## 1 Introduction  
Increasingly heavy traffic volumes require ongoing improvements in the performance of asphalt pavement. In order to achieve this goal, many measures have been taken, one of which is the modification of asphalt mixture. Tests show that the modification of asphalt mixture with nano-materials and basalt fibers can significantly improve and prolong pavement performance. Putting and fatigue tests of nano-modified asphalt mixtures were carried out by [PERSON] and [PERSON] [1]. The results showed that the addition of nano-TiO\({}_{2}\) can improve the adhesion and toughness of asphalt mixture, and improve the rutting resistance and fatigue life of asphalt mixtures significantly. Three kinds of inorganic nanoparticles, including titanium dioxide, were used to improve the performance of asphalt mixture. The microstructure of nano-modified asphalt mixture was studied with computed tomography (CT) scanning and scanning electron microscopy. The aging resistance of nano-modified asphalt was studied with the Fourier transform infrared spectroscopy and viscoelasticity test. The durability of the asphalt mixture was improved significantly by nano-particles [2]. [PERSON] et al. used nano-materials as modifiers to improve the performance of hot-mix asphalt mixture. Through a rutting test, indirect tensile test and indirect tensile fatigue test of nano-modified asphalt mixture, it was found that nano-TiO\({}_{2}\) significantly improved the mechanical properties of stone mastic asphalt (SMA) [3]. Basalt fiber, lignin fiber and polyester fiber were used by [PERSON] et al. to modify asphalt mixture and their high temperature stability, water stability and low temperature crack resistance were evaluated. The experimental results showed that basalt fiber is better than lignin fiber and polyester fiber in improving the performance of asphalt mixture [4]. The results showed that basalt fiber can significantly improve the crack resistance of asphalt mortar [5]. Improvement of the tensile strength of asphalt mixture by basalt fiber was evaluated by a splitting test. The results showed that basalt fiber can significantly improve the tensile strength of asphalt mixture [6]. [PERSON] and [PERSON], studying the improvement effect of basalt fiber on an asphalt surface layer, found that basalt fiber-modified asphalt has better performance in resisting permanent deformation and increasing pavement friction [7]. The fatigue life of modified asphalt was also evaluated. The results showed that basalt fiber could improve the low temperature performance of asphalt mixture [8]. [PERSON] et al. found that under the coupling of chloride ion erosion and a freeze-thaw (F-T) cycle, the low temperature flexural and fatigue properties of basalt fiber-modified asphalt mixture were obviously improved over those of ordinary asphalt mixture [9]. Because of climate influence in seasonally frozen areas, asphalt pavement will be affected by the frost heave force when the water in the pores freezes, and water loss when the pore water is thawed, leading to a continuous decline in the performance of the asphalt pavement. [PERSON] et al. studied the frost resistance, fatigue performance and durability of asphalt pavement in the Quebec area. It was found that the addition of fiber improved the frost resistance and fatigue performance of asphalt pavement [10; 11]. [PERSON] et al. studied the water sensitivity and degradability of glass aggregate asphalt mixture under F-T cycles in cold regions [12]. [PERSON] et al. studied the durability of rubber particle-modified asphalt mixture during F-T cycles. The results showed that the splitting tensile strength decreased, and the void increased with the increase of rubber particle content and the same F-T cycles [13]. [PERSON] et al. used three kinds of viscoelastic constitutive equations to determine the relaxation modulus of asphalt mixture. The experimental results showed that the Prony series is the most accurate method for predicting the relaxation modulus of asphalt mixture during F-T cycles [14].