# Investigation of Mechanical Properties for Group Anchors
## 4 Numerical Simulation  
At present, the physical test conditions of the anchors are difficult to directly observe the internal stress, displacement, and fracture evolution process of the model, and numerical simulation can better reveal the whole process of the model fracture evolution. In this section, the whole process of the group anchor test is studied through numerical simulation. The size and loading conditions of the numerical model are the same as the above physical test. In this section, RFPA-3D software is used to study the evolution law of the anchor drawing fracture process. The matrix size of the numerical model concrete is 250 mm \(\times\) 250 mm \(\times\) 160 mm, the calculation cell is divided into 125 \(\times\) 125 \(\times\) 100, the diameter of the anchor is 20 mm, the length is 200 mm, the exposure is 40 mm. The loading mode takes displacement as a variable, and the loading step is 0.02 mm. The strength of the rock matrix is 50 MPa and the elastic modulus is 10,000 MPa. The strength and elastic modulus of the anchor are 1400 MPa and 210,000 MPa. Figure 6 shows the failure process of the test models, the failure process of the group anchor and the single anchor has both similarities and differences. The similarities is that the three types are progressive damage from the surface to the inside as the load increases. The differences are that the model surface of the single anchor forms a circular displacement concentration area at the initial stage of loading, the model surface of the two-group anchors  
Figure 5: Pull-out test results of group anchor. forms an elliptical displacement concentration area, and the model surface of the three-group anchors forms a triangular displacement concentration area, as shown in Figure 6a. For the range size of the displacement concentration zone, the three-group anchor is greater than the two, and the two is greater than a single, which means that the group anchor has a larger influence range. With the continuous increase of displacement loading, the damage on the surface of the models is intensified, and the damage is transferred to the inside of the models, and the displacement concentration on the surface of the models is obviously weakened. When the displacement load is 50 mm, the damage on the surface of the three types is transformed into a complete failure, and all models form a failure area, and the shape of the failure area is the same as the displacement concentration area. The characteristics of the failure area are consistent with the above physical model test. This is in good agreement with the results of the above physical test, as shown in Figures 4c and 6b. Figure 7 shows the relationship curve between the load and displacement of three different types of test models. Numerical results show that the maximum pulling force of a single anchor is 76 kN, the maximum pulling force of the two-group anchors is 145 kN, and the maximum pulling force of the three-group anchors is 205 kN. In contrast, the maximum pulling force of the two-group anchor is 1.9 times that of a single anchor, and the three-group anchor is 2.7 times that of a single anchor. Compared with physical test, the performance of the two-group anchor change from 78% to 95% (145 kN:2 \(\times\) 76 kN), and the performance of the three-group anchor changes from 70% to 90% (205 kN:3 \(\times\) 76 kN). Figure 8 shows that the debonding failure process and characteristics of the anchors. Intuitively, the debonding failure process of the group anchor is almost the same as that of the traditional single anchor, which is a process of gradual debonding from the surface to the inside. Careful observation reveals that the debonding failure of the group anchor has some characteristics of its own. One of the characteristics is that the debonding length of the inner side of the rods is lower than that of the outer side; for example, when the two-group anchors is in step-24, the inner side of the rod is de-bonded by 40 mm, while the outer side is de-bonded by 50 mm.