## 4 Seismic Assessments with Capacity Spectrum Method
### Seismic Assessments with CSM  
According to the analysis process of CSM described in Section 4.1, the performance point of each bent specimen under different seismic levels is calculated in Section 4.3. Referring to the damage levels evaluated with lateral displacements in Table 6, the damage levels of the three tested bents can be obtained under each specific peak ground acceleration (PGA), as determined using the methods outlined in ASCE/SEI 7-10 [47]. The estimated lateral displacement \(\delta_{est}\), corresponding EVD factors \(\xi_{eq}\), and damage levels of the specimens are summarized in Table 7.  
The calculation results show that the three two-column bent specimens exhibit no damage when the PGA does not exceed 0.2 g. Upon increasing the PGA from 0.2 g to 0.5 g, all bents display slight damage, indicative of rebar yielding with the associated crack width being less than 1 mm. These findings indicate that the precast segmental two-column bent possesses sufficient structural resilience for applications in moderate- or low-seismicity regions. When PGA increases to 0.6 g, the damage state of the bent B2-PGS pier can be defined as extensive damage, while the other two bents show \"moderate damage\". When PGA reaches 0.7 g, all the bents fail.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **B2-CIP** & **B2-PGS** & **B2-PGT** \\ \hline No damage & 0.0–15.0 & 0.0–20.0 & 0.0–20.0 \\ Slight damage & 15.0–50.0 & 20.0–45.0 & 20.0–55.0 \\ Moderate damage & 50.0–60.0 & 45.0–55.0 & 55.0–70.0 \\ Extensive damage & 60.0–65.0 & 55.0–65.0 & 70.0–80.0 \\ Failure or collapse & \textgreater{}65 & \textgreater{}65 & \textgreater{}80 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Damage levels evaluated with lateral displacements (mm) of tested bents.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**B2-CIP**} & \multicolumn{3}{c}{**B2-PGS**} & \multicolumn{3}{c}{**B2-PGT**} \\ \cline{2-10}
**PGA (g)** & \(\delta_{est}\) & \(\xi_{eq}\) & **Damage** & \(\delta_{est}\) & \(\xi_{eq}\) & **Damage** & \(\delta_{est}\) & \(\xi_{eq}\) & **Damage** \\  & **(mm)** & **(\%)** & **Level** & **(mm)** & **(\%)** & **Level** & **(mm)** & **(\%)** & **Level** \\ \hline
0.2 & 14.37 & 3.60 & No & 13.38 & 7.04 & No & 17.25 & 3.42 & No \\
0.3 & 27.75 & 6.33 & Slight & 24.47 & 8.82 & Slight & 32.63 & 4.95 & Slight \\
0.4 & 36.88 & 8.80 & Slight & 33.66 & 11.39 & Slight & 42.82 & 6.80 & Slight \\
0.5 & 45.82 & 11.19 & Slight & 44.38 & 14.08 & Slight & 53.23 & 8.82 & Slight \\
0.6 & 56.41 & 13.87 & Moderate & 59.87 & 16.08 & Extensive & 66.56 & 10.84 & Moderate \\
0.7 & - & - & Failure & - & - & Failure & - & - & Failure \\ \hline \hline \end{tabular}
\end{table}
Table 7: Seismic assessment of the bent specimens.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Damage Level** & **Description** \\ \hline No damage & Before yielding of the rebar, no visible cracking. \\ Slight damage & The rebar yielding occurs, and the crack width is less than 1 mm. \\ Moderate damage & The crack width reached 1–2 mm, and the height of the concrete \\  & spalling zone is less than 1/10 of the cross-sectional height. \\ Extensive damage & The crack width is greater than 2 mm, and the height of the concrete \\  & spalling zone is less than 1/2 of the cross-sectional height. \\ Failure or collapse & The longitudinal rebar or stirrup fracture occurs, or the lateral \\  & load-carrying capacity drops to 85\% of the maximum value. \\ \hline \hline \end{tabular}
\end{table}
Table 5: Description of defined five damage levels.  
Through the above analysis, we can conclude that the seismic performance of the bent B2-PGS pier is the worst, while the performance of B2-PGT is similar to that of B2-CIP. This conclusion proves that the proposed GSS-GCT connection is a reliable connection method for a precast two-column bent, which is helpful to improve its seismic performance.