Research progress on train operation safety in Xinjiang railway under wind environment

Abstract

Railway lines in the Xinjiang wind area face severe wind disasters year-round, which seriously affects the safety and economy of the railway in China. Therefore, the wind characteristics and statistics of wind-induced accidents along the Xinjiang railway lines are presented and the basic research route for evaluating the train running safety under crosswinds and effective measures to improve the windproof performances of trains are proposed, which are meaningful to deal with wind-induced train accidents. Based on this research route, a series of numerical simulations are conducted to evaluate train safety and the corresponding measures are provided. The results show the following. The running safety of the train under crosswinds mainly depends on the aerodynamic loads acting on the train. The relationships between the safe speed limit and train type, the load weight, the embankment height, the road cutting depth, the railway line curve parameters, the yaw angle and other factors are obtained. The critical wind-vehicle speed relationship, as well as the engineering speed limit value under different running conditions, are determined. Large values of the aerodynamic and dynamic indices mainly appear in special locations, such as near earth-embankment-type windbreak walls, shallow cuttings and the transition sections between various types of windbreak walls. Measures such as increasing the height of the earth-embankment-type windbreak walls, adding wind barriers with reasonable heights in shallow cuttings and optimizing the design of different types of transition sections are proposed to significantly improve the safe speed limits of trains under crosswinds.

1. Introduction

Located in the hinterland of Asia, Xinjiang in China has a unique continental climate, with little rain, hot summers and cold winters. Affected by southward-moving cold air from Siberia and the Ural Mountains, there are high-frequency strong winds [1]. The historical meteorological data show that the main characteristics of gales along the Xinjiang railway lines (the Xinjiang railway in this paper mainly refers to the Lanzhou–Xinjiang Railway and the Southern Xinjiang Railway in Xinjiang, China) have high speeds, long periods, strong seasonality and fast variations [2,3]. In addition, the maximum transient wind speed exceeds 60 m/s in the Baili wind area. Therefore, the Xinjiang railway along such wind area is one of the railway lines with the highest wind speeds and the most severe wind disasters in the world.

Since the operation of the Xinjiang railway began, many wind disasters have occurred. According to the existing incomplete statistics, there have been a total of 38 traffic safety accidents caused by wind and sand during railway transportation in Xinjiang from 1960 to the present [4]. Moreover, the strong wind frequently forces the trains to stop, which not only significantly affects the transportation efficiency but also has a poor societal influence. For example, on 28 February 2007, passenger train 5807 overturned from Urumqi to Aksu, as shown in Fig. 1 [5]. In addition, window glass damage, cement hardening and rail wear and tear increase, and life reduction of the driving equipment caused by wind and sand are also very common phenomena. The data mentioned above show that the characteristics of wind and wind disasters in the wind area along the Xinjiang railway pose unique challenges.

Many researchers have already performed a considerable amount of work to study the crosswind characteristics based on full-scale tests, reduced-scale model tests (wind tunnel tests and moving model tests) and numerical simulations [5–14]. Full-scale tests are difficult and expensive to organize and implement, and the field test process is easily affected by other factors, such as climatic conditions [15]. Reduced-scale model tests are extensively used in the study of train aerodynamic characteristics [16]. They have the advantages of being well-developed experimental methods with high measurement accuracy and ease of airflow parameter control [17,18]. Numerical simulations are a research method of train aerodynamics with shorter implementation time, lower costs and easily controlled parameters, and these have also been adopted to study train aerodynamics under different conditions, although the results are essentially an approximate solution that needs to be validated by experiments [19,20]. Specifically, in the EN Standard 14067–6 [21], a deterministic methodology based on the ‘‘Chinese Hat’’ wind gust model was proposed to evaluate the dynamic response of a railway vehicle to crosswind action.

In recent years, the aerodynamic characteristics of trains and traffic safety have been widely studied in different infrastructure scenarios under crosswind environments, e.g. environments with flat ground, embankments, cuttings and bridges [22–25]. To ensure the safe operation of trains under strong crosswinds, different types of windbreak walls have been built along railways in windy areas based on the different terrain conditions [26,27]. In addition, other factors, such as the train vehicles' properties (type, shape and load), line conditions (embankment height, road cutting depth and curve radius) and wind speed and direction, also significantly affect the safety of trains operating under crosswinds [28–31]. Therefore, based on the wind area along the Xinjiang railway, the present work proposes a set of methods and ideas to study train operation safety with different parameters under crosswinds as well as relevant optimization strategies.

2. Features of wind distribution along Xinjiang Railway

2.1 Distribution of strong wind areas along Xinjiang Railway

Railway lines in windy areas in Xinjiang mainly include the Lanzhou–Xinjiang Railway, the Lanzhou–Xinjiang High-Speed Railway and the Southern Xinjiang Railway. Starting from the Hongliu River, the Lanzhou–Xinjiang Railway passes along the Gobi piedmont on the south side of the East Tianshan Mountains, enters Urumqi through the Baiyang River Valley and finally links with the Alataw Pass along the northern foot of the Northern Tianshan Mountains. The Southern Xinjiang Railway starts from Turpan along the branch of the Tianshan Mountains, enters Korla along valleys and finally proceeds along the southern margin of the South Tianshan Mountains to Kashgar.

The main wind areas along the Xinjiang Railway include the Baili wind area, Sanshili wind area, Alataw Pass wind area, front Baili wind area of the Southern Xinjiang Railway, Yandun wind area and Dabancheng wind area [4]. Among these wind areas, the first four are strong wind areas, which experience high-speed, high-frequency and long-duration wind. The wind speeds of the other windy zones, however, are slightly lower and the wind periods are also shorter.

Running trains are extremely affected by the strong winds from the Baili wind area, the Sanshili wind area and the front Baili wind area of the Southern Xinjiang Railway. The wind direction is almost perpendicular to the railway lines. Wind-induced train accidents have occurred mainly in these zones. To reduce the impact of the strong crosswinds on the safety of train operation, the Urumqi Railway Bureau has built different types of windbreaks along the Baili wind area, the Sanshili wind area and the front Baili wind area of the Southern Xinjiang Railway since the end of the 1980s [4]. The diagram of the distribution of the wind areas along the Xinjiang Railway is shown in Fig. 2.

2.2 Statistical analysis of wind features along front Baili wind area of Southern Xinjiang Railway

Several key indicators used for statistical analysis of wind features in wind areas mainly include transient wind speed, 2-min-average wind speed and 10-min-average wind speed in this study. The calculation methods of these three wind speed statistical characteristic values are defined as follows: (1) transient wind speed: calculating the sliding average value of N valid sampling samples within 3 seconds with a sampling interval of 0.25 seconds and a sliding step of 1 second; (2) 2-min-average wind speed: using the transient value calculated per second as the sample value and 1 second as the sliding step to calculate the sliding average value of N valid samples within 120 seconds; (3) 10-min-average wind speed: using the transient value calculated per second as the sample value and 1 second as the sliding step to calculate the sliding average value of N valid samples in 600 seconds.

Historical wind data monitored along the front Baili wind area of the Southern Xinjiang Railway from 2015 to 2018 were selected (a total of 17 wind monitoring points along the railway line). Fig. 3 shows the maximum values of the 10- and 2-min-average wind speeds and the transient wind speed. The maximum transient wind speed during the period appeared at the #10 monitoring point, which was 61.6 m/s, and the maximum 2-min-average wind speed appeared at the #6 monitoring point, which was 61.2 m/s. The figure also reveals that the transient wind speed and the 2-min-average wind speed fluctuated significantly along these monitoring points, while the 10-min-average wind speed changed relatively smoothly, as mentioned above. The 10-min-average wind speed gradually increased from monitoring points #1 to #6, and it exhibited an overall declining trend from monitoring points #6 to #17.

Table 1 shows the number of days when the wind speed of the monitoring points was greater than 17.2 m/s (level 8 wind) in the front Baili wind area of the Southern Xinjiang Railway. The windy days were concentrated at monitoring points #4 to #9, and the number of days in which the wind was greater than 17.2 m/s was at most 275 days a year, which occurred at monitoring point #6 in 2016. Hence, the annual average number of windy days along the Xinjiang railway was extremely large.

2.3 Analysis of wind- and sand-induced accidents in Xinjiang Railway

Wind and sand hazards along the Xinjiang Railway cause various issues, such as vehicle overturning, slipping of vehicles, tracks being buried by sand, window damage and damage of the railway operation facilities. In addition, trackbed compaction, increased wheel/rail abrasion, reduced service life of the operation equipment, decreased air quality in the passenger cars and engine problems in diesel locomotives are also common due to sandstorms [4].

Fig. 4 shows the frequency of various types of accidents. Among the 38 traffic accidents caused by wind and sand, 21 were derailed and overturned due to crosswinds, accounting for 55.3% [32]. These accidents mainly occurred in the Baili wind area, Sanshili wind area and front Baili wind area of the Southern Xinjiang Railway. The overturning sites are relatively fixed for the Sanshili wind area, and the accidents all occurred between Tianshan and Sangequan. This was mainly because the railway line is almost perpendicular to the wind direction and other sections of the railway line have small angles with the wind direction. Sand accumulation on the railway line has caused eight derailments, accounting for 21.1% of the total number of derailments, which mainly occurred in the Yandun wind area and Baili wind area of the Lanzhou–Xinjiang Railway. Three cases of trains slipping due to the strong crosswinds were recorded, accounting for 7.9% of the derailments. Two vehicle derailments were induced by tarpaulins being blown onto the railway line, accounting for 5.3% of the derailments. Three cases of containers of freight trains being blown off by crosswinds occurred, accounting for 7.9% of the derailments. The other 2.6% of the derailments occurred for other reasons. In total, 134 vehicles were derailed due to strong winds (116 vehicles were overturned and 18 vehicles were derailed), 13 vehicles were derailed due to sand accumulation, and 104 vehicles slipped due to strong winds (including three derailed vehicles). Tarpaulins blown onto the railway line caused 12 overturned and derailed vehicles (including four derailed vehicles and eight overturned vehicles in the rear due to the front vehicles). The above accident statistics reveal that wind-induced train accidents account for a significantly larger proportion than sand-induced train accidents, which highlights that the strong wind is the main cause of train accidents along railways in Xinjiang. Thus, the wind-induced effect on train safety and corresponding mitigation measures were investigated in detail in this study.

3. Research route of running safety of trains under crosswinds

Fig. 5 illustrates the process for studying the running safety of a train under crosswinds. Aerodynamic loads on the train under crosswinds have significant effects on the running safety of the train. These mainly include the side force, lift force and overturning moment [21]. Therefore, to study the running safety of a train under crosswinds, first, the aerodynamic loads on the train under crosswinds were obtained. Second, the aerodynamic loads were applied as an external excitation to the vehicle dynamics model to calculate indicators of the running safety of the trains, such as the overturning coefficient and the derailment coefficient. The critical wind curve (CWC) was then obtained, illustrating the critical wind speed corresponding to the train speed. Finally, the train speed limit, which could be realized and applied during dispatching, was obtained according to the requirements of the train operation command system. In extremely windy areas, it is necessary to design and optimize windbreaks to ensure the running safety of the train and transportation efficiency under crosswinds.

4. Aerodynamic loads of train under crosswinds

4.1 Research methods

At present, the research methods for studying the aerodynamic loads of trains under crosswinds mainly include numerical simulations, reduced-scale model tests (wind tunnel tests and moving model tests) and full-scale tests.

(1) Numerical simulations

There are numerous factors that affect the aerodynamic loads of a train under crosswinds, including the wind speed, wind direction, train speed and design parameters of the train, railways and windbreaks. Numerical simulations are a relatively new method of solving engineering problems of train aerodynamics, which can study the effects of each of the factors on the train aerodynamics and surrounding flow structures separately. Compared with reduced-scale model tests and full-scale tests, numerical simulations require less time and cost. Therefore, numerical simulations are the most important method for analysing the aerodynamic loads of a train under crosswinds. Reynolds-averaged Navier–Stokes equations (RANS), unsteady Reynolds-averaged Navier–Stokes equations (URANS), detached eddy simulation (DES) and improved approaches can be carried out to simulate the turbulent flow around the train [33,34].

(2) Reduced-scale model tests

In the research of train aerodynamics, reduced-scale model tests usually include moving model tests and wind tunnel tests, which are conducted on a reduced-scale train model in the moving-model test rig and wind tunnel, respectively. The results of reduced-scale model tests can verify those of numerical simulations. The conditions of reduced-scale model tests are easy to control, and thus more cases can be examined. The measurement accuracy of reduced-scale model tests is high, and these tests are more convenient and feasible than full-scale tests. Therefore, reduced-scale model tests have played an important role in the study of train aerodynamics, and they have become one of the most important and common methods of studying train aerodynamics. The aerodynamic loads and surface pressure distribution on the train under crosswinds can be obtained by reduced-scale model tests [35,36].

(3) Full-scale tests

The aim of a full-scale test under crosswinds is to evaluate the running safety of a train. At present, the aerodynamic loads of trains under crosswinds have been calculated with the discrete integration of the pressure difference distribution over the train in most of the full-scale tests in China [37]. Nearly 30 full-scale tests were carried out on the Lanzhou–Xinjiang High-Speed Railway, Lanzhou–Xinjiang Railway and Southern Xinjiang Railway, providing valuable data for the research of the running safety of trains under crosswinds. However, due to the ambient wind, terrain and railways, the aerodynamic loads fluctuate significantly and are difficult to repeat in full-scale tests [38].

By comparing the above-mentioned characteristics of three types of research methods for train aerodynamics, it can be concluded that the numerical simulation has advantages of shorter implementation times, lower costs and more easily controlled parameters than the other two methods. Thus, the numerical simulation was selected to explore the influence of different factors on train safety and design windproof measures for trains under strong wind. In this study, based on the three-dimensional, incompressible, unsteady N-S equations and the k-ε two-equations turbulence model employed in the commercial computational fluid dynamics software FLUENT, a series of numerical simulations were conducted to obtain the analysed data. Because the research in this paper involves multiple types of trains with complex structures, in order to improve the grid quality, a more adaptable unstructured grid is used to discretize the computational domain. Besides, a smaller grid size is used around the train body to capture the complex flow field structure around the train.

4.2 Influence factors on aerodynamic loads

Fig. 6 illustrates the definition of the resultant wind angle β (which is also called the yaw angle), where V is the train speed, W is the wind speed that is perpendicular to the train speed, and β is the angle between the train speed and the resultant wind velocity U.

4.2.1 Marshalling type of train

For calculation efficiency, a model composed of a locomotive with three carriages is usually used to study the aerodynamic loads on a train in numerical simulations. To analyse the influence of the marshalling type of the train on the aerodynamic loads, the aerodynamic loads on two models were compared on the windward railway line behind a 2.4-m-high earth embankment-type windbreak wall. One model was composed of a locomotive and three single-deck carriages (M3), while another was composed of a locomotive and eight single-deck carriages (M8). The aerodynamic loads were similar to those of other trains and the windbreak walls, and thus these analyses on other trains and windbreaks were not repeated here for brevity. The first carriage after the locomotive was named C1, the second carriage after the locomotive C2, and so on.

First, in order to explore the aerodynamic load difference of carriages at different marshalling positions in the same one-train model under crosswind, the overturning moment coefficients of each single-deck carriage in M8 train model as a function of the resultant wind angle are illustrated in Fig. 7. The overturning moment coefficient of each carriage was quite different for wind angles from 0 ° to 70 ° (for example, the difference between the maximum and the minimum was 23.4% at a resultant wind angle of 15 °). The overturning moment coefficient of C1 was larger than that of other carriages, while the difference between the other carriages was not evident. For the larger resultant wind angles, the difference of the overturning moment coefficient between the carriages decreased (for example, the difference between the maximum and the minimum was 11.0% at the resultant wind angle of 90 °).

To investigate the effect of the marshalling types of train models on the aerodynamic loads on the carriages at the same marshalling positions, Fig. 8 illustrates the comparisons of the overturning moment coefficients of the single-deck carriages in M3 and M8 train models, as mentioned above. C3-1, C3-2 and C3-3 in the figure represent C1, C2 and C3 in M3, respectively, while C8-1, C8-2 and C8-8 represent C1, C2 and C8 in M8, respectively. The overturning moment coefficients of the carriages in M3 were slightly larger than those of the corresponding carriages in M8. The difference between C3-1 and C8-1 was large, with a value of 11.1%. The differences between C3-2 and C8-2, and between C3-3 and C8-8 were not significant, and most were within 5%. Hence, a train model of the marshalling of a locomotive and three carriages being used to study the aerodynamic loads on the train using numerical simulations is feasible, and the results are biased toward conservative, safe estimates.

4.2.2 Height of embankment

M3 (the model composed of a locomotive and three single-deck carriages) was selected for analysis, as the overturning moment coefficients of the carriages in M3 were slightly larger than those of the corresponding carriages in M8, as mentioned above. Because the embankment heights have a significant effect on aerodynamic loads of train carriages under crosswind, the overturning moment coefficients of the single-deck carriage on the embankments with different heights (see Ref. [40] for the dimensions of the embankment) at different resultant wind angles are shown in Fig. 9. In the range of 15 °–45 °, the overturning moment coefficient showed a trend of increasing from 0 to 15 m. However, the overturning moment coefficient showed a trend of decreasing as the height of the embankment increased in the range of 60 °–90 °. The train speed was usually larger than the wind speed, and thus the resultant wind angle β was generally less than 45 °. Therefore, within this common range of resultant wind angles, as the height of the embankment increased, the overturning moment of the train increased and the running safety of the train worsened.

4.2.3 Depth of road cutting

For the train carriage running inside a road cutting, the carriage aerodynamic performance is significantly affected by the depth of road cutting, thus Fig. 10 shows the overturning moment coefficients of the single-deck carriage for cuttings with depths of 0 (flat ground), 3, 5 and 8 m. Besides, the road cutting for analysis in this study is symmetric [41]. The overturning moment coefficient showed a trend of decreasing as the road cutting depth increased from 0 to 8 m. Therefore, as the depth of the road cutting increased, the running safety of the train improved. The overturning moment coefficient was 2.552 for the road cutting with a depth of 3 m at the resultant wind angle of 90 °, while it was only 0.633 for the road cutting with a depth of 8 m. The latter was 75.2% less than the former.

4.2.4 Windbreak walls

Due to the different local terrain along the railway, the windbreak wall types are also diverse, such as the earth-embankment-type windbreak, reinforcement-type windbreak wall, and so on. Different types of windbreak walls may cause different aerodynamic loads on train carriages running behind it, thus the overturning moment coefficients of the single-deck carriage with different windbreak walls at different resultant wind angles are shown in Fig. 11, and the same height of 2.4 m was selected for different types of windbreak walls in the analysis. The overturning moment coefficient of the carriage was large and positive with the earth-embankment-type windbreak wall (i.e. the carriage tended to overturn away from the windbreak wall), and thus the windproof performance of the earth-embankment-type windbreak wall was not sufficient. The overturning moment coefficients were mostly negative for the other windbreak walls (i.e. the carriage tended to overturn toward the windbreak wall) so the windproof performance of these windbreak walls was excessive. Because the bridge-type windbreak wall was designed with holes, the absolute value of the negative overturning moment coefficient of the carriage behind the bridge-type windbreak wall was small. The reinforcement type, concrete type and plate-type concrete tie were straight windbreak walls with different thicknesses [42]. As the thicknesses of these straight windbreak walls increased, the windproof performance of the windbreak wall improved significantly. The thickness of the concrete-type windbreak wall was similar to that of the concrete tie with the plate-type windbreak wall. Thus, their windproof performances were not significantly different. The windproof performance of the reinforcement-type windbreak wall was the greatest because it was the thickest. In summary, the windproof performance of the earth-embankment-type windbreak wall was the worst, while that of the reinforcement-type windbreak wall was the best. In addition, other types of windbreak walls exhibited similar windproof performances.

5. Study on safe speed limit of train operation under crosswind conditions

5.1 Train running safety calculation model

The effects of the following forces should be considered when calculating the operation stability of a vehicle (Fig. 12) [43,44]:

1. Centrifugal force when the vehicle passes through the curve;

2. Gravity;

3. Vehicle's lateral vibration inertial force;

4. Wheel-rail force;

5. Aerodynamic lateral force caused by the crosswind. This was calculated by integrals of two components: the pressure distribution and viscous forces of the windward and leeward surfaces of the vehicle;

6. Aerodynamic lift force. This was also calculated by integrals of two components: the pressure distribution and viscous forces of the top and bottom surfaces of the vehicle.

Critical overturning illustrates that the wheel-rail vertical force on the one side of the vehicle is zero (P₁ = 0), i.e. D = 1. Therefore, D < 1 can prevent the vehicle from overturning. The Chinese standard GB 5599–85 [45] requires D < 0.8.

5.2 Train operating safety speed limit

5.2.1 Relationship between critical overturning wind speed and train types

Because different types of trains have significantly different geometry structures, the aerodynamic loads on train carriages for different types of trains are also obviously different under the same operating condition. In order to explore the overturning wind speed differences between different types of trains, the single- and double-deck passenger trains (type 25T), box wagons, open wagons, container cars, and tank cars with empty loads were considered. Their overturning wind speeds at different running speeds were calculated to study the relationship between the critical overturning wind speed and train type, as shown in Fig. 13. The critical overturning wind speeds of various train types varied considerably. For freight trains, the critical overturning wind speed of different freight trains was in the following order from high to low: open wagon, tank car, container car and box wagon. Compared with the double-deck passenger train, the critical overturning wind speed of the single-deck passenger train was higher, and the difference between the two gradually increased as the speed increased. The critical overturning wind speeds of the single-deck passenger carriage and the box wagon were relatively close. The critical overturning wind speed of the box wagon was slightly larger than that of the single-deck passenger car.

5.2.2 Relationship between critical overturning wind speed and vehicle load

The load of the passenger car did not change significantly. To better analyse the impact of the vehicle load on the critical overturning wind speed, the box wagon was considered here to analyse the relationship between the critical overturning wind speed and the vehicle load (with no wind barrier and straight-line conditions). The results are shown in Fig. 14. The greater the vehicle load, the higher the critical overturning wind speed became. For a train speed of 120 km/h, the critical overturning wind speed with an empty load was 30 m/s, and with loads of 10, 20, 30, 40 and 50 t, the corresponding critical overturning wind speeds were 35.0, 39.2, 42.4, 45.2 and 47.4 m/s, corresponding to increases of 16.6%, 30.6%, 41.4%, 50.8% and 58.0%, respectively, compared to the empty load. The relationship between the critical overturning windspeed |${V_w}$| and load change M can be expressed by the following fitted equation: |${V_w}$| = 0.3457M + 31.227 (R² = 0.9786).

5.2.3 Relationship between critical overturning wind speed and embankment height

The overturning wind speed of an empty single-deck train was calculated under conditions with no wind barrier, a straight railway line and different embankment heights to study the relationship between the critical overturning wind speed and the embankment height, as shown in Fig. 15. It can be seen that the relationship between the critical overturning wind speed and the embankment height depended highly on the speed of the train. When the speed of the train was within 0–110 km/h, the critical overturning wind speed of the train increased with the increasing height of the embankment at the same speed. When the speed was within 110–120 km/h, the critical overturning speed was basically equal. When the speed was within 120–160 km/h, the critical overturning wind speed of the train at the same speed decreased with the increase in the height of the embankment.

5.2.4 Relationship between critical overturning wind speed and depth of road cutting

To explore the relationship between the critical overturning wind speed and the road cutting depth, an empty single-deck train operating with no wind barrier and straight railway line under different road cutting depths was simulated and analysed in Fig. 16. It can be observed that the critical overturning wind speed increased with the road cutting depth, and it did not change significantly with the speed of the vehicle at the same road cutting depth. In the case of 160 km/h, the critical overturning wind speed at a depth of 0 (i.e. flat ground) was 38.4 m/s, and at depths of 3, 5 and 8 m, the corresponding critical overturning wind speeds were 50.7, 61.8, and 70.0 m/s, corresponding to increases of 32.1%, 61.0% and 82.3%, respectively, compared to flat ground conditions. The relationship between the critical overturning wind speed |${V_w}$| and the road cutting depth D can be expressed by the following fitted equation: |${V_w}$| = 4.0415D + 39.084 (R² = 0.9839).

5.2.5 Effect of line curvature on critical overturning wind speed

When the train is running on a curved line, centrifugal force affects the critical overturning wind speed of the vehicle, and the effect is closely related to the radius of the curve, the track superelevation, the direction of the curve and the speed of the train. The effects of these curved line factors on the critical overturning wind speed of the vehicle are discussed one by one here.

For discussion purposes, the direction of the curve is defined as an inward curve if the wind blows from the outside of the curve to the inside of the curve, and vice versa for an outward curve.

(1) Relationship between critical overturning wind speed and radius of curved line

To study the relationship between critical overturning wind speed and radius of curvature for the railway line (R is used to denote), the critical overturning wind speed of an empty passenger train was calculated, and the results are shown in Fig. 17. No wind barrier, a standard track superelevation, an inward curve, different speeds and flat ground conditions were applied in these simulations.

When an empty single-deck passenger train was running on an inward curved line, the curves of the critical overturning wind speed versus the vehicle speed for different track radius of curvature intersected at a speed of 60 km/h. This indicated that the ideal track superelevation corresponded to the vehicle speed of 60 km/h. The centrifugal force produced by the curve was opposite to the wind direction. When the speed was less than the corresponding speed of the ideal track superelevation, the train was in an over-superelevated state, and the centrifugal force was less than the centripetal force caused by the preset track superelevation. The unbalanced acceleration was consistent with the wind direction, so that the critical overturning wind speed of the train was lower than that of the straight line. The smaller the radius, the greater the reduction in the critical overturning wind speed became. That is, when the train was running on the inward curve at a speed less than the speed corresponding to the ideal superelevation, the critical overturning wind speed increased as the radius increased. When the speed was greater than the corresponding speed of ideal superelevation, the train was in a state of under-superelevation. Thus, the centrifugal force was greater than the centripetal force caused by the ideal superelevation and the unbalanced acceleration direction was opposite to the wind direction. The critical overturning wind speed of the vehicle was higher than that for the straight line, and the smaller the radius, the larger the amplitude of the increase became. That is, when the train was running on the inward curve and the speed was greater than the speed corresponding to the ideal superelevation, the critical overturning wind speed decreased with the increase in the radius.

Similarly, when the train was running on the outward curve, the situation was exactly opposite to that of the inward curve. The centrifugal force produced by the curve was consistent with the wind direction. When the speed was less than the corresponding speed of the ideal superelevation, the train was in an over-superelevated state. The centrifugal force was greater than the centripetal force caused by the preset superelevation, and the unbalanced acceleration direction was opposite to the wind direction. Thus, the critical overturning wind speed was higher than that in the straight-line condition. The smaller the radius, the greater the increase became; that is, when the train was running on the outward curve at a speed less than the speed corresponding to the ideal superelevation, the critical overturning wind speed decreased as the radius increased. When the speed was greater than the corresponding speed of the ideal superelevation, the train was in a state of under-superelevation. The unbalanced acceleration direction was consistent with the wind direction, so that the critical overturning wind speed was lower than that of the straight line. The smaller the radius, the greater the reduction became. That is, when the train was running on the outward curve at a speed higher than the speed corresponding to the ideal superelevation, the critical overturning wind speed increased as the radius increased.

(2) Relationship between critical overturning wind speed and track superelevation

In an actual operating line, setting of the rail superelevation is not based on the maximum speed allowed by the line but a ‘comprehensive vehicle speed’, which is determined by the actual operating speed, load, operating densities of different models and other actual conditions. The superelevation is to be determined based on different curve radii. As a result, the track superelevation for different lines will vary, and the values will also vary slightly from year to year.

To study the relationship between critical overturning wind speed and the track superelevation, an empty single-deck passenger train was considered. Its critical overturning wind speeds at different train speeds were calculated and are shown in Fig. 18. No wind barrier, a 2200-m curve radius with an inward curve and flat ground were applied in these simulations. As can be seen from Fig. 18, the critical overturning wind speed decreased with the increase in the track superelevation for the same radius, curve direction and running speed, but there was not much difference between the cases with different track superelevation.

Theoretically, increasing the rails’ superelevation is equivalent to increasing the ‘centripetal force’ of the vehicle, as it can balance a larger centrifugal force generated by the train operating on curves. When the train ran on an inward-curving line, the direction of this ‘centripetal force’ was the same as the wind direction, which was equivalent to slightly increasing the crosswind speed. The vehicle's critical overturning wind speed decreased with the increase in the track superelevation. When the curve was outward-curving, the ‘centripetal force’ generated by the superelevation was opposite to the wind direction, which was equivalent to slightly reducing the wind. The critical overturning wind speed of the vehicle increased with increase in the track superelevation. Based on the results, the impact on the critical overturning wind speed of the vehicle was not significant due to the limited range of track superelevation.

(3) Relationship between critical overturning wind speed and curve orientation

The direction of the centrifugal force acting on a vehicle varies when running on curves with different orientations, so the critical overturning wind speed is also different. To explore the relationship between critical overturning wind speed and curve orientation, the critical overturning wind speed of an empty single-deck passenger train was calculated under the condition with no wind barrier, a 2200-m curve radius, a standard track superelevation and flat ground. The results for various running speeds with different curve directions are shown in Fig. 19.

As shown in Fig. 19, the critical overturning wind speed change of an empty single-layer passenger train operating on curves with different orientations showed opposite variations, although they had the same curve radius. The curves in the plot corresponding to the inward- and outward-curving tracks intersected at the speed corresponding to the preset rail superelevation. When the running speed was less than the speed corresponding to the ideal superelevation, the critical overturning wind speed of the inward curve was lower than that of the outward curve, and when the vehicle's operating speed was greater than the speed corresponding to the ideal superelevation, the critical overturning wind speed of the inward curve was higher than that of the outward curve.

For the inward curve, the critical overturning wind speed decreased to a certain value with the increase in the vehicle speed and then increased. For the outward curve, the critical overturning wind speed decreased monotonically with the increase in the vehicle speed.

5.2.6 Relationship between critical overturning wind speed and yaw angle

The aerodynamic force of the train is related not only to the speed of the wind but also to the wind direction. The angle between the ambient wind and the train's forward direction is defined as the yaw angle. The wind angle was defined as 0 ° when the wind direction was consistent with the direction of the train motion, 90 ° when it was perpendicular to the train and 180 ° when it was in the direction opposite to the train motion. To analyse the effects of different yaw angles on the overturning wind speed, the critical overturning wind speeds in 11 conditions (yaw angle from 40 ° to 140 ° with 10 ° as a step) were calculated, and the yaw angle with the lowest critical overturning wind speed was called the most unfavourable yaw angle. Fig. 20 shows the critical wind speed of a train at different yaw angles. As can be seen from Fig. 20, the effect of the yaw angle on the critical overturning wind speed was related to the vehicle speed. When the vehicle speed was zero, the most unfavourable yaw angle was 90 °. With the increase in the vehicle speed, the most unfavourable yaw angle increased. At 160 km/h, the worst yaw angle was around 100 °.

5.3 Determination of safe speed limit of train

5.3.1 Determination of wind speed-train speed limit segment ranges and warning levels

The determination of reasonable wind speed-train speed limit ranges is a comprehensive trade-off process. The critical overturning wind speed curve of each train type under strong crosswinds with different lines and windproof conditions in the Xinjiang railway areas must be considered. At the same time, for convenience of applying the driving commands, the wind speed range should be uniformly divided, allowing different wind speed ranges to correspond to different speed limits of the train. Furthermore, the speed limit should be as close as possible to the speed limit standards of the line.

At present, the wind speed used for the Xinjiang wind railway driving command is based on a 2-min-average wind speed (referred to as the averaged wind speed) and the transient wind speed. In line with the principle of safety, we define the critical overturning wind speed calculated by the numerical values as the transient wind speed. The conversion relationship between the averaged wind speed and the transient wind speed in each wind area subdomain is based on the historical wind speed statistics. The 2-min-average wind speed was converted based on the critical overturning wind speeds of different train types in each wind area subdomain.

The critical overturning wind speeds of different trains at various speeds in each wind area were calculated and analysed under various windproof conditions. The results showed that the minimum critical wind speed was 21.0 m/s and the maximum wind speed limit for the running safety in the wind area determined by the sand-starting conditions was 42 m/s. Thus, the wind speed limit for the 2-min-average was determined to range from 21 to 42 m/s, i.e. when the ambient wind speed is below 21 m/s, the trains will not be affected, while all trains must be stopped when the ambient wind speed is greater than 42 m/s. The speed range of the passenger train was 0–160 km/h and of the freight train was 0–120 km/h.

According to the characteristics of the crosswinds along the Xinjiang railway, the wind speed increases faster when the wind speed is below 30 m/s. To improve the running safety and referring to the wind speed limit sub-range of domestic high-speed railways, the wind speed segment range was set at 5 m/s when the wind speed was less than 30 m/s. When the wind speed reached higher than 30 m/s, the wind speed increased slowly, and the segment range was set to 3 m/s. Combining on-site wind speed conditions and driving experience, the wind speeds were divided into seven levels. For the critical overturning wind speed curves versus the train speed in each sub-domain of the wind area, the train speed limit in each wind speed limit was determined for different train types. According to international general practice, the wind speed warning levels were expressed using four colours: blue, yellow, orange and red, and the different colour levels were further classified to improve the efficiency of safe transportation. The specific warning levels and their wind speed ranges are shown in Table 2.

Referring to the speed limit standard of the Urumqi Railway, the speed segments were set to 45, 60, 80, 100, 120, 140 and 160 km/h (maximum speed of existing traditional line), and the critical overturning wind speed corresponding to the speed of 45 km/h was the maximum wind speed for safe driving.

5.3.2 Determination method of wind speed-vehicle speed limits

The running safety of trains in strong crosswind environments is affected not only by the critical overturning wind speed but also by the sand carried by strong winds and the visibility. However, these effects were not included in this study, which mainly considered the critical overturning wind speed-train speed as an important basis for determining the operating safety of trains.

Fig. 21 shows the critical overturning wind speed of the vehicle and the basic method for determining the wind speed-train speed limit. The critical overturning wind speed-train speed indicates the vehicle's safe wind speed limit at different operating speeds, with dangerous areas above the curve and safe driving areas below. The critical overturning wind speed-train speed curve is continuous. However, based on the current driving command capabilities, it is not yet possible to achieve continuous real-time control. Thus, the wind and train speeds are divided into several levels, and the safe operation area is formed of a number of ‘steps’. Each step corresponds to a different wind speed range and train speed level. Below the ‘steps’ are the actual commands for the safe operation area. The finer the ‘step’ division, the higher the utilization rate of the safety zone and the greater the train passing capacity. However, the convenience of the driving commands will be reduced accordingly. The speed limits were determined as follows: if the wind speed is within 30–33 m/s, the train is allowed to run at 60 km/h; if the wind speed is within 25–30 m/s, the train is allowed to run at 100 km/h; if the wind speed is less than 25 m/s, the train is allowed to run at 160 km/h.

6. Analysis of effects of measures improving the train safety under crosswinds

6.1 Reform of windbreak facilities

A series of field tests, numerical simulations and field investigations were conducted, and the results revealed that the large values of the aerodynamic and dynamics indices of trains under crosswinds mainly appeared in some special terrain types, such as earth-embankment-type windbreak walls, shallow cuttings and transitions between different types of windbreak walls. Therefore, it is necessary to conduct detailed research on the flow field characteristics of these special terrain types and design some corresponding reasonable reforms for them. The measures adopted for the abovementioned issues mainly consisted of the following: (1) heightening the earth-embankment-type windbreak wall with a poor windproof effect, (2) optimizing and redesigning structures of the transition terrain section between different windbreak walls and (3) analysing the aerodynamic performances of trains in shallow cuttings, and adding a windshield with a reasonable height.

(1) Reform of earth-embankment-type windbreak walls

Fig. 22 shows the streamlined patterns projected on the middle cross-sections of the head car in the original earth-embankment windbreak walls and the reformed earth-embankment windbreak walls. As revealed in Fig. 22(a), due to the poor windproof effect of the original earth-embankment windbreak walls, a considerable part of the upstream flow climbed along the windward side of the earth-embankment windbreak walls and invades into the railway regions, which would directly impact the windward surfaces of train bodies. Thus, significant positive pressure regions were observed in the upper windward region of the train body, whereas significant negative pressure regions appeared in the top and bottom regions, especially the top region. Due to the flow separation, there was a large-scale vortex between the windward side of the train body and the leeward side of the windbreak wall. In addition, three vortices with smaller scales were observed on the leeward regions of the trains, two of which were close to the leeward surfaces of trains, and the other was on the leeward side of the subgrade. Hence, there were huge pressure differences between the windward and leeward sides of the train exposed in such a flow field, which caused the train to be subjected to enormous overturning forces and moments toward the leeward side and become prone to leeward overturning. The above analyses revealed that the windproof performances of the earth-embankment windbreak walls are poor, and reforms need to be conducted on the structures of the windbreak wall to improve their windproof performances.

The original earth-embankment-type windbreak wall was reformed by being heightened, and the corresponding flow pattern around the reformed windbreak wall is shown in Fig. 22(b). Due to the uplifting effect of the reformed earth-embankment-type windbreak walls on the airflow, the upstream airflow flowing through the reformed windbreak walls flowed over the top of the train body without directly impacting the windward side of the train surface. No significant positive and negative pressure regions were observed around the train, but weak negative pressures were almost evenly distributed on both sides of the train body, which effectively avoided the large pressure differences between the windward and leeward sides of the train body. In addition, compared with the flow pattern of the original earth-embankment-type windbreak wall, the two vortices close to the leeward side of the train body were not formed for such reformed windbreak walls.

In general, the safety and stability of trains operating behind earth-embankment-type windbreak walls can be effectively improved by reasonably heightening the original forms. Furthermore, it should be noted that in the actual construction and reform process, a reasonable heightening height of the original earth-embankment-type windbreak wall should be determined by the original form and surrounding terrain.

(2) Reform of shallow cuttings

The streamline patterns projected on the middle cross-sections of the head car in the original and reformed shallow cuttings are shown in Figs. 23(a) and (b), respectively. According to Fig. 23(a), because the height of the train body on the railway line was higher than the total height of the original shallow road cutting, the original shallow road cutting could not completely block the incoming flow. Therefore, the upstream incoming flow could easily enter the railway region and impact the train body, which was the main cause of train overturning to the leeward side. This reveals that the windproof performance of the original shallow road cutting was insufficient. For the train operating on the first railway line behind the original shallow road cutting, two large-scale vortices appeared: one in the windward region and one in the leeward region. Furthermore, the vortex on the windward side was closer to the train body, which caused the airflow to interact more significantly.

To improve the windproof performance of the original shallow road cutting, a windbreak wall was set on the top surface of the original road cutting. As shown in Fig. 23(b), due to the blocking effect of the reformed road cutting with a sufficient height on the airflow, the airflow was lifted upward and flowed above the train body, avoiding the direct impact on the train body, which indicated that the newly installed windbreak wall on the top surface could significantly improve the windproof performances of the original shallow road cutting. Behind the reformed road cutting, two main vortices with larger scales were observed in the windward and leeward regions of the train, and the pressure field around the train was dominated by an evenly distributed, weak, negative pressure, which was beneficial for the safety and stability of the train operation.

In addition, during the actual construction and reform process, a reasonable height of a newly installed windbreak wall on the top surface of the shallow road cutting should be determined according to the depth and slope of the original road cutting itself, as well as the surrounding terrain conditions.

(3) Reform of windbreak wall transitions

According to the results of field tests and field investigations on the Lanzhou–Xinjiang Railway in China, 335 cases of windbreak wall transitions in 16 different categories were found along the Baili wind area of the Lanzhou–Xinjiang Railway. To guarantee the stability and safety of the train operating in such strong wind regions, a specific reform plan was determined for each windbreak wall transition based on its type, structural parameters and terrain conditions. The specific details of the reformed design for different windbreak wall transitions were not discussed below for brevity [32].

6.2 Analysis of effect of reformed windbreak facilities

A large number of field tests and studies have been carried out to deal with the safety issues of trains operating in severe environments with strong crosswinds along railway lines in Xinjiang, China. Based on the above research results, a series of outstanding and meaningful achievements have been obtained, such as optimizing and modifying windbreak walls and other windproof facilities, gradually improving and revising the ‘Measures for Safe Operation of Trains in Windy Weather', avoiding and reducing gale accidents, and reducing the economic losses caused by factors such as the train suspension, speed limit, passenger detention, and cargo backlog. All these achievements not only ensure the safety of trains operating under strong crosswinds but also greatly improve the transportation capacity in the windy area, and bring greater economic benefits to railway transportation in windy areas. An empty box wagon is considered as an example. For the original windbreak facility, the train was forced to stop operating when the wind speed reached 30 m/s, whereas by reasonably reforming and redesigning these windbreak facilities, the wind speed value restricting the train operation could be increased by 40%; that is, when the wind speed was lower than 42 m/s, the train was still allowed to operate normally. Based on the statistical data of the train suspension time from 2011 to 2013, the suspension time for a train operating on the Lanzhou–Xinjiang Railway was reduced by 25.7 h in 3 years, and that for the Southern Xinjiang Railway was reduced by 436.2 h, which further indicated that the reform of the original windbreak facilities achieved remarkable results.

7. Conclusions

(1) Among the 38 traffic accidents caused by windy and sandy conditions in the gale area along the Xinjiang Railway, 21 cases were due to train derailment and overturning accidents caused by strong winds, accounting for 55.3% of the cases. The other accidents involved the derailment of trains caused by the accumulation of sand on the railway line, the slipping of the trains due to strong winds, train vehicle derailment caused by tarpaulin being blown onto the railway line and accidents in which a container was blown off by the wind.

(2) The operating safety of trains in a strong windy environment mainly depends on the aerodynamic loads acting on the train caused by the ambient wind. Thus, the speed limit to allow trains to operate safely and the variations of the aerodynamic loads of the train with the external environment and line conditions are basically consistent. Additionally, the speed limits for trains operating safely with variations of the embankment height, road cutting depth, vehicle type, vehicle load, line curvature and wind direction angle were determined.

(3) Based on field wind speed conditions and experience in commanding train operation, the 2-min-average values of the wind speed of the Xinjiang general-speed railway were divided into seven levels from 21 to 42 m/s. The operating speeds of passenger trains ranging from 45 to 160 km/h were also divided into seven levels, and the operating speeds of the freight train were divided into five levels from 45 to 120 km/h. In addition, a reasonable speed limit for the safe operation of trains was determined based on the relationship between the critical wind speed and the train operating speed for different train types.

(4) The results of field tests and field investigations revealed that the large values of the aerodynamic performance and dynamic indices of trains under crosswinds mainly appeared under special terrain sections, such as those with earth-embankment-type windbreak walls, shallow cuttings and transitions between different types of windbreak walls. Reform and optimization measures have been implemented for these special terrain types with poor windproof performances, mainly including heightening earth-embankment-type windbreak walls, installing windbreak walls with reasonable heights on top of the road cutting type and optimizing and redesigning different types of windbreak transitions. By implementing these reformed windbreak facilities, the speed limits for trains operating safely have been greatly enhanced. For example, the speed limit for the box wagon was enhanced by 40%.

Acknowledgements

We are grateful for resources from the High Performance Computing Center of Central South University. This work was supported by the National Key R&D Program of China (Grant No. 2020YFA0710903).

Conflict of interest statement

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References