KENTRACK: A RAILWAY TRACKBED STRUCTURAL DESIGN AND ANALYSIS PROGRAM

Jerry G. Rose, Ph.D., PE Professor of Civil Engineering

261 OH Raymond Building University of Kentucky

Lexington, Kentucky 40506-0281 USA jrose@engr.uky.edu

Bei Su, MSCE William B. Long, EIT Graduate Research Asst. in Civil Engineering Geotechnical Engineer

University of Kentucky US Army Corps of Engineers S016 OH Raymond Building 801 Broadway

Lexington, Kentucky 40506-0281 USA Nashville, Tennessee 37202-1070 USA beisu625@yahoo.com william.b.long@lrn02.usace.army.mil

KEYWORDS: hot mix asphalt underlayment, railroad trackbed support, trackbed structural design,

layer thickness, asphalt tensile strain, subgrade bearing capacity ABSTRACT:

The development and application of a layer elastic finite element computer program, KENTRACK, is described. The program is particularly applicable for the structural design of heavy axle load and high-speed trackbeds. The railroad trackbed is considered as a three-layer elastic system composed of ballast, sublayer, and subgrade. The sublayer can be composed of all-granular material or Hot Mix Asphalt (HMA). The wheel loads are transmitted to the layered system through rails, tie plates, and ties. The thickness design is governed by limiting the vertical compressive stress on the top of the subgrade to reduce permanent deformation. For designs incorporating HMA underlayment as a sublayer an additional limiting criteria can be determined; that being the horizontal tensile strain at the bottom of the HMA layer to prevent fatigue cracking. Excessive deformation of the subgrade is not desirable because it results in distortion of the track and requires frequent maintenance. Fatigue cracking of the HMA layer also is not desirable because it can result in infiltration of water and subsequent weakening of the subgrade. The effects of varying materials properties and layer thickness on the calculated stress and strain levels and the predicted life of the trackbed are presented in detail. Subgrade modulus, ballast/HMA thickness and axle load represent three variables that have significant effects on the predicted railroad trackbed service life. The method for measuring vertical pressures at various locations in the trackbed using earth pressure cells is described and typical values and presented for heavy axle loadings. The predicted values from the KENTRACK program and the measured trackbed values for similar conditions compare very favorably. The KENTRACK program provides the designer a rational method for designing trackbeds for various combinations of loadings and trackbed materials and layer thickness. The relative effects of varying loadings and trackbed materials and thickness also can be ascertained. A sample design sequence is presented.

INTRODUCTION Railroads have been in existence for over 170 years and during the period, train speeds, annual

gross ton-miles, and axle loads have increased significantly. On United States railroads, peak axle loads in common revenue service have increased to 36 tons. The 39-ton axle load is undergoing extensive research. To accommodate these changes, larger rails have been developed such as RE136 and RE140. Several types of premium ties are also used including the predominate wood tie, concrete tie and steel tie. Different types of fasteners are available to match the different types of ties. However, the other important track component, the traditional all-granular support layer, has changed very little except for ballast quality and thickness. Normally a subballast is included for new construction. During the past twenty years, several new trackbed designs and structures have been developed in different countries according to their transportation needs. In the United States, Hot Mix Asphalt (HMA) trackbeds have been developed mainly for freight lines to provide the heavy axle loads with strong support and reduced trackbed maintenance.

Inadequate trackbed support adversely affects track quality. Components of the railroad track structure are damaged resulting in deterioration of the track geometry. Currently, due to the complexity of the problem, it is still not clear the exact effect to track damage that different factors such as train speed, axle load and traffic volume impart to the structure. Most analyses in this field are based on existing experience. In fact, based on the experience achieved by United States railroads in the past twenty years, it is found that frequent track maintenance is necessary for heavy axle load rail lines (Lopresti, Davis and Kalay, 2002). Though frequently maintained, rapid deterioration of track geometry is still unavoidable especially when the track structure transverses weak soil areas.

To address this problem, HMA trackbeds have been developed and tested during the past twenty years. During this period, numerous test and revenue trackbeds using HMA have been built over many types of subgrades. Thickness of the HMA was purposefully varied. It has been shown that HMA trackbeds impart the following benefits to the track structure according to performance measurements acquired from test installations (Asphalt Institute, 1998):

♦ A strengthened track support layer below the ballast to uniformly distribute reduced loading stresses to the roadbed (subgrade); ♦ A waterproofing layer and confinement to the underlying roadbed that provides consistent load-carrying capability for track structures-even on roadbeds of marginal quality; ♦ An impermeable layer to divert water to side ditches, essentially eliminating subgrade moisture fluctuations; ♦ A consistently high level of confinement for the ballast so it can develop high shear strength and provide uniform pressure distribution; ♦ A resilient layer between the ballast and roadbed to reduce the likelihood of subgrade pumping without substantially increasing track stiffness; and, ♦ An all-weather, uniformly stable surface for placing the ballast and track superstructure. Based on above advantages, HMA trackbeds are not only ideal for freight railroad lines, but also

are equally applicable for light rail, commuter and high-speed passenger rail. These lines require tight adherence to track geometric standards. Currently, two types of HMA trackbed designs have been used. One is called “underlayment” because the asphalt is used as a mat or a sublayer between ballast and subgrade instead of all-granular subballast. The other one is called “overlayment” or “full depth” because the asphalt mat is placed directly on the subgrade and ties are placed directly on the top of asphalt. There is no ballast layer. Figure 1 depicts the traditional all-granular ballast trackbed and the two types of HMA trackbeds.

In practice, the underlayment design is preferred by engineers. This is because the underlayment design maintains the ballast within the structure so the track geometry can be easily adjusted. Besides, asphalt underlayment is maintained in a protected environment because it is buried under the ballast which provides protection to asphalt such as avoiding sunlight and keeping temperature variance in a

low level. Due to the these reasons, only underlayment is documented in this paper. Figures 2a and 2b contain typical views of HMA underlayment trackbeds.

All-Granular Ballast Trackbed

subgrade

ballast

wood tie

subballast

Overlayment HMA Trackbed

subgrade

HMA

wood tie

Underlayment HMA Trackbed

subgrade

HMA

wood tie

Figure 1 Sections of Three Types of Trackbed Designs

Figure 2a Placing an HMA Underlayment on Subgrade during the Construction of a Second Track next

to an Existing Ballast Track

Figure 2b Exposed HMA Underlayment in Trackbed with Ballast and Wood Tie Track

BACKGROUND

There are two methods for analyzing the relationships between railroad trackbed thickness and stress distribution. One of the methods is based on a simplified theoretical method such as Boussinesq elastic theory. It assumes the foundation is composed of an ideal material that is elastic and isotropic and is semi-infinite in thickness. It is also called single layered theory. The other method involves using

empirical equations which are based on experience. Presently, two equations are widely used and accepted for railroad trackbed structural analysis and design (Selig and Waters, 1994). They are the Japanese National Railways (JNR) equation and the Talbot equation.

The reasons for developing a new design method for HMA and ballast trackbeds are summarized as follows:

(1) The Boussinesq method only considers one layer under the tie; whereas the HMA trackbed and all-granular (containing ballast and subballast) trackbed are typical multi-layered systems. The properties of materials used in different layers vary greatly, which does not meet the assumption of Boussinesq theory. Even using highly simplified consideration, in which the ballast, HMA, and subgrade are combined as one layer and assigned a proper parameter, it is still not feasible, because HMA is a typical visco-elastic, temperature dependent material whose properties are significantly affected by the environment.

(2) The existing design equations were developed based on the all-granular all-ballast trackbed. Due to the different properties of ballast and HMA trackbeds, the application to current design is not appropriate.

(3) The JNR equation was developed based on tests performed on narrow gage railroad lines. There is some question as to whether it is applicable for standard gage railroad lines.

(4) The Talbot equation was derived from laboratory tests (Talbot, 1919). The test trackbed was built by putting the ballast on the sand cushion over the laboratory floor and setting the pressure cells in the ballast at different levels. A universal machine added load on the rail, and the pressures distributed in the ballast were recorded by cells. An equation relating the pressure to the thickness of the ballast was obtained from the test data. Since the test data was developed for ballast trackbeds, the application of this equation for HMA trackbeds is not valid. This method even has limitations when used for ballast trackbed design. The test was performed on the laboratory floor, which was composed of concrete, so the support for the test trackbed was very stiff. The subgrade modulus factor is not considered in the equation. However, the typical track subgrade (support) is resilient in practice, which has a significant effect on the stress distribution in the trackbed. This implies that the pressures calculated by this equation will lead to under-design in soft subgrade conditions and will be too conservative in strong subgrade conditions.

To address the deficiencies in the existing design methods, two computer programs intended for railroad track structure analysis were developed in the United States. These are ILLITRACK (Robnett, 1975) and GEOTRACK (Chang, 1980).

ILLITRACK is a computer program developed by the University of Illinois by using finite element method. It was developed for all-granular ballast trackbed and only contains longitudinal and transverse two-dimensional models. However, the actual trackbed is three-dimensional. This program can be considered as using a two-dimensional model to simulate a three dimensional situation.

GEOTRACK is a computer program developed at the University of Massachusetts. It uses multi-layered theory and a three-dimensional model for the trackbed. This model divides the trackbed as five layers and cannot be modified by the user. They are ballast, subballast, subgrade 1, subgrade 2 and bedrock. It can be used only for the analysis of all-granular ballast trackbeds and is not applicable to HMA trackbeds and slab trackbeds.

Therefore, it is necessary to develop a scientific rational analysis procedure to determine the stress distribution for both HMA and ballast trackbeds. The KENTRACK computer program was developed for this purpose. COMPUTER PROGRAM THEORY

A structural design computer program, KENTRACK, was developed for analyzing railroad trackbeds by the Department of Civil Engineering, University of Kentucky in early 1980s (Huang, Lin, Deng and Rose, 1984). Recently, this program has been modified from a previous version that utilized a Disk Operating System (DOS). The modification permits the user to change various properties of the

track structure much easier than previously when values were entered by DOS. A user-friendly Window’s based interface, Graphical User’s Interface, containing four descriptive forms (or screens), allows the user the option to enter varying values for the track structure components. Finite Element Method

Typically, the railroad track structure consists of rail, fastener, tie and a multi-layered support system from top to bottom, as shown in Figure 3. Among them, the multi-layered support system consists of trackbed, subgrade and bedrock. The trackbed is normally composed of two layers ---- the top one is ballast or slab, and the bottom one is granular material such as subballast or bound material such as asphalt mix. When several loads are applied to the rail, the stress, strain and deflection of rail and tie can be obtained by superimposing the effect of each load.

layer 4 bedrock

layer 3 subgrade

layer 2 sublayer

layer 1 ballast

Beam Element

Spring

Symmetry Line

Tie

Rail

Figure 3 Sketch of Railroad Track Model

When calculating the stress and strain of rails and ties, the finite element method is employed.

Rail and tie can be classified as beam elements and the spring element is used to simulate the tie plate and fastener between rails and ties. The finite element equation and stiffness matrix of the beam element can be written as following:

=

−

−

−

yj

j

yi

i

yj

j

yi

i

MP

MP

w

w

lEISymmetryl

EIlEI

lEI

lEI

lEI

lEI

lEI

lEI

lEI

θ

θ

4

612

264

612612

23

2

2323

where, E is Young’s modulus, I is moment of inertia of beam, is the distance of beam between nodes i and j, w

li is vertical deflection at node i, θyi is rotation about y axis at node i, Pi is the vertical force

applied at node i, and Myi is moment about y axis at node i. For one dimensional spring element, the stiffness matrix can be written as following:

=

−

−

j

i

j

i

ss

ss

PP

ww

kkkk

where, ks is spring constant. After calculation, the stress beneath ties can be determined. However, due to the necessity of the

multi-layered theory, the stresses are simplified as intent circular loads. The radius of this circle is obtained by using the contact area of one tie, A, divided by the total numbers of elements, m. This process was shown in Figure 3. Multi-layered System

For KENTRACK, only four layers are used ---- ballast, subballast or HMA, subgrade soil and bedrock ---- from top to bottom. Following is a brief introduction to this system. The details of multi-layered system solution method can be found in a related reference (Y. H. Huang, 1993).

The general equation for multi-layered system is as follows:

)1)(1( 2

2

2

2

2

2

2

24

zrrrrrrr ∂∂

+∂∂

+∂∂

∂∂

+∂∂

+∂∂

=∇σσσσσσσ

By using this general equation, the stresses in vertical, tangential and radial directions, the shear stresses, and the strains (displacements) in radial and vertical directions can be expressed and calculated. However, these values are not the actual stresses and displacements due to a uniform load q distributed over a circular area. To find the actual stresses and displacements under a uniform load distributed over a circular area, Hankel transform method should be used. Then the results obtained from the above equations can be converted to actual stresses and displacements by using the following equation:

∫∞

=0 1

*

)( dmHmaJ

mR

HqaR

where, R* is the stress or displacement due to the loading which can be expressed as –mJ0(mα); R is the stress or displacement due to load q; J is Bessel function and m is a parameter. Material Properties

An HMA railroad trackbed is composed of three different materials. They are ballast, HMA and subgrade soil. Although all of them are considered as elastic materials, different kinds of numerical equations are used to describe them due to their different inherent properties.

Ballast can be considered as either a non-linear or linear material. When a railroad trackbed is recently constructed and has not been compacted, ballast always behaves non-linearly. In this case, the constitutive equation for calculating the resilient modulus of granular material is governed by the following two equations:

21

KKE θ= )21( 0321 Kz ++++= γσσσθ

where, E is the resilient modulus; K1 and K2 are the coefficients; σ1, σ2 and σ3 are the three principle stresses; γ is the unit weight of material and K0 is lateral stress ratio.

If the trackbed has been used for a period and the ballast has become compacted, it is more reasonable to use the linear model rather than the nonlinear model for calculating the resilient modulus. In this case, the above equations are still applicable by setting K2 equal to 0.

HMA is a temperature dependent material. Its dynamic modulus can be calculated by using the method developed by the Asphalt Institute (Hwang and Witczak, 1979). Note that different temperatures should be used for different months or seasons.

Subgrade soils are always considered as linear elastic materials regardless of the type. However, the program permits using different kinds of soil to composite the total subgrade with different Poisson’s ratios and elastic modulus values. In the bottom layer, the program will consider it as an ideal material --- bedrock --- which has an infinite elastic modulus (incompressible) and 0.5 for Poisson’s ratio. Damage Analysis

To predict the service life of the railroad trackbed, a prediction function has been integrated into the program based on the Minor linear damage analysis criteria. The design life can be determined by the following equation:

∑=

=n

i da

p

orNNN

L

1

1

where L is design life in years, Np is predicted number of repetitions during each period, Na and Nd are allowable number of repetitions during each period, and n is the time period (1 = year, 2 = half year, 4 = season, and 12 = month).

Note that in the above equation, two failure criteria are employed due to the different properties of materials. For HMA, it is the tensile strain on the bottom of asphalt that controls asphalt life to prevent excessive cracking. For subgrade soil, it is the vertical deformation that controls subgrade life to prevent excessive deformation which is determined to maintain adequate track geometry. The service life of track structure is governed by the lesser one, either tensile failure of the HMA layer or vertical permanent deformation of the subgrade.

To determine the number of repetitions of HMA to failure (Na), the following equation is used from Asphalt Institute (Asphalt Institute, 1982):

853.0291.30795.0 −−= ata EN ε where εt is horizontal tensile strain at the bottom of the asphalt, and Ea is elastic modulus of asphalt in psi. The relationship was developed for asphalt layers in highway pavement environments and loading conditions, which is much more stringent than in railroad trackbed.

To determine the number of repetitons of subgrade to failure (Nd), following equation is used (Huang, Lin, Deng and Rose, 1984):

583.3734.3510837.4 −−−×= scd EN σ where σc is vertical compressive stress on the top of subgrade in psi, and Es is subgrade modulus in psi. METHODOLOGY

In order to develop a rational structural design method for railroad trackbeds, it is necessary to understand the effects of the various track components to trackbed performance. A typical HMA rail track section shown in Figure 4a is used. Also, a traditional all-granular railroad trackbed, shown in Figure 4b, is also evaluated for performance comparison with the HMA trackbed. Note that the components and factors used in both of the models are the values for a typical trackbed. When the analysis is performed for determining different values, these values may be changed.

Tables 1a and 1b record all the constant and variable trackbed components and factors used in this evaluation. The inputting parameters are also recorded in this table. Damage analysis is performed by season. Note that the temperatures used here for each season are the average temperatures for a moderate climate. When designing railroad trackbeds in frigid or tropical zones, lower or higher temperature value should be used.

axle load = 36 ton

rail = RE132

200 in. thick

subgrade modulus = 12,000 psi

6 in. thick

subgrade

HMA layer

wood tie

ballast layer

8 in. thick

Figure 4a Section of HMA Trackbed

rail = RE132

axle load = 36 ton

10 in. thick

ballast layer

wood tie

subballast layer

subgrade

4 in. thick

subgrade modulus = 12,000 psi

200 in. thick Figure 4b Section of All-granular Ballast Trackbed

Table 2 contains the standard design parameters for typical HMA and all-granular ballast

railroad track structures used in United States. These standard values were used in the KENTRACK program. Note that provisions are included for replacing standard wood ties with concrete ties. Also, the combined thickness of ballast plus HMA (for HMA trackbed) and ballast plus subballast (for ballast trackbed) are maintained at 14 inches.

The critical outputs for examples 1 and 2 are listed in Table 3. They are subgrade vertical compressive stress, HMA horizontal tensile strain (valid only for HMA trackbed), predicted service life of subgrade and predicted service life of HMA (valid only for HMA trackbed). The advantage of the HMA trackbed can be noted. It induces lower vertical compressive stress (11.8 psi) on the top of the subgrade compared with all-granular trackbed (13.6 psi). This results in a predicted 133% increase in subgrade service life for the HMA trackbed.

Table 1a Details of Components and Factors that Remain Constant Parameter Name Parameter Values

Wheel Load (pound force) Two@36000

Distance between Loads (inch) 70

Tie Spacing (inch) 20

Tie Dimension (inch) 102×7×9 (length×thickness×width)

Ballast Modulus (psi) 47000

Subballast Thickness (inch) 4

Subballast Modulus (psi) 20000

Poisson’s Ratio for Subballast 0.35

Poisson’s Ratio for HMA 0.45

Volume of Voids for HMA(%) 5.7

Temperature for HMA (°F)

50 (spring) 63 (summer) 37 (autumn)

20 (winter)

HMA Modulus (psi)

698000 (spring) 372000 (summer)

1250000 (autumn) 2260000 (winter)

Volume of Bitumen for HMA (%) 13.5

HMA Viscosity at 70 °F (poise) 2500000

Subgrade Thickness (inch) 200

Poisson’s Ratio for Subgrade 0.4

Poisson’s Ratio for Bedrock 0.5

Traffic Volume (MGT) 32

Table 1b Details of Components and Factors that Vary

Parameter Name Parameter Values

Rail Size RE100, RE115, RE132, RE140

Fastener Type Spike

Poisson’s Ratio for Ballast 0.35 (after compact) 0.25 (before compact)

Ballast Thickness (inch) 6, 8, 10, 12

HMA Thickness (inch) 4, 6, 8

Subgrade Modulus (psi) 3000, 12000, 21000, 30000

Table 2 Standard Design Parameters for HMA and Ballast Trackbeds Parameter Name HMA Trackbed Ballast Trackbed

Rail Size RE132

Tie Type (Fastener Type) Wood Tie (Spike)

Tie Spacing (inch) 20

Tie Dimension (inch) 102×7×9 (length×thickness×width)

Ballast Modulus (psi) 47000

Poisson’s Ratio for Ballast 0.35 (after compact)

Ballast Thickness (inch) 8 10

Subballast Thickness (inch) N/A 4

Poisson’s Ratio for Subballast N/A 0.35

HMA Thickness (inch) 6 N/A

Poisson’s Ratio for HMA 0.45 N/A

Temperature for HMA (°F)

50 (spring), 63 (summer), 37 (autumn), 20 (winter)

N/A

HMA Modulus (psi)

698000 (spring) 372000 (summer)

1250000 (autumn) 2260000 (winter)

N/A

Volume of Voids for HMA (%) 5.7 N/A Volume of Bitumen for HMA

(%) 13.5 N/A

HMA Viscosity at 70 °F (poise) 2500000 N/A

Subgrade Modulus (psi) 12000

Subgrade Thickness (inch) 200

Poisson’s Ratio for Subgrade 0.4

Poisson’s Ratio for Bedrock 0.5

Traffic Volume (MGT) 32

Table 3 Critical Outputs for Wood Tie Track (Standard HMA and Ballast Trackbeds)

Item Standard HMA

Trackbed (Figure 4.1)

Standard Ballast Trackbed

(Figure 4.2) Subgrade Vertical Compressive

Stress (psi) 11.8 13.6

HMA Tensile Strain (in./in.) 1.58×10-4 N/A Predicted Service Life of Subgrade

(year) 14 6

Predicted Service Life of HMA (year) 29 N/A

It should be noted that subgrade failure of a trackbed, due to overstressing of the subgrade

normally results in settlement of the subgrade and a depression in the track surface profile. This depression can be easily corrected by adding additional ballast and raising (pulling) the track to its original and desired elevation.

Failure of a highway pavement subgrade, however, is a more severe situation. It normally results in settlement of the pavement structure and fatigue cracking of the HMA. These conditions are not easily corrected and either one is considered as a definite failure of the pavement. The failure criteria utilized in the KENTRACK program was developed based on highway loading conditions and environments.

The actual subgrade service life for an HMA trackbed is likely to be much greater than the predicted service life indicated in Table 3 for two reasons. The first reason is due to the inherently lower subgrade stress level in the HMA trackbed. This fact is partially reflected in the Table 3 predicted service lives for HMA and all-granular ballast trackbeds. The KENTRACK failure mechanism for subgrade is due to repeated loading and fatigue of the subgrade. Therefore, the lower subgrade stress level on the HMA trackbed accounts for a predicted increase in service life for the HMA trackbed.

However, since a failure (settlement) of a railroad trackbed subgrade is not as significant relative to a highway subgrade, the actual service life of a railroad subgrade is likely to be much longer even before it needs significant maintenance or rehabilitation. Therefore, the predicted service lives in Table 3 can be considered conservative for railroad applications.

The second reason is that normally the settlement of a trackbed is due to weakening or softening of the subgrade due to water infiltrating the structure. This is very common for the all-granular (open) ballast trackbed.

However, the HMA trackbed provides an impermeable layer to shield the subgrade from water infiltration from the top. This type of trackbed is less likely to be adversely affected by weak or soft subgrades.

Previous studies (Rose, Brown & Osborne, 2000) have revealed that moisture contents of subgrades in HMA trackbeds remain very close to optimum. This provides for maximum strength and load carrying capacity throughout the life of the trackbed. Therefore, it is likely that an HMA trackbed will have a significantly longer actual service life than an all-granular trackbed that is subjected to varying moisture contents of the subgrade. The source of the varying moisture could be rainfall percolating through the granular material or fluctuations in ground water table. EFFECT OF AXLE LOAD AND SUBGRADE MODULUS

In the design and analysis of a railroad trackbed structure, the imposed axle loads cannot be neglected. It is considered as the very significant external factor. In this paper, the 36-ton axle load has

been considered as the standard design value. However, in the United States, 33-ton axle loads are also very common on many freight railroad lines and 39-ton axle loads are undergoing research and testing.

It is desirable to evaluate the performance of trackbeds under these varying axle loads. Two types of track structures were evaluated; the HMA trackbed shown in Figure 4a and ballast trackbed shown in Figure 4b. However, the axle load was varied from 33 to 39 tons. However, since subgrade modulus is believed to have a major influence on the predicted performances of both HMA and all-granular ballast trackbeds, the effects of four different subgrade moduli were evaluated. The moduli were 3000 psi for weak subgrade, 12000 psi for normal subgrade, 21000 psi for good subgrade and 30000 psi for excellent subgrade. Analytical results are shown in Figures 5a and 5b for subgrade vertical compressive stress, Figure 6 for HMA tensile strain, Figures 7a to 7c and Table 4 for predicted service lives of HMA and subgrades in HMA and all-granular ballast trackbed.

Figures 5a and 5b show the effects of different axle loads and subgrade moduli on the subgrade vertical compressive stress for HMA and All-granular ballast trackbed. It is obvious that the heavier axle load results in larger subgrade vertical compressive stress for both the HMA trackbed and all-granular ballast trackbeds. The stress increases by about 19% as the axle load increases from 33 to 39 tons for a given subgrade modulus.

According to Figures 5a and 5b, it can be noted that subgrade modulus has a major effect on the subgrade vertical compressive stress for both HMA and all-granular ballast trackbeds. Higher subgrade moduli, which represents strong subgrade, results in higher subgrade vertical compressive stress. For example, in HMA trackbed, when axle load are 33 ton and 39 ton respectively, the subgrade vertical compressive stresses increase 92% and 96% as the subgrade modulus increases from 3000 psi to 30000 psi.

Also from these two figures, for the same axle load and subgrade modulus, the subgrade vertical compressive stress in HMA trackbed is lower than that in all-granular ballast trackbed. For example, when axle load is 33 ton and the subgrade modulus is 3000 psi, the subgrade vertical compressive stress in all-granular ballast trackbed is 13% higher than that in HMA trackbed. For 39 ton axle load and 30000 psi subgrade modulus, it is 12% higher. This also illustrates that HMA trackbed can decrease the subgrade vertical compressive stress thus increase the service life of subgrade.

Figure 6 shows the effects of different axle loads and subgrade moduli on the HMA tensile stain. The heavier axle loads produce larger deformations of the HMA layer. Thus the HMA tensile strain increases slightly as the load increases.

Figures 7a to 7c and Table 4 show the effects of different axle loads and subgrade moduli on the predicted service lives of HMA and subgrade in HMA trackbed and all-granular ballast trackbed.

Since both of the subgrade vertical compressive stresses and the HMA tensile strain increase as the axle load increases, the predicted life of HMA and subgrade decreases. The decreases are significant. For example, as the axle load increases from 33 to 39 ton, the subgrade life in the HMA trackbed and in the ballast trackbed are both reduced by about 50%.

Another interesting finding in Figure 7 is that, in HMA trackbed and for the same subgrade modulus, even under 39 ton axle load, the predicted HMA subgrade service life is longer (0.3, 10, 43, 103 years for subgrade modulus equals 3000, 12000, 21000, 30000 psi respectively) than it would be in an all-granular ballast trackbed (0.3, 8, 35, 93 years for subgrade modulus equals 3000, 12000, 21000, 30000 psi respectively) under 33 ton axle load. This is another indication that the HMA trackbed is superior to the all-granular ballast trackbed, assuming the subgrade modulus values are equal. In addition, based on findings discussed previously, the subgrades in HMA trackbeds remain at optimum moisture and strength (modulus). This implies that HMA trackbeds will provide even longer service lives than those predicted by the KENTRACK program.

Table 4 contains the predicted service lives for HMA and ballast trackbeds having various subgrade moduli. The effect of increasing axle load is obvious. The predicted service lives are reduced by about 50% as the axle load is increased from 33 to 39 tons.

7.26 7.88 8.49

10.8611.85

12.8512.4313.61

14.7813.98

15.3216.66

0

6

12

18

24

33 36 39

Axle Load (ton)

Sub

grad

e V

ertic

al C

ompr

essi

veS

tress

(psi

)

subgrade modulus = 3000 psisubgrade modulus = 12000 psisubgrade modulus = 21000 psisubgrade modulus= 30000 psi

Figure 5a Effects of Axle Load and Subgrade Modulus on the Subgrade Vertical Compressive Stress in HMA Trackbed

8.21 8.94 9.68

12.4913.64

15.1614.3715.73

17.0915.61

17.1218.63

0

6

12

18

24

30

33 36 39

Axle Load (ton)

Sub

grad

e V

ertic

al C

ompr

essi

veS

tress

(psi

)

subgrade modulus = 3000 psisubgrade modulus = 12000 psisubgrade modulus = 21000 psisubgrade modulus = 30000 psi

Figure 5b Effects of Axle Load and Subgrade Modulus on the Subgrade Vertical Compressive Stress in All-granular Ballast Trackbed

2.672.93

3.18

1.431.58 1.72

1.08 1.19 1.30

0.91 1.00 1.10

0

1

2

3

4

5

33 36 39

Axle Load (ton)

HM

A T

ensi

le S

train

x10

-4 (i

n./in

.)subgrade modulus = 3000 psisubgrade modulus = 12000 psisubgrade modulus = 21000 psisubgrade modulus = 30000 psi

Figure 6 Effects of Axle Load and Subgrade Modulus on HMA Tensile Strain

0

50

100

150

200

33 36 39

Axle Load (ton)

Pre

dict

ed S

ervi

ce L

ife (y

ears

) subgrade modulus = 3000 psisubgrade modulus = 12000 psisubgrade modulus = 21000 psisubgrade modulus = 30000 psi

Figure 7a Effects of Axle Load and Subgrade Modulus on the Predicted Service Life of HMA in HMA Trackbed

0

50

100

150

200

250

33 36 39

Axle Load (ton)

Pre

dict

ed S

ervi

ce L

ife (y

ears

)

subgrade modulus = 3000 psisubgrade modulus = 12000 psisubgrade modulus = 21000 psisubgrade modulus = 30000 psi

Figure 7b Effects of Axle Load and Subgrade Modulus on the Predicted Service Life of Subgrade in HMA Trackbed

0

25

50

75

100

33 36 39

Axle Load (ton)

Pre

dict

ed S

ervi

ce L

ife (y

ears

) subgrade modulus = 3000 psisubgrade modulus = 12000 psisubgrade modulus = 21000 psisubgrade modulus = 30000 psi

Figure 7c Effects of Axle Load and Subgrade Modulus on the Predicted Service Life of Subgrade in All-granular Ballast Trackbed

Table 4 Effects of Axle Load on Predicted Service Life of HMA and Subgrade for HMA and All-granular Ballast Trackbed HMA Trackbed

(8 in. ballast, 6 in. HMA)

Ballast Trackbed (10 in. ballast,

4 in. subballast) Subgrade Modulus

(psi)

Axle Load (ton) HMA Life

(year) Subgrade Life

(year) Subgrade Life

(year) 33 5 0.5 0.3 36 4 0.4 0.2 3000 39 3 0.3 0.15 33 39 19 8 36 29 14 6 12000 39 22 10 4 33 93 82 35 36 67 59 25 21000 39 50 43 18 33 163 199 93 36 118 141 66 30000 39 88 103 48

EFFECTS OF HOT MIX ASPHALT THICKNESS

Hot mix asphalt is a common civil engineering material that has been used as a highway paving material since the early 1900s. During the past twenty years it has been introduced to the railroad industry as underlayment material for use instead of an all-granular subballast layer. For a normal ballast trackbed, the subballast often is embedded into or mixed with the subgrade soil due to the compaction acting of loads. When water infiltrates the trackbed, ballast pockets develop. This speeds up the attrition of subgrade soils and reduces subgrade bearing capability. Railroad engineers have been perplexed by this problem for a long time. However, using HMA as the sublayer can solve this problem due to the inherent properties of the asphalt layer.

To evaluate the effects of different HMA thicknesses on the track performance, a typical HMA trackbed model shown in Figure 4a is used. The total trackbed thickness (ballast thickness plus HMA thickness) is 16 inches and the HMA thickness varies from 4 inches to 6 inches to 8 inches. To simulate the different types of roadbeds, subgrade modulus is set as 3000 psi for poor support, 9000 psi for normal support, 15000 psi for good support, 21000 psi for strong support and 27000 psi for excellent support. Test results can be found in Figures 8 and 9 and service life predictions can be found in Table 5.

From Figure 8, it can be found that for thicker HMA trackbed, the pressure on the top of subgrade is less than that for thinner HMA trackbed. Increasing HMA layer thickness lowers the pressure transmitted to the subgrade, thus the subgrade service life will increase. Although using thicker HMA can increase track modulus, therefore protecting subgrade (very important for weak subgrade soils), it also increases the tensile strain on the bottom of HMA as noted in Figure 9. Note that generally, for weak subgrades, the subgrade fails earlier than the HMA layer. So in this case, it is desirable to use thicker HMA layer to reduce the pressure on the top of the subgrade. But for stronger subgrades, since subgrade soil has a higher bearing capability, it will last longer than HMA layer. So the thickness of asphalt should be reduced to increase the service life of HMA.

6

8

10

12

14

16

3000 9000 15000 21000 27000

Subgrade Modulus (psi)

Sub

grad

e V

ertic

al C

ompr

essi

ve S

tress

(psi

)

0 in. HMA4 in. HMA6 in. HMA8 in. HMA

Ballast thickness = 16 in. - HMA thickness

Figure 8 Effects of HMA Thickness on Subgrade Vertical Compressive Stress

0.8

1.2

1.6

2

2.4

2.8

3.2

3000 9000 15000 21000 27000

Subgrade Modulus (psi)

HM

A T

ensi

le S

train

x10

-4 (in

./in.

)

1 in. HMA4 in. HMA6 in. HMA8 in. HMA

Ballast thickness = 16 in. - HMA thickness

Figure 9 Effects of HMA Thickness on HMA Tensile Strain

Table 5 Effects of HMA Thickness on Predicted Service Life of

HMA and Subgrade Subgrade

Modulus (psi) HMA Thickness

(inches) Predicted Service

Life of HMA (year) Predicted Service Life of

Subgrade (year)

0 N/A 0.2

4 7 0.4

6 6 0.5 3000

8 5 0.6

0 N/A 4

4 34 7

6 28 9 9000

8 26 10

0 N/A 15

4 71 24

6 59 32 15000

8 56 43

0 N/A 36

4 121 58

6 106 81 21000

8 96 103

0 N/A 75

4 178 107

6 148 147 27000

8 140 198 Note: Total thickness of ballast and HMA is 16 inches and traffic volume is 32 MGT.

TRACKBED STRESS MEASUREMENTS TTCI Subgrade Stress Measurements

The Transportation Technology Center (TTCI) in Pueblo, Colorado has measured the vertical compressive stress on top of subgrade underneath asphalt underlayment systems (D. Li, J. G. Rose, and J. Lopresti, 2001). Geokon model 3500 hydraulic type earth pressure cells (Figure 10) were utilized for the in-track measurements. Figure 11 depicts the configuration of the components in the measurement system. Data taken from the TTCI Heavy Tonnage test site indicates a vertical compressive stress of approximately 7 psi directly beneath an 8-in. thick asphalt underlayment system. The tests involved 33 ton axle-loading and wood ties. The depth of ballast between tie and asphalt is approximately 8 inches. The test section at Pueblo is placed on top of a very weak subgrade possessing a modulus of elasticity of approximately 2,000 psi in the saturated condition. Figure 12 shows a longitudinal view of the test section. Test results are shown in Figure 13. It is interesting to note that KENTRACK calculates a vertical compressive stress of approximately 6 psi for a subgrade modulus of 2,000 psi. These results

compare closely, as minimal differences are noted between the vertical compressive stress as measured in the trackbed and those predicted by KENTRACK.

Figure 10 Pressure Cell

Junction Box

Pressure Cell Battery

Figure 11 Data Acquisition System

HMA

ballast

subballast4 in.4 in.

12 in.

4 in.

8 in.

8 in.

clay subgrade

10 ft350 ft350 ft

Figure 12 Longitudinal Section of Test HMA Trackbed at TTCI

0

3

6

9

12

15

18 in. granular track 4 in. HMA track 8 in. HMA track

Sub

grad

e S

tress

(psi

)

Figure 13 Test Result of HMA Trackbed in TTCI UK and TTCI HMA Stress Measurements

Peak dynamic stresses also have been measured on top of HMA underlayments (below the ballast) on a CSX Transportation heavy tonnage revenue line by University of Kentucky (UK) researchers and at the Fast Track test installations by TTCI researchers (Rose J., Li D., and Walker, L. 2002). The revenue and test track measurements compare favorably with TTCI under the 33 ton axle loads, ranging from 13 to 17 psi. Actually the stresses on the HMA layer in the trackbed are only two to three times greater in magnitude than the pressure existed by an average size person standing on an

asphalt pavement. The dynamic pressure test results from TTCI are shown in Figure 14. Those from CSX Transportation are shown in Figure 15.

0

5

10

15

20

2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

Time (s)

Com

pres

sive

Stre

ss (p

si)

subgrade surfaceHMA surface

Figure 14 Dynamic Compressive Pressures Measured on TTCI Test Track

Other field studies indicate that the in-situ moisture contents of the subgrade type materials

directly under the asphalt underlayments remain very close to optimum values for the respective materials even after many years of service (J. G. Rose, E. R. Brown and M. L. Osborne, 2000). This attests to the waterproofing attributes provided by the asphalt layer. For design purposes, it is reasonable to base subgrade strength and bearing capacity values at optimum conditions (moisture content and density) for the material under the asphalt. The unsoaked (optimum) moisture content condition is consistent with in-service trackbed conditions. SUMMARY

The KENTRACK computer program, utilizing finite element method and multi-layered theory, has been described and utilized throughout this paper. The recently developed user-friendly windows based Graphical User’s Interface version has been specifically evaluated. The program is determined to be applicable for the structural design of all-granular ballast and layered (containing a cemented asphalt-bound or HMA granular layer) trackbeds.

The effects of numerous variables on trackbed design and evaluations, as determined and predicted by the computer program, are presented in particular detail. The incorporation of an asphalt-bound layer (HMA underlayment) in the track structure, in place of a granular layer, has a particularly significant effect of reducing trackbed stresses and strains. This increases the service life of the track structure, thus reducing maintenance and rehabilitation costs and improving operating efficiencies.

The variable that has the most significant effect on the predicted railroad trackbed service life is the subgrade modulus. The importance of initially designing for and maintaining high subgrade moduli within the track structure cannot be over emphasized. A primary benefit of an HMA trackbed is the waterproofing effect it provides to the underlying subgrade, thus assuring high subgrade modulus.

Stress measurements obtained from instrumented test and revenue traffic trackbeds compare favorably with the computer program predictions. This provides a measure of credibility to the

applicability and adaptability of the KENTRACK computer program.

0

5

10

15

20

25

7 8 9 10 11 12 13 14 15 16 17

Time (s)

HM

A C

ompr

essi

ve S

tress

(psi

)Four 6-Axle Locos

Initial 5 Cars

8 in. ballast5 in. HMA

0

5

10

15

20

4 5 6 7 8 9 10 11 12 13 14 15

Time (s)

HM

A C

ompr

essi

ve S

tress

(psi

)

Four 6-Axle Locos

Initial 5 Cars

8 in. ballast8 in. HMA

Figure 15 Representative Dynamic Compressive Stress on HMA Layer Measured for Empty Coal Train on CSX Transportation Mainline at Conway, KY

All damage analyses for the subgrade and HMA within the track structure are based on damage

equations developed for highway pavements. The critical outputs are vertical compressive stress on the subgrade and horizontal tensile strain on the bottom of the HMA layer.

The actual service lives for the HMA and subgrade in railroad trackbed environments are likely to be several orders of magnitude greater due to the less severe trackbed loadings and environmental conditions. The predicted lives for railroad applications would thus be very conservative. FINDINGS AND CONCLUSIONS

The findings and conclusions emanating from the computer generated stresses and strains in the track structure, due to the effects of varying numerous variables, and the predicted track structure service lines, are contained in the following discussions. Varying Axle Load

As axle loads increase, the imposed subgrade vertical compressive stress increases. For example, increasing the axle load from 33 to 39 tons increases the stress by about 15%. In addition, stresses are about 15% greater on ballast trackbeds. HMA tensile strains are increased as the axle load is increased.

Increasing axle loads reduces the predicted service lives for both HMA and all-granular ballast trackbeds. Varying Subgrade Modulus

Increasing the subgrade modulus leads to a marginal incremental increases in subgrade vertical compressive stress. The range is 9 to 17 psi from a very weak to a very strong subgrade. Stresses are typically 15% higher in the all-granular ballast trackbed for a given subgrade modulus.

However, the increases in stress levels with increasing subgrade modulus are insignificant and possibly misleading. This is due to the fact that the higher modulus (stronger) subgrades are capable of withstanding higher stresses to a greater degree. Therefore, the predicted service lives for both HMA and all-granular ballast trackbeds are increased very significantly. The increase ranges from 1 to 53 years from a weak to a strong subgrade, respectively. Furthermore, the life of the HMA trackbed is typically twice that of a ballast trackbed for a given subgrade modulus.

HMA tensile strain is reduced as the subgrade modulus is increased. This is expected as the asphalt layer deflects less on the stronger subgrades and the tensile strains are less. Except for the very strong subgrades, the initial failure of an HMA trackbed will be due to subgrade failure rather the HMA cracking.

Obviously, one of the major objectives to consider in the design and selection of materials for railroad trackbeds, is to assume the maintenance of a high modulus subgrade. It must adequately support the overlying track and granular materials to minimize trackbed induced maintenance, increase service life and improve operating efficiency. Varying HMA Thickness

For a given total thickness of ballast plus HMA, increasing HMA thickness from 4 in. to 8 in. only reduces subgrade vertical compressive stress by about 10%. Increasing HMA thickness from 4 in. to 8 in., slightly increases the HMA tensile strain.

Increasing HMA thickness increases the predicted service life of the subgrade substantially, but does reduce the service life of the HMA only marginally. ACKNOWLEDGEMENTS

The research reported herein was supported financially by CSX Transportation. A portion of the data was obtained from the Association of American Railroads test facility at Pueblo, Colorado. This paper is a condensed version of a THESIS submitted by Bei Su in partial fulfillment of the requirements for the degree of master of science in Civil Engineering at the University of Kentucky, February 2003, directed by Dr. Jerry G. Rose.

REFERENCES Asphalt Institute, (1998), HMA Trackbeds – Hot Mix Asphalt for Quality Railroad and Transit Trackbeds. Information Series 137, 10 pages. Asphalt Institute, (1982), Research and Development of The Asphalt Institute’s Thickness Design Manual (MS-1) Ninth Edition, Research Report 82-2, 150 pages. Chang, C. S., Adegoke, C. W. and Selig, E. T. (1980) The GEOTRACK model for railroad track performance. Journal of Geotechnical Engineering Division, ASCE, Vol. 106, No. GT11, November, pp. 1201-1218. Huang, Y. H., (1993) Pavement Analysis and Design, 1st Edition, Prentice Hall, pp 735-738. Huang, Y. H., Lin, C., Deng, X., and Rose, J., (1984) KENTRACK, A Computer Program for Hot-Mix Asphalt and Conventional Ballast Railway Trackbeds. Asphalt Institute (Publication RR-84-1) and National Asphalt Pavement Association (Publication QIP-105), 164 pages. Hwang, D., Witczak, M.W., (1979) Program DAMA (Chevron), User’s Manual, Department of Civil Engineering, University of Maryland. Li, D., Rose, J., and Lopresti, J., (2001) Test of Hot-mix Asphalt Over Soft Subgrade Under Heavy Axle Loads, Technology Digest 01-009, Transportation Technology Center, April, 4 pages. Lopresti, J., Davis, D., Kalay, S. (2002) Strengthening the Track Structure for Heavy Axle Loads, Railway Track & Structures, September, pp. 21-26. Robnett, Q. L., Thompson, M. R., Knutson, R. M., and Tayabji, S. D. (1975) Development of a structural model and materials valuation procedures. Ballast and Foundation Materials Research Program, University of Illinois, report to FRA of US/DOT, Report No. DOT-FR-30038, May. Rose, J., Brown, E. and Osborne, M., (2000) Asphalt Trackbed Technology Development; The First 20 years. Transportation Research Record 1713, Transportation Research Board, pp 1-9. Rose, J., Li, D., and Walker, L., (2002) Tests and Evaluations of In-Service Asphalt Trackbeds. Proceedings of the American Railway Engineering and Maintenance-of-Way Association, 2002 Annual Conference & Exposition, September, 30 pages. Selig, E. T. and Waters, J. M., (1994) Track Geotechnology and Substructure Management, Thomas Telford, pp 10.31-10.32. Talbot, A. N., (1919) Stresses in Railroad Track, Reports of the Special Committee to Report on Stresses in Railroad Track, Second Progress Report, AREA, Vol 21, pp 297-453.