## 3 Numerical Simulation of UDRC Spallation
### Interface Bond Behavior Verification  
To address the potential influence of steel-concrete interface behavior on the simulation results, a comprehensive sensitivity analysis was conducted comparing the shared-node (perfect bond) assumption with a cohesive zone modeling approach.  
Cohesive elements were implemented at the steel-concrete interface to simulate realistic bond-slip behavior using the *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE_TIEBREAK formulation in LS-DYNA. The interface behavior was governed by a bilinear traction-separation law, with parameters calibrated based on established bond-slip relationships for steel reinforcement in concrete under dynamic loading conditions. The cohesive model was characterized by the following parameters:  
* Maximum normal stress: \(\sigma_{\text{max}}=1.5\sqrt{f_{ck}}\)
* Maximum shear stress: \(\tau_{\text{max}}=2.5\sqrt{f_{ck}}\)
* Critical normal displacement: \(\delta_{n,c}=0.1\) mm
* Critical shear displacement: \(\delta_{s,c}=0.15\) mm  
where \(f_{ck}\) represents the characteristic compressive strength of concrete. For the C40 concrete employed in this study (\(f_{ck}=40\) MPa), the theoretical maximum bond shear stress was calculated according to established design codes as follows:  
\[\tau_{\text{max}}=2.5\sqrt{40}=15.4\,\text{MPa} \tag{6}\]  
This value serves as the critical threshold for interface debonding under the given material conditions.  
The finite element simulations revealed that the actual interface shear stress reached a maximum of only 0.8 MPa, occurring at approximately \(t=261\) us (Figure 8). This peak stress is approximately 19 times lower than the theoretical bond failure threshold given in Equation (6), indicating that the interface remains well within the elastic range throughout the entire loading process. This substantial safety margin definitively confirms that bond slip or debonding phenomena are not of concern under the investigated loading conditions.  
Figure 8: Temporal evolution of interface shear stress at the steel–concrete interface. The peak stress of 0.8 MPa remains significantly below the theoretical bond failure threshold of 15.4 MPa.  
Figure 9 presents a quantitative comparison of stress triaxiality and Lode parameter distributions between the shared-node and cohesive zone models. Remarkably, the cohesive zone model yields stress states in the bulk concrete region (\(r>8\,\mathrm{mm}\)) that demonstrate improved consistency with the ideal uniaxial compression value of \(-1/3\) for stress triaxiality. This counterintuitive finding can be attributed to the slight compliance introduced at the interface through the cohesive formulation, which effectively reduces stress concentrations and promotes more uniform stress distribution throughout the concrete matrix. Consequently, the cohesive zone analysis actually reinforces rather than undermines the validity of the one-dimensional stress assumption underlying the pull-back method.  
In summary, the sensitivity analysis demonstrates that the influence of cohesive elements on the stress state becomes more pronounced with increasing interface stiffness, with the shared-node constraint condition representing the maximum possible influence on the stress state of concrete in the vicinity of the reinforcement. Therefore, the shared-node modeling approach is adopted throughout this study as it provides the most conservative assessment of the interface effects on the overall structural response while maintaining computational efficiency and ensuring that the method validation encompasses the most restrictive conditions.