## 4 Analysis of the Damage Pattern of Fiber Shotcrete Laminated Beams Based on the Thickness Ratio  
### Macroscopic Damage Pattern of Fiber Shotcrete Laminated Beams Based on the Thickness Ratio  
In the four-point bending test of concrete, the failure modes of fiber shotcrete beams were classified into shear failure, flexural failure, and mixed-mode failure based on the type of damage cracks [46,47] as shown in Figure 8. In order to investigate the failure modes of fiber shotcrete beams at different thickness ratios, the cracks of the final rupture of the specimens were sketched as shown in Figure 9, where S denotes shear failure and T denotes flexural failure. Figure 8: Concrete failure mode. Figure 9: _Cont._  
In Figure 9, we can see that the cracks in the damaged fiber shotcrete samples at each thickness ratio include vertical bending cracks and slanted shear cracks, indicating a mixed-mode failure. This defect happens because the bending moment and shear force acting together on the fiber shotcrete beams significantly contribute to the damage of the samples. The percentage of flexural failure increases gradually with the increase in the thickness ratio, which is caused by the tensile stress of concrete exceeding its tensile strength when the fiber shotcrete beams are subjected to bending moments, and the layered construction reduces the tensile properties of fiber shotcrete beams. The test indicates that the location of the split interface in the concrete stacked beams affects the failure mode of fiber shotcrete beams, and the damage type of the first layer of fiber shotcrete at \(\lambda_{h}=0\) and \(\lambda_{h}=1\) is mixed-mode failure. While fiber shotcrete beams are layered and the first layer of concrete is thinner (\(\lambda_{h}=2-5\)), the first layer of fiber shotcrete cracks are vertical upward-bending cracks, and the failure mode is a flexural failure. This is due to the fact that after the thickness ratio increases, the first layer of fiber shotcrete is thinner, the shear span ratio is larger, and the flexural failure is dominant. Under the upper load of the four-point bending test, cracks in the test members mainly appeared in the middle of the fiber-sprayed concrete beams. Compared to the thickness ratio \(\lambda_{h}=0\) (single-layer fiber-sprayed concrete beams), when the two-layer fiber-sprayed concrete beams at other thickness ratios were damaged, the crack development showed a significant change at the parting interface, and when the crack developed upward, it would be horizontally deflected at the parting interface, which would lead to a greater release of fracture energy. The main reason for this is that the shear stresses carried at the concrete beam parting interface are provided by friction, and the lower the position of the parting interface, the higher the shear stresses carried, and when the crack develops to the concrete parting interface, the release of larger forces leads to an increase in the offset distance. In particular, at thickness ratios \(\lambda_{h}=1\) to the thickness ratio \(\lambda_{h}=4\), the horizontal offset distance of cracks at the interfaces increases with the increase in the thickness ratio; at the thickness ratio \(\lambda_{h}=5\), the offset distance of cracks at the interfaces is smaller, which is mainly due to the fact that the thickness of the first layer of concrete is too thin, which results in the structural load-bearing capacity being provided by the second layer of concrete almost exclusively, and the crack damage morphology is close to that of the thickness ratio \(\lambda_{h}=0\). Figure 9: Failure modes of fiber shotcrete beams with different thickness ratios (green, red, and blue lines represent the dividing line, the crack, and the transverse mutation, respectively). The final damage pattern of concrete at thickness ratios \(\lambda_{h}=3-5\) shows that interfacial detachment of different layers of concrete occurs at the interface.