1

IMPACT OF VERTICAL TRACK STIFFNESS VARIATIONS

IN RAILWAY INFRASTRUCTURE MAINTENANCE

João Corrêa Mendes da Silva Ribeiro

Instituto Superior Técnico, Lisbon, Portugal, 2014

joao.s.ribeiro@tecnico.ulisboa.pt

Abstract: Efficient and strategic maintenance planning has become a key issue for railway infrastructure

administrators. Tools for better planning have become more necessary to achieve the desired levels of per-

formance and productivity of the railway system. Research has found great importance of track stiffness

due to its influence on dynamic impacts on the wheel-rail interface. Dynamic impacts lead to track geometry

degradation, therefore, new measuring stiffness techniques are being developed allowing to study the impact

of track stiffness on track geometry quality. The present work focus on a track section of the Iron Ore Line

(Malmbanan), in northern Sweden, the heaviest haul railway in Europe. The main goal is to evaluate the

influence of track stiffness variations on the quality of the track. First, spatial/temporal variations of vertical

stiffness measurements recorded with an innovative measuring vehicle are analysed. Despite low stiffness

values, stiffer track sections are verified in winter measurements. The importance of several track assets on

the existence of stiffness variations is also examined and confirmed. Another approach is the evaluation of

the relation between the maintenance history and track stiffness or events. Data indicate some connection

between tamping frequency and the considered conditions. It is finally made the assessment of the influence

of track stiffness variations on track quality and the rate of degradation of the longitudinal level, measured

in mm/year. Great dispersion is found although some statistically significant results are obtained through

linear regression between stiffness variation and average or maximum rate of degradation per track section.

Keywords: Vertical track stiffness, Stiffness temporal variation, Stiffness spatial variation, Railway track

maintenance, Track geometry degradation

1 INTRODUCTION

In today’s competitive and ever-changing market it is more and more important to achieve an effective and

efficient maintenance strategy. LCC (Life Cycle Cost) and RAMS (Reliability, Availability, Maintenance

and Safety) have been playing an important role to achieve more efficient maintenance decisions. The

achievement of an improvement on the maintenance planning strategy and its efficiency will enable higher

levels of performance and productivity of the whole railway system (Arasteh khouy, 2013; Karttunen,

2012). Within this scope, researchers have been trying to understand the degradation mechanism of the

railway structure. It is believed that track stiffness and track deflection measurements may have an important

role on determining the root cause of track failures or track response under different traffic conditions

(Berggren, 2009; Puzavac et al., 2012). Certain relations between track stiffness and variation of track

stiffness with track geometry degradation have been discovered, due to the effect of track stiffness devia-

tions on variations of the wheel/rail contact. Such variations increase the dynamic impact on the rail and

consequently contribute to track structure deterioration (Burrow et al., 2009).

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The present work analyses vertical stiffness measurements on the Iron Ore Line (Malmbanan) in northern

Sweden, and the influence of stiffness variations in track geometry degradation. Stiffness measurements

used in this paper were performed in 2012 with a new innovative method which aims to improve the speed

and cost without compromising the quality (Berggren et al., 2014).

2 VERTICAL TRACK STIFFNESS

Static vertical stiffness, k [kN/mm] (1), is translated by the maximum deflection due to a wheel load at a

given point (Teixeira, 2003), where Q [kN] is the concentrated load applied on the rail and z [mm] is the

maximum deflection of the track.

𝑘 =𝑄

𝑧 (1)

The rail deflection is influenced by the combination of all the track’s components stiffnesses. This increases

the difficulty of understanding track stiffness and its effect on track performance. Factors such as the non-

linearity of the stiffness of different components, such as the rail pads or subgrade (Berggren, 2009;

Hosseingholian et al., 2009; Teixeira, 2003), the variability with different hydrologic and climatic condi-

tions (Woodward et al., 2014), or the existence of voids beneath sleepers, lead to non-linear behaviour of

the track.

When a train starts moving, the track will experience immediately a dynamic load (Berggren et al., 2002).

The response given by the track structure to the dynamic vertical movements created by the rolling stock

on the rail is the dynamic vertical stiffness and it varies as a function of time. It is usually used its inverse,

track receptance, α [m/kN], function of the excitation frequency, f [Hz].

𝛼(𝑓) =𝑧(𝑓)

𝑄(𝑓) (2)

3 LITERATURE REVIEW ON TRACK STIFFNESS INFLUENCE

Spatial track stiffness variation is one of the main origins of track geometry deterioration (Hunt, 2005;

Puzavac et al., 2012). It was only on the 1970s that the first studies on the importance of track stiffness for

reducing the vehicle dynamic loads were published by Prud’homme when the author presented a set of

equations for calculating dynamic loads (Puzavac et al., 2012; Teixeira, 2003).

Low global stiffness may generate settlements on the platform and consequently on the ballast layer which

will considerably increase displacements and bending stress in the rails per unit force with lower dynamic

forces (Hunt, 2005; Li & Berggren, 2010; Teixeira, 2003). It may be related to insufficient compactness

of ballast and/or platform, ballast fouling or even poor drainage (Teixeira, 2003). On the other hand, stiff-

ness values higher than the optimal translate mean increases on the dynamic loads. This leads to faster

deterioration as vertical stresses on sleepers and ballast are higher and heavier due to high dynamic wheel-

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rail contact stress with low bending rail strains (Hunt, 2005; Puzavac et al., 2012; Teixeira, 2003). Re-

search thus concluded that a relatively high and constant track stiffness is needed for optimising track re-

sistance to the applied loads and limit the track deflection which may lead to wear and fatigue damage of

track structure components (Andersson et al., 2013). According to Sussman et al. (2001) and Li and

Berggren (2010), the optimum track stiffness for freight-traffic lines is between 70-80 kN/mm.

Irregularities on track stiffness mean that properties of the track structure are heterogeneous along the rail-

way and will affect the train-track dynamic interaction. As higher the axle load or speed, the more impact

the variations will have (Dahlberg, 2003). Experimental measurements on several tracks show that vertical

stiffness transitions sometimes are not gradual and in some cases they are particularly pronounced in rather

short distances. It often occurs that greater geometry defects tend to coincide with sections with sudden

stiffness variations (Teixeira, 2003). López Pita (2002) verified that an increase of about 30-50% on ballast

stress levels may be induced, which increase track geometry deterioration rate, by the variation of track

stiffness in two adjacent sections if compared to track sections with constant stiffness. Best known stiffness

heterogeneities are related to the existence of bridges or tunnels which usually have concrete platforms with

high vertical stiffness when compared with the granular layers that compose the ballasted track platform.

However recent research verified that there is no obvious correlation between high degradation rates of track

quality and track infrastructures such as bridges or turnouts (Berggren, 2013). That reveals that other

sources of irregular stiffness such as non-uniformly compacted ballast, drainage problems on the granular

layers or even variation of the subgrade structure can be found and may be more frequent than expected

(Berggren, 2013; Dahlberg, 2010; Gallage et al., 2013; Teixeira, 2003).

4 MEASURING METHODS

Standstill measuring methods are the most common and measure stiffness at discrete intervals. However, if

track vertical stiffness is to be investigated in large distances or even the whole track, standstill measure-

ments are virtually impossible to carry out as they are very time-consuming and expensive (Burrow et al.,

2009). Continuous measurement techniques are traditionally based in two main approaches: dynamic

measurements on a single axle or laser-measurement of vertical deflections due to applied loads

(Berggren, 2009; Burrow et al., 2009). Different existing measurement systems are unlikely to get the

same vertical track stiffness due to several reasons such as the applied loads, spatial resolution of the meas-

uring technique, excitation frequency or even the influence of track geometry irregularities (Berggren,

2009; Hosseingholian et al., 2009).

Stiffness data used on this work was measured with an innovative method, recently developed in Sweden

by EBER Dynamics. The IMV100 is an adapted track recording car on which a new inertial measurement

system was added to the existing mechanical three-point chord measuring system. The combination of the

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two systems is the basis for the EVS-method, which separates the unloaded track geometry from the loaded

track geometry, enabling the determination of both track deflection and track stiffness (Berggren et al.,

2014; Nielsen et al., 2013). This approach enables to significantly reduce stiffness measurement costs.

Initial price estimations identify a price reducing factor of 10 to 20 times, when compared to other existing

stiffness measurement vehicles. There is also the benefit of the possibility of measuring at higher speeds (up

to 100 km/h) as the method does not imply any speed limitation, in opposition to dynamic measurement

techniques (Berggren et al., 2014). Track vertical stiffness was measured at relatively high speeds (around

80 km/h) and filtered at wavelengths of 12 metres.

5 THE IRON ORE LINE

The Malmbanan line is the only European heavy haul railway and it has been recently upgraded to support

30-tonne traffic (Larsson, 2004; Schöch & Frick, 2007; Schöch et al., 2011). It is located in the EU’s

most important mining region which produces around 90% of the total iron ore production in Europe, still

with large growth plans (Lundberg et al., 2012). The case study focuses on the first about 18 km of the

railway section 118, starting near Boden. Due to its proximity to the Arctic Circle, the line is constantly

subjected to severe meteorological conditions such as snowstorms and extreme temperatures which may

vary from close to -40 ºC during winter and +25 ºC during summertime. This variability may result in

substructure instability that affects track geometry up to 30 cm below the superstructure as the frost that is

created during the cold season over the substructure melts, creating frost boils and drainage complications

(Arasteh khouy, 2013; Schöch & Frick, 2007).

6 TRACK STIFFNESS ANALYSIS

6.1 SELECTION OF DATA

Work focused only on the left rail, following other research on track stiffness (Berggren, 2006), (Li &

Berggren, 2010) and (Berggren et al., 2014). Even though stiffness data varies from date to date, stiffness

measurements along the track indicate that most of the track has stiffness values between 30 and 40 kN/mm.

Five different data recordings were originally available (2012: February, 25 and 29 April, August; 2013:

November). Maximum stiffness values, between 50 and 70 kN/mm, represented less than 5% of the total

studied extension in the four inspections from 2012. However, data from November 2013 had almost 10%

of vertical stiffness values above 50 kN/mm (5% were above 100 kN/mm) reaching maximum values of

470 kN/mm (!). Notice that in (Li & Berggren, 2010) a track considered has a stiff railway has stiffness

values of about 170 kN/mm. Therefore the fifth recording run was disconsidered in the analysis.

6.2 VARIATION OVER TIME

Boden’s 2012 temperature and precipitation levels were analysed. Only five months did not have sub-zero

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temperatures registered. Highest temperatures occurred during June, July and August, as usual. As previ-

ously referred, such temperature variations may involve freeze-thaw cycles which induce variations on track

stiffness. Precipitation levels may also influence track stiffness once track drainage is crucial for the effec-

tive functioning of track’s bearing capacity. Humidity conditions of the terrain may vary in each inspection

performance due to more or less precipitation during the preceding period. This possibility is confirmed by

research, which refers that frost boils and poor drainage are often cause for reduced substructure stability,

between April and July in the Malmbanan line (Arasteh khouy et al., 2013).

The influence of weather conditions was visible in the analysis of track stiffness variations on 200 metres-

long segments. However, in opposite to the expected, stiffness measurements performed in February, the

coldest month of the year and fifth straight month with sub-zero temperatures, are the set of data with lower

maximum values of global vertical stiffness. A reduction of stiffness between the two April measurements

was verified. Two major factors may explain such difference: according to climate reports, average temper-

atures increased from around 1 ºC to about 6 ºC between the two dates, and the largest precipitation day of

the month occurred in 27 April (9.14 mm). In rainy seasons water may accumulate near the track and infil-

trate the subgrade, and can soften the track structure (Tzanakakis, 2013). Also, there is indication of strong

correlation between effects of thaw and decrease of stiffness due to the presence of defrosting water in the

subgrade layers (Zufelt, 2013). August registers are in general lower than the previous, meeting the expec-

tations due to absence of frost in the region together with an increase of the average monthly precipitation.

6.3 SPATIAL VARIATION

The 18 kilometres were divided in three parts for better perception of stiffness variations. Averages and

standard deviations of 200 metres-long track segments were used to represent mean values by sector and to

identify the extensions on which track stiffness fluctuates the most. An example is shown in Figure 1. As

expected, steeper average increases are correlated with higher standard deviations and lower average gradi-

ents are thus correlated with small standard deviations (the stiffer part is located in kilometre 1156 -

80 kN/mm in April which coincides with the only standard deviation above 12 kN/mm). Some of the stiff-

ness variations found coincide with the existence of track events along the railway such as railway bridges,

embankments, culverts, etc.

6.4 METHODOLOGY FOR MEASURING TRACK STIFFNESS VARIATIONS

The methodology for assessing the stiffness variation on a given location was based on the maximum vari-

ation within a 25 metres distance window (±2.5m). As four different sets of data were available, with the

already characterised spatial and temporal variations, the criterion defined for obtaining a single variation

of vertical track stiffness on a certain location, was the average of the maximum variations of three registers,

excluding the most distant value within the four estimated stiffness variations.

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Figure 1 – Example of spatial distribution of stiffness averages and standard deviations (Part 1/3)

7 INFLUENCE OF TRACK EVENTS

Among the provided data was a list with the location of several assets along the railway, some of which

were selected on the basis of their probability of explaining some existing stiffness variations. Chosen events

were culverts (32), water pipes (4), embankments (32), level crossings (1) and abolished level crossings

(17) (since the rails may still have non-typical track support conditions although the last abolished one was

closed in 1997), railway bridges (3) and turnouts (17). In opposite to railway bridges, it is not possible to

see through Google Earth the extension of embankments or even to spot their location visually. This is

important to refer since it was found that data related to railway bridges in fact were coordinates of the start

and ending points of each bridge. Furthermore, geographic location of track events was not accurate, thus

events not easily spotted via satellite images may be in the wrong location. Figure 2 summarises stiffness

variations induced per track asset.

Though short length structures, the three existing railway bridges are easily identified by high stiffness

variations, with a minimum of 12 kN/mm within a range of 25 metres. The influence of embankments in

stiffness variations is observed where stiffness values are higher in April and lower in August, after defrost-

ing. The absence of information about the extension of these embankments did not enable a better assess-

ment. However, the highest values are related with two coincident embankment coordinates and a near

abolished level crossing. Data of depth and diameter of culverts and pipes was not available thus an evalu-

ation of the influence of this parameters was not possible. The studied track section has only one level

crossing still opened and seventeen abolished level crossings. There is a possibility of a complete renewal

of some of the track sections during the works for improving the bearing capacity of the track that would

eliminate the concrete slabs often existent on level crossings, which could explain lower variations in some

MEAN STIFFNESS WITHIN 200 METRES (kN/mm)

STIFFNESS STANDARD DEVIATION WITHIN 200 METRES (kN/mm)

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of the abolished level crossings. Still, the active level crossing produces a stiffness variation of 13 kN/mm

while four of the abolished ones coincide with variations above 18 kN/mm. In average, about 90% of the

existing turnouts on the track are responsible for sudden stiffness variations above 9 kN/mm and more than

50% produce stiffness variations above 12 kN/mm. Comparing with the other most frequent track assets

(culverts and embankments – 32 each), turnouts are verified to be the events responsible for higher varia-

tions of vertical stiffness, in average.

Figure 2 – Induced stiffness variation per selected track events

8 STIFFNESS INFLUENCE ON MAINTENANCE

The space-time distribution of tamping operations described on the database is quite variable and did not

allow to identify any distinct pattern. The extension of one intervened track segment varies from 25 metres

(October 2002) to 8 250 metres (October 2003) leading to very distinguished total number of track segments

intervened on a maintenance performance.

The track was divided into 10 metres-long segments for assessing the tamping frequency. It was verified

that almost 20% of the track was intervened only two times in eight years and only less than 7% of the

considered track segments were intervened a minimum of four times. It was also verified that the majority

of the 200 metres-long segments with none of the selected track events was subjected to only one interven-

tion in eight years (37%) while track sections with five or more track events within 200 metres had at least

four interventions, or, in average, at least one maintenance operation every two years. Unlike the majority

of the track, locations where stiffness varies are more susceptible to deteriorate into quality levels that re-

quire corrective maintenance.

The comparative analysis of the maximum stiffness variation per 10 metres-long segments and the tamping

frequency within the same extension revealed a variable range of stiffness variations per number of tamping

operations. The vast majority of the 10 metres-long segments has maximum variations lower than 6 kN/mm

and most of the total number of segments have been tamped only two times (less than 20% was tamped

more than three times). However, whenever higher stiffness variations happen, the importance of tamping

operations increases: less than 50% of the sections with stiffness variations below 9 kN/mm were tamped

0% 20% 40% 60% 80% 100%

Railway bridge

Culvert

Embankment

A. level crossing

Level crossing

Pipe

Turnout

STIFFNESS VARIATION (25 M) PER TYPE OF EVENT

[0-3] (kN/mm)

]3-6] (kN/mm)

]6-9] (kN/mm)

]9-12] (kN/mm)

]12-15] (kN/mm)

]15-18] (kN/mm)

]18-21] (kN/mm)

]21-24] (kN/mm)

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at least three times; segments with stiffness variations above 9 kN/mm required more tamping operations,

i.e. 52% of the track sections with stiffness variations between 9 and 12 kN/mm and 71% with stiffness

variations above 12 kN/mm were tamped more than three times within the same time period (25% were

tamped at least four times).

9 STIFFNESS IMPACT ON THE MEAN QUALITY OF THE TRACK

The influence of the mean value and standard deviation of vertical track stiffness on the longitudinal level

of the track, within 200 metres-long segments, was assessed through a multiple linear regression. The mean

longitudinal level was considered as the dependent variable while the mean and standard deviation of ver-

tical stiffness were considered as independent variables. The coefficient of determination estimated turned

out to be low (7%). Nonetheless, the model is statistically significant at a significance level of 5% as the F

statistic has a p-value below 0.05. The two independent variables are also statistically significant at a 95%

confidence. Thus it can be concluded that, despite the strong influence of other external factors not consid-

ered in the model due to lack of data (i.e. rolling stock speed, unsprung mass, MGT, wheel-rail interface

quality, climate conditions, components condition, etc.) vertical track stiffness influence the track quality of

the railway.

10 STIFFNESS INFLUENCE ON RATES OF DEGRADATION

10.1 LONGITUDINAL LEVEL RATES OF DEGRADATION

After an initial analysis of the available data, twenty-six sets of longitudinal level data from 2009 to 2013

were found suitable to work with. The estimation of the rates of degradation was made through simple linear

regression, considering the deterioration level as the dependent variable Y and time as the independent var-

iable X. The regression coefficient corresponded to the deterioration rate of a given defect, in mm/day

(mm/year if multiplied by 365). Only regressions with coefficients of determination (R2) above 0.70 were

considered; negative rates were not taken into account. The fact that no tamping pattern had been identified

when analysing the available track maintenance data was taken into account. The space-time irregularity of

tamping operations lead to the assumption that a large part of the maintenance operations are not preventive

but corrective operations due to punctual defects exceeding track quality thresholds. Thus it was conserva-

tively considered the existence of a maintenance operation whenever the defect measured on two consecu-

tive track inspections would drop to less than 95% of the previous measurement. No maximum time-window

for a new tamping operation was considered as several track segments were only tamped once or twice in

eight straight years.

The twenty-six validated sets of data were plotted in the same chart to get a better visual notion of the

longitudinal level spatial distribution. Visual standout longitudinal level peaks, i.e. kilometric points on

which values were clearly different from the surrounding longitudinal level pattern were selected. A total

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of 140 valid linear regressions (rates of degradation) for 53 selected points were obtained with the previous

methodology. Accordingly to other research (Andrade & Teixeira, 2011; Cabecinha, 2012; Rodrigues,

2013) the rates of degradation adjusted to a lognormal distribution with mean of 4.95 mm/year and

standard deviation of 4.75 mm/year.

10.2 INFLUENCE OF STIFFNESS VARIATIONS ON THE RATE OF DEGRADATION

Two approaches were considered for the evaluation of the impact of stiffness variations on the rate of deg-

radation. The first one considered absolute variation levels and the second relative variations, both within a

25 (±2.5) metres range. The estimation of vertical stiffness variations within 25 (±2.5) metres on each

location revealed different levels of variation for each rate of degradation estimated.

The first approach took in consideration the clustering of rates of degradation per range of stiffness variation,

absolute and relative. A trend for higher rates of degradation was identified for stiffness variations above

15 kN/mm, Figure 3-A. The same was identified for relative stiffness variations, above 45%. Due to the

variability of the sample sizes, the rates of degradation were divided into two groups in order to evaluate

the statistical significance of the identified trend, Figure 3-B. The goodness of fit test was significant for a

log-normal distribution in both cases. A Mann-Whitney U-test (α=95%) did not reject H0 = distribution of

both groups are identical. Therefore, despite the apparent correlation between higher absolute stiffness var-

iations and higher rates of degradation of longitudinal level, there was no statistical significance.

Figure 3 – Boxplots of rates of deterioration per absolute stiffness variations

However, the existence of several different rates of degradation on the same location may bias the results.

Therefore two different approaches were attempted, again, with no significant results. The approaches in-

volved the definition of a single representative rate of degradation: the average or the maximum rate for

each considered stiffness variation. A linear regression was made for both cases with the absolute and rela-

tive stiffness variations. Wide dispersion was verified in both cases. Nevertheless all the regressions were

proven to be statistically significant. These findings leave open the possibility of a correlation between

0

2

4

6

8

10

12

14

16

Rat

e o

f d

egra

dat

ion (

mm

/yea

r)

Stiffness variation (kN/mm)

RATES OF DETERIORATION PER

ABSOLUTE STIFFNESS VARIATION

9 41 30 21 11 14 6

0

2

4

6

8

10

12

14

≤15 >15Rat

e o

f d

egra

dti

on (

mm

/yea

r)

Absolute stiffness variation (kN/mm)

RATES OF DEGRADATION PER

ABSOLUTE STIFFNESS VARIATION

101 31

A B

10

higher rates of degradation of local defects and sudden stiffness variations. However, stiffness variations

alone will not explain the variability of the registered degradation. A different methodology for obtaining a

higher frequency of higher stiffness variations may be necessary on future research in order to have bigger

sample sizes to analyse.

11 CONCLUSIONS

The case study track segment is a soft line with average stiffness values around 30 to 40 kN/mm. It was

verified the existence of lower stiffness values during summer measurements than in winter recordings. It

was also shown that segments with higher average stiffness values tend to coincide with track sections with

higher standard deviations and track assets such as railway bridges, turnouts and (abolished) level crossings.

Sections such track infrastructures tend to be more frequently intervened.

A multiple linear regression between the average track quality and vertical stiffness (mean and standard

deviation) was performed. Results demonstrated that for soft tracks, higher and steadier stiffness values

have positive effect on the track quality. However, other not considered factors have to be considered for

predicting degradation levels. Rates of degradation of several track sections were estimated as well as the

corresponding stiffness variations. No significant correlations were found between the sudden absolute (or

relative) stiffness variation magnitudes and longitudinal level rates of degradation. However, linear regres-

sions considering one rate of degradation per stiffness variation (average or maximum rate) were found to

be statistically significant despite the substantial dispersion of results.

Further research should focus on measuring vertical stiffness variation, as well as assess its influence on the

rates of degradation by track section category, since different speeds and rolling stock may induce different

rates of degradation when interacting with vertical stiffness variations.

REFERENCES

Andersson, A., Berglund, H., Blomberg, J., Yman, O. (2013). The Influence of Stiffness Variations in

Railway Tracks. Bachelor Thesis in Civil Engineering, Chalmers University of Technology, Göteborg,

Sweden.

Andrade, A. R., Teixeira, P. F. (2011). Uncertainty in Rail-Track Geometry Degradation: Lisbon-Oporto

Line Case Study. Journal of Transportation Engineering, 137(3), 193–200.

doi:10.1061/(ASCE)TE.1943-5436.0000206

Arasteh khouy, I. (2013). Cost-Effective Maintenance of Railway Track Geometry – A Shift from Safety

Limits to Maintenance Limits. PhD Dissertation, Luleå University of Technology, Luleå, Sweden.

Arasteh khouy, I., Schunnesson, H., Juntti, U., Nissen, A., Larsson-Kraik, P.-O. (2013). Evaluation of Track

Geometry Maintenance for a Heavy Haul Railroad in Sweden: A Case Study. Proceedings of the

Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 228(5), 496–503.

doi:10.1177/0954409713482239

Berggren, E. G. (2006). Measurements of Track Stiffness and Track Irregularities to Detect Short Waved

11

Support Conditions. In Proceedings of International Conference on Railway Track Foundations. 11-

13 September, Birmingham, UK.

Berggren, E. G. (2009). Railway Track Stiffness – Dynamic Measurements and Evaluation for Efficient

Maintenance. PhD Dissertation, Royal Institute of Technology, Stockholm, Sweden.

Berggren, E. G. (2013). Beating Stiff Track. International Railway Journal.

Berggren, E. G., Jahlénius, Å., Bengtsson, B.-E. (2002). Continuous Track Stiffness Measurement: An

Effective Method to Investigate the Structural Conditions of the Track. In Proceedings from Railway

Engineering. 3-4 July, London, UK.

Berggren, E. G., Nissen, A., Paulsson, B. S. (2014). Track Deflection and Stiffness Measurements from a

Track Recording Car. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail

and Rapid Transit, 228(6), 570–580. doi:10.1177/0954409714529267

Bugarin, M. R., Novales, M., Orro, A. (2006). Modelling High Speed Turnouts. In Proceedings of 7th World

Congress on Railway Research. 4-8 June, Montreal, Canada.

Burrow, M. P. N., Teixeira, P. F., Dahlberg, T., Berggren, E. G. (2009). Track Stiffness Considerations for

High Speed Railway Lines. (N. P. Scott, Ed.)Railway Transportation: Policies, Technology and

Perspectives (pp. 1–55). Nova Science Publishers.

Cabecinha, L. (2012). Análise dos Padrões de Degradação da Qualidade Geométrica de Via para Apoio à

Estratégia de Manutenção - Caso de Estudo da Unidade Operacional Sul da Rede Ferroviária

Portuguesa. MsC Dissertation, Instituto Superior Técnico, Technical University of Lisbon, Lisbon,

Portugal.

Dahlberg, T. (2003). Railway Track Settlements – A Literature Review. Report for the EU Project

SUPERTRACK.

Dahlberg, T. (2010). Railway Track Stiffness Variations – Consequences and Countermeasures.

International Journal of Civil Engineering, 8(1), 1–12.

Gallage, C., Dareeju, B., Dhanasekar, M. (2013). State-of-the-Art: Track Degradation a Bridge Transitions.

In Proceedings of the 4th International Conference on Structural Engineering and Construction

Management (pp. 40–52). Kandy, Sri Lanka.

Hosseingholian, M., Froumentin, M., Levacher, D. (2009). Continuous Method to Measure Track Stiffness

A New Tool for Inspection of Rail Infrastructure. World Applied Sciences Journal, 6(5), 579–589.

Hunt, G. A. (2005). Review of the Effect of Track Stiffness on Track Performance. RSSB, Research Project

T372.

Karttunen, K. (2012). Mechanical Track Deterioration due to Lateral Geometry Irregularities. Licentiate

Thesis, Chalmers University of Technology, Göteborg, Sweden.

Larsson, D. (2004). A Study of the Track Degradation Process Related to Changes in Railway Traffic.

Licentiate Thesis, Luleå University of Technology, Luleå, Sweden. Le Pen, L., Watson, G., Powrie,

W., Yeo, G., Weston, P., Roberts, C. (2014). The Behaviour of Railway Level Crossings: Insights

Through Field Monitoring. Transportation Geotechnics. doi:10.1016/j.trgeo.2014.05.002

Li, M. X. D., Berggren, E. G. (2010). A Study of the Effect of Global Track Stiffness and Its Variations on

Track Performance: Simulation and Measurement. Proceedings of the Institution of Mechanical

Engineers, Part F: Journal of Rail and Rapid Transit, 224, 375–382. doi:10.1243/09544097JRRT361

López Pita, A. (2002). The Importance of Vertical Stiffness of the Track on High-Speed Lines. In

Transportation Research Board 81st Annual Meeting. 13-17 January, Washington D.C., Washington,

USA.

12

Lundberg, S., Lundberg, P., Persson, Å., Stensson, P. (2012). Measure Priority Study – Ore Transports

between the Kallak Mine and the Malmbanan Line. ÅF Infraplan.

Nielsen, J., Berggren, E. G., Lölgen, T., Müller, R., Stallaert, B., Pesqueux, L. (2013). Overview of Methods

for Measurement of Track Irregularities for Ground-Borne Vibration - Deliverable D2.5. Chalmers

University of Technology, Trafikverkt, DB, SBB, D2S International, Alstom, 1–49.

Optirail. (2013). D1.1. Knowledge Available on Maintenance Operations and Surveying Systems – High

Speed & Conventional Lines.

Puzavac, L., Popović, Z., Lazarević, L. (2012). Influence of Track Stiffness on Track Behaviour Under

Vertical Load. Promet - Traffic & Transportation, 24(5), 405–412.

Rodrigues, P. (2013). Análise e Modelação da Evolução de Defeitos Geométricos da Via Férrea - Caso de

Estudo da Linha do Norte Engenharia Civil Júri. MsC Dissertation, Instituto Superior Técnico,

Technical University of Lisbon, Lisbon, Portugal.

Schöch, W., Frick, A. (2007). Development of the Grinding Practice at Malmbanan. In IHHA Conference.

10-13 June, Kiruna, Sweden. Schöch, W., Frick, A., & Gustafsson, P. (2011). Research towards

Perfected Rail Maintenance at Malmbanan. In IHHA Conference, Calgary, Canada (pp. 1–8). 19-22

June, Calgary, Canada.

Sussman, T. R., Ebersöhn, W., Selig, E. T. (2001). Fundamental Non-Linear Track Load-Deflection

Behavior for Condition Evaluation. Transportation Research Record, 1742, 61–67.

Teixeira, P. F. (2003). Contribución a la Reducción de los Costes de Mantenimiento de Vías de Alta

Velocidad Mediante la Optimización de su Rigidez Vertical. PhD Dissertation, Escola Tècnica

Superior d’Enginyers de Camins, Canals i Ports de Barcelona, Polytechnic University of Catalonia,

Barcelona, Spain.

Tzanakakis, K. (2013). The Railway Track and Its Long Term Behaviour – A Handbook for a Railway Track

of High Quality (Vol. 2). Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-

36051-0

Woodward, P. K., Kennedy, J., Laghrouche, O., Connolly, D. P., Medero, G. (2014). Study of Railway

Track Stiffness Modification by Polyurethane Reinforcement of the Ballast. Transportation

Geotechnics, (Accepted Manuscript). doi:10.1016/j.trgeo.2014.06.005

Zufelt, J. E. (2013). ISCORD 2013: Planning for Sustainable Cold Regions. Proceedings of the 10th

International Symposium on Cold Regions Development, Anchorage, Alaska, (June 2-5, 2013)