© U.S. Department of Transportation Federal Railroad Administration PB B5- 1 5930 9 Correlation of Concrete Tie Track Performance in Revenue Service and at the Facility for Accelerated Service Testing Sp™n? archand Volume II Predictions And Washington, dc 20590 Evaluations of Track Settlement DOT/FRA/ORD-84/02.2 August 1984 Final Report This document is available to the U.S. public through the National Technical Information Service, Springfield, Virginia 22161 NOTICE This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for the contents or use thereof. NOTICE The United States Government does not endorse products or manufacturers. Trade or manufacturer's names appear herein solely because they are considered essential to the object of this report. Technical Report Documentation Page 1. Report No. FRA/ORD-82/44.2 2. Gennwrnt Accession No. 3. Recipient's Catalog No. 4. Title and Subtitle Correlation of Concrete Tie Track Performance in Revenue Service and at the Facility for Accelerated Service Testing - Volume II 5. Report Date August 1984 6. Perforating Organi lotion Cod* 7. Author's) Harry E. Stewart and Ernest T. Selig 8. Par forming Organization Report No. 9. Performing Organi lotion Name and Address Department of Civil Engineering University of Massachusetts Amherst, .Massachusetts 01003 10. Work Un.. No. (TRAIS) II. Contract or Giant No. R-4146(7187)-090 1 2. Sponsoring Agency Name and Addras* U.S. Department of Transportation Federal Railroad Administration Washington, D.C. 20590 '3. Typo of Report and Period Covered Final Report *4. Sponsoring Agency Code RRD-10 is. supplement.,. Not.. This is Volume II of the Final Report of the Concrete Tie Cor- relation Study. This study was conducted under subcontract from Battelle- Columbus Laboratories and the Federal Railroad Administration. 16. Abstract Predictions and evaluations of settlement were made for revenue and the Facility for Accelerated Service Testing (FAST) track, both containing concrete and wood tie sections. The ballast physical states were investiga- ted by field tests done before and after track maintenance. Borings were also taken to identify the subgrade conditions. The stress-dependent elas- tic and inelastic ballast behaviors were derived from repeated load triaxial tests and a ballast box device. Triaxial tests were also performed on the subgrade soils. A computer model, GEOTRACK, was used to estimate the stresses and defor- mations in the track foundations. In addition, revenue site track modulus values predicted with GEOTRACK were compared to measured values. Predictions of track settlement were then made based upon the laboratory test results and stresses estimated using the computer model. The predicted values were com- pared to field measurements obtained using ballast instrumentation and survey- ing from benchmarks. The predicted settlements were of the same order as the measured values, however, some differences in trends were observed. A discus- sion of the factors that were not included in the methodology is presented, along with the implications of these factors on track performance. 17. K«y words Ballast, computer model, eye lie properties, elastic deformation, FAST, permanent deformation, subgrade track structures, track performance, track loading, concrete ties. IS. Distribution Statement This document is avail- able to the public through the Nation al Technical Information Service, Springfield, VA. 22161. 19. Security C Us sit. (of this report) Unclassified 20. Security CI es si I. (of this page) Unclassified 21. No. or Poges 22. Pr For- DOT F 1700.7 (S-72> Reproduction of completed page authorized Digitized by the Internet Archive in 2012 with funding from University of Illinois Urbana-Champaign http://archive.org/details/correlationofcon84022stew PREFACE The research described in this report was done at the University of Mas- sachusetts under subcontract R-4146(7187)-090 from Battelle-Columbus Labora- tories (BCL) . This work represents a portion of the concrete tie correlation study sponsored by the U.S. Department of Transportation, Federal Railroad Ad- ministration, conducted under BCL contract no. DOT-FR-8164. Program Manager for this study was Howard G. Moody of the Federal Railroad Administration. Project Engineer for the prime contract and responsible for the Battelle portions of the work was Harold D. Harrison of Battelle-Columbus Laboratories. The University of Massachusetts research was conducted under the direc- tion of Ernest T. Selig, Professor of Civil Engineering, and Principal Inves- tigator. Donald R. McMahon served as Research Engineer for the field investi- gations and organized a large portion of the initial laboratory investiga- tions. Graduate students at the University of Massachusetts participated in this research. Harry E. Stewart focused on the prediction methodology which formed the basis for his doctoral dissertation. Ronald F. Bukoski assisted in the field tests and performed the laboratory studies on the subgrade. Deh C. Ho assisted with the computer analyses. Gillian M. Norman was responsible for the ballast box development and experiments, with assistance from Donna M. Feng. Thomas J. Siller participated in the field investigations and conducted the property tests on the ballasts from the field sites. Additional assis- tance with the field investigations was provided by Ching L. Kuo, Michael C. McVay and Robert S. Grout. The measurements of dynamic wheel loads and vertical track modulus were made by Battelle-Columbus Laboratories. Battelle also performed the optical survey measurements of vertical track settlement. Administrative assistance and schedule coordination at the University of Massachusetts throughout the contract period were the responsibility of Kris- tin J. Currier. Ms. Currier was also responsible for the preparation of the final report manuscript. Drafting of figures was done by Thomas E. Sikora. The following railroad personnel assisted with coordinating the field work: Mr. Dan Jerman from Amtrak, Mr. Bruce Dunseth from the Chessie System, and Mr. Steve Heath from the Atchison, Topeka and Santa Fe. TABLE OF CONTENTS Chapter Page 1. EXECUTIVE SUMMARY 9 2. INTRODUCTION 12 3. SITE DESCRIPTION 14 3.1 General Background 14 3.2 Track Structure 14 3.3 Ballast Materials and Physical States 14 3.4 Ballast Resilient Behavior 17 General Concepts 17 Staged Testing 20 Shear Stress Reversal Testing 23 Resilient Modulus Formulation 32 Resilient Modulus Validation 39 3.5 Ballast Inelastic Behavior 39 Introduction 39 Constant-Amplitude Tests 43 Variable-Amplitude Tests 45 Shear Stress Reversal Tests 45 3.6 Ballast Box Tests 56 General Description 56 Permanent Settlement 56 Horizontal Stresses 58 3.7 Subgrade Material Sampling Program Repeated-Load Testing for Revenue Sites Repeated-Load Testing for FAST Subgrade Selection of Wheel Loads 64 64 64 64 4. TRACK MODULUS 68 4.1 Introduction 68 4.2 Selection of Parameters 68 4.3 Comparison with Field Measurements "9 5. TRACK LOADING 82 5.1 Introduction °2 5.2 Measured Wheel Loads 82 5.3 Load Distribution Methodology °3 83 Number of Load Applications "5 Multiple-Axle Loadings OD TABLE OF CONTENTS (completed) Chapter Page 6. METHODOLOGY FOR DEFORMATION PREDICTIONS 90 6.1 Stress Path Determination 90 6.2 Strain Determination 92 First Cycle Strains 92 Strain Accumulation Rates 92 Superposition of Strains 94 6.3 Deformation Determination 96 7. PERMANENT DEFORMATION EVALUATION 97 7.1 Introduction 97 7.2 Field Measurements 97 Revenue Sites 97 FAST Measurements 99 7.3 Predictions of Track Settlement 105 General Considerations 105 R.evenue Site Predictions 108 FAST Predictions 108 7.4 Discussion 114 Stress Path Considerations 114 Track Vibrations ' 118 Other Factors 118 Ballast Recompaction 118 Ballast Degradation 119 Subgrade Effects 120 8. SUMMARY AND CONCLUSIONS 122 REFERENCES 127 LIST OF TABLES Table Page 1. FAST Track Section Conditions 15 2. Track Structural Properties for All Sites 3. Initial Test Conditions for Ballast Staged and Stress Reversal Tests 11. Regression Results for Compression and Extension Resilient Strains 12. Resilient Moduli for Granite Ballast 13. Resilient Moduli for Field Site Ballasts 14. Permanent Strain for First Stress Path Loading from Staged Tests 20. Number of Cycles per MGT at Prescribed Dynamic Wheel Loads for Ballast and Subgrade 16 22 4. Stress Levels for Staged Tests 24 5. Order of Applied Stress Paths for Staged Tests 25 6. Average Resilient Moduli and Strains for Staged Tests 26 7. Regression Equations for E as a Function of 6 29 8. Test Conditions for Stress Reversal Cyclic Tests 31 9. Measured Resilient Moduli from Stress Reversal Tests 10. Resilient Strains for Staged Tests and Stress Reversal Tests 34 36 40 41 44 15. Ballast Constants, C, for use in e = e (1 + C log N) 46 16. Measured and Predicted Vertical Track Modulus 75 17. Mean Static and Dynamic Wheel Loads 84 18. Relative Frequency of Occurrence Assigned to Dynamic Wheel Loads 84 19. Number of Cycles per MGT for Ballast and Subgrade 87 87 21. Uncorrected Vertical Track Settlement Measurements from BCL Survey 98 22. Parameters for Stress Path CB Predictions 1° 6 23. Parameters for Stress Path DE Predictions 107 24. Comparison of GEOTRACK and Box Test Stress Paths 116 LIST OF FIGURES Figure Page 1. Representation of Stress-Strain Curve from a Triaxial Sample Under Repeated Load 19 2. FAST Wyoming Granite Gradation 21 3. Resilient Modulus versus Maximum Bulk Stress from Staged Tests 27 4. Arithmetic Relationship of E as a Function of 28 r 5. Shear Stress versus Resilient Strain for Compression and Extension 35 6. Resilient Strain Contours for Full Unloading 38 7. Measured and Predicted Moduli for All Ballasts 42 8. Measured versus Calculated Permanent Strains from Triaxial Tests 47 9. Permanent Strain versus Number of Cycles for Staged Tests, 3 psi Confining Pressure 48 10. Permanent Strain versus Number of Cycles for Staged Tests, 6 psi Confining Pressure 49 11. Permanent Strain versus Number of Cycles for Staged Tests, 12 psi Confining Pressure 50 12. Representation of Stress-Strain Curves for Shear Stress Reversal 52 13. Comparison of Strain Development Rates for Tests With and Without Stress Reversal 53 14. Rate of Strain Accumulation as a Function of Stress Parameters 55 15. Box Test Apparatus 57 16. Horizontal Stresses on Side Panels [31] 59 17. Horizontal Stresses on End Panel [31] 61 18. Measured Horizontal Stress Distribution from Ballast Box Experiments [31] 62 19. Variation of K as a Function of Depth from Box Experiments 63 20. Resilient Modulus versus Depth for Leeds Wood and Concrete Tie Sections 65 21. Resilient Modulus versus Depth for Lorraine and Aberdeen 66 22. Layer Description for Leeds Wood Tie Section 70 23. Layer Description for Leeds Concrete Tie Section 71 24. Layer Description for Lorraine 72 25. Layer Description for Aberdeen 73 26. Measured and Predicted Track Moduli for Revenue Field Sites, 6- to 30-kip Load Range 76 LIST OF FIGURES Figure Page 27. Ballast Depth versus Track Modulus for Revenue Field Sites 77 28. Measured versus Predicted Differential Rail Deflections for 6- to 30-kip Load Range 80 29. Equivalent Track Loading for Wood and Concrete Tie Sections 89 30. Equivalent Stress Paths for Roadbed Points 91 31. Normalized First Cycle Strains as a Function of Stress Ratios 93 32. Method Used for Ballast Strain Calculations for Mixed Loading 95 33. Initial Track Deformations for Aberdeen 100 34. Ballast and Subgrade Deformations from Instrumentation at FAST Section 22 after 1979 Rebuild 102 35. Measured Ballast Deformations from FAST Instrumented Sections 103 36. Measured Subgrade Deformations from FAST Instrumented Sections 104 37. Measurements and Predictions of Track Settlement for Leeds Wood Tie Section 109 38. Measurements and Predictions of Track Settlement for Leeds Concrete Tie Section 110 39. Measurements and Predictions of Track Settlement for Lorraine 111 40. Measurements and Predictions of Track Settlement for Aberdeen 112 41. Measurements and Predictions of Track Settlement for FAST Section 22 After Rebuild 113 42. Comparison of Box Test and GEOTRACK Stress Paths 117 CHAPTER 1. EXECUTIVE SUMMARY The objective of this part of the FAST/revenue service correlation study was the development and application of the methodology for prediction of the geotechnical aspects of track performance. Track performance is defined in terms of vertical track settlement. The following field sites were evalua- ted: 1) in-service revenue track having concrete crossties at Streator (Leeds), Illinois, Richmond (Lorraine), Virginia, and Aberdeen, Maryland, 2) a revenue wood tie track section at Streator (Leeds), Illinois, and 3) wood and concrete tie sections at the Department of Transportation Facility for Accele- rated Service Testing (FAST) test track in Pueblo, Colorado. The Streator site is owned by the Atchison, Topeka and Santa Fe Railroad. The Richmond section is owned by the Chessie System. The Aberdeen test section is owned by Amtrak. A variety of field tests were conducted at these sites to assess the physical states of the ballast materials as they existed prior to a track maintenance (raising and tamping) operation. The ballast physical states were identified using the plate load test, ballast density test, and lateral tie push test. These physical state tests were repeated after the surfacing operation to determine the changes in the ballast physical properties caused by the maintenance. One of the primary effects of track maintenance was a loosening and disturbance of the traffic-compacted and stabilized ballast layer, both in the cribs and under the ties. The physical states of the bal- last found immediately after the maintenance were approximately independent of ballast type and initial condition. Ballast materials were recovered from the sites and subjected to repeated load triaxial testing to investigate the elastic and inelastic behavior. A granite ballast from FAST was also tested in a variety of repeated load condi- tions, including a mix of load levels. The elastic behavior was defined in terms of the resilient modulus. The resilient moduli values from extension tests were smaller than the moduli values from compression tests under similar stress conditions. When the ver- tical stresses were cycled between extension and compression states, the total resilient moduli fell between the individual extension and compressive values. The resilient behavior of the field site ballasts was not significantly depen- dent upon ballast type. The inelastic behavior of the ballast was found to be dependent upon the first cycle strain, Z. , and a material constant, C. This constant was inde- pendent of stress conditions for a particular ballast, but was not the same for all ballasts. The total permanent or inelastic strain developed in a ballast sample with a mix of loads was controlled by the maximum past load and was independent of the loading sequence. Subsequent applications of re- duced load as well as partial unloadings resulted in negligible increases in permanent strain. This means that the largest dynamic wheel loads cause most of the track settlement. A strain superposition method was developed to ac- count for the deformations that result from repeated applications of the mixed loading conditions present at the field sites. The inelastic behavior of ballast was also investigated using a box-type testing device, intended to simulate field behavior. The trends in ballast deformation from these box tests were similar to those observed from the tri- axial tests. The box tests also showed that relatively large horizontal 9 residual stresses can develop in the ballast, both in the crib and under the ties, as a result of cyclic loadings. Measurements of vertical track modulus at the revenue sites did not indi- cate that significant changes in the magnitude of track modulus occurred due to the maintenance. The major factors contributing to the magnitude of track modulus were ballast depth and subgrade stiffness. Also, the field measure- ments of track modulus showed that the uniformity of track support was not improved as a result of the surfacings. Among the important differences between the sites was the train loading imposed on the track systems. The dynamic wheel loads at each site were measured by BCL to characterize the mixed loading conditions. The static wheel load distributions for each site were obtained from consist data. Al- though the average static and dynamic wheel loads were about equal for a par- ticular site, the static wheel load distributions for the revenue sites were quite different from the dynamic distributions. One out of one thousand (0.1 percent exceedance level) dynamic wheel loads at Aberdeen was measured at 75 kips. At the 0.1 percent exceedance level at Leeds, Lorraine, and FAST, the dynamic wheel loads were about 46 kips. These very high dynamic loads at Aberdeen were a result of a combined effect of wheel tread irregularities and the high speeds of passenger trains. The loading environment at FAST was much more uniform than at the revenue sites, because of the controlled nature of the FAST experiments. The average static and dynamic wheel loads at FAST, however, were about 1.5 to 2 times larger than the average values measured at the reve- nue sites. Survey measurements were made at each of the field sites by BCL to deter- mine cumulative vertical track settlements. The survey data from Aberdeen and FAST were supplemented by inductance coil strain gauges embedded in the bal- last layer. The strain gauge instrumentation of the ballast layers lead to the conclusion that the zone of ballast disturbed by the maintenance operation was the primary source of track settlement, and that over the relatively short experimental time period, the subgrade contributions to track deformation could be neglected for these sites. The settlements at the Lorraine and Aberdeen sites continued to develop at what appeared to be a steady rate throughout the period of the measure- ments, after the initial traffic following maintenance. Although the total vertical settlements at all of the revenue sites continued to increase as tonnage accumulated, the roughness of the track profiles did not increase. The ballast deformations at FAST were found to be similar for both wood and concrete tie sections. This was true for the ballast measurements obtain- ed during the initial FAST experiments and for the ballast deformations fol- lowing the 1979 rebuild. A three-dimensional, nonlinear, elastic, multilayer model, GEOTRACK, was used to predict track deflections and track moduli for the revenue sites. The model predictions of vertical track deflection agreed well with field meas- urements, although the model tended to underestimate the field values. The methodology to predict the inelastic or permanent settlement of the field track sections used GEOTRACK nonlinear stress analyses of the field site track sections with stress-dependent ballast properties, representative sub- grade moduli, and multiple-axle combinations of the measured dynamic wheel loads. The predicted stresses from the computer analyses for each particular field site and loading condition were used, along with the permanent deforma- tion behavior of the ballasts from laboratory tests to estimate the resulting ballast strains. 10 The general magnitudes of the predicted deformations agreed with the measured values. The shapes of the deformation versus million gross tons predicted results did not agree as well. The predicted rate of deformation accumulation for the revenue sites was less than the survey measurements indicated, particularly for the Aberdeen and Lorraine sites. The settlement predictions made for FAST Section 22 agreed best with the field measurements. This was probably a result of the more controlled track loading and test conditions present at FAST. Uncertainties in both the first cycle strains and the representative stress paths could account for some of the differences between measured and predicted settlements. Deviations between measured and predicted track set- tlements could have resulted from other factors not considered in the method- ology. One of the most important factors not included is thought to be set- tlement induced by vibrations transmitted through the track superstructure to the ballast. Other factors that can have varying degrees of influence on track settlement and performance include ballast degradation, environmental effects and subgrade responses. Although these last three factors did not appear significant for the monitoring periods at the field sites investiga- ted during this study, they could be significant at other sites. 11 CHAPTER 2. INTRODUCTION In order to improve current track design methods and quantify track main- tenance life, research is necessary to understand the behavior of the track foundation under dynamic traffic loading. The repetitive loading and unload- ing of track structures due to the passage of train traffic causes settlement in the supporting ballast and subgrade. As the traffic history accumulates, these deformations continue to increase until the track has deteriorated to a state at which it can no longer perform at a desired service level. At this point, the track is surfaced (raised and tamped) to reestablish the necessary profile, and the deformation process starts again. The forcus of this report is on the prediction of track performance at four field sites. Track performance is assessed in terms of vertical track settlement and the factors that contribute to settlement. The sites consist of concrete tie revenue service track at Leeds, near Streator, Illinois; Lor- raine, near Richmond, Virginia; a site south of Aberdeen, Maryland; and wood tie track at Leeds. Wood and concrete tie track at FAST is included for com- parison. Differences in track structural characteristics and track foundation among the sites were identified, A variety of field tests were conducted to assess the physical states of the ballast materials as they existed prior to track maintenance. These physical state tests were repeated after a surfac- ing operation to determine the changes in the ballast properties that occur- red due to track maintenance. To complete the site characterization, stan- dard penetration and Dutch cone penetration tests were used to investigate the subgrade support characteristics of the revenue sites. These tests were done using a drill rig specially equipped with rail wheels so that the borings could be taken directly under the track structure. The results of these sub- surface explorations were used to help identify variations in strength and composition of the foundation layers over the depths influenced by train load- ings. Moisture changes in the top of subgrade were also monitored and corre- lated with weather conditions. A summary evaluation of these test results has been given in a companion Volume I [1]* to this report. The results of these tests will be explained further where necessary to support conclusions made within this report. Among the important differences between the revenue sites are the train loadings imposed on the track systems. To determine these, the dynamic wheel load distributions were measured by the prime contractor, Battelle-Columbus Laboratories (BCL) , for representative traffic at each of the sites. Since each site was subjected to a significant range of wheel loads rather than constant repetition of the same magnitude loading, a method was developed that can be used to account for the real mix of wheel loads. The ballast and subgrade soils from each of the field sites were tested to determine both the resilient and inelastic behavior of these materials under representative loading conditions. Both cyclic and repeated load tri- axial tests were used to determine the resilient modulus of the ballast ma- terial under full unloading, partial unloading, and shear stress reversal conditions. Undisturbed subgrade samples were also subjected to repeated load tests under anticipated field stress conditions to determine the ^Numbers in brackets [ ] denote references. 12 resilient modulus. The final estimates of the elastic properties of the track substructure were based on the results of the physical state, triaxial, standard penetration and cone penetration tests. The development of an analytical model that incorporates the fundamental track structural components and foundation characteristics is a necessary tool for assessing track performance. The model used in this study, GEOTRACK, is a three-dimensional, nonlinear, elastic, multi-layer track analysis program that emphasizes the geotechnical aspects of track. The GEOTRACK model is con- ceptually similar to the MULTA model developed by BCL, as explained in Ref . [40]. Measurements of vertical track modulus were taken before and after main- tenance at the field sites by BCL during the initial site visits. The track structural and foundation properties determined for the field sites were used with the GEOTRACK model to predict values of track modulus. The comparisons between measured and predicted elastic track moduli served as an additional validation of the model's elastic capabilities. The prediction of the vertical track settlement at each of the field sites was based upon inelastic behavior of the foundation soils, as measured in the laboratory under representative loading conditions. The inelastic be- havior of the foundation soils has been investigated using repeated load tri- axial tests and a ballast box device developed for this program for simulating field conditions. A method was developed that can be used to account for the deformations that occur from repeated applications of the mixed loading condi- tions present at the field sites. Predicted values of track settlement were then compared with the track settlements measured at the field sites. These field measurements were obtained using inductance coils that measure ballast strain and optical surveying from benchmarks. The report will conclude with a discussion of the various factors that have not been accounted for in the deformation prediction model, and the im- plications of these factors on track performance. 13 CHAPTER 3. SITE DESCRIPTIONS 3.1 General Background Four revenue service track locations and the experimental FAST track in Pueblo, Colorado were selected as test areas for this research project. The revenue service sites included three locations that contained concrete cross ties and a control section having wood cross ties. The wood tie control sec- tion and one concrete tie section are located at Leeds near Streator, Illi- nois, in the north-central section of the state. The remaining two concrete tie test sections are located at Aberdeen, Maryland and Lorraine near Richmond, Virginia. A more detailed description of each of these four sites was given in Refs. [1,2,3,4,5]. The FAST track contained both wood and concrete tie test sections. The FAST track sections 17, 18 and 19 were instrumented in 1976, when the track was originally constructed, in order to monitor track foundation defor- mations and stresses. The track conditions for these sections are given in Table la. The measurements made in these track sections are used in portions of the correlation study. Part of the FAST track was reconstructed after 400 million gross tons (MGT) traffic had accumulated over the original track at the site. The gene- ral rebuild procedure for these test sections consisted of: a) Undercutting the existing track. b) Removal of the existing track structure. c) Subgrade preparation, including grading and compaction where necessary. d) Building new skeletonized track on the subgrade. e) Dumping and tamping ballast and raising the track. f) Regulating the ballast, followed by surfacing and lining operations. Further details regarding the rebuild procedures can be found in Ref . [6]. Data for certain ballast physical state tests were available from the re- built sections 3 and 22. The track conditions for these sections are given in Table lb. The concrete ties used in section 22 were the RT7-SS2 type. 3.2 Track Structure The track structure for railroads has several mechanical components, the most obvious of which are the cross ties and rails. Rails are generally fas- tened to the wood ties using the conventional tie plate and cut spike system. Rails are attached to the concrete ties using a spring-type clip fastener sys- tem. Tie pads support the rail on concrete ties, and electrical insulators separate the steel rail from the steel rail clips. Table 2 lists the main track structural parameters for FAST and the revenue service test sections. Some of the structural characteristics which differ among the test sections are: a) tie type and dimensions, b) tie spacing, c) tie weight, d) rail sec- tion, e) rail fastener, and f) pad type. 3.3 Ballast Materials and Physical States A description of the ballast materials, along with the results of the 14 Table 1. FAST Track Section Conditions a) Original Track Tie Track Track Ballast Ballast Tie Spacing Section Geometry Type Depth (in.) Type (in.) 17C Curved Granite 15 Concrete 24.0 17E Tangent Granite 15 Concrete 24.0 18A Tangent Granite 21 Wood 19.5 18B Tangent Granite 15 Wood 19.5 20B Tangent Limestone 15 Wood 19.5 20G Tangent Trap rock 15 Wood 19.5 b) Reconstructed Track 3 Curved Granite* 20 Wood 19.5 17ABCDE Curved Granite 16 Concrete 24.0 22A Tangent Traprock 15 Wood 19.5 22B Tangent Traprock 15 Concrete 24.0 *Several types of granite were used, 15 CU 3 a •H 3 u u o ►J vf o CN m O O 3 rH NO !-H vO >* • O r-« m vO • • O 1 CM m rH • r^ CO CN CM 00 u CN CJ CN o 21 CN CM CN en TJ u rH rH rH rH CN 3 CO Oh CN o CN m m O s vO m rH CO • o r^ CN VO • • O vO co >. m vO Pd • • o 1 4J a) -d- <■ rH • r^ cn NO vO CN u CN •H M CN CN o 21 CN cn cn % M-l S-\ a •H O >-l • /^ .3 (H vO ^>» •H vO >> 4J rH cu 3 • •u ^■^ •H O £> 4-J O H CO 4-1 •H 3 •3 -Q 4-1 H rH CO rH X cu •w ■H ■H rH CO s^ r-l M 6 ■^-^ s s_^ X 3 00 X 3 CU • CO 00 00 O 4-J 3 3 3 3 u 3 .3 6 4-1 3 CN •H JB •H CN cu cu •H cO •H 4-) O X •H 3 4-1 00 "3 3 4-J 4-1 P* cu O 00 ■U 00 T3 •H O •H 3 •H CO CO M B CO 3 4-1 •H 3 1 CU CU cu 1 3 3 3 a cu o CU CU X> CO & PQ JO Pu fe Q. H CO rJ ea 2 CO rH rH s«/ rH rH rH v> rH rH X) CU cu CU cu CU CU rH •H •H •H M •H •H rH •H •H •H •H •H •H w cO 3 3 W 3 3 >—/ H H H H H H ed Od Pd a: Pd 16 ballast physical state tests was presented in Ref. [1]. A summary of the re- sults and conclusions will be presented here where relevant to the prediction methodology. The physical state tests used to characterize the ballast materials were ballast density, plate load, and lateral tie push. These tests were done be- fore and after the track was raised and tamped so that quantitative assess- ments of the change in ballast physical state could be made. The ballast density tests were done in the cribs and under the ties as close to the rail seat as possible. The plate load tests were done at similar locations. The lateral tie push tests were done on single ties located away from the density and plate load test areas. The ballast density test procedure has been described in Refs. [7 and 8]. The test results showed that the maintenance operation decreased the relative compaction of the ballast under the ties by 10-12% at the sites where a large raise was applied. Large raises of 1-1/2 to 2 in. were given to the Lorraine and Leeds wood tie section. The pre- and post-maintenance ballast densities were the same at the Aberdeen site, where the raise was only about 0.1 in. Plate load tests on the ballasts were done before and after maintenance at selected locations in the cribs and under the ties. Descriptions of the plate load test procedures and apparatus can be found in Refs. [8,9,10], The test results showed that the largest plate bearing resistances were under the ties near the rail seat areas. The pre-maintenance values were greatest at the Lorraine site, possibly because of the high degree of fouling and the greatest accumulation of tonnage since previous maintenance. The post-maintenance values of plate bearing index were very similar for all of the sites, with the exception of Aberdeen. The Aberdeen site showed the smallest change in plate bearing index at the under-tie location as a re- sult of the small raise. The largest decrease in plate bearing index due to maintenance was also at the Lorraine site. This site had the largest raise, about 2 in. , which would significantly disturb the ballast structure, particu- larly when the ballast is fouled. This was consistent with the observation that the Lorraine site also showed the largest decrease in relative compaction at the under-tie location. For all of the sites where significant trackbed disturbance under the ties resulted from raising and tamping, the plate load tests showed no significant difference in ballast stiffness, independent of ballast type. Values of the plate bearing index were also measured under the center of the tie. Again, the Lorraine site had the highest average value before the maintenance. The Aberdeen values at this location showed no change resulting from maintenance, but do show that the values under the center of the ties prior to maintenance were only 1/3 of the value measured under the tie at the rail seat. The plate load tests for all of the revenue sites showed that the ballast stiffnesses were always greater under the tie at the rail seat than under the tie center prior to maintenance. After the maintenance operations, the ballast stiffnesses under the tie were about the same at both locations, although still slightly greater near the rail seat areas. 3.4 Ballast Resilient Behavior General Concepts The behavior of a granular material under repeated loading conditions has generally been recognized as being nonlinearly stress-dependent, and very dif- ferent from the behavior of the same soil under monotonic loading conditions. 17 This type of behavior is shown in Fig. 1. During the primary loading of a granular soil such as ballast, the strain develops rapidly and is only par- tially recovered upon unloading. Each additional cycle contributes another increment of plastic or permanent strain. The magnitude of the increment generally decreases with the number of cycles. The difference between the maximum strain under peak load and the permanent strain after unloading for each cycle is the resilient or recoverable strain. The resilient modulus of materials is defined as the repeated deviator stress divided by the recovera- ble strain. The amount of resilient recoverable strain generally decreases with number of cycles. Research has shown that under moderate levels of repeated load, the re- silient strains become approximately constant after some number of cycles, and the material behaves elastically. Kalcheff and Hicks [11] have indicated that only a few hundred cycles are necessary for this stabilization to occur. However, Brown [12] and Morgan [13] have shown that several thousand load repetitions are necessary to reach constant values of resilient modulus. The magnitude of the resilient modulus is very much stress-state depen- dent. Several studies [14,15,16] have shown that the resilient response of unbound granular materials greatly increases as the confining pressure in- creases and is affected to a much smaller extent by the magnitude of repeated deviator stress. This has led to the conclusion that the resilient modulus can be related to the bulk stress state using the relationship _ K 2 E r = KjB , (1) where E = resilient modulus, r K.. ,K~ = soil constants determined from laboratory test results, and = bulk stress or the first invariant of stress. The bulk effective stress is defined by 6 " °1 + °2 + °3 = O + 20 for triaxial compression tests, where O , , O = major, intermediate and minor effective principal stresses, 1 ^ -* respectively. This formulation has been widely used [17,18,19] to characterize the resilient modulus of granular materials. The bulk stress formulation (Eq. 1) has been preferred for ballast mater- ial by Robnett, et al. [20] and Knutson [21]. Alva-Hurtado [22] has investi- gated the resilient response of a granite railroad ballast and determined that an arithmetic relationship was equally valid when relating bulk stress to resilient modulus. The relationship developed by Alva-Hurtado also showed that the initial compaction state affected the resilient modulus. Although it has been shown that granular materials exhibit high values of resilient modulus even when the applied deviator stress level is near fail- ure [23], the use of bulk stress cannot allow any distinction to be made be- tween the effects of deviator stress or cell pressure. Various combinations 18 Iff I CO CO UJ ac co cr o > UJ Q 0;= CONSTANT PRIMARY LOADING RESILIENT ^ MODULUS <^ INITIAL PLASTIC STRAIN ADDITIONAL PLASTIC STRAIN AXIAL STRAIN RESILIENT STRAIN Figure 1. Representation of Stress-Strain Curve from a Triaxial Sample Under Repeated Load 19 of cell pressure and deviator stress are assumed to achieve the same bulk, stress, i.e., low cell pressure - high deviator stress or high cell pressure - low deviator stress or medium cell pressure - medium deviator stress combina- tions, all can result in the same bulk stress. Staged Testing In order to study the resilient behavior of railroad ballast under more general loading conditions that would include partial unloading and shear stress reversal, two triaxial test series were performed. The first series of triaxial tests did not involve shear stress reversal so the major principal stress was always the vertical stress. These tests were called staged tests, since a sample was subjected to several stress paths involving full and par- tial unloadings and various combinations of maximum and minimum positive shear stress. Previous research by Hicks [14] and Allen [24] has indicated that one specimen can be used to measure the resilient response of granular materials over a range of stress levels, and that the sequence of applied stresses did not significantly affect the measured resilient response. The ballast material used for both test series was the Wyoming granite originally used at FAST in sections 17 and 18. This material was chosen for several reasons. The static compression stress-strain behavior was well docu- mented [22,25], data and bulk stress formulations for the resilient response had been generated by other researchers [17,22], and reproduceable sample preparation and compaction procedures had been established. The gradation curve for the granite ballast is shown in Fig. 2. This ballast can be classified as an AREA Number 5 material. The specification ranges for the AREA Number 5 ballast are shown in Fig. 2. All of the staged cyclic tests were done on compacted samples of ballast. The rubber-tipped impact hammer compaction method developed by Yoo, et al. [7] was chosen to prepare the laboratory triaxial samples. The method con- sisted of placing layers of ballast into a specially designed split compaction mold that was clamped together and placed around the triaxial cell base pedes- tal. The layer was then subjected to twenty blows from the rubber- tipped im- pact hammer. This compactive effort resulted in reproduceable density states. After each sample was compacted in the mold, the sample was aligned with the triaxial system loading piston and the mold was removed. A small vacuum was applied to the inside of the sample prior to removal of the mold in order to give the sample enough strength so that it would not collapse during fur- ther test preparation. The ballast was tested dry to provide for more rapid sample preparation and ease of testing. The effective isotropic consolida- tion pressures were achieved by increasing the vacuum applied to the inside of the sample, eliminating the need for an exterior fluid pressure surrounding the triaxial sample cylinder. The specific initial test conditions, sample dimensions, and dry densi- ties for the staged tests are given in Table 3, along with the results from tests involving shear stress reversal. As can be seen from the results given in Table 3, the compaction procedures gave reproduceable densities. The average dry density was 100.3 pounds per cubic foot (pcf) and had a coefficient of variation of only 0.7%. The average initial void ratio, e o , was 0.66. As previously stated, the purpose of the staged cyclic tests was to investigate the relationship between the applied stress level and resilient modulus for both full unloading and partial unloading. Full unloading for these tests will result from complete removal of any applied deviator stress, O -O . Partial unloading will result from cycling between two levels of devia- tor stress without allowing complete unloading. 20 100 o 40 < UJ o UJ CL o CO • o z I AREA No. 5 SPECIFICATIONS- FAST WYOMING GRANITE _ 1 1 i n PARTICLE DIAMETER (mm.) Figure 2. FAST Wyoming Granite Gradation 21 en cu H cO CO u cu > cu 0) en cu 4-1 Crt c cd T3 CU 60 CO 4-1 w -u) CO CO CO o en c o •H 4-1 •H T3 C3 o a en cu H CO •H 4-i c cu rH CO H >- a oomoo^ovo^vo^ONininmcoiri^o vO O VO vO vO vO vO ^O vO vO vO vO vO vO ^O ooooooooooooooo ^o m s vo »o »t vO vO vjO **0 vO *•© o o o o o o mi 13 cu !-i Q fONHN^O^HNHHHC^i^^ OCTiOOrHOOCTirHOOOOOO OOvOOOOOOnOOOCTiOO U CU 4-1 CO s 4-1 o 4J CN XI • 00 e •H •H CU rH 00 4J • •H r*. C LO i-^ 00 CNJ vD o O H II II o O a\ o O O rH 1-4. H H rH CO CU H (0 rH CO •H 4-1 CN IG en ex ooooooooooooooo COvOvOvOvOOvOCOCOcnflCNCNCNCN o o o o o o \D CT. CN CN CN in a T3 T3 T3 T3 -d T3 T3 TJ T3 T3 TJ -a T) T3 TJ o CU CU cu CO cu 4-1 4-1 4-1 4-1 4-1 4-1 4J 4J 4-1 4-1 4-1 4-1 4-1 4-1 O CJ CJ U CJ CJ a CJ a CJ a a o a O ■H CO CO CO CO CO CO to CO co CO CO CO CO CO CO TJ Cu a a CU a. a cu cu cu Cu cu cu a CU a c s s e B B a s E B B S S e E B o o o o o o o O o o o o o O o u CJ CJ o cj cj o CJ CJ o o CJ cj CJ CJ CJ -a tj TJ TJ TJ TJ cu a- u- rHcNcn CO u •H <4-l •H ■H O CU Cu o> en • ll •H 4-1 .H ■H (fl d •H •H 4-1 •H CU C 00 •H CO u II OJ > C < cu 22 Confining pressures of 3, 6 and 12 psi were selected for these staged tests. For each confining pressure, four levels of applied shear stress (q) were used. The various combinations of cell pressure, maximum shear stress, and minimum shear stress used for the test stress paths are given in Table 4. Table 4 also gives the maximum bulk stress, G, for each test, along with the stress ratio, q /q f > where q is the static compressive strength of the bal- last for a given effective cell pressure. Four individual staged tests were done at each confining stress. In each test, the order of stress application was varied to investigate any changes in resilient modulus that might result from variations in stress sequence. Per- manent deformation characteristics for each stress level and sequence were also analyzed. These results will be discussed in another section. The order of applied stress paths for each of the tests is given in Table 5. Each stress path was repeated for 1000 cycles of loading and unload- ing and the recoverable strain between the maximum and minimum applied shear stress was measured. The recoverable strains during cycling along any of the stress paths tended to decrease as the number of cycles increased, but had generally reached an equilibrium value after about 500 cycles of the stress path had been applied. The resilient modulus, E , resulting from any of the stress paths was calculated by dividing the resilient strain into twice the cyclic shear stress, Aq, according to e =^a , (2) re r where Aq = difference between maximum and minimum applied shear stress, and £ = resilient strain, r The averaged results of the resilient moduli for each of the individual stress paths are given in Table 6, along with the corresponding average resi- lient strains. The resilient moduli values given in Table 6 are plotted against the maximum bulk stress for each stress path in Fig. 3. There is no distinct relationship between bulk stress and resilient modulus evident when moduli values measured from partial unloading stress paths are included. A check was also made to see if the data fit the common log-log f ormulation. Again, there was good correlation between log of E and log of 9 if only the results from fully unloaded stress paths were used. Figure 4 shows the comparison between resilient moduli values obtained by Alva-Hurtado [22] and those obtained in this study. The arithmetic regres- sion equations for these two sets of data are given in Table 7a. Although both sets of moduli measurements were made on the same granite material at the same density state, the results obtained by Alva-Hurtado are higher than those obtained in this study. The reason for this is not known, but it could be from differences in detailed test conditions or from changes in ballast grada- tion and angularity caused by repeated use of the same material. However, the slopes of the two E vs curves shown in Fig. 4 are the same. The coeffi- cients for the log-log regression equations for the resilient moduli- bulk stress formulation from these sets of data are also given in Table 7b for comparison. Shear Stress Reversal Testing The resilient behavior of ballast under one-way repeated loading in which the full deviator stress was removed was shown to be related to the maximum bulk stress on the material. Partial unloading resilient moduli are not 23 Table 4. Stress Levels for Staged Tests Stress 3c o 1 q Aq e Max nnax Min Max Min Max Path (psi) (psi) 3.00 (psi) 6.12 (psi) 0.00 (psi) 1.56 (psi) 1.56 (psi) 12.12 q f OA 3.00 0.150 OB 3.00 9.26 0.00 3.13 3.13 15.26 0.301 OC 3.00 12.38 0.00 4.69 4.69 18.38 0.451 OD 3.00 15.51 0.00 6.26 6.26 21.51 0.602 AB 6.12 9.26 1.56 3.13 1.56 15.26 0.301 AC 6.12 12.38 1.56 4.69 3.13 18.38 0.451 AD 6.12 15.51 1.56 6.26 4.69 21.51 0.602 BC 9.26 12.38 3.13 4.69 1.56 18.38 0.451 BD 9.26 15.51 3.13 6.26 3.13 21.51 0.602 CD 12.38 15.51 4.69 6.26 1.56 21.51 0.602 O'a' 6.00 6.00 12.00 0.00 3.00 3.00 24.00 0.150 B 6.00 18.00 0.00 6.00 6.00 30.00 0.301 O'c' 6.00 24.00 0.00 9.00 9.00 36.00 0.451 O'D' 6.00 30.00 0.00 12.00 12.00 42.00 0.602 A"B' 12.00 18.00 3.00 6.00 3.00 30.00 0.301 A'c' 12.00 24.00 3.00 9.00 6.00 36.00 0.451 A D 12.00 30.00 3.00 12.00 9.00 42.00 0.602 B C 18.00 24.00 6.00 9.00 3.00 36.00 0.451 B D 18.00 30.00 6.00 12.00 6.00 42.00 0.602 C'D' 24.00 30.00 9.00 12.00 3.00 42.00 0.602 0"A" 12.00 12.00 18.00 0.00 3.00 3.00 42.00 0.084 0~B~ 12.00 24.00 0.00 6.00 6.00 48.00 0.168 0~C~ 12.00 30.00 0.00 9.00 9.00 54.00 0.252 0~D" 12.00 36.00 0.00 12.00 12.00 60.00 0.335 A^B" 18.00 24.00 3.00 6.00 3.00 48.00 0.168 k"or* 18.00 30.00 3.00 9.00 6.00 54.00 0.252 a"d" 18.00 36.00 3.00 12.00 9.00 60.00 0.335 z"c" 24.00 30.00 6.00 9.00 3.00 54.00 0.252 B~D~ 24.00 36.00 6.00 12.00 6.00 60.00 0.335 C"D" 30.00 36.00 9.00 12.00 3.00 60.00 0.335 24 m I en o CN pq cj \ \ PQ \ \ < \ \ CJ \ \ < \ \ \ \ \ \ CJ Q Q \ \ \ \ \ \ « « CJ ^ \ \ \ \ < v \ O Q U \ \ \ \ I o CN \ \ \ \ \ < \ \ pq \ r \ \ \ \ O <1 u o y-i en Xi u CO PL. CO CD CU U U C/3 -O cu •H iH a < o u CU M O m iH CO H ro I CN I CO cu £ 3 55 CO CU H -a cu oo| CO CO on I to l CO I CO I en 00 I C/i \ \ r \ \ \ \ \ \ \ \ \ r \ o \ \ r \ \ r \ \ \ \ \ \ \ \ PQ a a < pq CJ a CJ O Q Q CJ pq < CM \ r \ \ \ r \ \ \ r \ \ t \ i-H \ \ \ \ \ \ \ \ \ \ \ ^ \ \ O O o o < < < pq pq CJ O O O c \ \ \ \ \ \ \ \ ^ \ ^ \ \ \ O \ \ \ \ \ \ ^ \ \ \ \ \ \ \ • < pq CJ Q PQ CJ Q CJ Q Q O pq < c CN \ \ \ \ \ \ \ \ \ \ \ ^ \ \ iH \ \ \ \ r \ \ \ \ \ \ \ \ \ o O O CJ pq r O < < pq pq pq cj CJ CJ pq CJ a CJ O \ \ \ \ \ \ o II — o O O ■ * \m •H CO O- ■■ N_S r< o o / 00 \ J* / a \/ •H T3 cd O o "~ rH g 3 rH 03 r-l •H •H 1-4 3 4J r- • •H CO 14-1 Cfl CO a o O < CU o •H M • o iH CM X CO Cd 3 s rH 3 4J c CU •H o rH ^-K CO CU Ptf ro QJ o 3 00 •rH (fs^) a «snxnpow nua-piT-satf 27 o © o U-l es o iH § •H 4J O § O fa O r4 /~s cd CO a) 1 •H W CO a M-l o V o 00 1© a A £ CO CO CO c (1) o M •H «j 4J O CO « v£> iH M CU iH Ptf 3 « CJ •H 4J CU O J >3" 4J «H M < • O cu CN 3 oc •H fa (TS^l) a 'snxnpow ^uafXTsan 28 Table 7. Regression Equations for E as a Function of 9 a) Model: E = K + K K, Staged Tests 9690 449 0.92 Alva-Hurtado [22] (N = 10,000) 22685 425 0.94 b) Model: E = K o r 3 K. Staged Tests 3160 0.593 0.95 Alva-Hurtado [22 (N - 10,000) 5477 0.535 0.91 29 related to the bulk stress alone, and thus must be influenced by a combination of stress parameters. When triaxial samples are subjected to both positive and negative cyclic shear stresses, the resilient behavior is even more com- plicated. Cycling between positive and negative shear stresses causes a con- tinual reversal of the principal stress directions in a triaxial sample. For triaxial compression, the final stress state is such that the major principal stress acts in the vertical direction on a horizontal plane. For triaxial extension, the final major principal stress acts in the horizontal direction on a vertical plane. A "positive" shear stress, q = (a -a )/2, will be defined as the shear stress resulting from a major principal stress acting within ±45° from the vertical. Likewise, a "negative" shear stress occurs when the major principal stress is acting within ±45° from the horizontal. Thus, these triaxial compressional stresses produce positive shear stresses and these extensional stresses produce negative shear stresses. When the shear stresses are cycled from positive to negative, the orientation of the major principal stress and plane is abruptly rotated by 90° as the stresses pass through the isotropic condition. The sample initial dimensions, densities and void ratios for the stress reversal tests have been given in Table 3. The test conditions for these tests are given in Table 8. For these tests, O will mean the vertical stress acting on the sample, which can be the major principal stress, a , or the minor principal stress, o depending on the overall stress condition. Simi- larly, a will refer to the horizontal stress acting on the sample. All test samples were isotropically_ consolidated prior to shear application. For the isotropic condition, o =o=o=g=g, where O is the isotropic v h 1 3 c c consolidation pressure. ' Also given in Table 8 are the stress ratios, q/q f , for both the compressional_and extensional por- tions of the applied stress paths, and the mean stress, p, applied to the sample. For triaxial extension tests, the static shear strength is defined by c cos4> - °, f sin$ " • (3) 1 + sin4> l f where o f is the major principal stress at failure. For these triaxial exten- sion tests, 0=o=o , since the cell pressure was maintained con- , , It hi c , stant throughout the test. A cycle of loading for the stress reversal tests consisted of first ap- plying the axial compressive stress followed by unloading to the extensional stress, and then reloading to isotropic conditions. Loading is defined as any change of stress state where the mean stress increases, that is, p = (a +a )/2 increases. Unloading is defined as a decrease in p. During testing, the resilient strains resulting from loading to q and unloading to n max \ in were monitored. The resilient moduli calculations were based on = _Vn (4) re e re E =i^ax (5) re £ re 30 * >* o o O O O ■K c en o o O O © CO /~\ 3 «* rH o o O ON CO •H rH CM CO CO CO CO CU CO u a 4-1 v«^ co |co O O o o o © .*£ s vr m CM CO -* CO pa CM > N CO O o o O o o U c co O o o © © + •H s-\ 3 • • • • • • CO rH •H H CO CO CO CO CO ■ ^ PS cd CO 1 1 1 1 1 1 lo CU CO a u M v^ II X CO X O o o o © © w > ■K CO • • • • • • |CD 9 o" s CO ON CO VO ON ON /— \ pi C M-4 o cr co •H »*» CO § s G r^ o o o o o o u /^N 5 H o o o o o CU •H u •H 4J CO CO CO a «tf vO on ON ON CM rH X w CO (U u -*^ u o X O O o o © O •a B- MH 1 o. CO • • • • • • c a s on oo m 00 H sr CO o co rH rH t-i CM CM u c * o . <*> iH o 4J c >o- O O o o o CM •H s-^ a CO O o o © o T3 •H • • • • o • + d CO CM CO vO vO vO ON 4J o a . t-\ CO © *»• lo CU X O o O o O o H 4J > cd • • • • • • II CO o 2 CN r»» 00 ««r o CO CU H CM rH CM CO CO 1© H c o e O O O © o o •H • ^-\ •H • • f • • • • CO 00 ■H S vO ON CM CM CM m co CO rH rH rH <-i CU CU a- U iH •*_• a -O X o o O © O © s cd . •£ CO • • • • • • o H lo S vO ON CM rH CM rH CM rH m rH CJ CM CM rH rH rH O rH rH CO CO CO CM r*s oo vo vo vo m © o © o o o O rH G co vO ON CM CM CM m , -O 'cN o- rH rH rH rH © v— ^ II + lb II 4J rH CM CO »* m vO CO 1 1 t 1 1 1 O* | CU H © B B Hi o •K * CM 31 2(q -q . _ max n min E rt " E - £ ' (6) re re where E , E and E , are the extension, compression and total resilient re re rt , 1 . moduli, £ and e are the resilient strains resulting from extension and compression, and q and q . are the maximum and minimum shear stresses, max min The measured resilient moduli for these tests are listed in Table 9 for var- ious cycle numbers. These tabulated values show that the extensional resi- lient modulus is always less than the compressional modulus, which results in the total resilient modulus having a value intermediate to the compressional and extensional moduli. The general trend for these tests is that the moduli increase as number of cycles increases. In contrast, the results from the staged tests showed that the moduli reached approximately constant values after a fewer number of cycles. Resilient Modulus Formulation After many load-unload cycles, the behavior of railroad ballast becomes relatively elastic, in that the resilient strains become approximately con- stant. The elastic behavior is nonlinear, however. The resilient strains from the loading portions of the staged tests and the peak points of the shear stress reversal tests are given in Table 10. These points will be used to determine the resilient modulus formulation for situations involving full unloading and with shear stress reversal. The re- sults from the stress reversal test at 9 psi effective confining pressure are not included because equipment malfunction during testing invalidated some of the test results. Figure 5 shows the relationships between the applied shear stress levels and the vertical resilient strains. The resilient strains increase as cell pressure decreases, for a given shear stress level, for both extension and compression. The compressional resilient strains in Fig. 5 for each cell pressure were fit to an equation of the form q = A(U£ r ) B , (7) using the data listed in Table 10. Since intermediate data were not availa- ble for the extensional resilient strain curves, straight lines from the ori- gin through the peak extensional resilient strains were assumed. The resi- lient extensional strains were related to the negative shear stress by q = a (ye) . (8) The coefficients A, B and a for each cell pressure were subsequently fit to a log-log relationship as a function of cell pressure. Good agreement between the observed data and the assumed forms of the regression equations was found for the fitted data. The solid lines shown on Fig. 5 were based on the regres- sion equations, and are in close agreement with the observations. Table 11 lists the assumed form of each regression equation and the de- rived coefficients and coefficients of determination for the regressions. The resilient strain relationships given in Table 11 were used to define contours 32 co 4-1 CO CD Pi co CO (1) U 4-1 C/D s o u M-4 -a o S 4-1 S 0) •H rH •H CO CU (* XI cu u 3 CO n3 cu S3 o< CU rH CO H SO c CO •rl cu Tj rH CO u o >. ^ CJ o )-< •H cu 4-1 ■4-1 cO U-4 4-1 < CO 4J H w w CJ w w w w W w w w < CO a. & CO a. CO CM o co On CN m CO ^ o> co vO O CO rH rH CM o oo CM CN O r^ rH ON rH O CN CN m CM CM CO v£> m NO O 00 no m CN o CN O CO CO co m CN ON o co CM m CO r^ CJ 1 I l c_> 1 C_> X) c CO ft (3 ft o G •H o CO •H CO CO cu a u CU a 4J • X o CO CU a 3 rH fl C 3 •H •H T3 O CO CO 3 3 rH rH 4-1 3 3 CJ T3 T3 CU O O •H rH •H 4-1 4-1 CO a C CU CD • CU U •H •H rH rH rH •H •H CO CO CO 4-1 CU CU O u u 4-1 II II II cu a 4-> u u u w w w 33 Table 10. Resilient Strains for Staged Tests and Stress Reversal Tests a) Staged Tests co CO cu S-i u C/i M CO Q) JS w •H 35 Table 11. Regression Results for Compression and Extension Resilient Strains a) Compression ■Q Form of Equation: q ■ A(ye ) w 3 (psi) A B 3.0 2.486 x 10" 3 1.171 6.0 7.680 x 10" 3 1.079 12.0 13.914 x 10" 3 1.036 1.00 1.00 0.99 Equations for Parameters A, B: A = c(a 3 ) D C = 8.647 x 10 -4 B = E(a 3 ) F E = 1.2816 D = 1.145 -0.0883 r = 0.98 r = 0.96 b) Extension Form of Equation: q = a(ye ) r u 3 (psi) 6.0 12.0 15.0 a 3.921 x 10 -3 1.023 x 10 -3 1.639 x 10 -3 Equation for a - nY a = S(a 3 ) 3 = 2.535 x 10 ' y = 1.518 r 2 = 0.99 -4 36 of equal resilient strain as related to p = + 0, 2 and q = -0 ,/2 for full - , . ml .... . V h vh unloading cases. These resilient strain contours are shown in Fig. 6. This figure shows that for a given effective confining pressure, a positive shear stress results in smaller resilient strains than the application of the same magnitude negative shear stress. This means that the compressional resilient modulus will be larger than the extensional resi- lient modulus for isotropic tests cycled between ± q. The procedure for calculating the resilient modulus, E^ , for compres- sion loading from q = to a specified value of q loading to q = is as follows: 1) The expression relating shear stress, q as a function of effective confining pressure, to r -F re max max — followed by full un- to resilient strain, £ '3' can be rearranged re U£ rc -D max 3 (9) where C, D, E and F are the coefficients listed in Table 11. Substitu- tion of the coefficients results in - 0.088] ye rc -1.145 q °-5 max 3 ,-4 1.282 (10) (8.647 x 10 2) The compressional resilient modulus, E 2 v rc is then lax rc ue x 10 rc -6 (11) The procedure for calculation of the extensional resilient modulus, E , re for repeated loadings from q = to q. is as follows: 1) The expressions relating shear stress, q . , to resilient extensi_onal strains, £ , as a function of effective confining pressure, cr , can be rearranged to -Y ye. re Tnin 3 3 where 3 and Y are the coefficients listed in Table 11. the coefficients results in (12) Substitution of -1.518 ye mm 3 re ,-4 (13) 2.535 x 10 2) The extensional resilient modulus, E •:•; ■"■■■ 37 re is then to 3- 00 c •H m o 5 3 o CO u 3 o c o CO cd !-i 4-1 CO 4J c cu CO 8 (jj a cj u cu 4-1 14-1 CO CO J-i 4-1 co 0) > 4-1 C CU c cu Cm o O sO U"> en o m so on CN rH •* ON o CN >* H rH en sO rH <* m o 00 ON o O H m m o rH sO r-. O rH H co iH II O O o o o o o O o O O o S3 o o sO o CO CN o CN rH ON ON ON CN ■3- CN sO m 00 rH sO «* ^ cn m CO CN CN O CO «3- 00 CO o 3 H CM H | D en CM o o o o o o o o o o o O CO CO CO CO so sO sO so CM CM CN CM 00 ON H tH CO LO vO r^ co cn CO CO cn CO CO CO CN CO CO I CO m I CO 44 The resulting values for the coefficient C for each of the ballasts test- ed are given in Table 15. The results given in Table 15 show that all of the methods used were in very close agreement for the revenue site ballasts and for the staged tests done on the FAST granite. Since the four methods for determination of the coefficient C gave consis- tent results for the revenue site ballasts and the granite ballast tested most recently, the average values given in Table 15 were taken to be representative of those materials. These soil constants and the measured first cycle strains were used to calculate strains from Eq. 16 for comparison with the measured strains after 10,000 cycles for the revenue site ballasts and after 1000 cyc- les for the FAST granite. As indicated in Fig. 8, the agreement is very good. Variable-Amplitude Tests The results for the staged tests at effective confining pressures of a = 3, 6 and 12 psi are shown in Figs. 9, 10 and 11, respectively. The magnitude and sequence of the applied stresses used in these variable-amplitude tests are given in Tables 4 and 5. Several very clear trends were evident for the staged test results. They were: 1. For a given effective cell pressure, the permanent strain at the first cycle increased as the applied vertical deviator stress increased. 2. For a given applied vertical deviator stress, the permanent strain at the first cycle decreased as the effective confining pressure increased. 3. When the deviator stresses were increased to values greater than any past maximum values, the permanent strains continued to increase. 4. When the deviator stresses were reduced to values less than any past maximum values, negligible changes in permanent strain resulted with addition- al cycling. 5. Partial unloadings resulted in negligible increases in permanent strains with cycles. 6. For any given effective confining pressure, the sequence of applied stresses did not affect the final values of permanent strain so long as the total number of cycles at each stress level was held constant. Items 1 through 3 listed above are well known and easily understood. Items 4 through 6 deserve attention. The experimental results showed that the maximum stress history of a sample controls future stress-strain response. These ballast test results imply that the maximum wheel loads for a given maintenance life cycle will control the amount of strain accumulation. The observation that maximum load controls future cyclic deformations has been reported for other ballast materials [21,27]. However, past re- search on ballast behavior under repeated load [27] and other granular mater- ials [30] has indicated that the sequence of applied loads does have an ef- fect on the total permanent strain developed, and that a sequence beginning with high loads will result in larger final permanent strains. This was not evident from the staged test results presented here, because the terminal permanent strains were not related to the sequence of applied stresses. Con- sidering the accepted variability of sample preparation techniques and general ballast behavior, the strains measured at the end of all staged test series for similar effective confining stresses were in very close agreement. The small amount of permanent strain accumulation associated with partial unloadings was also observed by Shenton [27] for ballast material. Shear Stress Reversal Tests The linear relationship between permanent vertical strain and log number 45 O cu / — V 4J 13 •H 01 c 4-1 03 CJ M CO O a, 6 H o m o en c o o CO PQ CU T3 C •H 5-i S-i O o a. B o a CU X) co 4-1 QJ -a CU 4-1 OJ 5-i CJ a> o 03 kJ c CX o B CJ o a o co CN co O O m CN CN 40 CN CM m CO H XI 11 co 4-1 T3 "O a CU O o3 CU O Cu kJ 3 b O co co CO co co CO CO o xi o X, 4-1 cu S w Pd o CO CU CO u CU 46 £ = £-(1 + C log N) Line of Equality &•? OJ c •H co u u CO 0) c CO E Pu *a (U 3 05 CO Leeds, Concrete (C = 0.26) Leeds, Wood (C = 0.34) Aberdeen (C - 0.25) Lorraine (C - 0.40) FAST Granite (C = 0.29) Calculated Permanent Strain, £„ (%) N Figure 8. Measured versus Calculated Permanent Strains from Triaxial Tests 47 6-8 8-8 vO r-( m o o on CO 01 i-f a cj o CD 6C c o co ro w oj H •a •> <4-l o 5-i a) 01 3 CO 5-i CD > 5-1 co 4J c cu e CO CO CO Pi PL| ON 5-i •H N 3 'ujBaas T^T^JSA ^uauBnuaj 48 8>S 6^8 r*» <3> 6* 00 r^- rH • • r- o o • 6«8 o 00 / | oo\ / J, en cu u J-l cu ,0 I 60 3 •H C •H »4-l c o u en a vO cn •u CQ CU H T3 cu 60 03 4-1 CO o M-l cn cu iH eg >> u cu ■i 3 2 en 3 cn cu > CO c/s 4J c cu c etJ 6 u CU Cm O H 0) 3 •H N (%) 3 ^utfj^S T* T3* 3 A ^uauBnusa 49 6-9 s-s &-« m r>» vO -* en CO &-9 o o • o en y '4-1 O )-i •§ 3 Z 6C C •H C •H 14-1 o c_> •H CO a CN w ■u CO cu H T3 cu M CO ■u en u o U-l CO cu a co >> cu CJ 4-1 O M CU CO u 4-1 cu *-i ct3 co Cu cu QJ u 3 •r-l N 3 'ufBa^S T^IP^A ^uauBnuaj 50 of cycles was evident for these tests. The test samples all continued to de- velop increasing amounts of compressive axial strain after the first cycle. The general trends noted for the constant repeated stress tests with full un- loading were also observed for the stress reversal tests. As effective con- fining pressure increased, the accumulated permanent strains decreased for constant values of q and Aq. For constant effective confining pressures and equivalent levels of negative shear stress, the amount and rate of accu- mulation of permanent strain increased as the compressive shear stress levels increased. The permanent strain developed after the first cycle of loading for tests involving shear stress reversal was not as clearly defined as for the one-way loading tests. The strain at N = 1 was in fact extensional (negative) for one of the stress reversal tests. The sample did, however, still tend to compress for the subsequent cycles. The explanation for the negative axial permanent strains that could be developed for these stress reversal tests is clearly shown in Fig. 12. The permanent vertical strain developed due to compression loading fol- lowed by unloading with shear stress reversal is dependent upon not only the minimum negative shear stress, q. , but also the maximum positive shear stress. For the same level of q . , the vertical permanent strain at the end of the first cycle could be negative, zero, or positive, depending on the magnitude of the applied positive shear stress, such as q 1 or q_ shown on Fig. 12. The permanent axial strain at N = 1 for stress reversal ' tests was always less than that developed at N = 1 for the staged tests, which had no stress reversal. The rate of strain development with number of cycles was very clearly affected by the existence of shear stress reversals. Figure 13 shows compari- sons of tests having similar effective confining pressures and maximum posi- tive shear stress, both with and without shear stress reversal. As previously explained, the strains at N = 1 were always smaller for the stress reversal tests. However, the rates of strain accumulation were very much larger for the stress reversal series, although both types of test had positive rates of strain accumulation. It was shown previously that the slopes of the strain versus log N curves for repeated loading without shear stress reversal were proportional to the strain at the first cycle, £ , through the constant, C, and that C was unchan- ged for all stress levels. This was not the case for the stress reversal tests. The slopes of the e versus log N curves for the stress reversal tests were affected by both the ratio of cyclic shear stress, Aq, to maximum com- pressive shear stress, q , and the stress ratio (q I a.) , where q,. is the r . . n max , . , max f f static compressive shear strength for the prescribed effective confining pressure. The variation of the slopes of the curves shown in Fig. 13 as a function of these stress parameters are shown in Fig. 14. Note that Aq/q equal to 1.0 represents the condition of full un- loading without stress reversal discussed in the previous section. Fig- ure 14 shows that as the compressive failure stress ratios and amounts of stress reversal increase, the slopes of the e versus log N curves increase rapidly. The trends shown in Fig. 14 also support the observation from the staged tests that the strain accumulation would decrease rapidly for par- tial unloadings where Aq/q is less than unity. This trend, although not completely quantified, was also observed by Shenton [27]. 51 Shear Stress, q = (a ~ a u )/2 v h (Compression) (Extension) Vertical Strain (Compression) -q (Extension) Figure 12. Representation of Stress-Strain Curves for Shear Stress Reversal 52 Figure 13. Comparison of Strain Development Rates for Tests With and Without Stress Reversal 53 0.1 d) (6,3,3) 10 100 1000 I 10000 -0.1 5 -0.2 '(6,3,4.8) c (U c 04 0.4 e) °3 q max 0.3 - (15,9,12) ^^ 0.2 0.1 — — ^V *^~-~~~'' ^(15,9,9) 1 1 1 1 10 100 Number of Cycles 1000 10000 Figure 13. (Continued) Comparison of Strain Development Rates for Tests With and Without Stress Reversal 54 .0 <-^-< 1.1 0.0 < ""* < 1.0 •*- partial unloading max 1.0 >-±SL -*■ shear stress reversal max 0.15r- 55 0.10 00 o (jj < 0.05 C<1 /q^) Compression max n f 0.08 max Figure 14. Rate of Strain Accumulation as a Function of Stress Parameters 55 3.6 Ballast Box Tests General Description In the laboratory box tests, the ballast was loaded vertically using a simulated section of tie. The test setup is illustrated in Fig. 15. The main objectives of these tests were to investigate the settlement characteris- tics of the ballast under field loading conditions, and to evaluate the hori- zontal stresses that develop beneath the tie segment. Details regarding the box construction, base support conditions, instrumentation and complete test results can be found in Ref. [31]. Only the results which are pertinent to analysis in this report will be given here. The ballast box was constructed to represent a section of tie about 11 in, long located directly below a rail. The box was 24 in. long by 12 in. wide. The length was intended to represent one-half of the crib width on either side of the tie segment. The ballast depth was 12 in. below the base of the tie segment. A flexible bottom to simulate subgrade support was incorporated so that the deflection basin below the ballast layer could be represented. The box side and end panels were instrumented so that the lateral stresses in the ballast could be estimated under both loaded and unloaded conditions. The panel numbers and locations are shown on Fig. 15. The physical state of the ballast prior to the cyclic loadings was representative of the conditions found under the tie rail seat after a maintenance tamping operation. The load applied to the 11.5-in. by 9-in. tie segment was 4000 lb. The stress at the base of the tie segment from this load was equivalent to the stress at the base of the tie beneath the rail seat due to a 33-kip wheel load. Permanent Settlement The permanent settlement trends for these tests were similar to those ob- served in the repeated load triaxial tests in that the settlement was linearly related to the log of the number of cycles. The form of the expression for the settlement of the tie for these ballast box experiments was identical to that developed for the repeated load triaxial tests (Eq. 16), except that d and d were substituted for £.. and z , where d.. and d were the residual vertical deflections of the tie after the 1 st and N tn cycles, respectively. Tests on both compacted and uncompacted samples in- dicated that the rates of settlement for these two physical states were differ- ent, but still both could be expressed by the relationship d^ = d x (l + C b log N) , (17) where C, is the settlement coefficient for the box tests derived the same way as for the triaxial tests. The coefficients determined for the compacted and uncompacted ballast samples were Compacted Uncompacted C L = 0.35 C, = 0.63 be bu The coefficient C, for the compacted samples was in general agreement with the results found for the compacted ballast triaxial tests done on the reve- nue site and FAST granite ballasts. The uncompacted coefficient, C , was about double the compacted coefficient. 56 • LOAD PANEL NUMBER END PANELS X w^m S~ TIE ^SEGMENT — T — 4 in. (typ.) I 1 \*T: ^^T PANELS I h H BASE •H 24 in. a •H H A |< 9 in. — -> m 1 |< — 8 in. >| 1 A Figure 15. Box Test Apparatus 57 . The physical state of the ballast was assessed at the end of these cyclic box tests. Both ballast density and plate load tests showed increases compar- able to those measured from the field tests. The ballast densities increased by about 8% in the box tests. The changes between the pre- and post-mainte- nance ballast densities for the under-tie locations at the field sites were about 9 to 12%. Plate bearing resistances at 0.05-in. deformation were com- pared for the box tests and the field sites. The field sites showed changes in the range of 400 to 1200% due to traffic effects. The increases in plate load resistance measured in the box tests were on the order of 800% due to the cyclic loading. The changes in ballast density and bearing stiffness measured in the box tests indicated that the field loading conditions were being approx- imately simulated, and the field repeated-load mechanisms of ballast compac- tion were being reproduced in these laboratory tests. Staged loading tests were also done using the ballast box device. Loads of 2000, 4000 and 6000 lb were applied in various sequences. The 4000-lb load resulted in an applied stress at the base of the tie segment that was equivalent to the stress at the base of a tie beneath the rail seat due to a 33-kip wheel load, as determined using the GEOTRACK model. The 2000- and 6000-lb loads were selected as experimental values to demonstrate staged load- ing effects. The deformation trends for these tests were similar to those ob- served in the staged triaxial tests. The total amount of vertical deformation was found to be independent of the applied load sequence. Also, as in the tri- axial tests, negligible additional permanent deformation resulted due to cyc- ling of loads less than any maximum past load. Horizontal Stresses Estimates of stresses, strains and deflections for layered systems such as track and pavement are based upon an idealized continuum approach using either multilayer models, such as GEOTRACK, or finite element methods. In a layered system where the stiffness of the upper layer is greater than that of an underlying layer, all methods of analysis predict that the lower por- tions of the stiffer layer will develop significant incremental tensile stres- ses and strains. When the upper layer consists of an unbound granular layer, such as ballast, either a redistribution of these stresses must occur or the initial and therefore final stress state must be different than that predic- ted. These conclusions are physically rational since the unbound layer can- not sustain tensile stresses. The occurrence of tensile stresses in an un- bound granular layer would result in very large inelastic deformations with each load application. Such large inelastic deformations under each load ap- plication are not observed in a stable, layered system such as track. One of the primary purposes of the box tests was to measure the lateral stresses developed in a simplified layered system, with particular interest in the development of residual lateral stresses. It has been recognized that some residual lateral stress can develop in soils such as sands [32] and clays [33] due to compaction and previous load history, but the magnitudes of these residual stresses have not been fully described for such materials as ballast. Thus, the side and end panels of the ballast box were instrumented to provide a direct measure of the lateral stresses that developed under the simulated track loading conditions. Typical measurements obtained from the side panels of the box are shown in Fig. 16. The results indicated that there was a rapid build-up of horizon- tal compressive stresses upon initial loading, and that high residual stresses developed after only one cycle of loading. Furthermore, the horizontal 58 CO Q_ co CO UJ en t- co o M cc o X 4 - 2 * i 1 1 1 1 1 1 5 6 8 1000 10000 100 1000 10000 LOADED 3= L m LOADED BAR 8 10 I i 100 1000 NUMBER OF LOAD CYCLES 1 10000 Figure 16. Horizontal Stresses on Side Panels [31] 59 stresses in the loaded state decreased and the residual stresses increased up to about 100 cycles. After 100 cycles, the horizontal stresses tended to sta- bilize and the unloaded value tended to converge to the loaded value. This means that the horizontal stresses tended to become constant during a load cycle. The maximum horizontal stresses acting on the side panels occurred at about the mid-depth of the ballast. The minimum horizontal stress on the side panels occurred near the base of the ballast layer. The box tests showed no evidence of tensile stress development in the ballast under loaded conditions. The stress measurements from the instrumented panels also showed no tendencies for reduction in the horizontal stresses in the ballast due to the applied ver- tical load on the simulated layered system. The measured horizontal stresses for the end panels are shown in Fig. 17. Similar trends for rapid buildup of the lateral residual stresses were observed at the end of the ballast box. The maximum lateral stresses again occurred about 6 in. above the base of the ballast layer. The variations of the horizontal stresses under load and under no applied vertical load as a function of the height above the box base are shown in Fig. 18. In general, the loaded condition produced higher lateral stresses for the first cycle. After about 100 cycles, there were only slight differences be- tween the loaded and unloaded horizontal stress states. After 10,000 cycles, the residual stresses were almost identical to the stresses developed under full vertical load. The measured residual horizontal stresses from these experiments were used to calculate values of K , the ratio of lateral to vertical effective stress at rest in the unloaded state. Theoretically, the maximum re- sidual horizontal stress should be limited by the passive failure condition. The ratio of_major principal stress at failure, a 1f » to minor principal stress at failure, o„. at the passive failure " condition is defined by (18) for a strictly cohesionless material such as ballast. The calculated K values, based on the box test side and end panel meas- o urements, the unit wexghts of the ballast, and the static surcharge due to the tie segment weight are shown in Fig. 19. The very large values_of K for the upper portion of the side zone would require a friction angle, $ , of about 56.5°, which might appear unreasonable. However, considering the curved fail- ure envelopes, possible particle interlocking due to the ballast angularity, and the very low vertical stresses in the upper ballast zone, a friction angle of this magnitude may be possible. Certainly values of K =6 would be possi- ble, since the required friction angle would be only about 45.5°. The results of static triaxial tests have shown that this value would not be out- side the possible range of values for low effective confining pressures. These experimental observations of the high residual lateral stresses and cor- respondingly high K values justified the use of such values in the subsequent GEOTRACK analyses for predicting track response. 60 °lf v max = K 1 + sin(J> °3f O P 1 - sincf) TIE LOADED TIE UNLOADED CO CO CO cc co o M O 1- V UNLOADED LOADED BAR 3 i 10 100 JCZ + =L 1 .-L i ■ 2 3 4 1000 1000 10000 10000 10000 10000 NUMBER OF LOAD CYCLES Figure 17. Horizontal Stresses on End Panel [31] 61 UJ CO < A OD 16- X o ™ CQ 12- 2 — o cc 8- u. UJ o 4- z < \— n.. en o END 2 3 HORIZONTAL STRESS (PSD CYCLE I 16- 12- 8- 4- SIDE . LOADED RESIDUAL (UNLOADED) '2 -| 1 1 1 1 1 1 1 r>» 2 4 6 8 HORIZONTAL STRESS (PSI) CYCLE I HORIZONTAL STRESS (PSI) CYCLE 10,000 12- 8- 4- SIDE —I 1 1 1 1 I * ' 2 4 6 HORIZONTAL STRESS (PSD CYCLE 10,000 Figure 18. Measured Horizontal Stress Distribution from Ballast Box Experiments [31] 62 CVJ 00 vO CD CO CJ CJ CM c CD B •H CD CL X o pa e o a; Q U-l o a o •H 4-1 a § *4 4-1 o c o •H 4-> CO •H CO > Oi CD •H LO m (*uf) asBg 3AoqB aouerjsjQ 63 3.7 Subgrade Material Sampling Program Along with the standard penetration (SPT) and cone penetration (CPT) tests previously described in Volume 1 [1], undisturbed soil samples (UDT) were taken at locations near the SPT locations, generally only a few ties away along the centerline of the track. In addition to the samples recovered from the field sites, subgrade ma- terial was recovered from the FAST track. Undisturbed samples were not taken. Repeated-Load Testing for Revenue Sites Unconsolidated-undrained repeated-load triaxial tests, as well as static triaxial tests, were done on these recovered subgrade materials. The details regarding the triaxial testing and test results from the revenue service field sites, as well as index and classification test results, can be found in Ref. [34]. The stress states for the triaxial repeated-load tests on the samples re- covered from the revenue service sites were intended to match the total stress states estimated at the sample location depths under representative train load- ings. Three basic steps were necessary to define these stress states. The ini- tial total vertical geostatic stresses at required depths were calculated based on the average soil densities as determined from the tube samples. The coef- ficient of lateral stress, K, defined as the ratio of total horizontal stress to total vertical stress, was assumed to be 0.75 for the revenue site subgrade materials. The incremental stresses due to multiple-axle train loadings were estimated using the GEOTRACK computer model. The three-dimensional stress states at various depths of interest were converted to axisymmetric constant confining pressure triaxial stress states using the method of stress invar- iants [22]. The individual stress paths used for these triaxial tests, shown in terms of p = (o +a )/2 and q = (c,-cO/2, can be found in Refs. [34 and 35]. The resilient moduli values determined from these tests were correlated with the cone penetration and standard penetration test data. These correla- tions were necessary since it was not possible to perform a series of triaxial tests under a range of stress conditions for each of the identified soil stra- ta and develop stress-dependent modular relationships. This is particularly true since remolding of the undisturbed samples would have significantly chan- ged their properties. The cone soundings represented a continuous measure of the soil properties that could be used to extrapolate the properties measured in the lab to other depths. Based upon the correlations made and the test data presented in Refs. [34 and 35], ranges of resilient moduli values for the subgrade materials were determined. These ranges of resilient moduli are shown in Fig. 20 for the Leeds wood and concrete test sections and in Fig. 21 for the Lorraine and Aberdeen concrete test sections. Repeated-Load Testing for FAST Subgrade The FAST subgrade was also tested for resilient modulus parameters as well as for index properties and strength parameters. The subgrade at FAST is gene- rally uniform throughout the test sections. The material was classified as a moderately uniform medium-to-fine silty sand. The Unified Soil Classification System (USCS) designation of the FAST subgrade was SM. The classification based on the American Association of State Highway and Transportation Officials (AASHTO) was A-2-4(0). Since undisturbed samples were not available, remolded specimens of the silty sand were prepared at moisture contents of 9.4 to 10.0 64 (3J) 3TI AOjaa M3d9Q o CU cu n c o u •o c cd o o Ds CO CU CU ►J u o 4S 4-1 a CU o CO 3 CO u cu > CO 3 i-H 3 ■O O 2 CO cu o CM CU u 3 t>o •H mom rH ,H (3j0 3*FI Aojag ipdaa o CN 65 •H O co cm uJ CO 3 r-» 3 O s c 0) 05 CU m o CM (3J) 9TI Aoxsg ipdaa o CO w CO 3 «H 3 O s co a) OS o CO O CM C a) CU M CO 3 iH 3 T3 I CO CU OS CN CU u 3 50 •H ± in m o CM 66 percent. Two methods were used to prepare FAST subgrade soil samples. The first sample type was made using a Harvard miniature compaction mold. These sam- ples had dry unit weights, y,, of approximately 124 pcf (101% AASHTO T-99) . The other sample type was made using a specially fabricated sample mold and using a preparation technique similar to that described by Ladd [36] with which the soil density state could be controlled. The resulting dry unit weights, y , , using the controlled compaction technique were 112 pcf (91% AASHTO T-99). All soil samples had length-to-diameter ratios of 2.5:1. Specific details regarding testing procedures, index test results, and strength parameters for the FAST subgrade are given in Ref. [37]. The results from the FAST subgrade tests indicate that the type of compac- tion used to prepare samples can have an effect on the measured resilient modu- li values. Samples prepared using the undercompaction method resulted in gene- rally higher moduli than those prepared using the Harvard miniature method. However, the data from both of these methods were combined and used to deter- mine the modulus coefficient, K-. , and modulus exponent, K~, for the following resilient formulation: K 2 a A vibratory method of compaction was used to prepare the subgrade samples test- ed in Ref. [17]. Values for K and K were also obtained for the data from this source. The resulting parameters are as follows: Source 1 2 Stewart 877 1.10 Thompson [17] 654 1.08 The main difference is in the coefficient of K. . A possible explanation for this difference is that the resilient moduli values taken after 40,000 cycles were used from the tests in this study, where- as the values reported in Ref. [17] were based on staged test results taken after 5000-load repetitions following a stress state change. It was previous- ly shown that single stage testing generally results in increasing modulus with increasing number of cycles, but staged testing does not show a continuous in- crease with number of cycles. 67 CHAPTER 4. TRACK MODULUS 4.1 Introduction The use of track modulus for assessing track performance is common in the railroad industry. The theoretical formulation of track modulus is based on the assumption that the rail acts as a beam continuously supported on an elastic foundation. The track modulus is defined as the supporting force per unit length of rail per unit deflection in the track system. The resulting equation for track modulus is *y pT~ T 1 ' ( 6° ' EI ' (20) where u is the track modulus (units = F/L/L) , P is the applied load (units = F) , 6 is the vertical rail deflection (units = L) , and EI is the rail bending stiffness (units = FL^). An important difference between the actual track support and the ideali- zed formulation of a rail on an elastic support is that the rail load is actu- ally applied to the foundation through discrete supports, which are the ties, rather than through support distributed along the track foundation. Another difference, for concrete tie track systems, is the inclusion of flexible tie pads between the rails and the tie rail seats. Even though these differences exist between the actual track structure and the theoretical formulation, the track modulus has historically been used as a measure of track quality. Fur- ther details on the historical development and interpretation of track modulus can be found in Refs. [38 and 39]. This chapter will present the track structure and foundation properties selected for input into the GEOTRACK program in order to predict the track modulus at each of the revenue field sites. These predictions will be com- pared with field measurements, and the trends will be discussed. 4.2 Selection of Parameters The GEOTRACK model [40] was used to determine elastic track deflections for predicting values of track modulus for the revenue field sites. The GEO- TRACK computer program is a three-dimensional, multi-layer model for determin- ing the elastic response of the track structure, using stress-dependent proper- ties for the ballast, subballast, and subgrade materials. The output of the program provides rail seat loads, tie-ballast reactions, tie and rail deflec- tions, and tie and rail bending moments. In addition, the output provides ver- tical displacements and the complete three-dimensional stress state at selec- ted locations in the ballast, subballast and subgrade. The validity of this model for evaluating the resilient response of track was established by compar- ing measured foundation responses obtained from FAST instrumentation with pre- dictions made using the GEOTRACK model. Details regarding the model valida- tion, measured FAST foundation responses, and the results of parametric studies 68 done using the GEOTRACK model can be found in Refs. [41 and 42]. In order to make determinations of the elastic responses of the revenue sites, the structural and foundation properties were determined for each of the sites. The structural properties are given in Table 2. Figures 22 to 25 show the ballast and subgrade layer divisions and properties. The shear stress-resilient strain formulation developed in Chapter 3 was used to characterize the stress-dependent resilient moduli for these sites. The other ballast parameter values are shown in Figs. 22 to 25. The subgrade layer properties used for the GEOTRACK analyses were chosen based on the results shown in Figs. 20 and 21. Layer divisions for the sub- grades were made (Figs. 22 to 25) where there appeared to be significant chan- ges in the measured resilient properties. The average resilient modulus for each subgrade layer was used as the representative value for the layer. The moduli for the subgrade layers were held constant, since stress-state-depen- dent relationships were not available for the subgrade. The values of total unit weight were determined from the subgrade samples recovered from the un- disturbed tube sampling. The values of Poisson's ratio used for the subgrade were based upon static triaxial tests and were generally very close to 0.5. The ratio of lateral to vertical stress, K = 0.75, was estimated from the soil conditions as a reasonable value for the subgrade layers. An exception to these values was that a K =2 value was used for the upper granular subgrade at the Leeds sites. The parameter K is defined as the ratio of lateral effective stress to vertical effective stress in the granular layers under the condition of zero lateral strain. The values of K = 4 to 6 in the upper granular layers may appear to be unusually high. However, these values were based upon experimental observations of ballast behavior in a laboratory ballast box de- vice developed for simulating field conditions. 4.3 Comparison with Field Measurements Measurements of track vertical load-deflection response were made at each of the revenue field sites by Battelle-Columbus Laboratories (BCL) . For the test, a point load of known magnitude was simultaneously applied to both rails, using vertical hydraulic jacks reacting against a loaded freight car. Rail de- flections were measured by sighting a steel scale with a surveyor's theodolite. The scale was attached to the rail. Seven to ten measurements at random tie locations were made to assess the variability in the load-deformation respon- ses within the track sections. These measurements were made both before and after the maintenance operations to see what differences in track support re- sulted from the surfacing operation. Track load-deflection measurements were made at 7 to 10 tie locations at each site. The measured averages and standard deviations for the pre- and post-maintenance load-deflection curves were given in Volume 1 [1] . A small amount of slack between the bottom of the tie and the top of the ballast layer may have contributed to the nonlinear response in the initial portion of the load-deflection curves. Most of this initial slack was assumed to have been eliminated after about a 6-kip load was applied. To minimize this effect, the track moduli values used for this comparison were calculated for the 6- to 30- kip load range. The mean track moduli measurements and estimates of the standard devia- tion were made using the mean load-deflection curves and the deflections at ±1 standard deviation, both taken at the 6- and 30-kip load levels. The 69 Bottom of Tie »• { 12 2 y> in E = 6500 psi r l I v = 0.48 _ y T = 117 pcf K = 0.75 54 in — 1 ' E - 9000 psi r -. V - 0.48 1 < 1 » Y T - 124 pcf K - 0.75 8 — BALLAST T SUBGRADE Figure 25. Layer Description for Aberdeen 73 standard deviations of track modulus calculated in this way are not symmetri- cal about the mean value, and slightly underestimate the actual standard devia- tions. For the purposes addressed in this chapter, the standard deviations of the track moduli values will refer to the limits calculated, based on the standard deviations of the rail deflections. To determine track modulus with GEOTRACK, deflections were calculated for the single axle solution with loads of 6 and 30 kips. The difference in loads and difference in deflections were substituted into Eq. 20 to get track modu- lus. The measured values of track modulus and the estimated standard devia- tions for all of the revenue field sites are given in Table 16 and shown in Fig. 26, along with the predicted values based on the GEOTRACK analyses. Seve- ral items on Fig. 26 deserve attention. First, there was no significant change in the track moduli values as a result of the surfacing operations. However, the pre-maintenance values did seem to be less variable than the post-mainte- nance values. This variation was also apparent in the average load-deflection curves, where the scatter about the mean was visibly larger for the post-main- tenance values. The fact that the average measured values were greater in the Leeds wood and Lorraine sections after maintenance is probably not statisti- cally significant, since the estimated standard deviations all overlap. Another observation from Fig. 26 is that there did not appear to be a cor- relation between height of raise and post-maintenance track modulus. Raises of 1.5 to 2 in. were given to the Leeds and Lorraine sections and only about 0.1 in. to the Aberdeen section. In spite of this, the pre- and post-maintenance values for any one test section were approximately equal, and the Aberdeen val- ue was between the Lorraine and Leeds values. An explanation for the increased variability of the post-maintenance modu- li values as compared to the pre-maintenance values could be that the surfacing decreased the uniformity of track support conditions between tie locations. One purpose of track maintenance is to improve the overall track surface, mean- ing to smooth out the vertical track roughness. A larger amount of raise must be applied beneath the lowest ties to achieve a uniform surface. These varia- tions in the actual raises applied beneath the individual ties could cause lo- cal differences in the amount of ballast disturbance, hence variations in the ballast physical state from one tie to another. Part of the differences in absolute magnitude of the average field track modulus measurements can be explained in terms of the differences in the track substructures. The parametric study [41] using .the GEOTRACK model indicated that track modulus increased as ballast depth increased. The ballast profiles and the simplified layer characterizations used in the GEOTRACK analyses (Figs. 22 to 25) show that the Leeds wood section had only about 9 in. of ballast be- neath the tie, whereas the Leeds concrete section contained about 14 in. The Aberdeen site had 20 in. of ballast, and the ballast depth at Lorraine was es- timated to be 28 in. below the tie. This trend of increasing track modulus with increasing ballast depth for the field sites is clearly confirmed by the field measurements in Fig. 27. The track modulus is also influenced by the subgrade characteristics. The GEOTRACK model indicates that the compression of the ballast layer accounts for about 10 to 20% of the total vertical rail deflection. Most of the remain- ing 80 to 90% of the rail deflection is accounted for by the compression of the subgrade materials. Furthermore, 25 to 40% of the subgrade deformation indica- ted by GEOTRACK occurs below a depth of about 10 ft, even though the stresses below this depth are low [41] . 74 CO Pn CO 3 CD ■H 3 3 3 -a CU o > se CU Cd ^ CJ M CO O M iw H CO iH 3 cd o o •H •H 4-) 4J CO M •H 0) > > CU O -a cu *3 ■u U o CO •H -3 •a 3 0) CO h 4-1 P-. Ui -3 •3 C (U CO 4J CO *3 e CU •H u 4-1 3 CO CO w CO OJ •3 X 3 CO • CO vO CU iH 00 CO CU M iH CU ^3 > CO CO X < O I ►J 4-1 CO a o ■H Pm ^ b CO ON o a\ 1 1 • • » • O IX CM CM v£> <* o 4-1 1 vO 5-i O $ m CO • • 14-1 IX O 0) oc X 4-1 CO CS a\ o 3 l-i • • • M •H a) CM CO r^. o CO | 5 n 1 H CU PU D 1 IX i-l CM m CO -a- CO CO CU 4-t •H CO "3 iH CU •H CU 3 3 CU > o CO cu 3 CO > •3 CU 4-t CJ ■H CU en a ii 3 CD 4-> •H 5 CM m m m « 00 v£3 m CO CU 4-1 CU U •3 cj O 3 O O S CJ CU 3 3 (U A A ■H (U CO CO CO -3 •3 •3 >-i u CU cu H CU cu CU o XI h4 (J (J «* CU u •3 a O 3 O O S V cu 3 3 (U a A •H CU CO CO CO *3 •3 T3 M V4 CU CU Ij CU CU CU o .o ►J ►J ►J <: 75 T3 00 U CO 3 V-i CO CO CO \ / 1) •u o •H CO o p- c cu I) CU T3 60 M d cu CO .0 p3 < cu 13 u CO P-. O p. •H M 1 O en •u o CO i-> c P4 CU i c v© ■H CO A u CO u cu o 4J hJ «H CO T3 e (0 ■u o 13 «H CU JJ ■u co CO «H 6 > •H CU •u Q CO w +1 HH KH I— <^ M 00 v£> CN (•UT/'u-p/sdT^) (^ OC-9) snxnpow ?pvil w oj CU a c CU > •u cu cu CO 4J pei O 0- CU 1-1 o O C *4-l o CJ •H n 3 CO •o ■a CU s CU CU u h4 .* P-. CJ CO u H T3 CU 4J CJ ■H u T3 CO CU o •a u Pi o o p- £ T3 C •» CO CO *3 T3 OJ CU CU >4 CU h3 3 u CO p- CO • CM -! 3 60 Pn 76 12 10 •H CO o. •H 3 CO 3 iH 3 -a o s CJ CO S-i Lorraine Aberdeen . Leeds | , Concrete I I . Predicted Post Pre Range of Standard Deviations from pre- and post- mainte- nance tests (Fig. 26) 10 20 Ballast Depth (in.) 30 40 Figure 27. Ballast Depth versus Track Modulus for Revenue Field Sites 77 The Lorraine test section was found to have the greatest depth of ballast- type material and the stiff est subgrade. Correspondingly, the Lorraine sec- tion had the highest values of measured and predicted track modulus of these four revenue sites. As can be seen in Fig. 27, the predicted value of track modulus was higher than the average measured values, but well within the esti- mated standard deviations. The Aberdeen post-maintenance value was lower than the Lorraine value due to a combination of reduced ballast thickness and lower overall subgrade stiff- ness. The predicted track modulus for the Aberdeen site was in very close agreement with the measured values. For the Leeds sites, the predicted values of track modulus were higher than the field values. However, the field values appear to be unusually low. The lower ballast thickness at the Leeds sites can account for some of the difference between the Leeds sites and the other two field sites, but these differences in ballast layer thickness were not enough to cause the low values measured at both Leeds sites. Considering the similarity between the subgrade stiffnesses at the Leeds sites and the Aberdeen site, closer agreement between the field measurements from these sites would be expected. It is possible that the embankment in the Leeds wood section resulted in reduced subgrade confinement and hence increas- ed vertical deflections. This would result in lower values of track modulus. However, the concrete section at Leeds, which was built at grade, had compara- bly low track moduli values as well. Thus, the embankment condition must not have been a major factor. It would be necessary to reduce the subgrade stiffnesses that were used in the GEOTRACK analyses by at least 50% in order to match the field track modulus measurements at the Leeds test sections. However, no rational justi- fication for making adjustments of these magnitudes could be found. If the soil moduli were overestimated at the Leeds sites, a similar systematic error should have occurred with the Lorraine and Aberdeen subgrades. Since the pre- dicted Lorraine and Aberdeen values were in good agreement with the measure- ments, a similar adjustment to the subgrade moduli at those sites would shift the predicted values away from the measurements. The measured and predicted values of track modulus are dependent on seve- ral factors, one of which is the support condition of the tie. These support conditions are a function of track settlement and maintenance effects. The support conditions would affect concrete and wood ties in a different fashion. The GEOTRACK model uses uniform properties, throughout each layer, includ- ing the support and contact under all ties. The field plate load tests showed that the ballast stiffness was not uniform under the ties, but was greater near the rail seat areas than under the tie centers. Furthermore, after the maintenance the ballast physical state was more uniform than before mainte- nance. However, even uniform physical state or modulus does not result in uniform support conditions along the tie. After a maintenance operation in which a high raise was given to the track, the ballast physical properties would be more uniform. However, the tamping and raise during the maintenance is done only near the rail seats, which could cause a gap near the center of the ties. This causes the actual load bearing areas to be near the rail seats due to the lack of contact near the tie centers. This increased load bearing near the rail seats would cause higher rail deflections directly under the applied load than would result from a continuously supported condition. The GEOTRACK model uses continuous con- tact between the tie directly under the applied vertical load and the ballast surface, leading to a lower rail deflection and higher track modulus than 78 measured in the field after maintenance. As traffic accumulates over the track, the ballast beneath the rail seats is recompacted and becomes stiffer, but the tie contact approaches a continuous condition. The more uniform support across the tie leads to a lower rail de- flection and hence a higher track modulus. After a small maintenance raise, the initial ballast physical states may be less uniform under the tie than after a large raise. However, in the former case, the contact may be more continuous and the ballast will have greater stiffness. This would result in a higher track modulus after a small raise than after a large raise, or at least not much change in the pre- and post-maintenance values. Further traffic leads to a centerbound track, in which a greater portion of the rail load would be carried by the central portion of the ties than in non-centerbound track. A gap also tends to develop between the ballast and tie beneath the rail. If the gap is included in the deflection measurement, then the calculated track modulus would appear to decrease as a result of cen- terbinding. However, if the gap is eliminated by a seating load, then the track modulus would probably increase with centerbinding. The interactions between the variable ballast physical states, tie sup- port conditions, and structural factors such as tie stiffness and rail size make generalizations about track modulus uncertain. This is particularly true since the degree and type of maintenance disturbance and traffic history of a site can change the ballast physical states in varying amounts. The scatter of the field measurements were such that there were no clear trends distin- guishing the pre-maintenance track moduli values from the post-maintenance values. The predictions of track modulus using the GEOTRACK program are some- what limited by the uniform layer property and full contact representations, and the inability to represent the maintenance factors for the field sites. For these reasons, variations between the measured and predicted track moduli values for the sites can be expected due to the variations in ballast proper- ties and support conditions which were affected by the maintenance operations. The possible centerbinding and uniformity of support conditions beneath the tie bottom may not, however, be a significant contributing factor to the track modulus values, although the effects are physically rational. Differen- ces between the bending stiffnesses of the wood and concrete ties would also not result in large differences in track moduli. Since only 10 to 20% of the total track deformation occurs due to ballast compression, the subgrade deflec- tions appear to be much more important. It was shown in previous parametric studies [41,42] that variations in tie stiffnesses do not have a major effect on the vertical subgrade stresses beneath the rail seats. The effects of a concrete tie (EI - 1,740,000 to 2,360,000 K-in. 2 ) have shown that the vertical stress beneath the rail seat may be only about 1 psi greater than the wood tie (EI - 386,000 K-in. 2) for similar conditions. Thus, the subgrade contribution to track modulus should be about the same for wood and concrete ties. The FAST dynamic measurements of resilient subgrade deflection also showed no signifi- cant difference between the deflections in wood and concrete sections. This would indicate that although the stress distributions and deformations in the ballast layer were affected by tie stiffness and possibly centerbinding, the subgrade responses were controlled mainly by the subgrade properties for the same ballast layer thickness. A comparison between the measured and predicted values of the revenue site vertical rail deflection is shown in Fig. 28. The differential deflection equals the deflection at 30 kips wheel load minus the deflection at 6 kips. A change in rail deflection causes a larger change in the calculated value of 79 0.12 r- 0.10 - •H o 0.08 r-t Q •h 0.06 " T3 0) H 3 CO (0 2 0.04 - 0.02 0.02 0.04 0.06 0.08 Predicted Differential Rail Deflection (in.) 0.10 Figure 28. Measured versus Predicted Differential Rail Deflections for 6- to 30-kip Load Range 80 track modulus. For example, the predicted values of track modulus at the Leeds wood and concrete sections were in error by about 60 to 100%, but the errors in predicted rail deflections were less. Furthermore, the differences between predicted and measured deflections were small in absolute magnitude. Thus, the predicted values of the rail deflections were in reasonable agree- ment with the measured values. In fact, considering the complexity of soil behavior, the accuracy of deformation prediction obtained was very good. 81 CHAPTER 5. TRACK LOADING 5.1 Introduction Any methodology for predicting the accumulated permanent strains and set- tlement of track must take into account the actual loading conditions. The actual loading of a given track will consist of a mix of many different wheel loads which are defined by individual car weights and the dynamic response of the moving train. The approach taken in this study for determination of the mix of wheel loadings at the sites was based on the direct measurement of the actual wheel loads at each site, rather than the use of empirical load factors. The fol- lowing sections will present these measurements, and describe the method used to characterize the mix of wheel loads present at each of the field sites, in- cluding FAST. The static wheel load distributions for each of the sites were obtained from the railroad companies, based on the car weights and tonnage records. 5.2 Measured Wheel Loads Strain gauge instrumentation was installed on the rails to measure the actual wheel loads. This work was performed by BCL. Descriptions of the strain gauges, the calibration procedures, the instrument locations, and the data recording methods are given in [44] and in Volume 3 [43]. On the basis of past experience in wheel load detection, a sufficient number of loads were recorded at each site so that the load distributions were accurately defined. The data were reduced to the form of the percent of wheel loads that ex- ceeded a given load level. This is analogous to the cumulative distribution function (CDF) of random variables. The random variables in this case were the static and dynamic wheel loads. The percent exceeded level for the meas- ured wheel loads was converted to the CDF by F x ( x) = 1QQ - P^t exceeded = p(x < x) , (n) where F y (x) is the probability that the given wheel load, X, is assigned a value equal to or less than a specified value, x. This statement is equi- valent to the expression P(X <^ x) . The cumulative distributions for the static and dynamic wheel loads were given in Volume 1 [1] for the field sites at Leeds, Lorraine, Aberdeen, and FAST. Several trends were identified in these distributions. There were sig- nificant differences between the low frequency of occurrence wheel loads at the sites. These differences appeared as wide separations between the static and dynamic CDF's near the upper tails of the distributions. These separa- tions began at about the 80-90 percent exceeded level (CDF = 0.8 - 0.9) for the revenue sites. The largest variation between the low frequency of occur- rence static and dynamic wheel loads was at the Aberdeen site. The very high dynamic loads, a factor of 3 to 5 times greater than the mean dynamic load, are thought to be caused by tread surface irregularities and the high speeds of the passenger trains. 82 ■ The wheel load distributions for the Lorraine site showed two distinct traffic patterns. The breaks in the wheel load distribution curves for this site were due to the fact that approximately equal numbers of loaded and empty trains pass over this site. Most of this traffic consisted of unit coal trains that traveled full in one direction and returned empty along the single mainline track. The differences between the measured static and dynamic wheel loads were not as severe at FAST. The relatively close agreement between the static and dynamic wheel loads at FAST was due to the test control and well maintained equipment at that site. For example, tread surface irregularities are regular- ly repaired at FAST, eliminating a major cause of high dynamic impact loads. In addition, the static wheel loads at FAST were very uniform for the consist used. On the basis of the data collected by BCL, the mean dynamic and static wheel loads for each of the sites were calculated according to methods des- cribed in Ref. [45]. These mean static and dynamic wheel loads are given in Table 17 for the revenue sites and FAST. 5.3 Load Distribution Methodology Selection of Wheel Loads Although the complete dynamic load distributions were defined for the sites, it would not be practical to determine the effect that the continuous load spectrum would have on the track structures. To simplify the continuous load distributions and reduce the number of computer analyses necessary, dyna- mic wheel loads corresponding to the 50, 10, 1 and 0.1 percent exceeded levels were chosen to represent the entire dynamic load distributions. The meaning of the 0.1 percent exceeded level, for example, is that only 1 out of 1000 loads will be greater than the specified value. The CDF corresponding to the 50, 10, 1 and 0.1 percent exceeded levels were 0.5, 0.9, 0.99 and 0.999, res- pectively. More rigorous methods have been suggested to represent the loadings for highway systems, but the chosen levels of exceedance are sufficient to ade- quately cover the range of expected dynamic wheel loads. Once these CDF values were chosen, it was necessary to determine the rela- tive frequencies of occurrence for these dynamic load levels. The method used was such that the midpoint loads between two values of the CDF were those loads corresponding to the 50, 10, 1 and 0.1 load levels. The CDF ranges for each load level were chosen such that the average CDF values corresponded to the se- lected values of 0.5, 0.9, 0.99 and 0.999. Thus, the difference between any two successive values of the CDF was used to represent the relative frequency of occurrence for the given dynamic load. The procedure used was as follows: 1) Begin at the upper limit of the CDF, where F (°°) = 1. 2) Calculate the next value of F (x- ) such that A -L F (oo) - F (x ) — 2 = °* 999 * (22) Note that F x (oo) - F x (x ) = ?(x ± <_ X ± £ «>) = f^*-^ where f (x ) = relative frequency of occurrence for the 0.1 percent ex- ceeded load, and X.. = dynamic wheel load at the 0.1 percent exceeded level. 83 H ■H O H o m cn oo cj\ C/J • • en • • • • • S o CM < oo o oo CM oo fa en cn CO ■s o ►J CO a •H fa a «* •a- cn (n rH N_/ vO sr 00 00 •-N s n 0) r* ■> CO d 13 "0 oo O a CO ■H o 00 o O m tfl M rH CN r*. CO • • • • • o CO o pj M m C3N CM m m ►J s 4J CJ o *a- cn cn rH CO 1 hJ CO •H CO 3 CO Q CO m r>- m O CN a 3 13 • • • • 1 CO CO m r^ m vO cu -3- CO CM rH 0} CO r-1 C o >> c a CO M TJ U c CO 3 ctJ •H VO • vO o a o «J r-» r^ o •H H rH rH /•-s <3> o O o rH 4J M m • «H ^ • • • ■ CO >» oo rH .-J (J CJ 1 00 H CO rH ■8 4J e CO fa 13 CO i-H TJ CO • o rH • o • o o rH o> •H o CO > rH o o • 4J cO h CO CO o iH m o> a) i CO o a cy» 4J fa X ?! W a fa 84 3) Calculate the next value of F (x ) such that F (x ) - F (x ) -^— - 2 = °'" ' (23) Note that F x (x ) - F x (x 2 ) = P(x 2 < X 2 <_ x ) - f x ( x 2 ) where f (x~) and X are the relative frequency of occurrence and dyna- mic wheel load for the 1 percent exceeded level. 4) Continue this process for CDF = 0.9 and 0.5. 5) Since 1 the remainder of the loads below the 50 percent exceeded level must be accounted for. To do this, calculate f (x ) such that X _) 4 f x (x 5 ) = 1-1 f(x.) , (25) i=l where f (x ) = relative frequency of loads less than the 50 percent ex- x j ceeded level. The dynamic load, X,.» is the load where the CDF has a value given by F (x ) - F (-oo) F x (x 5 ) = -^—2 -± = 0.091 , (26) where F (-oo) = 0. x This method is somewhat arbitrary, but the approach is rational and should approximately represent the mix of wheel loads. The dynamic loads for the 0.1, 1, 10 and 50 percent exceeded levels for the field sites and FAST, along with the relative frequencies calculated using the above outlined procedure, are given in Table 18. Number of Load Applications In order to relate laboratory repeated load tests to the traffic levels at the sites, it was necessary to convert MGT values to an equivalent number of cycles of load application. The dynamic records obtained from instrumented sec- tions of the FAST track were studied [46], and it was concluded that each axle pair in a truck acts nearly as a single load cycle for the ballast layer of the track support system. At greater depths, the stress distributions from the ad- jacent axles overlap sufficiently so that the four axles from adjacent wheel trucks represent a single load cycle. Therefore, two axles will be used to rep- resent a load cycle for the ballast layers and four axles to represent a single load cycle for the subgrade layers. Now 1 MGT equals 2 x 10^ kips, and the number of kips per axle equals twice the wheel load in kips. Thus the number of axles per MGT is 10 6 N = t^t > (27) a E(X) 85 where N = number of axles per MGT, and a E(X) = expected or mean value of the static wheel load distribution, in kips. The mean static wheel load (Table 17) was used rather than the mean dynamic load, since railroad tonnage records are based upon the actual weights of the cars. The train's axle load in tons is numerically equal to the wheel load in kips, assuming equal distribution of load on both wheels. Since the axle load acts on both rails, the number of wheels passing a particular location per MGT is the same as that calculated using Eq. 27. Based upon the previous conclusions regarding the number of axles per cy- cle for the ballast and subgrade layers, the conversion from MGT to number of load applications for the ballast is N \ = y" , (28) and for the subgrade is N s 4 where N, and N are the number of load applications per MGT for the ballast and subgrade layers. Using the mean static wheel load for the sites as given in Table 17, the equivalent numbers of load applications per MGT for the indivi- dual field sites were calculated. These results are summarized in Table 19. The distributions of the dynamic loads as previously calculated were used to define the mix of wheel loads at each of the sites. To determine the num- ber of axle loads of the prescribed magnitudes, the relative frequency for that load level, f (x.), is multiplied by the equivalent number of cycles per MGT, as given by n m = W N b • (30) for the ballast, and by N sl =£ x (x.) Ns , (31) for the subgrade. The equivalent number of load cycles per MGT, at the pre- scribed dynamic wheel loads, is given in Table 20 for both the ballast and subgrade layers. Again, note that the single wheel load in kips is equal to the axle load in tons. Multiple-Axle Loadings The GEOTRACK computer model, to be used later in analyzing the track per- formance, was modified during this program to handle multiple-axle loads. A four-axle loading condition, representing two adjacent wheel trucks, was used to represent the dynamic loadings at the field sites. Since it was unlikely that actual train loadings would consist of several wheel loads of the same magnitude occurring sequentially, the complete representation of dynamic track loadings was defined by combining three axles of the mean dynamic load with one axle from the individual values of representative dynamic loads. 86 Table 19. Number of Cycles per MGT for Ballast and Subgrade Leeds Lorraine Aberdeen FAST Ballast, N u 31000 28000 27000 17000 b Subgrade, N 16000 14000 13000 8000 Table 20. Number of Cycles per MGT at Prescribed Dynamic Wheel Loads for Ballast and Subgrade P (kips) 6.2 15.0 27.3 35.7 43.5 Leeds N b 5700 20000 5200 500 63 N s 2800 10000 2600 250 31 P (kips) 5.5 15.0 32.0 39.8 45.0 Lorraine N b 5200 18000 4700 460 57 N s 2600 9000 2300 230 28 P (kips) 8.2 18.7 34.2 46.2 75.0 Aberdeen N b 4900 17000 4400 430 54 N s 2400 8500 2200 220 27 P (kips) 8.9 32.8 38.3 40.5 48.0 FAST N b 3000 11000 2700 270 33 N s 1500 5300 1400 130 17 87 The equivalent track loadings for track sections having wood ties are shown in Fig. 29a. The mean dynamic wheel loads were used on three of the axles. The fourth axle load was based upon the wheel loads determined for the 50, 10, 1 and 0.1 percent exceeded levels. The variable wheel loadings were placed second in the sequence. The load positions shown in Fig. 29a were used for the Leeds wood and FAST 22 wood tie sections, but the magnitudes of the mean and variable dynamic loads differed as indicated in Table 18. The equivalent track loadings for the sites having concrete ties are shown in Fig. 29b. Again, the load sequence used was the same for all con- crete tie sections, although the magnitudes of the applied dynamic loads used did vary among the sites, according to Table 18. 88 I* ft t^. 1 o tH 1 *^ w 3 C* CO C o •H U cu 3 CO C/3 CU •H H (11 00 o M 3 CO (U •H CJ o o ti "^1 s o c I vO I iw f-4 C •H -H a) a tH a) 5 tH CU •o CU a X (U 4J c CU CJ leu " «*" o 1 p 1 o o ■ bO C •H -a CO o a e*S „ u rJ 1 — 1 CU H W H vO 1 s— ' .2 1 * H M O tJ U o CU a tH • O O CO H r ""* 1 o o st • c m CM tH tft O jH * G CU rH CO > C7* 3 i • C «H T3 (d o tH o m 4J W (T> m <* CNJ • co — *- ^ i-4 *o a\ in which case N. becomes N.*. The result is N J J N.* = 10 J r e* T (i) e lj - 1 (34) 4. The total cumulative strain after N. cycles of stress level i plus an additional N. applications of stress level j is then given by e (i+j) = E [1 + C log (N.* + N.)] . (35) The method is illustrated in Fig. 32 for a case with two load levels, the second of which is greater than the first. The procedure may be repeated for all other successive stress levels, and can even be used for returning to stress level i. For the field site predictions, the first cycle strains for the 50, 10, 1 and 0.1 percent exceeded load levels will be used, along with the prescribed number of cycles at each load level, as given in Chapter 5. However, for com- parison with the field measurements, the calculated strains are plotted as a function of the actual number of cycles (or MGT) , not the equivalent number of cycles used for the superpositions. 94 C •H ea O hJ "O CO a o •H •U u CU > TJ CU U o CU u u o o d (N CU tH CO H CO d ni a (1 ■H 43 Ml -i ■H o > P4 a) O ri ■H T3 rl IU hfl T3 n a 01 cfl x: 4J u on o ^v u • d (U •H > vy ■H 4-1 CO CO CU rH 3 CO iH pS CO > en 4J CU CJ T3 v^ [fl CU CU a) Q T3 CO C d CU ,C 13 CU rH 00 l-i n •H 3 cO 4-1 4-4 O •a CU o Pi d Q n CO CU 4-1 4-1 C/3 o 00 CO P>. o o o a\ CO r-» vO m r*-. r*. CM CM en CN CO CO CO iH CN CM CN CM CM CM O o o O o o o O o o O O O o o -3- v£> o CX\ >* r^. O o 00 C^ O r» O o «tf sr o o sf o CN CN- O iH 3- iH CN CU •u CU u iH CM CO CO m vO tH CM T3 CJ O d O o * CJ CU d d CU M n •H CU CO co cO T3 T3 •o u U CU CU u CU CU CU o jq J -J i-3 < CU 3 rH CO > CU CJ d CU u CU 4-1 CU 1-1 u o c M 98 - The standard deviation of the track settlement as referenced to the ini- tial baseline profiles is also given in Table 21. The standard deviation val- ues were computed from the variations between the initial baseline and the sub- sequent profiles, as supplied by BCL. These values were small, indicating little change in track roughness with settlement. Since the zero reference surveys at the Leeds sites and at Aberdeen were taken after some amount of traffic following maintenance, a correction had to be estimated to account for the missing initial settlements for these sites. Fortunately, the strain coils installed in the ballast at the Aberdeen site were monitored frequently during the first field site visit. These strain coils allowed a direct measurement of the amount of raise at the site and sub- sequent deformations. However, the strain coil measurements would probably give an overestimate of the ballast deformations throughout the entire track section. The reason is that a 13-in. depth of ballast was excavated and re- placed when the coils were installed. Although the ballast in the areas under the ties and in the cribs was compacted with a portable mechanical tamper, the replaced material may not have been as compact and stiff as the undisturbed ballast at locations without strain coils. The effects of this ballast distur- bance at the strain coil locations could have resulted in greater track settle- ment at these locations than at the remaining tie locations. The initial deformations that developed in the upper 13 in. of ballast at the Aberdeen site are shown in Fig. 33. The coils indicated a surface raise of about 0.1 in., followed by a rapid initial settlement. The reference zero survey was made 10 days after the surfacing. The ballast strain coils indica- ted that there had been about 0.20 in. of vertical deformation in the ballast since the surfacing due to the first 0.4 MGT traffic. Therefore, the BCL sur- veys had to be adjusted by this amount to correct for the missed initial defor- mations. The similarity between the trends of the corrected survey measurements and the bal^ajt strain measurements supported the conclusion that the subgrade and deeper Laxlast settlements could be neglected. The two Leeds sites did not have strain coils embedded in the ballast, so the corrections to the survey measurements at these sites were uncertain. The amount of initial settlement at these sites, where the raise was about 1-% in., could only be estimated. Data from FAST indicated that about .25 in. of set- tlement occurred after 0.3 MGT of traffic had passed over section 22 following a comparable raise. Based on this information, the correction to the Leeds survey measurements was estimated at 0.2 in. The actual survey data will be used for the Leeds sites, and the estimated corrections shown as an increase. Thus the survey measurements represent a lower bound to the actual track set- tlements. For the Leeds sites, the probable corrections for initial settle- ments were on the same order as the subsequent settlements over the remaining 18 months. The survey was done directly after maintenance at the Lorraine site. How- ever, an interval of over 30 MGT elapsed from the zero reference point to the first follow-up survey. Thus, the shape of the settlement curve could not be defined, even though the end points were known for this traffic interval. FAST Measurements Measurements of vertical track settlement at FAST section 22 were obtained from both embedded foundation instrumentation and track surveys. Details of the FAST 22 instrumentation used after the 1979 rebuild can be found in Ref. [54]. 99 a CO o +J 4-J •H C P 00 4J cu (1) c o a a T< % OS o c cu 3 cs •H > 4J 1-4 u c; CO o 3 < i t4 <0 O o o o CN ■fi CtJ cu •J a: O o M CU ^r* 1 "• ►J a (Q c cu cu 13 U CU o 0] e CO a O MGT 1.5 r b) FAST 22 Concrete 1.0 - 0.5 " MGT 100 100 Figure 34. Ballast and Subgrade Deformations from Instrumentation at FAST Section 22 after 1979 Rebuild 102 o a c o CD en CO cu ■U CO V-i CO CU CO G •H T3 CO o rJ CO !» I CU c o o 0) 6«S cr < u s-s CO c/ cr en -h t> co CM CO CH 1 X /— \ CO •H S CO cr a N— • ^^ T3 CO cd a o iH hJ ^ s.^ J2 G N C CU 4J CO cn on vO vO cn cn so vO cn cn so so cn *o cn vO cn vO cn vC cn vO cn vO cn vO en cn cn sO cn vO cn m cn sO cn sO cn cn cn so so o o o o o o o o O O o o O o o O o o o o o o O O CM lH sj- ao CM CM o CM CM CTi sr m CM o rH O CJ\ CM cn o H CM SO rH in CO rH m sO CM rH m -3" cn rH o cn rH CO -a- m a c o o rH rH o o o rH rH CM sj- Ln O ►H rH CM rH CM CM n rH rH rH rH r- a a CO O CM cn rH CM cn cn cn m CM CM VO CM CM CT\ cn in o vO cn sO cr> CM O cn o cn O cn o m m o vO o VO m CM n rH CO in >* 1! o o o o o o O o © o o o o o o o o O O o o o o o t: CI en en cn cn \D vO CM CM vO CM vO CM o •3- o m CM IT, CM CN] m Cvl o en O cn o cn o cn o cn o cn o o cn cn c o o o o O O O O o O o o o o o o o o o o o O o o a IT> rH CM 00 CM CM o vo rH CTi ON 0\ rH rH r -i rH CTi ON cn cn sr -J- >3- >* X rH rH 1 1 rH rH 1 1 CM CM 1 1 CM 1 CM CM 1 CM 1 CM 1 o\ cn l cn i cn 1 cn 1 CM 1 CM C--! CM 1 CM i CN! 1 CM CM 1 1 c c rH CT. 00 vO cn <■ cr. CM CTi H m H r*. o r>* cn r-«. CM CO cn m sO rH vO 1" CC CM vf vO 00 rH cn - r— cn cn <* m so c E o cn r»» m O cn r*» LH o o 00 O r>» CN CN| o 00 cn m O 00 cn m o CJ m r>» rH CM m cn cn >a- rH CM m cn cn -a- m rH CM m o> cn co rH cn ^3 CM cn 00 cn o 00 CM cn cn o 00 a a u O • vO o • o • 00 O • 00 m • m • ir. U >4-l O • m o • o • 00 CM • •u n cn cn en CO cu 4-> CO ccj cu CO c •H CO O hJ >, CO I cu C3 O CO < s^s a CO s>« «0| H-4 s! cr CO -H D co CM •-N -a CO cO 0- O •H hJ .* w x: c N C cu -MM CO CO CO CO CO vO vO v© \© CO v© CO O CO CO v© v© CO v© •© CO CO v© v© CO v© CO CO CO vO vO v© CO v£> vO CO CO vO vO CO CO vO v© CO CO v© v© O O O O o o O O o o O O o O O O O o O O o o o o rH r-» v© 00 v© 00 v© rH CM m o v© rH 00 r-l rH v© O 00 o 00 CO O 00 CO ON O o 00 •* vO CO 00 00 v© CM «Jf cm sr 00 rH OOHN O o rH rH rH «* v© r-- o rH rH CO CM CM co d- CN 00 ON CNl CM rH CO rH CO CO ON r-» o CO m -H CM O o CM O vO CM oo cm m CM rH m v© o m r- rH r-« co cm r>» m vo O rH CN CO o o O r-l O m On O rH O O rH CO rH m •>* r^ O rH iH CM CM v© rH m CM CO -st vO COON rH rH oo o H CM CO rH rH 00 H H CM CO rH rH o rH co m cm rH rH CM 00 CO 00 ON vo r^ (-* 00 o cnMn o ro r-» m O o 00 o r«. CM CM O 00 ro m o 00 CO m o in mo en rH CM CO «* m rH cn liO CO CO » r*. O m o O 00 CM • • • • • • CO CO 3. 3 /-"N CO Orf > C/3 1 W rH v -' V_ ' PQ PQ U U o o o H O a o O o o (•ux) uoT^Fuiaojaa a o •H 4J U cu c/d cu •H H o o CO X) cu CU u o •4-1 c CU E CU i-H •u a •H x) cu M P-. c CO d. CU B cu V-4 CO CO en cu 3 •H 109 cu > u 3 co XI CU •u o cu u U o c cu B (U )-l 3 U CO CO CU CU •H S Xi •H CO CO O ru a CU a cu M 3 CO cO cu a >^ CU > 3 en X) cu +j CU u u o a o >, >. /*-\ CO CO OS CO Pi CO S I 5 I CO CO H H w pq W M Q O Q U o 3 O •H •U o CU CO CU •H H CU O c o CJ CO X) -( H M-l o CO a o •H a •H xi cu P-i X c CO a cu e cu l-l 3 CO cO cu IS CO ro cu 3 00 •H fa (*UT) UOT3BUUOJ3a 110 o O o m o O o CM 0) G •H (0 M u O .J o c e u CD o to H o e o •H ■Ul u H O a o5 Ui 1 en en rH en v-x >— • s_y Ed . H « Q Q o a CD 05 M o ) 2 + (o - a ) 2 + (a - a ) 2 ] y . x z y z a «. + ^ t «. oct oct a 3 = G oct oct EQUIVALENT AXISSYMMETRIC STRESS STATES a ± = 27.6 a x = 27.0 a 3 =15.1 a 3 = 6.0 p = 21.4 q = 6.3 p - 16.5 q = 10.5 116 CO JZ u cd PU oa 0) eeds, Wood Lorraine 0.086 0.103 0.52 0.83 The assumed influence depths, h, of the recompacted zones were the same as the disturbed ballast depths used for the strain predictions. As can be seen from the measured track settlements shown in Figs. 37 and 39, the above values of settlement due to recompaction of the ballasts are of the same order of magnitude as the field settlement measurements. The mechanisms of ballast recompaction are the same as those affecting all aspects of track settlement. All of these mechanisms occur simultaneously, i.e., cyclic loading, vibration, and possible horizontal shearing at the tie- ballast interface. Individual contributing factors cannot be separated easily, then analyzed, and finally recombined in an additive manner. Ballast Degradation . Breakdown of the ballast particles will cause settle- ment because of a decrease in volume of the assembly of particles, similar to the effect of compaction. The causes of long-term ballast degradation can de- rive from several sources. Particle breakage from the high intergranular con- tact stresses is one source. The susceptibility of different ballasts to such breakdown is currently not well defined, nor are the effects that such degra- dation would have on track performance. Research is currently underway at 119 • UMass to investigate the breakdown potential for various ballasts, including some of the materials used at both the revenue sites and FAST, so that better performance evaluations of ballast can be made. Ballast degradation also can be affected by factors not associated with trattic loadings, such as chemical attack and weathering. These factors af- fect different ballasts in different ways. Freeze- thaw cycles, in areas prone to such seasonal variations, could also contribute to particle breakdown. Ice intrusion into the small fissures in individual ballast particles could lead to increased cracking and reduced particle strength. A completely frozen ballast condition, where the indivi- dual particles were "cemented," could lead to higher stresses in the formation and hence increased particle breakage. Subgrade Effects. The contribution of subgrade to the total track settle- ment was neglected in the predictions. The relationship between the strain coil measurements at Aberdeen and the agreement between the FAST track survev and predictions partially justified this simplification. Another reason why the subgrade contributions were not included was that the measured permanent strains from the laboratory tests done on the revenue site subgrade samples were inconsistent with either the measured or expected settlements. In some cases, the strains developed in subgrade samples under assumed representative triaxial stress conditions became very large after a relatively small number of load cycles. This may have been the result of in- correct representative stress paths, sample disturbance, the fact that the cyclic loading conditions were undrained, or a combination of all these ractors. The undrained loading condition is reasonable for representing the train loading effects, but continued cycling without allowing the dissipation of any excess pore pressure that might develop is not representative of the field con- ditions The trains do not pass continuously over the sites, but are spaced at relatively long intervals. This allows pore pressure dissipation to occur be- tween load- ngs, and hence decreasesthe resulting permanent deformations. The radial strain developments in the triaxial tests with constant lateral stress would also lead to larger axial deformations than anticipated in the field where the subgrade soils are greatly confined by the surrounding ground. The extrapolation of the triaxial test permanent strain data would have provided excessively large predicted values of subgrade deformation. This was particularly true for the Aberdeen site, where it was found that there were negligible subgrade contributions to the track settlement. The effects of par- tial or intermittent drainage, plane strain versus triaxial testing, and stress path effects on the subgrade deformation characteristics are areas that require further study. H Other subgrade conditions can, however, have a large influence on overall track performance. Factors such as subgrade consolidation under static embank- ment loads and subgrade movements from frost and moisture changes would be im- portant in regions having subsurface conditions susceptible to these mecha- nisms. Even after many hundreds of MGT, soil embankments may continue to set- tle by lateral creep induced by the repeated traffic loads, even though con- fined subgrades are stable. The Lorraine site, in particular, may be suscep- tible to this condition. For newly built track, subgrade compaction from the cyclic traffic loads can be significant. The increases in penetration resistance in the FAST sub- grade resulting from the first 400 MGT clearly showed densif ication 120 Subgrade penetration into the ballast when inadequate soil filters or no filters are used to prevent particle migration is clearly another source of settlement. However, the field sites involved in this study did not appear to involve this problem. 121 CHAPTER 8. SUMMARY AND CONCLUSIONS The objective of this portion of the concrete crosstie correlation study was the prediction of vertical track settlement at four field sites Since the track systems selected for analysis were in different geographical locations and subjected to different loading and environmental conditions, it ZH"!? to perform a complete ballast physical state assessment and sub- grade investigation of the track foundations present at each site h«l W% bal -? S \ Phy8iCa i f tatC8 W6re identified "sing the plate load test, till of r T Y f ' lateral tle PUSh teSt ' A ^i-tenance cycle, consis- ting of raising and tamping the ballast layer, was performed at each of the e r md the resulting changes in ballast conditions were measured. One of the primary effects of the track maintenance was a loosening and disturbance IL ^J, r TTt\ C ° mV T ed ^ Stable ballaSt layer ' The ballas t structure was disturbed both in the cribs and under the ties. The amount of disturbance Zcrlft ^ tb 1. am ° Unt ° f the raise « ^ was found that for trackbeds sub- jected to a significant raise, say 1.5 to 2 in., the physical states of the ballast immediately after the raise were approximately independent of ballast type and initial condition. " _ Samples of the ballast materials were recovered from the sites and sub- fro m 6 FA^ rePeate " i° ad triaXial teStlng - Addi tionally, a granite ballast from FAST was tested in triaxial repeated load conditions with and without shear stress reversals. Partial unloading and sequential application of re- peated loads were also considered. It was found that the resilient moduli values for full unloading of compressive vertical stresses could be correlated for^r XimUm b U k Stre f ° n the Sample ' Elther the lo 8- lo 8 or an arithmetic formulation could be used to relate the compressive resilient Young's modulus to the maximum bulk stress. For partial unloadings, however, the resilient modulus was ^igher than that measured- under full unloading, and was not unique- ly related to the maximum bulk stress on the sample. -», - lu B reSU ^ S from the shear ^ress reversal repeated load testing showed that the resilient moduli from extension and compression stress states were quite different. The extensional resilient moduli values were smaller than the congressional moduli values under comparable stress conditions. When the vertical stresses were cycled between compression and extension states, the total resilient moduli values fell between the extensional and compressive values. This is believed to more closely represent actual track conditions than prior techniques, which did not include shear stress reversals A comparison of the resilient moduli of all the field site ballasts also leads to the conclusion that the moduli values were not significantly depen- dent upon ballast type. The inelastic behavior of the ballast was investigated using the repeated load triaxial tests and a box-type testing device. The permanent strain beha- vior of single-staged, constant-amplitude tests without shear stress reversal could be defined by the first cycle strain, e and the material constant, C. This constant was independent of stress conditions for a particular bal- last, but was not the same for all ballasts. Staged tests on the ballast were done involving sequential application of variable magnitude repeated loads. For these tests, the total permanent strain developed in a ballast sample was controlled by the maximum past load and was independent of the loading sequence, so long as the number of load repetitions 122 at each stress level was the same for each of the tests. This means that the heaviest wheel loads, generally produced by impacts from wheel tread irregularities, cause most of the settlement. Subsequent applications of re- duced load as well as partial unloadings resulted in negligible increases in permanent strain. When the repeated loads in the triaxial tests were cycled between exten- sion and compression, the permanent strains developed at rates significantly greater than the rates for one-way loading. The increased permanent strain development was dependent upon both the compressive failure ratio and the ra- tio of cyclic shear stress to the maximum shear stress resulting from compres- sion loading. The permanent deformation accumulation in the ballast box tests, which were intended to simulate field behavior, was a logarithmic function of the number of load cycles, the compaction state, and the first cycle deforma- tions. The trends in inelastic behavior were similar to those in the triax- ial tests. The relationship between permanent deformation and the log of the number of cycles was similar to the trend of permanent deformation ob- served at FAST. The box tests also showed that relatively large horizontal residual stresses can build up in the ballast as a result of cyclic loadings. These residual stresses can develop not only under the tie, but also in the crib areas. This may be a mechanism in the phenomenon of tie migration or skew- ing. The horizontal stress measurements made in the ballast box suggested that the ballast layer in track is subjected to extreme variations in cyclic stresses. The unloaded stress states may be close to the limiting passive failure stress conditions. Measurements of vertical track modulus were made before and after the revenue site maintenance operations. The major factors contributing to the magnitude of vertical track modulus were ballast depth and subgrade stiff- ness. Track modulus measurements made in the track sections at Leeds having wood txes spaced at 19.5 in. and concrete ties spaced at 24 in. were not sig- nificantly different. The field measurements did not indicate significant changes in the magnitude of track modulus due to maintenance. Since the bal- last is always stiff relative to the subgrade and since the relative contri- bution of the ballast deformation to the overall elastic track deflection is small, this result may be expected. The field measurements did show, however, that the uniformity of the sup- port along the track was not improved as a result of the surfacings. Although the property of the ballast under individual ties was made more uniform because of the raising and tamping, as reflected by the plate load tests, the uniformity of contact between the ties and the ballast surface may not be improved. The GEOTRACK model, with the stress-dependent ballast modulus formula- tion and constant subgrade moduli determined for each of the sites, was used to predict track deflections and track moduli. The 6- to 30-kip wheel load intervals were used for the comparisons since the field measurements showed some initial slack in the tracks. The model predictions of vertical track deflection agreed well with, although they tended to underestimate, the field measurements. The original use of track modulus was to enable track designers and en- gineers to determine the load-carrying capacity of track in a reliable manner. With structural components such as concrete crossties and flexible tie pads of selectable stiffness, the value of the calculated track modulus may not be useful as a performance indicator if the assessment is based only on the 123 average magnitude of track modulus. The variability of track, modulus be- tween tie locations would be a more useful standard of track quality, since the variability would be a direct measure of the uniformity of the track sup- port, which is very important. The measured dynamic track loadings were used to characterize the mixed loading conditions for each of the field sites. The dynamic wheel load meas- urements and static wheel loads obtained from consist data showed that the mean static and dynamic loads were approximately equal for a given field site. The distribution of these loads was, however, quite different. The dynamic loads below the 10 percent level of exceedance were not significantly differ- ent from the static loads. However, above this level, the dynamic loads were much greater than the static loads for a given percent exceedance due to the impacts resulting from wheel tread irregularities. At the 0.1 percent exceedance levels, the dynamic wheel loads at Leeds, Lorraine, and FAST were similar, averaging 45.5 kips, with a maximum differ- ence of only 4.5 kips. However, the 0.1 percent exceedance load at Aberdeen was 75 kips. The very high dynamic loads measured at the Aberdeen section were 3 to 5 times greater than the mean dynamic load. These high wheel loads are the result of a combined effect of wheel tread irregularities and the high speeds of passenger trains. The loading environment at FAST was much more uniform that at the revenue sites, because of the controlled nature of the FAST experiments. While both the mean dynamic and static loads at FAST were on the order of 1.5 to 2 times the average values measured at the revenue sites, the low probability, large loads were 0.5 to 0.8 times the comparable loads at the revenue sites. A method was developed to convert MGT into an equivalent number of load cycles for the ballast and subgrade. The equivalent number of load cycles per MGT for the ballast ranged from 27,000 to 31,000 at the revenue sites and was about 17,000 at FAST. For the subgrade, the corresponding numbers of cy- cles per MGT are one-half the numbers in the ballast. Fielc measurements of vertical track settlement were made by BCL at each of the revenue sites. These measurements were made using optical survey tech- niques. The survey data from the Aberdeen site were supplemented by inductance- type strain coils installed in the ballast layer. Measurements of track set- tlement at FAST were obtained from both optical surveys and embedded instru- mentation. Estimates of initial settlement at the Leeds wood and concrete tie sections were necessary to account for the effects of about 0.5 MGT of traffic having passed over the newly surfaced test sections prior to the initial base- line surveys. The ballast strain coils at the Aberdeen site allowed an accu- rate correction to be applied to the baseline survey at that site. Permanent ballast strain data acquired using the inductance coils indica- ted that the total track vertical deformations at Aberdeen could be accounted for by the upper ballast deformation alone, even though only minimal distur- bance of the ballast occurred there. This leads to the conclusion that the zone of ballast that was disturbed by the maintenance operation was the pri- mary source of track settlement, and that the subgrade contribution could be neglected. The settlements at the Lorraine and Aberdeen sites continued to develop at what appeared to be a steady rate throughout the period of the measurements, after the initial traffic following maintenance. Although the total vertical settlements at all of the revenue sites continued to increase as MGT accumula- ted, the roughness of the track profiles did not increase. 124 The ballast deformations at FAST were found to be similar for both wood and concrete tie sections. This was true for the ballast measurements obtain- ed during the initial FAST experiments and for the ballast deformations fol- lowing the 1979 rebuild. The measurements of total track settlement and bal- last layer deformations in FAST section 22 tended to support the conclusion that the subgrade contributions to the track settlement could be neglected. The methodology to predict the inelastic or permanent settlement of the field track sections used GEOTRACK nonlinear stress analyses of the field site track sections with stress-dependent ballast properties, representative subgrade moduli, and multiple-axle combinations of the measured dynamic wheel loads. The predicted stresses from the computer analyses for each particular field site and loading condition were used, along with the permanent deforma- tion behavior of the ballasts from laboratory tests to estimate the resulting ballast strains. The mixed dynamic field loading conditions were accounted for by a formu- lation similar to Miner's rule for fatigue analysis. The type of strain su- perposition was justified based upon the results of the staged-test laboratory experiments. The settlement caused by the ballast was then determined as the product of the ballast strain and the depth of ballast disturbed by mainte- nance. The disturbed ballast depth was taken to be only 6 to 8 in. below the bottom of the tie for the maintained track sections. The contributions of the subgrade to the total track settlement were neglected. Although the general magnitudes of the predicted deformations agreed with the measured values, the shapes of the deformation versus MGT predicted results did not agree as well. This was particularly true for the revenue sites. Considering all of the sites, the settlement predictions made for FAST section 22 agreed best with the field measurements. This was probably a result of the more controlled track loading and test conditions present at FAST. The method used to determine the ballast strains incorporated two alter- native types of stress paths, one that matched the peak shear stresses and one that matched both the peak shear stresses and mean stress of a typical roaobed point. There were no distinct trends to indicate that either of the assumed stress paths based on the GEOTRACK calculations led to more consis- tent agreement between measured and predicted response. Uncertainties in both the first cycle strains and the representative stress paths could account for some of the differences between measured and predicted settlements. The results from the box test experiments indicated very small or negligible horizontal stress increases from load application, even in the top few inches of the ballast layer. Stress paths derived from these conditions would predict failure stress states in the ballast layer. In contrast, the high K values assigned to the ballast and the substantial increases in horizontal stresses in the upper ballast predicted by the GEO- TRACK model resulted in very different stress paths and non-failure condi- tions. Such uncertainties in the actual ballast stress path make accurate determination of the first cycle strains difficult. The actual representa- tive stress paths for the track ballast layers may be intermediate to the bounds created using the box test and GEOTRACK results. Deviations between measured and predicted track settlements could have resulted from other factors not considered in the methodology. One of the most important factors not included is thought to be settlement induced by vi- brations transmitted through the track superstructure to the ballast, as well as the extremely low probability, large loads encountered in revenue track. 125 - Other factors that can have varying degrees of influence on track settlement and performance include ballast degradation, environmental effects and sub- grade responses. Although these last three factors did not appear signifi- cant for the monitoring periods at the field sites investigated during this study, they could well be significant at other sites. 126 REFERENCES 1. Harrison, H.D., Dean, F.E., Selig, E.T. and Steward, H.E., Correlation of Concrete Tie Track Perfomrance in Revenue Service and at the Facility for Accelerated Service Testing , Federal Railroad Administration, Office of Research and Development, 1984, Report No. DOT/FRA/84/Q2.1 . 2. 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