University of Birmingham Fatigue life losses of railway concrete sleepers due to surface abrasions

Railway concrete sleepers are one of the most signiﬁcant components of ballasted track. The failure of a concrete sleeper is considered to be the process of accumulated damage due to repeated loads over a long period of time. The fatigue life of concrete sleepers is a concerned question of operation and maintenance departments of railway line. Despite the importance of the eﬀects of wheel-rail interaction loads in the reduction of the life cycle and operation time of concrete sleepers has been realized, at present, there is no systematic procedure for the service life analysis of concrete sleepers under repeated loads. Based on the damage accumulation method, this paper presents a fatigue life assessment method for a prestre-ssed concrete sleeper, and researches the fatigue life losses caused from surface abrasions. Surface abrasion is one of the most common problems of the concrete sleepers will reduce its resistance capability, and then inﬂuence its fatigue life. The outcome of this study can be used to evaluate the service performance of the abrasive concrete sleeper and improve the rail track maintenance and inspection criteria.


Introduction
Development of railway transportation system is significant and continuously around world.Railway transportation plays a vital role for economy.Railway is also the safest transportation which gives highly enjoyable ride for both of passengers or freights.Conventional ballasted railway structure consists of superstructure and substructure.The superstructure includes rails, rail pads, fastening system and sleepers.The substructure consists of ballast, sub-ballast and formation.Railway sleeper (also called rail tie in North America) is very important component in rail track structure.The main functions of sleeper are [ ]: ) Support the rails and maintain the track gauge.
) Transfer and distribute vertical loads from superstructure to substructure.
) Withstand vertical and longitudinal movement of rails.
Railway sleepers can be manufactured by timber, steel, concrete and any other engineered materials.Nowadays, prestressed concrete is the most common type used in sleepers around the world, which it has good structural performance and low cost in maintenance.However, railway sleepers experience millions repeated loading in service life and the progress of cracking depends on cyclic behaviour which caused by the wheel-rail interaction force.Nowadays, the permissible stress (also called 'allowable stress') method is utilised for concrete sleeper design which the dynamic load is not considered in design accurately [ , ].For example, in Japan May , Zadar, Croatia th International Conference on Road and Rail Infrastructure concrete sleepers cracks happen frequently have been found in high quality track under severe loading environments [ ].Therefore, the fatigue limit state should be considered in design process.Amount of experiments about dynamic influence on prestressed concrete sleepers has been conducted in University of Wollongong, the crack damage due to fatigue were investigated [ -].This research aims at providing a principle understanding of cyclic behaviour of railway concrete sleepers.This study also presents prediction method of cyclic behaviour on railway concrete sleepers.The outcome of this research will provide appropriate design principle for the concrete sleepers and it will help improve track maintenance and inspection system.

Fatigue life and predict method . Structural performance
Fatigue is a time-dependent behaviour where the damage due to repeat load will be accumulated.The fatigue damage in railway sleeper generated from wheel-rail interaction and it is determined by wheel-rail stress.The damage is random but the performance of railway concrete sleeper will decrease due to material degradation.The service life of railway concrete is usually more than years.The life cycle performance of railway concrete sleeper is shown in Figure .R(t) is the resistance of concrete sleeper and S(t) is the effect of cyclic roads.The performance graph is presented by probability distribution function.It can be considered as probability of sleeper failure when R(t)<S(t) in risk measurement.From the curve, the probability of sleeper failure keeps increasing with time.
. Fatigue life time prediction The Miner's Rule is usually used in predicting accumulated damage in many design codes [ , ].The damage accumulation method will be used to predict fatigue life of railway concrete sleeper in this research.The cumulative damage index ∑Di in multi-cycles with variable amplitudes can be calculated by: Where n(∆σ i ) is the applied number of cycles for a stress range ∆σ i ; N(∆σ i ) is the resisting number of cycles for a stress range ∆σ i .
This method is used to predict fatigue life under constant amplitude cycle loads and it is based on damage accumulation method.The corresponding S-N curve shown Figure is utilised to determine the maximum applied number of cycles for single stress amplitude.

. Fatigue load
To determine the fatigue load is the first step to investigate the cyclic behaviour of railway concrete sleepers.The fatigue loads are generated from wheel-rail interaction which influenced by train speed, axle loads, curve radius of track, track quality and environments etc. wheel-rail interaction force is various even in same rail line.Therefore, it's hardly to obtain accurate fatigue load of railway sleeper through whole service life.Some researchers use the wheel dynamic load detector to obtain the wheel-rail interaction force in the railway (at least year in period).The data obtained from site which can be used to generate numerical

Section and material properties
The

Remaining fatigue life calculation
The failure analysis of fatigue of concrete sleeper can be divided into two stages.In first stage, there is no crack appeared in this stage.The relationship between stress and stain is assumed as linear for both of concrete and steel.The critical cracking moment can be calculated: In second stage, the crack happens and the neutral axis of cross-section will change.When the section is fully cracked, the prosperityof the section can be calculated.The distance from the center gravity of the effective transformed area to the top of the compressed area y CG can be calculated by:

( )
Where the S pcII is the first moment about the bottom fibre after cracking, the A' pi is area of the prestress steel in layer i, and d i is the distance from prestress steel in layer i to the bottom of tension area.
Using transformed area of concrete section A cII , the effective transformed section can be calculated: The moment of inertia of the fully cracked section: Where the I t is the moment of inertia of transformed section before cracking, M cr is the cracking moment, M max is the maximum bending moment at section under cyclic load.
And then, the tension stresses range in the first layer prestress steel at tension area: Where M min is the minimum bending moment at the section under cyclical loads.

Results
The damage index of each year (D i ) and accumulated damage (ΣD i ) are calculated and shown in Figure .The total cyclic impact between wheel and rail through a sleeper is assumed times for a year.From the gragh, in early age the damage increases sharply which could be leaded by loss of prestress.After years in service, the the loss of prestress due to material properties become steady then the damage increases slow.The accumulated damage index shows that the positive beding moment is about years, which means the fatigue life is years.

Figure 1
Figure 1 Life cycle performance of concrete sleeper

Figure 2
Figure 2 the corresponding S-N curveTherefore, the failure cycles of the prestressing steel under a constant amplitude cyclic load can be given by: detail of railway sleeper is shown on Figure .The material properties of railway sleeper is shown in Table .

Figure 4
Figure 4 Railseat and centre section of sleeper

Figure 5
Figure 5 The damage index of each year and accumulated damage with time

Table 2
Material properties of railway sleeper