Embededded Track Design and Performance
FIGURE 4 Idealizations for modeling.
FIGURE 3 Track section and associated model elements.
FIGURE 1 Configuration 1: Rail fully embedded in concrete (illustrated with Rail Boot).
FIGURE 2 Configuration 2: Rail embedded in a non-structural material supported by concrete slab
(illustrated with Rail Boot).
(illustrated with Rail Boot).
The industry is gravitating to concrete slabs for embedded track designs. Designs with concrete have proven economies in construction and long-term performance. Yet there are concerns, such as the following:
•Agencies press for minimum slab thickness to minimize conflicts with existing utilities;
•Configurations to meet criteria for stray current control and ground vibration control may effect track integrity;
•Design factors for future utility trenching around embedded track are inherently uncertain, potentially governing a design, or, if ignored, jeopardizing long-term track performance;
•The effects of elastomers on the slab performance have little research;
•Embedded track is among the least maintenance friendly. Improvements in design analysis will allow confidence in new low maintenance concepts.
This paper provides embedded track analysis methodology and results that are the basis for engineering decisions on, and increased confidence in, long-term embedded track performance.
The analysis method treats the rail and support slab as two continuous beams interacting through an intermediate pad, with the support slab on a continuous elastic foundation (soil). The method produces deflections, moments, and stresses independently for the rail and support slab, and pressures in the intermediate pad and supporting soil. This information allows long-term maintenance assessments (slab life, required soil load capacity, and pad criteria) of a design.
The methodology is explained and the results for the practical range of embedded track configurations are presented.
BACKGROUND
The purpose of this paper is to present analysis methodology and illustrative results for embedded track, and to identify criteria or guidelines useful for assessing the integrity of an embedded track design.
A central interest is in assessing performance differences between different embedded track arrangements including those with and without elastomeric elements between rail and slab.
The development of the analysis methodology established the following goals for the modeling:
•To reflect the individual behavior of the rail and the slab;
•To incorporate methods for realistic slab support (foundation modulus for the soils);
•To assess performance under service (fatigue, life expectancy);
• To allow single axle or multiple axle loading and thermal rail loading.
The model uses Beam-On-Elastic-Foundation (BOEF) theory.
This report treats the material in the following order:
•Track configurations and conditions;
•Description of methodology;
•Illustration of methodology results;
•Summary.
TRACK CONFIGURATIONS AND CONDITIONS
The general embedded track configurations are:
1.Rail fully embedded in concrete (Figure 1);
2.Rail embedded in a non-structural material supported by structural concrete slab (Figure 2).
•Agencies press for minimum slab thickness to minimize conflicts with existing utilities;
•Configurations to meet criteria for stray current control and ground vibration control may effect track integrity;
•Design factors for future utility trenching around embedded track are inherently uncertain, potentially governing a design, or, if ignored, jeopardizing long-term track performance;
•The effects of elastomers on the slab performance have little research;
•Embedded track is among the least maintenance friendly. Improvements in design analysis will allow confidence in new low maintenance concepts.
This paper provides embedded track analysis methodology and results that are the basis for engineering decisions on, and increased confidence in, long-term embedded track performance.
The analysis method treats the rail and support slab as two continuous beams interacting through an intermediate pad, with the support slab on a continuous elastic foundation (soil). The method produces deflections, moments, and stresses independently for the rail and support slab, and pressures in the intermediate pad and supporting soil. This information allows long-term maintenance assessments (slab life, required soil load capacity, and pad criteria) of a design.
The methodology is explained and the results for the practical range of embedded track configurations are presented.
BACKGROUND
The purpose of this paper is to present analysis methodology and illustrative results for embedded track, and to identify criteria or guidelines useful for assessing the integrity of an embedded track design.
A central interest is in assessing performance differences between different embedded track arrangements including those with and without elastomeric elements between rail and slab.
The development of the analysis methodology established the following goals for the modeling:
•To reflect the individual behavior of the rail and the slab;
•To incorporate methods for realistic slab support (foundation modulus for the soils);
•To assess performance under service (fatigue, life expectancy);
• To allow single axle or multiple axle loading and thermal rail loading.
The model uses Beam-On-Elastic-Foundation (BOEF) theory.
This report treats the material in the following order:
•Track configurations and conditions;
•Description of methodology;
•Illustration of methodology results;
•Summary.
TRACK CONFIGURATIONS AND CONDITIONS
The general embedded track configurations are:
1.Rail fully embedded in concrete (Figure 1);
2.Rail embedded in a non-structural material supported by structural concrete slab (Figure 2).
These basic configurations can be used to model any practical embedded track form (i.e., configurations) using one of these basic configurations, including track continuously in street, grade crossings, or track at grade (above ground slabs).
The analysis is specifically for track that contains concrete (other than concrete ties) as a structural support or as a fill material between the rails. Any other embedded track (e.g., ballasted track with asphalt in-fill) is designed simply using conventional ballasted track engineering, and is outside this discussion.
Configuration 1: Rail Fully Embedded
The first configuration, rail fully embedded, is the case where there is a base concrete slab and concrete fill to the top of rail (Figure 1).
This configuration includes construction that is poured as a monolith (single pour from base of slab to top of rail), or sequential pours (base slab poured first, followed by one or more top pours).
Also included within this configuration are trough track (troughs for rail are cast in, with rail, fasteners and trough infill material placed after the trough is complete), any form of direct fixation track where concrete is the infill material between limits of the fasteners (or covering the fasteners and rail, except rail head).
Some slab designers prefer reinforcement bar within or into the rail infill concrete, particularly if there are multiple pours; such additions of rebar are consistent with the assumptions in the analysis, but have no effect on analysis results.
Configuration 2: Rail on Concrete Slab
The second general configuration is that of a concrete slab supporting the rail, with or without non-structural infill or top pour material (Figure 2).
With this configuration, infill material between rails is considered non-structural, meaning that it has no consequence in supporting rail loads other than adding dead weight to the structural supporting slab.
This configuration includes any material as the “top pour” (from top of support slab to top of rail), such as asphalt paving, paver blocks, lightweight concrete, or paneling of any type. Any rail fastener arrangement is acceptable.
BEAM ON ELASTIC FOUNDATION ANALYSIS PROCEDURES
-Analysis Method and Idealizations
The methodology implemented in this paper is the BOEF theory generally used to analyze track, except this method allows two beams (the rail and slab) where the traditional analysis allows only one beam (the rail).
This method, developed by Hetényi (1), allows assessment of the rail and slab interaction through a continuous series of springs between the rail and slab.
These intermediate springs represent rail pads, rail fasteners, or any membrane (such as Rail Boot) that have measurable stiffness (spring constants).
The model can be used to represent any intermediate material, as well as the case with no intermediate material (a very stiff spring). An elastic material (the soil or aggregate) supports the slab in the model.
These idealizations, illustrated in Figures 3 and 4, can represent any continuous track, including floating slab track as well as embedded track.
This analysis is linear, which means that this analysis allows cumulative addition of individual effects, such as two adjacent axles on a truck where the effects of each axle are superimposed.
The model considers wheel loads as “point” loads, and loads from rail thermal expansion and contraction are “distributed” loads, placing a load continuously along the length of the slab. The effects of distributed loads can be superimposed on the wheel load results in this model implementation.
The analysis is specifically for track that contains concrete (other than concrete ties) as a structural support or as a fill material between the rails. Any other embedded track (e.g., ballasted track with asphalt in-fill) is designed simply using conventional ballasted track engineering, and is outside this discussion.
Configuration 1: Rail Fully Embedded
The first configuration, rail fully embedded, is the case where there is a base concrete slab and concrete fill to the top of rail (Figure 1).
This configuration includes construction that is poured as a monolith (single pour from base of slab to top of rail), or sequential pours (base slab poured first, followed by one or more top pours).
Also included within this configuration are trough track (troughs for rail are cast in, with rail, fasteners and trough infill material placed after the trough is complete), any form of direct fixation track where concrete is the infill material between limits of the fasteners (or covering the fasteners and rail, except rail head).
Some slab designers prefer reinforcement bar within or into the rail infill concrete, particularly if there are multiple pours; such additions of rebar are consistent with the assumptions in the analysis, but have no effect on analysis results.
Configuration 2: Rail on Concrete Slab
The second general configuration is that of a concrete slab supporting the rail, with or without non-structural infill or top pour material (Figure 2).
With this configuration, infill material between rails is considered non-structural, meaning that it has no consequence in supporting rail loads other than adding dead weight to the structural supporting slab.
This configuration includes any material as the “top pour” (from top of support slab to top of rail), such as asphalt paving, paver blocks, lightweight concrete, or paneling of any type. Any rail fastener arrangement is acceptable.
BEAM ON ELASTIC FOUNDATION ANALYSIS PROCEDURES
-Analysis Method and Idealizations
The methodology implemented in this paper is the BOEF theory generally used to analyze track, except this method allows two beams (the rail and slab) where the traditional analysis allows only one beam (the rail).
This method, developed by Hetényi (1), allows assessment of the rail and slab interaction through a continuous series of springs between the rail and slab.
These intermediate springs represent rail pads, rail fasteners, or any membrane (such as Rail Boot) that have measurable stiffness (spring constants).
The model can be used to represent any intermediate material, as well as the case with no intermediate material (a very stiff spring). An elastic material (the soil or aggregate) supports the slab in the model.
These idealizations, illustrated in Figures 3 and 4, can represent any continuous track, including floating slab track as well as embedded track.
This analysis is linear, which means that this analysis allows cumulative addition of individual effects, such as two adjacent axles on a truck where the effects of each axle are superimposed.
The model considers wheel loads as “point” loads, and loads from rail thermal expansion and contraction are “distributed” loads, placing a load continuously along the length of the slab. The effects of distributed loads can be superimposed on the wheel load results in this model implementation.
Slab Structural Analysis Method
The structural analysis procedures applied to model results are in accordance with applicable American Concrete Institute Code (2).
Fatigue Calculations
Fatigue is calculated as slab life in years of service. Fatigue is calculated at the design load, the nominal wheel load multiplied by a design factor (typically 2).
Fatigue for slabs under special trackwork (frogs, switches, and rail crossings) uses the full design load. This reflects a notion that loads are generally higher as wheels cross frog flangeways and flangeways in rail crossings. Outside special trackwork, the track slabs will endure infrequent loadings at the full design load.
The procedure incorporates a “load distribution factor,” a percentage of the design load, that may be used for fatigue analysis of normal embedded track.
Fatigue is calculated by methods developed by the Portland Cement Association (3).
Base Support Stiffness
The support stiffness of the base soils, gravel, or other material directly under the slab is critical in embedded track analysis.
The considerable literature on soils and foundations lacks data in terms required by embedded track analysis. The design guideline (ACI 360, Design of Slabs on Grade) requires field measurements to obtain the required modulus, not entirely useful for preliminary assessments, or for parametric studies of embedded track configurations. This requirement can hinder new track design processes unnecessarily because the track configuration is central to the design development of all other facilities associated with a railroad or transit. In reality, the urban environment provides new embedded track with engineered base materials (streets, previous rail routes) and ample past borings nearby to provide information suitable for track design.
A preferred available approach is to estimate support modulus for the assumed base materials, generate track designs compatible with all criteria, then confirm the track design when geotechnical data is eventually produced. Assuming base materials and their properties has little risk not only because the urban base material is well known, but also because there is reliable consistency in properties that effect embedded track design in existing urban environments.
In the cases where embedded track may be placed other than in existing infrastructure, it is then, by definition, virgin development that necessitates knowing the requirements for the embedded track base in advance of all other project parameters. The required base will then be engineered to meet track base requirements.
The available method for calculating a reasonable support modulus for a variety of circumstances is provided by Richart et al. (4) using straightforward selection of the soil type and the geometry of the slab and base course. The method’s authors developed a series of curves from tests relating soil shear modulus, soil void ratios, shear wave velocity, soil grain type, slab dimensions, and base course thickness to spring rates (foundation modulus). The method allows consideration of confining pressure (the pressure from adjacent soils on the base material when it deforms under load), important in embedded track applications. The method provides results for vertical spring rates, horizontal spring rates, and rocking spring rates (the stiffness against slab twist about its longitudinal axis).
The Richart et al. data and methodology are implemented in this analysis for base support stiffness.
Results Available from Analysis
The results of the BOEF analysis are estimates of the rail and, separately, the slab deflections, moments, and shear force. The results also include pressures between rail, rail support (elastomer, Rail Boot, rail pad, Direct Fixation fastener), slab, and slab support (gravel or soil base).
The analysis uses these fundamental results to calculate rail and slab stresses and strains, which in turn are used for fatigue life estimates.
The analysis also provides other useful values such as slab safety factors and allowable stresses, and estimates of rail and slab natural frequencies, as design or evaluation aides.
The analysis provides structural results for reinforced slabs and non-reinforced slabs, and calculates slab reinforcement for crack control.
BOEF ANALYSIS RESULTS
This section presents results from the BOEF analysis.
These results illustrate trends in slab reactions (deflections, moments, and stress) and performance (fatigue life). This demonstration explores these results for the following parameter ranges:
•Slab configurations: full slab (Configuration 1) and base slab (Configuration 2)
•Rail support stiffness (elastic property of the rail pad, Rail Boot, or Direct Fixation fastener): 100,000 lb/in. to 3,000,000 lb/in.
•Slab thickness below the rail: 6 in. to 20 in.
For perspective, Rail Boot static stiffness is about 400,000 lb/in. Direct Fixation fasteners typically have a stiffness between 100,000 and 200,000 lb/in, and rail pads generally have stiffness values between 750,000 and 3,000,000 lb/in.
All other parameters in the model are held constant (see Table 1) to allow a direct comparison of results, although a number of parameters such as soils, temperature variants, curvature, and so on would be adjusted in practice for particular circumstances.
The loading and vehicle parameters are typical of a high-floor North American light rail vehicle (LRV). The trends in these results are also indicative of that expected for heavy rail vehicle loading, because the heavy rail vehicle weights and capacities are within 20% of those for LRVs, and heavy rail higher speeds are insufficiently different to effect these types of analysis.
All results are from calculations of both single axle and double axle loads, where the higher value from either is used when appropriate for each parameter explored. Double axle loads are those from two adjacent wheels representing a single truck.
Track Modulus and Support Stiffness
This is a brief aside to clarify the physical meaning of track modulus and support stiffness, and how those apply in this analysis. A support stiffness and its associated foundation modulus are directly related but different.
The structural analysis procedures applied to model results are in accordance with applicable American Concrete Institute Code (2).
Fatigue Calculations
Fatigue is calculated as slab life in years of service. Fatigue is calculated at the design load, the nominal wheel load multiplied by a design factor (typically 2).
Fatigue for slabs under special trackwork (frogs, switches, and rail crossings) uses the full design load. This reflects a notion that loads are generally higher as wheels cross frog flangeways and flangeways in rail crossings. Outside special trackwork, the track slabs will endure infrequent loadings at the full design load.
The procedure incorporates a “load distribution factor,” a percentage of the design load, that may be used for fatigue analysis of normal embedded track.
Fatigue is calculated by methods developed by the Portland Cement Association (3).
Base Support Stiffness
The support stiffness of the base soils, gravel, or other material directly under the slab is critical in embedded track analysis.
The considerable literature on soils and foundations lacks data in terms required by embedded track analysis. The design guideline (ACI 360, Design of Slabs on Grade) requires field measurements to obtain the required modulus, not entirely useful for preliminary assessments, or for parametric studies of embedded track configurations. This requirement can hinder new track design processes unnecessarily because the track configuration is central to the design development of all other facilities associated with a railroad or transit. In reality, the urban environment provides new embedded track with engineered base materials (streets, previous rail routes) and ample past borings nearby to provide information suitable for track design.
A preferred available approach is to estimate support modulus for the assumed base materials, generate track designs compatible with all criteria, then confirm the track design when geotechnical data is eventually produced. Assuming base materials and their properties has little risk not only because the urban base material is well known, but also because there is reliable consistency in properties that effect embedded track design in existing urban environments.
In the cases where embedded track may be placed other than in existing infrastructure, it is then, by definition, virgin development that necessitates knowing the requirements for the embedded track base in advance of all other project parameters. The required base will then be engineered to meet track base requirements.
The available method for calculating a reasonable support modulus for a variety of circumstances is provided by Richart et al. (4) using straightforward selection of the soil type and the geometry of the slab and base course. The method’s authors developed a series of curves from tests relating soil shear modulus, soil void ratios, shear wave velocity, soil grain type, slab dimensions, and base course thickness to spring rates (foundation modulus). The method allows consideration of confining pressure (the pressure from adjacent soils on the base material when it deforms under load), important in embedded track applications. The method provides results for vertical spring rates, horizontal spring rates, and rocking spring rates (the stiffness against slab twist about its longitudinal axis).
The Richart et al. data and methodology are implemented in this analysis for base support stiffness.
Results Available from Analysis
The results of the BOEF analysis are estimates of the rail and, separately, the slab deflections, moments, and shear force. The results also include pressures between rail, rail support (elastomer, Rail Boot, rail pad, Direct Fixation fastener), slab, and slab support (gravel or soil base).
The analysis uses these fundamental results to calculate rail and slab stresses and strains, which in turn are used for fatigue life estimates.
The analysis also provides other useful values such as slab safety factors and allowable stresses, and estimates of rail and slab natural frequencies, as design or evaluation aides.
The analysis provides structural results for reinforced slabs and non-reinforced slabs, and calculates slab reinforcement for crack control.
BOEF ANALYSIS RESULTS
This section presents results from the BOEF analysis.
These results illustrate trends in slab reactions (deflections, moments, and stress) and performance (fatigue life). This demonstration explores these results for the following parameter ranges:
•Slab configurations: full slab (Configuration 1) and base slab (Configuration 2)
•Rail support stiffness (elastic property of the rail pad, Rail Boot, or Direct Fixation fastener): 100,000 lb/in. to 3,000,000 lb/in.
•Slab thickness below the rail: 6 in. to 20 in.
For perspective, Rail Boot static stiffness is about 400,000 lb/in. Direct Fixation fasteners typically have a stiffness between 100,000 and 200,000 lb/in, and rail pads generally have stiffness values between 750,000 and 3,000,000 lb/in.
All other parameters in the model are held constant (see Table 1) to allow a direct comparison of results, although a number of parameters such as soils, temperature variants, curvature, and so on would be adjusted in practice for particular circumstances.
The loading and vehicle parameters are typical of a high-floor North American light rail vehicle (LRV). The trends in these results are also indicative of that expected for heavy rail vehicle loading, because the heavy rail vehicle weights and capacities are within 20% of those for LRVs, and heavy rail higher speeds are insufficiently different to effect these types of analysis.
All results are from calculations of both single axle and double axle loads, where the higher value from either is used when appropriate for each parameter explored. Double axle loads are those from two adjacent wheels representing a single truck.
Track Modulus and Support Stiffness
This is a brief aside to clarify the physical meaning of track modulus and support stiffness, and how those apply in this analysis. A support stiffness and its associated foundation modulus are directly related but different.
The physical measure of an elastomeric material is its stiffness, a simple spring rate obtained from a measured load deflection curve. The modeling uses a related, but different value called the foundation modulus to represent the idealized series of springs.
Also, where traditional BOEF calculations have a single track modulus, this analysis has two, which are more correctly called the rail foundation modulus (between the rail and slab) and slab foundation modulus (the material supporting the slab).
In this paper, the term support stiffness refers to spring rate unless specifically qualified.
Slab Life Expectancy
Life expectancy is the most useful indicator of embedded track slab performance because it intuitively provides a sense of track degradation processes that escape clear definition in other terms.
The life estimates are those earlier referenced Portland cement concrete methods that depict concrete (as well as other roadway materials) cracking, and loss of useful structural integrity. The life estimates presented here are the predicted life to slab replacement. The life estimates apply equally to reinforced and non-reinforced concrete.
Normal, Non-Special Trackwork, Track on Base Slab (Configuration 2)
Life expectancy is presented first in figure 5 for the most common embedded track configuration: normal track (any track outside special trackwork) installed on a base slab. This is Configuration 2 (see the section on Track Configurations and Conditions).
Recalling the description of Configuration 2, the material surrounding and between the rails is not considered as contributing to the structural support, consisting of asphalt, paver blocks or road crossing panels. In this configuration, the rail is supported by a rail pad, a direct fixation fastener, or is surrounded by the rail boot.
Also, where traditional BOEF calculations have a single track modulus, this analysis has two, which are more correctly called the rail foundation modulus (between the rail and slab) and slab foundation modulus (the material supporting the slab).
In this paper, the term support stiffness refers to spring rate unless specifically qualified.
Slab Life Expectancy
Life expectancy is the most useful indicator of embedded track slab performance because it intuitively provides a sense of track degradation processes that escape clear definition in other terms.
The life estimates are those earlier referenced Portland cement concrete methods that depict concrete (as well as other roadway materials) cracking, and loss of useful structural integrity. The life estimates presented here are the predicted life to slab replacement. The life estimates apply equally to reinforced and non-reinforced concrete.
Normal, Non-Special Trackwork, Track on Base Slab (Configuration 2)
Life expectancy is presented first in figure 5 for the most common embedded track configuration: normal track (any track outside special trackwork) installed on a base slab. This is Configuration 2 (see the section on Track Configurations and Conditions).
Recalling the description of Configuration 2, the material surrounding and between the rails is not considered as contributing to the structural support, consisting of asphalt, paver blocks or road crossing panels. In this configuration, the rail is supported by a rail pad, a direct fixation fastener, or is surrounded by the rail boot.
FIGURE 5 Life expectancy for normal embedded track on a base slab, only (Configuration 2).
Figure 5 assumes all wheels will produce a load that is 95% of the design wheel load.
The idea is that actual wheel load populations will be lower than the design wheel load, with only incidental occurrences near the design wheel load from derailments or severely flat wheels.
The 5% reduction in wheel load is very conservative, where the actual population of fatigue loads would be expected to distribute the static vehicle load (wheel load is 17,000 lb in this case, or less than half the design wheel load).
This reduced loading is applied to the fatigue calculation only. The structural calculations use the full design wheel load.
This and following charts are truncated at 35-year life expectancy, representing infinite slab life for practical purposes.
Figure 5 shows that life expectancy increases with the base slab thickness in normal (non-special trackwork) track.
Insights from Figure 5 include:
•Rail Support Stiffness between 200,000 lb/in. and 600,000 lb/in. improves life expectancy for slabs less than 16 in. thick, compared to softer or harder rail support stiffnesses.
•Embedded track with rail support stiffness of 1,000,000 lb/in. or greater require a minimum base slab thickness of 14 in. to have any life expectancy, and 16 in. thickness to achieve reasonable life expectancy.
The idea is that actual wheel load populations will be lower than the design wheel load, with only incidental occurrences near the design wheel load from derailments or severely flat wheels.
The 5% reduction in wheel load is very conservative, where the actual population of fatigue loads would be expected to distribute the static vehicle load (wheel load is 17,000 lb in this case, or less than half the design wheel load).
This reduced loading is applied to the fatigue calculation only. The structural calculations use the full design wheel load.
This and following charts are truncated at 35-year life expectancy, representing infinite slab life for practical purposes.
Figure 5 shows that life expectancy increases with the base slab thickness in normal (non-special trackwork) track.
Insights from Figure 5 include:
•Rail Support Stiffness between 200,000 lb/in. and 600,000 lb/in. improves life expectancy for slabs less than 16 in. thick, compared to softer or harder rail support stiffnesses.
•Embedded track with rail support stiffness of 1,000,000 lb/in. or greater require a minimum base slab thickness of 14 in. to have any life expectancy, and 16 in. thickness to achieve reasonable life expectancy.
Special Trackwork on Base Slab (Configuration 2)
The next example in Figure 6 is for special trackwork loading on a base slab (Configuration 2). The only difference between Figures 5 and 6 is that Figure 6 assumes all wheel loads are at the design wheel load, whereas Figure 5 assumes the wheel loads are 95% of the design wheel load. This assumption reflects a belief that special trackwork will eventually, if not initially, produce increased loads on the embedded track, and the increased loads will approximate a full impact load (double the static load).
Figure 6 shows that
•Thicker slabs are required under special trackwork for equal life expectancy of normal track with the same loading.
•The minimum base slab thickness under special trackwork should be 16 in. to achieve reasonable life expectancy.
•Rail support stiffness has little influence on life expectancy for turnout loads.
The next example in Figure 6 is for special trackwork loading on a base slab (Configuration 2). The only difference between Figures 5 and 6 is that Figure 6 assumes all wheel loads are at the design wheel load, whereas Figure 5 assumes the wheel loads are 95% of the design wheel load. This assumption reflects a belief that special trackwork will eventually, if not initially, produce increased loads on the embedded track, and the increased loads will approximate a full impact load (double the static load).
Figure 6 shows that
•Thicker slabs are required under special trackwork for equal life expectancy of normal track with the same loading.
•The minimum base slab thickness under special trackwork should be 16 in. to achieve reasonable life expectancy.
•Rail support stiffness has little influence on life expectancy for turnout loads.
Normal, Non-Special Trackwork, Track, Full Slab (Configuration 1)
The increased strength of a full slab is beneficial to life expectancy, as would be expected, with all but the thinnest slabs (6 in.) having infinite life for all rail support stiffness values.
Special Trackwork, Full Slab (Configuration 1)
Analysis results for special trackwork assumptions (full impact load) with a full slab indicate that the minimum slab thickness under the rail for a full slab should be at least 12 in. where the base slab requires a minimum of 16 in.
The increased strength of a full slab is beneficial to life expectancy, as would be expected, with all but the thinnest slabs (6 in.) having infinite life for all rail support stiffness values.
Special Trackwork, Full Slab (Configuration 1)
Analysis results for special trackwork assumptions (full impact load) with a full slab indicate that the minimum slab thickness under the rail for a full slab should be at least 12 in. where the base slab requires a minimum of 16 in.
FIGURE 6 Life expectancy for special trackwork on a base slab, only (Configuration 2).
Fatigue Life and Slab Structural Design
The fatigue analysis applies equally to reinforced and non-reinforced slabs, and is not influenced by structural details of reinforcement.
The fatigue calculation and slab design calculations both use the slab maximum stress from the BOEF analysis. This means that the analysis selects the maximum bending moment (from which stress is calculated) from single-axle loading or two-axle loading, whichever produces the higher stress.The fatigue life and the slab structural design are based on the same basic parameters, bending moment and stress, but are calculated independently.
This approach identifies those designs that meet required criteria (safety factors, etc.) but have an undesirable life expectancy. In the foregoing fatigue life presentation, the configurations that have unsatisfactory life expectancies meet required criteria.
The separate calculation of fatigue life and structural safety factor allow the possibility that an increased structural safety factor may not result in a commensurate extension in fatigue life.
The fatigue analysis applies equally to reinforced and non-reinforced slabs, and is not influenced by structural details of reinforcement.
The fatigue calculation and slab design calculations both use the slab maximum stress from the BOEF analysis. This means that the analysis selects the maximum bending moment (from which stress is calculated) from single-axle loading or two-axle loading, whichever produces the higher stress.The fatigue life and the slab structural design are based on the same basic parameters, bending moment and stress, but are calculated independently.
This approach identifies those designs that meet required criteria (safety factors, etc.) but have an undesirable life expectancy. In the foregoing fatigue life presentation, the configurations that have unsatisfactory life expectancies meet required criteria.
The separate calculation of fatigue life and structural safety factor allow the possibility that an increased structural safety factor may not result in a commensurate extension in fatigue life.
Deflections, Moments, Shear Force, and Pressures
This section discusses response to loading.
The analysis shows cases where the peak or maximum rail deflections from two axles are less than from one axle, even though two axles obviously have twice the load. The second axle cancels a portion of the rail and slab bending, thereby reducing the deflections produced by a single axle. The stress in the slab is similarly reduced. This effect can be significant, depending on parameter values, with a 10% to 15% decrease in two-axle deflections and stress from that of a single axle.
This effect is more pronounced as the rail support stiffness is reduced below 1,000,000 lb/in. In other words, as the rail support becomes softer, beneficial stress reduction from two axles is greater compared to single axle deflections. As the rail support stiffness increases above 1,000,000 lb/in., the two-axle response (rail deflections, slab stress) is greater than the single-axle response because the increased rigidity defeats rail bending over the interval between axles.
These findings raise the point that the design of slab tracks must consider both single-axle and multiple-axle loading.
Although infrequent, derailments most likely will commence as a single-axle event. More frequent, wheels traversing frog points and rail crossings approach the single-axle load condition. These conditions will govern the design in many cases.
However, multiple-axle loading may govern the design where, for example, the rail support stiffness is high.
Importantly, the designer should analyze both the single axle and multiple axle cases because the specific configurations and choices of parameter values may end with either case producing the larger response, which then becomes the governing case for design.
Pressures: Rail Support
One of the unique results of this modeling method is the ability to calculate the pressure of the rail on its support (rail pad, Rail Boot, etc.), of the rail support material on the slab, and of the slab on the material under the slab.
This information is very useful in the design of elastomers for the rail support and design of the subbase layer under the slab, usually an engineered selection of gravel base course and select soils.
Figure 7 shows pressures by the rail on the rail support (Rail Pad, Rail Boot, etc.) for a base slab, with two axle loading.
The pressure by the rail is negative for the stiffer rail supports. The negative values mean that the slab is deflecting more than the rail. The negative values mean the rail and slab are placing the rail support material in tension.
The magnitude of these negative pressures can exceed 900 psi at the stiffest (3,000,000 lb/in.) rail support. Under this condition, any fastener holding the rail to the slab will incur significant loading because these pressures are continuous along the rail and any fasteners are necessarily discrete devices that must accommodate the fully developed pressure each side of its location. For example, the load on a pair of anchor bolts (holding the rail to the slab) is over 25,000 lb, or 12,500 lb per anchor bolt, and where anchor bolt pairs are spaced at 24 in. Slab anchor inserts typically are designed for a maximum 12,000 lb pull-out load. While typical anchor bolt configurations could be altered, it is better to use a softer rail support to avoid this condition.
This section discusses response to loading.
The analysis shows cases where the peak or maximum rail deflections from two axles are less than from one axle, even though two axles obviously have twice the load. The second axle cancels a portion of the rail and slab bending, thereby reducing the deflections produced by a single axle. The stress in the slab is similarly reduced. This effect can be significant, depending on parameter values, with a 10% to 15% decrease in two-axle deflections and stress from that of a single axle.
This effect is more pronounced as the rail support stiffness is reduced below 1,000,000 lb/in. In other words, as the rail support becomes softer, beneficial stress reduction from two axles is greater compared to single axle deflections. As the rail support stiffness increases above 1,000,000 lb/in., the two-axle response (rail deflections, slab stress) is greater than the single-axle response because the increased rigidity defeats rail bending over the interval between axles.
These findings raise the point that the design of slab tracks must consider both single-axle and multiple-axle loading.
Although infrequent, derailments most likely will commence as a single-axle event. More frequent, wheels traversing frog points and rail crossings approach the single-axle load condition. These conditions will govern the design in many cases.
However, multiple-axle loading may govern the design where, for example, the rail support stiffness is high.
Importantly, the designer should analyze both the single axle and multiple axle cases because the specific configurations and choices of parameter values may end with either case producing the larger response, which then becomes the governing case for design.
Pressures: Rail Support
One of the unique results of this modeling method is the ability to calculate the pressure of the rail on its support (rail pad, Rail Boot, etc.), of the rail support material on the slab, and of the slab on the material under the slab.
This information is very useful in the design of elastomers for the rail support and design of the subbase layer under the slab, usually an engineered selection of gravel base course and select soils.
Figure 7 shows pressures by the rail on the rail support (Rail Pad, Rail Boot, etc.) for a base slab, with two axle loading.
The pressure by the rail is negative for the stiffer rail supports. The negative values mean that the slab is deflecting more than the rail. The negative values mean the rail and slab are placing the rail support material in tension.
The magnitude of these negative pressures can exceed 900 psi at the stiffest (3,000,000 lb/in.) rail support. Under this condition, any fastener holding the rail to the slab will incur significant loading because these pressures are continuous along the rail and any fasteners are necessarily discrete devices that must accommodate the fully developed pressure each side of its location. For example, the load on a pair of anchor bolts (holding the rail to the slab) is over 25,000 lb, or 12,500 lb per anchor bolt, and where anchor bolt pairs are spaced at 24 in. Slab anchor inserts typically are designed for a maximum 12,000 lb pull-out load. While typical anchor bolt configurations could be altered, it is better to use a softer rail support to avoid this condition.
Pressures: Slab Support
Slab pressures on the slab support material (gravel, soils, etc.) range from 5 to 10 psi (Figure 8), acceptable for most soil conditions. It should be kept in mind that embedded track is used most often in urban streets where there are numerous underground utilities. Utility activity over the life of the slab can include trenching beside and burrowing under the slab. This activity can cause uneven slab support if not properly back-filled. The slab must therefore have reserve structural capacity for bridging unknown future support conditions.
Slab Natural Frequency
While not a dynamic model, the information in the model allows calculation of undamped natural slab frequencies, useful for understanding qualitatively at least the relationship ground vibration created from train vibrations. The slab structure will filter train vibrations greater than the slab’s natural frequency, will amplify any vibrations near the slab’s natural frequency, and will transmit all train-induced energy that occurs below the slab’s natural frequency.
For a 9 ft wide slab, a full depth slab (Configuration 1) will have a natural frequency between 13 and 17 Hz, with little variation among slab thickness values. Base slab (Configuration 2) natural frequency varies from 30 Hz for 8 in. thick slabs to 17 Hz for 20 in. thick slabs.
Slab pressures on the slab support material (gravel, soils, etc.) range from 5 to 10 psi (Figure 8), acceptable for most soil conditions. It should be kept in mind that embedded track is used most often in urban streets where there are numerous underground utilities. Utility activity over the life of the slab can include trenching beside and burrowing under the slab. This activity can cause uneven slab support if not properly back-filled. The slab must therefore have reserve structural capacity for bridging unknown future support conditions.
Slab Natural Frequency
While not a dynamic model, the information in the model allows calculation of undamped natural slab frequencies, useful for understanding qualitatively at least the relationship ground vibration created from train vibrations. The slab structure will filter train vibrations greater than the slab’s natural frequency, will amplify any vibrations near the slab’s natural frequency, and will transmit all train-induced energy that occurs below the slab’s natural frequency.
For a 9 ft wide slab, a full depth slab (Configuration 1) will have a natural frequency between 13 and 17 Hz, with little variation among slab thickness values. Base slab (Configuration 2) natural frequency varies from 30 Hz for 8 in. thick slabs to 17 Hz for 20 in. thick slabs.
FIGURE 7 Rail pressure on rail support, base slab.
FIGURE 8 Full slab pressure on its support (gravel layer, prepared soil base).
Additional Notes on the Analysis
This subsection explains how the model treats the rail support elasticity.
In the foregoing presentation, we observed circumstances that had the rail deflecting less than the slab, meaning that the slab and rail were separating. We would have expected the rail and slab to move together, and, if anything, the rail deflect a little more into its support elastomer than the slab because the rail has more of the direct load and is a much more slender beam than the slab. This expectation is realized when rail support stiffness is 600,000 lb/in. or less.
When the elastomer stiffness approaches or exceeds 1,000,000 lb/in., the rail modulus becomes much greater than the slab support modulus, creating the circumstance for slab to deflect more than the rail.
In the latter circumstance, the rail is of course fastened to the slab or constrained by embedment concrete, thus the rail will deflect with the slab. However, this circumstance induces tensile load in rail fasteners or shear forces in constrain concrete that could cause degradation or failure.
Evidence that the rail support is too stiff would be sprung elastic rail clips, loose anchor bolts (either pulled out from concrete or loss of bolt torque), or concrete cracks (where rail is fully embedded in concrete) parallel to and within about 7 in. of the rail.
Effects of Rail Thermal Loading on Embedded Track
The analysis includes estimates of loads produced by thermal contraction and expansion of the rail.
In horizontal or vertical curves, Continuously Welded Rail thermal effects create radial loads on the rail support. The force in horizontal curves is determined by rail temperature difference from the rail neutral temperature and the curve radius. In vertical curves, the force is determined by the rail temperature difference, the change of grade through the curve and the length of the vertical curve.
This force is inversely proportional to the curve radius (i.e., the smaller the radius, the higher the force). The rail size has a lesser effect.
This force is a distributed force, meaning that the force is uniform along the length of a curve and is stated in pounds per unit rail length. Figure 9 shows thermally induced rail loads on vertical curves for the practical range of grade changes and curve lengths.
For even the most severe grade change and shortest curve length, the distributed loads are fairly low (under 140 lb/rail foot) compared to vehicle loads, assuming a 90oF rail temperature difference from the rail’s neutral temperature.
Figure 10 shows the lateral rail force in horizontal curves for the practical range of curvatures and temperature differences. The horizontal loads on slabs from rail thermal effects can become significant for curves with a radius of 200 ft and less. A track assessment would consider whether this effect along with other circumstances present (wheel loads, rail pre-curving) is within the rail restraint capacity.
This subsection explains how the model treats the rail support elasticity.
In the foregoing presentation, we observed circumstances that had the rail deflecting less than the slab, meaning that the slab and rail were separating. We would have expected the rail and slab to move together, and, if anything, the rail deflect a little more into its support elastomer than the slab because the rail has more of the direct load and is a much more slender beam than the slab. This expectation is realized when rail support stiffness is 600,000 lb/in. or less.
When the elastomer stiffness approaches or exceeds 1,000,000 lb/in., the rail modulus becomes much greater than the slab support modulus, creating the circumstance for slab to deflect more than the rail.
In the latter circumstance, the rail is of course fastened to the slab or constrained by embedment concrete, thus the rail will deflect with the slab. However, this circumstance induces tensile load in rail fasteners or shear forces in constrain concrete that could cause degradation or failure.
Evidence that the rail support is too stiff would be sprung elastic rail clips, loose anchor bolts (either pulled out from concrete or loss of bolt torque), or concrete cracks (where rail is fully embedded in concrete) parallel to and within about 7 in. of the rail.
Effects of Rail Thermal Loading on Embedded Track
The analysis includes estimates of loads produced by thermal contraction and expansion of the rail.
In horizontal or vertical curves, Continuously Welded Rail thermal effects create radial loads on the rail support. The force in horizontal curves is determined by rail temperature difference from the rail neutral temperature and the curve radius. In vertical curves, the force is determined by the rail temperature difference, the change of grade through the curve and the length of the vertical curve.
This force is inversely proportional to the curve radius (i.e., the smaller the radius, the higher the force). The rail size has a lesser effect.
This force is a distributed force, meaning that the force is uniform along the length of a curve and is stated in pounds per unit rail length. Figure 9 shows thermally induced rail loads on vertical curves for the practical range of grade changes and curve lengths.
For even the most severe grade change and shortest curve length, the distributed loads are fairly low (under 140 lb/rail foot) compared to vehicle loads, assuming a 90oF rail temperature difference from the rail’s neutral temperature.
Figure 10 shows the lateral rail force in horizontal curves for the practical range of curvatures and temperature differences. The horizontal loads on slabs from rail thermal effects can become significant for curves with a radius of 200 ft and less. A track assessment would consider whether this effect along with other circumstances present (wheel loads, rail pre-curving) is within the rail restraint capacity.
FIGURE 9 Vertical rail force on slabs in vertical curves from thermal effects.
FIGURE 10 Lateral rail force on slabs in horizontal curves from thermal effects.
SUMMARY
Analysis of embedded track using a multi-layer model provides insight on performance of embedded track. The model is a static, linear representation (compared to dynamic, non-linear representation) of elasticity within the track system of rail, rail support elastomer, slab, and ground support of the slab. The analysis method incorporates subordinate methods for estimating ground support for a practical range of conditions, for determining rail thermal effects on slab loading, for determining slab natural frequencies, and for estimating track life.
The method is demonstrated for a practical range of slab thickness and rail support elastomer values.
The summary of these results is:
•Rail support stiffness, the spring rate (not the track modulus) between rail and slab, generally has a significant effect on slab life and stresses.
•Rail support stiffness of 400,000 to 600,000 lb/in. is the ideal range for overall slab response and performance.
•High rail support stiffness (above 1,000,000 lb/in.) creates high slab stresses requiring thicker slabs.
•Typical slabs (those with simple base support and a non-structural fill between rail) should be at least 14 in. thick in normal track and 16 in. thick in turnouts to avoid fatigue deterioration. Full depth slabs (concrete to top of rail) may be 6 in. thick in normal track and 12 in. thick in turnouts for acceptable life expectancy within the ideal rail stiffness range (above).
•Rail deflections are less than slab deflections when rail support elastomer stiffness is greater than 1,000,000 lb/in. In these circumstances, the rail will place upward force on the concrete and any rail fasteners. The upward force can exceed current fastener allowable force, or damage embedment concrete, at the stiffest elastomer values.
•Rail deflections from a single axle are generally greater than deflections from two axles when the rail support stiffness is less than 1,000,000 lb/in. This means that slab evaluations should analyze both single axle and two axle loading cases.
•Maximum allowable slab tensile stress will be exceeded when slab thickness (base slabs only) is less than 12 in. and the rail support stiffness is 3,000,000 lb/in. or greater.
•Slab natural frequencies (important to ground vibration issues) are estimated.
•Slab pressure on its support (gravel, engineered soils) is between 5 psi for thicker slabs to 10 psi for the thinnest slabs.
•Rail upward or downward force from thermal effects in vertical curves on slabs is innocuous, attaining 140 lb per rail foot for a 90oF temperature above a neutral temperature, 150 foot curve length, and 10% grade change.
•Rail lateral force from thermal rail effects in horizontal curves may require additional lateral restraint for curves with radius 200 ft and less. The effect on rail restraints should be assessed in combination with other circumstances (wheel curving loads, lack of rail pre-curving).
Analysis of embedded track using a multi-layer model provides insight on performance of embedded track. The model is a static, linear representation (compared to dynamic, non-linear representation) of elasticity within the track system of rail, rail support elastomer, slab, and ground support of the slab. The analysis method incorporates subordinate methods for estimating ground support for a practical range of conditions, for determining rail thermal effects on slab loading, for determining slab natural frequencies, and for estimating track life.
The method is demonstrated for a practical range of slab thickness and rail support elastomer values.
The summary of these results is:
•Rail support stiffness, the spring rate (not the track modulus) between rail and slab, generally has a significant effect on slab life and stresses.
•Rail support stiffness of 400,000 to 600,000 lb/in. is the ideal range for overall slab response and performance.
•High rail support stiffness (above 1,000,000 lb/in.) creates high slab stresses requiring thicker slabs.
•Typical slabs (those with simple base support and a non-structural fill between rail) should be at least 14 in. thick in normal track and 16 in. thick in turnouts to avoid fatigue deterioration. Full depth slabs (concrete to top of rail) may be 6 in. thick in normal track and 12 in. thick in turnouts for acceptable life expectancy within the ideal rail stiffness range (above).
•Rail deflections are less than slab deflections when rail support elastomer stiffness is greater than 1,000,000 lb/in. In these circumstances, the rail will place upward force on the concrete and any rail fasteners. The upward force can exceed current fastener allowable force, or damage embedment concrete, at the stiffest elastomer values.
•Rail deflections from a single axle are generally greater than deflections from two axles when the rail support stiffness is less than 1,000,000 lb/in. This means that slab evaluations should analyze both single axle and two axle loading cases.
•Maximum allowable slab tensile stress will be exceeded when slab thickness (base slabs only) is less than 12 in. and the rail support stiffness is 3,000,000 lb/in. or greater.
•Slab natural frequencies (important to ground vibration issues) are estimated.
•Slab pressure on its support (gravel, engineered soils) is between 5 psi for thicker slabs to 10 psi for the thinnest slabs.
•Rail upward or downward force from thermal effects in vertical curves on slabs is innocuous, attaining 140 lb per rail foot for a 90oF temperature above a neutral temperature, 150 foot curve length, and 10% grade change.
•Rail lateral force from thermal rail effects in horizontal curves may require additional lateral restraint for curves with radius 200 ft and less. The effect on rail restraints should be assessed in combination with other circumstances (wheel curving loads, lack of rail pre-curving).
NOTES
1.Hetényi, M. Beams on Elastic Foundation. The University of Michigan Press, Scientific Series Volume XVI, copyright 1974, pp.179-185.
2.American Concrete Institute, Building CodeRequirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02). However, ACI 318 specifically excludes structural at-grade slabs from the scope of its Code. The analysis incorporates Design of Slabs on Grade (ACI 360R-92), reapproved 1997, partially addressing some track slab design issues. The interpretation of ACI 318 and ACI 360 that is most appropriate for track slab design, and implemented in this work, is in The Structurally Reinforced Slab-on-Grade, published by the Concrete Reinforcing Steel Institute in Engineering Data Report Number 33 (1989), and re-published by ACI in Practitioner’s Guide, Slabs on Ground, American Concrete Institute PP-4 (1998). The results reported are by the “rational method.” Four other structural design procedures are available in the calculations.
3.Packard, R. G., and S. D. Tayabji. New PCA Thickness Design Procedure for Concrete Highway and Street Pavements, Proc., Third International Conference on Concrete Pavement Design and Rehabilitation. Purdue University, 1985, pp. 225-236.; as implemented by Dr. Yang H. Huang, P.E., Finite Element Analysis of a Proposed Trackbed, prepared for Iron Horse Engineering Company, Inc., Feb. 19, 1991, p. 2.
Richart, F. E., Jr., J. R. Hall, Jr., and R. D. Woods. Vibrations of Soils and Foundations. Prentice Hall, 1970, pp. 350-353
REFERENCE
LAURENCE E. DANIELS. Transportation Research Circular E-C058: 9th National Light Rail Transit Conference. 2003,Portland, Oregon (USA).
1.Hetényi, M. Beams on Elastic Foundation. The University of Michigan Press, Scientific Series Volume XVI, copyright 1974, pp.179-185.
2.American Concrete Institute, Building CodeRequirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02). However, ACI 318 specifically excludes structural at-grade slabs from the scope of its Code. The analysis incorporates Design of Slabs on Grade (ACI 360R-92), reapproved 1997, partially addressing some track slab design issues. The interpretation of ACI 318 and ACI 360 that is most appropriate for track slab design, and implemented in this work, is in The Structurally Reinforced Slab-on-Grade, published by the Concrete Reinforcing Steel Institute in Engineering Data Report Number 33 (1989), and re-published by ACI in Practitioner’s Guide, Slabs on Ground, American Concrete Institute PP-4 (1998). The results reported are by the “rational method.” Four other structural design procedures are available in the calculations.
3.Packard, R. G., and S. D. Tayabji. New PCA Thickness Design Procedure for Concrete Highway and Street Pavements, Proc., Third International Conference on Concrete Pavement Design and Rehabilitation. Purdue University, 1985, pp. 225-236.; as implemented by Dr. Yang H. Huang, P.E., Finite Element Analysis of a Proposed Trackbed, prepared for Iron Horse Engineering Company, Inc., Feb. 19, 1991, p. 2.
Richart, F. E., Jr., J. R. Hall, Jr., and R. D. Woods. Vibrations of Soils and Foundations. Prentice Hall, 1970, pp. 350-353
REFERENCE
LAURENCE E. DANIELS. Transportation Research Circular E-C058: 9th National Light Rail Transit Conference. 2003,Portland, Oregon (USA).
Portland, Oregon. A convoy of Light Rail Vehicles is traveling along SW 6th Avenue.
Portland, Oregon. An convoy of Light Rail Vehicles is traveling along SW 6th Avenue, where the Hilton hotel is located and where the ninth National Light Rail Transit Conference took place.
