# Seismic Performance of Reinforced Concrete Short Columns Subjected to Freeze-Thaw Cycles
## 3 Test Results and Analysis
### Skeleton Curves and Characteristic Values  
Figure 9 presents the envelope responses of the specimens and the average responses due to the asymmetry of the hysteresis behaviors in the two loading directions. To quantify the influence of  
Figure 8: Force-displacement responses. freeze-thaw damage, important characteristic values of the specimens are listed in Table 3 and defined as follows: \(F_{y}\) and \(\Delta_{y}\) denote yield force and drift, respectively, calculated through the equivalent energy method [35]; \(\Delta_{u}\) denotes ultimate drift, defined when the applied load declines more than 15% from the peak load (\(F_{p}\)); \(\Delta_{p}\) is the corresponding drift value of \(F_{p}\); \(\mu_{\Delta}\) denotes the displacement ductility coefficient, defined by the ratio of \(\Delta_{u}\) and \(\Delta_{y}\); \(\theta_{\rm P}\) (equals \(\Delta_{u}-\Delta_{y}\)) denotes the plastic rotation of columns. As shown in Figure 9, the skeleton curves were almost overlapped when the drift was less than 0.5%, which means the initial stiffness did not degrade even though the elasticity modulus of concrete decreased due to the freeze-thaw action as stated by [PERSON] et al. [9]. This is possible because the axial load ratio (\(\
u=N/\xi_{\rm c}\cdot A_{\rm g}\)) actually increased with the decrease of concrete strength after FTCs and constant axial force. However, the differences in the skeleton curves became more obvious in the post-peak portion as the numbers of FTCs increased. To be specific, the descending branch became steeper for the most damaged column ZD-2, indicating a more severe strength decay. On the other hand, compared with the control specimen ZD-0, the yield load decreased and the maximum load increased slightly for the specimen with 100 FTCs, ZD-1, as presented in Table 3. All drifts at critical levels increased while the ductility reduced. There are two reasons that could explain the increment in component strength despite the freeze-thaw damage. First, considering the whole test procedure, the specimen ZD-1 was submerged in water before undergoing the freeze-thaw attack, which would help the concrete strength growth of the whole section. Secondly, the freeze-thaw damage penetrated from the component surface to the core, and therefore for a specimen subjected to FTCs, the damage degrees for inner concrete and outer concrete were not the same. Therefore, the deterioration of concrete strength would be more severe for a smaller scale of section size. After 200 FTCs, all the characteristic values listed in Table 3 decreased as compared with the specimen ZD-0. Among them, the measured yield and peak load decreased by 11.8% and 9.8%, respectively, and corresponding drifts decreased by 4.8% and 24.5%. Apparently, this pattern did not agree with the trend exhibited when the number of FTCs was only 100. To explain this inconsistency, the bearing capacities of columns, basically determined by the comparison of flexure strength and \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Specimen** & \(F_{y}\) (kN) & \(\Delta_{y}\) (\%) & \(F_{p}\)(kN) & \(\Delta_{p}\) (\%) & \(\Delta_{u}\) (\%) & \(\theta_{\rm P}\) & \(\mu_{\Delta}\) & \(\xi_{y}\) & \(\xi_{p}\) & \(\xi_{u}\) \\ \hline ZD-0 & 116.87 & 0.71 & 138.01 & 1.46 & 2.77 & 2.06 & 3.91 & 0.02 & 0.06 & 0.10 \\ ZD-1 & 111.81 & 0.82 & 139.97 & 1.47 & 2.83 & 2.01 & 3.40 & 0.03 & 0.05 & 0.09 \\ ZD-2 & 103.05 & 0.67 & 124.45 & 1.10 & 1.79 & 1.12 & 2.65 & 0.02 & 0.04 & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Force and deformation of the tested columns (units: % and kN). Figure 9: Envelops of the hysteresis loops. shear strength, should be analyzed first. Since the freeze-thaw attack mainly affects the strength of concrete, the decay of shear strength would be greater than flexure strength for a column member because of the different contributions of concrete strength to the total bearing capacities.