## 4 Conclusions  
1. Compared with the intact sandstone, the strength and deformation properties of specimens with a square hole are decreased, and the decrease rate is closely related to hole angle. After filling, the mechanical parameters of the pre-holed specimens are strengthened, and the strengthening effect of relatively rigid inclusions is much stronger than that of weak inclusions. Moreover, virtual extensometers were arranged on hole boundaries by DIC to measure hole deformation. It is found that the inclusions can restrain the hole deformation, especially the rigid inclusion can gradually passively support the surrounding rock matrix with the increase of load, thereby effectively improving the mechanical behavior of the pre-holed specimen.
2. The crack behavior and final failure pattern of the specimens with a square hole, especially the crack initiation position, are affected by the filling mode and the hole angle. The crack pattern around the square hole can be categorized into four types, while the number of cracks around the square inclusion increases and the crack pattern is more complex, which can be mainly divided into five types. Furthermore, the interface debonding tends to occur at the inclusion interface parallel to major principal stress direction, and the interface slipping tends to propagate along the inclined interface. The fracture evolution of the specimen during uniaxial compression proceeds from primary tensile cracks through secondary cracks to shear cracks, and the rock failure is mainly caused by secondary crack propagation and shear crack coalescence. The failure mode can be generally considered as mixed tensile-shear failure, and the difference is dominated by tension or shear. Notably, the inclusion not only has a certain crack arrest effect on rock matrix, but also can effectively inhibit sidewall spalling.
3. The damage and fracture evolution during uniaxial compression tests on sandstone specimens can be qualitatively and quantitatively characterized by DIC and AE techniques, and their results are in good agreement with the rock mechanical behavior. The AE counts and cumulative AE counts can be roughly divided into five periods or intervals, which correspond to five stages in the stress-strain curve of the specimen, i.e., pore compaction stage, elastic deformation stage, stable crack growth stage, unstable crack growth stage and rock failure stage. By verifying the major principal strain fields obtained by DIC, the critical points between these characteristic periods or intervals can be identified as the crack stress thresholds.  
* Since the crack closure stress is hard to be directly determined by the strain field, an objective approximate estimation method based on stress-strain curves was proposed. In addition, based on the observation of strain localizations on specimen with inclusions, the crack initiation stresses of inclusion and rock matrix were defined. The crack stress thresholds of sandstone can be significantly reduced by the hole and improved by the inclusion. The improvement effect of inclusion increases with the increase of mechanical properties of filling materials and is affected by the hole angle. The hole angle has little effect on crack closure stress, damage stress levels and initiation stress of inclusion, but has obvious effect on crack closure stress levels, damage stress, initiation stress of rock matrix and corresponding stress levels.  
Conceptualization, D.L.; data curation, D.L.; funding acquisition, Q.Z. and D.L.; investigation, Q.Z.; validation, D.L.; writing--original draft preparation, Q.Z.; writing--review and editing, D.L. Both authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (No. 52074349), the Outstanding Youth Science Foundations of Hunan Province of China (No. 2019J20028) and the Fundamental Research Funds for the Central Universities of Central South University (No. 2019 zzts884).  
The authors declare no conflict of interest.