## 6 Conclusions  
A mix design of small particle-size (SPS) asphalt mixture for controlling cracks in pavement surfaces was studied. The gradation was improved SMA-II dense gradation, and the binder was asphalt-rubber binder with polyester fiber used to enhance crack resistance. The asphalt mixture presented in this paper can be used as a hot mix asphalt thin overlay, which is an effective preventive maintenance method or pavement surface layer to improve the crack resistance performance of asphalt pavement.  
According to the Marshall test results, the optimal fiber content and the optimal asphalt-stone ratio for SMA-II-1 were 0.18% and 6.6%, respectively. The optimal fiber content and the optimal asphalt-stone ratio for SMA-II-2 were 0.27% and 8.1%, respectively. The optimal fiber content and the optimal asphalt-stone ratio for SMA-II-3 were 0.21% and 7.1%, respectively. In the study of the key controlling indices of mix proportion, the passing rate of the 1.18-mm sieve had a more remarkable influence on the air void content of the mixture than the passing rate of 0.075-mm sieve. The recommended range of the filler-asphal ratio should be between 1.1% and 1.4%. The results above can be used as guidance for the mix design of asphalt mixture.  
Overall performances of SMA-II-1, SMA-II-2, SMA-II-3 can satisfy requirements of the Chinese specifications according to the high temperature test, the water stability test and the skid resistance test. The beam bend test and the bending strain energy density function were adopted to evaluate the low temperature performance of three kinds of mixtures. Test results show that SMA-II with high rubberized asphalt content has better adaptability for deformation and greater bending strain energy density than traditional SMA-I (SBS-modified mixture), which can demonstrate good crack resistance performance of SMA-II. Life-cycle cost analysis showed the better life-cycle economic benefit of the SPS asphalt mixture thin overlay compared with the traditional AC-13 thin overlay.  
The pavement performance of this SPS asphalt mixture needs to be further investigated in engineering practice. In fact, the design method for the material composition and thickness of the asphalt thin overlay still need improvement and innovation in theory, method and practice.  
Conceptualization, J.P., J.Z. and R.L.; Methodology, J.P., J.X. and L.S.; Software, J.X., L.S.; Validation J.X. and L.S.; Formal Analysis, R.L., L.S. and J.X.; Investigation, J.X. and L.S.; Resources, L.S. and J.X.; Data Curation, J.Z., L.S. and J.X.; Writing--Original Draft Preparation, J.X. and L.S.; Writing--Review & Editing, M.A., J.X.; Visualization, J.X.; Supervision, J.P.; Project Administration, J.P.; Funding Acquisition, J.P.  
The research was funded by the National Natural Science Foundation of China grant number 51378073 and 51408048, the Key Program for Science and Technology Projects of Shaanxi province grant number 2016 ZDJC-24, the China Postdoctoral Science Special Foundation grant number 2016T90880, and the Science and Technology Project of Shaanxi Provincial Communications Department grant number 15-35T. The authors also appreciate the support of China Scholarship Council (CSC) during the research at Waseda University. And the APC was funded by Basic Scientific Research of Central College of Chang'an University grant number 300102219308 and 300102219316. The authors declare no conflict of interest.  
The aggregates and filler used in this study are limestones which were produced in Xi'an City, Shaanxi Province. The technical indicators were shown in Tables 1-3.