to temperature changes throughout the day) and over the long
term (for example, owing to changing interactions between
the rail and the surrounding structure and factors such as rail
maintenance and train movement) (Kish et al. 1987). RNT in an
existing CWR system can be reset by conducting stress modi-
fication procedures for example, by cutting the rail that is in a
state of tension to release the axial stress and then pulling and
reconnecting (welding) the rail ends so that the system is at a
new RNT value. This procedure is destructive, labor-intensive,
and disrupts rail operation. As a result, such procedures are
used sparingly because of concerns about extreme stress states
in the rail. Nondestructive testing (NDT) methods that can
determine rail stress state are helpful to guide appropriate use
of such stress modifying procedures. Given the variation of
RNT value in a rail system, knowing stress or RNT with NDT
is critical to identify potential for high-stress situations in rail
sections and to address buckling risk in a timely fashion. NDT
methods that predict values of in-place rail strain provide a
strong representation of overall rail stress state because strain
can be used to compute rail stress and load (when the rail
cross-sectional area and steel Young’s modulus are known),
and RNT (when the rail temperature and thermal expansion
coefficient are known).
The use of nondestructive measurement technologies
has been recognized as an important component of good rail
stress or RNT management practice (Read 2005). Past studies
have considered a variety of physical phenomena for the
basis of NDT methods (Elliot 1979), but none of them satisfy
all the needed criteria or deliver acceptable accuracy (Huang
et al. 2023). In particular, several NDT techniques based on
rail vibration frequency have been explored, usually limited
to the low-frequency vibration range not exceeding 1 kHz.
For example, Boggs (1994) studied vibration frequencies of
an analytical rail dynamic model by adding a coefficient to
account for moderate effects of shear and rotational inertia,
and used multiple resonance frequencies to determine the
supporting stiffness and axial load. Béliveau (1997) compared
the relationship between resonance frequencies and axial load
predicted by various types of analytical rail dynamic models
where the results were evaluated with experimental data.
Recently, Belding et al. (2023) employed an artificial neural
network to estimate RNT that is trained by the experimental
low-frequency set of rail resonances. However, other studies
suggest that the mechanical characteristics of supporting
structures (for example, rail pads, anchors, clips, crossties, and
foundational bases) profoundly influence the vibration reso-
nance values of rail, especially in the frequency range below
5 kHz (Connolly et al. 2015 Thompson 2009). Understanding
this behavior, we explore the feasibility of using rail resonance
behavior at higher frequencies (20 kHz and above) to estimate
in situ rail axial strain and/or RNT more precisely, without the
disrupting effects of the supporting structure.
In this paper we present a practical vibration measurement
approach to collect vibration data from in-service CWR and
study the correlation between rail axial strain and frequency
of individual selected high-frequency resonance modes. The
goal is to identify vibration resonances for which the frequency
remains correlated to rail axial strain across different testing
times, temperatures, stress conditions, and rail locations. This
proposed approach offers advantages over existing measure-
ment technologies in that (a) a single reference-free mea-
surement provides estimates of in-place rail stress condition
(b) high-frequency vibrations are used, thereby avoiding the cor-
rupting influences from rail support structures and (c) the tests
are nondestructive and do not disrupt rail service. Our study
brings practical relevance because it demonstrates results using
rail temperature, strain, RNT, and vibration data collected from
an active instrumented track line over a period of two years.
Rail Instrumentation and Measurement
Field test data were collected from a commercial Class 1 rail
freight line in active service in central Illinois. The line main-
tains high traffic volume, loads, and train passage frequency.
The data were collected within a 3.2 km (2 mi.) tangent track
(straight track) section that runs in the east-west direction. The
CWR track structure comprises a nominal 136RE profile on
wood crossties where the rail is fastened by steel spikes and
rail anchors (see Figure 1). The track structure exhibits a typical
“every other tie anchor” (EOTA) configuration, although
varying physical condition, tie spacings, and tightness of spikes
are observed. The railhead has been worn through years of
service such that the actual in-place rail profile is equivalent
to an 132RE section. The rail profile was physically measured
at both test locations using a rail wear gauge and confirmed
by measuring a thin section of rail obtained after the cutting
procedure.
Two separate testing locations were identified on the same
rail, identified as the “East” and the “West” testing locations.
At both testing locations, rail temperature and axial strain
were monitored using a permanently mounted system. The
two measurement locations are located approximately 4 m
(160 in.) apart, which represents a distance of seven rail tie
spans, excluding the spans where the sensors are located.
The tie-to-tie spacings (spacing between the inner edges of
1 2
Figure 1. Part of the test site in Illinois showing the section reserved for
rail cutting, indicated by 1, and the span for instrumentation at the East
test location, indicated by 2. The location of the West test location is not
shown in this photo.
J A N U A R Y 2 0 2 4 • M A T E R I A L S E V A L U A T I O N 61
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ties) among the tie spans between the measurement sites
vary, ranging from 0.23 to 0.3 m (9 to 12 in.). Approximately at
the midpoint between the two measurement locations, a rail
de-stressing procedure (rail cut) was applied. The rail cut was
applied on the fourth tie span toward the west direction from
the East location, as shown in Figure 1.
At both testing locations, the rail web was instrumented
with two sets of strain gauge modules (active set and spare
set) and temperature sensors, as shown in Figure 2. At each
location, the strain measurement system uses a four-leg full-
bridge gauge comprising two axial and two transverse (vertical)
strain gauges, the output of which is modified to account for
transverse strains owing to temperature and the Poisson effect
when a value of Poisson ratio (0.285 was used to represent rail
steel here) is input to the system, the output value from the
gauges is an equivalent axial strain value ​​ ​ x​​​ This approach has
been well established in practice (Samavedam et al. 1986), and
values of ​​ ​ x​​​ obtained with such systems have been shown to
well represent the axial stress state in the rail owing to confined
thermal expansion (Liu et al. 2018). For the remainder of this
paper, the compensated equivalent strain output ​​ ​ x​​​ will simply
be referred to as axial strain or microstrain. Alongside the
strain gauge modules, one resistance temperature detector
(RTD) on each side of the rail at each location was installed for
monitoring the rail temperature. Together these sensors enable
the rail RNT to be calculated using the formula: ​ ​
(2)​ RNT =T − ​ ​ ε​x​​
α ​ ​
where ​ ​
ε​x​​​ is the equivalent axial strain, ​
α​ is the presumed linear thermal expansion coefficient 1.169
× 10–5/°C (6.5 × 10–6/°F), and
T is the rail temperature.
The rail temperature, axial strain, and RNT readings are
transmitted to a track-side solar-powered, stand-alone data
logging system. The entire measurement system was installed
and tested one day before the rail-cutting procedure. The
logging system has continuously reported the temperature,
strain, and RNT data every 15 min since it was installed.
The rail-cutting procedure was conducted on the morning
of 31 July 2019. The cutting process released the rail stress
(tension) around the cut region and then the rail was pulled
and connected with a thermite weld to set the RNT to a
desired value. Because the strain and temperature measur-
ing system was deployed and operating before the rail cut
occurred, the equivalent axial strain and RNT of the system at
the two measurement locations can be accurately measured
moving forward. All reported strain and RNT are referenced by
the original cutting procedure, and no subsequent rail-cutting
procedure or other gauge calibration processes were carried
out. Although sensor systems are known to exhibit errors,
such as value drift, over the long term, in this case it is reason-
able to presume that the overall drift of the multisensor full-
bridge strain system will likely provide insignificant changes
with respect to the stress-state changes the system measures,
because the random drift of individual sensors within the
combined full-bridge system are likely to cancel each other out
over the two-year measurement period. To check for possible
drift problems, we switched from active to spare strain sensor
sets mounted nearby after over one year of measurement and
found no significant change in the strain readings.
The rail vibration responses are generated by mechanical
impulse events, which are initiated using a small steel sphere
with a diameter of 12 mm (0.47 in.). The impulse is applied by
hand to the center top of the railhead at the midspan location
between the ties. The vibration responses are sensed by a
polarized condenser microphone pointing to the side of the
railhead at the same location where the impulse is applied,
as illustrated by Figure 3. The microphone has a sensitivity
of ±3 dB across a frequency range of 4 to 100 000 Hz. The
response signals measured by the microphone are ampli-
fied through a sensor signal conditioner using a gain of
10, and then transmitted to a multifunction I/O device for
data acquisition. Each collected time signal set up by the
mechanical impulse is 0.3 s in duration with a sampling rate
of 500 kHz with a total of 150 001 sample points including
10 000 pre-trigger samples.
Vibration tests were carried out on 1, 5, 15, and 29 August,
19 September, and 18 October in 2019 29 May and 8 October
in 2020 and finally 16 June in 2021. Vibration data from both
the East and West locations were measured, although the West
location was not tested on 29 May 2020. A wide range of the
RNT and strain conditions are represented during these test
days. All vibration test days started at approximately 9:00 a.m.
and ended around 3:00 p.m. or when the rail temperature
started to decrease because of reduced sun exposure. The
vibration measurements started at one test location and then
switched to the other location every 40 to 60 min during the
ME
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RAILROADS
RTD
Strain gauge modules
Figure 2. Sensors attached to the rail web: resistance temperature
detectors (RTD) and the two sets of strain gauges. Each set consists of
two strain gauge modules that contain two strain gauges, oriented in
the axial and transverse direction, each attached on both sides of the
rail web.
62
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