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59 CHAPTER 6 Examination of LTPP Database for Indications of an Endurance Limit Introduction 2. Design procedures that use the equivalent temperature concept but the axle load distribution for each axle type-- Flexible pavements have traditionally been designed to These procedures also use the cumulative damage con- limit load-related cracking. The more traffic, the thicker the cept to determine the amount of fracture damage for each HMA layer to limit the load-related cracks to some design structure. The PerRoad Program would fall within this limit. As noted, however, industry has been proposing the category (63). use of an endurance limit as a mixture property for HMA 3. Design procedures that calculate and use pavement tem- layers. The endurance limit is defined as the tensile strain peratures at specific depths over some time interval, gener- below which no fracture or fatigue damage occurs and applies ally less than a month--These procedures typically use the to cracks that initiate at the bottom of the HMA layer. Almost incremental damage concept to determine the amount of all design and analysis procedures that use the endurance fracture damage within specific time intervals and at spe- limit concept assume that one value applies to all HMA mix- cific depths within the pavement structure. The MEPDG tures and temperatures. Values that have been used vary from would fall within this category (64). 65 to 120 ms. This section of the report has three objectives: discuss the The equivalent temperature concept simply defines one incorporation of the endurance limit design premise into temperature for which the annual or seasonal damage equals mechanistic-empirical based pavement design procedures, the cumulative damage determined at monthly or more fre- confirm the reality and values suggested for the endurance quent intervals. The equivalent temperature is used to estimate limit, and recommend field studies to support use of this con- the dynamic modulus for calculating the tensile strain at the cept in the MEPDG software. bottom of the HMA layer on an annual or seasonal basis. All M-E based design procedures, regardless of the group, use Miner's hypothesis to calculate fracture damage, and Including the Endurance assume that wheel-load-related alligator cracks initiate at the Limit Design Premise into bottom of the HMA layer and propagate to the surface with Mechanistic-Empirical-Based continued truck loadings, with the exception of the MEPDG. Pavement Design Procedures In addition, all M-E based design procedures use the max- All mechanistic-empirical pavement design procedures can imum tensile strain at the bottom of the HMA layer as the be grouped into three types relative to wheel-load-induced pavement response parameter for calculating fracture damage cracking. These are as follows: and predicting the amount of alligator cracks. Those design procedures apply the endurance limit design premise in one 1. Design procedures that use the equivalent axle load and of three methods, which are summarized as follows: equivalent temperature concepts--The equivalent tem- perature is determined based on an annual or monthly 1. The introduction of the endurance limit design premise basis. These procedures typically use the cumulative dam- into those design procedures that use the equivalent tem- age concept to determine the amount of fracture damage perature and equivalent axle load concepts is straight for- over the design period for each structure. The DAMA Pro- ward. Stated simply, the maximum tensile strain is cal- gram would fall within this category (62). culated at the equivalent temperature and axle load and

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60 Standard Mix; Conv. Low Modulus, Conv. High Modulus, Conv. Standard Mix, Full-Depth Endurance Limit 180 Tensile Strain, Bottom of HMA, 160 140 120 micro-strains 100 80 60 40 20 0 7 8 9 10 11 12 13 14 15 16 17 18 19 HMA Thickness, inches Figure 6.1. Tensile strains calculated for an 18-kip single-axle load for the equivalent annual temperature for different HMA mixtures. compared to the endurance limit. The HMA layer thickness with this method is that the higher loads result in signifi- is simply determined for which the maximum tensile strain cantly higher damage indices; an increase in axle load will equals or is less than the endurance limit. Figure 6.1 illus- result in an increase in damage to a power of about four. trates the use of the endurance limit within this method. Thus, the probability of cracking is much higher than the 2. The introduction of the endurance limit into those design probability of a specific tensile strain being exceeded. procedures that use the equivalent temperature concept 3. Those design procedures that use the incremental dam- but use the actual axle load distribution is also fairly age concept establish a threshold value for the tensile straight forward. The maximum tensile strain is calculated strain, below which the fracture damage is assumed to at the equivalent temperature for each axle load within the be zero. In other words, the procedure simply ignores axle load distribution. The axle load distribution for each calculated tensile strains that are equal to or less than the axle type is used to determine the probability of the tensile value set as the endurance limit for determining the incre- strain exceeding the endurance limit. The designer then mental damage within a specific time period and depth. considers that probability of exceeding that critical value Successive runs have been made with the MEPDG to deter- in designing an HMA layer for which no fatigue damage mine the difference in calculated fracture damage with and would accumulate over time. Figure 6.2 illustrates the use without using the endurance limit as an HMA mixture of the endurance limit within this method. One concern property. Figures 6.3 and 6.4 illustrate the increasing Standard Mix, Conv. Low Modulus, Conv. High Modulus, Conv. Standard Mix, Full-Depth 105 Endurance Limit (65 micro- Probability of Exceeding 100 95 strains), % 90 85 80 75 70 7 8 9 10 11 12 13 14 15 16 17 18 19 HMA Thickness, inches Figure 6.2. Probability of exceeding the endurance limit for different HMA mixtures using typical axle load distributions and seasonal temperatures.

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61 Summer, 250 ksi E=450 ksi E=650 ksi Winter, 900 ksi Endurance Limit 160 Tensile Strain, Bottom of HMA 140 Layer, micro-strains 120 100 80 60 40 20 0 6 16 26 36 Single Axle Load, kips Figure 6.3. Increasing tensile strains for varying single-axle loads for different seasons or dynamic modulus within those seasons (HMA thickness equals 15 in.). maximum tensile strains for varying single-axle loads for ing in the wheel paths is assumed to initiate at the surface and different dynamic modulus values and HMA thicknesses, propagate downward. The MEPDG assumes that both types respectively. of cracking are caused by load-induced tensile strains. That hypothesis, however, has yet to be confirmed. Version 0.9 of the MEPDG did not include the endurance As noted above, the new MEPDG uses an incremental dam- limit design premise in the recalibration process of the design age index. Fracture damage is computed on a grid basis with methodology or software. In other words, Version 0.9 assumes depth for each month within the analysis or design period. that any tensile strain in the HMA layer induces some fac- Temperatures are computed with the Integrated Climatic ture damage. Two types of load-related cracking are pre- Model at specific depth intervals for each hour of the day. dicted for designing flexible pavements in accordance with These temperatures are then grouped into five averages at the MEPDG--alligator cracking and longitudinal cracking in each depth interval for each month. The fatigue cracking the wheel path. Alligator cracking, the more common crack- (alligator cracking) equation is used to calculate the amount ing distress used in design, is assumed to initiate at the bottom of fracture damage for each depth interval and month. The of the HMA layer. These cracks propagate to the surface with monthly damage indices are then summed over time to predict continued fracture damage accumulation. Longitudinal crack- the area of fatigue cracking at each depth interval. 8-kip Load 14-kip Load 18-kip Load 22-kip Load 28-kip Load 34-kip Load Endurance Limit 300 Maximum Tensile Strain, 250 micro-strain 200 150 100 50 0 6 8 10 12 14 16 18 20 HMA Thickness, inches Figure 6.4. Increasing maximum tensile strains for varying single- axle loads for different HMA thicknesses (HMA dynamic modulus equals 450 ksi; equivalent annual modulus).