## 1 Introduction  
Polymer-modified stone music asphalt (SMA) is widely used in highway pavements with high traffic volume in China to improve the overall surface layer performance at high temperature. The main reason is that SMA has good rutting assistance by the stone-to-stone aggregate skeleton structure for loading and transferring, in addition to the better performance of the modified binders over unmodified binders. With the increase in traffic volume and the appearance of extreme low temperature climate, more and more cracks appear in asphalt pavement. These cracks could be caused by repeated loading fatigue and low temperature shrinkage. Cracking at low temperature, as one of the cracks asphalt pavements suffer, destroys not only the continuity of the pavement but also the integrity of the pavement structure. It seriously affects the normal service life of asphalt pavement [1, 2]. The modified SMA has been approved as one of the asphalt mixtures that performed well in crack resistance. There are many factors influencing the low temperature crack resistance of asphalt mixtures, including the gradation and maximum nominal particle size of the mixture, the grade of asphalt binder, volumetric properties of the mixture, etc. [3, 4]. Research exist on how modified asphalt binders and gradation of aggregates affect the cracking resistance of asphalt mixtures. In addition, there are many tests and index to evaluate the crack resistance of asphalt mixtures. [PERSON] found that by using a modified asphalt binder of 4% rock asphalt with Pen 90 base asphalt, the asphalt mixtures reached a bending strain of 2403 \(\mu\epsilon\), meeting the design requirements of low temperature in cold regions in winter (\(\geq\)2300 \(\mu\epsilon\)) [5]. [PERSON] et al. found that the failure strain of the SBS/CRM hybrid-modified SMA-13 asphalt mixture of increased by about 14% compared with that of the SBS-modified one at \(-10\)\({}^{\circ}\)C [6]. [PERSON] et al. showed that the low temperature rheological properties of asphalt could be significantly improved by using a Sasobit modifier with a dosage of 3.0% [7]. [PERSON] et al. selected bis (2-ethylhexyl) adipate (DOA) as a plasticizer to modify base asphalt, and the results showed that when the amount of plasticizer was increased to 3.0%, the failure strain of modified asphalt increased by about 66% compared with base asphalt [8]. The failure strain increased by about 66% compared with the base asphalt. [PERSON] et al. adopted the improved Superpave design method to design a rubber asphalt anti-crack layer asphalt mixture, which could achieve a better function of absorbing and reflecting cracks [9]. [PERSON] studied the crack resistance of a rubber-asphal mixture with three gradation types of SMA-13, AC-13 and Novachip (ultra-thin wearing course) Type-B; the results showed that the splitting and bending strength of SMA-13 with a smaller void at a low temperature were greater than that of the Novachip Type-B rubber asphalt mixture with a larger void [10]. [PERSON] et al. analyzed the anti-reflection crack performance of AC-10 and CAM-10 asphalt mixtures of strength absorbing layers with different void ratios through the four-point bending test and overlay test. He found that the CAM-10 asphalt mixture with a target void ratio of 2% had the best anti-cracking performance at a low temperature [11]. [PERSON] et al. proposed the superiority of the low-temperature performance test of asphalt based on prefabricated notch three-point bending fracture mechanics [12; 13]. [PERSON] et al. applied the disc tensile test (DCT) to conduct a fracture test of the asphalt mixture at \(-12\)\({}^{\circ}\)C, and selected the fracture strain capacity limit as the evaluation index [14]. There are many research projects on the gradation, the NMS of gradation, and the shape of aggregates on the rutting resistance [15; 16; 17; 18; 19]. However, there is little research on the effect of gradation NMS on the low temperature crack resistance of the SMA mixtures.