Construction and Building Materials 43 (2013) 184–190
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UGR-FACT test for the study of fatigue cracking in bituminous mixes F. Moreno-Navarro, M.C. Rubio-Gámez ⇑ Construction Engineering Laboratory of the University of Granada, Granada, Spain
h i g h l i g h t s " UGR-FACT is a new test to analyze fatigue cracking in bituminous mixes. " The dispositive has been designed specifically as well as a test procedure. " The test simulates the loads sustained by a real pavement. " It induces a fatigue cracking process (crack initiation, propagation, and failure). " The test device is easy to reproduce at a low economic cost.
a r t i c l e
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Article history: Received 26 December 2012 Received in revised form 18 February 2013 Accepted 19 February 2013 Available online 15 March 2013 Keywords: Laboratory test Bituminous mixtures Fatigue cracking Mix design Dissipated energy
a b s t r a c t Fatigue cracking in bituminous mixes is one of the most common pathologies that affect roads all over the world. The improvement of the laboratory test methods used in their design is crucial to prolong the service life of pavements. This article describes a test method that simulates the stresses caused by fatigue cracking in pavements. The UGR-FACT Test, based on a device that produces controlled fatigue cracking process, makes possible to analyze the cracking propagation in the different phases (initiation, progression, and failure). The study of the material is performed in a representative volume, controlling horizontal and vertical deformations produced in the immediate proximity of the crack, after the application of each loading cycle. The energy dissipated by the material is analyzed to avoid the problems associated with the three-dimensional dispersion and randomness of fatigue cracking. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Fatigue cracking is one of most common pathologies in pavements all over the world and one of the main factors conducive to the end of the service life of a road. The appearance of fatigue cracking is mainly due to two deterioration mechanisms: traffic loading and the action of thermal gradients [1]. The medium and long-term consequences of this pathology can be extremely negative from a structural perspective (bad load transfers that eventually lead to deformations and shear failure; penetration of moisture and of other chemical agents that cause potholes, peeling, washing of fines, reduced bearing capacity, etc.). Fatigue cracking can also significantly reduce user comfort as well as safety (an uneven pavement surface makes driving more risky, increases noise level, and reduces tire friction) [1]. Despite the many studies on fatigue cracking, nowadays it is still a priority in road engineering research and particularly in ⇑ Corresponding author. Tel.: +34 958249443/445; fax: +34 958246138. E-mail addresses:
[email protected] (F. Moreno-Navarro),
[email protected] (M.C. Rubio-Gámez). 0950-0618/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2013.02.024
the design of bituminous mixes [2–4]. Currently, there are different tests used to evaluate fatigue cracking [5,6], but none of these tests is universally used as a standard. In contrast to other pavement pathologies such as rutting and pathologies caused by water action, there is not a common reference test to evaluate fatigue cracking in asphalt mixtures. On the one hand, the load conditions applied in certain tests do not correspond to the actual loads that the pavement must sustain during its service life (the majority of these tests only evaluate fatigue without specifically focusing on cracking, and do not use suitable geometries or loading and test conditions). Consequently, it is difficult to ascertain the real response of the material to this phenomenon, based on the test results. On the other hand, tests that are based on more realistic loading conditions are more sophisticated (in terms of load application, instrumentation, specimen manufacturing, etc.) and often very expensive (which prevents them from being widely applied to mix design). Although these tests lead to interesting one-off laboratory studies, the results obtained cannot be compared to those of other mixes elaborated under the same conditions in other research centers.
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Fig. 1. (a) Stresses due to the action of traffic loads [1]. (b) Weak point where fatigue cracking processes are most likely to occur in the wearing course [7].
Despite the fact that traffic loading is the most important design parameter for any bituminous mix (given that it is the main source of loads to be sustained by the pavement), there is no a standard test method that evaluates the mechanical performance of bituminous mixes in regards to this phenomenon. Consequently, in order to more effectively combat fatigue cracking, a simple, low-cost laboratory test would be very useful. This test should be capable of specifying general design criteria that guarantee the resistance of the pavement to cracking. For this purpose, an alternative test method was developed at the University of Granada, Spain (UGR-FACT, University of Granada – Fatigue Asphalt Cracking Test). This method tries to adapt the fatigue conditions generated by traffic loads, which lead to the appearance of fatigue cracking in pavements. The test device designed permits the initiation and propagation of a controlled fatigue cracking process. By studying a representative volume of the bituminous mix (in which the cracking occurs) and analyzing the energy dissipated during the process, this test method is able to accurately evaluate the damage produced as well as the mechanical performance of the mix. This means that it could be a useful tool for the improvement of mix design. On the other hand, the test method is able to control the cracking process in a representative volume by avoiding the problems of randomness and tridimensional dispersion of the phenomenon, which constitute a significant advantage to study the cracking process. Furthermore, the test device is easily adapted to any dynamic press, simple to operate, and from a technical viewpoint, it is easy to reproduce. The test specimens used are easily manufactured and manipulated during the test, their composition is homogeneous, and the test device is capable of evaluating both simple and compound materials of variable dimensions. This paper describes this test, by defining its main characteristics (i.e. the device developed, its geometry, and the calculation method). An example is also provided that analyzes the fatigue cracking behavior in two different types of bituminous mix (to explain how this test method is applied and the repeatability of its results).
2. Test development 2.1. Previous considerations The repeated passing of vehicles (which produce bending and shear stresses), along with the leverage effect generated by stresses due to temperature variation, triggers a fatigue process that
eventually leads to the appearance and propagation of cracks in the pavement (Fig. 1a, [1,7]). Moreover, defects in the lower pavement layers (such as thermal contraction cracks or potholes caused by failures in the bearing capacity of the aggregate base) or the presence of dilatation joints or pre-cracks (used to mitigate and control the appearance of cracks), create weak points where the stresses caused by traffic loads are more intense. As a result, the fatigue process at these critical points advances more rapidly, and as a result, they are generally the location where cracking begins to occur (Fig. 1b) [7]. The fatigue cracking processing in a bituminous mix initially begins with tiny micro-cracks that gradually spread and interconnect (meso-cracking) until they generate a dominant failure surface that finally propagates throughout the material (i.e. clearly visible macro-cracking) [8,9]. One of the difficulties of studying fatigue cracking is that the distribution of micro- and meso-cracks in the volume of the material where the process takes place, is random and dispersed in three dimensions [9]. The design of a laboratory test to evaluate the performance of bituminous mixes in regards to fatigue cracking due to traffic loading should be based on these considerations. In this sense, the test should be capable of adapting the stresses to be applied and of simulating the most unfavorable situations for the pavement. Furthermore, the test method should be able to evaluate the mechanical performance of the material during all of the phases of the cracking process. Finally, the geometry of the test should permit the study of bituminous mixes in specimens that are simple to manufacture, and the time consumed during the test should not be very long. Even more important, however, the test should be easily replicable at a low economic cost to permit its use in other research centers.
2.2. Description of the test device and characteristics Based on the previous considerations, a test device was designed that induces a controlled fatigue cracking process on a test specimen by simulating the stresses that the bituminous mix will have to sustain during its service life. The device is composed of a base (Fig. 2a), two sliding supports (Fig. 2b) and a load application plate (Fig. 2c). The base has a platform which is composed of two sloping surfaces and two rails that allow the sliding supports to change position without any pitching or residual movement (which could lead to errors in deformation measurements). These sliding elements are composed of two ball carriages that are adapted to the shape of the rails at the base (thus minimizing friction and leading to effective load transmission). On their
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Fig. 2. The test device from different perspectives.
surface are two support plates to which the test specimen is attached with epoxy resin. Furthermore, the horizontal supports have two auxiliary elements (one on each side) where the horizontal deformation gauges (LVDT) are located (Fig. 2g). It is also composed of two vertical spindles that are used to measure vertical deformations in the upper part of the test specimen with linear variable differential transformers or LVDTs (Fig. 2f). The distance between the sliding supports can vary, depending on the type of deterioration that is reproduced. It is thus possible to evaluate pavements in which the base layer is characterized by a certain discontinuity (e.g. a crack, pre-crack, or a dilatation joint) or pavements with important defects in the base (e.g. a pothole or patch). These separation distances are established with a system of bolts that fix the position of the carriages during the time that the test specimen is attached to them before the experiment is actually performed (Fig. 2d). Finally, the head of the load application is independent of the body of the device, which is attached to the upper part or crossbar of the press. It is composed of a piece of steel that is thick enough to prevent deformations during the load application (thus avoiding differential errors due to its own deformation and which are not related to the test specimen). It also provides a flat surface for the vertical deformation gauges (Fig. 2f). The simple geometry of the test device is capable of generating horizontal as well as vertical deformations in the test specimen. This reproduces the bending and shear stresses due to traffic loading (Fig. 2e) as well as tensile strains, thanks to the weight of the support elements, which simulate the leverage effect of thermal contractions (Fig. 3). It also simulates the different states of the pavement in which there is a point where cracks are most likely to appear (e.g. potholes, pre-cracks, dilatation joints). The UGR-FACT is performed at a controlled temperature inside a climate chamber. This makes it possible to evaluate the response
of the material to different visco-elastic or elastic states by applying stress-controlled, vertical cyclic loading in versed sine on prismatic test specimens of adaptable dimensions. The parameters (load amplitude, frequency, and rest periods) and test conditions (test temperature and distance between supports) can also be varied, depending on the evaluation of mix performance. The test ends when the macro-crack propagates throughout the entire specimen (failure cycle, Nf). This causes its failure and fractures it into two sections (Fig. 2). Alternatively, the test also ends when the number of loading cycles reaches 2,000,000. In that case, the limit of the material’s resistance to fatigue cracking is assumed to exceed the loading value applied. During each loading cycle, besides the load applied, the device records horizontal deformations (in the lower section of the specimen) and vertical deformations (in the upper section of the specimen). These deformations occur in the area near the stressed zone where the crack will develop and spread. These deformations are measured on both sides of the test specimen so as to obtain the mean deformation value of the representative volume studied (Fig. 4). Furthermore, measurements are also obtained of the phase angle between the applied load and the deformation as well as the number of loading cycles and the time employed in each one. Based on the values recorded, it is possible to determine the energy dissipated by the material in the volume studied (by calculating the area inside the load–displacement curve obtained from the charge and discharge in each cycle, using calculation software). The resulting measurement is quite accurate, thanks to the fact that the device controls the deformations in all directions. Material fatigue theory based on energy dissipation concepts (due to the hysteresis of the material) is then applied [10–13]. This leads to a more precise evaluation of the evolution of the damage produced in the material during the cracking process (controlling its randomness and three-dimensional distribution, Fig. 4). In this way,
Fig. 3. Stress simulation in the test specimen.
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Fig. 4. Process of fatigue cracking in the test specimen.
the test developed provides detailed information as well as a complete analysis of the cracking process. 2.3. Evaluation of cracking behavior based on the study of the dissipated energy By analyzing the number of cycles in the cracking process, the UGR-FACT could provide a tool to design more resistant mixes and to ascertain which mixes are less prone to cracking or those in which cracks are slower to propagate. Based on the test conditions (load amplitude, frequency, temperature, etc.), it is possible to evaluate the fatigue life (Nf, establishing the fatigue cracking limit of each material [14,15]) and mix’s degree of ductility and tenacity (factors that directly affect crack propagation speed). Furthermore, the analysis of the dissipated energy can offer an accurate measure of the damage associated to the cracking process in the material studied.
Given that UGR-FACT analyzes horizontal as well as vertical displacements on both sides of the specimen, an overall measurement can be obtained of the dissipated energy in the study volume. This provides a more precise evaluation of the damage in the material. Thus, the total dissipated energy of the system in each load cycle is calculated as the energy dissipated horizontally as well as vertically by the following equation:
xi ¼ xhi þ xv i
ð1Þ
where xi is the dissipated energy in cycle i (in J/m3), xhi is the horizontally dissipated energy in cycle i (in J/m3) and xvi is the vertically dissipated energy in cycle i (in J/m3). The greater the quantity of energy dissipated by the bituminous mix, the greater the damage produced in the test specimen. In other words, for the same level of damage, a more resistant material will dissipate more energy since it will need to use a greater amount of energy to reach that level of damage. Nevertheless,
Fig. 5. Dissipated energy and RDEC curves.
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Table 1 Characteristics of the mixes and the testing protocol. Mix type
AC Ophite
AC Limestone
Characteristics
Bitumen 40/50 Ophite 4.9 4.1 2.494 2
Bitumen 40/50 Limestone 4.4 4.7 2.485 2
Binder Aggregate composition Bitumen (%) Air voids (%) Density (g/cm3) Testing protocol No. of test specimens per loading step Load amplitude (kN) Frequency (Hz) Distance between supports (mm) Temperature (°C)
0.5; 1.0; 1.5; 2.0 0.5; 1.0; 1.5; 2.0 5 5 50 50 20
20
patterns (the growth of the crack can be larger or smaller and cause more or less damage). In this sense, the RDEC graph shows how the dissipated energy increases from one cycle to another. Nevertheless, this increase is not steady, but is sometimes greater or smaller. Using this concept, a more accurate way of quantifying the evolution of the cracking in the material during the test could be done by the representation of the cumulative RDEC (Eq. (3)). As a result, this research proposes a mean damage parameter (c) for the cracking process of each mix (Eq. (4)), which is defined by the total cumulative RDEC in the test divided by the number of cycles in the cracking process (Nf).
Cumulative RDEC ¼
Nf X
RDECi
ð3Þ
i¼1
the dissipated energy in a cycle depends on the dissipated energy in previous loading cycles, and is thus dependent on its loading history. Consequently, any damaged material is also characterized by a corresponding change in dissipated energy [12]. In fact, only the relative quantity of dissipated energy created by each additional loading cycle, excluding the dissipated energy associated with passive behaviors such as plastic deformation and thermal energy, will produce further damage [16]. Because of this, it is necessary to use the ratio of dissipated energy change (RDEC) (Eq. (2)) [16–18] to analyze the evolution and real quantification of crack damage in the mix.
RDECnþ1 ¼
xnþ1 xn xn
ð2Þ
where xn is the energy dissipation produced in loading cycle n (in J/ m3); and xn+1 is the energy dissipation in loading cycle n + 1 (in J/ m3). This parameter eliminates the energy that dissipates in other form without producing damage in the mix (the energy dissipated through passive behavior such as thermal energy). This provides a good indicator of the cracking damage produced from one loading cycle to another. A comparison of the graphs of energy dissipation and the RDEC per cycle (Fig. 5) shows how in both, there is a growing tendency that is accentuated when the macro-crack is produced (the results showed in this figure were obtained in a real UGR-FACT test). However, the values obtained in the RDEC correspond more closely to the real behavior of cracking processes. As shown in previous studies [19,20], cracks in bituminous mixes grow in a discontinuous (stepwise) manner and in different
c¼
Cumulative RDEC Nf
ð4Þ
3. Experimental study The objective of this section is to describe how the test method is applied as well as the type of results that can be obtained from it. For this purpose, the materials and testing protocol used during the study are described. Subsequently, the results obtained are analyzed, and the fatigue cracking behavior of the material is evaluated. Furthermore, the repeatability of the test obtained under the different conditions is shown. 3.1. Materials and testing program This study analyzed the behavior of two AC bituminous mixes (Standard EN 13108-1) with very similar characteristics. Both had a continuous coarse grain size, and a bitumen content of approximately 4.7% of the total weight of the mix, and only differed in the nature of the coarse aggregate (Table 1). The set of specimens manufactured with each mix were made from the same mass to guarantee their homogeneity. Each mass was divided into different parts, which were then compacted in the laboratory with a roller segment compactor (as specified in Standard EN 12697-33) in order to obtain prism-shaped specimens (408 256 60 mm). The dimensions of the final test specimens (200 60 60 mm) were obtained by sawing these prism-shaped specimens and previously eliminating their edges to avoid possible imperfections. Table 1 shows the test protocol followed to evaluate both mixes and analyzes their cracking behavior at different load amplitudes. Two specimens were tested at each level. 3.2. Analysis of the results The results obtained in the different tests, in terms of failure cycle and cumulative dissipated energy at the end of the test (x, Eq. (5)), are shown in the Table 2. As can be observed, the repeatability of the test under the different conditions is
Table 2 Results and repeatability of the UGR-FACT test. Load (kN)
Frequency (Hz)
Temperature (°C)
Parameter
Specimen 1
Specimen 2
Mean
Standard deviation
% Deviation from mean
AC Ophite 2.0
5
20
Nf
2160 17,646.88 8285 39,029.67 35,200 67,604.22 2,000,000 –
1455 15,882.43 7175 36,875.87 33,805 81,683.19 2,000,000 –
1808 16,765 7730 37,953 34,503 74,644 – –
498.51 1247.65 784.88 1522.97 986.41 9955.34 – –
27.58 7.44 10.15 4.01 2.86 13.33 – –
455 8197.90 1395 8203.03 17,960 26173.50 67,475 82,625.04
515 6977.31 1230 10,649.34 17,105 24844.10 75,715 74,191.90
485 7588 1312 9426 17,532 25,509 71,595 78,408
42.42 863.09 116.67 1729.80 604.58 940.03 5826.56 5963.13
8.75 11.37 8,89 18.35 3.45 3.68 8.14 7.61
x (J/m3) 1.5
5
20
Nf
x (J/m3) 1.0
5
20
Nf
x (J/m3) 0.5
5
20
Nf
x (J/m3) AC Limestone 2.0 5
20
Nf
x (J/m3) 1.5
5
20
Nf
x (J/m3) 1.0
5
20
Nf
x (J/m3) 0.5
5
20
Nf
x (J/m3)
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Fig. 6. (a) Fatigue cracking endurance limit and (b) mean damage parameter.
Fig. 7. Cumulative RDEC.
within the range of accuracy to consider that the results offered by the UGR-FACT are stables. Although more tests are carrying out to study its precision, the UGRFACT can be considered as a trustable test to evaluate the fatigue cracking behavior of asphalt mixes.
x¼
Nf X
xi
Finally, the mean damage parameter (c) obtained in the UGR-FACT can offer an accurate way to assess the fatigue cracking design of asphalt mixes. As can be observed the cracking damage grows exponentially with the load. Fig. 6b shows that for the same load amplitude, the cracking damage in the AC Limestone mixture is higher than the damage in the AC Ophite mix. Nevertheless, as the load amplitude decreases, the amount of cracking damage in the mixes became more similar.
ð5Þ
i¼1
4. Conclusions where x is the cumulative dissipated energy (J/m3) in the test. Results show that the AC Ophite mix performed better than the AC Limestone mix. The conventional phenomenological analysis based on the values of the Nf cycle (Fig. 6a) shows that the fatigue cracking limit of the AC Ophite mix (next to 0.5 kN) is higher than that of the AC Limestone mix (next to 0.25 kN). For the same test conditions, the cumulative dissipated energy is higher in the AC Ophite than in the AC Limestone. Consequently, more energy is required to induce the fatigue cracking failure of the AC Ophite. The mean values of the cumulative RDEC obtained under the different tests conditions appear in Fig. 7. For the same load amplitude, the cracking damage in the AC Limestone mixture propagates faster than in the AC Ophite mix. This is an evidence that the AC Ophite has a slower fatigue cracking propagation speed.
This paper describes a laboratory test method, UGR-FACT, developed at the University of Granada (Spain) for the evaluation of fatigue cracking in asphalt mixes. The initial sections of the article describe the general characteristics of the test, the device used to apply it, and the evaluation of the results. Moreover, as an example of the implementation of the test method, the paper also include the results of the analysis of the fatigue cracking behavior of two bituminous mixes. The main conclusions that can be derived from this study are the following:
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The testing device designed simulates the loads sustained by an actual pavement. It induces a controlled fatigue cracking process (crack initiation, propagation, and failure) in a test specimen manufactured with the bituminous mix. The geometry of the test device is easy to reproduce at a low economic cost (which means that it can be used in different research centers) and permits the study and design of materials with test specimens that are relatively simple to manufacture. By studying the cracking process in a representative volume of the material, the test provides an effective solution for the problems associated with the dispersion and randomness of fatigue cracking. The use of dissipated energy concepts in material fatigue processes establishes a series of parameters that accurately define the mechanical performance of a bituminous mix in relation to fatigue cracking. The parameters specified in this test method reflect the damage caused in the materials evaluated. The homogeneity and repeatability of the results is within the range of accuracy for the evaluation of fatigue cracking damage in bituminous mixes.
Although the UGR-FACT test method is currently in the process of being improved and refined, the results presented in this paper reflect its potential value as a tool in the evaluation of fatigue cracking. References [1] Colombier, G. Cracking in pavements: nature and origin of cracks. In: Vanelstraete A, Franckien L, editors. Prevention of reflective cracking in pavements – RILEM report 18; 1997, p. 1–15. [2] Pérez-Jiménez F, Valdés GA, Botella R, Miró R, Martínez A. Approach to fatigue performance using Fenix test for asphalt mixtures. Constr Build Mater 2012;26:372–80. [3] Botella R, Pérez-Jiménez F, Miró R. Application of a strain sweep test to asses fatigue behavior of asphalt binders. Constr Build Mater 2012;36:906–12. [4] Zhi S, Gun WW, Hui LX, Bo T. Evaluation of fatigue crack behavior in asphalt concrete pavements with different polymers modifiers. Constr Build Mater 2012;27:117–25.
[5] Hajj E, Sebaaly P, Loria L. Reflective cracking of flexible pavements. Phase II: Review of analysis models and evaluation test. Research report no. 13JF-1. Nevada: University of Nevada Reno; 2008. [6] García Carretero J. Procedimientos de Estudio en laboratorio. Jornadas sobre Reflexión de Grietas en Carreteras. CEDEX, Madrid: Centro de Estudios y Experimentación de Obras Públicas; 1992. [7] Zamora-Barraza D, Calzada-Pérez MA, Castro-Fresno D, Vega-Zamanillo A. Evaluation of anti-reflective cracking systems using geosynthetics in the interlayer zone. Geotextiles and Geomembranes 2010;29:130–6Thom N. Principles of pavement engineering. Thomas Telford Ltd.; 2008. p. 470. [8] Florence C, Étude experimentale de la fissuration reflective et la modelisation de la resistance de structures cellulaires. Ph.D. thesis. École National des Ponts et Chaussées; 2005. [9] Jenq YS, Perng JD. Analysis of crack propagation in asphalt concrete using cohesive crack model. Transportation Research Board, National Research Council, Transportation Research Record 1317; 1991. p. 90–99. [10] Li Q, Lee HJ, Kim TW. A simple fatigue performance model of asphalt mixtures based on fracture energy. Constr Build Mater 2012;27:605–11. [11] Pronk AC, Hopman PC. Energy dissipation: The leading factor of fatigue. In: Proc., conf. of the United States strategic highway research: sharing the benefits. Thomas Telford, London; 1991. p. 255–67. [12] Ghuzlan K. Fatigue damage analysis in asphalt concrete mixtures based upon dissipated energy concepts. Ph.D. thesis. Urbana, IL: University of Illinois at Urbana-Champaign; 2001. [13] Shen S, Airey G, Carpenter S, Huang H. A dissipated energy approach to fatigue evaluation. Int J Road Mater Pavement Des 2006;7(1):47–69. [14] Carpenter SH, Ghuzlan KA, Shen S. A fatigue endurance limit for highway and airport pavement. J Transport Res Record (TRR) 2003;1832:131–8. [15] Shen S, Carpenter SH. Application of the dissipated energy concept in fatigue endurance limit testing. Transportation Research Record 1929. Washington, DC: Transportation Research Board; 2005. p. 165–73. [16] Shen S, Carpenter SH. Dissipated energy concepts for HMA performance: fatigue and healing. In: Center of excellence for airport technology, COE Report No. 29. Technical Report of Research. Federal Aviation Administration. UrbanaChampaign, Urbana, IL: University of Illinois at March 2007. [17] Carpenter SH, Jansen M. Fatigue behavior under new aircraft loading conditions. In: Proc. aircraft pavement technology in the midst of change. Reston, VA: ASCE; 1997. p. 259–71. [18] Ghuzlan K, Carpenter SH. An energy-derived/damage based failure criteria for fatigue testing. Transportation Research Record 1723. Washington, DC: Transportation Research Board; 2000. p. 131–41. [19] Zhang Z, Roque R, Birgisson B, Sangpetngam B. Identification and verification of a suitable crack growth law. J Assoc Asphalt Paving Technol 2001;70:206–41. [20] Zhang Z, Roque R, Birgisson B. Evaluation of laboratory measured crack growth rate for asphalt mixtures. Transportation Research Record 1767. TRB. Washington, DC: National Research Council; 2001. p. 67–75.