On the representative volume element of asphalt concrete at low temperature

AASHTO M320-10: Standard method of test for performance-graded asphalt binder. American Association of State Highway and Transportation Officials (2010)

AASHTO T313-12: Standard method of test for determining the flexural creep stiffness of asphalt binder using the Bending Beam Rheometer (BBR). American Association of State Highway and Transportation Officials (2012)

AASHTO T322-07-UL: Standard method of test for determining the creep compliance and strength of Hot-Mix Asphalt (HMA) using the Indirect tensile test device. American Association of State Highway and Transportation Officials (2007)

Anderson, D.A., Kennedy, T.: Development of SHRP binder specification. J. Assoc. Asphalt Paving Technol. 62, 481–507 (1993)

Arnold, J.C.: The influence of liquid uptake on environmental cracking of glassy polymers. Mater. Sci. Eng. A, Struct. Mater.: Prop. Microstruct. Process. 197, 119–124 (1995)

Bažant, Z.P.: Scaling of Structural Strength, 2nd edn. Elsevier, London (2005)

Bažant, Z.P., Novák, D.: Energetic-statistical size effect in quasibrittle failure at crack initiation. ACI Mater. J. 97(3), 381–392 (2000)

Bažant, Z.P., Pang, S.-D.: Activation energy based extreme values statistics and size effect in brittle and quasibrittle fracture. J. Mech. Phys. Solids 55, 91–131 (2007)

Bažant, Z.P., Planas, J.: Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press, Boca Raton (1998)

Berryman, J.G.: Measurement of spatial correlation functions using image processing techniques. J. Appl. Phys. 57, 2374–2384 (1985)

Burgess, R.A., Kopvillem, O., Young, F.D.: St. Anne test road—relationship between predicted fracture temperatures and low temperature field performance. J. Assoc. Asphalt Paving Technol. 40, 148–193 (1971)

Cannone Falchetto, A., Turos, M., Marasteanu, M.O.: Investigation on asphalt binder strength at low temperature. Road Mater., Pavement Des. 13(4), 804–816 (2012)

Cannone Falchetto, A., Le, J.-L., Moon, K.H., Marasteanu, M.O.: Histogram testing for strength size effect in asphalt mixtures at low temperature. Road Mater., Pavement Des. 14(1), 52–64 (2013a)

Cannone Falchetto, A., Montepara, A., Tebaldi, G., Marasteanu, M.: Microstructural characterization of asphalt mixtures containing recycled asphalt materials. J. Mater. Civ. Eng. 25, 45–53 (2013b)

Cannone Falchetto, A., Wistuba, M.P., Marasteanu, M.O.: Size effect in asphalt mixture at low temperature: Type I and Type II. Road Mater., Pavement Des. 17(1) (2016), doi: 10.1080/14680629.2016

Cook, R.D., Weisberg, S.: Applied Regression Including Computing and Graphics. Wiley Series in Probability and Statistics. USA (1999)

da Vinci, L.: Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze. Elsevirii, Leiden (1730) English transaltion by T. Weston, London, pp. 178–181

Daniels, E.: The statistical theory of the strength of bundles and threads. Proc. R. Soc. A, Math. Phys. Eng. Sci. 183, 405–435 (1945)

Dongré, J., D’Angelo, J.: Effect of new direct tension test protocol on the superpave low-temperature specification for bitumen binders. In: Bearing Capacity of Roads and Airfields (1998)

Eriksen, K., Wegan, V.: Optical methods for the evaluation of asphalt concrete and polymer-modified bituminous binders. Note 244, Danish Road Institute (1993)

Fisher, R.A., Tippet, L.H.C.: Limiting forms of the frequency distribution of the largest and smallest number of a sample. Proc. Camb. Philos. Soc. 24, 180–190 (1928)

Fréchet, M.: Sur la Loi de Probabilité de l’Écart Maximum. Ann. Soc. Math. Pol., 1 Comment. Math. 6, 93–116 (1927)

Gonzales, R., Woods, R., Eddins, S.: Digital Image Processing Using MATLAB. Pearson Prentice Hall, New York (2004)

Jiao, Y., Stillinger, F.H., Torquato, S.: Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 76, 031110 (2007)

Le, J.-L., Bažant, Z.P., Bažant, M.Z.: Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures. I. Strength, static crack growth, lifetime and scaling. J. Mech. Phys. Solids 59, 1291–1321 (2011)

Marasteanu, M., Velasquez, R., Cannone Falchetto, A., Zofka, A.: Development of a simple test to determine the low temperature creep compliance of asphalt mixture. IDEA program final report NCHRP 133, July (2009)

Masad, E., Button, J.: Implications of experimental measurements and analyses of the internal structure of hot-mix asphalt. Transp. Res. Rec. 1891, 212–220 (2004)

Masad, E., Muhunthan, B., Shashidhar, N., Harman, T.: Internal structure characterization of asphalt concrete using image analysis. J. Comput. Civ. Eng. 13(2), 88–95 (1999)

McClave, J., Sincich, T.: Statistics. 9th edn. Prentice Hall, New York (2003)

Moore, D.S., McCabe, G.P., Craig, B.A.: Introduction to the Practice of Statistics. Freeman, New York (2009)

Moskala, E.J.: A fracture mechanics approach to environmental stress cracking in poly(ethyleneterephtalate). Polymer 39(3), 675–680 (1998)

Oehlert, G.W.: A First Course in Design and Analysis of Experiments. Freeman, New York (2000)

Rasband, W.: Image J 1.50c, National Institutes of Health, USA, http://imagej.nih.gov/ij/notes.html (2015)

Readshaw, E.E.: Asphalt specifications in British Columbia for low temperature performance. J. Assoc. Asphalt Paving Technol. 41, 562–581 (1972)

Rinne, H.: The Weibull Distribution: A Handbook. CRC Press/Taylor and Francis, Boca Raton (2009)

Schafer, A., Teyssen, T.: Size, shape and orientation of grains in sand stones—image analysis applied to rock thin-sections. Sediment. Geol. 52, 251–271 (1987)

Swartz, S.E., Siew, H.C.: Is load control suitable for fracture-energy measurements for concrete? Exp. Mech. 27(4), 359–365 (1987)

Torquato, S.: Modeling of physical properties of composite materials. Int. J. Solids Struct. 37, 411–422 (2000)

Torquato, S.: Random Heterogeneous Materials. Springer, New York (2002)

Turos, M., Cannone Falchetto, A., Tebaldi, G., Marasteanu, M.O.: Determining the flexural strength of asphalt mixtures using the bending beam rheometer. In: Proceeding of the 7th RILEM Conference on Cracking in Pavements, vol. 4, pp. 11–20 (2012)

Underwood, E.: Quantitative Stereology. Addison-Wesley, Reading (1970)

Velasquez, R., Cannone Falchetto, A., Marasteanu, M.: From mixtures to binders can the inverse problem be solved? Road Mater, Pavement Des. 11(1), 225–249 (2010)

Weibull, W.: The phenomenon of rupture in solids. Proc. R. Swed. Ins. Eng. Res. 151, 1–45 (1939)

Yue, Z., Bekking, W., Morin, I.: Application of digital image processing to quantitative study of asphalt concrete microstructure. Transp. Res. Rec. 1492, 53–60 (1995)