U.S. Department of 

Transportation 

Federal Railroad 

Administration

Development of Gage Widening 

Projection Parameter for the 

Deployable Gage Restraint 

Measurement System 

Office of Research 

and Development 

Washington, DC 20590 

DOT/FRA/ORD-06/13 October 2006 This document is available to the 

U.S. public through the National 

Technical Information Service 

Springfield, VA 22161 
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October 2006 Final Report: 2001 - 2005

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

Development of Gage Widening Projection Parameter for the 

Deployable Gage Restraint Measurement System

6. AUTHOR(S) 

Narayana Sundaram (1) and Theodore Sussmann (2)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION 

REPORT NUMBERS

(1) Ensco, Inc. (2) U.S. DOT/Volpe Center/RTV-3G 

5400 Port Royal Rd

Springfield, VA 22151 

Kendall Square 

Cambridge, MA 02142 

9. SPONSORING/MONITORING AGENGY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING AGENCY 

REPORT NUMBER 

U.S. Department of Transportation 

Federal Railroad Administration 

Office of Research and Development, MS 20 

1120 Vermont Avenue, NW

Washington, DC 20590

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

This document is available through National Technical Information 

Service, Springfield, VA 22161. 

13. ABSTRACT

Recent gage restraint measurement system (GRMS) developments include the redesign of GRMS vehicles to conduct 

testing from a deployable axle instead of using freight truck mounted axle and GRMS on hi-rail vehicles. This new 

test configuration results in boundary condition changes in the applied loads and split axle location; both of which 

influence the results. To ensure equivalent safety considering these significant changes, a comprehensive evaluation of 

the mechanistic basis for previous GRMS rulemaking, coupled with a fundamental investigation of factors influencing

GRMS performance and inspection accuracy, was conducted along with field-testing to verify conclusions. Results of

the investigation to date suggest a need for reconsideration of the gage widening ratio (GWR) equation, which treated 

vertical load as a constant parameter. With the new GRMS testing capability at a wider range of test loads, it is 

necessary to include vertical load in the GWR equation. GWR has been the leading source of discrepancies between

the inspections conducted by original GRMS design and redesigned vehicles over the same territory. This report

describes the analysis and recent field-testing to provide the fundamental basis for a proposed gage widening projection

formula.

14. SUBJECT TERMS 15. NUMBER OF 

PAGES

Railroad, ties, condition assessment, track maintenance, non-destructive testing, gage

widening, track gage

43 

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OF THIS PAGE 

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OF ABSTRACT 

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ABSTRACT

unclassified unclassified unclassified

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i 
METRIC/ENGLISH CONVERSION FACTORS 

ENGLISH TO METRIC METRIC TO ENGLISH

LENGTH (APPROXIMATE) LENGTH (APPROXIMATE) 

1 inch (in) = 2.5 centimeters (cm) 1 millimeter (mm) = 0.04 inch (in) 

1 foot (ft) = 30 centimeters (cm) 1 centimeter (cm) = 0.4 inch (in)

1 yard (yd) = 0.9 meter (m) 1 meter (m) = 3.3 feet (ft) 

1 mile (mi) = 1.6 kilometers (km) 1 meter (m) = 1.1 yards (yd)

1 kilometer (km) = 0.6 mile (mi)

AREA (APPROXIMATE) AREA (APPROXIMATE)

1 square inch (sq in, in2) = 6.5 square centimeters

(cm2) 

1 square centimeter (cm2) = 0.16 square inch (sq in, in2) 

1 square foot (sq ft, ft2) = 0.09 square meter (m2) 1 square meter (m2) = 1.2 square yards (sq yd,

yd2) 

1 square yard (sq yd, yd2) = 0.8 square meter (m2) 1 square kilometer (km2) = 0.4 square mile (sq mi, mi2) 

1 square mile (sq mi, mi2) = 2.6 square kilometers

(km2

) 

10,000 square meters (m2

) = 1 hectare (ha) = 2.5 acres 

1 acre = 0.4 hectare (he) = 4,000 square meters (m2) 

MASS - WEIGHT (APPROXIMATE) MASS - WEIGHT (APPROXIMATE)

1 ounce (oz) = 28 grams (gm) 1 gram (gm) = 0.036 ounce (oz)

1 pound (lb) = 0.45 kilogram (kg) 1 kilogram (kg) = 2.2 pounds (lb) 

1 short ton = 2,000 

pounds (lb)

= 0.9 tonne (t) 1 tonne (t) =

=

1,000 kilograms (kg) 

1.1 short tons

VOLUME (APPROXIMATE) VOLUME (APPROXIMATE) 

1 teaspoon (tsp) = 5 milliliters (ml) 1 milliliter (ml) = 0.03 fluid ounce (fl oz) 

1 tablespoon (tbsp) = 15 milliliters (ml) 1 liter (l) = 2.1 pints (pt) 

1 fluid ounce (fl oz) = 30 milliliters (ml) 1 liter (l) = 1.06 quarts (qt) 

1 cup (c) = 0.24 liter (l) 1 liter (l) = 0.26 gallon (gal)

1 pint (pt) = 0.47 liter (l) 

 1 quart (qt) = 0.96 liter (l) 

1 gallon (gal) = 3.8 liters (l) 

1 cubic foot (cu ft, ft

3

) = 0.03 cubic meter (m3) 1 cubic meter (m3) = 36 cubic feet (cu ft, ft3) 

1 cubic yard (cu yd, yd3) = 0.76 cubic meter (m3) 1 cubic meter (m3) = 1.3 cubic yards (cu yd, yd3)

TEMPERATURE (EXACT) TEMPERATURE (EXACT) 

[(x-32)(5/9)] °F = y °C [(9/5) y + 32] °C = x °F

QUICK INCH - CENTIMETER LENGTH CONVERSION

0 1 2 3 4

Inches

Centimeters 0 1 2 6 3 4 5 7 1 8 9 10 11 12

5

3

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSION

 -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°

 

°F

 °C -40° -30° -20° -10° 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and Measures. Price $2.50 SD Catalog No. C13 10286 Updated 6/17/98

ii 
Table of Contents 

List of Figures..................................................................................................................................v 

List of Tables ................................................................................................................................ vii 

Preface............................................................................................................................................ ix 

Executive Summary.........................................................................................................................1 

1. Introduction.................................................................................................................................3 

2. Background.................................................................................................................................5 

2.1 GRMS Technology .............................................................................................................. 5 

2.2 GRMS Mechanics................................................................................................................ 6 

2.3 Current Rules and GRMS Application ................................................................................ 8 

2.4 Vehicle Design Requirements............................................................................................ 10 

2.5 GRMS Technology Summary............................................................................................ 11 

3. GRMS Field Investigation ........................................................................................................13 

3.1 Summary of Test Conditions............................................................................................. 13 

3.2 Data Analysis..................................................................................................................... 14 

3.3 GWR Computation ............................................................................................................ 14 

4. Analytical Investigation............................................................................................................17 

4.1 Derivation of GWP ............................................................................................................ 17 

4.2 Summary of Analytical Investigation ................................................................................ 19 

4.3 Field Verification............................................................................................................... 20 

4.4 Gage Widening Projection................................................................................................. 22 

5. Evaluation of GWP Performance..............................................................................................23 

5.1 Comparison between GWR, GWP, and PTLF .................................................................. 23 

5.2 Field Data Comparisons..................................................................................................... 24 

6. Summary and Conclusions .......................................................................................................31 

7. Recommendations.....................................................................................................................33 

8. References.................................................................................................................................35 

Appendix A. Rail Spring Model and TRKLOD Derivations .......................................................37 

Appendix B. GWP and TRKLOD Model Comparison Analysis.................................................41 

Acronyms.......................................................................................................................................45 

iii 
iv 
List of Figures 

Figure 1. Risk of gage widening derailment when gage exceeds critical gage, 59 inches.............7 

Figure 2. Rail translation and rotation under weak and strong ties................................................ 8 

Figure 3. Permitted test loadings for gage restraint as per the AREMA guidelines ....................10 

Figure 4. T-18 GWR values for three different non-modified sites at different load 

configuration runs.........................................................................................................15 

Figure 5. Lateral load-deflection trends for different vertical loads ............................................ 18 

Figure 6. GW32 versus PTLF delta gage comparison for T-18 results from MMIR................... 20 

Figure 7. GW24 (a) and GW30 (b) versus PTLF delta gage comparison for T-18 results 

from MMIR................................................................................................................... 21 

Figure 8. Normalization of GWP showing that GWP is not dependent on the load severity ......22 

Figure 9. Comparison of the GWP with the GWR where the PTLF and the GWP agree 

with each other and the GWR does not ........................................................................23 

Figure 10. Sample wayside measurements used to measure the maximum deflection of a 

run for a particular location...........................................................................................24 

Figure 11. Layout of the weak spots on the repeatability zone......................................................25 

Figure 12. GWP repeatability tests comparison a zone of approximately 400 feet for the 

TrackSTAR and the T-18..............................................................................................25 

Figure 13. AREMA load plot for FRA’s T-18 and TrackSTAR ................................................... 27 

Figure 14. Comparison plot of GWP from the T-18 and TrackSTAR over a length of 400 

feet during the Phase 3 tests, March 2005 .................................................................... 28 

v 
vi 
List of Tables 

Table 1. Comparison of the exception count between the FRA T-6 and the Holland 

TrackSTAR from the test conducted in October 2002 on MMIR ................................... 14 

Table 2. Analysis of A-factor dependence on higher order terms................................................. 19 

Table 3. Percentage error of the delta gage measured by the GRMS vehicles compared to 

the wayside instrumentation measurement ...................................................................... 24 

Table 4. Exception count for both the GRMS vehicles using the GWP equation.........................28 

Table 5. Exception count for both the GRMS vehicles using the GWR equation......................... 29 

vii 
viii 
Preface 

Gage widening derailments have been a challenge to the continued improvement of rail safety. 

Once the single leading cause of derailments, research and development projects on equipment 

and procedures have dramatically improved rail safety by targeting improved track gage widening 

performance. Specific developments that have contributed to the enhanced safety of track relative 

to gage widening risk include: 

1. The gage restraint measurement system (GRMS), an automated mechanical inspection 

system that identifies locations with poor gage widening characteristics by exercising the 

gage strength of the track using a split axle in place of one of the standard axles on the 

freight truck. 

2. The lightweight track loading fixture, which is a handheld device used to test the track 

gage by applying loads to confirm GRMS identified exceptions. 

3. Track safety standards accommodating the application of GRMS technology. 

The original GRMS technology developed in the 1980s and adopted by the industry through the 

1990s. Recent advances in GRMS technology include the adaptation of the technology by 

Holland Company to a hi-rail GRMS using a single deployable split axle targeting reduced cost 

and GRMS inspections that are more convenient. Using the hi-rail concept, Holland Company 

has provided GRMS inspections to the industry for maintenance planning. Further, the Federal 

Railroad Administration developed a new rail bound inspection vehicle utilizing a deployable 

split axle design to improve safety, as well as operational cost and efficiency. 

The newly designed vehicles operate substantially the same as the original technology. The new 

improvements, however, appear to identify gage widening exceptions at substantially different 

loading magnitudes and configurations than originally conceived, thereby requiring modifications 

in Track Safety Standards to ensure an equivalent level of safety. This report summarizes the 

efforts made to investigate and improve the track safety standards GRMS provisions. 

ix 
x 
Executive Summary 

This report describes the development of the new Gage Widening Projection (GWP) formula as a 

replacement for the Gage Widening Ratio (GWR) parameter that has been used as an index of 

weak or strong tie and fastener condition. Gage restraint measurement systems (GRMS) use 

GWR and the Projected Loaded Gage (PLG) index to assess the risk of freight train derailment 

due to gage widening. Development of new GRMS systems and their subsequent evaluations, 

however, have identified inconsistency in the current GWR equations on the treatment of 

different loading conditions and different vehicle characteristics. A comparison test in October 

2002 between the Holland TrackSTAR, a deployable single split axle, hi-rail GRMS, and the 

FRA T-6, a railbound GRMS with a truck-mounted split axle, showed a significant difference in 

defect numbers reported by these vehicles. Analyses and field evaluations indicated that these 

discrepancies were attributed to various factors, including the GWR equation, measurement 

accuracy problems, and differences in the physical configuration of the vehicles. 

The Federal Railroad Administration (FRA) has procured the T-18 as a replacement of the T-6, 

and it is the first railbound GRMS vehicle to have a deployable loading axle, giving it much 

more flexibility than its predecessor. The evaluation and verification testing in November 2004 

in Front Royal, VA, on the Norfolk Southern Railroad (NS) included a set of tests with 25 

different loading configurations within the acceptable load range for GRMS testing. The results 

of this test indicated that the current GWR calculation does not treat different loading 

configurations similarly, even for the same vehicle due to treatment of vertical load as a constant 

not as a variable in the GWR equation. A new form for the GWR equation was developed 

keeping all these factors in mind, and it was tested using the T-18 with two different loading 

configurations on the Maryland Midland Railroad (MMIR) in February 2005. The correct 

extrapolation loads were arrived at using the results of this test. The resulting equation was 

named GWP and has extrapolation loads of L = 16 kips and V = 30 kips. A final conclusive 

comparison test between the FRA T-18 and the Holland TrackSTAR was performed in St. Louis, 

MO on the BNSF Railway (BNSF). The GWP and Projected Loaded Gage at 24 kips lateral 

load (PLG24) comparison was found to be excellent between both the GRMS vehicles. The 

GWP, which is a two variable dependent parameter, was also found to compare well with the 

finite element TRKLOD model. Results from these analyses indicated that the GWR equation in 

the Track Safety Standards (TSS) should be replaced with the GWP equation to accommodate 

the different applied vertical loads. 

1 
2 
1. Introduction 

FRA Office of Research and Development (R&D) has initiated and maintained its research effort 

in GRMS technology development to improve detection of railroad track gage defects that cause 

derailments. In the rail transportation industry, due to heavy lateral loads being applied to the 

rails, it has been a problem to maintain the established distance between the rails. Lateral 

restraint or the strength to withstand these loads comes from ties, tie plates, rails, spikes, and the 

supporting track foundation. The ties and fasteners play vital roles in maintaining the track gage. 

If the loads applied to the rails are high enough to overcome the rail restraint, it is possible to 

move the rails sufficiently apart to have the wheels of the car drop between the rails, causing a 

gage widening derailment. GRMS has used GWR and PLG index to assess the risk of train 

derailment. Both of these indices were developed based on research conducted with deflections 

resulting from different vertical and lateral loading configurations on rails that represented the 

minimum restraint criteria allowed on track. 

Comparative testing was conducted on the MMIR in October 2002 to evaluate the GRMS 

capabilities of FRA T-6 and Holland TrackSTAR. The FRA T-6 is a railbound vehicle, and the 

Holland TrackSTAR is a hi-rail GRMS. Based on initial test results, it was determined that the 

current GWR calculation did not produce comparable results between the two vehicles. The 

comparison testing was conducted by monitoring the testing capabilities of each vehicle over the 

same track, repeatability over particular sections, and accuracy comparisons. The TrackSTAR 

produced substantially more defects than the FRA T-6. The main differences between these two 

vehicles are the loading conditions: the FRA T-6 applies a lateral load of 14 kips and a vertical 

load of 21 kips (L/V = ~0.7) whereas the Holland TrackSTAR applies a lower load of 10 kips 

and a vertical load of 14 kips (L/V = ~0.7). The applied load severity, which is a measure of the 

effective lateral load when the restraining effect of the vertical load and friction combination is 

removed, is different for both vehicles. Other differences included the gage measurement 

system, structure of the cars, and load control used to apply the loads. The current GWR 

equation does not consider the effects of different vertical loads; it is extrapolated only to a 

limiting lateral load. Another major difference between the T-6 and TrackSTAR is that the T-6 

GRMS axle is a truck axle and the TrackSTAR has a single axle GRMS. A simulation using the 

TRKLOD, a finite element model, indicated that the T-6 would measure 12 percent less 

deflection when compared to the deflection from the same loads in a TrackSTAR configuration, 

due to the effect of the vertical load applied through the adjacent axle in the truck onto the rails. 

The current GWR was developed for a vehicle that applies a vertical load 18-21 kips; if the 

vertical load changes, the GWR value is not consistent. All these problems constituted the need 

for a new GWR parameter that is consistent for different vehicle configurations and normalized 

for different load configuration. This report describes the development of the new GWR 

computations, along with description of field-testing conducted to confirm analytical 

conclusions. 

The new GWR parameter will satisfy the following criteria: 

1. It should be loading configuration (load severity) independent. 

2. It should be extrapolated to working loads since GWR is an indicator of weak or strong 

tie and fastener condition rather than the ultimate strength of the track. 

3 
3. The same equation would be used for truck-mounted and single split axle GRMS 

vehicles. 

4. The threshold for the safety and maintenance exceptions should remain the same, 1.0 

inch and 0.75 inches, respectively as those found in TSS. 

4 
2. Background 

Since railroads were first used to move heavy equipment, maintaining the track gage by a system

of ties, fasteners, and ballast has been a great challenge. Ties are typically made of wood, 

concrete, or steel, and they perform three major functions. They hold the rails at the correct 

gage, distribute the loads applied by the train to the track foundation, and anchor the track 

against lateral movement. The fasteners attach the rails to the ties and are typically cut spikes, 

screw spikes, or some type of spring clip. When the forces generated by the train exceed the rail 

holding capacity of the ties and fasteners, the rails move apart either through rotation or

translation, allowing the wheels to drop between the rails. This is known as gage widening 

derailment. Gage widening-related accidents have been one of the top five causes of trackrelated accidents based on FRA’s Railway Accident/Incident Reporting System (RAIRS) since 

FRA started monitoring railroad accident statistics in the late 1960s. A program was developed 

at the Volpe National Transportation System Center (VNTSC) in 1980 to investigate minimum 

rail restraint characteristics of typical track. Field and laboratory tests were performed to 

develop performance-based rail restraint standards that eliminate the worst case scenarios of the 

applied trainloads and local track conditions that would lead to rail restraint failure. In 

conjunction with the field and laboratory tests, two prototype devices were developed that 

provide quantitative measurements of the rail restraint capacity: GRMS and the lightweight 

track loading fixture (LTLF). 

2.1 GRMS Technology 

GRMS is a vehicle that runs on the track with a split axle applying vertical and lateral loads 

while continuously measuring the change in gage. The prototype GRMS system developed by 

FRA used a spilt axle mounted in the truck of a 100-ton hopper car and used FRA’s 

instrumentation car T-6 to record the data as described by Carr and Stuart (1995). The two 

vehicle consist was commonly referred to as the T-6, and a locomotive towed it. The loads were 

applied through the split axle, which was mounted on a standard three-piece truck in the rear of 

the hopper car. The split axle applied the loads through its 33 inches flanged steel wheels and 

housed the sensors that detect the track deflection under loads. A passive load control used in 

the original GRMS vehicle combined with high internal friction, limited its response to rapid 

track changes. The LTLF is manually operated and applies the lateral load through the 

theoretical shear center of the rail cross-section while using a gage bar to measure the change in 

gage. LTLF and its successor, the portable track-loading fixture (PTLF) use a manual hydraulic 

pump and cylinder to produce a test load of 4 kips. The LTLF/PTLF provide a method to verify 

defects identified by GRMS. 

Holland Company’s TrackSTAR vehicle is a hi-rail based GRMS and is capable of measuring 

other track parameters like rail profile and track geometry. It utilizes a single deployable split 

axle between the vehicle driving axles for applying vertical and lateral loads and has an optical

rail measurement system to measure gage as described by McCarthy (1995). TrackSTAR uses an 

active load control to apply loads on the track and is able to rapidly respond to the changes in 

track conditions. 

FRA procured a new GRMS vehicle, the T-18, which utilizes a state-of-the-art deployable single 

split axle capable of applying variable lateral and vertical load combinations. The evaluation 

5 
testing of the T-18 on NS in Riverton, VA, indicated repeatable unloaded and loaded gage 

measurements as well as low standard deviations of the applied lateral and vertical loads. The T18 uses a mechanical gage measurement approach compared to the optical system being used in 

the Holland TrackSTAR. 

2.2 GRMS Mechanics 

The initial development of GRMS technology was based on field experience with a variety of 

derailments which indicated that gage widening failure had occurred under common track 

loading scenarios. A field study near Logan, OH, defined the track characteristics of minimally 

adequate in-service track to define the boundary between acceptable and unacceptable track, tie, 

and fastener conditions (Jeong and Coltman, 1983). Unacceptable conditions were noted as 

those where the track, tie, and fastener conditions were not adequate to safely support track 

loads. The main characteristic of an unsafe tie is an inability to restrain the spike or fastener 

from movement under load. Load-deflection characteristics of minimally adequate track 

conditions were developed from data analysis at various test sites. Knowledge of track failure 

modes indicated that rail restraint characteristics and track forces were critical parameters. A 

series of vehicle-track interaction tests was conducted in Bennington, NH, to define the limits of 

tolerable track geometry irregularities based on the response of a common vehicle type. Lateral 

and vertical loads were measured to determine the lateral to vertical load ratio (L/V), and it was 

found that peak wheel-rail forces reached 22 kips and were relatively insensitive to vehicle speed 

(5 to 20 mph) (Coltman and Weinstock, 1988). Lateral loads of 24 kips on the high rail and 16 

kips on the low rail have been measured on track with geometry that passed FRA TSS during the 

test according to Blader (1983). Track maintained to minimum levels should be able to 

withstand 24 kips ultimate lateral load without gage change adequate to cause wheel drop. The 

loads from the field study in Bennington, NH, defined the target load regime for the development 

of GRMS to detect track, tie, and fastener conditions not meeting the minimally adequate criteria 

used by Jeong and Coltman (1983). 

2.2.1 Track Response to Applied Loads 

A new track structure with appropriate ballast and good geometrical alignment can support 

typical train loading. As each track component is worn and degraded over time, however, 

subsequent loading, deformation, and environmental effects diminish the restraint capacity. 

Track with a high percentage of structurally degraded ties typically exhibits geometry 

perturbations, particularly gage, cross-level, and alignment. These geometry imperfections 

create dynamic interactions between the train and the track that can produce high lateral wheelrail forces. When combined with a weakened track structure, high lateral loads can cause 

sufficient spreading of the rails to allow wheel drop. This occurs when the loaded gage exceeds 

the critical safety limit defined by the physical dimensions of a wheel set. The critical safety 

limit is defined by the minimum acceptable flange thickness, minimum acceptable back-to-back 

wheel dimension, standard tread dimension, and a notch in the rim including half of the rim tread 

radius. The combination of these dimensions is a critical safety limit of 59 inches, as shown in 

Figure 1. 

6 
Figure 1. Risk of gage widening derailment when gage exceeds critical gage, 59 inches 

The gage can approach this limit if the high rail, low rail, or both rails move under load. This 

motion can be separated into two components: translation and rotation, as shown in Figure 2(a). 

Poor performing ties, fasteners, or large dynamic forces cause each motion. Rotation is 

controlled by the location and magnitude of the applied loads, the fastener holding stiffness, the 

rail section geometry and torsional stiffness, and the wheel-rail interface geometry. Translation 

is controlled by the lateral stiffness of the tie and fasteners, rail section geometry and lateral 

bending stiffness, and the frictional force induced by the applied vertical load. 

The overall railhead deflection is influenced much more by the track properties (ties, fasteners, 

ballast) than by the rail mechanical properties (material properties, rail geometry, rail weight). 

This is significant when evaluating a measured head deflection under load and relating it to the 

rail restraint capacity. The resulting railhead deflection is caused by foundation deficiencies, not 

rail material or geometry defects. 

Figure 2(b) shows a rail segment under vertical and lateral loading on a strong tie. Since the tie 

is assumed to be strong, all the rail, tie plate, and spike gaps are taken up by the initial rail 

movement. On the other hand, Figure 2(c) shows the rail under loading on a weak tie. As with 

the strong tie, all the initial gaps are removed. In this diagram, the tie plate has translated 

laterally, as the tie can no longer support the spikes. This weakened restraint capacity can vary 

from the worst case, represented by missing ties or spikes, to light degradation with small plate 

movement and no spike pull. 

7 
Figure 2. Rail translation and rotation under weak and strong ties 

2.2.2 Load Severity 

Load severity is a representation of the effective lateral force applied to the rail that removes the 

resistance offered by the combination of the vertical force and friction between the rail and tie 

plate (Manos, at al., 1982), given by: 

S = L − μV [1]

Where: 

S = track load severity (kips)

L = applied lateral force (kips) 

V = applied vertical force (kips) 

μ = coefficient of friction between tie and rail, approximated as 0.4. 

The load severity concept is a useful tool to estimate the net load applied to the track that is not 

balanced by friction at the rail-tie interface and must therefore be restrained by the fastener. 

2.3 Current Rules and GRMS Application 

2.3.1 Projected Loaded Gage 24 (PLG24) 

The PLG at 24 kips ultimate loading condition (PLG24) parameter considers the combination of 

the rail deflection and unloaded gage and is indicative of the overall ability of the tie and fastener 

system to maintain gage under severe loads of L = 24 kips and V = 32 kips. The extrapolation 

loads were derived from an investigation by VNTSC (Kish et al., 1984), which surveyed loads 

experienced by high and low rails during various tests and analysis of cars in severe curve 

conditions. PLG24 is computed according to: 

PLG24 = ULG + A⋅(LDG −ULG) [2]

8 
Where: 

ULG = unloaded gage (in), 

LDG = loaded gage (in), and 

A = an extrapolation factor computed from: 

2 ( 0.258 ) 0.009 ( 0.258 )

13.513

L V L V

A − ⋅ − ⋅ − ⋅ = [3]

L = applied lateral force (kips) 

V = applied vertical force (kips). 

2.3.2 GWR 

The current definition of GWR is based on two concepts: 

1. The track gage compliance originally proposed as the deflection rate, which was the 

inverse of stiffness and indicated the allowable deflection per unit load and thus 

conveyed the response of track gage to load. 

2. GWR used the deflection rate concept, multiplied by a factor corresponding to the 

ultimate load condition, to develop limiting deflection criteria at an ultimate load 

condition. 

These concepts indicate that GWR is a limiting condition representing the amount of movement 

in the track under working loads. The current GWR equation is stated as: 

⋅16 − = L

LDG ULG GWR [4]

Where: 

ULG = unloaded gage (in) 

LDG = loaded gage (in) 

L = applied lateral force (kips) 

Rearranged in a similar manner to the PLG24 equation, GWR can equivalently be represented 

as: 





 



 = − ⋅ L

GWR LDG ULG 16 ( ) [5]

In a manner similar to PLG24, GWR thus uses the factor 16/L as an extrapolation factor to a 

higher load condition from the test load. In this manner, 16 may represent the GWR ultimate 

lateral load condition. 

The current TSS set the exception thresholds to 0.75 inches for maintenance and 1.00 inch for 

safety. The scale factor 16 kips in the GWR equation was determined as being the extrapolation 

load at which the deflection of minimally acceptable track at a nominal FRA’s T-6 applied 

lateral force would yield a GWR value of 1.00 inch. Field tests reported by Jeong and Coltman 

(1983) indicated that for low lateral loads (up to 15 kips), rail-base displacements account for 70 

percent to 90 percent of the total railhead displacements. A high rail-base displacement would 

9 
indicate that the tie, tie-plate, or the spikes are not in good condition, and hence the GWR value 

closely indicates the rail fastening condition at a specific location. 

2.4 Vehicle Design Requirements 

The minimum design requirements specified by FRA TSS, Part 213, for a GRMS vehicle specify 

that gage restraint should be measured between the heads of rail at an interval not exceeding 16 

inches. The applied vertical load should be no less than 10 kips per rail, and the lateral and 

vertical test load combinations should be such that they provide an L/V ratio between 0.5 and 

1.25. An L/V ratio of greater than 0.8 has been found by experience to be more prone to 

derailment; hence, vehicles operating in this zone of lateral load and vertical load combination 

exercise caution. The American Railway Engineering and Maintenance-of-Way Association 

(AREMA) Manual for Railway Engineering is more detailed, and it specifies the gage 

measurement requirements, as shown in Figure 3. Unloaded gage should be measured at least 5 

feet behind or 10 feet ahead of any load applying source greater than 350 pounds in either lateral 

or vertical directions. The loaded gage measurement should take place within 1 foot of the 

applied load. Lateral and vertical load applied by a GRMS vehicle should fall in zone II or zone 

IV as illustrated in Figure 3. Caution should be used during testing as risk for derailment is 

higher in zone IV due to high L/V ratio. 

Ambiguity in the vehicle requirements has led to different designs. An evaluation of the hi-rail 

and railbound designs to assure consistency in load and displacement measurements is necessary. 

This evaluation is a major step in the advancement of new GRMS design, as described in this 

report, for the current design change to single split axle with variable test loading combinations 

from truck split axle with constant vertical test load. 

Figure 3. Permitted test loadings for gage restraint as per the AREMA guidelines 

10 
2.5 GRMS Technology Summary 

Recent changes in the design of GRMS vehicles include the Holland TrackSTAR and the FRA 

T-18, which are single axle GRMS systems as opposed to the truck mounted split axle devices 

used for GRMS testing. The TrackSTAR used a laser-based non-contact gage whereas the T-6 

and the T-18 used a contact-based gage measurement system. The T-6 and T-18, as well as other 

GRMS vehicles used in the railway industry, apply a nominal lateral load of 14 kips and a 

nominal vertical load of 21 kips whereas the TrackSTAR applies a lateral load of 10 kips and a 

corresponding vertical load of 14 kips. The L/V ratios of the different load combinations used 

are approximately 0.7. The applied load severity is different for TrackSTAR when compared to 

the T-6 and the T-18. 

Loading conditions during measurement of gage restraint play a critical role in obtaining

accurate and repeatable data. Track gage widening load-deflection behavior is nonlinear and is 

controlled by many factors, including rail size, tie type, and condition. Confirmation of the 

capabilities of different systems with distinct test loads to accurately measure gage restraint is 

important to ensure track safety. 

11 
12 
3. GRMS Field Investigation 

Good comparison between present GRMS vehicles and their repeatability, as well as reliability, 

is very important in making GRMS a good tool to test gage restraint. A comparison test was 

carried out between the FRA T-6 and the Holland TrackSTAR in October 2002 on MMIR. 

Substantial differences between the two vehicles in design and performance led to considerable 

disparity in the test results. The TrackSTAR found more safety and maintenance exceptions than

the FRA T-6 in the GWR and PLG24 category. Both vehicles have some measurement errors. 

For example, the T-6 was slow in reacting to gage changes, and the TrackSTAR had a drifting 

lateral load sensor. It was concluded that investigation of GWR and PLG24 was needed to 

ensure accuracy for varying load conditions. A detailed report on the MMIR comparison test 

was developed, which included the analysis of the test results (Choros et al., 2003). 

Development of the FRA T-18 and its qualification testing was conducted in November 2004 on 

NS. The ability of the T-18 to test at different loading configurations was used to investigate the 

relation between GWR and load severity. A length of about 50 miles of track was tested at two 

different load severities: one loading configuration being the FRA T-6 nominal loads and the 

other being the TrackSTAR’s nominal loads. Repeatability of the T-18 was found to be 

excellent when the two loading configurations were compared over subsequent runs. Based on 

the investigation of the influence of load severity on GWR, a new equation, GWP, was 

developed. Using the GWP equation, a comparison of the TrackSTAR and the T-18 was 

conducted on the River Subdivision of BNSF between St. Louis, MO, and Cape Girardeau, MO, 

during, March 7-11, 2005. Excellent repeatability was found between both the vehicles in terms 

of the new form of GWR (which is called GWP) and PLG24. 

3.1 Summary of Test Conditions 

The MMIR track was predominantly Class II with 115 American Railway Engineering 

Association design (RE) rail section with a few exceptions where lighter rail was used, usually 

less than one rail length. Timber ties were used predominantly for the track structure, with the 

exception of a few sections where steel ties were used. Timber tie condition varied from new to 

degraded, typical of Class II track. When MMIR was retested with the T-18 in February 2005, 

the tie and rail conditions were found similar to those when tested in October 2002. Detailed 

information about the track for the October 2002 tests can be found in Choros et al. (2003) 

report. 

The November 2004 test with the T-18 was conducted at NS on Class II track with 136 RE rail 

section. The track length was about 2,600 feet and had a few weak locations due to weak timber 

ties and some lost spikes. Locations of weak gage restraint capacity were created by removing 

the spikes of a tie for both rails and using a flat steel plate with the same thickness as the regular 

tie plate instead of a regular tie plate. These spots were created with an objective of obtaining 

the same coefficient of friction between the rail and the tie for all the created defects. The 

number of consecutive ties with flat steel plates instead of normal tie plates determined the 

relative severity of the poor gage restraint condition. The GRMS vehicle applied loads through 

five such locations of increasingly poor gage restraint using additional flat steel plates.

13 
Similarly, the comparison test between the T-18 and the TrackSTAR in March 2005 carried out 

on the BNSF River Subdivision between St. Louis and Cape Girardeau, MO, had a repeatability 

phase of testing where defects were created using the same procedure followed at the evaluation 

testing at NS. The repeatability comparison testing was carried out on 132 RE rail section, and 

the over the road run comparison was conducted on a combination of 115 RE, 132 RE, and 136 

RE rail sections. 

3.2 Data Analysis 

Results from the first comparison test at MMIR between the FRA T-6 and the TrackSTAR 

indicated that both vehicles were repeatable at their respective nominal loads. The Holland 

TrackSTAR, however, identified a greater number of reportable exceptions, GWR and PLG24, 

for safety and maintenance. The principal difference between the numbers of exceptions from

the two GRMS vehicles was GWR safety. The TrackSTAR found 10.17 times more GWR 

safety exceptions than the T-6. For GWR maintenance, PLG24 maintenance, and the PLG24 

safety, the TrackSTAR’s numbers of reported exceptions were higher by 2.63, 6.33, and 7.89 

times, respectively, as shown in Table 1. 

Table 1. Comparison of the exception count between 

the FRA T-6 and the Holland TrackSTAR from the test 

conducted in October 2002 on MMIR 

Exception Type Safety Maintenance

T-6 Holland T-6 Holland

GWR 78 814 329 125

PLG24 9 71 42 266

Some measurement errors existed in both the vehicles, which the comparison report details. 

Accounting for measurement errors still did not bridge the gap between the two vehicles. A 

simulation using the TRKLOD model shows that the T-6 would measure 12 percent less 

deflection when compared to the deflection from the same loads in a TrackSTAR configuration 

due to the effect of the vertical load applied through the adjacent axle in the truck onto the rails. 

The current GWR was developed for a vehicle that applies 18-21 kips vertical load, and if the 

vertical load changes, the GWR value is not consistent. 

3.3 GWR Computation 

Development of new design GRMS and distinct loading configurations has spurred the need to 

improve the GWR’s reliability between vehicles. The current GWR equation is computed using 

Equation 4 and does not currently include a vertical load term. New vehicle designs and 

operating loads make it necessary to include the vertical load to get good repeatability between 

two different GRMS equipment for the GWR parameter. 

The T-18 repeatability testing over the same stretch of track at different speeds on NS 

(November 2004) found the GWR to be 0.045inches at the five different speeds. After the 

preliminary results, a stretch of track (about half a mile) was tested at 25 different load 

combinations of acceptable vertical and lateral loads. Figure 4 shows the change in GWR with 

14 
respect to applied load severity at three different weak locations (locations where no tie-plates 

were substituted). The coefficient of friction chosen was 0.258, and it is equal to the c value 

derived by Blader (1983) to approximate the minimal rail restraint curve. These locations were 

chosen such that they were roughly about 0.8 inches GWR at nominal T-6 load severity of 7 

kips, therefore closely representing minimally acceptable track. It is clearly observed that the 

GWR graph has a positive slope; hence, it is not normalized for different loading configurations, 

and hence the GWR equation is inconsistent for vehicles that apply different nominal load 

combinations. 

Figure 4. T-18 GWR values for three different non-modified sites at different load 

configuration runs 

15 
16 
4. Analytical Investigation 

The present GWR computation does not take into account the applied vertical load; thus it was 

found not to perform well in vehicle comparison tests. Therefore, a thorough analysis of the 

fundamental GWR computation was conducted with the goal of developing a new computation 

procedure that would perform equally well for a variety of load configurations representing the 

new generation GRMS systems and provide an equivalent level of safety. The applied load 

severity, a good representation of the effective lateral load resistance, results in different GWR 

values when loads vary even at the same location. The form of the new GWR equation was 

developed using three different approaches involving various physical and analytical track 

models, along with consideration of established conditions of minimally acceptable track 

conditions. The result of the analysis was a new equation termed the GWP index to avoid 

confusion with the earlier GWR, which it is intended to replace. 

4.1 Derivation of GWP

Since the PLG24 equation performed better than GWR in the comparison test between the 

different GRMS vehicles, the PLG24 analysis procedures were investigated to determine if the 

extrapolation procedure could improve the performance of the current GWR equation. The 

PLG24 equation includes an extrapolation factor to estimate gage for extreme loading situations, 

which would be detrimental to track conditions if the loading was applied in the field during 

testing. Due to the potential track damage at the higher loads, the A-factor was developed as the 

ratio of two non-linear equations with the numerator being the limiting conditions (L = 24 kips 

and V = 32 kips) and the denominator being the applied conditions. The A-factor is given as 

follows: 

2

2

( 0.258 ) 0.009 ( 0.258 )

( 0.258 ) 0.009 ( 0.258 )

L V L V

L V L V A c c c c

− ⋅ − ⋅ − ⋅

− ⋅ − ⋅ − ⋅ = [6]

Where: 

 Lc = critical lateral load set at 24 kips 

 Vc = critical vertical load set at 32 kips 

 0.258 = coefficient of friction, identified from the lines of constant deflection as the 

slope of the lateral load-vertical load graph, termed mL,V

Based on the lines of constant deflection developed for the PLG A-factor from TRKLOD 

analysis, shown in Figure 5, the E-factor was developed as the extrapolation factor for estimating 

gage widening under GWR ultimate load. The slope of the lines of constant deflection relating 

lateral load and deflection govern the relationship together with the spacing between the constant 

vertical load lines. The slope of the deflection versus lateral load lines is 0.0663 in/kip on 

average as shown on the graph. The slope of the plot of deflection versus vertical load for the 

single axle loading condition was found to be -0.167 in/kip of vertical load on average. The 

negative value of this ratio appeared reasonable since less deflection would be expected for an 

increase in vertical load. The deflection equation was then developed as: 

17 
D m L m V [7] L D V D = ⋅ − ⋅ , ,

Where: 

 D = deflection 

 mL,D = slope of the lateral load, deflection plot, (0.663 in/kip lateral load) 

 L = lateral load 

 mV,D = slope of the vertical load, deflection plot, (-0.167 in/kip vertical load) and

 V = vertical load

1.2

V = 10 k V = 20 k

1.0 V = 0 k

Deflection (inches) 0.8

y = 0.0663x 

0.6 V = 30 k

0.4

0.2

0.0

0 5 10 15 20 25

Lateral Load (kips)

Figure 5. Lateral load-deflection trends for different vertical loads 

Since the PLG24 and GWR are ratios of deflection at a limiting condition to the deflection at the 

test load conditions, similarly the E-factor was computed as a ratio of the deflection computed 

for the ultimate load to the field test load conditions. The limiting conditions for GWR analysis

were assumed as 16 kips lateral and 32 kips vertical; the 1 inch deflection at the limiting 

condition is a constant in the E-factor equations. The E-factor for a single axle test load 

condition can be computed according to: 

 m L m V ( ) L V L V L V

m L m V

D

D

E

L D V D

c L D c V D c

− ⋅

− ⋅ = − ⋅ = − = ⋅ − ⋅

⋅ − ⋅ = = 0.257

16 0.257 32

0.257

7.75

0.066 0.017

0.512

, ,

, , [8] 

Where 

 Dc is the critical deflection, and then GWR would be computed as: 

GWR = ∆Gage ⋅ E [9]

Where 

∆Gage = LDG-ULG 

Another approach using the PLG A-factor resulted from simplifying the A-factor by neglecting 

the higher order terms: 

18 
L 0 258 V

L 0 258 V A c c

1 − ⋅

− ⋅ = .

. [10]

Where 

GWP Gage A1 = ∆ ⋅

The equation simplifies to a ratio of load severities for the given coefficient of friction, denoted 

in this analysis as mL,V of 0.258: 

S

S A c

1 = [11]

Where 

 Sc = critical load severity 

S = test load severity 

Neglecting the higher order terms results in a difference between the original A-factor and the Afactor without higher order terms (A1) of 12 percent for the condition of reduced load severity 

where the GWR does not perform well, as shown in Table 2. Otherwise, A1 could properly 

extrapolate to the ultimate load conditions within 10 percent error. 

Table 2. Analysis of A-factor dependence on higher order terms 

Lc

kips 

Vc

kips 

L 

kips 

V 

kips 

A-factor A1 Percent

Error 

24 33 14 21 1.68 1.80 7

24 33 10 21 3.03 3.38 12

24 33 17 21 1.28 1.33 4

Two other methods were investigated to verify the nature of the GWP equation, namely the 

Simple Rail Spring Model and the TRKLOD analysis, which Appendix A describes in detail. 

4.2 Summary of Analytical Investigation 

For all the three approaches, the values of the critical vertical load Vc are not known. The 

critical lateral load Lc is set to 16 kips, the same as used before in the original GWR equation. 

The forms of the equations are: 

m L m V

m L m V

D

D

E

L D V D

c L D c V D c

⋅ − ⋅

⋅ − ⋅ = =

, ,

, , [12]

which is previous equation 8 and 

L m V

L m V

S

S A

V L

c c V L c

1 − ⋅

− ⋅ = =

,

, [13]

This is previous equation 10, again with mV,L equal to the coefficient of friction of 0.258. These 

computation procedures fall into two categories, the application of a ratio of deflection for 

19 
equation 12 and a ratio of load severity for equation 13 to extrapolate from field test load to 

ultimate load condition.

4.3 Field Verification 

One criterion not achieved yet is that the GWP equation should keep the safety limits set in TSS 

the same. A test was conducted again on MMIR in February 2005 with the T-18 being operated 

at two different loading configurations, one with the nominal T-6 loads (L = 14 kips and V = 21 

kips) and the other with nominal TrackSTAR loads (L = 10 kips and V = 14 kips). The 

exceptions were computed using equation 13 with Lc = 16 kips and Vc = 32 kips. Forty-nine of 

these exceptions were tested using the PTLF loaded to 4 kips and a gage bar to measure rail 

deflection. Good correlation was observed on the plot of GW32 (32 refers to Vc) versus PTLF 

delta gage (loaded at 4 kips) for both the load configurations, as shown in Figure 6. 

Figure 6. GW32 versus PTLF delta gage comparison for T-18 results from MMIR 

It is noticed that the 0.625 inches PTLF delta gage line intersects the two load configuration runs 

at about 0.9 inches of GW32. The 0.625 inches delta gage for a 4 kips PTLF loading has been 

considered a safety exception for comparison purposes. Therefore, 32 kips is not the critical 

vertical load since the threshold would have to be changed to 0.9 inches from 1.0 inch. Two 

more critical vertical loads, 24 kips and 30 kips, were also plotted, and it was found that GW30 

provided the best results in keeping the thresholds the same as the old GWR thresholds. Figure 7 

(a) and (b), respectively, show these two plots. 

Normalization was also investigated by plotting GW30 versus load severity for the same three 

locations, which were used in Figure 4 when plotting GWR versus load severity. Figure 8 shows 

that GW30 is independent of load severity and hence the different loading configurations applied 

by the different vehicles. The combination of maintaining the threshold the same as GWR and 

normalization achieved by GW30 makes it satisfy all the requirements for a parameter that 

20 
identifies weak tie fastener system efficiently for a variety of test configurations and load 

magnitudes. 

(a) 

(b) 

Figure 7. GW24 (a) and GW30 (b) versus PTLF delta gage comparison for T-18 results 

from MMIR 

21 
Figure 8. Normalization of GWP showing that GWP is not dependent on the load severity 

4.4 Gage Widening Projection 

The form of the GWP equation is based on a ratio of load severity according to equation 13 with 

critical lateral and vertical loads of 16 kips and 30 kips, respectively, and is stated as follows: 

L V Gage L V

GWP Gage − ⋅ = ∆ ⋅ − ⋅

− ⋅ = ∆ ⋅ 0.2588.26

0.258

16 0.258 30 [14]

Selecting the vertical load at 30 kips instead of 33 kips used in the derivation of the A-factor will 

allow the TSS safety limits to remain the same, 0.75 inches for maintenance and 1.00 inch for 

safety defects. 

22 
5. Evaluation of GWP Performance 

5.1 Comparison between GWR, GWP, and PTLF 

The GWP equation results were compared to GWR values and PTLF results to evaluate the 

changes resulting from the new equation. The analysis was conducted to determine if the new 

equation addressed the previously identified problems with the GWR equation. It was found that 

the GWP equation compared well with the PTLF limit of 5/8-inch deflection when the applied 

force is increased from 0 to 4 kips. The PTLF was applied to two locations during the BNSF test 

to obtain an estimate of the accuracy of both the T-18 and TrackSTAR to measure gage strength. 

Figure 9 shows one of these locations, where the PTLF 4 kips deflection was a 0.5 inches and 

thus not an exception according to the TSS, CFR 213.110(m). The GWR flags it a safety 

exception where the GWP value does not deem it a safety exception. 

Figure 9. Comparison of the GWP with the GWR where the PTLF and the GWP agree 

with each other and the GWR does not 

The T-18, as well as the TrackSTAR, gage measurements were compared to wayside 

measurements to ensure correct measurements by the sensors on the vehicles. Wayside 

instrumentation was set up on three out of the five weakened spots to compare the measurements

of the GRMS vehicles. String potentiometers were instrumented to the rail to facilitate the 

displacement measurements on both sides of the rails. Figure 10 shows a sample measurement 

by one of the potentiometers. Both the vehicles showed good comparison (tabulated in Table 3) 

with the wayside instrumentation of TrackSTAR being the better of the two on average. 

23 
Figure 10. Sample wayside measurements used to measure the maximum deflection of a 

run for a particular location 

Dis

placement (inches)

Time (seconds) 

Min

Max 

First truck 

Second 

truck 

Table 3. Percentage error of the delta gage measured by the GRMS vehicles compared to 

the wayside instrumentation measurement 

GRMS Test Results Loads 

(kips) 

Average 

Error 

Std Dev 

T-18 All Runs Combined Error -9.08% 13.79% 

T-18 Day 1 Average Error 10L 14V -18.99% 8.32% 

T-18 Day 2 Average Error 14L 21V 4.13% 6.05% 

TrackSTAR Average Error 10L 14V -6.05% 14.59% 

5.2 Field Data Comparisons 

The comparison test between the T-18 and the TrackSTAR at St. Louis, MO, consisted of the 

following three phases of testing. 

5.2.1 Verification and Calibration 

Verification and calibration of both vehicles were performed for all GRMS fundamental 

measurements, namely unloaded gage, loaded gage, left and right vertical and lateral loads, and 

distance measurement. A load cell fixture was used to verify and calibrate the load 

measurements. A gage bar was used at 20 different locations to calibrate and verify GRMS 

loaded and unloaded gage measurements. A measured 1,000-foot section was used to calibrate 

the distance encoders used by each GRMS vehicle. Both the FRA T-18, as well as the Holland 

TrackSTAR, showed good calibration of the basic GRMS measurements. 

24 
5.2.2 Repeatability 

After the calibration was performed and the measurement capabilities of both the vehicles were 

verified, a repeatability test was conducted for both the vehicles. A test section of about 1,500 

feet was chosen, and the T-18 was tested at five different speeds and the TrackSTAR at three 

different speeds, all within the operating track speeds. Weak spots were generated by removing 

tie plates in increasing number and replacing the tie plates with flat steel plates. Four weak spots 

were created in tangent section and one weak spot in the curve section; Figure 11 shows the 

layout of weak spots. 

LOC2

3 tie plates 

removed 

638 ft

LOC1

2 tie plates 

removed 

510 ft

LOC5

4 tie plates 

removed 

1193 ft

LOC4

5 tie plates

removed 

770 ft

LOC3

4 tie plates 

removed 

695 ft

Start 1 in curve 

4 sites in tangent 

Figure 11. Layout of the weak spots on the repeatability zone 

Both vehicles were found to be highly repeatable. Figure 12 shows the GWP values for both the 

vehicles over a 400-foot section of the repeatability zone. No exceptions were found on the 

repeatability segment that the vehicles tested. 

Figure 12. GWP repeatability tests comparison a zone of approximately 400 feet for the 

TrackSTAR and the T-18 

25 
5.2.3 Over the Road Test 

The last phase of the comparison testing included testing both GRMS vehicles over about 40 

miles of Class III track with both vehicles applying their respective nominal loads. Figure 13 

shows the loads applied by the both vehicles on the AREMA plot. It can be seen that both the 

vehicles adhere to the AREMA specifications of applying test loads to the track. The acceptable 

zones on the AREMA plot are Zone II and Zone IV for test load application. 

Figure 14 shows a plot comparing GWP from the TrackSTAR, as well as the T-18, and it is 

observed that the comparison is very good. PLG24 safety exceptions were based on a PLG24 

threshold of 59 inches, and GWP safety exceptions were based on a GWP threshold of 1.00 inch. 

The exception count for both the vehicles compared very well and is tabulated in Table 4. GWP 

comparison between the two GRMS systems in terms of exceptions counted by location and feet 

were found to be very good (five for TrackSTAR and eight for T-18 when counted by location). 

Consecutive feet exceptions were counted as one exception by location. Table 5 shows the 

exception count considering the previous equation of GWR and safety threshold of 1.00 inch. It 

is observed that the maintenance and safety exception counts show greater disparity than the 

GWP numbers. 

26 
Figure 13. AREMA load plot for FRA’s T-18 and TrackSTAR 

Standard

deviation (kips)

GRMS 

Vehicles

Lateral Vertical 

TrackSTAR 0.76 1.04 

T-18 0.27 0.47 

27 
400 450 500 550 600 650 700 750 800

Feet

 0.0

 0.2

 0.4

 0.6

 0.8

 1.0

GWP (inches)

TS Run 10L 14V MP 49 to 63

 W15: Comparison of GWP between T-18 and TrackSTAR

T18 MP 49 to 63 14L 21V

Figure 14. Comparison plot of GWP from the T-18 and TrackSTAR over a length of 400 

feet during the Phase 3 tests, March 2005 

All three phases of the comparison testing between the FRA T-18 and the Holland TrackSTAR 

concluded that the GWP was an excellent measure to use when testing with GRMS vehicles with 

different loading configurations and systems. Further, by utilizing the GWP equation, both 

GRMS vehicles are capable of performing gage widening strength tests to determine the integrity 

of the track structure to withstand applied service loads. 

Table 4. Exception count for both the GRMS vehicles using the GWP equation 

GRMS 

Vehicle 

GWP 

Safety 

GWP 

Maintenance

PLG 

Safety 

PLG 

Maintenance 

Loaded 

Gage 

Exceptions by Feet

TrackSTAR 13 225 5 1154 0

T-18 23 244 5 2480 163

Exceptions by Location

TrackSTAR 5 85 3 280 0

T-18 8 75 3 439 46

28 
Table 5. Exception count for both the GRMS vehicles using the GWR equation 

GRMS 

Vehicles

GWR 

Safety 

GWR 

Maintenance

PLG 

Safety 

PLG 

Maintenance 

Loaded 

Gage 

Exceptions by Feet

TrackSTAR 245 1277 5 1154 0

T-18 154 907 5 2480 163

Exceptions by Location

TrackSTAR 69 322 3 280 0

T-18 45 225 3 439 46

By comparing the two exception numbers obtained from the GWP and the GWR, it is observed 

that the cumulative (safety and maintenance combined) of GWP numbers for TrackSTAR are 90, 

and for the T-18, it is 83 with the TrackSTAR identifying 8 percent more exceptions. The same

cumulative numbers for the GWR are 391 for the TrackSTAR and 270 for the T-18, providing a 

ratio of 1.45. In addition, in the case of GWP, it is observed that the safety exceptions are 

greater for the T-18 whereas the maintenance numbers are greater for the TrackSTAR. It is 

noticed that the GWR favors the vehicle applying a lower load severity (TrackSTAR) over the 

vehicle applying a higher load severity (T-18). In contrast to that, the GWP is a much better 

comparison between two different vehicles applying different load combinations. The GWP 

exceptions from the St. Louis test noted by both the vehicles were overlaid with the TRKLOD 

model for the minimally acceptable track conditions. The GWP exceptions compare excellently 

with the TRKLOD model, and Appendix B describes the analysis in detail. 

29 
30 
6. Summary and Conclusions 

The GWP equation was developed as a two variant dependent parameter that aims to satisfy the 

requirements from which the original GWR was developed. Shortcomings of the original GWR 

were analyzed in depth, and analysis and field verification were used to determine the form of

the present GWP equation. A test with the FRA T-18 was conducted on MMIR with different 

loading configurations to arrive at the exact value of the critical vertical load, which was 

determined to be 30 kips. The GWP achieves normalization of gage widening values at different 

loading configurations. It also keeps the original threshold of 1.00 inch as the safety exception 

limit and the maintenance limit, is retained at 0.75 inches. Excellent correlation exists between 

the GWP and the delta gage measured using the PTLF loading up to 4 kips. The theoretical 

TRKLOD model was also found to have good comparison with the GWP values from the 

comparison test between the FRA T-18 and the Holland TrackSTAR. GWP is a better 

extrapolation equation than the GWR, which normalizes the differences in applied loads 

common in the various designs of the GRMS vehicles present today. Advantages of the GWP 

over the GWR and its merits as an excellent tool for measuring track gage widening warrant its 

inclusion in the TSS. 

31 
32 
7. Recommendations 

It is recommended to apply the GWP equation described in this report in place of GWR for all 

GRMS analysis. Specifically, the GWP should be used in place of GWR for any redesigned 

GRMS operating at a loading different from the originally applied nominal 14 kips lateral, 21 

kips vertical load combination, or for GRMS systems where the split axle is not located in the 

position of the leading axle of the trailing truck. The recommended GWP equation is: 

L 0 258 V

8 26 GWP Gage − ⋅ = ∆ ⋅ .

. [15]

33 
34 
8. References 

AREMA (1999). Manual for Railway Engineering, American Railway Engineering and 

Maintenance of Way Association, Landover, MD. 

Blader F. (1983). “Analytic Studies of the Relationship Between Track Geometry Variations 

and Derailment Potential at Low Speeds,” FRA/ORD-83/16, September. 

Carr, G. and C. Stuart (1995). “Performance-Based Tie/Fastener Inspection Technique Using the 

Gage Restraint Measurement System,” Nondestructive Evaluation of Aging Railroads, 

International Society for Optical Engineering (SPIE), Proceedings, Vol. 2458, June. 

Choros, J., Fateh, M., Sussmann, T., and E. Curtis (2003). “Gage Restraint Measurement 

System Comparison Tests: Railbound and Hi-Rail Vehicles,” FRA/ORD-03/29, December 

2003. 

Coltman, M. and H. Weinstock (1988). Vehicle/Track Interaction Test at Bennington, NH, 

DOT/FRA/ORD-87/1, revised. 

Coltman, M., Dorer, R., and P. Boyd (1988). “The Development of Automated Survey 

Techniques for Evaluating Tie and Rail Fastener Performance,” Applied Mechanics Rail 

Transportation Symposium, American Society of Mechanical Engineers, AMD-Vol. 96, RTDVol. 2. 

Jeong, D. and M. Coltman (1983). “Analysis of Lateral Rail Restraint,” U.S. Department of 

Transportation, Federal Railroad Administration, Report No. FRA/ORD-83/15, September. 

Kish, A., Jeong, D., and D. Dwonczyk (1984). “Experimental Investigation of Gauge Widening 

and Rail Restraint Characteristics,” DOT/TSC/FRA-84-05, FRA/ORD-84/12. 

Manos, W. P., Scott, J. F., Choros, J., and A. M. Zarembski (1982). “Development of an 

Improved Vehicular Loading Characterization, Associated with Gage Strength of Track,” 

American Railway Engineering Association, Bulletin 686, Volume 83. 

McCarthy, W. (1995). “TSAR High-Rail System for Measurement of Rail Lateral Restraint,” 

Nondestructive Evaluation of Aging Railroads, International Society for Optical Engineering 

(SPIE), Proceedings, Vol. 2458, June. 

35 
36 
Appendix A. Rail Spring Model and TRKLOD Derivations 

A-1. Derivation of Rail-Spring Model Factor 

A simple physical model of the rail was also used to derive an equation for predicting rail 

deflection and hence a form for the GWP equation. The rail is assumed to be restrained against 

lateral movement by a single lateral spring with stiffness K. Furthermore, interaction of the rail 

with the tie plate due to the vertical force will cause a frictional force that reduces the effective 

lateral force by a factor depending upon the frictional coefficient between the tie and the tie 

plate. The value of the frictional coefficient can be found from the constant deflection lines for 

tests performed in the past on rail deflections with varying application of lateral and vertical 

force combinations. 

L

V

K

μV

Figure A-1. Simple rail-model represented by the rail restrained by a single lateral spring 

against a lateral and vertical force combination 

Based on analysis of this model, an equation for an extrapolation factor was developed that is 

given by equation 10 and similar to equation 11, thus confirming the nature of the analysis of the 

PLG A-factor development. 

x

x

I

K

L μ V

x

K

L - μ V

x

F L - μ V

F K x

gw

gw gw

gw

=

− ⋅ =

⋅ =

= ⋅

= ⋅

(L V)

(L V ) I gw gw

− μ ⋅

− μ ⋅ =

37 
In the above derivation, it is assumed that the rail deflections are equal for both rails. The 

extrapolation factor, I, for this model is the ratio of the deflection expected at the target load 

severity, noted with the sub, gw, in the equations, to the deflection obtained by the GRMS 

vehicle for the applied load severity and thus is equivalent to equation 10, the ratio of load 

severities for the ultimate and test load conditions. 

A-2. Derivation Based on the TRKLOD Analysis 

TRKLOD is a finite element model with each node representing a tie and the rail modeled as a 

beam element using three piecewise linear springs. The restraints are one lateral spring and two 

vertical springs, which adequately represent the displacements and rotations experienced by the 

rail under the any loading conditions, as shown in Figure 5 (a). More information about the 

TRKLOD model and its working can be obtained from the TRKLOD manual (Jeong and 

Coltman, 1982). 

Both vertical and lateral springs are considered to be piecewise linear, as illustrated in Figure A2 (b) and A-2 (c). The TRKLOD model takes inputs for the breaking points of the springs in the 

form of F and δ combinations. 

The TRKLOD model was run for a series of load combinations representing the load spectrum of 

interest for GWR and spring constants representing minimally acceptable track conditions 

developed by analysis presented in Manos, W. P., Scott, J. F., Choros, J., and A. M. Zarembski 

(1982); Coltman, M., Dorer, R., and P. Boyd (1988); and Jeong, D. and M. Coltman (1983). The 

model was then used to obtain predicted deflections. The deflections shown in Figure 5 are the 

deflection for a single rail presented by Coltman, M., Dorer, R., and P. Boyd (1988) and used in 

the development of PLG24. The total gage change is obtained by doubling the single rail 

deflection. 

38 
V

K

K2

K 3 1

(b)

(c)

(a)

L

Figure A-2. Schematic of the TRKLOD model element and its cross-section (a), lateral 

piecewise linear spring (b), and vertical piecewise linear spring (c) 

Given the deflection values from TRKLOD, an extrapolation factor ETRKLOD was defined as the 

ratio of the deflection at the critical loads to the deflection at the applied loads, Equation 8 where 

D is the expected deflection at the test load for the minimally acceptable track conditions used 

for the spring constants in TRKLOD. The analysis procedure is similar to the analysis of the 

data from Figure 5 and was used to develop the E-factor in Section 4.1. 

39 
40 
Appendix B. GWP and TRKLOD Model Comparison Analysis 

The GWP results were compared to the TRKLOD model using a series of simulation runs of the 

model using soft springs as the definition of minimally acceptable track with 115 lb rail, 18 

inches tie spacing, and load application using a single axle GRMS vehicle. Table B-1 gives the 

breaking points of the soft spring model, and the parameters of the 115 lb rail were taken from

the TRKLOD manual. 

Table B-1. Coordinates of breaking points of the soft spring used for the TRKLOD model 

K1, K3 Vertical 

Springs (Five 

Breaking Points) 

K2 Lateral spring 

(Seven Breaking 

Points) 

δ F 

-100.0 -2500.0

0.0 0.0

0.2 2.0

1.5 0.0

100.0 0.0

δ F 

-110.67 -484.00

-10.67 -404.00

-10.00 -400.00

0.00 0.00

10.00 400.00

10.67 404.00

110.67 484.00

Figure B-1 (a) and B-1 (b) show data from safety and maintenance GWP exceptions from T-18 

and TrackSTAR, respectively overlaid on top of constant deflection lines of the TRKLOD 

model. The colors of the data points are indicative of the deflection measured of a single rail 

during the GRMS testing. The mean and standard deviation of the difference between actual 

measured delta gage and the TRKLOD predicted delta gage based on the applied lateral and 

vertical loads were calculated and are tabulated in Table B-2. 

Table B-2. Average and standard deviation of the difference between the measured and 

TRKLOD predicted delta gage for T-18 and TrackSTAR 

T-18 

Safety Maintenance

Mean 0.20 -0.05

Standard Deviation 0.12 0.06 

TrackSTAR 

Safety Maintenance

Mean 0.18 -0.03

Standard Deviation 0.11 0.04 

41 
(a) 

(b) 

42 
Figure B-1. TrackSTAR data points from exception locations overlaid with the TRKLOD 

models constant lines of deflection 

A positive value of the average difference between the predicted and the measured is noticed for 

both the vehicles for the safety exceptions, and a slightly negative value (less than zero) is 

observed for both the vehicles for maintenance exceptions. A positive value of the difference 

indicates that the measured delta gage is higher than the expected or predicted delta gage. Hence 

the track at that location is weaker than minimally acceptable track and therefore a safety 

exception. A slightly negative value of the difference, which is observed with the maintenance 

exceptions, indicates that the track at that location is a slightly stronger than minimally 

acceptable track but is still weak and requires maintenance. The GWP value consistently shows 

the difference between the safety and maintenance exceptions for different vehicles with 

different loading configurations. 

43 
44 
45 

Acronyms 

AREMA American Railway Engineering and Maintenance-of-Way Association 

BNSF BNSF Railway (formerly Burlington Northern Santa Fe Railway) 

Delta gage Gage change between loaded and unloaded gage measurements 

FRA Federal Railroad Administration 

GRMS Gage Restraint Measurement System 

GWP Gage Widening Projection 

GWR Gage Widening Ratio 

LTLF Lightweight track loading fixture 

MMIR Maryland Midland Railroad 

NS Norfolk Southern Railroad 

PLG Projected Loaded Gage 

PLG24 Projected Loaded Gage at 24 kips lateral load 

R&D Research & Development 

RAIRS Railway Accident/Incident Reporting System 

RE American Railway Engineering Association rail section design 

T-18 FRA GRMS test vehicle with deployable split axle, commissioned May, 2004 

T-6 FRA GRMS test vehicle with truck mounted split axle, replaced by T-18 

TrackSTAR Holland’s Company hi-rail GRMS with deployable split axle 

VNTSC Volpe National Transportation System Center