## 2 Test Preparation and Procedures  
### Specimen Preparation  
The rock matrix material in our test is green sandstone taken from Neijiang, Sichuan province of China. The sandstone was identified as fine-to-medium-grained sandstone with clastic texture and massive structure. It is mainly composed of quartz (28%), plagioclase (24%), potassium feldspar (19%), chlorite (18%), siliceous debris (7%), calcite (2%) and iron (2%), with a grain size distribution of 0.04-0.4 mm. The prismatic sandstone specimen was processed to have the geometric dimension of 120 mm (height 'H') \(\times\) 60 mm (width 'W') \(\times\) 30 mm (thickness 'T'), and the end surfaces of the specimens were polished according to the standards of the International Society for Rock Mechanics (ISRM) [28]. The height-to-width ratio of the specimen was 2.0 to minimize the end friction effect under uniaxial compression, and the designed thickness could ensure the consistency of surface fracture and internal damage [29]. A square hole with the side length of 13.3 mm was fabricated in the center of sandstone specimens using a high-pressure water jet cutting system, and two inclination angles of 0\({}^{\circ}\) and 45\({}^{\circ}\) were considered to investigate the relationship between the crack behavior and the hole angle. The prefabricated square holes in the specimens were filled with two types of cement mortar with different mixture proportions: Type I and Type II inclusion, which were mainly composed of 42.5 Portland cement, quartz sand with particle size less than 0.425 mm, purified water and 0.5% expansion agent. The mixture mass ratio of Type I inclusion was 1:4:0.75 (cement: sand: water), while that of Type II inclusion is 1:2:0.45. After curing for 28 d at a temperature of 20\({}^{\circ}\) and a humidity of 95%, some essential physical and mechanical properties of the tested sandstone and inclusions are listed in Table 1. The longitudinal wave velocity of the sandstone and filling materials was measured by the wave velocity measurement system (ZT801 model). The uniaxial compressive strength (UCS), Poisson's ratio and Young's modulus were obtained by testing standard cylindrical specimens with a size of \(\varphi 50\times 100\) mm using the Instron-1346 testing system. The Brazilian tensile strength was calculated by testing standard Brazilian disc specimens with a size of \(\varphi 50\times 25\) mm under radial compression. The mode I fracture toughness of sandstone was obtained by three-point bending test on semi-circular bend (SCB) sandstone specimens. However, since it was difficult to prepare fracture test specimens with filling materials, the fracture toughness of filling materials was not measured. The results show that the UCS and Young's modulus of Type I inclusion are much lower than the sandstone, so it can be treated as weak filling materials in rocks. While Type II inclusion is a kind of filling material with relatively stronger strength and stiffness, such as calcium or siliceous fillers. In addition, intact specimens and specimens with open holes were also prepared for testing for comparison purposes. Therefore, three filling modes were considered, including no inclusion, Type I inclusion and Type II inclusion, which are represented by letters A, B, and C respectively. The geometric sketch and photographic images of the prepared specimens are shown in Figure 1. Table 2 lists the geometrical sizes and mechanical parameters of the tested specimens. The specimen number describes