Culverts are very common in recent railway lines. Wild life corridors and  drainage conducts often fall in this category of partially buried structures. Their dynamic  behavior has received far less attention than other structures such as bridges  but its  large number makes that study an interesting  challenge from the point of view of safety  and savings. In this paper a complete study of a culvert, including on-site measurements  as well as numerical modelling, will be presented.  The structure belongs to the high speed railway line linking Segovia and Valladolid, in  Spain. The line was opened to traffic in 2004. Its dimensions (3x3m) are the most frequent  along the line. Other factors such as reduced overburden (0.6m) and an almost right  angle with the track axis make  it an interesting example to extract generalized  conclusions.  On site measurements have been performed in the structure recording the dynamic  response at selected points of the structure during the passage of high speed trains at  speeds ranging between 200 and 300km/h.   The measurements by  themselves provide a good insight into the main features of  the  dynamic behaviour of the structure. A 3D finite element model of the structure,  representing its key features was also studied as it allows further understanding of the  dynamic response to the train loads . In the paper the discrepancies between predicted  and measured vibration levels will be analyzed and  some advices on numerical   modelling will be propose

Alarcón Álvarez, Enrique

Fraile de Lerma, Alberto

Hermanns, Lutz Karl Heinz

Vega Domínguez, Jaime

Archivo Digital UPM

Dynamic Effects On Culverts for High Speed Trains

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

Congress on Numerical Methods in Engineering 2011 
Coimbra, 14 to 17 June, 2011 
© APMTAC, Portugal, 2011 
 
 
DYNAMIC EFFECTS ON CULVERTS FOR HIGH SPEED TRAINS 
Jaime Vega1*, Lutz Hermanns2, Enrique Alarcón2 and Alberto Fraile2 
1: Centro de Modelado en Ingeniería Mecánica.  
Fundación para el Fomento de la Innovación Industrial 
 José Gutierrez Abascal 2. 28006 Madrid. 
e-mail: jvega@etsii.upm.es 
 
2: Departamento de mecánica estructural y construcciones industriales. 
Escuela Técnica Superior de Ingenieros Industriales.  
Universidad Politécnica de Madrid. 
José Gutierrez Abascal 2. 28006 Madrid. 
e-mail: lhermanns@etsii.upm.es, {enrique.alarcon, alberto.fraile}@upm.es  
 
 
Keywords: Underpass, dynamic effects, high speed train 
Abstract Culverts are very common in recent railway lines. Wild life corridors and 
drainage conducts often fall in this category of partially buried structures. Their dynamic 
behavior has received far less attention than other structures such as bridges  but its 
large number makes that study an interesting challenge from the point of view of safety 
and savings. In this paper a complete study of a culvert, including on-site measurements 
as well as numerical modelling, will be presented. 
The structure belongs to the high speed railway line linking Segovia and Valladolid, in 
Spain. The line was opened to traffic in 2004. Its dimensions (3x3m) are the most frequent 
along the line. Other factors such as reduced overburden (0.6m) and an almost right 
angle with the track axis make  it an interesting example to extract generalized 
conclusions. 
On site measurements have been performed in the structure recording the dynamic 
response at selected points of the structure during the passage of high speed trains at 
speeds ranging between 200 and 300km/h.  
The measurements by  themselves provide a good insight into the main features of  the 
dynamic behaviour of the structure. A 3D finite element model of the structure, 
representing its key features was also studied as it allows further understanding of the 
dynamic response to the train loads . In the paper the discrepancies between predicted 
and measured vibration levels will be analyzed and  some advices on numerical  
modelling will be proposed.  
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
 2
1. INTRODUCTION 
 
Culverts and underpasses are very common in recent railway lines, including high speed 
railway lines (HSRL). Wild life corridors and drainage conducts often fall in this category of 
partially buried structures. According to Eurocode, they are not simple structures for which 
the impact factor may be obtained using simplified formulas. Therefore, the amount of 
analysis required in their design is similar to the analysis associated to non conventional 
bridges, while their cost should be orders of magnitude smaller. 
 
This lack of consistency between cost and design effort is being addressed by Spanish Public 
Works Office. As a first step, the dynamic response of a set of real structures in the HSRL 
linking Segovia and Valladolid has been monitored. A preliminary set of the results of these 
work has already been presented [1], [2]. This paper deals with one of these structures, which 
dimensions have been found to be very frequent. The first part of this paper presents both the 
structure and the layout set for the monitoring. Also, the most important features of the 
recordings obtained during the passage of a series of high-speed trains will be summarized.  
 
In order to gain insight into the dynamic behavior, the structure has been modeled using finite 
element (FE) techniques. A set of two FE models, one representing the superstructure, the 
second representing the structure, the embankment and a portion of the soil, will allow 
performing simulations resulting in time history estimations of some response parameters. All 
issues regarding FE models, which are different from the ones formerly used by some of the 
authors [3], will be covered in the second part of the paper.  
2. STRUCTURE PRESENTATION AND LAYOUT 
The structure selected for monitoring has a square cross section. Its inner opening is 3m wide, 
and the walls are 0.2m thick. It is build up of 8 precast blocks, each of them being 2m long. 
Therefore, the total length of the structure is 16m. The mean distance between the ballast base 
and the upper plane of the structure is 0.6m. The geotechnical information available indicates 
that the soil is granular, with medium density. The number of blows in standard SPT test 
varies almost linearly from 10 at 1m depth to 90 at 5m.  
 
Statistical analysis of the inventory of all culverts and underpasses in the HSRL linking 
Segovia and Valladolid revealed that this dimensions were the most commonly found. Three 
other factors lead to the choice of the structure. First, it is almost perpendicular to the track 
axis. Second, its reduced overburden. Third, the topological conditions of the surroundings 
that allowed both suitable access and good visibility of trains using the line. 
 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
 3
 
Figure 1. Structure's geometry and sensor positioning. 
  
Both the structure and superstructure have been monitored with piezoelectric accelerometers. 
In the structure, 6 sensors have been placed in the middle section of three different precast 
blocks. In each position, a sensor has been positioned vertically at midpoint of the roof, and 
another horizontally at mid-height of the wall. The relative distances between sensors and 
track axis are shown in Figure 1.  
 
In the superstructure, sensors have been placed vertically on sleepers (close to the exterior 
rail-pads) and on the rail foot (at mid-span between two sleepers). Four couple of sleeper and 
rail sensors have been placed, two on each track. In each case, one sleeper is placed 
approximately over the underpass mid-span, and the other one is three sleepers further to the 
north (Valladolid).  
 
In this document, the focus will be on the dynamic behavior of the underpass roof, and only 
measurements from three sensors (A, B and C in Figure 1) will be taken into consideration.   
 
3. MONITORING RESULTS SUMMARY 
 
The structure was monitored for slightly more than 24 hours. During that time, 46 trains 
travelled the line. Four different passenger trains were operating in the line. Their nominal 
axis loads and distances are presented in Figure 2. 
 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
 4
 
Figure 2. Characterization of trains travelling the line. 
 
A sample of recording obtained is shown in Figure 3. It was obtained during the passage of a 
s-130 train, which is the RENFE code for Talgo 250, with an estimated speed of 200km/h. 
Speeds have been estimated in two ways. First, from video recordings of the trains during the 
tests. Second, measuring time lapses between peaks associated with each axis in root mean 
square (RMS) acceleration records. 
   
 
Figure 3. Sample acceleration recording obtained. 
 
Acceleration records show important differences in measured levels depending on the sensor 
(Figure 4). In this case, the biggest response has been measured close to the center of the 
structure. Spectral analysis of this signal shows that energy distributes in a wide range 
between 0 and 120Hz. Analysis of the decay portion of the record indicate a free vibration 
frequency of about 40Hz. This is interesting because, EC0-A2 [4] indicates that peak 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
 5
acceleration levels must be calculated considering frequencies below the highest  value 
among 30Hz, or1.5 times the fundamental mode and the third vibration mode. In this case it is 
difficult to establish de vibration modes of the ensemble structure - embankment. However it 
is clear that there is an important amount of energy far above 1.5*40=60Hz. 
 
 
Figure 4. Spectral density from a sample acceleration recorded at the roof of the culvert. 
 
Figure 5 shows an overview of all measurements performed. It shows, for each sensor, the 
peak acceleration value as a function of train speed. Different symbols (circles, squares, stars 
and diamonds) have been used for each train type. Also, different colors have been used for 
each sense (track): from Valladolid to Segovia or from Segovia to Valladolid.  
 
 
Figure 5. Peak acceleration for each sensor. 
 
It is interesting to notice that speeds for a given train type are in almost all cases very similar. 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
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This is logical considering trains operate almost always at nominal speed. Considering each 
group of similar samples (a given train at a given speed)  the scatter in peak acceleration 
values seems important. It is also clear that track, that is circulation sense, is important in the 
response level. As it will be proven, relative distance between sensor and track explain this 
differences. 
 
Depending on the sense of circulation, relative distances between sensor and circulating track 
are different. Measurements obtained from both senses of circulation can be considered 
together if this relative distance is considered. As shown in Figure 6, considering relative 
distances, the number of available positions increases since the central sensor is not 
symmetrically placed.    
 
 
Figure 6. Identification of relative positions of sensors from track axis. 
 
 
Figure 7 presents a plot of peak vertical acceleration as a function of relative sensor position, 
along the roof of the underpass. In order to reduce all other sources of scatter, only s-130 
trains at around 200km/h have been considered. Each sense of circulation has been plotted in 
different colors, consistent with the coding in Figure 5. From the figure, it is clear that, at 
positions ±5m, both senses of circulation lead to similar acceleration levels. Thus proving the 
importance of relative position in explaining response values. 
 
Figure 7 is interesting because it proves the unequal distribution of acceleration response 
along the middle plane of the underpass axis. It is clear that demand is much greater below the 
circulating track than in the opposite track. Next section describes the FE models built in 
order to have a more detailed description of response levels along the roof.  
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
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Figure 7. Peak acceleration as a function of relative position along the roof transverse axis. 
( s-130 trains at around 200km/h). 
 
4. FINITE ELEMENT MODELS 
Vibration levels at different points of the structure will be predicted using a two step method. 
First, for a given train and a given speed, reaction force records in the ballast-subballast 
interface will be evaluated at discrete points along the track axis. These points will be 
considered as source terms in the second calculation step, where the acceleration record at the 
point of interest is obtained. This is performed by considering as many transfer functions as 
source points considered. 
 
The first step is performed using a finite element model representing half the track 
superstructure. In this model the rail is modeled using beam elements. Sleepers are modeled 
as lumped masses. Spring dashpot elements are used to model both the fastening system and 
the ballast-embankment ensemble.  
 
A lumped mass representing the unsprung mass of half an axle is set to move at the train’s 
speed. A spring dashpot element is used to model contact. A moving load representing axle 
load is linked to this mass. Time integration of the motion equation allows obtaining reaction 
force histories at discrete points of the ballast sub-ballast interface. Since all considered 
elements are linear, time histories for different axle loads can be obtained by scaling. 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
 8
Moreover, considering axle distances and train velocity, time lags can be computed making it 
possible to build the complete history of reaction forces when the train passes.  
 
Figure 8. Finite element model used for obtaining reaction forces at interface points bellow each sleeper. 
 
 
Rail roughness has been modeled by considering a profile consistent with Braun & 
Hellenbroich spectral density model [5]:  
 
 
 
ω−⎛ ⎞= ⎜ ⎟⎝ ⎠rr rr 0 0
nG (n)  G (n )
n
 (1)  
 
where n0=1/2π, and ω=3.5. From this profile, considering the train speed and the properties of 
the contact element, a moving self equilibrated couple of reaction forces can be defined. This 
couple is considered in a second time history analysis, allowing new reaction force histories to 
be obtained. Since this contribution to reaction force is independent on axle load, only time 
lags need to be considered when building the complete time history of reaction forces 
produced by rail roughness when the train passes. These values can be added to previous ones 
thus obtaining the total reaction force histories at each point of the ballast- subballast 
interface. 
 
The second step is performed in the frequency domain considering transfer functions from 
force at each emitter point of the ballast-subballast interface and acceleration at the reference 
point. For each sleeper, two emitter points have been considered, one bellow each rail. It is 
assumed that each rail contributes only to its closer emitter point.  
 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
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Transfer functions are computed by performing harmonic analysis with a finite element model 
of the culvert plus the embankment and the ground. For a given frequency, all transfer 
functions are calculated simultaneously taking advantage of the reciprocity principle. A 
unitary force is applied at the node which response is desired while displacements are 
measured at all source points considered. Due to the symmetry of the problem, only one half 
of the geometry is modeled.  
 
The model mesh is presented in Figure 9. Five different materials have been defined: the soil, 
the embankment, the backfill, the ballast and the concrete. Elements in Figure 9 have been 
colored depending on their material. It contains 20 node solid elements, and dashpots in the 
boundaries properties of which are set to avoid reflection of incident waves. In some portions 
of the backfill, the mesh has been built with 10 node tetrahedra.  
 
 
Figure 9. FE mesh used for obtaining transfer functions. 
 
Element sizes have been set such that there are at least 4 elements per wavelength at 120Hz, 
considering the embankment as the softest element  . The number of degrees of freedom of 
the model has been limited in order for the computer to deal with the problem using only 
RAM memory (the computer machine used in calculations has 6Gb). Otherwise computing 
time increases dramatically. The model extends 15.5m at both sides, perpendicular to the 
track axis, and 10.8m in its direction and has ∼1 million degrees of freedom.   
 
Using the two models described previously, simulations have been performed. Figure 10 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
 10
shows a comparison between one set of recordings and simulations for an s-130 train with 
v=200km/h. Comparisons are performed using RMS values (1s windows). The reasons for 
using the latter value for comparisons are twofold. First, peak acceleration is highly dependent 
on the high frequency content of the signal, and the simulations have energy up to 120Hz . 
Secondly, peak values are usually linked to highly non linear phenomena such as shocks of 
wheels against the rail, and these are not modeled. The agreement is quite good although no 
adjustment of FEM parameters have been performed.  
 
 
 
Figure 10. Comparison of recordings and simulations. Train s-130 with v=200km/h 
 
 
More simulations have been performed in order to assess the response in points where no 
measurements were performed. Figure 11 shows a plot where measurements for s-130 trains 
at 200km/h  are compared with predictions at mid-points of each pre-cast block. Predictions 
have been performed considering two different roughness levels, in order to identify an upper 
and a lower bound for the response. In this case, the lower bound is associated to the lowest 
roughness level (best quality) in the Braun and Hellenbroich model. The upper bound is 
associated with an intermediate roughness level.  
 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
 11
 
Figure 11. Simulations vs. measurements along the roof midline. 
 
 
5. CONCLUSIONS 
This work presents a set of measurements and models providing clues to understanding the 
dynamic behavior of frequently encountered underpasses.  
 
Measurements have proved that acceleration scatter is quite important. Also, response 
distribution along the underpass axis has been found to be non-uniform, with the relative 
position between track axis and sensor being very important.  
 
Finite element techniques have been useful to model the dynamic behavior of this structure, 
using a set of two models: one for the superstructure and another for the ensemble structure- 
embankment- soil. These models have allowed assessing a detailed distribution of response 
along the upper plane of the structure.  
 
Jaime Vega1*, Lutz Hermanns2 , Enrique Alarcon2 and Alberto Fraile2 
 12
5. ACKNOWLEDGEMENTS 
This research was supported by Spanish Ministerio de Fomento, Direccion general de 
Ferrocarriles, under contract No. A-V-ENC-E-119.  
 
 
REFERENCES 
[1] Alarcon E, Vega J, Montañes E, Fraile A. "Dynamic effects on culverts for high speed 
trains", in the "Workshop on dynamics, structural and earthquake engineering: 
research and practice." Ispra, Italy, 16th july 2010. 
[2] Fraile A, Hermanns L, Chirino F, Alarcon E. "Dynamic Effects of High Speed 
Trains on Underpasses" Proceedings of the Sixth International Conference on 
Computational Structures Technology, B.H.V. Topping and Z. Bittnar (Editors), 
Civil-Comp Press, Stirling, Scotland. Septiembre 2002. 
[3] Fraile A, Hermanns L, Alarcon E. " Estudio de vibraciones en la estación de 
Segovia". Hormigón y acero Volumen 61, nº 258, 7-23. ISSN: 0439-5689. Octubre-
diciembre 2010. 
[4] EN 1990. Annex 2: Application for Bridges.. 
[5] Braun, H., and Hellenbroich, T. 1991. Messergebnisse von Strassenunebenheiten. VDI 
Berichte 877, VDI-Verlag, Dusseldorf, Germany. pp. 47-80. [In German.]. 


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Dynamic Effects On Culverts for High Speed Trains

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