## 2 Numerical Simulation  
### Numerical Modeling  
The numerical model of impact testing included a drop hammer, bearing plate, impact head, and concrete plate. Solid164 solid elements were used for each part, and all were divided by hexahedral meshes. The numerical models of the impact tests under different working conditions are shown in Figure 2, in which the types of drop hammer impact heads included a single impact head, three impact heads, and four impact heads. Among them, there were two working conditions for the four-impact-head tests; one where the long axis of the impact head was along the diagonal direction of the concrete slab (Condition I), and the other where the long axis of the impact head was along the direction of the symmetry axis of the concrete slab (Condition II). Working Condition I was consistent with the actual micro-crack crushing process during the rehabilitation of concrete pavement. For the numerical simulation process of the on-site concrete pavement homogenized microcrack crushing construction and the indoor concrete slab drop-weight impact tests [9], the main material parameters are shown in Table 1 and the parameters of different impact test conditions are shown in Tables 2 and 3. In the process of modeling and analyzing with LS-DYNA, it was necessary to deal with the collision and contact problems of each part. When defining the contact of each part, the contact surface was defined as a set of quadrilateral and triangular regions, where one surface was defined as the master surface and the corresponding surface was the slave surface. In order to ensure correct contact of  
Winfrith (MAT84) concrete constitutive model, with relatively few model parameters, was selected by referring to the research results of others [16; 17; 18; 19]. This model was developed by [PERSON] in the 1980s [22; 23], and the plastic shear failure adopts the following Ottosen four-parameter mode:  
\[\gamma(I_{1},J_{2},J_{3})=\alpha J_{2}+\lambda\sqrt{J_{2}}+bI_{1}-1 \tag{1}\]  
\[\lambda\begin{cases}k_{1}\cos\left[\frac{1}{3}\cos^{-1}(k_{2}\cos(3\theta)) \right]&\cos(3\theta)\geq 0\\ k_{1}\cos\left[\frac{\pi}{3}-\frac{1}{3}\cos^{-1}(-k_{2}\cos(3\theta))\right]& \cos(3\theta)\leq 0\end{cases} \tag{2}\]  
\[\cos(3\theta)=\frac{3\sqrt{3}}{2}\frac{J_{3}}{J_{2}^{3/2}} \tag{3}\]  
where the four parameters \(a\), \(b\), \(k_{1}\), and \(k_{2}\) are all functions of the ratio of tensile to compressive strength (\(f_{i}/f_{c}\)), which can be determined by uniaxial tension (\(\theta=60^{\circ}\)), uniaxial compression (\(\theta=0^{\circ}\)), biaxial compression (\(\theta=0^{\circ}\)), and triaxial compression (\(\theta=60^{\circ}\)).  
Since the Winfrith model does not define tensile failure, MAT_ADD_EROSION was added to define material failure [24; 25]. Under impact, the strength of concrete changes with the strain rate, which mainly produces compressive failure. Therefore, the principal strain was used as the failure criterion for the concrete materials. Concrete usually shows tensile failure or shear failure, in which the hydrostatic pressure is positive for pressure and negative for tension; therefore, hydrostatic pressure failure was used to give the minimum pressure that the concrete could withstand. If the hydrostatic pressure was less than the minimum pressure, then the material would fail.