## 1 Introduction  
Asphalt pavement is influenced by freeze-thaw cycles in the middle and lower reaches of the Yangtze River and some seasonally frozen areas of China in winter. Many studies have shown that freeze-thaw cycles significantly affect the performance of asphalt mixtures [1; 2; 3]. The freeze-thaw process would lead to the loss of adhesion between binder and aggregates, which can also change the properties of aggregate, such as strength, compressibility, porosity, and permeability [2], as well as reduce the strength and stiffness of asphalt mixtures. Therefore, it can cause various forms of premature pavement distress [3]. Some asphalt pavements were discovered to have grave freeze injury during construction right away or after the construction process is completed [4; 5]. Hence, effective analysis of the freeze-thaw cycles on the performance of asphalt mixtures is necessary [6; 7; 8].  
General studies are mainly focused on the influence of freeze-thaw cycles and the macro performance of asphalt mixtures under simple stress states including resistance, stiffness, stability, fatigue life, low-temperature properties, etc. [9; 10; 11; 12; 13; 14; 15]. They have made contributions to improve the accuracy of asphalt pavement design parameters. And a number of studies on the damage evolution of asphalt mixtures during freeze-thaw cycles from the basis of micro-level were reported in Ref. [16; 17].  
Furthermore, a lot of models were established to characterize the mechanical performance of asphalt mixtures after multiple freeze-thaw cycles under simple stress states [18; 19].  
However, the asphalt mixtures are not only affected by the freeze-thaw cycles, but also by the complex stress states in the site [20; 21]. Therefore, the uniaxial tensile test, uniaxial compression test, bending test, and indirect test under one-dimensional or two-dimensional stress states cannot reflect the failure modes of asphalt mixtures in three-dimensional stress conditions in the asphalt pavement structures [22; 23; 24]. Generally speaking, the tensile properties of asphalt materials should be emphasized at relatively low temperature. While the conventional triaxial test is available only for the triaxial compressive stress state with confining pressure if the first principal stress \(\sigma_{1}\) equal to the second principal stress \(\sigma_{2}\), the triaxial tensile tests cannot be carried out [25; 26; 27]. As it is difficult to study the multi-axial strength properties of asphalt mixtures [28; 29], the three-dimensional failure criterion of asphalt mixture after freeze-thaw cycles has not been developed.  
The objective in this paper is to study the effects of the complex stress states and freeze-thaw in asphalt pavement in the laboratory, as well as to perform triaxial tests (especially triaxial tensile testing) for AC (Asphalt Concrete)-13 and SMA (Stone Mastic Asphalt)-13 asphalt mixtures after freeze-thaw cycles with the self-developed triaxial test method. In addition, the nonlinear and linear failure criterions under three-dimensional stress states are established to evaluate the impact of stress and freeze-thaw cycles on the performance of these asphalt mixtures. From the strength point of view, the SMA-13 asphalt mixture exhibits better freeze-thaw resistance under complex stress condition compared with the AC-13 asphalt mixture. Therefore, it is recommended as the upper surface layer material of pavement structure.