Deviatoric stress-strain curves and Overall deformation of crushed gangue under triaxial compression: The deviatoric stress-strain curve and overall deformation of crushed gangue under different confining pressures are shown in Fig. 3 and Fig. 4, respectively. It can be concluded from the Fig. 3 and Fig. 4 that in the triaxial compression process of crushed gangue, with the increase of axial deformation, its deviatoric stress gradually increases with the increase rate decreasing. The simulation results under confining pressure of 0.1MPa are consistent with that in literature [34]. Hence, the accuracy of the numerical simulation model is reliable. Under the same strain condition, the deviatoric stress of crushed gangue increases with the confining pressure increasing. When ε = 0.4, the maximum axial stress σ1 of crushed gangue is 3.50 MPa, 4.63 MPa, 5.66 MPa and 6.44 MPa under confining pressures of 1.0 MPa, 1.5 MPa, 2.0 MPa and 2.4 MPa, respectively. It indicates that the bearing capacity of crushed gangue increases with the confining pressure increasing. In addition, the bulging deformation is most obvious at the low confining pressure. With the increase of confining pressure, the degree of bulging deformation gradually decreases. The reasons are as follows: the larger the confining pressure, the higher the restraint degree of the block in the sample, the more difficult the lateral deformation of the block. As a result, the bulging deformation of the sample is less significant.
Vertical movement evolution law of block of crushed gangue under triaxial compression: The vertical movement of the block in the crushed gangue are obtained considering different strain states at σ3 = 0.1MPa, as shown in the cloud map of Fig. 5. The vertical movements of the block considering different confining pressures at ε = 0.4 are shown in Fig. 6. It can be concluded from Fig. 5 and Fig. 6 that
① The vertical movement amount of the block in the crushed gangue decreases from the top to the bottom of the gangue sample in the process of triaxial compression. This is because the block at the top of the gangue sample is first disturbed by the loading plate, and the displacement is the largest. With the increase of the distance between the block and the loading plate, the disturbance degree gradually decreases and the displacement decreases gradually.
② The vertical movement of gangue block increases gradually with the increase of compression deformation. However, due to the constraint of the rigid loading plate and rigid base, the “triangle area” of the block displacement appears at the top and bottom of the sample, and the “triangle area” becomes more and more obvious with the loading process. The vertical displacement of the block in the top “triangle area” is significantly greater than other blocks in the same layer; the vertical displacement of the block in the bottom “triangle area” is small, which is obviously lower than other blocks. The above results show that: the vertical displacement of blocks in the same layer is different in the process of triaxial compression. In other words, when the vertical displacement of block occurs in the sample, the adjacent blocks have obvious dislocation.
③the triangular area of vertical displacement at the top of the crushed gangue sample decreases with the increase of confining pressure. The reasons are as follows: the greater the confining pressure, the higher the restraint degree of the block in the sample, the more difficult the lateral displacement of the block, and the less significant the dislocation between adjacent blocks in the same cross section. Finally, the “triangle area” of vertical displacement at the specimen top is less obvious.
Lateral movement evolution law of block of crushed gangue under triaxial compression: The lateral movement of the blocks in the crushed gangue are obtained considering various strain states at σ3 = 1.0 MPa, as shown in the cloud map of Fig. 7. The lateral movement of the blocks are obtained considering different confining pressures at ε = 0.4, as shown in Fig. 8. It can be concluded from Fig. 7 and Fig. 8 that
① The lateral movement of the gangue block changes from gathering towards the axis to expanding outward in the process of triaxial compression, when the axial deformation is increased. Under the restriction of confining pressure, the block in the sample moves towards the axis. At the same time, under the axial load, the sample is gradually compacted, but the compaction degree of the specimen orderly decreases along the axial direction of the sample. As a result, the difficulty of lateral movement of the block also decreases gradually from top to bottom. With the loading process, the lateral movement of the block is difficult to be restrained by the confining pressure. Under the action of axial load, the block begins to move outward, and the closer to the edge of the sample, the more significant the displacement. Moreover, due to the constraint of the rigid loading plate and rigid base, the lateral displacement of the middle location of the block is obviously larger than that of the two ends. Then a “triangle area” inside the block is formed both sides of the sample. With the axial deformation increasing, the “triangle area” of lateral displacement becomes more and more obvious. The above results reveal the deformation evolution mechanism of the crushed gangue samples from “extruding to the axis” to “bulging to the periphery” during the loading and compression from the perspective of mesoscopic fabric evolution of block movement in Section 3.2.
② With the increase of the confining pressure, the “triangle area” of lateral displacement of crushed gangue sample decreases. This is because the greater confining pressure leads to higher degree of restraint on the block in the sample and the greater difficulty of block lateral displacement. Finally, the “triangle area” of lateral displacement of the crushed gangue sample becomes smaller.
Skeleton force chain evolution law of the specimen under triaxial compression: In the triaxial compression process, most of the external load is mainly borne by the skeleton force chain. Under the condition of confining pressure of 1.0 MPa, the sample composed of crushed gangue are compressed to different strain states (ε = 0.0, 0.1, 0.2, 0.3 and 0.4), then the skeleton force chain distribution characteristics in the crushed gangue samples are obtained, as shown in Fig. 9. Furthermore, the relations of contact number-axial strain and maximum contact force-axial strain in the specimens are also discussed in Fig. 10. Under the confining pressures of σ3 = 1.0 MPa, 1.5 MPa, 2.0 MPa and 2.4 MPa, the crushed gangue samples are compressed to ε = 0.4, and the evolution characteristics of skeleton force chain distribution are obtained, as shown in Fig. 11. The relations of contact number-confining pressure and maximum contact force-confining pressure in the specimens are also discussed in Fig. 12. The red chains in the Fig. 9 and Fig. 11 represent the skeleton force chain, other colors reflect general contact forces, and the thickness of the skeleton force chain shows the magnitude of the contact force. It can be seen from Fig. 9 to Fig. 12 that
① With the skeleton force chain structure gradually formed, the process of “failure - reconstruction” begins to occur continuously. However, the stability of the skeleton force chain structure becomes stronger with the axial strain increasing. This is because the most of the external load is borne by the skeleton force chain structure. With the increase of the external force, the block in the load-bearing framework is first crushed due to the stress concentration, which leads to the instability and failure of the bearing skeleton structure. Then, a series of phenomena, such as displacement, rotation of the block in the sample, and filling of the small block into the gap between the large blocks are caused. As a result, the stability of the large block is improved, the internal structure of the sample is adjusted and optimized, and a more stable skeleton force chain structure is formed. Therefore, the bearing capacity and deformation resistance of the sample are improved.
② Confining pressure affects the stability of skeleton chain structure of the samples during triaxial compression. With the confining pressure increasing, the stability of the skeleton force chain structure gradually improved, the total contact number and maximum contact force between particles also gradually increase. The reasons are as follows: the greater the confining pressure, the higher the degree of restraint on the block in the sample, the greater the difficulty of block movement during the compression deformation, the more stable the block in the skeleton force chain structure. This will result in a more stable and stronger skeletal force chain structure which greatly improved the bearing capacity of crushed gangue sample. When the crushed gangue samples are loaded to ε = 0.4 under the conditions of σ3 = 1.0 MPa, 1.5 MPa, 2.0 MPa and 2.4 MPa, the total number of contacts in the samples are 79246, 87659, 92687 and 99568, respectively, with an increase of 25.6%. The maximum contact forces in the samples are 7271 N, 9556 N, 12794 N and 14556 N, respectively. It can be deduced that increasing confining pressure can significantly enhance the bearing capacity of crushed gangue.
Block fragmentation evolution law of the specimen under triaxial compression: When the confining pressure is σ3 = 1.0 MPa, crushed gangue samples is compressed to ε = 0.1, 0.2, 0.3 and 0.4, and then the spatial-temporal distribution characteristics of blocks are obtained, as shown in Fig. 13. The crushed block number are also counted in the Fig. 14. Under the confining pressure of σ3 = 1.0 MPa, 1.5 MPa, 2.0 MPa and 2.4 MPa, the crushed gangue sample is compressed to ε = 0.4, and the spatial distribution characteristics of blocks are obtained, as shown in Fig. 15. The test results are shown in Fig. 16. It can be seen from Fig. 13 to Fig. 16 that
① under the triaxial compression condition, with the loading process, the block fragmentation in the sample is gradually developed, and the amount of fragmentation increases gradually. Besides, the following spatial distribution characteristics are presented: the fragmentation amount of the block gradually decreases (except for the bottom) from the top to bottom and show an obvious distribution characteristic of top > bottom > middle. This is due to the end effect at the top and bottom of the sample, and the strength of the rigid loading plate and rigid base is much higher than that of the gangue block. When the top and bottom blocks of the sample contact with the rigid loading plate and the rigid base, the gangue blocks are more likely to be broken. At the same time, the external load is transmitted gradually from the specimen top to the bottom, and most of the load is transferred through the skeleton force chain structure. The block in the skeleton force chain bears the higher load and is more likely to be crushed.
② Confining pressure has a significant influence on the fragmentation degree of gangue specimens. The higher the confining pressure, the higher the fragmentation degree. When the crushed gangue samples are loaded to ε = 0.4 for σ3 = 1.0 MPa, 1.5 MPa, 2.0 MPa and 2.4 MPa, the number of crushed gangue samples is 5639, 7822, 9678 and 11146, respectively, with an increase of 97.7%. This is because the higher the confining pressure, the higher the restraint degree of the block, and the stronger the stability of the skeleton force chain structure formed in the sample. When the specimen is loaded to the same strain state, the greater the pressure, the higher the indirect contact force of the block, and the more likely the block to be crushed.