# Mechanical Properties of Marble Under Triaxial and Cyclic Loading Based on Discrete Elements
## 5 Micromechanical Response and Analysis  
### Microrack Number Evolution  
During the loading process, rock materials undergo complex deformation and damage, with the generation and propagation of microcracks playing a crucial role in influencing the mechanical properties and failure mechanisms of the rock. DEM is used to track and record cracks, and the change in the number of microcracks is monitored in real time to analyze the law of the evolution of damage in rock specimens. In the parallel bonding model, when the normal stress or tangential stress applied during compression exceeds its corresponding bonding strength, the contact bond between particles will break, and this fracture process leads to the formation of microcracks. These fractures can be classified into tensile cracks and shear cracks based on the dominant stress direction, as illustrated in Figure 14 below [36]. Figure 14: Schematic representation of microcrack formation. Figure 13: Comparison of the mechanical parameters for two loading paths: (**a**) peak strength; (**b**) Poisson’s ratio; and (**c**) elastic modulus. The development of the number of microcracks under conventional triaxial is shown in Figure 15a. Based on Figure 16, it can be observed that the evolution of the number of microcracks in rock specimens under varying circumferential pressures follows a similar pattern. The development curves for the total number of cracks, tensile cracks, and shear cracks exhibit an \"S\"-shaped growth trend, with their abrupt changes correlating well with the elastic, plastic, and failure phases of the stress-strain curve. At the beginning of loading, the rock specimens are in the elastic phase and the number of microcracks is low; the number of microcracks gradually increases as the rock specimen is loaded until it enters the plastic phase. When the axial strain exceeds the peak strain, the microcracks grow dramatically and penetrate each other, leading to macroscopic damage to the rock specimen. After entering the residual stage, the number of microcracks gradually becomes stable. In the pre-peak stage, the higher circumferential pressures correspond to fewer microcracks, indicating that the circumferential pressures can inhibit the propagation of microcracks during this phase. Additionally, as the circumferential pressures increase, the stage of rapid microcrack growth is progressively delayed, suggesting that the circumferential pressures moderate the rapid development of cracks to some extent. When the rock specimens are loaded to the residual stage, the cumulative number of microcracks increases with the increase in the circumferential pressures, and at the end of the test, the total number of cumulative microcracks under each circumferential pressures is 824, 1412, 1819, and 2017, which is primarily due to the circumferential pressures exerting a limiting effect on the lateral deformation of the rock specimen, which hinders its destruction. As a result, the accumulation of microcracks in the rock specimen increases by the end of the test. Figure 15: Microcrack evolution diagram for two loading paths (20 MPa): (**a**) conventional triaxial; and (**b**) cyclic loading. The evolution of microcracks under cyclic loading is depicted in Figure 15b. As shown in Figure 17, the number of internal microcracks in the rock specimens increases in a stepwise fashion with the increase in axial strain under varying circumferential pressures. In the pre-peak stage, there are few microcracks, and the number development shows obvious \"memory\" characteristics; in other words, the number of microcracks remains stable in a horizontal line before the axial strain reaches the maximum strain of the last cycle when the axial stress is reloaded after unloading. When cyclic loading reaches near to the peak strength, the microcrack number curve shows a non-\"memory\" behavior, and the number of microcracks begins to increase before the axial strain reaches the previous maximum.