# Cyclic Tests and Numerical Analyses on Bolt-Connected Precast Reinforced Concrete Deep Beams
## 4 Numerical Study
### Parametric Analysis Study  
A parametric analysis was performed to summarize the effects on geometrical and material parameters based on the verified numerical modeling method in Section 4.1. The following parameters were considered: height-to-length ratio (\(\alpha\)), height-to-thickness (\(\beta\)) and material type of concrete. The height of RDBs is determined as 900 mm, which is the same as the test specimens. The thickness of RDB includes 60 mm, 80 mm and 100 mm. The height-to-length ratio of RDB is ranged from 0.75 to 2.0. The compressive strength of concrete includes three types: 25 N/mm\({}^{2}\) (C25), 30 N/mm\({}^{2}\) (C30) and 35 N/mm\({}^{2}\) (C35). Table 4 presents the detailed information of these RDB models. The effects on lateral loading-displacement curves with parameters of height-to-length ratio, height-to-thickness and material type of concrete are shown in Figure 13.  
Figure 11: Comparison of the load-displacement relationship between the test and FEM results.  
As the results presented in Figure 13a show, it can be concluded that the height-to-length ratio of the RDB is showing a high contribution to the shear resistance of the RDBs. A higher height-to-length ratio of the RDB results in a higher shear resistance throughout all of the loading levels, as demonstrated by the test results. According to Figure 13b, it can be seen that the shear resistance of RDB is increasing with the increase in compressive strength of the concrete material. However, the increment is decreasing with the increase in the compressive strength. The shear resistance of RDB is obviously increasing with the decrease in the height-to-thickness ratio of RDB (see in Figure 13c), and such increment is increasing with the decrease in the height-to-thickness ratio of RDB.  
Therefore, it can be concluded that the shear resistance of RDB can be efficiently strengthened by a large margin by decreasing the height-to-length ratio and increasing the height-to-thickness ratio of RDBs. However, the material type of concrete shows little effect on the seismic performance of RDBs.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimens** & **Effects** & **\(h\)/mm** & **\(t\)/mm** & **\(l\)/mm** & **Concrete** & **\(\mathbf{\kappa}\)** & **Parameters** \\ \hline RDB-1 & & 900 & 60 & 450 & C30 & 2.0 & 15 \\ RDB-2 & Height-to-length ratio of RDB & 900 & 60 & 600 & C30 & 1.5 & 15 \\ RDB-3 & (\(\alpha=h/l\)) & 900 & 60 & 750 & C30 & 1.2 & 15 \\ RDB-4 & (\(\alpha=h/l\)) & 900 & 60 & 900 & C30 & 1.0 & 15 \\ RDB-5 & & 900 & 60 & 1050 & C30 & 0.75 & 15 \\ \hline RDB-6 & & 900 & 60 & 600 & C25 & 1.2 & 15 \\ RDB-7 & Strength of concrete material & 900 & 60 & 600 & C35 & 1.2 & 15 \\ \hline RDB-8 & Height-to-thickness ratio & 900 & 80 & 600 & C30 & 1.5 & 11.25 \\ RDB-9 & (\(\beta=h/l\)) & 900 & 100 & 600 & C30 & 1.5 & 9 \\ \hline \hline \end{tabular} Note: \(h\), \(l\) and \(t\) are the height, length and thickness of the RDB, respectively.  
\end{table}
Table 4: Parameters analyzed for RDBs.  
Figure 12: Failure pattern comparison of the tests and FEM predictions.