Experimental and Theoretical Determination of the Frost-Heave Cracking Law and the Crack Propagation Criterion of Slab Track with Water in the Crack  
[PERSON]  
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[PERSON]  
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[PERSON]  
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[PERSON]  
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[PERSON]  
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[PERSON]  
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Footnote 1: email: {[EMAIL_ADDRESS],  
propagation in cold regions is equivocal. Therefore, this maintenance standard did not consider the influence of external temperature (\(T\)) and moisture content on crack propagation. Consequently, it is of great significance to reveal the evolution laws of frost-heave crack propagation, establish reasonable evaluation criteria for the crack-propagation state, and provide important theoretical and experimental support for crack maintenance and the prevention of the frost-heaving of slab-track. Slab-track cracks with frost-heave are shown in Figure 1.  
Research on frost-heave crack propagation has mainly concentrated on the mechanism of frost heave and the value of the frost-heave force in cracks. [PERSON] [5] analyzed the mechanisms of frost damage to concrete pore structures using ultrasonic nondestructive testing, image analysis, and scanning electron microscopy. [PERSON] [6] investigated the types of damage to slabs under the effect of static ice pressure, and clarified the mechanism of frost-heave damage using a theoretical model. It is generally acknowledged that the frost-heave force produced by the water-ice phase transition causes cracks to propagate [7]. However, there have been very few studies regarding evaluation criteria for frost-heave crack propagation in slab tracks. In recent years, the mileage of slab-track has been increasing steadily in China. Investigation of crack damage to slab-tracks in cold areas of China has found that cracks with a width of 0.2-0.4 mm have appeared in the supporting layer (base slab) of slab-track, and the maximum width of cracks can reach 2 mm. Cracks with a width of 0.1-0.2 mm have appeared on the surface of the slab-track, 80% of which are transverse penetrating cracks [8; 9; 10]. In areas of severe cold and high humidity, once crack damage occurs in a slab-track structure, the cracks will inevitably experience frost heave [7]. Considering the disadvantages of cracks for the durability of slab-tracks, scholars have conducted in-depth research on the factors involved in frost-heave crack propagation. For example, the moisture content in cracks, the width of cracks, and temperature are all significant factors that affect frost heave. As the temperature decreases and the moisture content in cracks increases, the speed of frost-heave crack propagation will accelerate [11; 12; 13; 14; 15]. In spite of the mounting effort that is being put into the topic, the timing of crack propagation, the state of cracks, and the law of crack propagation under the influence of external factors are still not exactly known. In order to evaluate the state of crack propagation and reveal the evolution laws of frost-heave crack propagation, many theoretical studies have been conducted on the value of the frost-heave force [16; 17]. Additionally, some researchers have experimentally measured the frost-heave force in cracks [18; 19], and proposed the use of stress intensity factors at the crack tip as the criterion for the initiation of concrete cracks. The value of the stress-intensity factor at the crack tip depends not only on the magnitude of the external load on the crack, but also on the magnitude of crack cohesion. Additionally, initiation toughness is also controlled by the crack initiation load and the equivalent length of the  
Figure 1: Slab-track cracks with frost heave. crack. However, the value of the frost-heave force measured by different test methods differs greatly. The reason for this may be that the small size of crack tips makes it difficult to implant pressure sensors. With the advancement of monitoring technology, the testing methods for damage to concrete structures have been constantly improved.