## 1 Introduction  
Permanfrost and seasonal frozen soil are predominantly found in the western and northern regions of China, covering over 70% of the land area. With the rising demand for transportation infrastructure and energy development, more rock mass projects are expanding into cold regions. After geological evolution and tectonic movement, a rock mass is rich in joints and fissures, posing significant challenges to rock mass engineering in cold regions. For instance, regions such as Haixi, Nsari, Nagqu, and Yushu experience 140 days per year with a temperature difference of more than 15 \({}^{\circ}\)C between day and night and undergo up to 200 freeze-thaw cycles annually (Figure 1) [1]. In cold regions, fractured rock masses in highways, railways, tunnel slopes, and mining slopes of large open-pit mines experience various disasters due to freeze-thaw cycles and cyclic loading [2, 3, 4, 5]. Examples include freeze cracks in open tunnel sections [6], landslides [7], and rockfalls [8, 9], significantly affecting the long-term stability of rock mass engineering in these areas. The primary mechanisms underlying rock freeze-thaw damage include ice volume expansion [10], hydraulic stress from unfrozen water in micropores [11], and internal stress induced by crystal growth [12]. Numerous scholars have conducted extensive laboratory tests and studies. It is widely accepted that porosity [13; 14], saturation [15; 16; 17], freeze-thaw cycle frequency [18; 19], pH value [20; 21; 22; 23], and confining pressure [24; 25] are the primary factors influencing freeze-thaw damage in rocks. Based on this, scholars have used damage theory to establish rock freeze-thaw damage models, employing factors such as the elastic modulus [26], pore structure [27; 28], and ultrasonic longitudinal wave velocity [29; 30]. They have also developed corresponding structural models [31; 32]. Apart from being susceptible to freeze-thaw geological disasters, rock engineering faces significant challenges from construction-related disturbances and periodic fatigue deformation induced by traffic load cycles during operation [33]. Consequently, research on the mechanical behavior of rocks under fatigue and dynamic loads has emerged as a prominent area of focus [34; 35]. [PERSON] [36; 37; 38] and [PERSON] [39] analyzed how different stress amplitudes, upper bound stresses, and loading waveforms affect the evolution of rock fractures. [PERSON] and [PERSON] et al. [40; 41] proposed the fatigue threshold theory to assess the fatigue failure of rock masses. [PERSON] et al. [42] examined the evolution of rock fatigue damage variables using the Weibull probability distribution function. [PERSON] et al. [43] explored the damage law of rocks under cyclic loading based on dissipated energy. [PERSON] et al. [44] developed a constitutive model for rock fatigue deformation by comparing it with the long-term creep of rocks. However, in cold regions, cracked rock masses often experience simultaneous effects of freeze-thaw cycles and periodic loading during the damage accumulation process. Recent studies have primarily focused on either freeze-thaw or cyclic load damage [45; 46; 47]. This study aims to bridge this gap by examining the combined effects. This paper conducts a freeze-thaw cycle (F-T) test on double-fractured granite, followed by a uniaxial fatigue load test. The pore distribution of the samples at different stages was analyzed through NMR scanning. High-speed photographic monitoring was used to explain the fracture evolution behavior of macroscopic cracks during uniaxial fatigue loading. This study investigates the combined effects of freeze-thaw and fatigue loading on the damage and failure characteristics of cracked granite. Additionally, a damage constitutive mathematical model is developed, taking into account the combined influence of prefabricated cracks, freeze-thaw cycles, and fatigue loading. These findings contribute to a deeper understanding of the damage and failure mechanisms of fractured rock masses in seasonally frozen areas.