## 3 Results and Discussion
### Cumulative Vertical Displacement  
Figure 6 illustrates the curves correlating the CVD with the number of loading cycles at elevated temperatures. These CVD-number of loading cycle curves visually demonstrate the connection between the ultimate deformation of the granite and the number of loading cycles. The progression of CVD can be categorized into three distinct stages: an initial rapid growth stage, a subsequent stable growth stage, and finally, an accelerated growth stage. At 25 \({}^{\circ}\)C, the CVD of granite samples gradually increases as the number of loading cycles increases, as demonstrated in Figure 6. Notably, for samples exposed to an equivalent cycle number, the CVD exhibits an upward trend alongside an increase in the upper load limit. Furthermore, it is worth highlighting that failure and nonfailure samples exhibit differences in the stages of cyclic loading at which CVD occurs, as observed by [PERSON] et al. [46]. For instance, in cases where the samples do not fail, a significant portion of the CVD is concentrated in the initial phase of cyclic loading. In fact, the cumulative deformation resulting from the first 50 cycles accounts for approximately 60% of the total deformation. On the other hand, in cases where the samples do fail, the CVD primarily occurs during the failure stage, which corresponds to the latter part of the cyclic loading process and accounts for roughly 50% of the total displacement. Similar findings have also been reported in previous research conducted by [PERSON] et al. [23] and [PERSON] et al. [47]. In the early loading phase, the internal primary fractures and cracks undergo continuous compaction, leading to irreversible plastic deformation. As a result, the curve exhibits a significant upward trend during this initial loading phase. In the failure stage, microcracks within the sample continue to propagate and merge over multiple cycles, while damage defects accumulate. In the few cycles preceding sample failure, a rapid escalation in CVD leads to a sudden sample failure when it reaches a critical value. It should be noted that  
Figure 6: The cumulative vertical displacement (CVD) evolution curves with the number of loading cycles at different increased temperatures. (**a**) 25 \({}^{\circ}\)C; (**b**) 200 \({}^{\circ}\)C; (**c**) 300 \({}^{\circ}\)C; (**d**) 400 \({}^{\circ}\)C.  
when the upper load limit is set to a low value, sample failure may not occur. Consequently, the CVD of the sample only displays the initial rapid growth and stable stages, with no occurrence of an accelerated growth stage. In most cases, the CVD tends to rise with an increase in the number of loading cycles. Nevertheless, a different trend emerges at 200 \({}^{\circ}\)C and 300 \({}^{\circ}\)C, where the CVD of granite samples initially decreases before subsequently increasing as the number of loading cycles rises, as depicted in Figure 6b,c. These findings highlight temperature and cyclic loading impacts on granite's physical and mechanical characteristics. In the early phases of cyclic loading, the temperature elevation triggers sample expansion, resulting in the closure of internal microcracks and the enlargement of the compressive region, which is in agreement with the observations of [PERSON] et al. [48]. The compressive region expansion and the increased elastic modulus within the samples indicate a thermal hardening effect, as suggested by [PERSON] et al. [49]. As the number of loading cycles increases, the sample's microcracks steadily increase, and the damage deformation gradually accumulates. Over time, the thermal expansion effect becomes insufficient to compensate for the accumulated plastic deformation, leading to a subsequent increase in CVD. As the sample approaches failure, a noticeable, sharp upturn in CVD is observed, as shown in Figure 6, which indicates sample failure. At 400 \({}^{\circ}\)C, the cumulative vertical deformation remains relatively stable during the initial cycles and significantly increases only upon sample failure.