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A comparison of railway track foundation design methods
Article in Proceedings of the Institution of Mechanical Engineers Part F Journal of Rail and Rapid Transit · March 2007
DOI: 10.1243/09544097JRRT58
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A Comparison of Railway Track Foundation Design
Methods
Date Written: January 2006.
Date of revision: May 2006.
Authors:
Dr. M. P. N. Burrow, MA, PhD;
Dr. D. Bowness, BEng, MSc, PhD;
Dr. G. S. Ghataora, B.Eng. PhD. MIMM, MILT, FMES
Position/Affiliation of Authors:
Dr. M. P. N. Burrow; Senior Research Fellow in the Department of Civil Engineering,
School of Engineering, the University of Birmingham.
Dr. D. Bowness; Senior Research Fellow in the School of Civil Engineering & the
Environment, University of Southampton.
Dr. G. S. Ghataora; Senior Lecturer in the Department of Civil Engineering, School of
Engineering, the University of Birmingham.
Contact Address of Lead Author: Railway Research Centre, Gisbert Kapp
Building, School of Engineering, University of Birmingham, Edgbaston,
Birmingham, B15 2TT.
Telephone: 0121 414 2626
Email: m.p.n.burrow@bham.ac.uk
Number of Words: 5, 900
Fax: 0121 414 3675
Number of Tables: 4
Number of Figures: 10
Key words: Subgrade, ballast, sub-ballast, trackbed layers, granular material,
design procedure, analytical design, material performance, resilient modulus
Abstract
One of the primary functions of the layers which make up the trackbed in a
conventional railway track system is to distribute the high wheel/rail contact forces so
that the stresses in the subgrade are of an acceptable level. To ensure that the
trackbed layers perform this task adequately, there are a number of design procedures
that may be used to calculate an appropriate thickness of the layers. This paper
describes and compares five such design procedures from the USA, UK, Europe and
Japan. The comparisons show that the design procedures give large differences in the
calculated layer thicknesses which are due to the design methodologies used in each
procedure. Consequently, to enable an appropriate design procedure to be adopted for
a given set of conditions it is necessary to have a thorough knowledge of the
methodologies employed together with their inherent assumptions.
1
INTRODUCTION
Conventional railway track combines a number of components, including the rail,
fastening system, sleepers, ballast and sub-ballast, in a structural system (Figure 1).
The structure should be designed to withstand the damaging effects of railway traffic
and climate so that the subgrade is adequately protected and that railway vehicle
operating costs, safety and passenger comfort are kept within acceptable limits during
the design life [1, 2].
The cumulative effect of repeated traffic loads is to deteriorate the track substructure
over time. However, whilst the ballast lends itself to periodic maintenance to adjust
track line and level, subgrade related problems are less easily rectified. Consequently,
a primary objective of design is to protect the subgrade and to this end the trackbed
layers (ballast and sub-ballast) should be of an appropriate thickness for the traffic
and subgrade conditions at hand. If they are of insufficient thickness then the large
train induced repetitive stresses in the subgrade are likely to cause excessive subgrade
deformation, significantly increasing maintenance requirements, whereas
unnecessarily thick trackbed layers will be inefficient in terms of construction and
maintenance costs [3].
The trackbed usually is composed of at least two distinct ballast and sub-ballast
layers. The ballast is crushed granular material, of uniform size, placed as the top
layer of the substructure in which the sleepers are embedded (Figure 1). The most
important functions it performs are; resisting vertical, lateral and longitudinal forces
applied to the sleepers to maintain track in its desired position; provision of resiliency
and energy absorption for the track; provision of drainage, reduction of traffic induced
stresses and facilitating maintenance operations [4]. The sub-ballast is a granular
layer between the ballast and the subgrade which also helps to reduce the traffic
induced stresses to acceptable levels and facilitates drainage. In addition, the subballast layer prevents interpenetration of the subgrade and ballast, prevents upward
migration of fine material emanating from the subgrade and helps prevent subgrade
attrition by ballast (see below) [4]. There are a number of design procedures for
determining appropriate trackbed layer thickness, including standards issued by
infrastructure operators and research published in the literature. As the structural
properties of the ballast and sub-ballast layers are similar such procedures usually
recommend a single thickness for the trackbed layers and the proportion of ballast and
sub-ballast is not specified. As the ballast is more expensive than the sub-ballast, it is
assumed that a minimum thickness of ballast, usually between 0.2 and 0.3 m, will be
used to facilitate maintenance operations which are carried out periodically to readjust
the line and level of the track.
This paper describes five such procedures and compares the calculated thicknesses for
a variety of conditions. The methods analysed are from the USA (a method proposed
by Li et al. [5]); Europe (The International Union of Railways standard UIC 719R
[6]); the United Kingdom (a method developed by British Rail Research [7] and the
current Network Rail code of practice [8]) and Japan (the West Japan Railway
Company standards for high speed and commuter lines [9, 10]).
1.1 Subgrade failure caused by repeated loading
The primary modes of traffic-induced deterioration in the subgrade are attrition by the
ballast (subgrade erosion), progressive shear failure (cess heave), an excessive rate of
settlement through the accumulation of plastic strain and massive shear failure (i.e.
where the weight of the train and track superstructure may cause the underlying
subgrade to shear) [4]. These modes are mostly associated with fine grained soils
such as clays. Problems due to subgrade attrition, progressive shear failure and an
excessive rate of settlement through the accumulation of plastic strain are associated
with the upper most part of the subgrade where cyclic shear stresses are likely to be at
their highest. Attrition arises when the ballast penetrates and wears away the
subgrade surface whilst progressive shear failure occurs where the cyclic stresses are
sufficiently high to cause the soil to be sheared and remoulded (Figure 2). An
excessive rate of settlement may cause ballast pockets to form (Figure 3) as a result of
the vertical component of shear deformation of the subgrade surface [4]. Water can
collect in the pockets further weakening the subgrade and possibly resulting in mud
pumping (wet spots). Attrition may be prevented using an appropriately thick subballast layer and progressive shear failure occurs at stress levels below that causing
massive shear. Therefore, foundation design methods should explicitly prevent
progressive shear failure and excessive plastic deformation. Several approaches may
be adopted to help prevent these failure modes including using non-ballasted track
forms, introducing an asphalt layer, increasing the flexural rigidity (EI) of the rail and
using techniques, such as soil stabilization, to permit higher stresses [11]. Usually
however, the use of appropriate thicknesses of the trackbed layers is likely to be
effective and economical [3]. Procedures which adopt the latter approach are the
subject of this paper and are described below.
2
DESIGN PROCEDURES
2.1 Li et al.
The method proposed by Li et al. [5] aims to prevent both progressive shear failure
and excessive plastic deformation. This is achieved by limiting the stresses in the
subgrade such that plastic strain is of an acceptable level. Subgrade stresses are
determined using an analytical model of the track system, whilst the allowable
stresses are determined from an equation that relates plastic strain to the number of
loading cycles. For design purposes the trackbed is considered as a single
homogenous granular layer.
2.1.1 Track Model
A three-dimensional, multilayered, elastic model known as GEOTRACK [4] was built
to determine the subgrade stress distribution under various traffic loadings. The
model simplifies the track substructure as a single granular layer overlying an
homogenous subgrade. To account for the increase in track loading that results from
track and vehicle irregularities, Li et al. suggest that dynamic loads should be used.
Where this information is unavailable, they prescribe the use of the following
empirical equation, suggested by the American Railway Engineering Association
(AREA), to modify static wheel loads:
K  1
0.0052  V
D
(1)
where K is the ratio of dynamic to static wheel loads, V is the train speed (km/h) and
D is the wheel diameter (m).
2.1.2 Subgrade performance
To determine allowable plastic strains and deformations under repeated loading,
cyclic load triaxial tests were conducted on various fine grained soils [12]. From
these it was found that the subgrade cumulative plastic strain (p) could be related to
soil deviator stress (d) and the number of repeated stress applications (N) as follows:
m
 
 p %   a d  N b
s 
(2)
where σs is the compressive strength of the soil and a, b and m are parameters
dependent on the soil type. Integrating over the depth of the deformable part of the
subgrade, the total cumulative deformation can be determined as:
T
    p dt
0
where T is the subgrade layer depth in metres.
(3)
For design purposes Li et al. suggest that p and  should be limited to 2 % and 25
mm respectively. These values are used for the comparisons described below.
2.1.3 Design Charts
Equations 2 and 3, together with GEOTRACK, were used to produce two sets of
design charts [5]. The first set of charts give a minimum thickness of the trackbed
layers to prevent progressive shear failure and are functions of trackbed layer and
subgrade resilient moduli (defined as the repeated deviator stress divided by the
recoverable (resilient) axial strain), soil type and traffic loading. The second set of
charts, which are additionally a function of subgrade depth, give a thickness of the
trackbed layers to prevent excessive plastic deformation.
2.2 The International Union of Railways method
UIC 719 R [6] is a set of recommendations for the design and maintenance of the
track substructure. Specifications are given for a single thicknesses of the ballast and
sub-ballast (i.e. trackbed layers) and for the prepared subgrade (Figure 4).
2.2.1 Basis for design
UIC 719 R specifies that the substructure may contain some or all of the following
layers: ballast; a granular sub-ballast; a geotexile; prepared subgrade (Figure 4).
The combined thickness of the granular layer (i.e. trackbed layers) is determined from
the type of soil forming the subgrade, traffic characteristics, track configuration and
quality and thickness of the prepared subgrade. No information is given on how the
individual thicknesses of the ballast and sub-ballast should be determined. The
prepared subgrade is the layer below the sub-ballast which has been treated to
improve its engineering properties. Its inclusion in the design is optional, unless the
subgrade requires improvement (see below). A geotexile may also be used.
2.2.2 Soil quality
The type of soil forming the subgrade is classified according to a simple system based
primarily on the percentage of fines in the soil. There are four quality classes of soil:
QS0, for soil that is deemed to be unsuitable without improvement; QS1, for “poor”
soils which are considered acceptable in their natural condition subject to adequate
drainage and maintenance, although improvement should be considered; QS2 for soils
of “average” quality and QS3 for soils which are considered to be “good”. Poorer
quality soils require thicker trackbed layers.
2.2.3 Traffic
To characterize the traffic using a line, UIC 719 R refers to UIC 714 [13]. UIC 714
classifies a particular line as a function of the tonnage hauled, tonnage of tractive
units, line speed, traffic mix (i.e. freight and/or passenger) and wear effects of
vehicles. According to the classification determined using UIC 714, lines which carry
faster and heavier traffic are required to have thicker trackbed layers.
2.3 British Rail method
British Rail research developed a method which sought to protect against subgrade
failure by excessive plastic deformation [7]. To this end, a series of design charts
were produced to relate the required thickness of the trackbed layers to a measure of
the strength of the subgrade known as the threshold stress. The charts were developed
by combining traffic induced subgrade stresses predicted from a linear elastic model
of the track system with soil threshold stresses determined by laboratory testing.
2.3.1 Track model
A single layer elastic model of the track, (i.e. the trackbed layers and subgrade are
treated as homogenous), was developed to predict the stress distribution in the
subgrade for various assumed sleeper spacings and contact pressures. Measurements
of stresses at a site on the UK’s East Coast Main Line were used to verify the model.
2.3.2 Subgrade performance
In order to determine a suitable material parameter for use in design, a series of cyclic
triaxial compression tests were performed on London Clay. The results of the tests
indicated the existence of a threshold stress, above which repeated load applications
cause large permanent deformations that increase exponentially with the number of
loading cycles. Below this threshold stress, the plastic strain associated with each
load cycle reduces until a stable condition is reached where the permanent
deformations are small.
2.4 Network Rail Code of Practice
Recommendations for the thickness of the trackbed layers on the UK network are
incorporated in a recent Network Rail code of practice, RT/CE/C/039 “Formation
treatments” [8]. The code recognises that the condition of the railway substructure
affects track geometry and maintenance requirements. Based on this premise, and
where track geometry has been adequate in the past without the need for excessive
maintenance, the code suggests that the subgrade possesses adequate strength and
stiffness. Where this has not been the case, the required thickness of the trackbed
layers can be determined from a chart given in the code.
2.4.1 Trackbed layers thickness chart
The chart relates the required thickness of the trackbed layers to undrained subgrade
modulus (or Young’s modulus) for three different values of the dynamic sleeper
support stiffness (30, 60 and 100 kN/mm/sleeper end). The values of the dynamic
sleeper support stiffness relate to minimum requirements for existing main lines both
with and without geogrid reinforcement and new track, respectively.
No technical details of how the chart was derived are given, although the document
states that it was “derived using a combination of empirical data and multilayer elastic
theory”.
2.5 West Japan Railways
West Japan Railways have issued construction and maintenance standards for
Shinkansen and commuter lines [9, 10]. The Shinkansen lines are of standard gauge
(i.e. 1435 mm) and are dedicated for high speed passenger trains operating at average
speeds of 200 km/h. The commuter lines on the other hand use a narrow gauge (1067
mm) and may carry mixed traffic. For both types of line the required depth of the
trackbed layers is given in Table 1 and the substructure is assumed to have a bearing
capacity (b) of 288 kPa and where it is less than this value ground improvement is
required. (Note a bearing capacity of 288 kPa equates to a compressive strength (s)
of approximately 112 kPa assuming a cohesion model plastic solution to a simple
strip footing where b = 2.57 s.).
3 METHODOLOGY
A comparison of the design methods was made by determining the combined
thickness of the trackbed layers specified by each method under a variety of
conditions relating to:

Subgrade

Axle load

Speed

Cumulative tonnage.
A summary of the factors accounted for in these comparisons is given in Table 2.
3.1 Subgrade
For the study, the subgrade was assumed to be a clay soil with a high percentage of
fines and of high plasticity and is typical of problematic soils in the UK. The
condition of the soil was represented by its resilient modulus and was assumed could
vary from 15 MPa to 100 MPa. As some of the procedures use measures of soil
condition other than the resilient modulus it was necessary to have a means of
determining the resilient modulus from these measures in order to be able to compare
the procedures. For the clay considered herein, an empirically founded relationship
between the resilient modulus, Es and the ultimate compressive strength (Li et al.’s
method), σs of the form Es  250  σs was used (see [4]). The threshold strength
(British Rail method) was related to the resilient modulus by assuming that it was
equal to the half of the compressive strength [4]. For the European Standard UIC 719
R guidelines relating the measure of soil quality used in the standard to any
engineering measures of soil performance, such as the resilient modulus or strength,
are not given. Rather, as described above, the guidelines relate the soil quality to the
percentage of fines in the soil and these suggest that a soil with more than 40 % of
fines (such as a clay) should be considered as a class QS1 type soil. Consequently, it
was assumed that the quality of the subgrade was class QS1 and that the subgrade had
not been prepared. The Young’s Modulus, necessary for the Network Rail Code, was
assumed to be equal to the resilient modulus, which is a more common means of
expressing the modulus of materials subjected to repeated applications of stress. For
the WJRC standard the subgrade was assumed to have been improved to the
minimum required bearing capacity of 288 kPa (see above).
Concerning the traffic loading, two different scenarios were considered. Both
assumed a mixture of 50 % freight and 50 % passenger traffic, the characteristics of
which were representative of a Class 66 locomotive pulling fully laden wagons
travelling at 125 km/h with axle loads of 250 kN, and a high speed locomotive-hauled
passenger train travelling with an axle load of 170 kN [14]. However, for one
scenario, the passenger train was assumed to travel at 200 km/h, and for the other at
300 km/h. These were considered to be representative of conditions on a main line in
the UK and a high speed line such as the Channel Tunnel Rail Link (CTRL)
respectively. Whilst Li et al.’s method and UIC 719 R account for mixed traffic the
other procedures do not. Consequently, for these procedures a train with a 250 kN
axle load travelling at 200 km/h and one at 300 km/h were used to represent the
traffic. A design life of 60 yrs was used with a design loading of 900 MGT (i.e. 15
MGT/yr for 60 years) as this is similar to that of the CTRL [15]. The results of the
study are shown in Figure 5. For the case of a passenger train travelling at 300 km/h
only the results using Li et al.’s procedure are shown as the thickness of trackbed
layers determined using the other four methods are the same for a passenger train
travelling at 200 km/h compared to one at 300 km/h.
3.2
Axle load
The axle load study was carried out for a design on a clay subgrade with a resilient
modulus of Es = 40 MPa and the results of the study are shown in Figure 6. The
relationships described above for the subgrade condition study were used to determine
the other required measures of soil strength. To simulate freight traffic, a train speed
of 125 km/h was chosen with axle loads varying from 140 kN to 350 kN, the latter
figure is just above the current 343 kN (35 tonnes) limit in the USA. As the current
axle load limit is 250 kN (25.4 tonnes) in the UK, for the British Rail and Network
Rail comparisons the load was limited to this value. The design life was chosen to be
60 yrs with a design loading of 900 MGT.
For the Network Rail procedure the desired dynamic sleeper end stiffness was
assumed to be 100 kN/ mm/sleeper end as this corresponds to a line speed greater
than 160 km/h [8]. The West Japan standards for commuter traffic were used in the
study as the chosen line speed was 125 km/h (cf. Table 1).
3.3 Speed
The study of design thickness with speed was made for a high speed locomotive with
a 170 kN axle load (this is similar to that of the Eurostar high speed trains operating
on the CTRL). The required thickness of the trackbed layers was determined for
speeds between 80 – 350 km/h (see Figure 7).
For the West Japan Railways design thicknesses appropriate to Shinkansen trains
were used for speeds above 200 km/h and those for commuter lines for all other
speeds. The subgrade conditions and design life were the same as those for the axle
load comparison described above.
3.4 Cumulative tonnage
The cumulative tonnage study used Class 66 locomotive pulling fully laden wagons
travelling at 125 km/h with axle loads of 250 kN and subgrade conditions as those for
the axle load comparison. The cumulative tonnage was varied from 30 MGT to 900
MGT with an assumed annual tonnage of 15 MGT/yr (Figure 8).
4 DISCUSSION
From the comparisons shown in figures 5 to 8 two general observations may be made:
1. For each comparison there is a large variation in the specified thickness of the trackbed
layers amongst the procedures.
2. The design thickness specified by each procedure is a function of at least one of the four
variables considered (subgrade resilient modulus, axle load, speed and cumulative
tonnage). However, only Li et al.’s method gives a variation in required thickness with
all of the variables.
The reasons for these differences, although complex, may be explained in part with reference to
the approach to design adopted. Each of the procedures have varying amounts of empirical and
analytical elements. In an analytical approach to design two main processes are combined [16].
In the first process, stresses, strains and deflections induced by traffic loading in the subgrade
are determined using an analytical model of the track system. In the second process critical, or
allowable, stresses, strains and deflections are determined, often from experimentation on the
subgrade soils. Induced stresses, strains or deflections, are compared with the allowable to
formulate the design. The approach is summarized in Figure 9.
The characterization of traffic
4.1.1 Axle loads
Traffic characterization requires the magnitude, frequency, configuration and duration of all
loads to be modelled. In terms of the magnitude of the wheel loads, both static and dynamic
components should be considered (see above) [4]. Research suggests that the dynamic
component is a function of speed, vehicle mass and sources of irregularity in the wheel, running
surface or vertical track geometry. Dynamic effects have been shown to increase significantly
track loading especially where vehicles which have out of round wheels are operating at high
speeds [17, 18]. Since the stresses transmitted to the subgrade, and therefore the strains and
deflections in the subgrade, are a function of the load, it may be expected that the thickness of
the trackbed layers specified by any procedure is a function of the axle load. For the static
component, it is evident for Figure 6 that this is the case for all of the procedures considered,
expect for the WJRC and Network Rail ones. Further, it can be seen from Figure 6 that even for
the four procedures which consider the static load as a design parameter, the thickness of the
trackbed layers recommended are not in close agreement. The reasons for this concern the
analytical models used and how these simulate the distribution of the train load through the
substructure as discussed in section 4.2.1.
Concerning the dynamic component, as it is a function of speed the comparison of thickness of
the trackbed layers with design speed (Figure 7) may be used to help determine whether
dynamic loading has been considered.
As described above, Li et al.’s method consider dynamic effects through equation 1. This is
reflected in Figure 7 which shows, for their method, that the thickness of the trackbed layers is a
continuous function of speed. However, the formula described by equation 1 is based on
empiricism and is believed to overestimate the dynamic increment (and therefore the required
thickness of the trackbed layers) at high speeds [15].
The recommended thickness of the trackbed layers determined using UIC 719 R, the Network
Rail standard and the WJRC standards are irregular functions of speed. For UIC 719R, the
increase in traffic loading with speed is taken into account using UIC 714 (see above) and for
the Network Rail standard higher speed lines are required to have a greater sleeper support
stiffness and consequently a greater thickness of the trackbed layers. As mentioned earlier, the
WJRC standard for commuter lines is not a function of speed however a thicker trackbed layer
is specified for the faster Shinkansen lines. Whether the requirement to increase the thickness
with speed, for both the Network Rail and WJRC procedures, is due to setting higher standards
of ride quality for high speed lines or whether its is because the procedures recognise that
damage to the subgrade increases with speed therefore necessitating thicker trackbed layers is
unclear.
In the British Rail method design thickness is not a function of speed. However, it was
recognised that dynamic loads should be considered and it was reported that work was being
undertaken to this end, although the results of this work were unavailable for incorporation in
the procedure when it was published.
4.1.2 Traffic mix
The traffic using a particular line may be a mixture of trains with different axle loads travelling
at different speeds and for design purposes it is important to consider the effect of this spectrum
of loads on the system. However, only the Li et al. and UIC 719R methods account for the
variation in loads which may occur, whilst the design of other procedures is based on the
consideration of a single axle load.
To account for the variation in traffic Li et al. convert the estimated spectra of wheel loads over
the design life to the number of repetitions of a single design load that causes an equivalent
amount of damage[19, 4]. UIC 719 R adopts the approach developed by the UIC [13] which
enables daily traffic to be represented in terms of a theoretical traffic load.
4.2 Analytical model and layer characterization
4.2.1 Analytical model
In an analytical design procedure it is assumed that the railway substructure can be modelled as
a system of elastic layers characterized by two properties, the elastic modulus and Poisson’s
ratio. The elastic modulus is usually taken to be the resilient modulus, and it may be determined
from laboratory tests on the materials, either directly, or from an analysis of the response
measured in situ [20]. Poisson’s ratio is usually estimated.
Three of the procedures state that an elastic model was used to formulate their designs. Li et
al.’s model consisted of separate trackbed and subgrade layers with stress state dependent
resilient modului. The model used to develop the British Rail procedure represented the
substructure by a single layer with a single value of resilient modulus, whilst the Network Rail
code used multilayer elastic theory. The effect of these models on thickness of the trackbed
layers may be seen with reference to Figure 5. This figure shows that whilst all three procedures
give similar functions of design thickness with resilient modulus, the thicknesses recommended
are not the same. The thickness of the trackbed layers given by British Rail is greater than for
the other two, partly because their single layer model neglects both the effect of the much higher
stiffness of the trackbed layers and also the changes in resilient modulus which occur with
loading. Given the limited information available about Network Rail’s model it is difficult to
determine whether the differences in design thickness in relation to other procedures given by
the Network Rail code are due to the model used or to other factors.
It is not known if models were used to formulate the specifications given by the UIC and WJRC,
however as mentioned previously it is believed that these standards are largely based on
empiricism.
4.2.2 Layer characterization
Since weaker subgrades can withstand lower stress levels, it would be expected that the
thickness of the trackbed layers recommended by a procedure is a function of the engineering
properties of the subgrade (Figure 5). This is the case for the Li et al., British Rail and Network
Rail procedures. However, it is not the case for the UIC 719 R and WRJC standards. As
mentioned above, the UIC 719 R design thickness is a function of the soil class which is related
to the percentage of fines in the soil. Using this system, two soils of different stiffness or
strength are classified as the same if the percentage of fines in each is similar. For the example
shown in Figure 5, even though the soil resilient modulus varies from 15 MPa to100 MPa,
according to UIC 719 R the soil is always classified as poor. Clearly this may be inappropriate
and it is notable that the recommended thickness of the trackbed layers obtained using UIC 719
R is the largest of the procedures for all four of the comparisons (figures 5 to 8). As described
previously, the WJRC recommendations are based on the requirement for the subgrade bearing
capacity to be greater than 288 KPa. However, this may result in an overly conservative design
when the bearing capacity is greater than this value.
4.3 Material performance
In an analytical approach to design it is necessary to determine a measure of material behaviour
which may be compared to the subgrade stresses, strains or deflections predicted by the
analytical model to formulate the design. For the procedures described here, Li et al. use plastic
strain and cumulative deformation (equations 2 and 3), UIC 719R a measure of soil “quality”,
the BR method uses threshold stress, the Network Rail code the Young’s modulus and the
WJRC a nominal subgrade bearing capacity.
Ideally these measures of performance should be determined by testing subgrade material under
conditions which match the field situation as closely as possible. The methods proposed by Li
et al., British Rail and Network Rail used repeated load triaxial tests. Such tests however, are
unable to replicate the rotation of the principal stresses which occur in the soil under traffic
loading [20, 21]. As a consequence, research suggests that the performance of many materials
may be overestimated resulting in the under design of the trackbed layers [21]. The effect of the
replication of principal stresses on material performance is the subject of on-going research in
this project.
The contrasting measures of material performance used by Li et al. and the British Rail
procedure are of particular interest. Li et al.’s procedure incorporates a model of material
fatigue under cyclic loading to determine allowable stresses and strains. Such models relate
subgrade deformation to the expected number of applications of load, using relationships of the
form of equation 2, and are widely used in the design of roads [2]. The British Rail procedure,
on the other hand, uses the threshold stress concept, which suggests that provided the stresses in
the subgrade are always less than the threshold stress, the subgrade may in theory undergo an
infinite number of load cycles before failure. Evidently, using the former approach it is
necessary to specify a design life, whilst for the latter it is not. This is demonstrated by Figure 8
which shows that the design thickness recommended by Li et al.’s method only is a function of
cumulative traffic (and therefore design life). The concept of threshold stress is not well
understood. However, its use in both railway and highway engineering is currently gaining
credence as more research is undertaken to better understand the concept [20].
4.4 Case studies
In the UK lines exist with a thickness of trackbed layers from less than 300 mm to 1000 mm or
more. For example the CTRL, whose trackbed layer design was based on UIC 719 together
with French TGV best practice, has a thickness of the trackbed layers (ballast + sub-ballast +
prepared subgrade) on ballasted sections approximately between 0.85 and 1 m [22]. The lower
thickness is for sections of the track where the subgrade is Folkestone sand and the upper
thickness for sections on heavily overconsolidated clay subgrades. In addition, for the sections
constructed on heavily overconsolidated clays subgrades, 0.65 m of the clay below the base of
the prepared subgrade was dug out and replaced with Folkestone sand sandwiched between
geotextiles. Since opening in September 2003 there have been no reported problems with the
substructure and it has been suggested that the interval between planned tamping and
realignment maintenance of every 3 yrs is increased [23]. This would therefore indicate that the
thickness of the trackbed layers on the CTRL is adequate.
The CTRL sections constructed on overconsolidated clays correspond approximately, in terms
of traffic loading and subgrade conditions, to the 300 km/h subgrade study (Figure 5) with a
compressive strength of 100 kPa [22]. Using these values and assuming a resilient modulus
value of 25 MPa (see section 3.1) the thickness of the trackbed layers determined from each
procedure are given in Table 3. From this table it may be seen that the trackbed layer
thicknesses recommended by the British Rail procedure is similar to UIC 719 R, although the
former was not produced with high speed lines in mind. Li et al.’s procedure on the other hand
gives a value greater then the UIC 719 R one by approximately 31 %, which may be attributed
in part to the use of the AREA equation (1) which it is believed may over estimate dynamic
wheel loading at very high speeds [15]. However, as mentioned above the overconsolidated
clay subgrade on the CTRL was replaced with sand, to a depth of 0.65 m, which is likely to have
somewhat larger compressive strength and resilient modulus values than the clay. Therefore, it
may be argued that a truer thickness of the trackbed layers for the CTRL built on the
overconsolidated clays is somewhere between 1 m and 1.65 m (i.e. 1 + 0.65 m), depending on
the engineering properties of the Folkestone sands and the thickness given by the Li et al.
procedure is within these limits. Network Rail’s procedure gives a smaller value than UIC 719
R by approximately 20 % and may suggest that the code may not be suitable for designing high
speed lines. A very low thickness, in comparison with UIC 719 R, is given by the WJRC
procedure but the subgrade would require improvement to achieve the required 288 kPa bearing
capacity (see section 2.5).
A further example is a mixed traffic line near Leominster in Herefordshire which has been
investigated for some time prior to and during the current project [24]. The trackbed layer
thickness varies along the site from approximately 900 to 1300 mm and has increased from its
original thickness over time due to continued ballast replacement. Sections of the site show
large amounts of deterioration and there is a need for frequent maintenance. The deterioration is
believed to be due to poor drainage causing localised softening; fines migration into the ballast;
heterogeneous dynamic sleeper support stiffness and consequent non-uniform track settlement
(see Figure 10). Lower bound estimates of the subgrade strength and resilient modulus values
found at the site are 100 kPa and 25 MPa respectively [22]. The design line speed for the
section concerned is 128 km/h (although there are speed restrictions in place) and the annual
tonnage at the site is approximately 6 MGT/yr. Using these values, and assuming 50 % of the
traffic is freight, the trackbed layer thicknesses recommended by the five procedures are given
in Table 4. It may be seen from this Table that the recommended thicknesses given by Li et al.
and UIC 719 R are similar, but the British Rail thickness is approximately 15 % greater than
these thicknesses and the Network Rail and WJRC recommendations are significantly lower.
The greater thickness given by the British Rail method may be attributed to their single layer
model of the track substructure which neglects the effect of the much higher stiffness of the
trackbed layer (see 4.2.1). All of the recommendations are less than, or at the lower end in the
case of the British Rail procedure, the 0.9 to 1.3 m trackbed layer thickness found at the site.
This would suggest that if the thickness of the trackbed layers is the sole consideration in
trackbed design then there should be no need for the excessive maintenance which has occurred.
However, the fact that there has been a large amount of maintenance illustrates that other factors
should be taken into account in any design process. These include appropriate drainage, the
prevention of subgrade attrition (through the use of a suitable sub-ballast layer) and the
necessity to ensure a uniform track stiffness (which as Figure 10 illustrates is not the case at
Leominster).
To better understand these factors as well as the relationship between the thickness of the
trackbed layers and track performance a number of sites are being monitored in this project,
including the CTRL. The sites monitored and the techniques used are described in a companion
paper [25].
5 CONCLUSION
This paper presented five different procedures which may be used to determine the thickness of
the trackbed layers for railway foundation design. For each procedure, comparisons were made
of the thickness as a function of subgrade condition, axle load, speed and cumulative tonnage.
The comparisons were made to reflect existing UK conditions and to enable extrapolation to
future traffic loading conditions. For all comparisons the procedures show a large variation in
recommended thickness of the trackbed layers and that for four out of five of the methods, the
thickness is not a function of all of the factors examined. Reasons for this were discussed with
reference to the approach to design adopted by the methods. This showed that Li et al.’s
procedure follows most closely an analytical methodology. The research presented has also
shown that there are a number of areas which require additional research. These include traffic
characterization, methods used to determine material properties to reflect accurately field
conditions, models used to specify material behaviour under repeated loading and the use of the
methods for heavier axle loads and faster speeds than those which currently occur on the UK
network.
Accordingly, it is hoped that this paper will help the reader to understand the scientific basis and
inherent assumptions of the five design procedures described and will assist in selecting and
modifying, where appropriate, any procedure to give an appropriate design for a given set of
conditions.
6 ACKNOWLEDGEMENTS
The financial support of the Engineering and Physical Sciences Research Council is noted with
gratitude. The authors are grateful to Mr Alan Stirling, Dr Nick O’Riordan (Arup), Professor
Chris Clayton and Dr Amanda Burrow for their advice and support.
7
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Track Formation Subgrade for High Speed Railways, Rail Technology for the Future,
ICE, London.
16. Ullidtz, P. (2002) Analytical tools for pavement design. Key note address, 8th
International Conference on Asphalt Pavements, Copenhagen, Denmark, August 2002.
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List of tables
Table 1: Required depth of trackbed layers for the West Japan Railway Company
Table 2: Factors accounted for in the design procedures reviewed.
Table 3: CTRL trackbed layer thickness.
Table 4: Leominster trackbed layer thickness.
List of figures
Figure 1: Simplified components of conventional ballasted railway track
Figure 2: Subgrade progressive shear failure (after [4])
Figure 3: Excessive subgrade plastic deformation (after [3])
Figure 4: Calculation of the minimum thickness of the track bed (after UIC, [6])
Figure 5: Variation in design thickness with subgrade condition
Figure 6: Variation in design thickness with axle load
Figure 7: Variation in design thickness with train speed
Figure 8: Variation in design thickness with cumulative tonnage
Figure 9: Analytical design (after [2])
Figure 10: Track stiffness at Leominster (after [24])
Tables
Table 1: Required depth of trackbed layers for the West Japan Railway Company
Line
Annual tonnage (MGT1/yr)
Shinkansen
10 ≤ MGT
10 > MGT
1
MGT stands for million gross tonnes.
Commuter lines
NA
Required trackbed
layer depth (mm)
300
250
200
Table 2: Factors accounted for in the design procedures reviewed.
Li et al.
from GEOTRACK
model used to
formulate their design
charts
Via GEOTRACK
UIC 719R
Yes
Rail section
Speed
Via GEOTRACK
by using a dynamic
axle load (can use the
AREA equation)
No
Yes
Annual tonnage
Yes
Cumulative tonnage
from annual tonnage
multiplied by the
design life
charts are provided
for different subgrade
types in terms of the
resilient modulus and
soil strength
Static axle load
Sleeper type, length
& spacing
Subgrade condition
NR Code 039
No – but 25.4 tonne
axle load limit on UK
network
WJRC
No
No
No
No
Via minimum
requirements for the
dynamic sleeper
support stiffness.
Also 125mph is
fastest speed on UK
network
No
No
crude variation –
Shinkansen has
greater depth than
commuter lines
Yes
BR Method
From an elastic model
– charts only go up to
an axle load of 24
tonnes
No difference in
stresses found for
sleeper spacings of
630–790 mm
No
No – field results
showed response was
quasi-static up to
100km/h, but could
be incorporated by
using a dynamic axle
load
No
No
No
No
Yes (using soil
quality determined
primarily from the
number of fines in the
soil)
Using a threshold
stress for the material
in question
Undrained subgrade
modulus or undrained
shear strength
Yes
for commuter lines
only
No
Bearing capacity of
subgrade assumed to
be 288kPa otherwise
ground improvement
must be carried out
Table 3: CTRL trackbed layer thickness.
Depth of trackbed layers (m)
Li et al.
UIC 719 R
British Rail
Network Rail
WJRC
1.31
1.001
0.97
0.79
0.302
1
Including prepared subgrade
2
Subgrade improvement required as bearing capacity of soil is likely to be less than the
minimum of 288 kPa (see section 2.5).
Table 4: Leominster trackbed layer thickness.
Depth of trackbed layers (m)
Li et al.
UIC 719 R
British Rail
Network Rail
WJRC
0.86
0.82
0.97
0.49
0.203
3
Subgrade improvement required as bearing capacity of soil is likely to be less than the
minimum of 288 kPa (see section 2.5).
Figures
Fastening system
Axle load
Concrete, wooden, or
steel sleeper
Rail
Ballast
Trackbed
layers
Sub-Ballast
Sub-structure
Subgrade
Figure 1: Simplified components of conventional ballasted railway track
Shearing and remoulding
of subgrade
Figure 2: Subgrade progressive shear failure (after [4])
Original subgrade surface
Subgrade
Ballast pocket
containing water
Figure 3: Excessive subgrade plastic deformation (after [3])
Figure 4: Calculation of the minimum thickness of the track bed (after [6])
0
Li et al. (200 km/h)
UIC 719 R
West Japan Railways
0.1
0.2
British Rail
Network Rail
Li et al. (300 km/h)
0.3
0.4
0.5
Thickness of trackbed layers (m)
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
15
25
35
45
55
65
75
85
95
Resillient Modulus (MPa)
Figure 5: Variation in design thickness with subgrade condition
0
Li et al.
UIC 719 R
West Japan Railways
Thickness of trackbed layers (m)
0.2
British Rail
Network Rail
0.4
0.6
0.8
1
1.2
1.4
140
190
240
290
340
Axle load (KN)
Figure 6: Variation in design thickness with axle load
0
0.1
Li et al.
British Rail
UIC 719 R
Network Rail
West Japan Railways
Thickness of trackbed layers (m)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
80
130
180
230
280
330
Speed (Km/h)
Figure 7: Variation in design thickness with train speed
0
0.1
Li et al.
British Rail
UIC 719R
Network Rail
West Japan Railways
Thickness of trackbed layers (m)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
100
200
300
400
500
600
700
800
900
Cumulative tonnage (MGT)
Figure 8: Variation in design thickness with cumulative tonnage
Traffic Characterization
Track Model
Predicted stresses and strains
Allowable stresses and strains
Predicted within acceptable?
Shearing and remoulding
of subgrade
Y
Y
Design too conservative?
N
End
Figure 9: Analytical design (after [2])
View publication stats
Mileage (Miles,Yards)
Figure 10: Track stiffness at Leominster (after [24])
839
849
860
871
882
893
904
915
926
937
948
959
970
981
992
1003
1014
1024
1035
1046
1057
1068
1079
1090
1101
1112
1123
1134
1145
1156
1167
1178
1189
1199
1210
1221
1232
1243
1254
1265
38m1276
Effective Stiffness (kN/mm/sleeper end)
95.00
85.00
75.00
65.00
55.00
45.00
35.00
25.00
15.00