#054 rail life analysis and its use in planning track mtce - railway tech inter 1993

Rail Technology International 1993 1

Rail Life Analysis and its Use in Planning Track Maintenance

Allan M. Zarembski Ph.D., P.E President

ZETA-TECH Associates, Inc. In recent years, there has been an increasing trend toward acquiring "hard" data about track component conditions, as well as a better understanding of the failure mechanisms for key track components, such as rail. This has led to an increased ability to predict how and when these components will fail, and thus when they must be replaced. In turn, this information allows for the accurate forecasting of track component replacement and hence budgetary requirements. In addition, it allows for a more accurate planning and scheduling of track maintenance activities, since the times and locations for the key production activities is more accurately known. This type of maintenance planning is becoming increasingly important in light of the growing cost of track maintenance for railway systems. As these systems become larger and more complex, and as the cost of maintenance continues to increase, the ability to properly plan and execute track maintenance programs in an efficient and cost-effective manner becomes increasingly important. Component Degradation Relationships A critical part in the implementation of a Usable track maintenance planning system is the development of effective track component degradation or failure relationships. These relationships represent the transition from the data base, which is an expression of the current condition o the track system and subsystems to the future condition of the track and its key components. It is this projection of component condition and "life" that provides the information on which maintenance planning is based. There are two basic types; of component life or failure models that are traditionally developed: mechanistic models or empirical models. Mechanistic models are mathematical models that attempt to simulate the actual failure mechanism or mechanisms in order to determine degradation or failure of the component. This approach attempts to define the actual mechanical properties of the components and their complete loading environment so that the interaction between the loads and the materials can be mathematically simulated to represent the mechanism(s) of failure. This approach generally is quite sophisticated, often requiring complex (and time consuming) computer algorithms to simulate each of the potential failure mechanisms. However, this approach provides a good understanding of the actual behavior of the track and its components, as well as determining which properties are most important in extending the performance of the component or system. As such, these models are very effective for designing systems or developing improvements in these components. They also tend to require more detailed input data, some of which may not be readily available in a realistic track data base configuration.


Empirical models are relatively simple models based on experimental or observational data to obtain relationships between key factors that affect the component lives. These models are generally derived from statistical approaches, by which a large volume of experimental or observational data is collected and correlated. Often a mechanistic model is used to help define the most critical variables with the statistical or empirical analyses providing for the relationships between these variables. Empirical models are often relatively simple in final form, and as such, tend to require less computational time than the mechanistic models. They also tend to be very highly dependent on the data used to develop them, and as such cannot be readily extended outside the range of behavior which is represented by that data. The actual relationships that are used .for the calculation of component life are by nature component and failure mechanism specific. Thus, separate relationships are required for each of the key track components, including:

rail life

tie life

track geometry (or alternately ballast and subgrade)

turnouts/special trackwork

other components as required In addition, for each component or set of components, it is often necessary to develop failure mechanism specific relationships to correspond to the various modes of failure of a component. Thus for the case of rail there can be as many as four failure mechanisms at work on mainline track (where the rail will fail mechanically, rather than "rust out... as can occur on light density trackage). These mechanisms are:

* Rail wear

* Rail fatigue (internal)

* Rail fatigue (surface)

* Rail End Failure (joint or weld) These mechanisms in fact can act concurrently, i.e. the rail can simultaneously be subject to wear, internal defects, surface defects such as corrugations or spalling and weld batter and fatigue. Depending on the relative rate of failure of each mechanism, the actual failure mechanism will vary, based on the specific set of track and traffic conditions. Thus, it is often necessary to calculate the life under all of the affected mechanisms with the shortest predicted life being used for the maintenance planning activity.


The final step in the development of a set of usable degradation equations is the calibration for specific railroad conditions and experience, so as to reflect actual component lives on that property. This is a critical activity, since railroad maintenance practices and conditions can significantly affect the component life. Rail Failure Models Rail represents one of the largest, if not the largest, maintenance expenditure items in the maintenance of way budgets of heavy freight railroads. The most common failure modes for rail, and consequently the ones that are most frequently modeled are: rail wear; rail fatigue; and rail end failure (for bolted or welded rail). In general, rail life models tend to be based on a defined set of data in which one of the above failure modes tends to dominate. This type of behavior is illustrated in Figure 1 where rail life based on wear limits is compared to rail fatigue life for different axle (or wheel) loading environments. Thus, it can be seen that in the lighter axle load environments, rail wear is the dominant failure mode (i.e. most rails would be removed because of wear criterion), while in the heavier axle load environments (most commonly associated with high tonnage freight railroads) fatigue emerges as the dominant replacement criterion. This relationship is based on tangent track. In curved track, the behavior changes as rail wear becomes a more important replacement criterion, depending on the curvature, loading, and level of maintenance of the system. Attempts to develop a single general life model to represent all of the failure mechanisms have, in actuality, been based on a single dominant mechanism. Since the critical failure mechanisms noted above are not additive, but rather are alternate failure mechanisms, the idea of simply combining all of their effects into one equation is not effective. Rather, it is necessary to develop failure relationship~ for each of the critical mechanisms (wear, fatigue, etc.) and to run all of the models, and see which produces the shorter life. In this manner, the actual life and the mode of failure is calculated. In order to illustrate this concept, two rail failure modes will be examined in detail: rail wear and rail fatigue. Rail Wear Rail wear is the loss of rail head metal resulting in a decrease in size (and strength) of the railhead. Rail wear is generally defined in terms of allowable wear limits (or conversely minimum remaining head size). These wear limits have been defined in several interrelated ways, including: vertical head loss; side head loss; linear combinations of the two; head area loss; and maximum angle of side wear. Rail wear models have been developed using both of the approaches outlined earlier: empirical and mechanistic. In the case of mechanistic models, these models attempt to develop degradation relationships for each of the possible wear modes such as adhesive/abrasive wear, plastic flow, surface fatigue, and corrosion. They then calculate the damage (wear) occurring under individual wheel loading cycles, determine the cumulative wear, and calculate the rail wear life. These


models are relatively complex and are generally cumbersome to apply in a large data base, whose objective is to forecast component life for a large number of locations or segments of track. The empirical model approach has been a commonly utilized one for rail wear. The general form of one such rail wear equation is:

Rail Life = a * f (C,H,L,S ,Sb) * R ' * J ' --------------------------------------------

g (D) * h(G) * F(P,S) where: a = Calibration Constant ** f(C,H,L,S,Sb) = Function of Curvature (C), Rail Hardness

(H), Lubrication (L), Speed (S), and Balance Speed (Sb) R' = Function of Rail Size

J ' = Function of Jointed or CWR Track g(D) = Function of Annual Density (D) h(G) = Function of Grade (G) F(P,S) = Function of Axle Load (P) and speed (S)

and This set of equations was calibrated to specific railroad practices by means of direct wear measurements taken on the line during site inspection. Rail Fatigue Rail fatigue failure represents the failure of the rail through the development of fatigue defects, which reduce the strength of the rail so that the rail can no longer safely support traffic loading. If these defects are not removed, they can result in failure (breaking) of the entire rail section. Fatigue analysis models have taken the form of both mechanistic and empirical (and even statistical) models. The mechanistic models have attempted to analyze the cumulative fatigue damage developed in a given critical location (usually the point of maximum combined stresses) in the rail head. Thus by having an effective representation of the loading environment, converting the loading to localized stress distribution (for all relevant stresses such as bending, contact and thermal stresses), combining the stresses and comparing them with the material properties, a calculation of the fatigue damage, and consequent fatigue life can be carried out. These models are extremely complex models that require a significant amount of computational time for each analytical application, and hence, may not be appropriate for use in a data base application where a large number of iterations of the model(s) is required. Empirical models for rail fatigue have been developed using forms similar to that presented for rail wear. However, the major difficulty in applying this type of model to rail fatigue is that, unlike in the case of rail wear, rail fatigue, which results in the development of individual fatigue defects, does not require the removal from track of an entire segment of rail. Rather individual


rail lengths, usually between 13 and 39 feet in length, are removed for each defect. Thus, an entire rail segment is usually removed from track, only when the number of defects is such that it is economically more attractive to remove the entire segment rather than replacing it piecemeal. Noting this, an alternative approach using probability distribution theory to predict the occurrence of the individual fatigue defects, has emerged as a viable technique for predicting the fatigue life of rail. This approach has been successfully applied to freight railroad traffic in the "Weibull" statistical analysis approach.

PD(MGT) = 1 - exp [ - (MGT/) ] where: PD = Probability of a defect occurring at tonnage level MGT,

= slope of the Weibull line = Weibull intercept, corresponding to the MGT value at which 63.2% of the

rails will contain a defect and Using this approach to forecast the occurrence of fatigue defects, using historical defect data such as found in an effective data base, represents a practical and implementable approach for the: prediction of rail fatigue defects and corresponding defect life. However, this equation requires the availability of the complete defect and tonnage history for the segment under analysis. This is not always available. However, information regarding the defect rate for a given line segment, particularly corresponding to the last several years of service, is generally available. This data can be used to generate a set of Weibull parameters (, ) by using the defect rate equation (corresponding to the first derivative of the Weibull equation) as follows:

DR = [a / ( ) ] MGT - l where: DR = Rate of defect occurrence in defects/rail/MGT In order to use this equation directly for the prediction of the rail life, it is necessary to first solve for the Weibull parameters and . Once these are known or defined, then the life of the rail in track can be obtained for a given defect rate (DR) as follows:


DR * Life (MGT) = [-----------------------------] l / (- l )

where:

= Alpha, the Weibull slope = Beta, the Weibull intercept DR = the defect rate in defect/rail/MGT Life (MGT) = fatigue life of the rail in cumulative MGT corresponding to the

defined defect rate It should be noted that this Weibull relationship is affected by railroad maintenance policies, particularly rail profile grinding programs. This behavior again suggests that any such predictive relationship must be adapted and calibrated to the specific railroad's maintenance practices and policies. Rail Life Analysis for Representative Freight Railway These wear and fatigue life relationships were applied to a 140 mile long stretch of heavy axle load freight railroad to demonstrate this planning capability. This stretch of track carries primarily unit coal traffic in 100 ton unit trains with varying annual traffic densities along the route. In order to perform such an analysis, the track was divided into homogeneous segments where all of the key track and traffic parameters that affect the component (rail) life remain constant throughout that segment. These include the following parameters:

- Rail Type - Rail Size - Curvature - Grade - Operating speed - Super-Elevation - Lubrication - Rail Hardness - Traffic Density - Installation Date

This division of the track was carried out in a manner consistent with the existing railroad data base. Note: for the 141 mile section of track analyzed, there were over 1100 such segments. (Note: this was considered to be a high curvature section of railroad, and thus represents a very large number of homogeneous segments per mile.) In addition to the specific segment data noted above, rail defect history data and location specific rail wear data was collected. The former was used in the Weibull analysis and the latter was used in the calibration of the rail life model to reflect railroad behavior and practice.


After calculating both rail wear and rail fatigue life, the actual rail replacement date was determined using the lower of the two calculated lives. Thus, when the wear life was less than the fatigue life, such as or moderate and sharp curves, the wear life value was used to calculate the rail replacement date. When the fatigue life was the lower value, such as on tangents, this value was used to calculate the rail replacement dates. The resulting wear and fatigue lives were combined with the rail installation dates to calculate rail replacement cycles and the amount of rail required for replacement for each future year. The actual forecast replacement date is presented on a segment by segment basis in Figure 2. Note that the historical rail replacement cycles can be clearly seen as a pattern of predicted rail replacement year. In order to accommodate the railroad's policy of laying rail in long stretches, the rail replacement cycles shown in Figure 2 were consolidated into 3.5 mile long stretches of track, corresponding to the railroad's defined minimum rail relay length. This consolidated rail relay program is presented in Figure 3. As can be seen from this figure, the rail replacement points are well defined and form a progression along the track, thus lending themselves directly to a long term rail replacement plan. It should be noted that the track at MP 245 to 260 has a significantly lower traffic density than the rest of the line, thus accounting for its very long replacement life (replacement in year 2040). Short, Intermediate, and Long Term Planning Rail life relationships can be used to predict the replacement point of rail along defined segments of track, provided that basic information about the history, condition, and traffic are known. These life predictions, in turn, lend themselves for use within the scope of a maintenance planning structure, so as to predict both short and long term planning needs. In general these planning horizons can be divided into three broad categories: Short term; Medium term; and Long term. Short term applications for rail replacement planning employ the information immediately, up to a one year period from the time of data acquisition and analysis. Because of the almost real time nature of this application, rail forecasting models have the least application here. Rather, direct measurement and exception data (wear, defects, corrugations, etc.) are most applicable in this time frame. Medium term applications generally have a one to two year horizon, which lend themselves to MOW planning for both capital and maintenance programs. Within this time frame, data can be analyzed to predict "next year's" rail program requirements by defining the required amount and type of rail, its location, and an optimum replacement schedule. This data can also be used to evaluate alternate rail programs, identify areas where maintenance, such as grinding, is required, and establish priorities in the event of budget cuts.


However, it is in the final category, that of long term applications, that this type of forecasting is most appropriate. With a time horizon of two to ten (or more) years, forecasting models permit the development of long term programs and budgets. Thus, multi-year budgets can be developed for 3 year, 5 year, 10 year, or longer planning horizons. In addition, this long term application of component degradation analysis allows for the determination of the consequences of not installing the needed rail (or other components). Thus, the effect and long term consequences of budget cuts and deferred maintenance can be more realistically assessed. Finally, alternate long term maintenance programs, practices, and strategies can be evaluated and assessed. This type of planning can likewise be carried out for other key track components to include ties, ballast (or alternatively track geometry), turnouts, special trackwork, bridges, etc. It may therefore be concluded from this that the development and use of track component degradation relationships, within the context of an overall track maintenance planning activity, permits railway maintenance officers to properly and effectively plan their future maintenance requirements and develop cost- effective long term track maintenance programs.

#054 rail life analysis and its use in planning track mtce - railway tech inter 1993

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