## 4 Anchor Bolt Pull-Out Analysis
### Effect of Installation Conditions on the Fracture Mode
At the upper part, the constraint from the surrounding concrete is relatively low. Micro cracks and major radial cracks can both be found in this area. Thus, the bond stress in this area decreases at an earlier stage [12; 15]. In Figure 12c,d, where the adhesive stress limit is 12 MPa, crack development and bond stress distributions are similar to the previous case. With the increase of adhesive stress limit, the cone area at the upper part of the anchor bolt when \(x=225\) um is larger than that in Case 1. The final fracture pattern changed from bond fracture to bond-cone complex fracture. In Figure 12e,f, where the bond stress is 16 MPa, the crack development and the bond stress distribution of \(x=75\) um is similar to previous cases. When \(x=300\) um, the crack reaches the surface of the concrete block, and the bond stress on the lower part of the anchor bolt decreases, forming a cone shaped fracture pattern. The load-displacement relationship of Case 1, 2, and 3 is shown in Figure 13, where it shows that, with the increase of the maximum bond stress, the maximum load is increasing. For the case with bond stress of 8 MPa where the fracture pattern is bond fracture, the shape of the load-displacement curve is similar to the bond-stress curve mentioned in Figure 3b. For the case with bond stress of 12 MPa where the fracture pattern is compound fracture, it can be found that the area of the load-displacement curve is larger than the previous curve, indicating that the energy consumed in compound fracture is larger than in bond fracture. For the case with bond stress of 16 MPa, the maximum load is larger than the previous cases, and the area of the load-displacement curve, or the energy consumed, is even larger. Because of concrete cracks generated in this process, more noise can be observed in the curve. Figure 11: Effect of adhesive stress on the fracture pattern. For case 2, 6, and 7, when increasing the diameter of the anchor bolt, the damage pattern changed from bond damage to cone damage, shown in Figure 14, and the load-displacement relationship is shown in Figure 15. When the diameter of the anchor bolt increases, more bond force is provided by the increased interface area between anchor bolt and concrete. This bond force is subjected to the same amount of concrete in a cone-shaped area; thus, more concrete is damaged with more bond force by the pull-out process. Figure 14: Effect of anchor bolt diameter on the fracture pattern. Figure 12: Crack development and bond stress distribution. (**a,b**) Case 1. (**c,d**) Case 2. (**e,f**) Case 3. Figure 13: Load-displacement relationships with different bond stress. For case 2, 4, and 5, when changing the embedment depth of the anchor bolt from shallow to deep, the damage pattern changed from cone damage to bond damage, shown in Figure 16, and the load-displacement relationship is shown in Figure 17. When the embedment depth of the anchor bolt increases, the volume of the cone-shaped area also increases. Although more bond force is provided by the increased interface area, the fracture pattern changes from cone fracture to bond fracture due to more concrete participating in resisting the bond force. To summarize, the analysis cases with bond stress of 12 MPa and their final crack pattern are listed in Table 5 and Figure 18. In this figure, the horizontal axis is the ratio between embedment depth \(l_{e}\) and the anchor bolt diameter \(d\), while the vertical axis is the maximum load \(P\) in the pull-out process. When \(l_{e}/d<3\), the fracture pattern is cone fracture; when \(l_{e}/d>3\), the fracture pattern is bond fracture; and, when \(l_{e}/d=3\), the fracture pattern is cone-bond complex fracture. This figure shows the tendency that, in this study, with the increase of the value of \(l_{e}/d\), the fracture pattern changes from cone fracture to bond fracture. Figure 16: Effect of embedment depths on the fracture pattern. Figure 12.0 Load-displacement relationships with different embed depths.