4 NUMERICAL SIMULATIONS
In the support mode S4 (shotcrete and systematic rock bolts), two kinds of specimens were simulated by 3DEC. Displacement constraints are applied at the bottom and around the model, and the loading rate at the top of the model is calculated as 1 × 10−3 mm/step.
The 3DEC simulation results are compared with the stress–strain curves obtained by the laboratory experiments, as shown in Figure 8, and the numerical simulation and the experimental results are found to be in good agreement. The stress–strain curve of the specimens with a bedding angle of 0° shows different degrees of fluctuation at the post-peak stage, and the stress falls rapidly after the specimens with a bedding angle of 90° reach their peak strength values, which is caused by the failure process and the failure mode of the specimens. The specimens with a bedding angle of 0° primarily show the shear failure controlled by rock materials. The existence of the bedding surfaces causes the specimens to produce secondary cracks along the bedding surfaces or at a certain angle to the bedding surfaces, and the occurrence of secondary cracks causes the stress–strain curves to fluctuate. The failure of the specimens with a bedding angle of 90° is primarily controlled by the bedding surfaces, which indicates the tension failure along the bedding surfaces. When the load level reaches the peak strength of the specimen, the specimen rapidly deforms along the bedding surface.
The numerical simulation failure mode of 3DEC is shown in Figure 9. The simulation results show the influence of bedding on the failure mode. That is, in addition to the single inclined plane shear failure of the specimens with a bedding angle of 0° (Figure 9(a)), more failure areas are observed along the bedding surfaces. The failure of the specimens with a bedding angle of 90° is primarily controlled by the bedding surfaces, and the failure areas are distributed along the vertical bedding. The 3DEC simulated the failure of the specimens along the bedding or joint surfaces, such as slippage and cracks, and visually showed the deformation of the specimens along the bedding or joint surfaces (such as the cracks along the virtual joint and the bedding as shown in Figure 9(a) and (b)).
As shown in Figure 10, the deformation of holes and shotcrete obtained by the 3DEC simulation is quite similar to the results obtained in laboratory tests.
The 3DEC was used to further simulate the triaxial tests of the two specimens under the above support modes in order to observe the damage and fracture of the specimens with holes and anchors and to determine the behavioral characteristics of the support structures. Displacement constraints were applied at the bottom of the model, the confining pressures applied in the X and Y directions were MPa and MPa, respectively, and the loading rate at the top of the model was 1 × 10−3 mm/step.
The numerical simulation tests have obtained the evolution process of the damage and fracture of the specimens with bedding angles of 0° and 90° under the stress-damage coupling, as shown in Figure 11. The cracks of the specimen with a bedding angle of 0° started from the top and bottom of the hole, mainly for tensile failure, and then the shear failure occurred on both sides of the hole. Then, the tensile failure areas at the top and bottom of the hole and the shear failure areas on both sides of the hole extended to the inside of the specimen along the horizontal bedding direction, which thus formed a failure area of a certain depth around the hole. The failure process of the simulated specimen with a bedding angle of 90° is different from that of the specimen with a bedding angle of 0°. The specimen cracked due to the shear failure of the two sides of the specimen. Thereafter, the cracks developed along the shear failure on both sides of the specimen to the deep part of the specimen; when the cracks developed to the vertical bedding surface, the failure type turned to a mixed vertical shear and split failure along the bedding surface. However, due to the influence of the confining pressure, the specimen did not form a through-crack along the bedding surface, but a shear failure occurred, which shows that the existence of the bedding surface can affect the failure process of the rock mass and the distribution of secondary cracks under triaxial compression, but it cannot affect the final failure mode.