ABSTR ACT
Continuously welded rails are connected without
stress relief joints and, thus, thermally induced rail
movement is constrained, which can result in the
development of excessive axial stress and risk of
rail failure. Nondestructive testing (NDT) methods
that estimate in-place rail stress state or rail neutral
temperature are desired. Some methods have been
developed, but none satisfy the requirements for ideal
monitoring in practice. We propose an NDT technique
based on impulse-generated vibration, seeking high-
frequency rail vibration resonances whose frequency
maintains a consistent correlation with rail axial
stress/strain across different temperatures, stress
states, and rail support conditions. Rail temperature,
axial strain, and vibration data were collected
from an active Class 1 commercial rail line over a
period of nearly two years. The frequencies of four
consistent and clear resonance modes of the rail were
monitored. One of the identified modes demonstrates
a unique linear relation with axial strain across a
range of temperatures and stress states at each of the
two measurement locations. The developed linear
relations were used to predict in-place strain and rail
neutral temperature with acceptable accuracy across
all the measurement data, although each test location
exhibits a unique relation.
KEYWORDS: acoustic sensing, NDT, rail neutral temperature,
rail buckling, spectral analysis
Introduction
Continuously welded rail (CWR) is the prevailing type of
railroad track structure in the United States. CWR comprises
long sections of continuous rail steel that are welded together
at the ends. The CWR structure also contains rail fastener
and foundational components such as rail crossties, clips,
and anchors and thus represents a mechanically constrained
system without stress-relief joints. Although CWR offers
advantages such as smooth transit at high speed, it constrains
the free thermal expansion of the rail and therefore tends to
build up high levels of axial stress when the rail experiences
temperature extremes. In particular, high levels of axial com-
pression build up at high rail temperatures, which can cause
rail buckling events. According to a report from the Federal
Railroad Association (FRA), “track alignment irregularities
(buckled/sun kink)” is among the leading track-related factors
that cause train accidents (US DOT n.d.). Rail buckling is also
associated with a high risk of large-scale train derailment
(Wang et al. 2020), which entails rail operation suspension,
damage, and even casualties. Therefore, monitoring thermally
induced axial stress state in CWR is important for railway oper-
ations and safety.
The parameter rail neutral temperature (RNT) is broadly
used by track engineers to characterize the stress state of CWR.
RNT represents the rail temperature at which the rail is totally
free of axial stress, and it provides a quick sense of the load
level by comparing the present rail temperature to RNT. Larger
differences between the present rail temperature and RNT
indicates higher levels of load in constrained systems, follow-
ing the relationship derived from linear thermal expansion: ​ ​
(1)​ ​ P
AE​
=​ ε​x​​ =α(T ​ − RNT)​​,
where
P is the thermally induced axial force,
E is the Young’s modulus of the rail steel,
A is the cross-sectional area of the rail, ​ ​
ε​x​​​ is the equivalent axial strain, ​
α​ is the coefficient of linear thermal expansion of the rail
steel, and
T is the in situ rail temperature.
The RNT of a track structure is set at the time of rail instal-
lation, but it can vary over the short term (for example, owing
PREDICTING AXIAL STRESS STATE IN
CONTINUOUSLY WELDED RAIL USING
IMPULSE-GENERATED VIBRATION
MEASUREMENTS
CHI-LUEN HUANG* AND JOHN S. POPOVICS*†
*Department of Civil and Environmental Engineering, University of Illinois at
Urbana-Champaign, Urbana, IL 61801
† johnpop@illinois.edu
Materials Evaluation 82 (1): 60–66
https://doi.org/10.32548/2024.me-04377
©2024 American Society for Nondestructive Testing
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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.
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