The current practice of determining arc radii in lateral direction when constructing new lines or modernization was based on certain catalogue schemes specified in standards dedicated to some railway lines or feasibility studies (Bałuch 1983). The lateral wear of rails in arches with small radii is very intense, therefore they should be limited at the design stage, and in operation by using special lubricants reducing friction. This also has its drawbacks, as the grease is transferred to the wheel of a railway vehicle and in extreme cases reduces the friction coefficient between the wheel and rail also on a straight section, it can also affect track circuits. The function describing the wear of rails in arches was developed on the basis of many years of observation and experimental research (Bałuch 1983) and takes the form: where: R -adopted arc radius [m], λs -function correcting rail durability in arches.
Based on the above dependencies, a graphic form describing the rail durability depending on the radius of the arc can be developed (Fig. 2). Assuming the standard 190 and 300 m turnout radii, it can be read that the durability of 60E1 rails will be respectively 69 and 142 Tg. For 49E1 rails it will be 34 and 71 Tg being half the life of the 60E1 heavy rail. Therefore, it is necessary to strive to maximize the value of the radius of arches in the lateral tracks of turnouts. The exception may be the track systems of the Technical and Holding Station (THS), where due to the limited surface area there is no technical possibility to use such a solution (Fig. 3). The figure above shows the radii of lateral arches enabling the train to enter the holding and repair hall. The difference in the radius of the arc results from the geometry and layout of the tracks enabling the way to service facilities, limited significantly by the accessibility of the terrain. However, the restrictions on the minimum arc radius for this type of vehicle R = 60 m have been respected.

Analysis due to maintenance costs
The selection of the minimum radius of the circular arc can affect the cost of the entire pavement. Determining the approximate factor increasing the expenditure on maintaining the railway surface depending on the arc radius used can be read from Fig.  6 (Bałuch 1983). The assumptions assume that the expenditure on maintaining a straight track is equal to w = 1. Based on the graph, you can see what value of the factor increasing the expenditure on maintaining the track located in a circular arc should be taken depending on the radius of the circular arc used on the open line or in the turnout head. Of course, these are theoretical assumptions, because each infrastructure manager has its own maintenance policy and probably has precise data on the costs actually incurred for the repair and maintenance of railway infrastructure, including track. Decisions on carrying out infrastructure repairs and its maintenance should be made based on diagnostic measurements and ongoing observations, taking into account the assessed parameters, among others: synthetic track condition indicator, horizontal, vertical unevenness, and wear of surface elements. Therefore, in the design process of track geometrical systems and track connections, the maximum radius values obtainable under existing limitations should be used. This approach will extend the life of the rail infrastructure and partially reduce the number of repairs.

Analysis due to capacity
Low capacity is also often due to point speed restrictions: on crossings, engineering objects, switches, used railway traffic control devices, additional track additions, etc. Reconstruction of track systems is an investment that requires significant financial outlays. The first stage on the way to improving capacity may be the modernization of traffic control devices, use of modern passenger trains with a high acceleration of start up to 1,2 m/s 2 , large proportion of the door surface (at least 25% in relation to the length of the vehicle) with a width of at least 1,2 m. An important element in rolling stock to support agglomeration is the floor height at the same level as the platform. However, this is still a serious problem until the reconstruction of platform heights to one height standard of 760 mm or 550 mm for re-gional stations and passenger stops. All these activities can allow for faster exchange of travellers at the passenger stop or railway station, thus reducing the time taken by the train to take the platform edge. The capacity of a new or modernized system can be calculated in an analytical manner or with the use of specialized computer applications, e.g. using microsimulation tools (Open Track, RailSys). For example, the capacity of the Warszawa Srodmiescie passenger stop in its present shape was calculated as well as for the reconstruction proposal (Figures 4  and 5). Substituting formulas (5) and (6)  where: signs as in formulas (4), (5) and (6).

Capacity analysis for the existing state (ac-
Let us calculate the capacity for the Warszawa Srodmiescie passenger stop for the current situation. It was assumed that due to the specificity of the line, no non-essential train traffic or shunting operations occur. So lpn and lpm is equal to 0. Due to the fact that we analyse the capacity of a passenger stop, there is also no such thing as a converging route. Therefore, lps is also equal to 0. Formula (7) therefore takes the following form: where: signs as in formula (4).
To be able to calculate the capacity, we need to calculate the occupancy time of the track node. In the minimal version it will be time consisting of three components: where: twj -time of train entering the entire length into the distance at which the platform is located [min], tp -passenger exchange time [min], tzo -time when the distance at which the platform is located is released by the train [min].
Train entry time was calculated using train motion kinematics -this is the assumption made for the purposes of this article. The braking time from 60 km/h to 0 km/h will last 18,52 s and it will take place on the road 154,35 m. Due to the fact that the distance is 200 m and the trainset composition length is 195 m, it means that we still need to calculate the occupation time of the section with a length of 240,65 m, which the train will overcome at a speed of 60 km/h -14,44 s. So twj will be equal to 32,96 s. Taking into account various factors (including device reliability), it is assumed that this time will be assumed at twj = 40 s. Passenger exchange time for the Warszawa Srodmiescie passenger stop, railway undertakings accept at tp = 90 s. The last factor is the time when the distance is released, which should be calculated for the length of the adopted trainset composition. Therefore, the first element is the acceleration of the train for 18,52 s on the road 154,35 m. We must add the time of uniform motion at 60 km/h on the route 40,65 m, which is equal to 2,44 s. So tzo = 20,96 s. Taking into account various factors (including reliability of devices) it is assumed that this time will be adopted for tzo = 25 s. Substituting the above data into formula (6) Please note, that the above calculations are made for a passenger stop (track node). The capacity of the railway line passing through this stop, which will determine the final number of trains that will pass through this expedition point, has not been calculated. , for which acceleration of start-up and deceleration during braking is equal to 0,9 m/s 2 (average value for vehicles containing apparatus of MEDCOM company) (Biliński et al. 2009), − it was assumed that a typical trainset composition is 3 EN57AKM (maximum composition), so the length of one composition is about 195 m (which is close to the length of one distance equal to half of the braking distance, − it was assumed that the turnouts have a 1:9 slant and a 300 m radius; therefore, rides in a lateral direction at a speed of 40 km/h. Analysing formula (7), it can be determined that we do not deal with the movement of non-basic trains and shunting rides. Thus, lpn and lpm is equal to 0. We are dealing with converging routes at the time of departure. It is not possible to carry out outgoing rides at the same time. Therefore, in this situation, the formula for calculating the capacity will be as follows:

Capacity analysis for the designed state (ac-
where: signs as in formulas (4) and (6).
There are two unknowns in the meter. The first is the number of converging routes lps, while the second is the duration of the converging routes tps. The number of converging routes lps will be equal to half the number of trains that can be handled in the current (existing) system shown in Fig. 3 In addition, it was assumed that tps = tzw = 0,96 min.
Having the above data, it is possible to calculate the capacity of the Warszawa Srodmiescie station using the formula (16) Please note, that the above calculations are made for a station (track node). The capacity of the railway line passing through this station, which will determine the final number of trains that will pass through this expedition post, has not been calculated.

Summary
The issues presented in the article discuss important elements that should be taken into account when designing or rebuilding station and line track infrastructure. The analysis took into account aspects of durability, maintenance costs as well as technical parameters related to design. The article also includes the capacity aspect that affects the functionality of the line or point railway infrastructure. Analyses related to the selection of radii of circular arches show that one should strive for the maximum value of this radius not only on the open line but mainly in track systems of stations or passenger stops. By using this solution, we gain a longer life cycle (inter-repair cycle). For example, using an arc radius of R = 300 m instead of R = 200 m, we gain more than a double extension of rail life. This will be important in the case of large railway stations, or technical and holding stations, where dozens of turn-outs will often be built, and then maximizing the lateral tracks radius can significantly reduce their maintenance costs. The arc radius is also important from the point of view of kinematic parameters and the comfort of the train passing through this curvature. This affects the maximum train speed at turnouts. This is important when increasing the capacity of a line or station. The larger radius of the lateral track allows faster descent from the main track to the secondary track, allowing the next train to enter. This is important on heavily loaded railway junctions, such as the Warsaw Railway Junction mentioned in the article. The presented capacity calculations for station track systems with different types of turnouts and arc radii used show that we can achieve a higher capacity of almost 1,4 times. To gain a comprehensive improvement in the quality of service in the railway area, it is necessary to take into account various factors and elements not only of the track system and its geometry, but also minimize maintenance costs at the design or reconstruction stage. The analyses are preliminary assumptions for the development of tools supporting the assessment of design solutions, among others in terms of capacity, durability, maintenance costs of track infrastructure or due to technical requirements.