Continuous Welded Rail

The performance of continuous welded rails, before buckling takes place, is now well known and one is aware that in the case of ambient temperatures different from the laying temperatures there will be an area in the middle of the track without any movement.

From: Railroad Track Mechanics and Technology , 1978

THE MECHANICS OF RAIL FASTENERS FOR CONCRETE SLAB TRACK

Bernard Bramall , in Railroad Track Mechanics and Technology, 1978

4 OTHER MODES OF ELASTICITY

Today, continuous welded rails are taken as normal for main lines. Where rail joints must be incorporated, the so-called breathing lengths must move in the fasteners. Either a frictional or elastic grip can in principle limit the movement. Before slip occurs there is usually a small elastic deformation and this is useful in distributing tractive or braking forces to the slab and without provoking rail creep. Eisses [7] has made a particular study of longitudinal elasticity in relation to precast slab track, and suggests that a fastener should permit 2.8 mm movement before slip occurs.

Two other modes of elastic restraint remain possible, both torsional and in longitudinal planes, namely horizontal and vertical. The first of these has wielded importance by contributing to resistance against lateral buckling. A slab is eminently suitable for taking over that function. However, even in a slab track there remains a tenable role for these restraints by influencing vibration within the audio range.

However complicated may be deformations of the rails in the vicinity of the wheels, it is obvious that vibration can endure after the passage of a train, according to several modes of natural frequency. Indeed any railway man knows they can be excited ahead of a train, providing a strictly unauthorized listening post. Amongst these pervasive vibrations are some with nodes at every fastener. Table 2 shows primary frequencies of bending both vertically and horizontally, assuming the supports permit free angular movement. Any restraining of angular movement would raise the frequencies.

TABLE 2. NATURAL VIBRATION OF RAILS WITH NODES AT FASTENINGS

RAIL VERTICAL FREQUENCY HORIZONTAL FREQUENCY
Type Weight Second Moment of Spacing of supports Spacing of supports
Vertical Horizontal 60 cm 65 cm 70 cm 60 cm 65 cm 70 cm
Kg/m cm4 cm4 Hz Hz Hz Hz Hz Hz
s 49 49.43 1819 320 1200 1020 880 500 428 370
s 54 54.54 2073 359 1220 1040 900 510 432 373
s 60 60.4 2760 454 1310 1120 960 542 461 398
uic 54 54.43 2346 414 1300 1110 950 546 465 401
uic 60 60.34 3055 513 1400 1200 1030 578 491 424
s 64 64.92 3252 604 1400 1190 1030 605 514 444
AREA 14c 69.4 4029 1510

NOTE: f= ( π/2L 2 ) EI / m in general units or F= ( 713.000 / D 2 ) J/W where F in Hz is frequency, D in cm is spacing, J in cm4 is second moment of area, W in kg/m is rail weight.

All these frequencies are well within the range of human hearing and the rail is a fairly large loud speaker. Moreover, those emitted waves which might have been absorbed by ballast are reflected by a hard concrete slab. Human sensitivity tends to be most acute at frequencies of about 1,000 Hz, diminishing gradually for frequencies below or above.

In this mode, the frequencies of horizontal bending are entirely below 1,000 Hz. Thus there is absolutely no merit in seeking to raise them by intentionally increasing angular restraint. The vertical vibrations are above 1,000 Hz for closely spaced fasteners, so rotational stiffness in a vertical plane has some slight acoustic merit.

Lower frequencies excited by the passage of trains inevitably have longer distances between nodal points, which may travel along the rail. Between nodes the rail must move within the fasteners. Thus the restraining stiffness of the fasteners exerts its effect on frequency. Travelling in a train over a series of different test lengths as at Radcliffe-on-Trent gives a surprisingly convincing subjective impression how the dominant tone tends to rise with stiffness. Evidence can be discerned from power spectral analysis, even if the total noise is unchanged. In turn that leads into the fascinating study of human preferences.

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THE EXPERIMENTAL DETERMINATION OF THE AXIAL AND LATERAL TRACK-BALLAST RESISTANCE

Pierre Dogneton , in Railroad Track Mechanics and Technology, 1978

3.1.3 Thermal Stresses

On condition that appropriate fastening devices are used accompanied by an adequate and well-maintained ballast bed, the continuous welded rails may be submitted to considerable thermal stresses without risk of buckling caused by high temperatures (compressive forces) or breakage by low temperatures (tensile forces).

The performance of continuous welded rails, before buckling takes place, is now well known and one is aware that in the case of ambient temperatures different from the laying temperatures there will be an area in the middle of the track without any movement. In this area, designated as "neutral area," expansion is prevented throughout; the thermal stresses will reach their maximum values there at extreme temperatures. On either side of this neutral area, expansion is only partly prevented. There are movements, which attain their maximum amplitude at the ends of the rails, where the thermal stresses are then equal to zero. These two areas at the ends of the rails are called "breathing areas."

For a difference in temperature of 1 o, the stress in the rail equals Eα, E being Young's modulus for the rail steel considered and α the corresponding thermal expansion coefficient. The Eα value has been tentatively measured using extensometers and the range of variation obtained is comprised between 0.210 and 0.255 daN/mm 2 .

The force developed in a rail equals E A α Δ T. Thus, at a difference in temperature of 45°, which generally corresponds to the maximum difference which may be encountered, one obtains a maximum force of 650 kN in the case of a U36 rail and of 780 kN in the case of a U80 rail. These values must be multiplied by 2, to obtain the corresponding axial force in the track.

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Railway Engineering

William W. Hay , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

V.I.3 Other Field Procedures

A full ballast section with a 6- to 12-in. shoulder beyond the tie ends is required to withstand thermal forces in CWR and lateral and vertical displacement or sun kink. Surfacing and tie renewals should not be undertaken when the rail is in compression (trying to expand), or at least only a few feet of track should have ties and ballast disturbed at a time. When a sun kink occurs, the rail is shrunk by cooling or a portion is cut out and a field weld or joint bars is applied. Pull-aparts (usually in cold weather) are repaired by applying joint bars, by heating and expanding, or by cutting in a short section of rail (10   +   ft) held by joint bars or a Thermit weld.

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Models for infrastructure costs related to the wheel–rail interface

E. Andersson , J. Öberg , in Wheel–Rail Interface Handbook, 2009

Reference information

There is a mix of 50   kg and 60   kg rails, with a predominance of 50 kg. Most tracks, if weighted by actual traffic volume, have continuous welded rails (CWR) resting on concrete sleepers. Permissible axle load is mostly 22.5 tonne, but some lines are upgraded to 25 tonne. The iron ore line allows for 30 tonnes axle load. The total route length is 10 000  km, of which about 1900   km is double or quadruple track. Sidings on stations and yards are not included in these figures. The routes include some 11 400 switches.

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Thermal Expansion

David R.H. Jones , Michael F. Ashby , in Engineering Materials 1 (Fifth Edition), 2019

Continuous welded railroad track

Traditional railroad track is hot rolled to the correct cross section in the steel mill, and cut into standard lengths for easy transportation. When the track is laid, the lengths are joined end to end using "fishplates"—short lengths of steel plate overlapping the joint, and bolted to the ends of the rails (Figure 31.6).

Figure 31.6

Figure 31.6. A fishplated rail joint—note expansion gaps.

At each joint there must be a short gap (≈ 1/8″) between the rail ends, to allow for longitudinal thermal expansion of the rails on hot days. Fishplate joints are unsatisfactory for high-speed lines, and these now use continuous welded rail (CWR). Rail from the mill is delivered to site by train in long prewelded lengths, laid on reinforced concrete ties (sleepers), and finally site welded into still longer lengths (many km long). Figure 31.7 is a close up of a section of rail showing the ties, and the spring clips that hold the rail down onto the ties.

Figure 31.7

Figure 31.7. Continuous welded rail.

The rail is subjected to a range of temperatures, from the coldest temperatures in winter to the hottest days in summer. In continental US or Europe this can easily be −   10 to +   30°C (ΔT  =   40°C), giving a thermal strain αΔT of 12   ×   10−   6  ×   40, or 0.48   ×   10−   3 (α value of steel taken from Table 31.1). Over a 3-km length of CWR, this would produce a length change of 1.44   m! Clearly, something has to be done to stop the rail expanding/contracting.

For each km of track, there will approximately 2000 ties, so there are 2000 clips bearing down on each rail. The combined friction of all these clips stops the rail sliding over the ties. The ties themselves are very heavy, and are set in tightly packed ballast consisting of self-locking chips of broken stone (e.g., granite). This means that the ties do not move over the ground either, so the track is unable to expand or contract. The thermal strain is neutralized by an equal and opposite elastic strain, which produces a locked-in thermal stress given by

(31.7) σ = Eα Δ T

For ΔT  =   40°C, σ  =   200   ×   103  MN   m−   2  ×   0.48   ×   10−   3  =   96   MN   m−   2 (E value of ferritic steel taken from Table 3.1). This is much less than the yield stress of the steel, so the rail stays elastic.

There is one complication, though. On very hot days, the compression force in the rail can cause buckling—the track moves sideways, and tight snaking curves develop which will derail a train. We have already looked at the elastic buckling of beams in Chapter 7. The critical buckling load is given by

F cr = C EI L 2

Modern rail sections have a large second moment of area I, so this helps to stop buckling. However, the rail is very long (large L), so if the rail is not prevented from moving sideways, it will buckle very easily. In practice, the heavy ties and strong ballast generally stop the rail moving sideways as well as lengthways, and the risk of buckling is small. However, in practice, this risk is further reduced by ensuring that the rail spends a lot of its time in tension. After the rail is laid, but before it is site welded and clipped to the ties, it is pretensioned using powerful hydraulic jacks. Of course, after a long patch of warm weather—when the stock of rail has had time to warm up—this pretensioning may not be needed. The service temperature at which the rail neither expands nor contracts is called the "zero-stress temperature," and this is generally chosen so as to engineer a low risk of buckling at the maximum design temperature, while ensuring that the rail does not pull through the spring clips at the minimum design temperature.

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THE DEVELOPMENT OF ANALYTICAL MODELS FOR RAILROAD TRACK DYNAMICS

D.R. Ahlbeck Researcher , ... R.H. Prause Associate Section Manager , in Railroad Track Mechanics and Technology, 1978

Recent Track Measurements

Track dynamic response measurements were made on high-speed tangent track under both summer and winter ambient conditions during a recent AAR Track Train Dynamics Program task. Although the task was aimed primarily at the measurement of dynamic track gauge, tie plate loads and rail vertical and lateral absolute deflections were also measured. This provided an additional opportunity to compare actual measurements with computed values from the analytical track models.

The track at the measurement site consisted of 133 lb/yd (66 kg/m) continuous welded rail on 8 × 14-in. l:40-cant tie plates, a processed phosphate-ore ballast with at least a 24-in. depth, and a subgrade of uniform fill material (probably crushed lava rock and sand). Estimated track parameters used to calculate the track stiffness ( eqs. 2 through 7) are given in Table 2. From these parameters, the individual and overall stiffnesses of the track structure are calculated from linear theory, and are listed in Table 3.

Table 2. Estimated Values of Track Parameters

Parameter Numerical Values
Rail weight 133 lb/yd 66 kg/m
Flexural rigidity, EI 24.9(10) 8 lb-in2 7.15(10) 8 MN-m2
Tie spacing, l t 23 in. 58.4 cm
Tie tamped area, At 360 in.2 2323 cm2
Tie width, w 9 in. 22.9 cm
Ballast depth, h 24 in. 61.0 cm
Ballast modulus, Eb 30,000 lb/in.2 207 MN/m2
to 40,000 lb/in.2 276 MN/m2
Subgrade modulus, KO 150 lb/in.2 1.03 MN/m2
to 500 lb/in2 3.45 MN/m2
Ballast densit, ρb 2200 lb/ft3 35,200 kg/m3
Subgrade density, ρs 2500 lb/ft3 40,000 kg/m3

Table 3. Calculation of Track Stiffness and Deflections Under Load

Calculated Parameter Numerical Values
kb (ballast stiffness) 944,000 lb/in 165 MN/m
to 1,260,000 lb/in 220 MN/m
ks (subgrade stiffness) 229,000 lb/in 40 MN/m
to 762,000 lb/in 133 MN/m
kbs (combined stiffness) 184,000 lb/in 32 MN/m
to 475,000 lb/in 83 MN/m
Kt (assumed tie stiffness) 1(10)6 lb/in 175 MN/m
K (track modulus, per rail) 3,650 lb/in 25 MN/m/m
to 8,350 lb/in 58 MN/m/m
β (inverse characteristic length) .0246 in−1 .97 m−1
to .0303 in−1 1.2 m−1
Kr (track stiffness to point load, per rail) 297,000 lb/in 52 MN/m
to 551,000 lb/in 97 MN/m
λ (influence coefficient) * 0.13
to -0.01 (uplift)
y (total vertical deflection) * .125 in 3.2 mm
to .059 in 1.5 mm
(*)
Based on a 33,000-pound wheel load and a 72-inch axle spacing (100T car)

Typical force and deflection traces are shown in Fig. 12 for heavy 100-ton (LC3) and 125-ton (LC4) covered hopper cars, and 6-axle radio-controlled diesel units, at a train speed near 50 miles per hour. In Fig. 13 a group of empty 100-ton covered hopper cars are shown near 60 miles per hour. Both of these recordings were made under winter ambient (frozen ballast) conditions. To check the comparison between the measured and computed deflection shapes, the idealized deflection curves were plotted, based on two identical cars coupled together: two loaded 125-ton cars (P = 39,200 lb), and two empty 100-ton cars (P = 8,000 lb). Points from typical measured deflection curves were then plotted over these linear, idealized curves (in reality, a time-variation compared with an ideal spatial variation). Results of these plots are shown in Fig. 14. It is immediately apparent from this plot that track modulus (K) exhibits a nonlinear, "hardening" spring rate quite similar to an elastomeric pad in compression. While the deflection under maximum wheel load (purposely matched by choice of a track modulus of 5500 lb/in/in, or 38 MN/m/m) agrees well in magnitude and shape, the deflection under light wheel load is actually three times greater than calculated. The slight increase in deflection from a 39,000-lb. wheel load (LC4 car) over the 33,000-lb. wheel load (LC3 car) is indicative of the very high tangent stiffness under load.

Fig. 12. Tie Plate Vertical Load and Rail Vertical Deflection Under Heavy Freight Cars and Locomotives of Unit Train (Train Speed 50 mph, 80 kph)

Fig. 13. Tie Plate Vertical Load and Rail Vertical Deflection Under Empty and Lightly-Loaded Freight Cars (Train Speed 60 mph, 97 kph)

Fig. 14. Comparison of Idealized (Linear Beam on Elastic Foundation) and Measured Rail Deflection Shapes Under Wheel Loads of Coupled Cars

To pursue this further, representative data points were plotted for a range of wheel loads under both summer and winter conditions. Ranges of tie plate vertical loads and corresponding vertical absolute rail deflections are shown in Fig. 15. From an average value of locomotive-induced tie plate loads (assumed to be 33,000-pound vertical wheel loads, and limited to lower-speed recordings), the instrumented tie plate was found to support about 33 percent of the wheel load in summer, about 48 percent in winter. Tangent stiffness values under maximum static wheel loads (per rail) were calculated from these tie plate-to-wheel load ratios, assuming (for the locomotives) a negligible influence from adjacent wheels. Choosing nominal, linear stiffness values from these curves (rail deflection under heavy wheel load), "secant" values of 290,000 lb/in (51 MN/m) for summer, and 425,000 lb/in (74 MN/m) for winter are calculated, which fall reasonably close to the calculated values of Table 3. The tangent stiffness, however, for small oscillations about the static load, is seen to be roughly twice the calculated stiffness.

Fig. 15. Tie Plate Load Versus Rail Vertical Deflection Downward From Rest Position, 133 lb/yd Rail

It is apparent from the deflection traces of Figs. 12 and 13 that the track structure is highly damped under vertical load. Even the high impact load of a flat wheel on one diesel unit (Fig. 12) is very quickly damped. Oscillation frequencies of 20 to 25 Hz were observed, as well as higher-frequency oscillations of 88 to 100 Hz under impact loads, with higher static wheel loads. Under light cars (6000 to 9000-pound wheel loads), impact oscillations of 50 to 70 Hz were observed.

Experimental measurements of rail lateral stiffness were also conducted by applying a lateral force to the rail in increments of 1000 pounds up to 10,000 pounds maximum, simultaneously with a 33,000–pound vertical wheel load. A patch of Teflon tape and a witch's brew of Molykote and EP grease were applied under the wheel to reduce lateral frictional hysteresis. Under these conditions, a lateral stiffness of 330,000 lb/in (58 MN/m) was measured at the rail head, reasonably linear up to this load level. Lateral oscillations in dynamic gauge were noted in recordings, particularly at rail temperatures near or above the "laying" temperature, ranging from 20 Hz under heavy wheel loads (particularly locomotives), down to 15 Hz under the light wheel load of a caboose. Absolute lateral oscillations near 10 Hz were occasionally seen under impact loading.

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A review of railway infrastructure monitoring using fiber optic sensors

Cong Du , ... Xingwei Wang , in Sensors and Actuators A: Physical, 2020

4.1 Rails

Ping et al. [116 ] utilized two FBGs as bi-directional sensor attached on the rail track in vertical and longitudinal directions to accurately determine longitudinal force measurement in continuous welded rail as shown in Fig. 13(a). The experiment was conducted for 23 h at two selected points on the subgrade of a Chinese high speed railway. One point was situated at approximately 150 m away from the rail intersection and the other point was located at over 70 m from the abutment of a bridge. The sensors were calibrated for temperature variations. The maximum differences obtained between measured values and theoretical values at these two points were 7.5 kN and 10.9 kN, respectively. The experimental results obtained were in agreement with the theoretical analysis with a measurement accuracy of over 95 %. Minardo et al. [117] utilized a slope assisted Brillouin optical time-domain analysis (SA-BOTDA) technique to monitor the railway traffic condition in real time by attaching a single-mode optical fiber along a rail track of about 60 m length with an outer diameter of 900 μm on the Italian regional line San Severo-Peschici (Fig. 13(b)). A test train with a total length of about 42.66 m and a maximum speed of approximately 110 km/h was used. The total number of axles was eight and the total mass of the train was 50 tons + 50 tons (two wagons). In the experiment, the sampling rate of 1 gigasample (GS)/sec, 100 m sensing length and 128 averages for the Brillouin gain traces were selected. The acquisition rate obtained was 31.4 Hz and a spatial resolution of 1 m was achieved for the strains induced during the train passage. The collected data from SA-BOTDA identified the location of trains, counted the number of axles, measured the train velocity and monitored the dynamic loading conditions for dynamic strain measurements in order to calculate the rail bed modulus.

Fig. 13

Fig. 13. Several FOS placement approaches to monitor rail track. (a) Layout of FBG sensors and its installation on site (modified from [116]), (b) Layout of the glued fibers used for rail track monitoring (modified from [117]).

Bao et al. [118] used a pulse pre-pump Brillouin optical time domain analysis (PPP-BOTDA) to monitor the strain and temperature at the joint of rail tracks, which utilized a single mode fiber as distributed sensing element (Fig. 14(a)). The field test was conducted on a length of 25 km rail track. The results in their experiments presented that the strain and temperature coefficient of PPP-BOTDA were 5.19 × 10-5 GHz/μԑ and 1.03 GHz/°C respectively. The spatial resolution obtained was nearly 2 cm. The measurement range of the distributed optical fiber obtained was roughly up to 12,000 μԑ (1.2 %) or higher. The results concluded that the gage length of the sensor required should be at least 1.5 mm to incorporate the changes due to very low temperature (-30 °C to−45 °C). Klug et al. [119] conducted two field tests to monitor local strain, local track displacement and derived vertical and horizontal deformations of tracks based on the principle of Brillouin backscattering. The first test was conducted on a 34 m rail track to monitor lateral rail deformations due to large vertical loads caused by natural events such as landside, avalanche, mudflow or rockslide. The results indicated the measurement of strain changes on the outer and inner track side with a maximum strain measurement of about 600 μԑ. The second test focused on monitoring vertical deformations such as local strain and local track displacement. The test was performed under two different load cases; (1) a locomotive with a length of 19.28 m and a weight of 80 tons; and (2) a passenger wagon with a length of 26.40 m and a weight of 46 tons. The results obtained showed that, in case of locomotive, the vertical deformation measured was less than 2 mm and the four axles were hard to determine. For the passenger wagon, the sensor length was increased to match the longer length of wagon and the vertical deformation was measured over 5 mm indicating that the foundation soil was not well compacted in that particular area. Wheeler et al. [120] applied OFDR based on Rayleigh backscattering technique to measure displacements during rail traffic. For laboratory test, rail displacements were measured by instrumenting and loading a 2.8 m long section of simply supported rail (Fig. 14(b)) and comparing the results by conducting static and dynamic tests using three DIC cameras and five linear potentiometers (LP). The results indicated that the displacement measured with OFDR had a difference of 0.3 mm when compared to DIC and LP. Moreover, OFDR failed to monitor rail displacement under high vibration generated due to fast moving train as the quality factor of the recorded fiber optic strain data obtained was below the manufacturer's minimum recommended threshold. However, OFDR based distributed FOS was promising in monitoring rail displacements under low vibration conditions.

Fig. 14

Fig. 14. Distributed FOS approaches to monitor rail track. (a) Schematic of the placement of distributed FOS (modified from [118]), (b) Layout of optical fiber installed on the rail (modified from [120]).

Kang et al. [121] developed a FBG sensing system and a graphic user interface (GUI) for real-time monitoring of gauge change procedures on wheels and verified through a 1/6th subscale model test. They attached two FBG sensor arrays composed of five FBGs each (grating length 10 mm, reflectivity 90 % (10 dB)) on rail track (Fig. 15) to measure the strains in real-time when a train passes from standard gauge to broad gauge. The wheel speed was controlled by a remote controller with a range from 0 to 60 rpm. The weight of the wheel set was 70 kg. The sampling rate of the system was 5 Hz. The results showed that such optical gauge changing monitoring system can be very helpful for railway industry. Zhang et al. [122] proposed a track temperature prediction system based on FBG sensors and relevance vector regression theory and developed a system for real-time online monitoring of railway track temperature, displacement and strain to deploy it as an early warning system of Guangzhou-Shenzhen-Hong Kong high-speed railway track condition. The monitoring area was 1960 m long with 285 FBG sensors attached on the high speed railway. This included 42 FBG temperature sensors, 117 FBG displacement sensors and 126 FBG stress and strain sensors. 65 out of 117 FBG displacement sensors were installed to measure the relative displacement between the rail and the track bed. The remaining FBG displacement sensors were employed to monitor relative displacement between the bed plate and the bridge. Two 16 channels FBG demodulators were utilized with a frequency of 50 Hz. The results demonstrated that the system can effectively monitor and predict the health status of the track structure under harsh environment and sudden weather changes.

Fig. 15

Fig. 15. Schematic of the real-time monitoring system of the railway gauge change procedures (modified from [121]).

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High-speed railway ballast flight mechanism analysis and risk management – A literature review

Guoqing Jing , ... Xiang Liu , in Construction and Building Materials, 2019

3.3.1 Ballast profile

Track engineering measures could be developed to reduce the risk of ballast flight. Some measures are often used in engineering: compacting and stabilizing the top layer of ballast; ensuring that ballast aggregates are washed and free of dust; reducing shoulder ballast height while maintaining CWR stability; and decreasing the ballast airflow interaction to diminish the aerodynamic effects. The crib ballast top should be 2–4 cm lower than the sleeper top level and larger ballast aggregates are preferred on top of the ballast bed surface (as this affects ballast tamping); moreover, ballast should be swept off the sleeper top surface, where the ballast can easily be picked up due to the higher vibration of the sleeper [24].

Lowering the ballast profile by 2–4 cm below the sleeper top is a risk mitigation strategy adopted by several countries, such as Japan, China, France, and Spain [7,70,26,71] . As discussed previously, ballast particles are more prone to be picked up if on the surface of the sleeper. This solution has appeared to have good results, but in France, this solution caused an increase in the tamping frequency. This could be explained by the fact that a lower ballast profile also implies a lower lateral resistance. It should be noted that the ballast shoulder height reduction leads to a tamping maintenance frequency increase, and results in a potential lack of lateral resistance for the Continuous Welded Rail, as well as the crib ballast reduction. All the potential ballast profile engineering methods should be tested with reference to Le et al. [50], which investigates ballast-sleeper interactions.

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