# Tensile Properties of Granite Under Cyclic Thermal Shock and Loading
## 3 Test Results and Analysis
### Elastic Stiffness  
Elastic stiffness is a characteristic parameter that reflects the ability of granite to resist deformation. In order to ensure that both the starting and ending points of the approximate linear segment of elastic stiffness are within the loading curve, the elastic stiffness of the loading segment is defined as the slope between the two points corresponding to 30% and 70% of the load upper limit on the hysteresis loading segment of the load-displacement curve [43].  
Figure 12 shows the variation of elastic stiffness of granite as a function of cyclic loading-unloading cycles in the Brazilian splitting test following different numbers of cyclic water-cooling shocks. The elastic stiffness initially increases markedly, then stabilizes, and ultimately decreases with additional loading-unloading cycles. The sharp initial increase in elastic stiffness is attributed to the compaction of internal pores during the first loading, which enhances granite density and its deformation resistance, accounting for approximately 80% of the total stiffness gain [38]. During the next few cycles, as the  
internal structure becomes progressively compacted, elastic stiffness increases slightly, corresponding to the rapid growth stage of peak displacement observed in Figure 13. Thereafter, although loading-unloading cycles continue, elastic stiffness remains nearly constant, corresponding to the slow growth stage of peak displacement. In the final cycles before failure, accumulation of internal damage due to continued cyclic loading causes elastic stiffness to decrease; at this stage, significant plastic deformation occurs in the granite, and peak displacement increases with cycle number until specimen failure, corresponding to the failure stage of peak displacement.  
In addition, it is observed from Figure 13 that under the same preset load upper limit, the increase in elastic stiffness after the first loading shows a trend of gradually increasing with the number of water-cooling shocks. For instance, under a 70% load upper limit, the elastic stiffness of granite after the first cyclic loading is 51.55 kN/mm, 36.14 kN/mm, 30.54 kN/mm, 29.46 kN/mm, and 25.86 kN/mm after 0, 1, 3, 5, and 7 water-cooling shocks, respectively; after the first cyclic loading, the elastic stiffness increases to 52.53 kN/mm, 41.28 kN/mm, 36.18 kN/mm, 35.72 kN/mm, and 33.92 kN/mm, corresponding to an increase of 2%, 14%, 18%, 21%, and 31%, respectively. Similarly, under the same number of cyclic loading-unloading cycles, with the increase in the number of water-cooling shocks, the elastic stiffness of granite exhibits a decreasing trend. The aforementioned phenomena are attributed to the fact that the water-cooling shock exacerbates the generation and propagation of microcracks within the granite, and these microcracks continue to propagate during the cyclic water-cooling process. In particular, after multiple thermal cycles, the further expansion of microcracks reduces the integrity of the internal structure of the rock, thereby diminishing its elastic stiffness [44; 45].  
Figure 13: Relationship between elastic stiffness of granite and number of cyclic loading-unloading cycles under cyclic loading-unloading conditions. (**a**) 65% load upper limit; (**b**) 70% load upper limit (**c**) 75% load upper limit; (**d**) 80% load upper limit.