## 5 Damage State Evaluation of RC Columns  
In the previous subsection, the damage state of RC columns after impact is evaluated qualitatively. Due to the lack of quantitative standards, it is not convenient for engineering applications. In this section, a quantitative evaluation standard for the damage state of components after impact will be given. In 2010, [PERSON] et al. [26] found a good linear relationship among impact energy \(\mathbf{E}_{k}\), maximum displacement \(\mathbf{u}_{\text{max}}\) and static ultimate load-bearing capacity \(\mathbf{F}_{\text{su}}\) through the drop-weight experimental results of 21 RC beams with final bending failure, and summarized the following formula:  
\[\mathbf{F}_{\text{su}} =0.522\frac{E_{k}}{\mathbf{u}_{\text{max}}} \tag{10}\]  
Since then, international drop-weight impact test research teams, such as [PERSON] [27; 28], [PERSON] and [PERSON] [29; 25], have verified its reliability through experiments or a large number of collected data on RC beam drop-weight experiments and obtained satisfactory results. In the above study, the ultimate flexural failure of RC beams, as shown in Figure 11(a), is actually characterized by the formation of a plastic hinge at the mid-span impact position, and its failure mechanism is similar to that of RC columns in this study, as shown in Figure 11(b). In the actual project, due to the energy absorption of the anti-collision device, only part of impact kinetic energy is converted into the deformation energy \(E_{\text{ab}}\) of the RC column. Therefore, the impact energy of the structure can be better reflected by using \(E_{\text{ab}}\). The calculation of \(E_{\text{ab}}\) is shown in Figure 22.  
According to the above method, based on the impact simulation of RC column specimens under impact in ref. [30] by ABAQUS, \(\mathbf{E}_{\text{AB}}\) and \(\mathbf{u}_{\text{max}}\) of the specimen are obtained, and the equivalent static load \(\mathbf{F}_{\mathbf{eq}}\) (calculated by Formula (11)) is defined and compared with its maximum static load-bearing capacity \(\mathbf{F}_{\text{su}}\) (calculated by finite element in Point 2.3). All calculation results are listed in Table 5.  
\[\mathbf{F}_{\text{eq}}=\frac{\mathbf{E}_{\text{ab}}}{\mathbf{u}_{\text{max}}} \tag{11}\]  
Figure 21: Failure diagram of reinforced concrete members under load. Figure 23 shows the \(F_{\text{eq}}/F_{\text{su}}\) ratio of all specimens. It can be found that for specimens DZ150-4 and DZ180-3 with small impact speed, the damage after horizontal impact is very slight, which means that the whole specimen does not enter the plastic stage, and the ratio \(F_{\text{eq}}/F_{\text{su}}\) is basically below 0.4. For the specimen DZ150-7 with high impact speed, the damage is more serious after horizontal impact, and the ratio \(F_{\text{eq}}/F_{\text{su}}\) exceeds 1.1. In general, except that the ratio \(F_{\text{eq}}/F_{\text{su}}\) (=0.75) of specimen DZ120-3 does not agree well with the experimental damage state (complete failure), the other specimens are in good agreement. Therefore, 0.4 and 1.1, two specific values of \(F_{\text{eq}}/F_{\text{su}}\), were taken as the critical values to divide the states of slight damage, the plastic stage and failure.