## 4 Analysis of Results
### Size Effect of the Mechanical Properties of Basalt Blocks
#### 4.1.4 Size Effects of Failure Modes  
Figure 13 shows the failure modes of basalt samples of various sizes with hidden cracks under uniaxial compression obtained from FDEM simulations and laboratory tests or field observations, where the black, red, and cyan lines represent yielded cracks, shear failure cracks, and tensile failure cracks, respectively, and the marker points I-V represent different failure stages. Figure 13: Fracture evolution and failure modes of basalt samples of different sizes with hidden cracks under uniaxial compression. (**a**) Fragmentation failure of intact basalt; (**b**) structure-controlled failure of medium-sized basalt with local fractures; (**c**) splitting failure of REV-sized basalt with sufficient fractures. As shown in Figure 13a, for a small-sized basalt sample (i.e., 50 mm \(\times\) 100 mm) with few hidden cracks, a fragmentation failure mode under uniaxial compression appears, in which the longitudinal and transverse tension cracks are closely interlaced, accompanied by a loud noise and violent ejection, and many fragments appear after failure, indicative of extremely evident brittle characteristics. Basalt has good homogeneity at the grain scale owing to the features of dense arrangement, high strength, and small particle size. Under axial loading, the pre-peak stress field is relatively uniform, and the stress value is small, which is insufficient to reach the local strength of the rock material to form local fractures, without resulting in fractures. When the axial stress approaches the peak strength, the overall stress level is high, and a slight nonuniform stress field occurs. A small number of yielded cracks, which are randomly distributed, appear once the local stress exceeds the local strength of the rock material. The axial stress reduces sharply after the peak, and a prominent heterogeneous stress field, including local stress relief zones and stress concentration zones, is formed, in which more yielded cracks emerge in the stress concentration areas, and the shear and tensile failure cracks in the stress-relief areas initiate instantaneously due to the sliding and opening of crack elements, and they continue to propagate and coalesce to form macro-fractures, accompanied by a large number of fragments. Therefore, the failure process of the entire intact basalt is short, showing a fragmentation failure mode, which is consistent with the experimental results; that is, a tensile failure mechanism caused by high stresses plays a leading role. As shown in Figure 13b, for the medium-sized basalt sample (i.e., 100 mm \(\times\) 200 mm) with a small number of local hidden cracks, the failure mode can be tension failure, tension-shear composite failure, or shear failure. Basalt with local hidden cracks is a typical heterogeneous rock material. Due to the difference in the elastic modulus between the matrix and hidden cracks, a slight heterogeneous stress field occurs near the cracks in the initial loading stage, because of which the local strength of the rock material cannot be reached to form local fractures. With the increase in the loading, a significant stress concentration area is formed near the hidden cracks in the pre-peak loading stage; that is, a tensile stress concentration zone appears in the upper and lower tips of the hidden cracks, and a compressive stress concentration zone appears on both sides. Shear failure occurs first on the hidden crack surfaces due to the low shear strength, and then, a tensile crack (i.e., wing crack) approximately parallel to the loading direction appears at the hidden crack tips once the local tensile stress exceeds the tensile strength of the rock material. In the post-peak stage, the microcracks formed continue to expand and penetrate, leading to a macro-failure of the sample.