## 3 Results and Discussion
### Comparative Analysis of Fracture Law with Indoor Low-Velocity Impact Tests  
In the indoor low-velocity impact tests on concrete slabs, under impact-cracking conditions using a single impact head, three impact heads, and four impact heads (Condition I), the concrete slab failed. The crack development is shown in Figure 14.  
In the indoor tests of low-velocity impact cracking of concrete slabs, under the low-velocity impact of a single impact head, there was a compressive shear failure zone on top of the concrete slab regardless of whether the concrete slab was 50 mm thick or 80 mm thick. The bottom of the concrete slab first cracked, the crack developed upwards until the main crack ran through the concrete slab, and then the concrete slab specimen failed [9]. When three impact heads were used for impact tests, the initial crack appeared at the bottom of the concrete slab; the crack first extended forward along a main crack, and then multiple branch cracks appeared. When the concrete slab finally failed, a triangular fracture core was usually formed in the center of the slab. Under the impact of four impact heads (Condition I), the bottom of the concrete slab cracked first, and a nearly quadrilateral fracture core generally appeared in the center of the concrete slab, while the top surface of the concrete slab cracked at a later time than the bottom. The sides of the cracked core were approximately parallel to the edge of the concrete slab, and cracks appeared along the long axis of the impact head and developed to the edge of the concrete slab.  
Through numerical simulation, the crack propagation forms of concrete slabs under the conditions of a single impact head, three impact heads, and four impact heads were analyzed. Figure 15 shows the failed concrete slabs of a single impact head, three impact heads, and four impact heads (Condition I). Under the impact of the single impact head, cracks first appeared at the bottom of the concrete slab, a compression shear zone appeared on the top of the slab, and stress concentration appeared on the four sides and vertices of the impact head. Cracks at the bottom of the concrete slab extended to the top of the slab, and when the main crack ran through the concrete slab, the concrete slab failed. At this time, the stress concentration around the impact head dissipated; however, the stress concentration mainly occurred in the compression-shear zone just below the impact head. Under the impact of three impact heads, the crack first developed along the long axis of each impact head. Due to the stress concentration at the vertex of the rectangular impact head, the fracture first occurred at the vertex; then, cracks expanded along the shortest distance from the adjacent vertex of the impact head, and finally, a triangular cracked core was formed. Cracks also appeared in the long axis direction of the outer edge of the impact head until the cracks developed to the edge of the concrete slab, causing the specimen to fail. Four impact heads were used to impact the concrete slab, with the long  
Figure 14: Fracture forms of concrete slabs impacted by different impact heads. (**a**) Single impact head; (**b**) Three impact heads; (**c**) Four impact heads (condition I).  
axis of the impact head being along the diagonal direction of the concrete slab (Condition I). When the concrete slab failed, a quadrangular fracture core was formed in the center of the concrete slab. The four sides of the cracked core were approximately parallel to the edges of the concrete slab. The cracks in the cracked core developed to the edge of the slab, and some cracks extended to the edge of the concrete slab. At this time, the specimen would have failed.