STRUCTURAL DESIGN OF RAILWAY TRACKBEDS RELATIVE EFFECTS OF VARIOUS FACTORS

Transcription

1 JRC docx D R A F T Proceedings of the ASME/ASCE/IEEE 2011 Joint Rail Conference JRC2011 March 16 18, 2011 Pueblo, Colorado, USA STRUCTURAL DESIGN OF RAILWAY TRACKBEDS RELATIVE EFFECTS OF VARIOUS FACTORS J.G. Rose University of Kentucky Lexington, KY USA JRC M.C. Trella, II University of Kentucky Lexington, KY USA ABSTRACT Layer-elastic, finite-element computer programs are available for performance-based structural design and analysis of railway trackbeds. This paper utilizes the KENTRACK design program. It is possible to consider the fatigue lives of the various layers relative to the imposed wheel loads, tonnages, environmental conditions and other factors. The service lives of the individual components of the trackbed are predicted by damage analysis for various combinations of traffic loadings, accumulated tonnages, subgrade support, and component layer properties and thicknesses. The results are presented graphically. The latest version, KENTRACK 3.0, is utilized. It is coded in C#.NET a popular computer language for achieving accuracy and efficiency. The graphical user interface in the KENTRACK 3.0 provides a technique to analyze trackbeds as structures. It is possible with KENTRACK 3.0 to select individual trackbed layers and associated thicknesses to satisfy roadbed and trackbed performance requirements. In addition, it is possible to performance-rank different track sectional designs based on the relative importance of the particular track section and track type. The types of roadbed and trackbed configurations are selected to meet each of the various performance ranks. INTRODUCTION Excessive deflections and subsequent permanent track settlements have considerable effects on the ultimate quality and geometric features of trackbeds. These must be controlled within reasonable limits. The design and construction of the trackbed support structure largely influences the long-term performance of the track relative to maintaining adequate 1 N. K. Agarwal University of Kentucky Lexington, KY USA geometric features for efficient and safe train operations. Performance-based design methods provide design criteria to assess the relative effects of various factors affecting longterm performance of different trackbed designs. It is possible for designers to select trackbed support layer thicknesses and constituent materials to satisfy roadbed performance requirements with a performance-based design method. Specifically, by considering each layer s fatigue life related to the number of load repetitions, axle loads, and tonnages, a method is available for designing thicknesses of various layers and selecting materials according to the importance of a particular section of track. Thus the predicted design life for various design criteria and failure modes can be determined. The properties and thicknesses of the various layers comprising the track structural support largely determine the quality of the trackbed substructure and its ability to adequately withstand the various loading intensities. Minimizing track deflections under loading and essentially eliminating subsequent permanent track settlements are desired attributes to be executed by an adequate design system. A primary influencing factor is the level of substructural support. Specifying specific design parameters and construction techniques for track on earthen structures are extremely important for controlling track settlement and dynamic deflection and the ultimate performance of the track. These factors largely influence the ultimate quality of the track. Performance based design methods provide design criteria to assess the relative effects of various factors affecting long-term performance of different track designs. These designs involve selecting layer thicknesses and

2 constituent materials possessing various properties inherent to influencing long-term quality performance of the track. KENTRACK KENTRACK is a computer program based on layer elastic finite element; this program was specifically developed for performance-based structural design and analysis of railway trackbeds. Kentrack was initially developed (Huang, et al., 1984) as a DOS Program to analyze traditional all-granular layered trackbeds and asphalt layered trackbeds. It was subsequently expanded to analyze trackbeds containing a combination of granular and asphalt layers (Rose, et al., 2010). The principle factor in the analysis is to limit vertical compressive stresses on the subgrade. In addition, it is possible to consider the fatigue lives of the various layers relative to the effects of wheel loads, tonnages, environmental conditions and other factors using appropriate failure criteria. The service lives of the individual components of the trackbed are predicted by damage analysis for various combinations of traffic, tonnages, subgrade support, component layer properties and thicknesses. The latest Windows version, KENTRACK 3.0, is coded in C#.NET, a popular computer language. The graphical user interface in the KENTRACK 3.0 provides a technique to analyze trackbeds as structures. The development of KENTRACK Version 3.0 is described in an Application Tutorial (Rose, et al., 2010) THEORY The basic theory, on which KENTRACK Version 3.0 is based, is described elsewhere (Rose, et al., 2010). The primary single failure criterion for the all-granular trackbed is the cumulative effects of the vertical compressive stresses on the subgrade leading to excessive permanent deformation. However, since an asphalt-bound layer can resist deformation as a function of its tensile strength, an additional failure criterion tensile strain at the bottom of the asphalt layer is included in the analysis of asphalt trackbeds to limit asphalt cracking. The subgrade vertical compressive stress failure criterion is also applicable for asphalt trackbeds. The loading configuration in KENTRACK uses the Superposition Principle and Track Symmetry for distributing the wheel loads over several ties (Huang, et al., 1984). The Damage Factors are calculated based on highway failure criteria used in the DAMA program ( Institute, 1982; Hwang & Witczak, 1979). This program is widely applied for the structural design and analysis of highway pavements. Additional aspects and discussion of the loading configuration and failure criteria analyses are presented in (Huang, et al., 1987), (Rose, et al., 2003), and (Rose and Konduri, 2006). The asphalt damage factors obtained from the highway developed DAMA program are believed to be more severe relative to railroad environments. Previous analyses have indicated that the asphalt layer in the insulated trackbed environment weathers at an extremely slow rate (Rose and Lees, 2008). Ultraviolet and oxygen-induced effects are minimized by the ballast cover. Also, temperature extremes in 2 the asphalt layer are minimized due to ballast cover (Rose, 2008). Thus, the predicted design lives for the asphalt trackbeds reported herein are likely very conservative. APPLICABILITY KENTRACK is applicable for analyzing three types of trackbed structures as depicted in Figure 1. The traditional All-Granular trackbed consists of four layers ballast, subballast, subgrade, and bedrock. The primary failure criterion is the vertical compressive stress on the subgrade. The Underlayment trackbed contains a layer of asphalt in place of the granular subballast in a traditional trackbed. It also has four layers ballast, asphalt, subgrade, and bedrock. trackbeds are being widely accepted and commonly considered as an alternate to the traditional allgranular trackbed. The asphalt layer is similar in composition to the asphalt mix used for highway pavements. Documented benefits are that the asphalt layer 1) strengthens trackbed support reducing subgrade stress, 2) waterproofs the roadbed to reduce subgrade moisture contents and fluctuations, and 3) provides a consistently high level of confinement for the ballast enhancing the shear strength of the ballast (Anderson and Rose, 2008), (Rose and Lees, 2008) (Rose and Bryson, 2009). The Combination trackbed contains five layers ballast, asphalt, subballast, subgrade, and bedrock. The subballast layer can be considered as an improved subgrade. This design is an alternate to the Underlayment trackbed and contains subballast between the asphalt layer and subgrade. DATA PORTRAYAL KENTRACK is applicable for calculating stresses and strains in the trackbed and associated design lives for a specific set of design parameters. In addition, selected parameters can be varied in magnitude and the relative influences evaluated. Data derived from the program is provided in Table 1 for the default thicknesses of the trackbed layers and loading conditions indicated in Figures 2 and 3 respectively. Traffic density is assigned 200,000 repetitions per year of a 286,000- lb car, or 28.6 MGT/year. This is utilized for the subgrade and asphalt life predictions. Each car is considered equivalent to one load application. modulus was varied from a weak 3000 psi (20.7 MPa) to a strong 30,000 psi (207 MPa). Also, an average subgrade modulus of 12,000 psi (83 MPa) and a moderately strong 21,000 psi (145 MPa) subgrade modulus were included. Standard design axle loads of 33 and 36 tons and the anticipated 39-ton axle load were selected for evaluations. Specific input parameters are contained in reference (Rose, et al., 2010) EFFECTS OF SUBGRADE AND LOADING VARIABLES Data contained in Table 1 and depicted in Figures 4 through 9 assesses the effects of two primary variables Modulus and Axle Loads for the three types of track designs. The three track designs and associated layer dimensions, shown in Figure 2, identify the X-sectional dimensions for the All-Granular,, and Combination track designs. The combined trackbed thickness of 14 in. (35

3 cm) for the ballast and subballast/ asphalt layers was selected for the All-Granular and designs. The Combination design utilizes the design plus a 4-in. (10 cm) thick subballast layer for a total trackbed thickness of 18 in. (46 cm). Effect of Varying Modulus Table 1 contains data showing the effects of varying Axle Loads and Modulus on the calculated Compressive Stresses and Tensile Strains, along with associated predicted design lives, for the All-Granular, and Combination Trackbeds. Stresses, depicted in Figure 4a for the 36-ton axle load, are relatively low, even for the All-Granular Trackbed, ranging from 8 to 20 psi (55 to 138 kpa). stresses are even lower for the Trackbed, an indication of the positive influence of the asphalt layer. The addition of the subballast layer in the Combination trackbed results in even lower stresses for a given subgrade modulus. All of the calculated stress values on the subgrade, from the weakest to strongest subgrade, are less than the stress (vertical pressure) exerted on a highway pavement by a passenger car typically 30 psi (207 kpa). This attests to the effective stress reducing capabilities of the rail/tie/ballast portion of the track section. In-track pressure (vertical compressive stress) measurements utilizing in-bedded pressure cells compare favorably with the KENTRACK calculated stresses (Rose, et al., 2004). Based on the output from the KENTRACK design, pressure levels within the track structure are quite low and only marginally affected by variable axle loads. Therefore, differential trackbed performance is likely a function of the quality of the support, defined as the stiffness modulus of the subgrade. Figure 4b indicates that the Tensile Strains at the bottom of the asphalt layer decrease as the subgrades become stiffer. This is expected since the asphalt layer deflects less over stiffer subgrades. The additional subballast layer in the Combination trackbed further reduces tensile strains. The asphalt tensile strain levels are very low in magnitude relative to highway pavement applications. This is likely due to the fact that the imposed loading stresses in the trackbed are very low as well. Also, previous studies have revealed that the asphalt layer in the insulated trackbed weathers, or hardens, at a very slow rate compared to highway pavement applications (Rose and Lees, 2008). Furthermore, the temperature extremes in the insulated trackbed environment are lessoned compared to exposed asphalt highway pavements. Figure 5a shows the effects of varying Modulus on the Predicted Design Life for the three types of trackbeds. Rail traffic is 28.6 MGT/year and a 36-ton axle load. As the subgrade stiffness increases the predicted subgrade design life increases significantly for all three trackbed designs. This occurs even though the subgrade stress increases as subgrade stiffness increases. The advantage of stiffer subgrades is readily apparent. The addition of the 3 asphalt layer results in a quantum increase in subgrade design life relative to the all-granular trackbed. Figure 5b shows the effects of vary Modulus on the Predicted Design Life for the three types of trackbeds. As the subgrade stiffness increases, the predicted asphalt design life increases significantly for both types of asphalt trackbed designs. The stiffer subgrades minimize the deflection of the asphalt layer and the resulting tensile strains, thus the increased design life expectancy prior to a crack in the asphalt layer. The positive effect of stiff subgrades relative to extending the design life of the asphalt layer is apparent. The importance of maintaining a stiff, high-modulus track support is readily apparent. Soft subgrades (support) require frequent surfacing to correct track settlement and deformation, as indicated by the low predicted design lives. Effect of Varying Axle Loads Figures 6a, 6b, and 6c show the effects of varying Axle Loads and Modulus on Compressive Stresses for the three types of trackbed designs. As indicated previously in Figure 4a, subgrade compressive stress increases as subgrade modulus increases for all three types of trackbeds. This is the case for 33 and 39-ton axle loads in addition to the previously detailed 36-ton axle load. Typically the increase in subgrade stress is 7 to 11 psi (48 to 76 kpa). Increasing axle loads from 33 to 39 tons slightly increase subgrade compressive stresses for a specific subgrade modulus. Typically the increase in subgrade stress is only 1 to 2 psi (7 to 14 kpa). Therefore, the effect of increasing axle loads results in minimal increases in subgrade compressive stresses for a given subgrade modulus and trackbed design. Figures 7a, 7b, and 7c show the effects of varying Axle Loads and Modulus on Design Lives for the three types of trackbed designs. These correspond to the subgrade compressive stresses indicated in Figures 6a, 6b, and 6c for the All-Granular, and Combinations trackbeds, respectively. The All-Granular trackbed subgrade Design Life predictions in Figure 7a indicate the extremely significant effect of variable subgrade modulus on Predicted Design Lives. Predicted subgrade design life is substantially increased as subgrade modulus increases. These trends are similar for the and Combination trackbeds. Also, increasing axle loads indicate reductions in subgrade life. In addition, the predicted subgrade design lives, for a given axle load and subgrade modulus, increase significantly for the trackbed (Figure 7b) and increase even more for the Combination trackbed (Figure 7c). Figures 8a and 8b show the effects of varying axle loads and subgrade modulus on Tensile Strain for the two types of asphalt trackbed designs. As indicated previously in Figure 4b, asphalt tensile strain decreases as subgrade modulus

4 increases for both types of asphalt trackbeds. This is the case for the 33 and 39-ton axle loads in addition to the previously detailed 36-ton axle load. Typically the decrease in asphalt tensile strain is Increasing axle loads from 33 to 39 tons slightly increase asphalt tensile strains for a specified subgrade modulus. Typically the increase in strain is only , therefore the effect of increasing axle loads results in minimal increases in asphalt tensile strains for a given subgrade modulus and trackbed design. Figures 9a and 9b show the effects of varying axle loads and subgrade modulus on Design Lives for the two types of asphalt trackbed designs. These correspond to the asphalt tensile strains indicated in Figures 8a and 8b for the and Combination trackbeds, respectively. The trackbed design life predictions in Figure 9a indicate the extremely significant effect of variable subgrade modulus on predicted design lives. Predicted asphalt design life is substantially increased as subgrade modulus increases. In addition, increasing axle loads indicate reductions in asphalt design life. These trends are similar for the and Combination trackbeds. In addition, the predicted asphalt design lives, for a given axle load and subgrade modulus, increase significantly for the Combination trackbed (Figure 9b) relative to the trackbed (Figure 9a). This personifies the structural advantage of the subballast layer in the Combination trackbed design. EFFECTS OF LAYER THICKNESS VARIABLES The thicknesses of the ballast and asphalt layers were varied to indicate the effects on calculated stresses/strains and predicted design lives. The data is presented in Tables 2, 3 and 4. Effect of Varying Ballast Thickness for All-Granular Trackbeds Figure 10a shows the Effect of Varying Ballast Thickness and Modulus on Compressive Stresses for All- Granular Trackbeds. The axle loading and subballast thickness are constant. Increasing ballast thickness from 4 to 12 in.(10 to 30 cm) decreases subgrade stress by about 20% for the lowest modulus subgrade. The effect is even more significant for the higher modulus subgrades. For the 30,000 psi (207 MPa) modulus subgrade, the reduction in subgrade stress is nearly 50% for a comparable ballast thickness increase. The stiffer subgrades provide the level of support necessary for the ballast to develop sufficiently high shear strength for proper dissipation of stresses. Thus the potential benefit of the ballast can be achieved. Figure 10b shows the Effects of Ballast Thickness and Modulus on the Predicted Design Life of the. For the 3000 psi (21 MPa) subgrade modulus, predicted subgrade lives are substantially less than one year, regardless of the ballast thickness, even though the imposed stresses are reasonably low in magnitude (Figure 10a). This 4 situation is personified in existing trackbeds when track sections overlying the weak subgrades must be raised and surfaced by maintenance forces multiple times during the year. However, for the stiffer subgrades, the Predicted Life is increased substantially, particularly for the stiffer subgrades. Effect of Varying Thickness for Trackbeds Figure 11a shows the Effect of Varying Thickness and Modulus on Compressive Stress for Trackbeds. The axle loading, 36 tons, and ballast thickness, 8 in. (20 cm), are constant. As the asphalt layer thickness increases, the subgrade stress decreases. Also, comparing subgrade stress values, with the 8-in. (20 cm) thick ballast section for the All-Granular trackbed, indicate further reduction in subgrade stresses. This personifies the added advantage of the incorporation of an asphalt layer within the track structure. Figure 11b shows the comparable Effects of Varying Thickness and Modulus on the Predicted Design Life of the. Increasing asphalt thickness from 3 to 9 in. (8 to 23 cm) typically increases predicted design life of the subgrade by 5 to 6 times. This is due to the reduced subgrade stresses as asphalt thickness increases, as noted in Figure 11a. Also, the effect of higher values of subgrade modulus to increase predicted subgrade life is very apparent, as was noted previously in Figures 5a and 7b. In addition, comparing the predicted subgrade design lives for the Trackbeds (Figure 11b) with those for the All-Granular Trackbeds (Figure 10b) indicates significant advantages of the Trackbed design. Figure 11c shows the Effect of Varying Thickness and Modulus on Tensile Strain for Trackbeds. As the asphalt layer thickness increases, the tensile strain decreases. Tensile strain reductions also occur as the subgrade modulus increases. These are typical findings from numerous highway research studies stiffer subgrade/base support reduces asphalt tensile strain levels. Figure 11d shows the comparable effects on Predicted Design Life. Thicker asphalt layers increase predicted design lives for the asphalt layer. For weak subgrades and thin asphalt layers, the predicted asphalt design life is greater than that of the subgrade. However, as the subgrade modulus increases and the asphalt layer thickness increases, the predicted subgrade life is greater than the predicted asphalt life. This is indicative of the ability of stiff subgrades to accommodate substantially more axle loads while sustaining less damage. Effect of Varying Ballast Thickness for Trackbeds Figure 12a shows the Effects of Varying Ballast Thickness and Modulus on Compressive Stress for Trackbeds. The axle loadings, 36 tons, and asphalt

5 thickness, 6 in. (15 cm), are constant. As the ballast thickness increases, the subgrade stress decreases. The values and trends are very similar to those in Figure 11a for Trackbeds as the asphalt thickness increases, for a constant ballast thickness, the subgrade stress decreases. Therefore, both ballast and asphalt serve to decrease imposed subgrade stresses for Trackbeds. Figure 12b shows the comparable Effects of Varying Ballast Thickness and Modulus on the Predicted Design Life of the. Increasing ballast thickness from 4 to 12 in. (10 to 30 cm) typically increases predicted design life of the subgrade by 5 to 7 times. This is due to the reduced subgrade stresses as ballast thickness increases, as noted in Figure 12a. Also, the effect of higher values of subgrade modulus to increase predicted subgrade life is very apparent as was noted previously in Figures 5a and 7b. Figure 12c shows the Effect of Varying Ballast Thickness and Modulus on Tensile Strain for Trackbeds. As the ballast thickness increases, the tensile strain decreases. Tensile strain reductions also occur as the subgrade modulus increases. Figure 12d shows the comparable Effects on Predicted Design Life. Thicker ballast sections increase predicted design lives for the asphalt layer. For the weaker subgrades and thinner ballast sections, the predicted asphalt design life is greater than that of the subgrade. The effect of increasing ballast thickness from 4 to 12 in. (10 to 30 cm), for a constant asphalt layer thickness of 6 in. (15 cm) (Figure 11), is similar to the effect of increasing asphalt thickness from 3 to 9 in. (8 to 23 cm), for a constant ballast thickness of 8 in. (20 cm) (Figure 12). Typical asphalt trackbed designs, currently in common use, specify asphalt layer thickness of about 6 in. (15 cm) and ballast thickness of 8 to 12 in. (20 to 30 cm). Closure The Effects of Specifically Varying and Ballast Thicknesses for Combination Trackbeds are not presented herein. However, it is obvious from Figures 4 and 5 that the addition of a 4-in. (10 cm) thick subballast layer below the asphalt layer thus the distinction Combination Trackbed provides additional subgrade stress and asphalt tensile strain reductions. Concurrently, predicted subgrade and asphalt design lives are increased. Most in-track (existing) asphalt trackbeds, which have been rehabilitated by replacing a portion of the trackbed support with asphalt, have an effective subballast layer composed of degraded ballast, sand, cinders, etc. Thus the trackbeds classify essentially as combination trackbeds. Most asphalt trackbed designs on new alignments/embankments specify that the upper portion of the subgrade be select material. The select material designation implies the layer is similar to a subballast layer. CONCLUDING COMMENTS The KENTRACK program was utilized to determine the effects of varying track parameters on track stress/strain indices and predicted design lives of the track components. Three types of trackbed designs were evaluated; All-Granular,, and Combination. Highway failure criteria were utilized for predicting the design lives for the subgrade and asphalt layers for a 28.6 MGT/yr traffic density. For a given type of trackbed, the effect of subgrade stiffness (modulus) is the most significant factor influencing the design. Although, for a given loading configuration, stiffer subgrades produce slightly higher subgrade stresses, the predicted design lives for the stiffer subgrades are increased by several orders of magnitude. tensile stresses, however, are lower for the stiffer subgrades and the design lives are increased proportionally. Increasing axle loadings result in increased subgrade stresses and reduced predicted subgrade life for all three types of trackbeds. tensile strains are marginally increased and the predicted asphalt lives are marginally reduced. The effects of the higher axle loads can be offset by increasing the effective stiffness (modulus) of the subgrade. An trackbed results in lower subgrade stress than a similar thickness of All-Granular trackbed. This is more pronounced when subballast is added to the trackbed, known as a Combination trackbed. Predicted subgrade design lives are higher for both the and Combination trackbeds as compared to the All-Granular for a given level of subgrade support and axle loading. The results indicate that selecting and maintaining a stiff, high modulus subgrade is extremely important. This can be obtained by selecting subgrade materials commensurate with achieving desired performance. Preventing water from accessing and saturating the subgrade in concert with maintaining adequate drainage will greatly assist in assuring high-quality support is provided for the ballast and track. This will provide trackbeds that will promote long-term stability and maintenance of desired track geometric parameters. ACKNOWLEDGEMENTS Several graduate students have been involved with further development and updating of the program since the initial development. Those involved during the interim include Charles Khoury, Bradley Long, Bei Su, Frank Twehues, Kumar Peddu, Karthik Konduri, Shweta Padubidri, Juntin Brown and Neeharika Ilavaia. REFERENCES Anderson, J.S. and J.G. Rose, (2008). In-Situ Test Measurement Techniques Within Railway Track Structures, 2008 ASME/IEEE/ASCE Joint Rail Conference Proceedings, Wilmington, DE, 21 pages. 5

6 Institute (1982). Research and Development of The Institute s Thickness Design Manual (MS-1) Ninth Edition, Research Report 82-2, 150 pages. Hwang, D. and Witczak, M. (1978). Program DAMA (Chevron) User s Manual, Department of Civil Engineering, University of Maryland, September, pp Huang, Y.H., Lin, C., Deng, X. and Rose, J. (1984). KENTRACK, A Computer Program for Hot-Mix and Conventional Ballast Railway Trackbeds, Institute (Publication RR-84-1) and National Pavement Association (Publication QIP-105), 164 pages. Huang, Y.H., Rose, J. and Khoury, C. (1987). Thickness Design for Hot-Mix Railroad Trackbeds, Paving Technology 1987 AAPT, Vol. 56,pp Rose, J. (2008). Test Measurements and Performance Evaluations of In-Service Railway Trackbeds, Proceedings of the Transportation Systems 2008 Workshop, Phoenix, 17 pages. Rose, J., Agarwal, N., Brown, J., and N. Ilavaia, (2010). Kentrack, A Performance-Based Layered Elastic Railway Trackbed Structural Design and Analysis Procedure A Tutorial, ASME, IEEE, ASCE, AREMA, & TRB 2010 Joint Rail Conference. Paper JRC , Urbana, IL, 38 pages. Rose, J.G. and L.S. Bryson. (2009). Optimally Designed Hot Mix Railway Trackbeds Test Measurements, Trackbed Materials, Performance Evaluations, and Significant Implications, 2009 International Conference on Perpetual Pavements, Ohio Research Institute for Trans. and Envir., Columbus, 19 pages. Rose, J. and Konduri, K. (2006). KENTRACK A Railway Trackbed Structural Design Program, Proceedings of the 2006 AREMA Annual Conference, 31 pages. Rose, J. and Lees, H. (2008). Long-Term Assessment of Trackbed Component Materials Properties and Performance, Proceedings of the 2008 AREMA Conference, 28 pages. Rose, J., Su, Bei, and Long, W. (2003). KENTRACK: A Railway Trackbed Structural Design and Analysis Program, Proceedings of the 2003 AREMA Annual Conference, 25 pages. Rose, J., Su, Bei, and Twehues, F. (2004). Comparisons of Railroad Track and Substructure Computer Model Predictive Stress Values and In-situ Stress Measurements, Proceedings of the 2004 AREMA Annual Conference, 17 pages. Table 1. Effect of Varying Axle Load and Modulus on Trackbed Stresses, Strains, and Predicted Design Lives Axle Load (ton) Trackbeds All-Granular Trackbed Trackbed Combination Trackbed Modulus (psi) Layer 3 Compressive Stress (psi) Layer 3 Predicted Life (years) Layer 2 Tensile Strain Layer 3 Compressive Stress (psi) 6 Layer 2 Predicted Life (years) Layer 3 Predicted Life (years) Layer 2 Tensile Strain Layer 4 Compressive Stress (psi) Layer 2 Predicted Life (years) Layer 4 Predicted Life (years) Note: Compressive Stresses and Tensile Strains are Calculated. and Lives are Predicted based on Highway Design Failure Criteria. and Life Predictions based on 28.6 MGT/year. Subballast thickness for All-Granular and Combination Trackbeds is 4 in. 10 psi = 69 kpa, 1000 psi = 6.9 MPa.

7 Table 2. Effect of Varying Ballast Thickness and Modulus on Compressive Stress and Predicted Design Life for All-Granular Trackbeds. Ballast Thickness (in.) Modulus (psi) Layer 3 Compressive Stress (psi) Note: Compressive Stresses are Calculated. Lives are Predicted based on Highway Design Failure Criteria. Life Predictions are based on 28.6 MGT/year. Subballast Thickness is 4 in. Axle Load is 36 tons. 1 in. = 2.54 cm, 10 psi = 69 kpa, 1000 psi 6.9 MPa. Layer 3 Predicted Life (years) Table 3. Effect of Varying Thickness and Modulus on Compressive Stress and Tensile Strain and Predicted and Design Lives for Trackbeds Thickness (in.) Modulus (psi) Layer 3 Compressive Stress (psi) Layer 3 Predicted Life (years) Note: Compressive Stresses and Tensile Strains are Calculated. and Lives are Predicted based on Highway Design Failure Criteria. and Life Predictions based on 28.6 MGT/year. Ballast Thickness is 8 in. Axle Load is 36 tons. 1 in. = 2.54 cm, 10 psi = 69 kpa, 1000 psi = 6.9 MPa. Layer 2 Tensile Strain Layer 2 Predicted Life (years)

8 Table 4. Effect of Varying Ballast Thickness and Modulus on Compressive Stress and Tensile Strain and Predicted and Design Lives for Trackbeds Ballast Thickness (in.) Modulus (psi) Layer 3 Compressive Stress (psi) Layer 3 Predicted Life (years) Note: Compressive Stresses and Tensile Strains are Calculated. and Lives are Predicted based on Highway Design Failure Criteria. and Life Predictions based on 28.6 MGT/year. Thickness is 6 in. Axle Load is 36 tons. 1 in. = 2.54 cm, 10 psi = 69 kpa, 1000 psi = 6.9 MPa. Layer 2 Tensile Strain Layer 2 Predicted Life (years) All-Granular Combination Figure 1. Three Types of Ballasted Trackbed Structures Applicable for KENTRACK. 8

9 Traffic = 28.6 MGT/year All Granular Traffic = 28.6 MGT/year Traffic = 28.6 MGT/year Combination Figure 2. Default Thicknesses for the Trackbed Layers and Loading Conditions. (1 in. = 2.54 cm) Wheel load For one car the total weight The number of repetitions assumed per year The traffic per year = 36,000 lb/wheel = 36,000 lb/wheel x 8 = 286,000 lb/rep = 143 ton/rep = 200,000 rep/yr = 200,000 rep/yr x 143 ton/rep = 28,600,000 GT/yr = 28.6 MGT/yr Figure 3. Million Gross Tons Per Year Calculation. 9

10 Figure 4a. Effect of Modulus on Compressive Stress. Figure 4b. Effect of Modulus on Tensile Strain. 10

11 Figure 5a. Effect of Modulus on Design Life. Figure 5b Effect of Modulus on Design Life. 11

12 Figure 6a. Effect of Axle Load on Compressive Stress in All-Granular Trackbed. Figure 6b. Effect of Axle Load on Compressive Stress in Trackbed. Figure 6c. Effect of Axle Load on Compressive Stress in Combination Trackbed. 12

13 Figure 7a. Effect of Axle Load on Design Life in All-Granular Trackbed. Figure 7b. Effect of Axle Load on Design Life in Trackbed. Figure 7c. Effect of Axle Load on Design Life in Combination Trackbed 13

14 Figure 8a. Effect of Axle Load on Tensile Strain in Trackbed. Figure 8b. Effect of Axle Load on Tensile Strain in Combination Trackbed. 14

15 Figure 9a. Effect of Axle Load on Design Life of Layer in Trackbed. Figure 9b. Effect of Axle Load on Design Life of Layer in Combination Trackbed. 15

16 Figure 10a. Effect of Ballast Thickness and Modulus on Compressive Stress for All-Granular Trackbed. Figure 10b. Effect of Ballast Thickness and Modulus on Design Life for All-Granular Trackbed. 16

17 Figure 11a. Effect of Thickness and Modulus on Compressive Stress for Trackbed. Figure 11b. Effect of Thickness and Modulus on Design Life for Trackbed. 17

18 Figure 11c. Effect of Thickness and Modulus on Tensile Strain for Trackbed. Figure 11d. Effect of Thickness and Modulus on Design Life for Trackbed. 18

19 Figure 12a. Effect of Ballast Thickness and Modulus on Compressive Stress for Trackbed. Figure 12b. Effect of Ballast Thickness and Modulus on Design Life for Trackbed. 19

20 Figure 12c. Effect of Ballast Thickness and Modulus on Tensile Strain for Trackbed. Figure 12d. Effect of Ballast Thickness and Modulus on Design Life for Trackbed. 20