- Email: [email protected]
Design of Railway Track for Speed and High-speed Railways
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 91 (2014) 256 – 261
XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP) (TFoCE 2014)
Design of Railway Track for Speed and High-speed Railways Stanislav Hodasa* a
University of Žilina, Fac. of Civil Engineering, Dept. of Railway Engineering, Univerzitná 8215/1, SK-01026 Žilina, Slovak Republic
Abstract The design of railway lines under the current standard STN 73 6360 [1] including the comparison of railway line parameters to the European Standard EN 13803-1 and a new proposal in accordance to the new prepared standard STN 73 6360-1 [2] of Slovak Railways (ŽSR). Specifications of the basic design parameters of these standards: designing minimum radius values of horizontal and vertical alignment radii within these standards, for example at speeds: V = 160 km/h, V = 200 km/h and V = 250/300 km/h. The routes shown in the 3D model terrain surface. Dynamic spatial design of railway lines and their routing designs in 3D drawings, their development in the terrain and comparison according to the selected speed parameters. © 2014 The Authors. Published by Elsevier Ltd. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil (http://creativecommons.org/licenses/by-nc-nd/3.0/). Engineering (23RSP). Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP) Keywords: railway track design; comparison of parameters; high-speed lines; 3D model.
1. Introduction A designer that designs reconstruction, modernization or newly built railway tracks must consider the 3D design of digital design documentation and design parameters of the currently valid standards. In the European countries there are valid railway track design standards for the CEN members, for example EN 13803-1, adopted by the EU Member States as STN EN 13803-1 [2]. Besides this, some countries have adopted regional standards that regulate design parameters with regard to the conditions of a particular country, while respecting the basic framework criteria of the European standards. For example, the currently valid STN 73 6360 [1] in the Slovak Republic which will be replaced by the new STN 73 6360-1 [3] in 2014. The new standard [3] will have to consider new higher speed limits of RP5 and RP6 (in Slovak standards referred to as RP) for the speed and high-speed tracks for V 300 km/h also using the other standards for buildings that are parts of the railway tracks (tunnels, bridges, catenary, safety and signaling equipment, railway superstructure and railway subgrade, etc.). The current standard [1] contains the speed limits RP1 to RP4 for V 160 km/h, the new standard proposal [3] will modify these design criteria and complete them with other limits, RP5 for V 230 km/h and RP6 V 300 km/h.
* Corresponding author. Tel.: +421-41-513-5847. E-mail address: [email protected]
1877-7058 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP) doi:10.1016/j.proeng.2014.12.056
Stanislav Hodas / Procedia Engineering 91 (2014) 256 – 261
257
The higher the speed, the more stringent design criteria of the track geometry and also of the deformation resistance of the railway subgrade body [7, 8] are required. The final project documentation for the construction of railway track must be elaborated in a very high quality of processing, not only graphics but also software solutions utilized for its creation. The design documentation standards for project documentation drawings are required as prior mandatory criteria for their form and content. In the Slovak Republic the modernization of main railways corridors for V 160 km/h is now being performed. The railway lines for V > 250 km/h are worldwide considered high-speed in all new constructions or when the existing rail corridors are reconstructed for V 200 km/h. In the upcoming STN [3] and the existing STN EN [2] these speed limits are also included, but common practice in Slovakia is different, i.e. the modernization takes place only at V 160 km/h and new buildings such as tunnels and bridges are designed for V 200 km/h (for example, the double track railway tunnel “Turkish Hill - Turecký vrch” on the main corridor of the track Žilina - Bratislava at the railway station Trenþianske Bohuslavice), [6]. On the upgraded railway corridors it will be possible to drive at V 200 km/h using passenger train sets with tilting bodies, as they allow driving through curves at higher speed. In Slovakia we are currently limited by the maximum permissible track speed Vmax 160 km/h stated by railway traffic regulations. 2. Basic design parameters of curves of railway tracks The design parameters of the railway line project and the optimized location of this track body are closely related. The more difficult conditions of complicated terrain or dense area (population, objects and industrial parks), the more difficult is to satisfy the criteria of parameters for designing the railway line and there is also a reduction in driving comfort (especially in the case of passenger transport). Therefore, in the proposal we exclude the minimum design radius rmin (designated as Rlim in EN 13803-1) despite the allowed values of the norm and we aim to maximize the optimization criteria and reduce the energy intensity of lines in future operations (adjustment of horizontal and vertical curvature of track line, new train sets, propulsion systems of train sets, etc.). If the railway line is only used by passenger trains, for example in the speed limit RP6 (230 < V 300 km/h), it is possible to use maximum longitudinal gradients of vertical alignment of the lines and maximum cant of rails in curves. The passenger trains are light, short, have a low center of gravity of wagons, aerodynamic shape etc. On these tracks freight trains and heavy trains would not be able to run. In the case of mixed traffic, the line is also used by slower trains (e.g. freight trains) and these trackage parameter values would not be suitable for them. Therefore it is necessary to make a compromise between the assumed fastest and slowest trains of the particular designed rail line, for example this implies the proposed radius r between rmin and rmax according to (1), also the cant p [mm] of the track can be calculated from (1) (designated as D in STN EN [2]) the cant deficiency Imax [mm] or cant excess Emax [mm] and other parameters such as longitudinal gradient [‰], etc. 11.8 11.8 2 2 Vmax drd Vmin p I max p Emax
(1)
The track designer must also consider the weight which will be transported on the track. We consider the sum of weights of all the powered railway vehicles (PRV) and transported vehicles (TV) and their load weight: brutto = tarra + netto. To transfer the values between longitudinal gradient of the track sections, towable mass of vehicles and their speeds we can use the tables of technical normative weights for the particular PRV. The tables of towable masses are developed for various types of driving resistance (types R, S, T, U, details are in the regulation SR 1013 [4]), which take into account the analytical calculations and load diagrams (Koref´s nomogram) for the particular operated PRV. The axis alignment of the route with large radius values requires increased investment costs and complicated structural and engineering solutions (large number of tunnels, bridges, walls, etc.). Nowadays, the proposals of rail tracks are only developed in digital 3D format using computer technology and software products specialized in railway engineering [11, 12]. The development of the railway route depends on the type of railway track with its different specified standard parameters for the design of the route of the speed and high-speed lines.
258
Stanislav Hodas / Procedia Engineering 91 (2014) 256 – 261
In the case of reconstruction, the railway track follows the original body and only improves certain elements of the track, but in the case of modernization, e.g. for V = 160 km/h, the track route usually leaves the original body in some sections of the new railway track, as there is the axis alignment of the route under ŽSR Z10 [5]. The speed and highspeed tracks have their own specified criteria of design parameters [2] and are typically designed on a new body or with certain completely redesigned sections of the original route (according to [2] - large values of radii rmin = C.Vmax2/(D + Ilim), where C = 11.8 mm.m.h2/km2, cant D = 160 mm, possibly limit of D = 180 mm, cant deficiency Ilim = 100; 130 mm for Vmax = 300 km/h, but for tilting railway cars running at V 260 km/h the values are Ilim = 275; 306 mm). If the terrain is mountainous, it is appropriate to consider the optimal location of the route in the terrain. In a mountain area the route requires a lot of bridges, tunnels, supporting and retaining walls and other objects. It is not necessary to circumvent mountains and valleys, as it was in the past. A possible development of the railway route is presented by basic examples in Fig. 1 as two typical options for routing. The pictures can be viewed as construction of two routes for speeds of V = 140; 100 km/h and V = 300 km/h, where various structural and technological solutions will be applied. Or we can consider that the original track for V = 140; 100 km/h was rebuilt to a track of higher quality, in this case to a high-speed track for V 300 km/h. In Fig. 1a the route is built for V = 140 km/h as a hillside route and circumvents transverse mountain ridge or mountain range. For the above mentioned speed according to [1] the minimum radius rmin is proposed for mixed traffic as (2).
rmin
6.5 pd 2 max
2 Vmax
6.5 1402 150
849.33 | 850 m
(2)
The proposed radii are greater r1 = 2500 m, r2 = 1250 m and r3 = 900 m, thus the particular cants will be in the new curves smaller than the ones considered in the calculation for rmin in (2). The high-speed tracks require rmin as (3) in [2].
C 2 Vmax p I max
rmin
11.8 3002 160 100
4084.62 | 4500 m
(3)
The design of the track axis radius is greater than (3) and has value of r = 6000 m (whole 500 m above).
a)
b) Fig. 1. Railway track - (a) mountain range; (b) valley, transverse valley.
rmax
C 2 Vmin p Emax
11.8 1602 150 100
6041.60 m
(4)
If the track is going to be used by slower trains such as freight trains running at Vmin = 160 km/h, it is necessary to consider the design of the radius with respect to the cant excess Emax of the slowest train in (4) for rmax of [2], where cant p = 160 mm, in [3] p = 150 mm. These values are valid for the recommended limits which secure the driving comfort of passengers and also the safety of goods transport. Maximum permissible limit values are also acceptable by the standard [2], but in this way the driving comfort is reduced. The route requires the tunnel advancement through the rock mass. In Fig. 1b the route development across the valley or transverse valley is presented. The railway route for V = 140; 100 km/h follows the contours around the hillside and the track for V = 300 km/h passes through a compulsory
259
Stanislav Hodas / Procedia Engineering 91 (2014) 256 – 261
bridge object and then leads to the tunnel tube. If the speed is V = 100 km/h (for the speed limit RP3) for mixed traffic, the minimal radius rmin is designed according to [2] for the relevant speed limit (5), other values from Fig. 1.
rmin
7.1 pd1max
2 Vmax
7.1 1002 150
473.33 | 475 m
(5)
The smallest designed radius of the reconstructed track route is r3 = 475 m in Fig. 1b. Then the present design values of the cants of the particular curves p1, p2 and p3 are calculated. The principle and basic differences of particular tracks are shown in Fig. 2, where the track is reconstructed for V 140 km/h (RP4), the modernized track for V 160 km/h, the speed track for V 200 km/h (RP5) and the highspeed track for V 300 km/h (RP6). Some technologically advanced countries in Europe and in the world are able to operate high-speed lines at V = 320 to 360 km/h (the world record is V = 574.8 km/h on the conventional railway corridor TGV - LGV East in France, dated 3.4.2007).
=140
26 5
km/h 200m /h min =1 km
min
=850m
m =1600
240
=250 km/h
min
=5000m
250
245
245
255
250
60 =1
250
0 26
Fig. 2. Railway tracks - comparison of route development by speed limits RPi.
When designing curves, grade lines with continuous height shape, i.e. non-linear grade lines or lines with constant line shape (Table 1), are inserted between the non-canted part of rail and the canted part of the same rail (due to climbing of the cant p). In Slovakia, we may design cosine spiral with non-linear grade line for speed limit zones RP5 and RP6 in accordance with [3] for the speed of V > 160 km/h up to V 300 km/h. Under restricted conditions with speed 80 < V 300 km/h we may design Bloss spiral with non-linear grade line for RP3 to RP6. The standard [3] recommends cubic parabola with linear grade line for RP1 to RP6. Table 1. Transition spirals and grade lines for speed limits RP1 to RP6 in accordance with [3]. Types of spirals and grade lines
Speed limit zone
Equations of the transition spirals
Cubic parabola with linear grade line*
RP1 to RP6 0 > V 300 km/h
y
Bloss spiral with non-linear grade line*
RP3 to RP6 80 > V 300 km/h
y
Cosine spiral with non-linear grade line*
RP5 and RP6 200 > V 300 km/h
y
Shapes of grade lines
x3 6 r lp x4 4 l p2 r
x5 10 l 3p r
l 2p x2 4r 2rS2
§ · ¨ cos S x 1¸ ¨ ¸ lp © ¹
3. Dynamic design of spatial position of railway track The directional curvature of railway track including basic specifications of its structural elements such as curve radii (blue), shape and length of transition spirals (green), straight sections between the curves (red), etc., must be consistent with the design values of railway track according to STN [1] or STN EN [2]. Consequently, the principles of dynamic track design are characterized in the graphical environment with 3D terrain, using software tools
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Stanislav Hodas / Procedia Engineering 91 (2014) 256 – 261
accepted by railway practice [11, 12] etc. The values of the radii and transition spirals can be selected directly in the design of the tangent polygon either sequentially or we can design a minimum radius with the length of the transition spiral for all the curves and within the final solutions we modify the values in the software database tables (the whole 3D line model will be automatically modified after each modification of the basic parameters). In the drawing with 3D contours in Fig. 3 the tangent polygon (gray) will be designed, including the following minimum radii for RP4 V = 160 km/h (orange line), for RP5 V = 200 km/h (green line), for RP6 V = 300 km/h (blue line) according to (9) to (10). The presentation of the speed limit zones of railway lines is shown in Fig. 2. For rail route with V = 160 km/h according to STN [1] for cant pmax = 150 mm:
rmin
rmin
2 0.0472Vmax
2 6.5 Vmax
pd 2
0.0472 u1602
6.5 u160 150
1208.32 | 1250 m
(6)
2
1109.33 | 1200 m
(7)
Compared to the values in accordance with EN STN [3] for cant p = 150 mm, Imax = 100 mm, C = 11.8:
rmin
C 2 Vmax p I max
11.8 1602 1208.32 | 1250 m 150 100
(8)
The result is a design of all the radii above the value ri 1250 m of the track for V = 160 km/h in Fig. 4 (orange). The tangent polygon route can be modified by moving its top points VBi and by changing the parameter values ri, li and other design elements by shifting them directly in the drawing in Fig. 3.
Fig. 3. Railway track - dynamic solution design in 3D.
For the track RP6 Vmax = 250 km/h according to Standard [3], supplemented by Standard [1], pmax = 150 mm, where the slow trains run at the speed of Vmin =140 km/h: for the speed Vmax = 250 km/h, cant p = 150 mm and cant deficiency Imax = 100 mm:
rmin
C 2 Vmax p I max
11.8 2502 150 100
2950.00 | 3000 m
(9)
for Vmin = 140 km/h, cant p = 150 mm and cant excess Emax = 110 mm:
rmax
C 2 Vmin p Emax
11.8 1402 150 110
5782.00 | 5500 m
(10)
The result is a design of the radius 3000 m ri 5500 m of the track curves for V = 250 km/h (RP6) in Fig. 4. During the designing we are supposed to check that all the radii ri values are in the interval rmin ri rmax, (1). The design of the minimum radius in our example for V = 160 km/h is according to (6) to (8) and for V = 250 km/h according to (9) applying (10). It must be considered whether the freight and slow passenger trains will be allowed on high-speed lines, because the high-speed line requires quality and stable geometric position and height of the track and these freight trains would have a significant influence on the track and increase the costs of the trackage
Stanislav Hodas / Procedia Engineering 91 (2014) 256 – 261
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maintenance during its operation. The final designs of both railway lines are shown in Fig. 4.
Fig. 4. Railway tracks - layout design.
4. Conclusion
The design works include complicated procedures, while the railway track components must comply with all design criteria of the currently applicable standards and regulations. In principle the route design of slow tracks such as RP1 to RP4 is equally challenging to prepare as for the speed and high-speed lines of RP4 and RP6 speed limits, but the internal basic design parameters are different for each particular project. With increasing track speed we must also increase and secure its safety during operation which is much more expensive. Nowadays the development of quality and precise design documentation is not possible without computer technology using 3D variant solutions. The project design documentation contains many complex structural objects required for the railway operation and crossing with other modes of transport (bridges, tunnels, railway stations, terminals, intermodal terminals, humps and others [6]) and all of them must have an exact spatial position [8 to 10] given by the coordinate and height system (ETRR/89, S-JTSK, etc.). References [1] STN 73 6360 Geometric position and arrangement of the track standard gauge railways, 1999, update No.1 2003. [2] STN EN 13803-1 Railway applications. Track. Track alignment design parameters. Track gauge 1435 mm and wider. Part 1: Plain line, SK, (In accordance with EN 13803-1), 2010. [3] STN 73 6360-1 Geometric position arrangement of 1435 mm gauge Railways, Research and development institute of Railways, Slovak Railways - ŽSR, http://www.zsr.sk, Slovakia, before issuing 2014/2015. [4] SR 1013 Technical specifications of traction rolling stocks, ŽSR, 2006, SK, update No.11 2013. [5] Z10 Rules of technical operation of the railway infrastructure (PTPŽI), SK, 2014. [6] L. Ižvolt, S. Hodas, Modernisation of railway infrastructure in the Slovak Republic, COMPRAIL XIII - Computer system design and operation in the railway and other transit systems, New Forest, UK, organised by WESSEX Institute of Technology, http://www.wessex.ac.uk, http://www.witpress.com, Southampton, United Kingdom, 2012, ISBN 978-1-845564-616-5, e-ISBN 978-1-84564-617-2, pp. 211-223 [7] S. Hodas, L. Ižvolt, Modelling of temperature regime of railway track structure and its comparison with the results of experimental measurements, COMPRAIL XIV - Railway engineering design and optimization, Rome, Italy, organised by WESSEX Institute of Technology, http://www.wessex.ac.uk, http://www.witpress.com, Southampton, United Kingdom, 2014, ISBN 978-1-84564-766-7, eISBN 978-1-84564767-4, pp. 253-265. [8] L. Ižvolt, P. Dobeš, M. Meþár, Contribution to the methodology of the determination of the thermal conductivity coefficients Ȝ of materials applied in the railway subbase structure, Communications, Scientific letters of the University of Žilina, http://svf.uniza.sk/kzsth, Žilina, Slovakia, ISSN 1335-4205, Vol. 15, No. 4 (2013), pp. 9-17. [9] J. Ižvoltová, A. Villim, Identification of observations errors by Gauss-Jacobi algorithm, Civil and environmental engineering, Scientific technical journal, ISSN 1336-5835, Vol. 8, No. 1 (2012), Faculty of Civil Engineering, ŽU Žilina, Žilina, Slovakia, 2012, pp. 13-17. [10] J. Ižvoltová, Coordinate and datum transformation, Analele universităĠii din Oradea, Fascicula construcĠii úi instalaĠii hidroedilitare, ISSN 1454-4067, Vol. 13, (2010), Oradea, Romania, 2010, pp. 201-206. [11] AutoCAD Civil 3D 2015 CZ EDU, Software, AUTODESK, http://students.autodesk.com. [12] RailCAD, Software for arrangement and design of the track geometry, VÚT Brno, http://www.railcad.cz, Brno, Czech Republic, 2003-2014.
ScienceDirect Procedia Engineering 91 (2014) 256 – 261
XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP) (TFoCE 2014)
Design of Railway Track for Speed and High-speed Railways Stanislav Hodasa* a
University of Žilina, Fac. of Civil Engineering, Dept. of Railway Engineering, Univerzitná 8215/1, SK-01026 Žilina, Slovak Republic
Abstract The design of railway lines under the current standard STN 73 6360 [1] including the comparison of railway line parameters to the European Standard EN 13803-1 and a new proposal in accordance to the new prepared standard STN 73 6360-1 [2] of Slovak Railways (ŽSR). Specifications of the basic design parameters of these standards: designing minimum radius values of horizontal and vertical alignment radii within these standards, for example at speeds: V = 160 km/h, V = 200 km/h and V = 250/300 km/h. The routes shown in the 3D model terrain surface. Dynamic spatial design of railway lines and their routing designs in 3D drawings, their development in the terrain and comparison according to the selected speed parameters. © 2014 The Authors. Published by Elsevier Ltd. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil (http://creativecommons.org/licenses/by-nc-nd/3.0/). Engineering (23RSP). Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP) Keywords: railway track design; comparison of parameters; high-speed lines; 3D model.
1. Introduction A designer that designs reconstruction, modernization or newly built railway tracks must consider the 3D design of digital design documentation and design parameters of the currently valid standards. In the European countries there are valid railway track design standards for the CEN members, for example EN 13803-1, adopted by the EU Member States as STN EN 13803-1 [2]. Besides this, some countries have adopted regional standards that regulate design parameters with regard to the conditions of a particular country, while respecting the basic framework criteria of the European standards. For example, the currently valid STN 73 6360 [1] in the Slovak Republic which will be replaced by the new STN 73 6360-1 [3] in 2014. The new standard [3] will have to consider new higher speed limits of RP5 and RP6 (in Slovak standards referred to as RP) for the speed and high-speed tracks for V 300 km/h also using the other standards for buildings that are parts of the railway tracks (tunnels, bridges, catenary, safety and signaling equipment, railway superstructure and railway subgrade, etc.). The current standard [1] contains the speed limits RP1 to RP4 for V 160 km/h, the new standard proposal [3] will modify these design criteria and complete them with other limits, RP5 for V 230 km/h and RP6 V 300 km/h.
* Corresponding author. Tel.: +421-41-513-5847. E-mail address: [email protected]
1877-7058 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of organizing committee of the XXIII R-S-P seminar, Theoretical Foundation of Civil Engineering (23RSP) doi:10.1016/j.proeng.2014.12.056
Stanislav Hodas / Procedia Engineering 91 (2014) 256 – 261
257
The higher the speed, the more stringent design criteria of the track geometry and also of the deformation resistance of the railway subgrade body [7, 8] are required. The final project documentation for the construction of railway track must be elaborated in a very high quality of processing, not only graphics but also software solutions utilized for its creation. The design documentation standards for project documentation drawings are required as prior mandatory criteria for their form and content. In the Slovak Republic the modernization of main railways corridors for V 160 km/h is now being performed. The railway lines for V > 250 km/h are worldwide considered high-speed in all new constructions or when the existing rail corridors are reconstructed for V 200 km/h. In the upcoming STN [3] and the existing STN EN [2] these speed limits are also included, but common practice in Slovakia is different, i.e. the modernization takes place only at V 160 km/h and new buildings such as tunnels and bridges are designed for V 200 km/h (for example, the double track railway tunnel “Turkish Hill - Turecký vrch” on the main corridor of the track Žilina - Bratislava at the railway station Trenþianske Bohuslavice), [6]. On the upgraded railway corridors it will be possible to drive at V 200 km/h using passenger train sets with tilting bodies, as they allow driving through curves at higher speed. In Slovakia we are currently limited by the maximum permissible track speed Vmax 160 km/h stated by railway traffic regulations. 2. Basic design parameters of curves of railway tracks The design parameters of the railway line project and the optimized location of this track body are closely related. The more difficult conditions of complicated terrain or dense area (population, objects and industrial parks), the more difficult is to satisfy the criteria of parameters for designing the railway line and there is also a reduction in driving comfort (especially in the case of passenger transport). Therefore, in the proposal we exclude the minimum design radius rmin (designated as Rlim in EN 13803-1) despite the allowed values of the norm and we aim to maximize the optimization criteria and reduce the energy intensity of lines in future operations (adjustment of horizontal and vertical curvature of track line, new train sets, propulsion systems of train sets, etc.). If the railway line is only used by passenger trains, for example in the speed limit RP6 (230 < V 300 km/h), it is possible to use maximum longitudinal gradients of vertical alignment of the lines and maximum cant of rails in curves. The passenger trains are light, short, have a low center of gravity of wagons, aerodynamic shape etc. On these tracks freight trains and heavy trains would not be able to run. In the case of mixed traffic, the line is also used by slower trains (e.g. freight trains) and these trackage parameter values would not be suitable for them. Therefore it is necessary to make a compromise between the assumed fastest and slowest trains of the particular designed rail line, for example this implies the proposed radius r between rmin and rmax according to (1), also the cant p [mm] of the track can be calculated from (1) (designated as D in STN EN [2]) the cant deficiency Imax [mm] or cant excess Emax [mm] and other parameters such as longitudinal gradient [‰], etc. 11.8 11.8 2 2 Vmax drd Vmin p I max p Emax
(1)
The track designer must also consider the weight which will be transported on the track. We consider the sum of weights of all the powered railway vehicles (PRV) and transported vehicles (TV) and their load weight: brutto = tarra + netto. To transfer the values between longitudinal gradient of the track sections, towable mass of vehicles and their speeds we can use the tables of technical normative weights for the particular PRV. The tables of towable masses are developed for various types of driving resistance (types R, S, T, U, details are in the regulation SR 1013 [4]), which take into account the analytical calculations and load diagrams (Koref´s nomogram) for the particular operated PRV. The axis alignment of the route with large radius values requires increased investment costs and complicated structural and engineering solutions (large number of tunnels, bridges, walls, etc.). Nowadays, the proposals of rail tracks are only developed in digital 3D format using computer technology and software products specialized in railway engineering [11, 12]. The development of the railway route depends on the type of railway track with its different specified standard parameters for the design of the route of the speed and high-speed lines.
258
Stanislav Hodas / Procedia Engineering 91 (2014) 256 – 261
In the case of reconstruction, the railway track follows the original body and only improves certain elements of the track, but in the case of modernization, e.g. for V = 160 km/h, the track route usually leaves the original body in some sections of the new railway track, as there is the axis alignment of the route under ŽSR Z10 [5]. The speed and highspeed tracks have their own specified criteria of design parameters [2] and are typically designed on a new body or with certain completely redesigned sections of the original route (according to [2] - large values of radii rmin = C.Vmax2/(D + Ilim), where C = 11.8 mm.m.h2/km2, cant D = 160 mm, possibly limit of D = 180 mm, cant deficiency Ilim = 100; 130 mm for Vmax = 300 km/h, but for tilting railway cars running at V 260 km/h the values are Ilim = 275; 306 mm). If the terrain is mountainous, it is appropriate to consider the optimal location of the route in the terrain. In a mountain area the route requires a lot of bridges, tunnels, supporting and retaining walls and other objects. It is not necessary to circumvent mountains and valleys, as it was in the past. A possible development of the railway route is presented by basic examples in Fig. 1 as two typical options for routing. The pictures can be viewed as construction of two routes for speeds of V = 140; 100 km/h and V = 300 km/h, where various structural and technological solutions will be applied. Or we can consider that the original track for V = 140; 100 km/h was rebuilt to a track of higher quality, in this case to a high-speed track for V 300 km/h. In Fig. 1a the route is built for V = 140 km/h as a hillside route and circumvents transverse mountain ridge or mountain range. For the above mentioned speed according to [1] the minimum radius rmin is proposed for mixed traffic as (2).
rmin
6.5 pd 2 max
2 Vmax
6.5 1402 150
849.33 | 850 m
(2)
The proposed radii are greater r1 = 2500 m, r2 = 1250 m and r3 = 900 m, thus the particular cants will be in the new curves smaller than the ones considered in the calculation for rmin in (2). The high-speed tracks require rmin as (3) in [2].
C 2 Vmax p I max
rmin
11.8 3002 160 100
4084.62 | 4500 m
(3)
The design of the track axis radius is greater than (3) and has value of r = 6000 m (whole 500 m above).
a)
b) Fig. 1. Railway track - (a) mountain range; (b) valley, transverse valley.
rmax
C 2 Vmin p Emax
11.8 1602 150 100
6041.60 m
(4)
If the track is going to be used by slower trains such as freight trains running at Vmin = 160 km/h, it is necessary to consider the design of the radius with respect to the cant excess Emax of the slowest train in (4) for rmax of [2], where cant p = 160 mm, in [3] p = 150 mm. These values are valid for the recommended limits which secure the driving comfort of passengers and also the safety of goods transport. Maximum permissible limit values are also acceptable by the standard [2], but in this way the driving comfort is reduced. The route requires the tunnel advancement through the rock mass. In Fig. 1b the route development across the valley or transverse valley is presented. The railway route for V = 140; 100 km/h follows the contours around the hillside and the track for V = 300 km/h passes through a compulsory
259
Stanislav Hodas / Procedia Engineering 91 (2014) 256 – 261
bridge object and then leads to the tunnel tube. If the speed is V = 100 km/h (for the speed limit RP3) for mixed traffic, the minimal radius rmin is designed according to [2] for the relevant speed limit (5), other values from Fig. 1.
rmin
7.1 pd1max
2 Vmax
7.1 1002 150
473.33 | 475 m
(5)
The smallest designed radius of the reconstructed track route is r3 = 475 m in Fig. 1b. Then the present design values of the cants of the particular curves p1, p2 and p3 are calculated. The principle and basic differences of particular tracks are shown in Fig. 2, where the track is reconstructed for V 140 km/h (RP4), the modernized track for V 160 km/h, the speed track for V 200 km/h (RP5) and the highspeed track for V 300 km/h (RP6). Some technologically advanced countries in Europe and in the world are able to operate high-speed lines at V = 320 to 360 km/h (the world record is V = 574.8 km/h on the conventional railway corridor TGV - LGV East in France, dated 3.4.2007).
=140
26 5
km/h 200m /h min =1 km
min
=850m
m =1600
240
=250 km/h
min
=5000m
250
245
245
255
250
60 =1
250
0 26
Fig. 2. Railway tracks - comparison of route development by speed limits RPi.
When designing curves, grade lines with continuous height shape, i.e. non-linear grade lines or lines with constant line shape (Table 1), are inserted between the non-canted part of rail and the canted part of the same rail (due to climbing of the cant p). In Slovakia, we may design cosine spiral with non-linear grade line for speed limit zones RP5 and RP6 in accordance with [3] for the speed of V > 160 km/h up to V 300 km/h. Under restricted conditions with speed 80 < V 300 km/h we may design Bloss spiral with non-linear grade line for RP3 to RP6. The standard [3] recommends cubic parabola with linear grade line for RP1 to RP6. Table 1. Transition spirals and grade lines for speed limits RP1 to RP6 in accordance with [3]. Types of spirals and grade lines
Speed limit zone
Equations of the transition spirals
Cubic parabola with linear grade line*
RP1 to RP6 0 > V 300 km/h
y
Bloss spiral with non-linear grade line*
RP3 to RP6 80 > V 300 km/h
y
Cosine spiral with non-linear grade line*
RP5 and RP6 200 > V 300 km/h
y
Shapes of grade lines
x3 6 r lp x4 4 l p2 r
x5 10 l 3p r
l 2p x2 4r 2rS2
§ · ¨ cos S x 1¸ ¨ ¸ lp © ¹
3. Dynamic design of spatial position of railway track The directional curvature of railway track including basic specifications of its structural elements such as curve radii (blue), shape and length of transition spirals (green), straight sections between the curves (red), etc., must be consistent with the design values of railway track according to STN [1] or STN EN [2]. Consequently, the principles of dynamic track design are characterized in the graphical environment with 3D terrain, using software tools
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accepted by railway practice [11, 12] etc. The values of the radii and transition spirals can be selected directly in the design of the tangent polygon either sequentially or we can design a minimum radius with the length of the transition spiral for all the curves and within the final solutions we modify the values in the software database tables (the whole 3D line model will be automatically modified after each modification of the basic parameters). In the drawing with 3D contours in Fig. 3 the tangent polygon (gray) will be designed, including the following minimum radii for RP4 V = 160 km/h (orange line), for RP5 V = 200 km/h (green line), for RP6 V = 300 km/h (blue line) according to (9) to (10). The presentation of the speed limit zones of railway lines is shown in Fig. 2. For rail route with V = 160 km/h according to STN [1] for cant pmax = 150 mm:
rmin
rmin
2 0.0472Vmax
2 6.5 Vmax
pd 2
0.0472 u1602
6.5 u160 150
1208.32 | 1250 m
(6)
2
1109.33 | 1200 m
(7)
Compared to the values in accordance with EN STN [3] for cant p = 150 mm, Imax = 100 mm, C = 11.8:
rmin
C 2 Vmax p I max
11.8 1602 1208.32 | 1250 m 150 100
(8)
The result is a design of all the radii above the value ri 1250 m of the track for V = 160 km/h in Fig. 4 (orange). The tangent polygon route can be modified by moving its top points VBi and by changing the parameter values ri, li and other design elements by shifting them directly in the drawing in Fig. 3.
Fig. 3. Railway track - dynamic solution design in 3D.
For the track RP6 Vmax = 250 km/h according to Standard [3], supplemented by Standard [1], pmax = 150 mm, where the slow trains run at the speed of Vmin =140 km/h: for the speed Vmax = 250 km/h, cant p = 150 mm and cant deficiency Imax = 100 mm:
rmin
C 2 Vmax p I max
11.8 2502 150 100
2950.00 | 3000 m
(9)
for Vmin = 140 km/h, cant p = 150 mm and cant excess Emax = 110 mm:
rmax
C 2 Vmin p Emax
11.8 1402 150 110
5782.00 | 5500 m
(10)
The result is a design of the radius 3000 m ri 5500 m of the track curves for V = 250 km/h (RP6) in Fig. 4. During the designing we are supposed to check that all the radii ri values are in the interval rmin ri rmax, (1). The design of the minimum radius in our example for V = 160 km/h is according to (6) to (8) and for V = 250 km/h according to (9) applying (10). It must be considered whether the freight and slow passenger trains will be allowed on high-speed lines, because the high-speed line requires quality and stable geometric position and height of the track and these freight trains would have a significant influence on the track and increase the costs of the trackage
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maintenance during its operation. The final designs of both railway lines are shown in Fig. 4.
Fig. 4. Railway tracks - layout design.
4. Conclusion
The design works include complicated procedures, while the railway track components must comply with all design criteria of the currently applicable standards and regulations. In principle the route design of slow tracks such as RP1 to RP4 is equally challenging to prepare as for the speed and high-speed lines of RP4 and RP6 speed limits, but the internal basic design parameters are different for each particular project. With increasing track speed we must also increase and secure its safety during operation which is much more expensive. Nowadays the development of quality and precise design documentation is not possible without computer technology using 3D variant solutions. The project design documentation contains many complex structural objects required for the railway operation and crossing with other modes of transport (bridges, tunnels, railway stations, terminals, intermodal terminals, humps and others [6]) and all of them must have an exact spatial position [8 to 10] given by the coordinate and height system (ETRR/89, S-JTSK, etc.). References [1] STN 73 6360 Geometric position and arrangement of the track standard gauge railways, 1999, update No.1 2003. [2] STN EN 13803-1 Railway applications. Track. Track alignment design parameters. Track gauge 1435 mm and wider. Part 1: Plain line, SK, (In accordance with EN 13803-1), 2010. [3] STN 73 6360-1 Geometric position arrangement of 1435 mm gauge Railways, Research and development institute of Railways, Slovak Railways - ŽSR, http://www.zsr.sk, Slovakia, before issuing 2014/2015. [4] SR 1013 Technical specifications of traction rolling stocks, ŽSR, 2006, SK, update No.11 2013. [5] Z10 Rules of technical operation of the railway infrastructure (PTPŽI), SK, 2014. [6] L. Ižvolt, S. Hodas, Modernisation of railway infrastructure in the Slovak Republic, COMPRAIL XIII - Computer system design and operation in the railway and other transit systems, New Forest, UK, organised by WESSEX Institute of Technology, http://www.wessex.ac.uk, http://www.witpress.com, Southampton, United Kingdom, 2012, ISBN 978-1-845564-616-5, e-ISBN 978-1-84564-617-2, pp. 211-223 [7] S. Hodas, L. Ižvolt, Modelling of temperature regime of railway track structure and its comparison with the results of experimental measurements, COMPRAIL XIV - Railway engineering design and optimization, Rome, Italy, organised by WESSEX Institute of Technology, http://www.wessex.ac.uk, http://www.witpress.com, Southampton, United Kingdom, 2014, ISBN 978-1-84564-766-7, eISBN 978-1-84564767-4, pp. 253-265. [8] L. Ižvolt, P. Dobeš, M. Meþár, Contribution to the methodology of the determination of the thermal conductivity coefficients Ȝ of materials applied in the railway subbase structure, Communications, Scientific letters of the University of Žilina, http://svf.uniza.sk/kzsth, Žilina, Slovakia, ISSN 1335-4205, Vol. 15, No. 4 (2013), pp. 9-17. [9] J. Ižvoltová, A. Villim, Identification of observations errors by Gauss-Jacobi algorithm, Civil and environmental engineering, Scientific technical journal, ISSN 1336-5835, Vol. 8, No. 1 (2012), Faculty of Civil Engineering, ŽU Žilina, Žilina, Slovakia, 2012, pp. 13-17. [10] J. Ižvoltová, Coordinate and datum transformation, Analele universităĠii din Oradea, Fascicula construcĠii úi instalaĠii hidroedilitare, ISSN 1454-4067, Vol. 13, (2010), Oradea, Romania, 2010, pp. 201-206. [11] AutoCAD Civil 3D 2015 CZ EDU, Software, AUTODESK, http://students.autodesk.com. [12] RailCAD, Software for arrangement and design of the track geometry, VÚT Brno, http://www.railcad.cz, Brno, Czech Republic, 2003-2014.