## 5 Experimental Study with Numerical Methods
### Crack Type and Number Analysis  
Figure 9 shows the evolution of the number of tensile and shear microcracks in numerical tests on the intact, hole-containing, and filled specimens. The onset of microcracks within the specimens was observed when the intact test loading was approximately 55% of the peak value, corresponding to a strain of 0.14%. Tensile microcracks exhibited a gradual growth trajectory prior to the peak, subsequently undergoing a substantial escalation post-peak, culminating in a final count of 1411. The onset of shear microcracks was observed to occur prior to the peak, and their growth was found to commence only after the peak. The proportion of microcracks at the time of the peak was found to be 6% of the total microcracks, and the final total number of microcracks was determined to be 1501.  
The initial increase in microcracks within the hole-containing specimens remained minimal until a stress level of 67 percent of the peak value was attained, at which point the strain reached 0.07 percent, marking the onset of microcracks. Tensile microcracks exhibited a gradual increase until they reached their peak, with a final count of 753. Shear cracks also increased only slowly until the peak value was reached. Subsequent to this, although the increase became more pronounced, the number of shear microcracks was a mere 7.04% of the total number of cracks, and the ultimate total number of microcracks was 810.  
The onset of microcracks within the specimens was observed when the cement-filled specimens were loaded to approximately 55% of the peak value, corresponding to a strain of 0.14%. The number of tensile microcracks increased to 4136 upon reaching the peak. The increase in shear microcracks was relatively gentle, and the final total number of microcracks was 4397, with shear microcracks accounting for 5.94% of this total.  
In summary, the prevalence of microcracks in all three specimens was predominantly characterized by tensile microcracks, with shear microcracks exhibiting negligible presence [26]. The cement-filled specimens demonstrated the highest number of total microcracks, followed by the intact specimens, and the specimens containing a hole exhibited the lowest number. The earliest cracking point was observed in the cement paste-filled marble, and the filled area produced a greater number of cracks during the destructive process, which aligns with the performance of the rock specimens in the indoor test.  
The relationship between the number of microcracks and axial strain for the hole-containing specimens was fitted to an exponential curve with a strong correlation (R\({}^{2}\) = 0.9194), as shown in Figure 10. This high goodness-of-fit indicates that the model  
Figure 9: Variation in number of microcracks: (**a**) Intact specimens. (**b**) Hole-containing specimens. (**c**) Filled specimens.  
reliably captures the progressive development of microcracks during loading. The fitted curve quantitatively characterizes the nonlinear accumulation of microdamage, where the increasing slope reflects the transition from stable crack initiation (Stage I) to unstable crack propagation (Stage II). This aligns with the classic \"three-stage\" damage evolution theory [39]. This provides a predictive tool for estimating rock failure precursors in engineering applications.