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.