Fig. 30. Direction of magnetic field lines generated by the heating wire

would increase.

31.

This is the first model of induction heating of a rail forming part of a turnout to be developed by these authors. It was designed to demonstrate what phenomena occur when the rail is under the impact of a magnetic field. The rail and the wire do not form a full, closed magnetic loop. The magnetic field around the wire partly escapes into the air. As a result, penetration of the magnetic field into the rail structure is weaker and the magnetic induction on the rail surface is low. This weakened magnetic field may be insufficient to produce high eddy current densities in the rail and, in effect, it will be impossible to use induction heating for turnouts. Greater intensity of the magnetic field may improve the value of induction yet power losses associated with dispersion effects

Intensity of the magnetic field generated by the current across the coil is shown in Figure

The following assumptions underlie simulatiton testing of a rail at the time of induction heating in FLUX 3D software26 27:

The sample results were obtained in the simulation process at 650H frequency and 11.14 MA/mm2 density of the current across the wire. Set ranges of frequency and rms values of the current across the wire can be varied as part of this model.

Figure 29 presents a sample distribution of the absolute values of magnetic induction as obtained in the simulation process.

Fig. 29. Distribution of magnetic induction in the rail and its environment

Magnetic induction on the lateral web surface and on its foot reached a maximum of 0.037 T. This low value is due to the fact that an air gap appeared between the rail and the heating wire, impeding and dispersing the magnetic field. The wire itself was circular and its entire surface did not adhere to the rail, therefore magnetic field penetration into the rail was not effective.

Figure 30 shows the direction of magnetic field lines with regard to a rail placed inside the magnetic field of the heating wire.

26Femm, User′s Manual, 2009

27Flux3d, *User′s guide,* vol. 1-4, 2009

The following assumptions underlie simulatiton testing of a rail at the time of induction

 electric and magnetic parameters of a rail: electrical resistivity **ρ**, prime magnetising curve **B** = f (**H**) or **J**=f (**H**), intensity of the coercion field **Hc**, loss factors of eddy currents

The sample results were obtained in the simulation process at 650H frequency and 11.14 MA/mm2 density of the current across the wire. Set ranges of frequency and rms values of

Figure 29 presents a sample distribution of the absolute values of magnetic induction as

magnetic field description in 3D space with the aid of scalar magnetic potential,

heating in FLUX 3D software26 27:

obtained in the simulation process.

effective.

magnetic field of the heating wire.

26Femm, User′s Manual, 2009 27Flux3d, *User′s guide,* vol. 1-4, 2009

constant density of current across the heating wire,

the current across the wire can be varied as part of this model.

Fig. 29. Distribution of magnetic induction in the rail and its environment

Magnetic induction on the lateral web surface and on its foot reached a maximum of 0.037 T. This low value is due to the fact that an air gap appeared between the rail and the heating wire, impeding and dispersing the magnetic field. The wire itself was circular and its entire surface did not adhere to the rail, therefore magnetic field penetration into the rail was not

Figure 30 shows the direction of magnetic field lines with regard to a rail placed inside the

**w** and of magnetic hysteresis loop **h**, zero boundary conditions: **n**·**H** = 0.

Fig. 30. Direction of magnetic field lines generated by the heating wire

This is the first model of induction heating of a rail forming part of a turnout to be developed by these authors. It was designed to demonstrate what phenomena occur when the rail is under the impact of a magnetic field. The rail and the wire do not form a full, closed magnetic loop. The magnetic field around the wire partly escapes into the air. As a result, penetration of the magnetic field into the rail structure is weaker and the magnetic induction on the rail surface is low. This weakened magnetic field may be insufficient to produce high eddy current densities in the rail and, in effect, it will be impossible to use induction heating for turnouts. Greater intensity of the magnetic field may improve the value of induction yet power losses associated with dispersion effects would increase.

Intensity of the magnetic field generated by the current across the coil is shown in Figure 31.

Application of 3D Simulation Methods to the Process of Induction Heating of Rail Turnouts 331

*Badania eksploatacyjne wodnego system ogrzewania rozjazdów typu MAS-Guben*, CNTK

Binns K.J., Lawrenson P.J., Trowbridge C.W. (1995). *The Analytical and Numercial Solution of*

Bolkowski S., Stabrowski M., Skoczylas J., Sroka J., Sikora J., Wincenciak S. (1993).

Brodowski D., Andrulonis J.(2000). *Efektywność ogrzewania rozjazdów kolejowych*, CNTK,

Brodowski D., Andrulonis J. (2002). *Ogrzewanie rozjazdów kolejowych*, *Problemy kolejnictwa*,

Gawrylczyk K.M. (2007). *Analiza wrażliwościowa pola elektromagnetycznego z użyciem metody elementów skończonych*, Instytut Naukowo-Badawczy ZTUREK, Warszawa

Gozdecki T., Hering M., Łobodziński W. (1979). *Urządzenia elektroniczne. Elektroniczne urządzenia grzejne*, Wydawnictwa Szkolne i Pedagogiczne, Warszawa Grobelny M. (2009) *Budowa, modernizacja, naprawa i remonty nawierzchni kolejowej – urządzenia*

*Instrukcja eksploatacji i utrzymania urządzeń elektrycznego ogrzewania rozjazdów*, PKP Polskie

Jianming J. (1993). *The finite element method in electromagnetic*, A Wiley-Interscience

Jiles D. (1991). *Introduction to Magnetism and Magnetic Materials*, Chapman & Hall, ISBN 0-

Kiraga K., Szychta E., Andrulonis J. (2010). *Wybrane metody ogrzewania rozjazdów kolejowych –*

Kuryłowicz J. (1962). *Badania materiałów magnetycznych*, Wydawnictwo Naukowo-

Leśniewska E. (1997). *Zastosowanie symulacji pól elektromagnetycznych w projektowaniu przekładników*, Zeszyty Naukowe Politechniki Łódzkiej, Nr 766, Łódź Materiały seminaryjne CNTK. (2004). *Wodne ogrzewanie rozjazdów kolejowych typu MAS*,

Mendrela E., Łukaniszyn M., Macek-Kamińska K. (2002). *Tarczowe silniki prądu stałego z*

Praca zbiorowe: *Studium na temat wyboru optymalnego systemu ogrzewania rozjazdów*,

Sajdak Cz., Samek E. (1985). *Nagrzewanie indukcyjne. Podstawy teoretyczne i zastosowanie*,

Sikora R. (1997). *Teoria pola elektromagnetycznego*, Wydawnictwo Naukowo-Techniczne,

*komutacją elektroniczną*, Wydawnictwo Gnome, Katowice

*artykuł przeglądowy,* PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 86

Gignoux D., Schlenker M.(2005). *Magnetism Fundamentals*, Springer, Grenoble

*i elementy,* RYNEK KOLEJOWY, 2009-03-09

Publication, John Wiley & Sons, INC., New York

Linie Kolejowe S.A., Warszawa, 2007

412-386-30-5,New York

Techniczne, Warszawa

Warszawa, 21-22 Kwiecień

*Prospekt informacyjny o otulinach firmy Haet Point*, 2009.

Wydawnictwo "Śląsk", Katowice

COBiRTK, 1971

Warszawa

NR 2/2010

*Electric and Magnetic Fields*, A Wiley-Interscience Publication, John Wiley & Sons,

*Komputerowe metody analizy pola elektromagnetycznego*, Wydawnictwo Naukowo –

**8. References**

Warszawa, Styczeń 2004

Techniczne, Warszawa

zeszyt 135, CNTK

INC., New York

Warszawa

Femm, *User′s Manual, 2009*  Flux3d, *User′s guide,* vol. 1-4, 2009

Fig. 31. Intensity of the magnetic field generated by the current across the heating wire

It is easy to read the value of magnetic field intensity arising from the heating wire: it approaches 11000A/m in the centre of the wire and reduces to 3000A/m at the contact of the rail and the wire after covering a distance of circa 1 centimetre (drag).

The air gap must be fully eliminated in continuing research and, should it prove impossible, the gap needs to be minimised in order to reduce magnetic field dispersion as much as practicable.

### **7. Conclusion**

This chapter has presented elementary knowledge concerning 3D model illustrations of induction heating as applied to rail turnouts. It should be borne in mind, however, that a simulation model can differ widely from reality due, for instance, to simplifications discussed by the authors. The magnetic model itself must be modified in order to solve the issue of the air gap, for example.

It is also necessary to verify simulation results against those obtained in an actual model of turnout induction heating. Work on developing an actual model is in progress.

At the present stage, the magnetic model developed by the authors in Flux3D provides for observation of electric and magnetic effects in the rail's internal structure triggered by flow of eddy currents. The model will be utilised to determine the depth of magnetic field penetration into the rail structure as dependent on variations of magnetising current frequency and will serve to determine a temperature distribution along the rail in the process of heating. Knowledge of this temperature distribution or, to be more exact, of maximum temperature values attained by the individual rail sections is the key to success of this research.

### **8. References**

330 Infrastructure Design, Signalling and Security in Railway

Fig. 31. Intensity of the magnetic field generated by the current across the heating wire

the rail and the wire after covering a distance of circa 1 centimetre (drag).

practicable.

**7. Conclusion**

this research.

issue of the air gap, for example.

It is easy to read the value of magnetic field intensity arising from the heating wire: it approaches 11000A/m in the centre of the wire and reduces to 3000A/m at the contact of

The air gap must be fully eliminated in continuing research and, should it prove impossible, the gap needs to be minimised in order to reduce magnetic field dispersion as much as

This chapter has presented elementary knowledge concerning 3D model illustrations of induction heating as applied to rail turnouts. It should be borne in mind, however, that a simulation model can differ widely from reality due, for instance, to simplifications discussed by the authors. The magnetic model itself must be modified in order to solve the

It is also necessary to verify simulation results against those obtained in an actual model of

At the present stage, the magnetic model developed by the authors in Flux3D provides for observation of electric and magnetic effects in the rail's internal structure triggered by flow of eddy currents. The model will be utilised to determine the depth of magnetic field penetration into the rail structure as dependent on variations of magnetising current frequency and will serve to determine a temperature distribution along the rail in the process of heating. Knowledge of this temperature distribution or, to be more exact, of maximum temperature values attained by the individual rail sections is the key to success of

turnout induction heating. Work on developing an actual model is in progress.

**13**

*France*

**EMC Analysis of Railway Power Substation**

*1Université Lille 1 Sciences et Technologies, USTL, IEMN/TELICE Laboratory*

The first part of the chapter will present the global aspect of the railway power infrastructures and specially the power supply substation. The goals of this study consist in proposing a high frequency model of the railway systems and verifying by simulation the conformity with the EMC standards. Thus, each component of the railway power infrastructure (transformer, power rectifier) is modeled and the simulation results of the conducted emissions are

A railway system might pollute, in an electromagnetic sense, the surrounding environment, disturbing radio and communication systems which can be not related to the railway itself. In this case the whole railway can be considered as a source of Electromagnetic Interference (EMI). In order to avoid the disruption of the electronic equipments near to the railway, the overall field generated by railway system must be kept below certain safety values given by standards [1]. Obviously, there are many sources of the electromagnetic field and their

compared to measurements on a reduced scale of the power supply substation.

because of power circuits that might become a source of emissions.

**1. Introduction**

**2. EMI sources in railway system**

contributions can come from:

kilohertz up to one gigahertz.

**Modeling and Measurements Aspects**

*2Université Lille 1 Sciences et Technologies, USTL, L2EP Laboratory,*

S. Baranowski1, H. Ouaddi1, L. Kone1 and N. Idir2

*F-59650 Villeneuve d'Ascq,*

strona internetowa szyn: www. inzynieria-kolejowa.dl.pl.

## **EMC Analysis of Railway Power Substation Modeling and Measurements Aspects**

S. Baranowski1, H. Ouaddi1, L. Kone1 and N. Idir2 *1Université Lille 1 Sciences et Technologies, USTL, IEMN/TELICE Laboratory 2Université Lille 1 Sciences et Technologies, USTL, L2EP Laboratory, F-59650 Villeneuve d'Ascq, France*

### **1. Introduction**

332 Infrastructure Design, Signalling and Security in Railway

Wielgosz R. (2009). *Łączenie bezstykowych szyn kolejowych,* MECHANIKA CZASOPISMO

Wincenciak S. (1998). *Metody i algorytmy optymalizacji kształtu obiektów w polu elektromagnetycznym*, Oficyna wydawnicza Politechniki Warszawskiej, Warszawa Wróbel R. (2000). *Analiza wpływu parametrów obwodu magnetycznego i elektrycznego na pracę*

TECHNICZNE, Wydawnictwo Politechniki Krakowskiej, 2-M/2009, Zeszyt 6, Rok

*silnika tarczowego prądu stałego z magnesami trwałymi i elektronicznym komutatorem,*

strona internetowa szyn: www. inzynieria-kolejowa.dl.pl.

Rozprawa doktorska, Łódź

106.

The first part of the chapter will present the global aspect of the railway power infrastructures and specially the power supply substation. The goals of this study consist in proposing a high frequency model of the railway systems and verifying by simulation the conformity with the EMC standards. Thus, each component of the railway power infrastructure (transformer, power rectifier) is modeled and the simulation results of the conducted emissions are compared to measurements on a reduced scale of the power supply substation.

### **2. EMI sources in railway system**

A railway system might pollute, in an electromagnetic sense, the surrounding environment, disturbing radio and communication systems which can be not related to the railway itself. In this case the whole railway can be considered as a source of Electromagnetic Interference (EMI). In order to avoid the disruption of the electronic equipments near to the railway, the overall field generated by railway system must be kept below certain safety values given by standards [1]. Obviously, there are many sources of the electromagnetic field and their contributions can come from:

However, a train might be or be not compliant to field standards depending on the line characteristics and on its position on the railway. Nowadays, trains are designed to meet EMC rules, but the non-compliances can be remedied thanks to identification of the different resonances frequency, which can occur mainly in a frequency range from some kilohertz up to one gigahertz.

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 335

EN 50121-3-1 limit

Resonance due to Infrastructure or train

0.01 0.1 1 **Frequency (MHz)**

As presented previously, the aim of the standards is to limit the disturbance of the external environment produced by the railway infrastructure but also on the railways system itself. Indeed, the new generation of rolling stock is equipped with safety communication systems with on board antennas which must not be disturbed neither. These elements of safety system operate in frequency range from 10 kHz to 30MHz, which constitute the frequency range considered in this study but also above, for example, the GSMR signal frequency is around 900MHz. Thus, it becomes important to know which source can introduce the

Besides, sensitivity of these communication systems must also be evaluated for the resonant

A schematic representation of the railway infrastructure is shown in Fig. 3. In this figure, we can see that the power supply system constituted by the substation, the rails, the catenaries and the train which constitutes the load of the power line. This figure also shows a location system based on telecommunication between on board antenna and

power transformer, sometimes static converters, and cables, bus bars...etc.

The railway power supply system is generally composed by two main systems:

lines, multi-conductors structures, conductivity of the ballast, ...)

0

**2.2 Effect of the resonances**

**3. Railway power infrastructures**

antenna along the track.

Fig. 2. Example of the measured magnetic field

20

**H (dBµA/m)**

disturbances.

frequencies.

40

60

### **2.1 Description of standards EMI measurement methods**

The EMC standard EN 50121 [1] is used to characterize the EM environment, in the railway systems; it notably aim to limit the EMI levels from the railway infrastructures to the external environment. This standard EN 50121 describes the methodologies and the limits to apply, relating to the EM radiations and immunity of railway equipments, vehicles and infrastructures. The emissions of the whole railway system, including vehicles and infrastructure, are dealt with the section 2 of the EN 50121. The objective of the tests specified in this standard is to verify that the EM emissions produced by the whole railway systems do not disturb the neighboring equipments and systems.

The methodology then consists in measuring the radiated EM emissions at a distance of 10 m from the middle of the tracks and at about 1.5 m from the floor (Fig.1) and in comparing them with the maximum levels (limit curve in red in Fig.2). The measurements protocol and the limits are specified for the frequencies varying from 9 kHz to 1 GHz.

For each frequency band (9kHz-150kHz; 150kHz-30MHz; 30MHz-1GHz), the standards define among others:

During measurements of the electromagnetic field radiated at 10 m from the railway track, we can observe that, sometimes, for some frequency, the standards limit can be exceeded. An example of measurement from 10 kHz to 1 MHz is given in fig. 2. The exceeding is characterized by resonance phenomena which appeared for some frequencies of the power supply current.

Fig. 1. On site measurement of the electromagnetic radiation of the train (stationary and moving)

Fig. 2. Example of the measured magnetic field

### **2.2 Effect of the resonances**

334 Infrastructure Design, Signalling and Security in Railway

The EMC standard EN 50121 [1] is used to characterize the EM environment, in the railway systems; it notably aim to limit the EMI levels from the railway infrastructures to the external environment. This standard EN 50121 describes the methodologies and the limits to apply, relating to the EM radiations and immunity of railway equipments, vehicles and infrastructures. The emissions of the whole railway system, including vehicles and infrastructure, are dealt with the section 2 of the EN 50121. The objective of the tests specified in this standard is to verify that the EM emissions produced by the whole railway

The methodology then consists in measuring the radiated EM emissions at a distance of 10 m from the middle of the tracks and at about 1.5 m from the floor (Fig.1) and in comparing them with the maximum levels (limit curve in red in Fig.2). The measurements protocol and

For each frequency band (9kHz-150kHz; 150kHz-30MHz; 30MHz-1GHz), the standards

During measurements of the electromagnetic field radiated at 10 m from the railway track, we can observe that, sometimes, for some frequency, the standards limit can be exceeded. An example of measurement from 10 kHz to 1 MHz is given in fig. 2. The exceeding is characterized by resonance phenomena which appeared for some frequencies of the power

Fig. 1. On site measurement of the electromagnetic radiation of the train (stationary and

1.5 m

**2.1 Description of standards EMI measurement methods**

systems do not disturb the neighboring equipments and systems.

define among others:

be measured,

supply current.

moving)

as shown until 1MHz in fig.2

10 m

the limits are specified for the frequencies varying from 9 kHz to 1 GHz.

As presented previously, the aim of the standards is to limit the disturbance of the external environment produced by the railway infrastructure but also on the railways system itself. Indeed, the new generation of rolling stock is equipped with safety communication systems with on board antennas which must not be disturbed neither. These elements of safety system operate in frequency range from 10 kHz to 30MHz, which constitute the frequency range considered in this study but also above, for example, the GSMR signal frequency is around 900MHz. Thus, it becomes important to know which source can introduce the disturbances.

Besides, sensitivity of these communication systems must also be evaluated for the resonant frequencies.

### **3. Railway power infrastructures**

A schematic representation of the railway infrastructure is shown in Fig. 3. In this figure, we can see that the power supply system constituted by the substation, the rails, the catenaries and the train which constitutes the load of the power line. This figure also shows a location system based on telecommunication between on board antenna and antenna along the track.

The railway power supply system is generally composed by two main systems:

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 337

**Sim ulations Measurem ents**

**0 0.5 1 1.5 2 -110**

Fig. 5. Example of obtained results (corrsponding to the Fig. 4 configuration). The generator

In the world, many kind of railway power supply exist: alternative (AC) or direct current (DC), with various amplitudes: 1500kV, 3kV, 25kV… Then, we have worked on a general power substation constituted by a transformer and a power converter as

In case of AC power supply substation, there is no AC/DC converter. The power

In order to propose a high frequency model of the whole system, it's necessary to determine a model for each element, especially of power transformer, which accuracy will be highly dependent of the accuracy of each primary model. The low frequency model of the transformer, defined at 50Hz, is not valuable when the frequency increases. Indeed, some phenomena can be predominant in high frequencies as the Eddy current, which depends on the variation of the magnetizing impedance and the winding resistance, but also the

**Freque ncy (MHz)**

**-105 -100 -95 -90 -85 -80 -75 -70 -65**

**5. Power supply substation**

presented in fig. 6.

give a sinusoidal signal of 1V amplitude.

Fig. 6. Schematic circuit of a railway substation

transformer constitutes the main device of the substation.

**Normalized magnetic field H/V**

**in (db S/m)**

Fig. 3. Simplified diagram of railway infrastructure

### **4. Problem of EMC in railway**

In order to avoid EMI with high levels of electromagnetic disturbances, measurements are usually performed. Test results can lead to different comments and from an industrial point of view, it is important to distinguish the disturbances due to the railway power supply infrastructure (substation – line catenaries/rail) and others due to the train itself. Indeed, it is important to know which kind mitigations solutions have to be done to reduce the disturbances and who should do that: the train manufacturer or the power supplier.

In a previous research project [2], the lines system has been modeled. The proposed model enables to estimate the field radiated by the power line taken into account various parameters like the geometry of the line; the conductivity of the soil … The model is based on line theory, the train is the load (Ztrain) and a generator feeds the lines.

An example of the simulation conditions and the obtained results is given in figures 4 and 5

This model gives good results and many details on how each parameter has been taken into account can be found in [2]. But it is only a model of the lines and the generator used in this simulation is a sinusoidal one with constant amplitude.

Then, it was necessary to model the power substation to obtain a more realistic generator and this has constituted the goal of the CEMRAIL project of which some results are presented here.

Fig. 4. Simplified model of the power supplier line

Fig. 5. Example of obtained results (corrsponding to the Fig. 4 configuration). The generator give a sinusoidal signal of 1V amplitude.

### **5. Power supply substation**

336 Infrastructure Design, Signalling and Security in Railway

In order to avoid EMI with high levels of electromagnetic disturbances, measurements are usually performed. Test results can lead to different comments and from an industrial point of view, it is important to distinguish the disturbances due to the railway power supply infrastructure (substation – line catenaries/rail) and others due to the train itself. Indeed, it is important to know which kind mitigations solutions have to be done to reduce the

In a previous research project [2], the lines system has been modeled. The proposed model enables to estimate the field radiated by the power line taken into account various parameters like the geometry of the line; the conductivity of the soil … The model is based

An example of the simulation conditions and the obtained results is given in figures 4 and 5 This model gives good results and many details on how each parameter has been taken into account can be found in [2]. But it is only a model of the lines and the generator used in this

Then, it was necessary to model the power substation to obtain a more realistic generator and this has constituted the goal of the CEMRAIL project of which some results are

disturbances and who should do that: the train manufacturer or the power supplier.

on line theory, the train is the load (Ztrain) and a generator feeds the lines.

simulation is a sinusoidal one with constant amplitude.

Fig. 4. Simplified model of the power supplier line

Fig. 3. Simplified diagram of railway infrastructure

**4. Problem of EMC in railway**

presented here.

In the world, many kind of railway power supply exist: alternative (AC) or direct current (DC), with various amplitudes: 1500kV, 3kV, 25kV… Then, we have worked on a general power substation constituted by a transformer and a power converter as presented in fig. 6.

Fig. 6. Schematic circuit of a railway substation

In case of AC power supply substation, there is no AC/DC converter. The power transformer constitutes the main device of the substation.

In order to propose a high frequency model of the whole system, it's necessary to determine a model for each element, especially of power transformer, which accuracy will be highly dependent of the accuracy of each primary model. The low frequency model of the transformer, defined at 50Hz, is not valuable when the frequency increases. Indeed, some phenomena can be predominant in high frequencies as the Eddy current, which depends on the variation of the magnetizing impedance and the winding resistance, but also the

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 339

In order to analyze the behavior or the railway substation we have built a test bench which

The experimental setup is composed with a three phase power transformer, a diodes rectifier and loads. The transformer is a 15 kVA - 220 V/110 V with Δ connected high voltage (HV) winding and Δ connected low voltage (LV) winding. The power rectifier is designed with twelve power diodes and is connected to 47 Ω resistor. All these elements are placed over a common ground plane (Fig. 8). The different devices are connected using 1m

A high frequency model of the power transformer, which takes into account the various physical phenomena has been studied [4][8]. Figure 9 presents this model applied to the

Starting from an ideal transformer model with transformation ratio η, the proposed model takes into account, for each phase, the leakage inductances, the skin effects, the magnetizing impedance and stray capacitances of which become significant at high frequency. Moreover the iron core has been considered linear at frequency above 10 kHz [12] [13] consequently its

The subject of the work is to identify the important physical parameters which contribute to induce resonance phenomena. We have chosen to propose a model as physical as possible

Loads

Ground Plane

Rectifier Power

transformer

15kVA three phase power transformer used in the laboratory test bench (fig.8).

This model is valid in the frequency band varying from 40 Hz to 30 MHz.

and after, if necessary, to add black box to model more intricate phenomena.

**6.2 Laboratory test bench**

**6.3 Transformer model**

long cable.

reproduces the substation in small scale.

effect can be neglected at high frequencies.

Fig. 8. Circuit diagram and photo of the test bench

parasitic capacitances which appear between windings due to the insulated parts of the transformer. The analysis of the transformer behavior shows that it's possible to use an equivalent electrical circuit model which is valid in the considered frequency band.

During the past decades, many models of power transformer have been studied for several applications. Most of those models, often in a reduced frequency band, are based on the representation of the transformer by an arrangement of resistive, inductive and capacitive elements which can take into account the physical behavior of power transformer [3]; some others are wide band models established using the black box principle [7]. Obviously, it's also possible to apply the FEM (Finite Element Method) method to have a precise model, but in this case, the exact constitution of the transformer must be known. Some additional difficulties are found in the studied problem: how to found the appropriate data sheet when the transformer is operated in the railway system since many years? In the following sections, we will present the proposed equivalent model and two techniques used to identify the transformer parameters.

### **6. High frequency model of transformer**

### **6.1 Preliminary study**

Making measurements in railways power substation is not easy, then preliminary investigations have been done on various power transformers. Primary and secondary winding impedances measurements in various configurations have been done on two different transformers:

Figure 7-a (15kVA transformer) and Fig. 7-b (2.38MVA transformer) show the secondary winding impedance measured when the primary is short circuited for these two transformers.

These two impedances have been measured in the same frequency band: 100 kHz to 40MHz. We can note that these two responses are globally identical. Thus, we will model, in the first time, a low power transformer before to apply this model to a real substation transformer.

Fig. 7. Secondary winding impedance measurements when the primary is short circuited for two tested transformers (a- 15kVA and b- 2.38MVA)

### **6.2 Laboratory test bench**

338 Infrastructure Design, Signalling and Security in Railway

parasitic capacitances which appear between windings due to the insulated parts of the transformer. The analysis of the transformer behavior shows that it's possible to use an

During the past decades, many models of power transformer have been studied for several applications. Most of those models, often in a reduced frequency band, are based on the representation of the transformer by an arrangement of resistive, inductive and capacitive elements which can take into account the physical behavior of power transformer [3]; some others are wide band models established using the black box principle [7]. Obviously, it's also possible to apply the FEM (Finite Element Method) method to have a precise model, but in this case, the exact constitution of the transformer must be known. Some additional difficulties are found in the studied problem: how to found the appropriate data sheet when the transformer is operated in the railway system since many years? In the following sections, we will present the proposed equivalent model and two techniques used to

Making measurements in railways power substation is not easy, then preliminary investigations have been done on various power transformers. Primary and secondary winding impedances measurements in various configurations have been done on two

Figure 7-a (15kVA transformer) and Fig. 7-b (2.38MVA transformer) show the secondary winding impedance measured when the primary is short circuited for these two

These two impedances have been measured in the same frequency band: 100 kHz to 40MHz. We can note that these two responses are globally identical. Thus, we will model, in the first time, a low power transformer before to apply this model to a real substation transformer.

Fig. 7. Secondary winding impedance measurements when the primary is short circuited

equivalent electrical circuit model which is valid in the considered frequency band.

identify the transformer parameters.

**6.1 Preliminary study**

different transformers:

transformers.

**6. High frequency model of transformer**

for two tested transformers (a- 15kVA and b- 2.38MVA)

In order to analyze the behavior or the railway substation we have built a test bench which reproduces the substation in small scale.

The experimental setup is composed with a three phase power transformer, a diodes rectifier and loads. The transformer is a 15 kVA - 220 V/110 V with Δ connected high voltage (HV) winding and Δ connected low voltage (LV) winding. The power rectifier is designed with twelve power diodes and is connected to 47 Ω resistor. All these elements are placed over a common ground plane (Fig. 8). The different devices are connected using 1m long cable.

### **6.3 Transformer model**

A high frequency model of the power transformer, which takes into account the various physical phenomena has been studied [4][8]. Figure 9 presents this model applied to the 15kVA three phase power transformer used in the laboratory test bench (fig.8).

Starting from an ideal transformer model with transformation ratio η, the proposed model takes into account, for each phase, the leakage inductances, the skin effects, the magnetizing impedance and stray capacitances of which become significant at high frequency. Moreover the iron core has been considered linear at frequency above 10 kHz [12] [13] consequently its effect can be neglected at high frequencies.

This model is valid in the frequency band varying from 40 Hz to 30 MHz.

The subject of the work is to identify the important physical parameters which contribute to induce resonance phenomena. We have chosen to propose a model as physical as possible and after, if necessary, to add black box to model more intricate phenomena.

### Fig. 8. Circuit diagram and photo of the test bench

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 341

**Note:** The proposed model can be used to model a single phase transformer by using only

The experimental results, in time or in frequency domain presented in the next sections, allow determining the various parameters of the proposed model. Figure 10 shows an

Fig. 10. Comparison within measurements and simulation results (impedance of the

The determination of each parameter of the equivalent circuit (Fig.9) of the transformer model is realized from impedance measurements versus frequency, in different test

The magnetizing impedance of each phase is modeled by a resistance in parallel with an inductance; their values are deduced from the impedance measured on the primary

**7. Determination of the various elements of the transformer model**

fitting method; details are given in [4-5-6].

primary winding, the secondary being open)

configurations [7] [8].

**7.1 The magnetizing impedance**

example of modeling results compared to experimental data.

one circuit by phase.

**6.4 Validation results**

Fig. 9. High frequency model of three-phase power transformer

Each element of the equivalent circuit will be detailed and the method used to determine these parameters will be presented in the next section.

	- Turn-to-turn capacitance of the primary and secondary windings: Ca1, Ca2, Cb1, Cb2, Cc1, Cc2,
	- Capacitances between windings (divided in two capacitances): Ca31, Ca32, Cb31, Cb32, Cc31, Cc32,
	- Capacitance between the input of the primary winding and the output of the secondary: Car, Cbr, Ccr,

**Note:** The proposed model can be used to model a single phase transformer by using only one circuit by phase.

### **6.4 Validation results**

340 Infrastructure Design, Signalling and Security in Railway

Fig. 9. High frequency model of three-phase power transformer

these parameters will be presented in the next section.

resp.) [14].

[16], [17] :

Cc1, Cc2,

Cc31, Cc32,

secondary: Car, Cbr, Ccr,

Each element of the equivalent circuit will be detailed and the method used to determine

course, the magnetizing impedance changes with the frequency [7] [15].

The experimental results, in time or in frequency domain presented in the next sections, allow determining the various parameters of the proposed model. Figure 10 shows an example of modeling results compared to experimental data.

Fig. 10. Comparison within measurements and simulation results (impedance of the primary winding, the secondary being open)

### **7. Determination of the various elements of the transformer model**

The determination of each parameter of the equivalent circuit (Fig.9) of the transformer model is realized from impedance measurements versus frequency, in different test configurations [7] [8].

### **7.1 The magnetizing impedance**

The magnetizing impedance of each phase is modeled by a resistance in parallel with an inductance; their values are deduced from the impedance measured on the primary

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 343

Leakage

inductance with

skin effects

Fig. 12. Primary impedance with secondary short circuited (phase A)

Fig. 13. Equivalent circuit of the leakage impedance

of measurements.

for the studied transformer.

is supposed equivalent to phase A)

Li in

The leakage impedance can be modeled using a R-L ladder network as shown in Fig. 13

In order to have an efficient approximation, the parameters of the equivalent circuit are computed with a less square algorithm; the identification being performed with the results

Table1 presents the parameters of the equivalent circuit of the leakage impedance obtained

Ri in R1 R2 R3 R4 R5 R6 R7 R8 Phase A 0.6 58 49 132 45 472 746 679 Phase B 0.6 58 0.001 33 37 1082 15 39

mH L1 L2 L3 L4 L5 L6 L7 L8 Phase A 1.1 1.08 3.6 100 13 11 54 14 Phase B 1.1 2.3 2.4 2.5 8.3 11 36 69 Table 1. Parameters of the leakage impedance model of the laboratory transformer (phase C

winding, at low frequency, when the secondary winding is open as shown in Fig 11. The values of these parameters for the phase A and B are given as following:

Ram= 13.44 kΩ, and Lam=31.19 mH, Rbm= 15.87 kΩ and Lbm=32.14 mH

However, if we take into account the geometry of the transformer, phases A and C are considered, to have the same behavior, then the corresponding parameters are supposed to have the same value.

### **7.2 The leakage impedance**

The leakage inductance and the wire resistance (the skin effect) of the winding can be determined by measuring the primary impedance when the secondary winding is shortcircuited. Winding losses can be estimated from the impedance measured in the low frequency band as shown in Fig. 12.

Fig. 11. Primary winding impedance when the secondary is opened (measuremens on the Phase A of the test bench transformer)

winding, at low frequency, when the secondary winding is open as shown in Fig 11. The

However, if we take into account the geometry of the transformer, phases A and C are considered, to have the same behavior, then the corresponding parameters are supposed to

The leakage inductance and the wire resistance (the skin effect) of the winding can be determined by measuring the primary impedance when the secondary winding is shortcircuited. Winding losses can be estimated from the impedance measured in the low

Fig. 11. Primary winding impedance when the secondary is opened (measuremens on the

values of these parameters for the phase A and B are given as following:

Ram= 13.44 kΩ, and Lam=31.19 mH, Rbm= 15.87 kΩ and Lbm=32.14 mH

have the same value.

**7.2 The leakage impedance**

frequency band as shown in Fig. 12.

Magnetizing impedance

Phase A of the test bench transformer)

Fig. 12. Primary impedance with secondary short circuited (phase A)

The leakage impedance can be modeled using a R-L ladder network as shown in Fig. 13

In order to have an efficient approximation, the parameters of the equivalent circuit are computed with a less square algorithm; the identification being performed with the results of measurements.

Fig. 13. Equivalent circuit of the leakage impedance

Table1 presents the parameters of the equivalent circuit of the leakage impedance obtained for the studied transformer.

Table 1. Parameters of the leakage impedance model of the laboratory transformer (phase C is supposed equivalent to phase A)

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 345

The impedance characteristics presented in Figures 11 and 12 show the same evolution at high frequency (above 3 MHz) with fast variations and consequently it costs time to model. Thanks to "augmented method" [5], it is possible to consider this part by using an inductance in parallel with a "black box". The "black box" is elaborated by using the principle of the "vector fitting" [13]. This algorithm consists in approximating a frequency response with a rational function, expressed by a sum of partial fractions. This principle is implemented in the IdEM® software [6] [18] used for our study. This code generates a macro-model which could be integrated in software like Pspice. Figure 9 presents the main equivalent circuit of the transformer with the added impedance issued from "augmented model" (Fig.15) which takes into account the high frequency effects. Figure 16 shows the effect of this 'augmented model impedance' on the HF accuracy of the model, by

MACRO HF

R=300 Ω

Fig. 16. Primary impedance with secondary short circuited (Phase A). Comparison between measurement and simulation result with and without the augmented model (named black

Fig. 15. Equivalent circuit for high frequency behavior of the transformer.

This circuit is repesented by a component named "augmented model" in figure 9.

L=4.8 uH

**7.4 The augmented model impedance**

box in the figure).

comparison of the measurements results with the model ones.

### **7.3 Stray Capacitances**

The stray capacitances of each phase of the transformer are estimated separately. As an example, here, the phase A (A0A1-a0a1) is studied. The transformer is modeled as a "black box", and it's necessary to determine the capacitance Ca1, Ca2, Ca31, Ca32, Car, Ca1g and Ca2g. Their effects are located in high frequencies so they will be evaluated in this frequency range.

For each phase, seven measurement configurations are necessary to determine these capacitances. Thus, they provide seven equations which unknowns are the capacitances of the equivalent circuit. Following, the equation system is solved using mathematical tools. Figure 14 presents the seven measurements configurations with the associated equations, in the case of the phase A. The arrows show the measurements points, the short circuits are presented by the lines and Cme represents the measured capacitance. As well as the magnitude, the phase of the impedance is measured in order the make an efficient characterization.

Moreover some precautions are taken for example it is proper to short-circuit the two other phases when the third is characterized in order to inhibit their influences.

Fig. 14. Measurement configuration used for determining capacitances (example for phase A)

#### **7.4 The augmented model impedance**

344 Infrastructure Design, Signalling and Security in Railway

The stray capacitances of each phase of the transformer are estimated separately. As an example, here, the phase A (A0A1-a0a1) is studied. The transformer is modeled as a "black box", and it's necessary to determine the capacitance Ca1, Ca2, Ca31, Ca32, Car, Ca1g and Ca2g. Their effects are located in high frequencies so they will be evaluated in this frequency

For each phase, seven measurement configurations are necessary to determine these capacitances. Thus, they provide seven equations which unknowns are the capacitances of the equivalent circuit. Following, the equation system is solved using mathematical tools. Figure 14 presents the seven measurements configurations with the associated equations, in the case of the phase A. The arrows show the measurements points, the short circuits are presented by the lines and Cme represents the measured capacitance. As well as the magnitude, the phase of the impedance is measured in order the make an efficient

Moreover some precautions are taken for example it is proper to short-circuit the two other

Fig. 14. Measurement configuration used for determining capacitances (example for phase A)

phases when the third is characterized in order to inhibit their influences.

**7.3 Stray Capacitances**

range.

characterization.

The impedance characteristics presented in Figures 11 and 12 show the same evolution at high frequency (above 3 MHz) with fast variations and consequently it costs time to model. Thanks to "augmented method" [5], it is possible to consider this part by using an inductance in parallel with a "black box". The "black box" is elaborated by using the principle of the "vector fitting" [13]. This algorithm consists in approximating a frequency response with a rational function, expressed by a sum of partial fractions. This principle is implemented in the IdEM® software [6] [18] used for our study. This code generates a macro-model which could be integrated in software like Pspice. Figure 9 presents the main equivalent circuit of the transformer with the added impedance issued from "augmented model" (Fig.15) which takes into account the high frequency effects. Figure 16 shows the effect of this 'augmented model impedance' on the HF accuracy of the model, by comparison of the measurements results with the model ones.

Fig. 15. Equivalent circuit for high frequency behavior of the transformer.

This circuit is repesented by a component named "augmented model" in figure 9.

Fig. 16. Primary impedance with secondary short circuited (Phase A). Comparison between measurement and simulation result with and without the augmented model (named black box in the figure).

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 347

and the Fourier calculation of the current which can be calculated through a FFT algorithm for all measurements. The various impedances of the equivalent circuit shown in Fig. 9 can

then be determined through various configurations of the transformer.

Fig. 18. Voltage waveform in primary winding when the secondary is open

Fig. 17. Measurement bench in time domain

### **8. Characterization of the transformer in frequency domain**

As detailed in the previous section, the determination of the proposed model parameters is based on impedance measurements which can easily be done in frequency domain with impedance or network analyzer.

This method gives good results for low power transformer but there are some problems to make this kind of measurement with very high power transformer as the ones used in railways substation, which are the followings:

We propose a measurement method, carried out in time domain and based on the injection of higher level signals in the transformer. The principle of the proposed method and the obtained results are presented in the next section. [9]

### **9. Characterisation in time domain**

### **9.1 Measurements principle**

A square voltage waveform is applied at terminals of the transformer in the various configuration tests. The input current and input voltage are measured in time domain and determined in frequency domain via Fourier transforms and then the corresponding impedance can be deduced.

This experimental method has been applied in reduced scale on the laboratory test bench, to characterize the 15kVA three phases transformer. For this characterization, a square signal of magnitude 30 V with a period equal to 30µs, duty cycle equal to 0.5 and the rise time and fall time equal to 10ns. A differential voltage probe (bandwidth: 100MHz) is used to measure the voltage at the generator terminals. The current is measured with a current probe (bandwidth: 100MHz). The connection wires between the generator and the transformer are chosen as short as possible. Figure 17 shows a diagram of the measurement bench; we can see the generator, one phase of the transformer and the position of measurements probes.

Figure 18 and 19 show respectively the waveforms of the primary voltage and current of one phase of the transformer, in the configuration described in figure 17 when the voltage signal is applied at the primary winding with the secondary being open. These measurements allow determining the magnetizing impedance. The sample frequency used for these measurements is 125 Msample/s. All impedances can then be measured with this technique, but now the data have to be processed.

### **9.2 Impedance calculation**

The measurements results obtained in time domain will be converted in frequency domain. The impedance can be expressed as the ratio between the Fourier calculation of the voltage and the Fourier calculation of the current which can be calculated through a FFT algorithm for all measurements. The various impedances of the equivalent circuit shown in Fig. 9 can then be determined through various configurations of the transformer.

Fig. 17. Measurement bench in time domain

346 Infrastructure Design, Signalling and Security in Railway

As detailed in the previous section, the determination of the proposed model parameters is based on impedance measurements which can easily be done in frequency domain with

This method gives good results for low power transformer but there are some problems to make this kind of measurement with very high power transformer as the ones used in

A square voltage waveform is applied at terminals of the transformer in the various configuration tests. The input current and input voltage are measured in time domain and determined in frequency domain via Fourier transforms and then the corresponding

This experimental method has been applied in reduced scale on the laboratory test bench, to characterize the 15kVA three phases transformer. For this characterization, a square signal of magnitude 30 V with a period equal to 30µs, duty cycle equal to 0.5 and the rise time and fall time equal to 10ns. A differential voltage probe (bandwidth: 100MHz) is used to measure the voltage at the generator terminals. The current is measured with a current probe (bandwidth: 100MHz). The connection wires between the generator and the transformer are chosen as short as possible. Figure 17 shows a diagram of the measurement bench; we can see the generator,

Figure 18 and 19 show respectively the waveforms of the primary voltage and current of one phase of the transformer, in the configuration described in figure 17 when the voltage signal is applied at the primary winding with the secondary being open. These measurements allow determining the magnetizing impedance. The sample frequency used for these measurements is 125 Msample/s. All impedances can then be measured with this technique,

The measurements results obtained in time domain will be converted in frequency domain. The impedance can be expressed as the ratio between the Fourier calculation of the voltage

one phase of the transformer and the position of measurements probes.

**8. Characterization of the transformer in frequency domain**

impedance or network analyzer.

railways substation, which are the followings:

seen, especially at high frequency.

**9. Characterisation in time domain**

but now the data have to be processed.

**9.2 Impedance calculation**

**9.1 Measurements principle**

impedance can be deduced.

obtained results are presented in the next section. [9]

Fig. 18. Voltage waveform in primary winding when the secondary is open

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 349

The obtained results show a good agreement between these methods. However, we note a small difference, in the impedance variation between these methods in low frequency, which may be due to two reasons: the low accuracy of measurement equipments in the time domain (oscilloscope, probes ...) and the behavior of the magnetic material at low frequency. We can say that these results validate the proposed temporal method. This method is based on measurement of the voltage and current waveforms in the study system by reference to the method of Frequency Response Analysis FRA [10] which is based on the determination of the transfer function and voltage measurements. In the proposed method, the injection of

higher current values allows us to obtain the nominal operating of the transformer.

The test bench (Fig. 8) is composed by the 15 kVA power transformer, a rectifier (twelve diodes) and a load constituted by four power resistances. The high frequency model of the

The output current of the power transformer is measured for each phase using an

Figure 22 shows an example of current measured for phase A and obtained by the simulation. The test bench is simulated by using the high frequency equivalent circuit of the power transformer, presented previously, loaded with twelve diodes which model is available in the components library of the software simulator (SPICE) and four resistors.

Fig. 22. Measured (left) and simulated (right) output current of the power transformer (Phase A)

**10. Application to the test bench**

**10.1 The laboratory setup without the line**

power transformer is used in this simulation.

Fig. 21. Circuit diagram of the test bench

oscilloscope and current probe.

Fig. 19. Current waveform in primary winding when the secondary is open

Figure 20 shows the comparison between the impedance measured at the primary winding when the secondary is short circuited measured directly in frequency domain with impedance analyzer and the impedance issued from the data processing applied to measurements in time domain.

Fig. 20. Comparison between measurement of impedance in frequency domain and with temporal method applied to impedance of the primary winding, the secondary being short circuited.

The obtained results show a good agreement between these methods. However, we note a small difference, in the impedance variation between these methods in low frequency, which may be due to two reasons: the low accuracy of measurement equipments in the time domain (oscilloscope, probes ...) and the behavior of the magnetic material at low frequency.

We can say that these results validate the proposed temporal method. This method is based on measurement of the voltage and current waveforms in the study system by reference to the method of Frequency Response Analysis FRA [10] which is based on the determination of the transfer function and voltage measurements. In the proposed method, the injection of higher current values allows us to obtain the nominal operating of the transformer.

### **10. Application to the test bench**

348 Infrastructure Design, Signalling and Security in Railway

Fig. 19. Current waveform in primary winding when the secondary is open

measurements in time domain.

circuited.

Figure 20 shows the comparison between the impedance measured at the primary winding when the secondary is short circuited measured directly in frequency domain with impedance analyzer and the impedance issued from the data processing applied to

Fig. 20. Comparison between measurement of impedance in frequency domain and with temporal method applied to impedance of the primary winding, the secondary being short

### **10.1 The laboratory setup without the line**

The test bench (Fig. 8) is composed by the 15 kVA power transformer, a rectifier (twelve diodes) and a load constituted by four power resistances. The high frequency model of the power transformer is used in this simulation.

Fig. 21. Circuit diagram of the test bench

The output current of the power transformer is measured for each phase using an oscilloscope and current probe.

Figure 22 shows an example of current measured for phase A and obtained by the simulation. The test bench is simulated by using the high frequency equivalent circuit of the power transformer, presented previously, loaded with twelve diodes which model is available in the components library of the software simulator (SPICE) and four resistors.

Fig. 22. Measured (left) and simulated (right) output current of the power transformer (Phase A)

EMC Analysis of Railway Power Substation Modeling and Measurements Aspects 351

These curves show that the model seems very good until 10MHz. These results on a reduced scale power system are very encouraging and this study has to be continued on a real

The results obtained with a laboratory power transformer show a good agreement between

Depending on the application, the measurements approach, in frequency domain, is often used and gives good results. However, for the high power system it is not possible to use to impedance analyzer (specific apparatus) thus other methods can be used as the Frequency Response Analysis (FRA). Nevertheless, the power necessary for these experimental determinations is low and can be a problem when the goal of the measurements is to define a model functioning at high power level for a large frequency band. The proposed experimental method, in time domain, allows making measurements with high injected power. The preliminary results, obtained on a laboratory transformer are very interesting.

This work has been done with the help of V. Deniau and J. Rioult from IFSTTAR LEOST laboratory and G Nottet from Alstom Transport within CEMRAIL project, with

[1] European Standards EN 50121: 2006 Railway applications – Electromagnetic

[2] A Cozza, "Railways EMC : assessment of infrastructure impact" PhD thesis Lille and

[3] C. Andrieu, E. Daupahant and D. Boss, "A frequency- Dependant Model for a MV/LV

[4] H. Ouaddi, S. Baranowski, N. Idir "High frequency modelling of power transformer :

[5] J. Kolstad, C. Blevins, J. Dunn, A. Weisshaar, " NewCircuit Augmentation Method for

[7] S. Chimklai, J.R Marti, "Simplified Three-Phase Transformer Model for Electromagnetic

[8] H. Ouaddi, S. Baranowski, N. Idir " High frequency modelling of power transformer:

(Electrical Review), ISSN 0033-2097, R.86 May 2010. pp 165-169.

Transformer", IPST'99 – International Conference on Power Systems Transient,

application to railway substation in scale model", XIV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering,

Modeling ofInterconnects and Passive Components", IEEE Trans, Advanced

Transient Studies", IEEE Trans, Power Delivery, vol. 10, no. 3, July 1995, pp. 1316-

Application to railway substation in scale model" Przegląd Elektrotechniczny

simulations and experimental results in time and in frequency domain.

railway power substation

**12. Acknowledgment**

**13. References**

competitiveness cluster I-TRANS

Compatibility.

Torino , 2005

June 20-24,1999, Budapest

[6] www.emc.polito.it section IDEM®.

1325.

Arras, France, September 2009.

packaging, Vol. 29, no.1, February 2006

**11. Conclusion**

As shown in Figure 22, we note a good agreement between the measured and simulated currents. Nevertheless, the waveform of the measured current is disturbed by digital noise of the oscilloscope. Moreover in our simulation we used sources without noise which does not exist in real case.

### **10.2 The laboratory setup with the line**

As a conclusion of the laboratory study, we have realized a complete simulation of a railway power system by adding a power line and a power load to the transformer. Fig. 23 shows the experimental setup.

Fig. 23. Laboratory test bench simulating a railway power infrastucture

The test bench is constituted by the previous laboratory transformer (15kVA) used in one phase transformer configuration (the two others phases are short circuited), connected to a 5.6m power line and load by power resistances.

This system is fed by a network analyzer (connected to port 1) which allows measuring the current in the power line via the S21 parameter as presented in figure 23, thru a current sensor (connected to the port 2 of the analyzer) .

Figure 24 shows a comparison between measurements and modeling for two extreme positions of the current sensor: near the transformer (z = 0) and near the load (z = 5.6m).

Fig. 24. Comparison between measurement and modeling : frequency variation of the current in the power line for two positions of the sensors

These curves show that the model seems very good until 10MHz. These results on a reduced scale power system are very encouraging and this study has to be continued on a real railway power substation

### **11. Conclusion**

350 Infrastructure Design, Signalling and Security in Railway

As shown in Figure 22, we note a good agreement between the measured and simulated currents. Nevertheless, the waveform of the measured current is disturbed by digital noise of the oscilloscope. Moreover in our simulation we used sources without noise which does

As a conclusion of the laboratory study, we have realized a complete simulation of a railway power system by adding a power line and a power load to the transformer. Fig. 23 shows

The test bench is constituted by the previous laboratory transformer (15kVA) used in one phase transformer configuration (the two others phases are short circuited), connected to a

This system is fed by a network analyzer (connected to port 1) which allows measuring the current in the power line via the S21 parameter as presented in figure 23, thru a current

Figure 24 shows a comparison between measurements and modeling for two extreme positions of the current sensor: near the transformer (z = 0) and near the load (z = 5.6m).

**z=0 m z=5,6 m**

Fig. 24. Comparison between measurement and modeling : frequency variation of the

Fig. 23. Laboratory test bench simulating a railway power infrastucture

5.6m power line and load by power resistances.

sensor (connected to the port 2 of the analyzer) .

current in the power line for two positions of the sensors

not exist in real case.

the experimental setup.

**10.2 The laboratory setup with the line**

The results obtained with a laboratory power transformer show a good agreement between simulations and experimental results in time and in frequency domain.

Depending on the application, the measurements approach, in frequency domain, is often used and gives good results. However, for the high power system it is not possible to use to impedance analyzer (specific apparatus) thus other methods can be used as the Frequency Response Analysis (FRA). Nevertheless, the power necessary for these experimental determinations is low and can be a problem when the goal of the measurements is to define a model functioning at high power level for a large frequency band. The proposed experimental method, in time domain, allows making measurements with high injected power. The preliminary results, obtained on a laboratory transformer are very interesting.

### **12. Acknowledgment**

This work has been done with the help of V. Deniau and J. Rioult from IFSTTAR LEOST laboratory and G Nottet from Alstom Transport within CEMRAIL project, with competitiveness cluster I-TRANS

### **13. References**

**Part 3**

**Signalling, Security and Infrastructure**

**Construction in Railway**

## **Part 3**

## **Signalling, Security and Infrastructure Construction in Railway**

352 Infrastructure Design, Signalling and Security in Railway

[9] H. Ouaddi, S. Baranowski, G. Nottet, B. Demoulin, L. Koné, "Study of HF Behaviour of

[10] WG A2.26 report. "Mechanical condition assessment of transformer windings using

[11] H. Ouaddi, G. Nottet S. Baranowski, L. Koné, N. Idir, 'Determination of the high

[13] B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain response

[14] B.Cogitore, J. P. Kéradec, "The two-winding transformer: an experimental method to

[15] T. Noda, H. Nakamoto, S. Yokoyama, "Accurate modeling of core-type distribution

[16] F. Blache, J. P. Kéradec, B. Cogitore, "Stray capacitance of two winding transformers:

[17] H.Y. Lu, J.G. Zhu,V.S. Ramsden, S.Y.R. Hui, "Measurement and modeling of stray

[18] I. A. Maio, P. Savin, I. S. Stievano, F. Canavero, " Augmented models of high frequency

instrumentation and measurement, Vol. 43, No. 2, April 1994.

transactions on Powers Electronics Specialists Conference,, 1994.

Electronics Specialists Conference, Vol. 2, Page(s): 763 – 768, 1999.

frequency response analysis (FRA)" Electra n°228 October 2006.

IEEE VPPC 2010, Lille, 1-3 September 2010. proceeding sur clef USB [12] A. Oguz Soysal, "A method for wide frequency range modelling of power transformers

Appl. Phys., 53, 3 (2011) 33603-1-7 February , 2011

1802–1810, October 1993.

delivery, Vol.17, October2002.

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2009.

Railway Power Substation in Physical and Geometrical Scale" European Phys. J.,

frequency parameters of the power transformer used in the railway substation',

and rotating machines", IEEE Transactions on Power Delivery, vol. 8, No. 4,pp.

by Vector Fitting", IEEE Trans, Power Delivery, vol. 14, no. 3, July 1999, pp. 1052-

obtain a wide frequency range equivalent circuit", IEEE transactions on

transformers for electromagnetic transient studies", IEEE transactions on power

equivalent circuit, measurements, calculation and lowering", IEEE tr IEEE

capacitance in high frequency transformers", IEEE transactions on Powers

transformees for SMPS", Proceeding, 20th Int. Zurich Symposium on EMC, Zurich

**14**

*Spain*

*University of Castilla-La Mancha*

, (1)

**Criteria for Improving the Embankment-**

Inmculada Gallego, Santos Sánchez-Cambronero and Ana Rivas

**Structure Transition Design in Railway Lines**

In the design of a railroad track there are some situations in which the introduction of a structure in the track is needed, for example a bridge, a viaduct or a pontoon. This circumstance is even more frequent in the High Speed lines, since the design criteria, fundamentally slopes and radius, are stricter than those for conventional lines. The introduction of a structure determines the appearance of a point with an abrupt change in

The experience has shown that these transition zones between embankment and structure are the source of many problems (related to safety, passengers' comfort, maintenance expenses, etc.), causing differential settlements among adjacent track cross sections and

In order to diminish this unfavorable effect, the well known "technical blocks" are designed in a length determined between the structure and the embankment of access to this one. However, in spite of this structural disposition, it has not been found yet any design solution that notably reduces the track geometrical quality defects that have been observed in the mentioned zones. This is an important issue, because they produce a relevant increase in the maintenance expenses of the High Speed lines and they affect the availability of the

originating which is known as "dip" (European Rail Research Institute, ERRI., 1999)

**2. Theoretical foundation of embankment-structure transition behavior**

The wheel load transmitted by a train to the track does not correspond to the static load; instead, random dynamic overloads appear due to the sprung and un-sprung masses. Among the great amount of existing formulations relative to these overloads, there is an outstanding contribution made by Prud 'Homme (Prud`Homme, 1970) according to the expression (1)

> 0.45 100 *NS V*

where: σ(ΔQNS) is the standard deviation of the dynamic overloads due to the un-sprung masses of the material; *V* is the running speed of the vehicle; *b* is a variable related to the track defects and to the vehicle defects; *m* is the un-sprung mass of the vehicle; *k* is the

*Q b mK*

the vertical stiffness from a track cross section to another.

track (Gallego, López, Ubalde, & Texeira, 2005).

vertical track stiffness; φ(ε) is Damping of the track.

**1. Introduction**

## **Criteria for Improving the Embankment-Structure Transition Design in Railway Lines**

Inmculada Gallego, Santos Sánchez-Cambronero and Ana Rivas *University of Castilla-La Mancha Spain*

### **1. Introduction**

In the design of a railroad track there are some situations in which the introduction of a structure in the track is needed, for example a bridge, a viaduct or a pontoon. This circumstance is even more frequent in the High Speed lines, since the design criteria, fundamentally slopes and radius, are stricter than those for conventional lines. The introduction of a structure determines the appearance of a point with an abrupt change in the vertical stiffness from a track cross section to another.

The experience has shown that these transition zones between embankment and structure are the source of many problems (related to safety, passengers' comfort, maintenance expenses, etc.), causing differential settlements among adjacent track cross sections and originating which is known as "dip" (European Rail Research Institute, ERRI., 1999)

In order to diminish this unfavorable effect, the well known "technical blocks" are designed in a length determined between the structure and the embankment of access to this one. However, in spite of this structural disposition, it has not been found yet any design solution that notably reduces the track geometrical quality defects that have been observed in the mentioned zones. This is an important issue, because they produce a relevant increase in the maintenance expenses of the High Speed lines and they affect the availability of the track (Gallego, López, Ubalde, & Texeira, 2005).

### **2. Theoretical foundation of embankment-structure transition behavior**

The wheel load transmitted by a train to the track does not correspond to the static load; instead, random dynamic overloads appear due to the sprung and un-sprung masses. Among the great amount of existing formulations relative to these overloads, there is an outstanding contribution made by Prud 'Homme (Prud`Homme, 1970) according to the expression (1)

$$
\sigma(\Delta Q\_{\rm NS}) = 0.45 \frac{V}{100} b \sqrt{m K \rho(\varepsilon)} \,\,\,\,\,\tag{1}
$$

where: σ(ΔQNS) is the standard deviation of the dynamic overloads due to the un-sprung masses of the material; *V* is the running speed of the vehicle; *b* is a variable related to the track defects and to the vehicle defects; *m* is the un-sprung mass of the vehicle; *k* is the vertical track stiffness; φ(ε) is Damping of the track.

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 357

This revision of the solutions employed, shows a lack of homogeneity of the design criteria: each Railway Administration uses different designs for the longitudinal sections of the

The previous analysis shows a lack of homogeneity in the design criteria. Besides, it must be added what the experience has pointed out, a remarkable deterioration of the quality in the transitions. These two facts, lead to think about two reflections: a) it does not exist a precise knowledge of the behavior of transitions, and b), the current designs have certain limitations since they are unable to reduce in a remarkable way the deterioration experimented in these areas. The first reflection invites us to deepen in the knowledge of the deterioration process and the second one induces us to consider two more aims: 1) introducing new design criteria and 2) giving an analytical basis to the already existent, to overcome some of those limitations. In order to achieve those aims a numerical modelization of the embankment-

Therefore, within the scope of this work it is sought to carry out a model of finite elements which simulates the behavior of embankment-structures transitions. This model will enable to quantify the vertical stiffness of the track according to the type of disposition of the materials which the transition is carried out with (PA and PB, Fig 1) as well as the

Rail steel 2.1x1011 0.3 - - 7.5 104 Elastic bearing 2.952x108 - - - -

element 1 8.01x1010 0.25 - - -

element 2 5.02x1010 0.25 - - -

element 3 3.68x1010 0.25 - - - Ballast 1.3x108 0.2 0 45 1.9x104 Sub-ballast 1.2x108 0.3 0 45 1.9x104 Track bed 8.107 0.3 0 35 2x104 Material QS1 1.25x107 0.4 15000 10 2x104 Material QS2 2.50x107 0.3 10000 20 2x104 Material QS3 8x107 0.3 0 35 2x104

Rock 3x109 0.2 2.7x104

Table 1. Values of geotechnical parameters considered in the models

1.6x108 0.25 2.3x104

**(0)**  **(N/m3)**

structure transition is shown in this chapter (Gallego & López, , 2009)

geotechnical characteristics of these materials (See Tab 1 and Tab 2).

**Material E (N/m2) υ** *c* **(N/m2)**

embankment-structure transitions.

**3. Motivation of the chapter**

Sleeper

Sleeper

Sleeper

Cement-treated granular material

Expression (1) introduces a new criterion to reduce the mutual aggressiveness between track and vehicle. From that it is deduced the importance of having a low value of the vertical stiffness of the track *(K)* and of the un-sprung mass of the vehicle *(m)* to avoid increasing the dynamic overloads due to the un-sprung masses. This influence is a more relevant fact in high speed trains.

In addition, it is not only the stiffness value which determines the dynamic overloads. They are also influenced by the variation of the stiffness value that might exist from one sleeper to another.

The first studies carried out to deal with this problem were carried out by Amielin, 1974, later on in the eighties they stand out those by Lopez, 1983, Hettle, 1986, Hunt, 1997, Esveld, 2001, López A. , 2001 or Teixeira, 2003 shown that as the difference between the stiffness values of two consecutive sleepers increases, the reaction on the sleepers increases, thereby increasing the load on the sleeper. On the other hand, next to these increments of stress, the experience has proved that some differential settlements are originated. As a result of these two factors hanging sleepers can be developed that in turn increase the stress on the ballast. In order to avoid this deterioration experimented in the transitions, these sections are built the well known "technical blocks", whose aim is achieving a gradual increase in the stiffness from one sleeper to the following one, as we reach the structure.

Now, it is interesting to know: How are these designs? What criteria are used to define them? To answer these questions a revision of the designs used by the different European Railway Administrations has been made. Five types of the most used measures have been identified. They are enumerated next, being the first one the most frequently employed:

Along with these measures, they have been also identified a variety of track formation materials behind the abutment. There are three types that stand out, just as it is schematized in Fig 1. The first two types are the more frequently used, and with regard to that work they will be called slope type PA and slope type PB.

Fig. 1. Types of dispositions of the backfill behind the abutment in embankment-structure transitions.

This revision of the solutions employed, shows a lack of homogeneity of the design criteria: each Railway Administration uses different designs for the longitudinal sections of the embankment-structure transitions.

### **3. Motivation of the chapter**

356 Infrastructure Design, Signalling and Security in Railway

Expression (1) introduces a new criterion to reduce the mutual aggressiveness between track and vehicle. From that it is deduced the importance of having a low value of the vertical stiffness of the track *(K)* and of the un-sprung mass of the vehicle *(m)* to avoid increasing the dynamic overloads due to the un-sprung masses. This influence is a more relevant fact in

In addition, it is not only the stiffness value which determines the dynamic overloads. They are also influenced by the variation of the stiffness value that might exist from one sleeper to

The first studies carried out to deal with this problem were carried out by Amielin, 1974, later on in the eighties they stand out those by Lopez, 1983, Hettle, 1986, Hunt, 1997, Esveld, 2001, López A. , 2001 or Teixeira, 2003 shown that as the difference between the stiffness values of two consecutive sleepers increases, the reaction on the sleepers increases, thereby increasing the load on the sleeper. On the other hand, next to these increments of stress, the experience has proved that some differential settlements are originated. As a result of these two factors hanging sleepers can be developed that in turn increase the stress on the ballast. In order to avoid this deterioration experimented in the transitions, these sections are built the well known "technical blocks", whose aim is achieving a gradual increase in the stiffness

Now, it is interesting to know: How are these designs? What criteria are used to define them? To answer these questions a revision of the designs used by the different European Railway Administrations has been made. Five types of the most used measures have been identified. They are enumerated next, being the first one the most

Backfill behind the abutment either with materials of a high compression level or

Along with these measures, they have been also identified a variety of track formation materials behind the abutment. There are three types that stand out, just as it is schematized in Fig 1. The first two types are the more frequently used, and with regard to that work they

Fig. 1. Types of dispositions of the backfill behind the abutment in embankment-structure

 Use of a transition slab built with reinforced concrete or another material. Introduction of horizontal layers on a track formation of different materials.

Use of geosynthetics to achieve an abutment reinforced backfill.

Treatment of the track bed and sub-ballast with cement.

from one sleeper to the following one, as we reach the structure.

granular material treated with cement.

will be called slope type PA and slope type PB.

high speed trains.

frequently employed:

transitions.

another.

The previous analysis shows a lack of homogeneity in the design criteria. Besides, it must be added what the experience has pointed out, a remarkable deterioration of the quality in the transitions. These two facts, lead to think about two reflections: a) it does not exist a precise knowledge of the behavior of transitions, and b), the current designs have certain limitations since they are unable to reduce in a remarkable way the deterioration experimented in these areas. The first reflection invites us to deepen in the knowledge of the deterioration process and the second one induces us to consider two more aims: 1) introducing new design criteria and 2) giving an analytical basis to the already existent, to overcome some of those limitations. In order to achieve those aims a numerical modelization of the embankmentstructure transition is shown in this chapter (Gallego & López, , 2009)

Therefore, within the scope of this work it is sought to carry out a model of finite elements which simulates the behavior of embankment-structures transitions. This model will enable to quantify the vertical stiffness of the track according to the type of disposition of the materials which the transition is carried out with (PA and PB, Fig 1) as well as the geotechnical characteristics of these materials (See Tab 1 and Tab 2).

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 359

Fig. 2. General schematic of an embankment–structure. The transition is the zone adjacent to

Suitable accuracy can be achieved by modeling only a transition section. However, the track section chosen to be modeled should be such that possesses the fundamental characteristics of a transition. However, the track section chosen for modeling should have the fundamental characteristics of a transition. For both slope types considered (PA and PB), these characteristics occur when the material changes from one material to another, either at the beginning or end of the slope (see Fig 2). Thus, the sections to be modeled are those

Fig. 3. Schematic of the beginning and end of the technical block in the slope of type PB and PA

The directions considered for the model are the following ones: the axis *x* indicates the

sleeper direction, the axis *y* the vertical and the axis z the rail direction (see Fig 2).

the structure (see Gallego I.,2006)

shown within the rectangles in Fig 3.

**4.2 Geometry of the analyzed domain**

\*MGT = Cement-treated granular material

Table 2. Geometric and geotechnical parameter considered in the model

### **4. Description of the numerical model and the work assumptions**

In order to quantify the vertical track stiffness value and the incidence that the disposition and type of material of the track formation have on it, it is considered more accurate to analyze the track as a whole system. So as to carry out this analysis, the most appropriate approach is to apply the finite elements method. This method enables the numerical simulation of different materials and diverse boundary conditions, facilitating the study of the interaction among the different elements that compose the railway superstructure and infrastructure.

The employment of the finite elements method is accurate to evaluate the global behavior of the track structure, but it is very limited to quantify the efforts in the ballast: the intergranular stress is very different from stress and strain assumed in a continuous medium. However, the use of a discrete elements model, or a mixed one, finite and discrete elements, implies a tremendous computational cost and an enormous complexity.

In the Railway field, the finite elements method has been used by authors as López A. , 1977, Sauvage & Larible, 1982, Profillidis, 1983, Sahu, Rao, & Yudhbir., 1999 Mira, Férnández, Pastor, Nasarre, & Carrillo, 2000, among others. Some studies developed in the eighties stand out, such as Profillidis, 1983, since the results of those works were integrated by the Committee D-117 of the ORE in the Record (Comité D-117 (ORE), 1983). The sizing graphics of the track bearing structure are collected in this work. Together with the previous works, it is also worth mentioning those carried out by the "Ministerio de Fomento Español", which have been the basis for making some recommendations for the Railways track construction.

In order to generate the model proposed in this chapter, the contributions collected in the different models of Railways track formations carried out so far and enunciated previously have been taken into consideration.

### **4.1 Description of the analyzed domain**

The length of an embankment-structure transition depends on the type of structure and the height of the access embankment. In the case of embankment heights around 15 meters, the technical block can reach lengths of up to 85 meters (Fig 2). A 3D Model for such that length require an extremely powerful software and hardware, implying a huge computational cost due to the long time calculation that would be needed.

**GEOTECHNICAL PARAMETERS**

PA 1:1 QS2/QS3 QS1 H7PA11QS2QS3QS1

In order to quantify the vertical track stiffness value and the incidence that the disposition and type of material of the track formation have on it, it is considered more accurate to analyze the track as a whole system. So as to carry out this analysis, the most appropriate approach is to apply the finite elements method. This method enables the numerical simulation of different materials and diverse boundary conditions, facilitating the study of the interaction among the different elements that compose the railway superstructure and

The employment of the finite elements method is accurate to evaluate the global behavior of the track structure, but it is very limited to quantify the efforts in the ballast: the intergranular stress is very different from stress and strain assumed in a continuous medium. However, the use of a discrete elements model, or a mixed one, finite and discrete elements,

In the Railway field, the finite elements method has been used by authors as López A. , 1977, Sauvage & Larible, 1982, Profillidis, 1983, Sahu, Rao, & Yudhbir., 1999 Mira, Férnández, Pastor, Nasarre, & Carrillo, 2000, among others. Some studies developed in the eighties stand out, such as Profillidis, 1983, since the results of those works were integrated by the Committee D-117 of the ORE in the Record (Comité D-117 (ORE), 1983). The sizing graphics of the track bearing structure are collected in this work. Together with the previous works, it is also worth mentioning those carried out by the "Ministerio de Fomento Español", which have been the basis for making some recommendations for the Railways track construction. In order to generate the model proposed in this chapter, the contributions collected in the different models of Railways track formations carried out so far and enunciated previously

The length of an embankment-structure transition depends on the type of structure and the height of the access embankment. In the case of embankment heights around 15 meters, the technical block can reach lengths of up to 85 meters (Fig 2). A 3D Model for such that length require an extremely powerful software and hardware, implying a huge computational cost

**Original ground**

QS2 QS3 ROCA

**Type material of transition (type1/type2)**

QS3/MGT\*

**4. Description of the numerical model and the work assumptions**

Table 2. Geometric and geotechnical parameter considered in the model

implies a tremendous computational cost and an enormous complexity.

**Name of case studies H embankment (H7)- Disposition – value of the slope- material 1 material2-original ground**

**GEOMETRIC PARAMETERS**

> **Slope value (H:V)**

PB 3:1 QS2/MGT\*

\*MGT = Cement-treated granular material

have been taken into consideration.

**4.1 Description of the analyzed domain**

due to the long time calculation that would be needed.

**Type of design (Fig 1)**

infrastructure.

Fig. 2. General schematic of an embankment–structure. The transition is the zone adjacent to the structure (see Gallego I.,2006)

Suitable accuracy can be achieved by modeling only a transition section. However, the track section chosen to be modeled should be such that possesses the fundamental characteristics of a transition. However, the track section chosen for modeling should have the fundamental characteristics of a transition. For both slope types considered (PA and PB), these characteristics occur when the material changes from one material to another, either at the beginning or end of the slope (see Fig 2). Thus, the sections to be modeled are those shown within the rectangles in Fig 3.

### **4.2 Geometry of the analyzed domain**

The directions considered for the model are the following ones: the axis *x* indicates the sleeper direction, the axis *y* the vertical and the axis z the rail direction (see Fig 2).

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 361

The model also sought to make the vertical stiffness equal for all of the elastic bearings (see Fig 4). The vertical dimension and the modulus of elasticity were fixed so that the vertical stiffness of the element coincided with the stiffness of the elastic bearing provided by the manufacturer. For the high-speed Madrid–Seville line, the elastic bearings have a stiffness of

Because the sleeper section is not constant along its entire length, the dimensions of its most representative section were used for the sleeper model elements. For each element (See Fig 5),

To obtain homogeneity in the calculations, the elements of the model had to have a constant width, which is not the case in the real sleeper. Thus, the model width must be considered to be an average width. This average width must be such that the load bearing surface in the

The sleeper–ballast contact zones contain a high concentration of strains. This local phenomenon requires refining of the mesh used to model these zones. However, applying this procedure is sometimes impossible because of the computational resources and model complexity needed. The most common alternative to modeling the contact zones is to use bounded degrees of freedom. In fact, this solution was adopted by ORE Committee D-117

*E I EI model model real real* (2)

the modeled flexural stiffness must be equal to the real flexural stiffness, as follows

Fig. 4. Model of the rail and elastic bearings carried out in this study

Fig. 5. Schematic of a real sleeper and a modeled sleeper

model is equal to that in reality.

**4.4 Sleeper–ballast contact**

nearly 500kN/mm (López A. , 2001)

### **4.2.1 Transverse section**

The measures adopted for the transversal section are the ones used in the High Speed line Madrid-Sevilla, but considering the track as simple and applying symmetry with respect to the plane *x* = 0.

The slope of the embankment varies with the type of material from which it is made; between H/V=3/2 and 1/2. The value 3/2 has been adopted in the model, because it was employed in the Madrid–Seville line.

### **4.2.2 Vertical direction**

In the vertical direction (axis y) not only all the elements that compose the super structure are considered but also the, sub-ballast , the formation layer, 7m for the embankment and 3m for the original ground.

Values of 30, 25, and 60 cm, respectively were adopted for the thicknesses of the ballast under a sleeper, the sub-ballast the formation layer. These values are the same values as those applied in the transversal section of the High Speed line between Madrid and Seville.

### **4.2.3 Longitudinal direction**

For domain analysis, the load applied on a sleeper is transmitted to the adjacent sleepers through some transmission coefficients. These coefficients clearly decrease as the distance from the point of load application increases; the coefficient is only 7 per cent in the third sleeper, when the first sleeper is defined as the one on which the load is applied (Comité D-117 (ORE), 1983)

To determine the real value of the settlement of the head of the rail when the load acts on it, one must not only solve for that load but also consider the history of the previous loads that have affected that sleeper. The load applied on a sleeper transmits it to the two adjacent sleepers. In order to observe the behavior of two consecutives sleepers with different stiffness under a load, while taking into account their load history also, four successively loaded sleepers (T5, T6, T7, and T8) were considered in order to analyze the behavior of sleepers T7 and T8.

In 1983, a test in Derby showed that important phenomena are apparent up to the fourth sleeper from the one loaded (Comité D-117 (ORE), 1983). Therefore, four unloaded sleepers were introduced at both ends of the model. This set-up avoided artefacts and yet included a substantial number of sleepers onto which the load could be applied. This approach required consideration of a transition sector comprising 12 sleepers, leading to a model system with a total length of 7.20 m.

### **4.3 Modelling rail track, elastic bearing, and sleeper section**

In order to model the rail track, its resistance to bending was simulated in the most accurate way possible (Fig 4), which is why the inertia of the modelled rail must be equal to that of the real rail.

The measures adopted for the transversal section are the ones used in the High Speed line Madrid-Sevilla, but considering the track as simple and applying symmetry with respect to

The slope of the embankment varies with the type of material from which it is made; between H/V=3/2 and 1/2. The value 3/2 has been adopted in the model, because it was

In the vertical direction (axis y) not only all the elements that compose the super structure are considered but also the, sub-ballast , the formation layer, 7m for the embankment and

Values of 30, 25, and 60 cm, respectively were adopted for the thicknesses of the ballast under a sleeper, the sub-ballast the formation layer. These values are the same values as those applied in the transversal section of the High Speed line between Madrid and

For domain analysis, the load applied on a sleeper is transmitted to the adjacent sleepers through some transmission coefficients. These coefficients clearly decrease as the distance from the point of load application increases; the coefficient is only 7 per cent in the third sleeper, when the first sleeper is defined as the one on which the load is applied (Comité D-

To determine the real value of the settlement of the head of the rail when the load acts on it, one must not only solve for that load but also consider the history of the previous loads that have affected that sleeper. The load applied on a sleeper transmits it to the two adjacent sleepers. In order to observe the behavior of two consecutives sleepers with different stiffness under a load, while taking into account their load history also, four successively loaded sleepers (T5, T6, T7, and T8) were considered in order to analyze the behavior of

In 1983, a test in Derby showed that important phenomena are apparent up to the fourth sleeper from the one loaded (Comité D-117 (ORE), 1983). Therefore, four unloaded sleepers were introduced at both ends of the model. This set-up avoided artefacts and yet included a substantial number of sleepers onto which the load could be applied. This approach required consideration of a transition sector comprising 12 sleepers, leading to a model

In order to model the rail track, its resistance to bending was simulated in the most accurate way possible (Fig 4), which is why the inertia of the modelled rail must be equal to that of

**4.2.1 Transverse section**

**4.2.2 Vertical direction**

3m for the original ground.

**4.2.3 Longitudinal direction**

employed in the Madrid–Seville line.

the plane *x* = 0.

Seville.

117 (ORE), 1983)

sleepers T7 and T8.

the real rail.

system with a total length of 7.20 m.

**4.3 Modelling rail track, elastic bearing, and sleeper section**

Fig. 4. Model of the rail and elastic bearings carried out in this study

The model also sought to make the vertical stiffness equal for all of the elastic bearings (see Fig 4). The vertical dimension and the modulus of elasticity were fixed so that the vertical stiffness of the element coincided with the stiffness of the elastic bearing provided by the manufacturer. For the high-speed Madrid–Seville line, the elastic bearings have a stiffness of nearly 500kN/mm (López A. , 2001)

Because the sleeper section is not constant along its entire length, the dimensions of its most representative section were used for the sleeper model elements. For each element (See Fig 5), the modeled flexural stiffness must be equal to the real flexural stiffness, as follows

$$E\_{model} I\_{model} = E\_{real} I\_{real} \tag{2}$$

Fig. 5. Schematic of a real sleeper and a modeled sleeper

To obtain homogeneity in the calculations, the elements of the model had to have a constant width, which is not the case in the real sleeper. Thus, the model width must be considered to be an average width. This average width must be such that the load bearing surface in the model is equal to that in reality.

#### **4.4 Sleeper–ballast contact**

The sleeper–ballast contact zones contain a high concentration of strains. This local phenomenon requires refining of the mesh used to model these zones. However, applying this procedure is sometimes impossible because of the computational resources and model complexity needed. The most common alternative to modeling the contact zones is to use bounded degrees of freedom. In fact, this solution was adopted by ORE Committee D-117

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 363

 In the vertical plans limits of the model, z=0 and z=7.20m, the boundary condition adopted is to impose the nullity of movement in the perpendicular direction to these

 In the vertical plans limits of the model, x=0 and x=18.45m, the boundary condition is, like the previous one, to impose the nullity of movement in the perpendicular direction

In the horizontal inferior plan of the model y=-3m, the condition to be imposed is the

An elastic, isotropic, and linear model was used to develop a mechanic model of the rail tracks, elastic bearings, sleepers, and the granular material processed with cement. In contrast, a perfect plastic model, i.e. the Drucker–Prager model (Oliver & Arlet, 2000), was used to model the rest of the materials, including the ballast, sub-ballast, track bed, embankment fill, and original ground. Finite strain was used to simulate the kinematics of

Granular material treated with cement is considered to behave elastically, at least until it reaches a substantial percentage of its stress limit; one can assume its modulus of elasticity

To model the embankment material on which the track is laid, a perfect elasto-plastic behavior was assumed. This assumption implies that reloading occurs in the same way as downloading, and that the material experiences no hardening (hardening parameter *H=0*). For modeling of the yield surfaces, the most accurate approach is to use a model dependent on hydrostatic pressure. These models are the Drucker–Prager and Mohr–Coulomb models, which limit the material behavior for states of hydrostatic stress (in traction). For the present study, the Drucker–Prager model was selected because it has been used in several elasto-plastic models

The principle formulated by Drucker and Prager in 1952 includes the influence of pressure through the first invariant of the stress tensor *I*1 and the internal friction angle . It also depends on the second invariant *J*2 of the deviatoric stress tensor, as well as on two parameters: the friction angle among particles and the cohesion *c*. This criterion is expressed by means of the principal stress invariant and *J2* (the second invariant of

F , , ; ( ) K( , ) 0 1 2 1 2 *IJc I J*

K( , ) 6 ( ) cos /(3 3 3 sen )

( ) 2sen /(3 3 3 sen )

 *c* (4)

 (5)

, (3)

>

used to design railway projects, and it has been validated by ORE Committee D-171.

plans (uz=0).

to these plans (ux=0).

**4.6 Material constitutive model**

the continuous medium.

deviatoric stress), as follows:

where

and

null vertical displacement (uy=0).

to remain essentially constant under normal stress.

and was used by the Railway Track Formations Project in its recommendations on railway track construction (Ministerio de fomento, 1999).

The use of bounded degrees of freedom requires the introduction of different nodes for each material at the contact surface. These nodes must move equivalently in the direction perpendicular to the contact plane (see Fig. 6). However, these nodes can move at different values in the directions parallel to the contact plane.

This solution is effective because it solves the tensional discontinuities that appear at the interface between two materials that differ significantly in their stiffness. In this model, bounded degrees of freedom were used at the sleeper–ballast contacts.

Fig. 6. Schematic of the ballast-sleeper contact

#### **4.5 Boundary conditions**

The model in this study differs from many existing models of railway track construction (Gallego, López, Ubalde, & Texeira, 2005), in which all vertical planes are constrained in all directions. In the Supertrack project (European comunity, 2005) and in this work, the planes that shape the slopes of embankments are left completely free, with no restrictions. In particular, the boundary conditions used here are as follows (see Fig. 7):

Fig. 7. Boundary conditions

### **4.6 Material constitutive model**

362 Infrastructure Design, Signalling and Security in Railway

and was used by the Railway Track Formations Project in its recommendations on railway

The use of bounded degrees of freedom requires the introduction of different nodes for each material at the contact surface. These nodes must move equivalently in the direction perpendicular to the contact plane (see Fig. 6). However, these nodes can move at different

This solution is effective because it solves the tensional discontinuities that appear at the interface between two materials that differ significantly in their stiffness. In this model,

The model in this study differs from many existing models of railway track construction (Gallego, López, Ubalde, & Texeira, 2005), in which all vertical planes are constrained in all directions. In the Supertrack project (European comunity, 2005) and in this work, the planes that shape the slopes of embankments are left completely free, with no restrictions. In

track construction (Ministerio de fomento, 1999).

values in the directions parallel to the contact plane.

Fig. 6. Schematic of the ballast-sleeper contact

**4.5 Boundary conditions**

Fig. 7. Boundary conditions

bounded degrees of freedom were used at the sleeper–ballast contacts.

particular, the boundary conditions used here are as follows (see Fig. 7):

An elastic, isotropic, and linear model was used to develop a mechanic model of the rail tracks, elastic bearings, sleepers, and the granular material processed with cement. In contrast, a perfect plastic model, i.e. the Drucker–Prager model (Oliver & Arlet, 2000), was used to model the rest of the materials, including the ballast, sub-ballast, track bed, embankment fill, and original ground. Finite strain was used to simulate the kinematics of the continuous medium.

Granular material treated with cement is considered to behave elastically, at least until it reaches a substantial percentage of its stress limit; one can assume its modulus of elasticity to remain essentially constant under normal stress.

To model the embankment material on which the track is laid, a perfect elasto-plastic behavior was assumed. This assumption implies that reloading occurs in the same way as downloading, and that the material experiences no hardening (hardening parameter *H=0*).

For modeling of the yield surfaces, the most accurate approach is to use a model dependent on hydrostatic pressure. These models are the Drucker–Prager and Mohr–Coulomb models, which limit the material behavior for states of hydrostatic stress (in traction). For the present study, the Drucker–Prager model was selected because it has been used in several elasto-plastic models used to design railway projects, and it has been validated by ORE Committee D-171.

The principle formulated by Drucker and Prager in 1952 includes the influence of pressure through the first invariant of the stress tensor *I*1 and the internal friction angle . It also depends on the second invariant *J*2 of the deviatoric stress tensor, as well as on two parameters: the friction angle among particles and the cohesion *c*. This criterion is expressed by means of the principal stress invariant and *J2* (the second invariant of deviatoric stress), as follows:

$$\mathcal{F}(I\_1, I\_2, c; \phi) = \overline{\alpha}(\phi)I\_1 + \sqrt{I\_2} - \overline{\mathcal{K}}(\kappa; \phi) = 0 \tag{3}$$

where

$$\overline{\mathbf{K}}(\kappa, \phi) = \mathbf{6} \ c(\kappa) \cos \phi \,/\, \left(\mathbf{3} \sqrt{\mathbf{3}} + \sqrt{\mathbf{3}} \sin \phi\right) \tag{4}$$

and

$$
\sqrt{\alpha}(\phi) = 2 \operatorname{sen} \phi \mid \left( 3 \sqrt{3} + \sqrt{3} \operatorname{sen} \phi \right) \tag{5}
$$

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 365

To simulate the constructive process of an embankment and to ensure convergence of the solution, the first load state (only the material weight) was divided into 250 substeps of the gravitational load application and 50 balance iterations for each one. For railway loads, 15 sub-steps proved to be sufficient to achieve convergence. The program used is ANSYS

To carry out the calculations, the load of only one axle was considered while assuming the

The increased value of the dynamic overloads was calculated using Prud'Homme's formulation, with 1mm used as the value for *b* and the speed set to be 300 km/h. With this approach, the value of a dynamic overload was obtained according to the dynamic stiffness, which is unknown because its calculation requires knowing the value of the point dynamic load on the track. It is customary to carry out railway calculations assuming that the dynamic stiffness has a value similar to that of the static stiffness; this assumption has been validated by experience and confirmed by calculations (Ministerio de fomento, 1999). Thus, this assumption was also made in the present study, and numerical tests were used to justify

Fig. 10. Schematic of the different load states

Structural, which enables nonlinear analysis.

effects of the remaining axles to be negligible.

this choice.

When the function that defines the yield surface (3) is represented in the main stress space, a cone is obtained, the axis of which is the hydrostatic axis (see Fig 8).

Fig. 8. Schematic of yield surfaces Drucker–Prager

Of the elements used, a quadratic 'brick' element of 20 nodes was selected; this is the most common type of element in three-dimensional models used to design railway tracks. The final meshes are shown in Fig 9.

Fig. 9. Finite-element model for transitions with slopes of type PA31 and PB11

### **4.7 Hypothesis adopted**

The load application must be carried out in several stages. In the first stage, only the material's own weight is considered until reaching the stress balance, while at later stages the loads due to the train are also taken into account. The stresses and displacements of interest are the ones that correspond to the application of the train loads; therefore, they can be calculated from the difference between the totals obtained after applying the train loads to the first stage.

Here, it was convenient to apply four load states due to the train passage, matching each state to the application of the static load per wheel in the four central sleepers of the model: T5, T6, T7, and T8 (See Fig 10).

When the function that defines the yield surface (3) is represented in the main stress space, a

Of the elements used, a quadratic 'brick' element of 20 nodes was selected; this is the most common type of element in three-dimensional models used to design railway tracks. The

Fig. 9. Finite-element model for transitions with slopes of type PA31 and PB11

The load application must be carried out in several stages. In the first stage, only the material's own weight is considered until reaching the stress balance, while at later stages the loads due to the train are also taken into account. The stresses and displacements of interest are the ones that correspond to the application of the train loads; therefore, they can be calculated from the difference between the totals obtained after applying the train loads

Here, it was convenient to apply four load states due to the train passage, matching each state to the application of the static load per wheel in the four central sleepers of the model:

cone is obtained, the axis of which is the hydrostatic axis (see Fig 8).

Fig. 8. Schematic of yield surfaces Drucker–Prager

final meshes are shown in Fig 9.

**4.7 Hypothesis adopted**

T5, T6, T7, and T8 (See Fig 10).

to the first stage.

Fig. 10. Schematic of the different load states

To simulate the constructive process of an embankment and to ensure convergence of the solution, the first load state (only the material weight) was divided into 250 substeps of the gravitational load application and 50 balance iterations for each one. For railway loads, 15 sub-steps proved to be sufficient to achieve convergence. The program used is ANSYS Structural, which enables nonlinear analysis.

To carry out the calculations, the load of only one axle was considered while assuming the effects of the remaining axles to be negligible.

The increased value of the dynamic overloads was calculated using Prud'Homme's formulation, with 1mm used as the value for *b* and the speed set to be 300 km/h. With this approach, the value of a dynamic overload was obtained according to the dynamic stiffness, which is unknown because its calculation requires knowing the value of the point dynamic load on the track. It is customary to carry out railway calculations assuming that the dynamic stiffness has a value similar to that of the static stiffness; this assumption has been validated by experience and confirmed by calculations (Ministerio de fomento, 1999). Thus, this assumption was also made in the present study, and numerical tests were used to justify this choice.

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 367

H7PA11QS2QS3 11.242 17.227 37.206 42.752

H7PB11QS2QS3 18.847 19.957 36.054 39.325

H7PA31QS2QS3 10.800 16.380 34.139 39.744

H7PB31QS2QS3 14.015 19.296 34.519 38.512

H7PA11QS2MGT 15.380 25.499 43.859 47.795

H7PB11QS2MGT 28.721 32.644 37.657 40.000

H7PA31QS2MGT 13.182 18.275 36.549 42.077

H7PB31QS2MGT 21.524 25.961 35.777 38.592

H7PA11QS3MGT 32.193 53.563 71.692 75.374

H7PB11QS3MGT 54.186 59.936 69.294 70.473

H7PA31QS3MGT 29.354 51.068 70.875 74.650

H7PB31QS3MGT 48.668 58.069 70.340 73.444

Table 3. Values of vertical static track stiffness at the beginning of transition *KI* (kN/mm)

**ORIGINAL GROUND QS2**

( *K QS* ( 2) ) 10.186 15.717 33.226 38.433

( *K QS* ( 3) ) 28.899 50.929 70.606 74.027

( *K MGT* ( ) ) 67.782 73.676 83.214 87.800

Table 4. Values of vertical static track stiffness *K* for conventional embankments (kN/mm)

**ORIGINAL GROUND QS3**  **ORIGINAL GROUND ROCK**

**ORIGINAL GROUND QS1**

ORIGINAL GROUND QS2

ORIGINAL GROUND QS3 ORIGINAL GROUND ROCK

TRANSITION TYPE

for all cases studied

**EMBANKMENT MATERIAL**

**FULL QS2**

**FULL QS3**

**FULL MGT**

ORIGINAL GROUND QS1

### **5. Results from the model: Presentation and critical analysis**

This modeling study was carried out in two phases with different aims. In the first phase, different case studies were analyzed numerically, and the results were studied. These results then determined whether to carry out more case studies or proceed with the second phase. The main objective of the first phase was to observe how changing from a less rigid material to a more rigid one would affect the vertical stiffness of the track.

In the second phase, variations caused by the different stiffness values were analyzed for all the case studies from the first phase.

### **5.1 First phase**

In the first phase, the main differences among the designs of the embankment–structure transitions are the types of materials used and the construction design. This justifies defining two types of case studies based on different geotechnical and geometrical parameters.

The geometrical parameters include the type and grade of slope; the latter is defined, e.g., as 1 : 1 and 3 : 2 (*H* : *V* , horizontal and vertical). The geotechnical parameters are the modulus of elasticity of the materials that compose the embankment fill and the original ground. For the modulus of elasticity, a range of values was used, matching those adopted in the numerical model presented by ORE Committee D-117. The values coincide with the lower limit values corresponding to the material types QS1, QS2, QS3, and rock (see Tab 1).

To fill the embankment, granular material processed with cement (MGT) was added to the model, since this material is so frequently used. Combining all these values with the technical block and the four load states already described, yielded a total of 48 case studies (see Tab 2). The modeling results for the case studies are shown in Tab 3.

To make additional comparisons, the stiffness was calculated for cases in which the fill corresponded to conventional embankments made with the same type of material (see Tab 4).

1. It is useful to apply stiffness values not only at the beginning but also at the end of the technical block; therefore, the cases corresponding to the ends of the technical blocks were calculated. Since the calculated stiffness values in the first 48 cases were similar for original ground QS1 and QS2, and for QS3 and rock, it was sufficient to calculate the cases corresponding to QS2 and QS3, thereby reducing the number of cases from 48 to 24 (see Tab 5).

### **5.2 Second phase**

The second phase involved analyzing the results of the first phase. The criteria were to limit the following:

This modeling study was carried out in two phases with different aims. In the first phase, different case studies were analyzed numerically, and the results were studied. These results then determined whether to carry out more case studies or proceed with the second phase. The main objective of the first phase was to observe how changing from a less rigid material

In the second phase, variations caused by the different stiffness values were analyzed for all

In the first phase, the main differences among the designs of the embankment–structure transitions are the types of materials used and the construction design. This justifies defining two types of case studies based on different geotechnical and geometrical

The geometrical parameters include the type and grade of slope; the latter is defined, e.g., as 1 : 1 and 3 : 2 (*H* : *V* , horizontal and vertical). The geotechnical parameters are the modulus of elasticity of the materials that compose the embankment fill and the original ground. For the modulus of elasticity, a range of values was used, matching those adopted in the numerical model presented by ORE Committee D-117. The values coincide with the lower limit values corresponding to the material types QS1, QS2, QS3,

To fill the embankment, granular material processed with cement (MGT) was added to the model, since this material is so frequently used. Combining all these values with the technical block and the four load states already described, yielded a total of 48 case studies

To make additional comparisons, the stiffness was calculated for cases in which the fill corresponded to conventional embankments made with the same type of material (see

1. It is useful to apply stiffness values not only at the beginning but also at the end of the technical block; therefore, the cases corresponding to the ends of the technical blocks were calculated. Since the calculated stiffness values in the first 48 cases were similar for original ground QS1 and QS2, and for QS3 and rock, it was sufficient to calculate the cases corresponding to QS2 and QS3, thereby reducing the number of cases from 48 to 24 (see

The second phase involved analyzing the results of the first phase. The criteria were to limit

(see Tab 2). The modeling results for the case studies are shown in Tab 3.

**5. Results from the model: Presentation and critical analysis**

to a more rigid one would affect the vertical stiffness of the track.

the case studies from the first phase.

**5.1 First phase**

parameters.

Tab 4).

Tab 5).

**5.2 Second phase**

 The upper value of the vertical stiffness The lower value of the vertical stiffness The value of the longitudinal variation

the following:

and rock (see Tab 1).

Table 3. Values of vertical static track stiffness at the beginning of transition *KI* (kN/mm) for all cases studied

Table 4. Values of vertical static track stiffness *K* for conventional embankments (kN/mm)

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 369

The analysis identified some problems related to the type of material. Based on these, the

 Excessive deformations were observed in the rail when material of type QS1 exists in the original ground (see Fig 11). These deformations reached 14mm under the rail when transitions QS2 and QS3 were used (Tab 7). In these cases, the deformations were large, as were the deformation values between adjacent sleepers. For this reason, it is appropriate to substitute the original ground material of type QS1 with another material or to treat the existing QS1 material in such a way as to obtain a modulus of

In transitions from material of type QS2 to treated granular material, which occurs commonly in buried structures, the stiffness increased significantly at the beginning of the technical block when there was a relatively compressible material in the original ground. The solution with the smallest increase in the stiffness value was PA31. Fig 12 shows this value to be 16.4% which is too large. For this reason, transition-type QS2/MGT is not

elasticity corresponding to that of a material of at least type QS2.

**6. Proposed design recommendations**

most relevant recommendations include:

appropriate for use in the surface structure.

Fig. 11. Deflection of the head of loaded rails

Table 5. Values of vertical static track stiffness at the beginning *KI* and end of transition *KF (kN/mm)* for all cases studied

These criteria were applied in two steps. Initially, the first two criteria were applied, and solutions were discarded if they resulted in either very high stiffness values, which generate elevated dynamic overloads, or very low stiffness values, which generate excessive rail deformations of the rail. To determine whether the stiffness values were high or low, they were compared to the values for designs using the same original ground material and the same materials as the simulated transition. Tab 6 shows the solutions remaining after this elimination process.

Table 6. Transition types obtained after eliminating the transition types that with extreme stiffness values

The second step consisted of applying the third criterion, limiting the longitudinal variation value. From among the case studies, the cases selected were those with the smallest increase in the K value at the beginning and end of the technical blocks. In this way, the most appropriate solutions were obtained for each type of original ground material (QS2 and QS3). This approach yields certain design recommendations, which are described in the following section.

### **6. Proposed design recommendations**

368 Infrastructure Design, Signalling and Security in Railway

**H7PA11QS2QS3** 17.227 37.581 37.206 61.927 **H7PB11QS2QS3** 19.957 47.071 36.054 64.276 **H7PA31QS2QS3** 16.380 41.982 34.139 65.175 **H7PB31QS2QS3** 19.296 49.312 34.519 67.536

**H7PA11QS2MGT** 25.499 62.550 43.859 72.812 **H7PB11QS2MGT** 32.644 66.571 37.657 80.345 **H7PA31QS2MGT** 18.275 68.029 36.549 76.708 **H7PB31QS2MGT** 25.961 69.294 35.777 79.658

**H7PA11QS3MGT** 53.563 68.278 71.692 79.658 **H7PB11QS3MGT** 59.936 71.145 69.294 78.319 **H7PA31QS3MGT** 51.068 71.418 70.875 82.844 **H7PB31QS3MGT** 58.069 71.009 70.340 82.115

Table 5. Values of vertical static track stiffness at the beginning *KI* and end of transition *KF*

These criteria were applied in two steps. Initially, the first two criteria were applied, and solutions were discarded if they resulted in either very high stiffness values, which generate elevated dynamic overloads, or very low stiffness values, which generate excessive rail deformations of the rail. To determine whether the stiffness values were high or low, they were compared to the values for designs using the same original ground material and the same materials as the simulated transition. Tab 6 shows the solutions remaining after this

> ORIGINAL GROUND QS2

> > PB31 PA11

> > PB31 PA11

> > PB31 PA11

Table 6. Transition types obtained after eliminating the transition types that with extreme

yields certain design recommendations, which are described in the following section.

The second step consisted of applying the third criterion, limiting the longitudinal variation value. From among the case studies, the cases selected were those with the smallest increase in the K value at the beginning and end of the technical blocks. In this way, the most appropriate solutions were obtained for each type of original ground material (QS2 and QS3). This approach

ORIGINAL GROUND QS3

> PB11 PA31

> PB11 PA31

> PB31 PA31

ORIGINAL GROUND ROCK

> PB11 PA31

> PB11 PA31

> PB31 PA31

ORIGINAL GROUND QS1

PA11

PA11

PA11

**ORIGINAL GROUND QS2 ORIGINAL GROUND QS3 BEGINNING (** *KI* **) END (** *KF* **) BEGINNING (** *KI* **) END (** *KF* **)**

**TRANSITION TYPE**

*(kN/mm)* for all cases studied

elimination process.

QS2/QS3 PB31

QS2/MGT PB31

QS3/MGT PB31

Materials of transition: Type1/Type 2

stiffness values

The analysis identified some problems related to the type of material. Based on these, the most relevant recommendations include:

 Excessive deformations were observed in the rail when material of type QS1 exists in the original ground (see Fig 11). These deformations reached 14mm under the rail when transitions QS2 and QS3 were used (Tab 7). In these cases, the deformations were large, as were the deformation values between adjacent sleepers. For this reason, it is appropriate to substitute the original ground material of type QS1 with another material or to treat the existing QS1 material in such a way as to obtain a modulus of elasticity corresponding to that of a material of at least type QS2.

In transitions from material of type QS2 to treated granular material, which occurs commonly in buried structures, the stiffness increased significantly at the beginning of the technical block when there was a relatively compressible material in the original ground. The solution with the smallest increase in the stiffness value was PA31. Fig 12 shows this value to be 16.4% which is too large. For this reason, transition-type QS2/MGT is not appropriate for use in the surface structure.

Fig. 11. Deflection of the head of loaded rails

Criteria for Improving the Embankment-Structure Transition Design in Railway Lines 371

Fig. 12. Analysis of the stiffness variations assuming material transition from type QS2 to

 Near the abutment, the stiffness increased abruptly when using a granular material treated with cement as fill (MGT, 3% by weight). In fact, the stiffness value of the abutment could oscillate between 200KN/mm and 300KN/mm. The maximum of 87.8 KN/mm obtained for the case of treated granular material (Tab 4) is outside of that range. In this case, it is necessary to put a material with greater stiffness than MGT next

 A direct transition from QS2 or QS3 material to the structure is not recommended. At best, the stiffness is 38.43 KN/mm when the embankment material is QS2 and 74.027 KN/mm if it is QS3 (see Tab 4), as compared to200-300 KN/mm of vertical stiffness on

 It is sometimes necessary to build the embankment adjacent to the abutment before building the structure. For example, this occurs when the original ground adjacent to the abutment is preloaded, and the load is removed immediately before building the transition. In that case, a slope of type PA (right column) is used instead of a slope of type PB (left column) in the transition from embankment material QS2 to QS3. In this research, a suitable value is obtained for the slope of the transition for each type (PA, PB). For that reason, it is necessary to distinguish between both slope types when considering whether a better approach would be to build the embankment before or

In this way, based on these analyses, this study can make some recommendations about construction designs. Moreover, this study has proposed some ideas relating to the geometric designs of the different materials and has classified the designs according to the original ground and according to when the adjacent embankment is built, either before or

granulartreated material

to the abutment.

the abutment.

after fabricating the structure.

after the construction of the structure (Fig 13).

Table 7. Settlements of rail for the different load steps. Case study: original ground QS1

LOADED SLEEPER 5 **-0.0083** -0.0077 -0.0069 -0.0063 LOADED SLEEPER 6 -0.0104 **-0.0106** -0.0100 -0.0091 LOADED SLEEPER 7 -0.0113 -0.0117 **-0.0118** -0.0112 LOADED SLEEPER 8 -0.0117 -0.0120 -0.0123 **-0.0125**

LOADED SLEEPER 5 **-0.0050** -0.0045 -0.0038 -0.0032 LOADED SLEEPER 6 -0.0054 **-0.0057** -0.0052 -0.0044 LOADED SLEEPER 7 -0.0051 -0.0057 **-0.0060** -0.0055 LOADED SLEEPER 8 -0.0049 -0.0054 -0.0059 **-0.0062**

LOADED SLEEPER 5 **-0.0086** -0.0081 -0.0074 -0.0069 LOADED SLEEPER 6 -0.0111 **-0.0114** -0.0109 -0.0101 LOADED SLEEPER 7 -0.0121 -0.0126 **-0.0129** -0.0124 LOADED SLEEPER 8 -0.0127 -0.0131 -0.0136 **-0.0139**

LOADED SLEEPER 5 **-0.0067** -0.0062 -0.0055 -0.0049 LOADED SLEEPER 6 -0.0079 **-0.0083** -0.0078 -0.0071 LOADED SLEEPER 7 -0.0083 -0.0089 **-0.0092** -0.0087 LOADED SLEEPER 8 -0.0085 -0.0090 -0.0096 **-0.0099**

LOADED SLEEPER 5 **-0.0061** -0.0056 -0.0048 -0.0043 LOADED SLEEPER 6 -0.0072 **-0.0074** -0.0069 -0.0062 LOADED SLEEPER 7 -0.0074 -0.0079 **-0.0082** -0.0077 LOADED SLEEPER 8 -0.0076 -0.0080 -0.0084 **-0.0087**

LOADED SLEEPER 5 **-0.0032** -0.0027 -0.0020 -0.0015 LOADED SLEEPER 6 -0.0030 **-0.0032** -0.0027 -0.0020 LOADED SLEEPER 7 -0.0026 -0.0029 **-0.0031** -0.0026 LOADED SLEEPER 8 -0.0022 -0.0025 -0.0028 **-0.0030**

LOADED SLEEPER 5 **-0.0071** -0.0066 -0.0059 -0.0053 LOADED SLEEPER 6 -0.0086 **-0.0089** -0.0084 -0.0077 LOADED SLEEPER 7 -0.0091 -0.0096 **-0.0099** -0.0094 LOADED SLEEPER 8 -0.0094 -0.0098 -0.0103 **-0.0106**

LOADED SLEEPER 5 **-0.0043** -0.0038 -0.0031 -0.0025 LOADED SLEEPER 6 -0.0044 **-0.0047** -0.0042 -0.0034 LOADED SLEEPER 7 -0.0040 -0.0045 **-0.0048** -0.0043 LOADED SLEEPER 8 -0.0036 -0.0040 -0.0045 **-0.0048**

LOADED SLEEPER 5 **-0.0029** -0.0025 -0.0020 -0.0016 LOADED SLEEPER 6 -0.0028 **-0.0031** -0.0027 -0.0022 LOADED SLEEPER 7 -0.0024 -0.0029 **-0.0032** -0.0028 LOADED SLEEPER 8 -0.0021 -0.0025 -0.0029 **-0.0032**

LOADED SLEEPER 5 **-0.0017** -0.0014 -0.0010 -0.0007 LOADED SLEEPER 6 -0.0015 **-0.0017** -0.0014 -0.0010 LOADED SLEEPER 7 -0.0011 -0.0015 **-0.0017** -0.0014 LOADED SLEEPER 8 -0.0008 -0.0011 -0.0015 **-0.0017**

LOADED SLEEPER 5 **-0.0032** -0.0028 -0.0022 -0.0018 LOADED SLEEPER 6 -0.0031 **-0.0035** -0.0031 -0.0025 LOADED SLEEPER 7 -0.0028 -0.0033 **-0.0036** -0.0033 LOADED SLEEPER 8 -0.0025 -0.0029 -0.0034 **-0.0037**