Random distribution characteristics of peak dynamic stress on the subgrade surface of heavy-haul railways considering track irregularities

doi:10.1016/j.soildyn.2018.10.013

Soil Dynamics and Earthquake Engineering

Volume 116, January 2019, Pages 205-214

https://doi.org/10.1016/j.soildyn.2018.10.013 Get rights and content

Highlights

•
Dynamic stresses on the subgrade surface were asymmetric along the track centerline.
•
Peak dynamic stress on subgrade surface follow normal distribution along the track.
•
The maximums of peak dynamic stresses on subgrade surface were forecasted.

Abstract

The dynamic response of the subgrade surface under moving train loads provides information for subgrade settlement prediction, condition evaluation and so forth. In this paper, a 3D dynamic finite element (FE) model that considers the interactions among the wagon, track and subgrade was built. Then, the irregular vertical track spectrum of the three major lines in China was applied to simulate track irregularity. Through numerical calculation, the influence of vertical track irregularity on the dynamic stress of subgrade surface was investigated. The distributions of peak dynamic stresses at three subgrade surface locations (under each of the two rails and at the track center) along the track under the passage of trains with various axle loads were statistically acquired. The normal distributions of the peak dynamic stresses on the subgrade surface were verified. The maximum peak dynamic stresses were forecasted. The results indicated that the dynamic stresses on the subgrade surface were asymmetric along the center of subgrade surface due to the random distribution of track irregularities, and the peak dynamic stresses were found to follow a normal distribution. With the increase of axle load, the dispersion of peak dynamic stresses increased gradually, and the distribution curve of peak dynamic stresses gradually became steeper. The computed peak dynamic stresses aligned well with the field test data, indicating that the 3D dynamic FE model and statistical analysis method were reasonable. The research results will provide a basis for the reliability analysis of the dynamic deformation and accumulated settlement of subgrade surface.

Introduction

Heavy haul railways have great freight conveying capacity and have created great social and economic benefits. Improving the performance and longevity of the heavy-haul railway system has long been a research focus for rail transport all over the world. Because subgrade accounts for more than 70% the total length of the heavy haul railway, it plays a key role in the security of railway transportation.

The dynamic stress response of subgrade caused by moving trains is the starting point for strength and deformation stability analysis. The main factors contribute to dynamic stress response of subgrade have been identified and include the speed of train [1], [2], axle load [2] and track irregularity [3]. Heavy-haul trains run slower (generally under 120 km/h) than high-speed trains. Two more factors may play a great role in the dynamic stress response of subgrade.

Two general methods are commonly adopted to study the dynamic stress response of subgrade: field tests [2], [4], [5] and model tests [6], [7], [8], [9]. Dynamic stress can be measured using these two methods, but the tests are expensive. With the development of computer technology and vehicle-track coupled dynamics [10], [11], numerical simulation has become an effective way to investigate the dynamic behavior of subgrade surface due to railway traffic. There are two types of numerical modeling for railway subgrade: track-subgrade modeling and train-track-subgrade coupled modeling; the former simplifies the train loading to some extent. Some scholars assume traffic load is a cyclic load acting on fixed points [12], [13], while other scholars simulate train loading through the definition of stationary loads moving on rail surface [14], [15]. Track-subgrade modeling is simple and requires less computation than train-track-subgrade coupled modeling; however, it only considers the quasi-static interactions of the wheel and track and neglects the dynamic interactions of the train and track.

To overcome the shortcomings in the current analysis of the dynamic responses of railway substructures, Zhai proposes the theory of vehicle-track coupled dynamics and builds a full train-track model [10], [11], which is widely used in the dynamic analysis of train-track interaction. Subsequently, some train-track-subgrade coupled models have been built to analyze the dynamic stress responses of subgrade [16], [17] with good results.

In summary, the numerical analysis of the vehicle, track and subgrade in high-speed railway systems mainly focuses on the interactions between the train and track. There are few studies regarding the dynamic stress response of subgrade surface in heavy-haul railways, and the distribution of dynamic stress along the track has not been sufficiently investigated regarding track irregularities. In this paper, a 3D dynamic FE model of wagon, track and subgrade was developed using ABAQUS, and the irregular vertical track spectrum of China's three major lines is applied to simulate track irregularity. The dynamic responses of subgrade were analyzed. The distribution of peak dynamic stresses on the subgrade surface along the track (under each of the two rails and at the track center) were statistically obtained. The peak dynamic stresses on the subgrade surface were found to follow a normal distribution according to the Kolmogorov rule. The maximum peak dynamic stresses on the subgrade surface were forecasted based on the triple standard deviation principle.

Section snippets

Wagon model

In this study, the wagon was simulated as a full wagon model with a double suspension system, where the wagon body, bogie and wheelset forming the wagon system were considered rigid bodies. The full wagon model can reflect the superposition of vibration between the wheelsets, which is reasonable. The wagons were connected to bogies by primary suspensions, and the bogies were connected to wheelsets by secondary suspensions. The suspension systems were simulated as springs and dampers.

Zhai [11]

Probability analysis of the peak dynamic stress on the subgrade surface

As mentioned, the groundwater table is relatively low, there is little rainfall in the K361 + 784–904 section of the track, and the filling of the subgrade bed is a coarse-grained soil, which has high permeability. Therefore, the stress calculated in the FE analysis refers to the effective stress.

Unless otherwise specified, in this paper, ‘dynamic stress’ refers to dynamic stress in vertical direction, and the downward direction is positive. According to the literature [16], the peak dynamic

Conclusions

In this paper, a wagon-track-subgrade system is modeled using the finite element method. The irregular vertical track spectrum of China's three major lines is applied to simulate track irregularity. Using numerical calculation, the distributions of the peak dynamic stresses along the track under the passage of the wagons at three locations of subgrade surface (beneath each rail and at the track center) are statistically acquired. Four conclusions can be drawn:

1)
The track irregularity leads to the

Acknowledgements

This work is financially supported by the National Natural Science Foundation of China (grant number 51678572, 51878666), Specialized Scientific Research Fund Projects of Shenhua Group Corporation Ltd. (grant number SHGF-14–55) and Graduate Innovation Project of Central South University (2017zzts156). The contributions of anonymous reviewers and editors are also acknowledged.

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When simulating loading, the above requirements of regulatory documents are supplemented by accounting for the properties of the track structure. For example, in (Xu et al., 2018; Mei et al., 2019) the rail, sleepers, and ballast layer were modeled as elastic media, while the substructures were simulated as elastoplastic media using the Mohr–Coulomb constitutive model. In addition, when estimating the service life of the subgrade, it is advisable to take into account changes in the properties of the ballast and subballast materials that determine the load on the subgrade soil.
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View full text

Random distribution characteristics of peak dynamic stress on the subgrade surface of heavy-haul railways considering track irregularities

Highlights

Abstract

Introduction

Section snippets

Wagon model

Probability analysis of the peak dynamic stress on the subgrade surface

Conclusions

Acknowledgements

Dynamic stress analysis of a ballasted railway track bed during train passage

J Geotech Geoenviron Eng

Track-bed mechanical behaviour under the impact of train at different speeds

Soils Found

Analytical model to predict dynamic responses of railway subgrade due to high-speed trains considering wheel-track interaction

Int J Geomech

Deformation measurement on a heavy haul track formation

Int Heavy Haul Conf

Deformation characteristics of railway roadbed and subgrade under moving-wheel load

Soils Found

Experimental settlement and dynamic behavior of a portion of ballasted railway track under high speed trains

J Sound Vib

Full-scale model testing on a ballastless high-speed railway under simulated train moving loads

Soil Dyn Earthq Eng

Experimental study on dynamic load magnification factor for ballastless track-subgrade of high-speed railway

J Rock Mech Geotech Eng

Analysis and design of vertical dynamic parameters of wheel/rail system with low dynamic interactions

J China Railw Soc

Vehicle-track coupled dynamics

Three-dimensional numerical modelling of ballasted railway track foundations for high-speed trains with special reference to critical speed

Transp Geotech