## 5 Experimental Study with Numerical Methods
### Failure Pattern  
Figure 8 shows the crack development of intact rock specimens, hole-containing rock specimens, and cement-filled hole rock specimens at 70% of peak stress, at peak stress, at 45% after the peak, and in the residual stage. At 70% of peak stress, sporadic microcracks appeared inside the intact specimen. As the experiment continued, tensile microcracks began to increase in number, and shear microcracks appeared on rare occasions. At 45% of peak stress, tensile microcracks increased dramatically, and thorough cracks were formed, resulting in an obvious damage surface. The shear microcracks also began to increase suddenly and mainly appeared in the vicinity of the damage surface. The number of microcracks gradually stabilized and their increment decreased after entering the residual stage. Figure 8: _Cont_. Figure 7: Comparison of stress–strain curves: (**a**) Hole-containing specimens. (**b**) Cement paste-filled specimens. Two tensile cracks sprouted simultaneously near the top and bottom of the hole center at 70% of peak stress in the hole-containing specimens. This observation aligns with the literature [35; 36], which states that sporadic microcracks initially manifest in the stress concentration area. Additionally, a few microcracks emerged in the far field of the hole, exhibiting a predominant tensile crack type. As the axial load increased to reach the peak stress stage, wing-type cracks began to appear on both sides of the hole. In addition, the cracks continued to develop axially, with two distinct tensile cracks appearing above and below the hole, while fewer shear microcracks appeared, which is consistent with the description in the literature [37]. At 45% of peak stress, the tensile microcracks underwent a sharp increase, resulting in the formation of a penetration, which led to the emergence of an obvious rupture surface. At this juncture, the macroscopic cracks formed, and the shear microcracks began to increase, primarily manifesting near the rupture surface. Subsequently to entering the residual stage, a new rupture surface emerged, and the two rupture surfaces, in conjunction with a tensile macrocrack above the hole, collectively formed an inverted \"Y\"-shaped macrocrack damage surface. This pattern of broken discourse is the same as the results of the literature [38]. Cement-filled specimens initially exhibited sporadic microcracks at the periphery of the apertures and within the cement slurry. As the specimens approached the peak stage, microcracks continued to develop at the primary fracture surface of the rock samples and in the filled slurry. The distribution of cracks was significantly denser than in the first two rock sample types, the hole filling had a higher concentration of cracks compared with intact rock, and wing cracks began to develop in the axial direction. As the specimen progressed to 45% of peak stress, the cracks were essentially complete, and obvious rupture surfaces emerged. This was accompanied by the formation of significant macroscopic cracks, while a substantial number of microcracks manifested within the filling area. A comparative study of indoor tests and numerical tests was conducted to reproduce the stress-strain pattern, strength characteristics, and macroscopic damage patterns of the intact rock samples, the hole-containing rock samples, and the cement paste-filled rock samples. The numerical analyses demonstrated a high degree of similarity between the models and the actual rock samples. This indicates that the numerical models of the three types of rock samples established in this paper can appropriately reflect the crack extension development path and the microscopic damage mechanism of this rock material in uniaxial compression tests. A comparison of the crack extension process revealed that the cracks in the cement paste-filled rock samples were significantly influenced by the cement paste-filled portion.