Top-Down Cracking of Hot-Mix Asphalt Layers: Models for Initiation and Propagation (2010) / Chapter Skim
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B-ii TABLE OF CONTENTS page TABLE OF CONTENTS ............................................................................................................ B-ii APPENDIX B DEVELOPMENT OF THE HMA-FM-BASED MODEL ...................................................B-1 B.1 Introduction ....................................................................................................................B-1 B.1.1 HMA Fracture Mechanics Model ........................................................................B-1 B.1.1.1 HMA fracture mechanics ...........................................................................B-1 B.1.1.2 HMA fracture mechanics-based crack growth simulator ..........................B-2 B.1.1.3 Energy ratio approach ................................................................................B-4 B.1.1.4 Modified energy ratio approach ................................................................B-5 B.1.1.5 Summary of existing HMA-FM model .....................................................B-6 B.1.2 Material Property Models ....................................................................................B-6 B.1.2.1 Binder aging model ...................................................................................B-7 B.1.2.2 Dynamic modulus model ...........................................................................B-7 B.1.2.3 Tensile strength model ...............................................................................B-8 B.1.2.4 Healing model ............................................................................................B-8 B.2 Development of Model Components ...........................................................................B-11 B.2.1 Material Property Model ....................................................................................B-11 B.2.1.1 AC stiffness (creep compliance)
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B-iii B.3.2.4 Model predictions without thermally induced damage ...........................B-46 B.3.2.5 Model predictions with thermally induced damage ................................B-48 B.4 Creep Compliance Master Curves from the SuperPave IDT .......................................B-52 B.5 Determination of Crack Initiation Time .......................................................................B-55 B.6 List of References ........................................................................................................B-59
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B-1 CHAPTER 2 DEVELOPMENT OF THE HMA-FM-BASED MODEL B.1 Introduction B.1.1 HMA Fracture Mechanics Model The continuing development of the HMA fracture mechanics (HMA-FM) model, which was determined to be necessary to include effects of aging, healing, and thermal stress on topdown cracking performance, represented a significant proportion of the effort of the researchers at the University of Florida (UF)
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B-2 Where, St is the tensile strength of the mixture. It has been shown that DCSEf is independent of mode of loading.
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B-3 the location(s) of possible crack initiation specified; (ii)
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B-4 Create model of structure and boundary conditions Numerical Analysis Obtain: σ, ε, u Calculate DCSE in critical zones from this load cycle (i.e. DCSE/cycle)
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B-5 Where, m and D1 are the creep compliance power law parameters (determined using SuperPave IDT creep compliance test at 10 °C) , and parameter A is a function of tensile strength St and tensile stress in the asphalt concrete pavement, which is expressed as follows: ( )
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B-7 B.1.2.1 Binder aging model Asphalt aging is sometimes quantified by change in binder viscosity, which is directly related to the prediction of dynamic modulus and the creep properties, as discussed below. The binder viscosity at mix/laydown condition (t = 0)
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B-8 developed by Witczak and Fonseca (30) is one of the most comprehensive mixture dynamic modulus models available today.
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B-9 controlled displacement crack growth testing in asphalt concrete mixes modified with various additives. They found an increase in work was required to open cracks after rest periods due to both relaxation in the uncracked body and chemical healing at the micro-crack and macro-crack interface.
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B-10 presents healing results at 20 °C for different applied DCSEs in the same mixture. Based on these results, they defined a healing rate hr, which can be expressed as ( )
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B-11 B.2 Development of Model Components The model components developed in this project included: material property models, pavement response models, and pavement fracture models. Detailed descriptions of each of the developments are summarized in the sections below: B.2.1 Material Property Model As can be seen from Section B.1 (Introduction)
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B-12 As an example, Figure 2-6 gives three predicted AC stiffness curves as a function of time (in days) , i.e., daily lowest, mean, and highest AC stiffness at surface of the pavement section of Washington D.C.
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B-13 0 50 100 150 200 250 300 350 1.5 2 2.5 3 3.5 4 t (day)
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B-14 an example, Figure 2-9 (c) shows the variation of AC tensile strength with age at the surface of the pavement section.
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B-17 0 2 4 6 8 10 0 10 20 30 40 50 Time (year)
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B-18 As a further step, possible improvements to this model for application in real pavement sections were investigated, which resulted in the development of a simplified empirically-based healing model for use in this research. A model based on laboratory healing tests As stated in Section B.1 (Introduction)
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B-19 As shown in the table, a constant healing period of 300 s was introduced between every 300 loading cycles. Each of the loading cycles was composed of 0.1 s of haversine loading and 0.9 s rest period.
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B-20 However, it is emphasized that this model may not be suitable for direct application in field conditions due to the following reasons: • Variation of hnr (i.e., healing rate) with age was not taken into account in the model.
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B-21 where, S(t,z) is the general expression for AC stiffness, and S(t)
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B-22 where, DCSEd_induced is the dissipated energy induced during the day, and DCSEd_remain is the dissipated energy remaining at the end of the day after healing, which can be obtained by rearranging Eqn (0-9) as follows, ( )
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B-23 The corresponding daily lowest stiffness Slow for five successive years (each year was started from July 1st) , after taking the effects of aging into account, are plotted in Figure 2-15.
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B-24 Yearly-based healing criterion In the daily-based healing criterion, the damage generated in any particular day will be healed only once during that day, after which no healing will be applied to remaining damage. This does not agree well with the observation from laboratory healing tests (32)
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B-25 model. A 9-kip circular load was applied repeatedly to the surface of a pavement to simulate the cyclic traffic load.
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B-26 where ( ') E ξ ξ− is the relaxation modulus at reduced time 'ξ ξ− ; and the reduced time ξ is: / Tt aξ = where Ta is the temperature shift factor.
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B-27 and longitudinal thermal stresses was caused by different boundary conditions to which the AC layer is subjected in these two directions: • The AC layer is subjected to a fixed boundary condition in the longitudinal direction, which can induce very high longitudinal thermal stresses, which are the main cause of thermal cracking. • However, the AC layer can move in the transverse direction once the maximum friction provided by the base is reached.
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B-28 In the crack initiation model, the load-associated damage and thermal-associated damage is obtained based on the pavement response models as follows, • The load-associated damage per cycle (or, DCSEL/cycle) is calculated as: ( )
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B-29 B.2.3.2 Crack growth model The crack growth model was developed on the basis of a two-dimensional (2-D) displacement discontinuity boundary element (DDBE)
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B-30 • Potential crack path: The potential crack path was predefined in front of the crack tip at the beginning of crack growth simulation. It was composed of a series of zones of constant length heading toward the bottom of the AC layer.
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B-31 B.3 Integration of Model Components B.3.1 Integration of Healing Model The material healing model was integrated into the performance model by determining the two critical values for daily lowest AC stiffness on the basis of a full-scale test conducted in the FDOT's APT facility using the HVS. B.3.1.1 Background of experiments for evaluating healing effect Since Accelerated Pavement Testing (APT)
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B-32 (testing track 1) composed of a dense-graded mixture on limestone base and sand subgrade was divided into three test sections: 1A, 1B, and 1C.
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B-33 (i.e., only slightly aged)
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B-34 Table 2-32. IDT test results (at 10°C)
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B-35 B.3.1.3 Model predictions without healing Stage one: crack initiation When healing effect was not considered, the predicted load passes to induce crack initiation for the aged and unaged sections are given in Figure 2-21. As seen in the figure, predicted number of loads to cracking for the unaged section was only about 41,700, which was much less than the 128,300 loads for the aged section.
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B-36 02/06 02/08 02/10 02/12 02/14 02/16 02/18 02/20 02/22 02/24 0 0.2 0.4 0.6 0.8 1 1.2 D C S E no rm Time (mm/dd) Aged Unaged Figure 2-22.
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B-37 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 0 50 100 150 200 250 300 350 Load repetition ( x 103 )
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B-38 B.3.1.4 Determination of critical values for daily lowest AC stiffness In order to determine these two critical values Scr1 and Scr2, the daily lowest AC stiffness curves in the aged and unaged sections are plotted in Figures 2-25 and 2-26, respectively. As shown, the stiffnesses of the aged section are much higher than the unaged section.
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B-39 the definitions of healing zones, the Slow values for this section should be close to Scr1. As a result, Scr1 was selected to be 320 ksi (see Figure 2-26)
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B-40 passes of 140,000 when the first crack was observed. The predictions in Figure 2-28 show the same trend: crack occurred in the aged section after about 12 days, and no crack occurred in the unaged section.
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B-41 Stage two: crack propagation Performance predictions accounting for healing were continued in the crack propagation stage. As shown in Figure 2-29, the crack in the aged section reached the critical crack depth after 296,600 passes of HVS loading.
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B-42 -0.25 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 0 5 10 15 20 25 30 Time (day)
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B-43 A limited investigation indicated that thermal damage induced in pavement sections subjected to a non-freeze climate as that of Florida was not high enough to alter the predicted top-down cracking performance of these sections. Therefore, a freeze-thaw climate as that of Washington, D.C., was selected to demonstrate the importance of including the thermal response model.
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B-44 The variation of asphalt concrete (AC) modulus with time was estimated using the AC stiffness (creep compliance)
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B-45 0 50 100 150 200 250 300 350 -10 0 10 20 30 40 50 time (days)
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B-47 Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 0 0.2 0.4 0.6 0.8 1 1.2 Damage accumulation at Yr12 D C S E no rm Time (month) Figure 2-35.
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B-48 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 Time (year)
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B-49 0 100 200 300 400 0 2 4 6 8 10 σT at Yr10 ( z = 0" )
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B-50 Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 0 0.2 0.4 0.6 0.8 1 1.2 Damage accumulation at Yr10 D C S E no rm Time (mon) Figure 2-38.
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B-51 cracking in this pavement. Clearly, the thermal effect cannot be ignored for accurate prediction of crack initiation.
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B-52 that the FE limit (DCSE limit) aging model played an important role in determining the time of crack initiation and the average crack grow rate.
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B-53 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5000 10000 15000 20000 25000 30000 D (1 /G pa )
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B-54 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 5000 10000 15000 20000 25000 30000 D (1 /G pa )
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B-55 B.5 Determination of Crack Initiation Time The crack initiation time for each of the eleven Florida sections (see Table 2-38) was determined on the basis of crack rating history (see Figures 2-46 to 2-51)
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B-56 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 C ra ck R at in g Time (year) I75-1A I75-1B Crack Initiation at Year 12 Crack Initiation at Year 10 Figure 2-46.
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B-57 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 C ra ck R at in g Time (year) SR80-1 SR80-2 Crack Initiation at Year 13 Crack Initiation at Year 22 (linear extrapolation)
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B-58 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 C ra ck R at in g Time (year) SR471 SR19 Due to resurfacing, crack rating returned to 10 (at Year 4)
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B-59 B.6 List of References 1. Zhang, Z., R
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B-60 11. Button, J
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B-61 22. Sangpetngam, B
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