Fractal analysis of effect of air void on freeze–thaw resistance of concrete Shanshan Jin a,b,⇑ , Jinxi Zhang c , Baoshan Huang b a Beijing University of Civil Engineering and Architecture, Beijing 100044, China b Department of Civil and Environmental Engineering, The University of Tennessee, Knoxville, TN 37996, USA c Beijing Key Laboratory of Trafﬁc Engineering, Beijing University of Technology, Beijing 100124, China highlights  A fractal model was built to characterize the air voids size-distribution.  The fractal model was validated more reliable than previous model.  The air voids size-distribution showed signiﬁcant inﬂuence on frost resistance.  A regression model between fractal dimension and durability factor was obtained. article info Article history: Received 18 November 2011 Received in revised form 27 April 2013 Accepted 30 April 2013 Keywords: Concrete Air void Freeze–thaw resistance Fractal analysis Box-counting dimension abstract Pore structure is one of the major characteristics inﬂuencing the freeze–thaw resistance of concrete. Although the air-void spacing factor associated to the porosity features of concrete is known as a widely used parameter to assess the freeze–thaw resistance, controversies on the determination of critical values of air-void spacing factor still exist in many related studies. Moreover, it is reported that the pore-size distribution in concrete also signiﬁcantly affects its freeze–thaw resistance. In this study, a fractal model was established to characterize the air voids size-distribution in concrete, and the corresponding fractal dimension obtained from the fractal model was validated for its effectiveness in describing the air voids size-distribution quantitatively. By comparison to a fractal model presented in a previous study, the frac- tal model proposed in this study was found more reasonable and reliable. Based on the theoretical prin- ciple, correlations between air voids size-distributions and the measured freeze–thaw resistances of concrete were established through laboratory experiments. The results revealed that air voids size-distri- bution exhibited more signiﬁcant inﬂuence on the freeze–thaw resistance of concrete than the air-void spacing. Furthermore, a regression equation with fairly high correlation coefﬁcient between the fractal dimension of air voids size-distribution and the durability factors of concrete was obtained from the results. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Due to the pore structure of concrete, freezing and thawing is one of the major reasons leading to its deterioration or failure. Based on the hypothesis of hydrostatic pressure proposed by Pow- ers [1], a direct relationship can be found between the freeze–thaw resistance and the air-void spacing of concrete, and the spacing factor of air voids is proposed to be less than 250 lm to obtain the adequate freeze–thaw resistance for the concrete. Numerous researches have been reported on the relationship between the freeze–thaw resistance and the spacing factor in recent decades [2–6]. Although the signiﬁcance of the inﬂuence of spacing factor on the freeze–thaw resistance is illustrated in many studies, there are still some controversies on the determination of critical values of the spacing factor (i.e. the maximum air-void spacing over which frost damage occurs under given conditions) among the conclusions. For example, Pigeon and Malhotra [4] conducted the freeze–thaw test and air-void test on roller compacted concrete. The research results indicate that the critical spacing factor of 250 lm is not necessary for obtaining the adequate freeze–thaw resistance. This conclusion was also validated by Gao et al. [5] through experiments. For another example, the research con- ducted by Zhang et al. [6] shows that the critical spacing factor is related to the strength grade of concrete, and the higher strength grade corresponds to the greater critical spacing factor. In order to ﬁnd a better indirect method to evaluate the freeze–thaw resis- tance, many other parameters associated with the characteristics of pore structure, such as the pore volume, ﬂow length, median pore diameter and shape of pore have been utilized to characterize the freeze–thaw resistance of concrete [7–10]. The effects of 0950-0618/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2013.04.040 ⇑ Corresponding author at: Beijing University of Civil Engineering and Architec- ture, Beijing 100044, China. Tel.: +86 13811452725. E-mail address: shanshanjin3@gmail.com (S. Jin). Construction and Building Materials 47 (2013) 126–130 Contents lists available at SciVerse ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat