## 4 Statistical Analysis on Database of Experimental Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Code**} & \multirow{2}{*}{**Horizontal Shear Strength**} & \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Interface Roughness**} & \multirow{2}{*}{**Limitations**} \\ \cline{3-4}  & & & **Smooth** & & **Rough** \\ \hline \multirow{4}{*}{ACI 318 [27]} & \multirow{2}{*}{\(v_{nh}=c+\mu\rho_{v}f_{y}\)} & c (MPa) & 0.56 & 1.8 & \(v_{nh}\leq 3.5\) MPa \\ \cline{3-4}  & & \(\mu\) & - & 0.6 & \(A_{v(\min)}\) or rough surface \\ \cline{2-4}  & & \(\mu\) & 0.6 & 1.0 & \\ \cline{2-4}  & & \(v_{n}=\mu\,\rho_{v}f_{y}\) & \(K_{1}\) & 0.2 & 0.2 & \(v_{n}\leq K_{1}f_{c}^{\prime}\) \\ \cline{2-4}  & & \(K_{2}\) (MPa) & 5.5 & \(3.3+0.08f_{c}^{\prime}\) & \\ \hline \multirow{4}{*}{AASHTO LRFD [29]} & \multirow{2}{*}{\(v_{n}=c+\mu\big{(}\rho_{v}f_{y}+\sigma_{c}\big{)}\)} & c (MPa) & 0.52 & 1.65 & \\ \cline{2-4}  & & \(\mu\) & 0.6 & 1.0 & \(v_{n}\leq K_{1}f_{c}^{\prime}\) \\ \cline{2-4}  & & \(K_{1}\) & 0.2 & 0.25 & \(v_{n}\leq K_{2}\) \\ \cline{2-4}  & & \(K_{2}\) (MPa) & 5.52 & 10.34 & \\ \hline PCI [28] & \(v_{n}=\mu_{c}\,\rho_{v}f_{y}\) & \(K_{1}\) & 0.2 & 0.25 & \(v_{n}\leq K_{1}f_{c}^{\prime}\) \\ \cline{2-4}  & & \(K_{2}\) (MPa) & 5.5 & 6.9 & \(v_{n}\leq K_{2}\) \\ \hline \multirow{4}{*}{MC 2010 [30]} & \multirow{2}{*}{\(\tau_{u}=\tau_{c}\sqrt[3]{f_{ck}}+\mu(\sigma_{n}+k_{1}\rho_{v}f_{y})\)} & c & 0.1 & \\ \cline{2-4}  & & \(\mu\) & 0.6 & 0.7 & \\ \cline{1-1} \cline{2-4}  & & \(k_{1}\) & 0.5 & 0.5 & \\ \cline{1-1} \cline{2-4}  & & \(k_{2}\) & 1.1 & 0.9 & \\ \cline{1-1} \cline{2-4}  & & \(\beta vf_{c}^{\prime}\) & 6.19 & 10.46 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of parameters and limitations in design codes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Investigator**} & \multirow{2}{*}{**Quantity**} & \multirow{2}{*}{**Interface**} & \(A_{cv}\) & \(f_{c}^{\prime}\) **for [PERSON]** & \(\rho_{v}f_{y}\) \\  & & & **(mm2)** & **(MPa)** & **(MPa)** \\ \hline \multirow{2}{*}{[PERSON] et al. [12]} & 12 & Uncracked & 32,300 & 26–31 & 1.5–9.2 \\ \cline{2-4}  & 6 & Uncracked & 32,300 & 27–29 & 1.5–9.6 \\ \hline \multirow{2}{*}{[PERSON] et al. [12]} & 19 & Pre-cracked & 32,300 & 16–30 & 1.5–9.2 \\ \cline{2-4}  & 6 & Pre-cracked & 32,300 & 27–29 & 1.5–9.1 \\ \hline \multirow{2}{*}{[PERSON] and [PERSON] [13]} & 4 & Rough & 92,920 & 65–71 & 0.4–1.7 \\ \cline{2-4}  & 6 & Rough & 31,930 & 34–52 & 6.4 \\ \hline \multirow{2}{*}{[PERSON] et al. [17]} & 4 & Rough & 103,460–106,420 & 40 & 2.0–3.1 \\ \cline{2-4}  & 3 & Rough & 247,740 & 40 & 2.3 \\ \hline \multirow{2}{*}{[PERSON] [15]} & 4 & Rough & 103,480–106,450 & 40 & 1.9–3.1 \\ \cline{2-4}  & 18 & Smooth & 35,930 & 40–106 & 1.8–9.3 \\ \hline \multirow{2}{*}{[PERSON] and [PERSON] [19]} & 3 & Smooth & 31,930 & 52 & 6.4 \\ \cline{2-4}  & & \(\beta vf_{c}^{\prime}\) & 6.19 & 10.46 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: List from experimental database by push-off tests. Table 5 shows strength ratios of the push-off tests as the average value, standard deviation, and coefficient of variation. The ratios were found to have an average value of 1.18 to 2.95 and a coefficient of variation of 9.0 to 45.1% with respect to surface roughness. It is considered that all design code equations are capable of evaluating the horizontal shear strength of the specimen with adequate safety. However, the push-off test on the smooth surface of the interface showed a higher value than the horizontal shear strength calculated by the design code equation, and all design codes underestimate.