Bridge bearings experience numerous smallamplitude displacements under environmental loads. The continuous cyclic accumulations of these smallamplitude displacements will result in severe wear on the polytetrafluoroethylene (PTFE) plates in the bridge bearings, which seriously endangers the service life of bearings. Traditional method directly uses the linear wear rate of cumulative displacements in a short period to evaluate the wearing life, but the linear wear rate only in a short period such as several days may not represent the characteristics in the whole bridge service life. Hence, this research takes the spherical steel bearings of the Nanjing Dashengguan Yangtze River Bridge as a study object. The cumulative dynamic displacement (CDD) under the action of a single train and the cumulative bearing travel (CBT) under the continual actions of many trains are studied using the monitored longitudinal displacement data from spherical steel bearings. Furthermore, the probability statistics and the Monte Carlo sampling simulation for CDD are studied, and the safety evaluation method for bearing wear life in the real environment is proposed using a reliability index regarding the failure probability of monitored CBT over the wear limit during service lifetime. In addition, safety evaluation on the bearing wear life was performed to assess the condition of spherical steel bearings in the real service environment. The results can provide an important reference for analysis on the bearing wear life of longspan railway bridge structures.
As the service time of railway bridges increases, some bridge components may suffer from the aging and damage problems due to the influence of external environment loads. Among these bridge components, the bridge bearing is an important loadbearing component in largespan railway bridge structures, which can suffer from a series of diseases, such as the disengagement of bearings, the uneven compression, the twisting and fracturing of the bearing plate, and the weld cracking, which directly threaten the safety of railway bridges [
Current research on bearing damage in highspeed railway bridges mainly concentrated on the following three aspects: (1) the causes of bearing damage and prevention methods [
The latest studies revealed that bridge bearings experienced numerous smallamplitude dynamic displacements under dynamic loads [
Therefore, this research takes the spherical steel bearings of the Nanjing Dashengguan Yangtze River Bridge as a study object as shown in Figure
The components of spherical steel bearing.
The Nanjing Dashengguan Yangtze River Bridge is a largespan highspeed railway steel truss arch bridge. It is designed for river crossing of the BeijingShanghai highspeed railway and the ShanghaiWuhanChengdu highspeed railway, as shown in Figure
Locations of the longitudinal displacement sensors
Therefore, 12 LVDT displacement sensors (namely linear variable differential transformers) are installed at the upstream and downstream sides of the six groups of bearings (i.e.,
The monitored longitudinal displacement data at the
The monitored result of
Because the monitored longitudinal displacement data contain static longitudinal displacements induced by the temperature field and dynamic longitudinal displacements induced by dynamic loads as well, the dynamic longitudinal displacements need to be extracted from the monitored data first. Note that the static and dynamic longitudinal displacements are in different frequency bands. The static longitudinal displacement is greatly influenced by temperature changes, so the cycle period is about one day (i.e., the corresponding frequency is 1/86400 Hz). To ensure that the frequency of static longitudinal displacements is completely within the band range, the upper limit of the frequency band is designed to be 5/86400 Hz, namely (0, 5/86400] [
The wavelet packet decomposition method can use a pair of filters to decompose the monitored longitudinal displacement into different frequency bands scale by scale [
Tree structure of the wavelet packet coefficients.
Taking Figure
Decomposition result of monitored longitudinal displacement. (a) Component caused by temperature field. (b) Component caused by dynamical loads.
The continuous accumulation of smallamplitude dynamic displacements will induce serious fatigue wear, which can severely decrease the service lifetime of bearings. Thus, it is necessary to carry out study on the cumulative characteristics of smallamplitude dynamic displacements. The CDD caused by a single passed train was calculated to evaluate the contribution of this train to the cumulative wear. The CDD caused by the
Calculation of variables
Variable  Calculation equation 














The dynamic displacement of
The monitored data from August 10th to August 31st in 2017 is selected for analysis. A total of 3495 trains passed over the Dashengguan Yangtze River Bridge over this period, and each train corresponds to one value of
Each value of
The
The number of monitored CDDs are not enough to satisfy the requirement of large sample for safety evaluation of bearing wear life. Therefore, it is necessary to perform sampling simulation of CDDs using probabilistic statistics of the monitored CDDs to obtain adequate data.
Figure
The cumulative probabilities of
The cumulative distribution function is fitted in a leastsquares manner using the cumulative probabilities of
The cumulative probability of
GEVDs of
Based on the method above, the best cumulative distribution functions of
Since
Based on the sampling simulation method above, the simulation results of 3495
The simulated
Furthermore, the simulated 3495 values of
The simulated
The CBT relates to the bearing wear condition. If the CBTs exceed the wear limit in the service lifetime, the spherical steel bearing is totally damaged and cannot be used for longitudinal thermal expansion any longer. Therefore, it is necessary to analyze whether the CBTs at bridge site can exceed the wear limit in the service lifetime.
The failure probabilities of spherical steel bearings in the service lifetime (i.e., the probabilities of CBT over the wear limit in the service lifetime) are calculated as follows:
or
By referring to the sampling simulation method in the Section
The cumulative probability characteristics for the
After
If the calculated reliability level
Figure
After the three parameters are determined, the bearing wear life is evaluated by the following seven steps:
The values of
All the 8434300 values of
Steps (1) and (2) are repeated 1000 times to obtain 1000 values of
The cumulative probability of
The failure probability
The reliability level
Because the linear growth rate of CBT for
The 1000 values of
Based on the monitored dynamic displacement data of steel truss arch bridge bearings, the CDD under the action of a single train and the CBT under the continual actions of many passed trains are investigated. Furthermore, the probability statistics and the Monte Carlo sampling simulation method for CDD are studied, and the safety evaluation method for the bearing wear life is proposed using a reliability index regarding the failure probability of monitored CBT over the wear limit in the service lifetime. The main conclusions are drawn as follows:
Through monitored data analysis, the monitored longitudinal displacement data mainly consist of temperatureinduced static displacements and traininduced dynamic displacements. The wavelet packet decomposition method can effectively extract the smallamplitude dynamic displacements caused by train loads from the monitored data. All the CDDs contain uniform and random characteristics, and all the CBTs have an obvious linear correlation with the number of passed trains, but their linear growth rates are different.
Through probability statistics analysis, GEVD can well describe the cumulative probability characteristics of CDD. The Monte Carlo sampling simulation was performed using GEVD to simulate CDD and CBT, and the results show that the simulated cumulative probabilities of CDD have agreement with the monitored ones of CDD, and the simulated linear growth rates of CBT have agreement with the monitored ones of CBT.
Through safety evaluation analysis, the safety evaluation method for the bearing wear life is proposed using a reliability index, and it is finally judged whether the CBTs can exceed the wear limit in the service lifetime. The evaluation results show that all the spherical steel bearings do not exceed the wear limit in the service life.
cumulative bearing travel
cumulative dynamic displacement
cumulative probability
monitored longitudinal displacement data at the
monitored longitudinal displacement data at the
dynamic displacement caused by the
cumulative distribution function with assigned value
cumulative distribution function with assigned value
general extreme value distribution
cumulative distribution function of
cumulative distribution function of
cumulative distribution function of
cumulative distribution function of
linear variable differential transformer
average value of 3495 CDDs for each
average value of 3495 CDDs for each
CBT caused by
CBT of
CBT of
wear limit of
wear limit of
cumulative travel of bearing caused by the
set of
set of
simulated CDDs of
simulated CDDs of
total number of
total number of
number of CDDs in
number of CDDs in
normal distribution
polytetrafluoroethylene
CP of the
CP of the
failure probability
value of cumulative probability
Weibull distribution
wavelet packet coefficient in the
target reliability level.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
The authors thank the Natural Science Foundation of Jiangsu Province of China (BK20180652) and the China Postdoctoral Science Foundation (2017M621865).