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1、and Robert L. Lytton, Ph.D., P.E., F.ASCE3Abstract：asphalt mixtures have been demonstrated to be anisotropic materials in both laboratory and field tests. The anisotropy of asphalt mixtures consists of inherent anisotropy and stress-induced anisotropy. In previous work, the inherent anisotropy of as

2、phalt mixtures was quantified by using only the inclination angles of the coarse aggregate particles in the asphalt mixtures. However, the inclination of fine aggregates also has a contribution to the inherent anisotropy. Moreover, the contribution to the inherent anisotropy of each aggregate may no

3、t be the same as in the previous work but will depend on the size, orientation, and sphericity of the aggregate particle. This paper quantifies the internal microstructure of the aggregates in asphalt mixtures by using an aggregate-related geometric parameter, the vector magnitude. The original form

4、ulation of the vector magnitude, which addresses only the orientation of coarse aggregates, is modified to account for not only the coarse aggregate orientation, but also the size, orientation, and sphericity of coarse and fine aggregates. This formulation is applied to cylindrical lab-mixed lab-com

5、pacted asphalt mixture specimens varying in asphalt binder type, air void content, and aging period. The vertical modulus and the horizontal modulus are also measured by using nondestructive tests. A relationship between the modified vector magnitude and the modulus ratio of the vertical modulus to

6、the horizontal modulus is developed to quantify the influence of the inherent microstructure of the aggregates on the anisotropy of the mixtures. The modulus ratio is found to depend solely on the aggregate characteristics including the inclination angle, size, and sphericity, and it is independent

7、of the asphalt binder type, air void content, and aging period. The inclination angle, itself, proves to be insufficient to quantify the inherent anisotropy of the asphalt mixtures.DOI: 10.1061/（ASCE）MT.1943-5533.0000325. 2011 American Society of Civil Engineers.CE Database subject headings: Asphalt

8、s; Mixtures; Anisotropy;Microstructures; Aggregates; Field tests.Author keywords: Asphalt mixtures; Microstructure; Aggregate; Vector magnitude; Modulus ratio.Introduction The anisotropy of a material is the property of being directionally dependent. Theanisotropy of an asphalt mixture can be define

9、d as the difference in physical properties, such as modulus and Poissons ratio, when the asphalt mixture is measured in different directions. According to the origins of anisotropy, granular materials,such as soils, aggregate base, and asphalt mixtures, consist of two types of anisotropy: （1） inhere

10、nt anisotropy; and （2） stressinduced anisotropy （Adu-Osei 2000; Masad et al. 2002; Kim et al.2005; Underwood et al. 2005）. The inherent anisotropy of anasphalt mixture is attributed to the preferential orientation of aggregates.Because the aggregates tend to “lie flat” during the compaction of aspha

11、lt mixtures, the major axis （i.e., longest diameter） of the aggregate has a preferential direction in the horizontal plane. The stress-induced anisotropy is the result of crack growth under load applications. The increase of the crack surface area leads to the loss of the intact material area, which

12、 causes the modulus degradation.The crack growth speed differs in different directions,which results in different modulus degradation in different directions and produces the stress-induced anisotropy in the asphalt mixture. Because the two types of anisotropy have different mechanisms, the inherent

13、 anisotropy and the stress-induced anisotropy must be investigated separately. The focus of this paper is investigating the inherent anisotropy of asphalt mixtures. To avoid the influence of the stress-induced anisotropy and to obtain the pure inherent anisotropy, all asphalt mixture specimens were

14、tested within small strains in this study so that no cracks grew in the asphalt mixture specimens during the test. The inherent anisotropy of the asphalt mixture has been demonstrated to be significant in both laboratory and field tests. Levenberg and Uzan （2004） conducted small strain （i.e., below

15、150 microstrains） hydrostatic compression tests on lab-compacted cylindrical samples and found that the asphalt mixture was 1.5 times stiffer vertically than horizontally. Motola and Uzan （2007） conducted compressive dynamic modulus tests on eight field-cut specimens and illustrated that the vertica

16、l modulus was 40% greater than the horizontal modulus. They suggested modeling the asphalt mixture as a cross-anisotropic material whose properties are symmetric about the vertical direction and are identical in the horizontal plane that is perpendicular to the compaction direction. Ramos- Aparicio

17、（2004） and Oh et al. （2006） backcalculated 106 groups of ground penetrating radar （GPR） data and falling weight deflectometer （FWD） field tests of asphalt pavement and found the anisotropic modulus ratio （i.e., the ratio of the vertical modulus to the horizontal modulus） to be an average of 1.26. As

18、phalt mixtures exhibit significant inherent anisotropy only under compression;under tensile loading, an asphalt mixture behaves approximately isotropically （Underwood et al. 2005; Wagoner and Braham 2008）.Therefore, this paper studies the inherent anisotropy of asphalt mixtures under compressive loa

19、ding only.The inherent anisotropy of the asphalt mixture needs to be accounted for during the performance analysis of asphalt pavements because both fatigue cracking and plastic deformation may be underestimated if assuming that asphalt mixtures are isotropic in compression. Wang et al. （2005） condu

20、cted triaxial tests on cubic field samples and showed significant differences in vertical and horizontal stiffness. They further analyzed the pavement responses in a finite element pavement program by using the anisotropic moduli and the isotropic modulus, separately. They found larger tensile and s

21、hear stresses in the pavement when using the anisotropic moduli than when using the isotropic modulus. Oh et al. （2006） modeled the asphalt pavement with both the anisotropic moduli and the isotropic modulus for the asphalt layers. Their modeling results indicated that the pavement rutting predicted

22、 by the anisotropic moduli matched well with the measured pavement rutting, which exceeded the rutting predicted by the isotropic modulus. To address the preferred orientation of geological structures, a parameter of vector magnitude was first introduced by Curray （1956） for quantification of two di

23、mensional orientation data. Subsequent researchers （Oda and Nakayama 1989; Oda 1993）addressed the inherent anisotropy of soils for the inclination of soil particles by using the concept of vector magnitude, which was then used to formulate a microstructure-based fabric tensor to modify the effective

24、 stress in the soils during a continuum damage analysis.The similar fabric anisotropy concepts were employed to describe the granular sands and soils properties such as the inherent anisotropy, the directions of principal stresses, and the anisotropic elastic deformation （Wong and Arthur 1985; Houqu

25、e and Tatsuoka 1998; Yoshimine et al. 1998）. Recently, by direct application of the fabric tensor, the anisotropic behavior of granular soils was successfully simulated by a number of elastoplastic constitutive models （Li and Dafalias 2002; Dafalias et al. 2004; Lashkari and Latifi 2007;Loukidis and

26、 Salgado 2009）. The same formulations of the vector magnitude and the fabric tensor were applied to asphalt mixtures （Masad et al. 2002; Masad and Button 2004; Tashman et al. 2005; Dessouky et al. 2006; Saadeh et al. 2007）. The preferential orientation of the coarse aggregates in the asphalt mixture

27、s was evaluated with X-ray computed tomography （CT） and was then quantified by using the vector magnitude. Subsequently, the fabric tensor was formulated on the basis of the vector magnitude to modify the effective stress in the asphalt mixture during a continuum damage analysis. The fabric tensor f

28、ormulated by using the vector magnitude proved to be an effective indicator of the inherent anisotropy of asphalt mixtures. Accounting for the inclination of coarse aggregates in the continuum damage model produced more accurate predictions of pavement rutting. The inherent anisotropy of asphalt mix

29、tures is not attributed only to the inclination of coarse aggregates. The inclination of fine aggregates also has a contribution to the inherent anisotropy. Moreover, the contribution to the inherent anisotropy of each aggregate may not be the same but will depend on the size, sphericity, and orient

30、ation of the aggregate particle. All three parameters must be addressed when quantifying the inherent anisotropy of an asphalt mixture. In other words, the microstructure-based fabric tensor should address not only the inclination of coarse aggregates but the size,orientation, and sphericity of both

31、 coarse and fine aggregates whose size is between 1.18 and 4.75 mm. To characterize the fine aggregates, an imaging system with high resolution is required for scanning the asphalt mixtures. The images produced by the X-ray CT may not have a high enough quality in dots per inch （DPI）. Consequently,

32、other imaging methods that can provide higher quality images need to be investigated. In addition, instead of indirectly addressing the inherent anisotropy by using the fabric tensor to modify the effective stress in the material, it would be desirable to establish a direct relationship between the inherent anisotropy and the anisotropic moduli of the asphalt mixtures. This paper investigates the inherent anisotropy of asphalt mixtures for the size, the orientation, and the sphericity of aggregate particles. These geometric