# Studies on Seismic Performance of Precast Concrete Columns with Ground Splice Sleeve
## 3 Test Results and Discussion
### Discussion on Test Results
#### 3.2.3 Stiffness Degradation Curves  
The stiffness of the column will degrade after cracking. Under low cyclic repeated horizontal loading, the computational formula of its stiffness can be expressed as  
\[K_{i}=\frac{\left|+P_{i}\right|+\left|-P_{i}\right|}{\left|+\Delta_{i}\right| +\left|-\Delta_{i}\right|} \tag{1}\]  
where \(K_{i}\) means the secant stiffness of the specimen under the \(i\)th level load; \(+P_{i}\), \(-P_{i}\) are the peak load values of the first circulation under the \(i\)th level load and \(+\Delta_{i}\), \(-\Delta_{i}\) are their corresponding displacements. Due to the small number of load levels in the low cyclic repeated loading stage, the stiffness degradation in the failure stage is considered simultaneously, and the stiffness value is obtained from Equation (2) whose calculated results can qualitatively reflect the change tendency of stiffness degradation during the whole loading process.  
\[K=\frac{P}{\Delta} \tag{2}\]  
Calculate the stiffness value of specimens at each loading stage, including initial stiffness \(K_{30}\), cracking stiffness \(K_{cr}\), yield stiffness \(K_{y}\), and ultimate stiffness \(K_{u}\). Since the reading of the displacement sensor has a large relative error at the beginning of the test, the secant stiffness at the end of the first stage of the low cyclic repeated loading is regarded as the initial stiffness \(K_{30}\), and the secant stiffness at the end of the second stage of the low cyclic repeated loading is denoted as \(K_{130}\). Then calculate the relative stiffness of \(K_{130}\), \(K_{cr}\), \(K_{y}\), and \(K_{u}\) with respect to \(K_{30}\). The stiffness of each specimen at each loading stage is shown in Table 5. It can be concluded from Table 5 that the cast-in-situ columns have a faster velocity of stiffness degradation. Column 5# has the most successful grouting and its stiffness degradation process after yielding is similar with that of the cast-in-situ columns.  
For the sake of comparing and analyzing, the stiffness degradation curves of each specimen are drawn in the same coordinate system shown in Figure 13. It is shown that the stiffness of the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & **Cracking Load (kN)** & **Yield Load (kN)** & **Ultimate Load (kN)** \\ \hline
1\# (cast in situ) & 25.43 & 47.45 & 54.19 \\
2\# & 27.57 & 48.60 & 59.81 \\
3\# & 28.54 & 47.77 & 65.55 \\
5\# & 27.38 & 37.54 & 40.53 \\
6\# (cast in situ) & 26.17 & 47.87 & 56.29 \\
7\# & 27.04 & 28.93 & 39.76 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Load-carrying capability of the specimens.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Specimen** & \(K_{30}\) & \(K_{130}\) & \(K_{130}/K_{30}\) & \(K_{cr}\) & \(K_{cr}/K_{30}\) & \(K_{y}\) & \(K_{y}/K_{30}\) & \(K_{u}\) & \(K_{u}/K_{30}\) \\ \hline
1\# (cast in situ) & 40.37 & 14.21 & 35.20/\(\
u\) & 11.26 & 27.89\% & 6.17 & 15.28\% & 2.52 & 6.24\% \\
2\# & 47.9 & 33.57 & 70.08\% & 22.58 & 47.14\% & 18.71 & 37.93\% & 6.68 & 13.95\% \\
3\# & 43.96 & 28.14 & 64.01\% & 21.03 & 47.84\% & 16.64 & 37.85\% & 3.98 & 8 specimens is relatively large at the first stage of low cyclic repeated loading, while it diminishes as the number of loops increases. At the second stage, since cracks appear and propagate, steel bars would slip longitudinally with respect to the adjacent concrete. Meanwhile, the velocity of stiffness degradation accelerates caused by the plastic deformation that occurred in the concrete. After the specimens achieve yield stress, the stiffness is reduced further but its velocity begins to slow down, and finally the stiffness degradation tends to be steady.