## 2 Finite Element Simulation
### Calibration of CDP Parameters  
When the concrete damage plasticity model is used to simulate the cracking behavior of concrete, two parameters--the dilation angle and the viscosity parameter--need to be calibrated to ensure the accuracy of the simulation. The dilation angle \(\psi\) in the CDP model of this paper is set to simulate the volume expansion of concrete as a brittle material due to inelastic strain when subjected to tension. A larger dilation angle indicates more brittle concrete. [PERSON] et al. [20] defined the dilation angle for reinforced concrete, and its value was specified from \(31^{\circ}\) to \(42^{\circ}\). The recommended values in the ABAQUS user manual [11] are \(30\)-\(45^{\circ}\). The viscosity parameter \(\mu\) is a time-dependent parameter that controls the convergence of the model and the accuracy of the calculation. When \(\mu\) is equal to \(0\), the material is purely plastic; when \(\mu\) is equal to \(1\), the material is purely elastic. The smaller the value, the more precise the accuracy, and the more the speed of the calculation decreases. The recommended values in ABAQUS [11] range from \(0.00001\) to \(0.005\). For the experiments of [PERSON] et al. (2019), the parameters are calibrated based on the S1 slab. Figure 12a shows the results from simulations with different dilation angles. All of the dilation angle results in Figure 12a were obtained at \(\mu=0.0001\), where \(\mu\) is at a relatively accurate level, and the curves for \(\psi=30^{\circ}\) and \(\psi=35^{\circ}\) both have peaks and fall rapidly, demonstrating that damage to the slab has occurred and does not fit with the experimental curve. The comparison shows that \(\psi=40^{\circ}\) can simulate the experimental  
Figure 11: Uniaxial stress–strain curves for concrete: (**a**) uniaxial compressive stress–strain curve of concrete; (**b**) uniaxial tensile stress–strain curve of concrete. results relatively accurately. Figure 12b shows the simulation results for different viscosity parameters. The smaller the viscosity parameter, the more accurate the results. Figure 13 shows a good correlation between the post-processed cloud image and the photographs of the cracks. The results of Figure 13 are simulated for \(\psi=40^{\circ}\), \(\mu=0.0001\). The numerical simulation can accurately simulate tangential cracks on the face of the slab, and the ring cracks are formed outside the shear reinforcement region (the red bar is the location of the shear studs), which is consistent with the description of the experimental results. Therefore, \(\psi=40^{\circ}\), \(\mu=0.0001\) was finally determined and applied to all of the model simulations of [PERSON] et al. For [PERSON] and [PERSON]'s experiment, relatively accurate simulation results were obtained using \(\psi=40^{\circ}\), \(\mu=0.005\). The results of the comparison of the experimental results from P1 to P5 with the simulated values can be seen in Figure 20.  
to the experimental results. When comparing the photos to the experimental results, the cracks are visibly in similar locations. The experimental results are similar to the cracks in the simulated plates with concentric force (i.e., S2 and S7). A visible ring of closed cracks is formed around the column, which is typical of punching shear damage. The crack simulation results for the eccentric force plate S3 are consistent with the experimental results, with an asymmetric shape of the cracks due to eccentric loading. However, the crack patterns of S4 and S8, which are also subjected to eccentric forces, can show circular cracks near the columns, but the overall crack similarity is different. This may be due to the increase in the number of shear studs, which leads to sliding in the outer two rings of the shear studs in the plate under actual conditions. While the ABAQUS simulation assumes that the reinforcement and concrete are embedded constraints, this is an ideal state. Because there is no relative slip, the cracking is symmetrical, and the cracks on the eccentric force side are more developed.