## 2 Experimental Program
### Material Characteristics  
The compressive strengths of each brick and joint mortar are shown in Table 1. As shown in the table, the compressive strength of the red brick was higher than that of the cement brick in both the single unit and 3-layered prism tests. In addition, the 3-layered prism compressive strengths of the cement and red bricks are about 43% and 41% of the single unit compressive strengths, respectively. The compressive strength of the joint mortar was considerably higher than those of the 3-layered prism of the masonry. Some factors are needed to evaluate an in-plane rocking strength of URM masonry walls: an adhesive strength and a friction coefficient between the brick unit and mortar. Adhesive strengths \(\tau_{0}\) and friction coefficients \(\mu\) can be obtained from the relationship between shear stress \(\tau\) and axial stress \(\sigma_{0}\) based on the well-known Mohr's circle, as shown in Figure 4. As shown in Figure 4 and Equation (1), it is assumed that the shear stress and the axial stress are linearly related in the region where the axial stress is not high (the hatched part); hence, the slope and \(y\)-intercept are the friction coefficient \(\mu\) and adhesive strength \(\tau_{0}\), respectively [30]. In this study, the bed joint sliding tests were conducted using the 3-layered prism specimens to investigate the adhesive force and friction coefficient. Figure 5 shows the test overview. In this test, the experimental parameter is the axial stress \(\sigma_{0}\) of 0.3, 0.5, and 0.7 N/mm\({}^{2}\); the axial force corresponding to the axial stress was applied with four steel bars, as shown in Figure 5. The target axial force was confirmed by the value measured from the strain gauges attached to each steel bar. The strain value for each axial force was calculated using Equations (2) and (3). The Young's modulus of the steel bar was obtained from an additional tensile test. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**Cement Brick**} & \multicolumn{2}{c}{**Red Brick**} \\ \cline{2-5}  & **Brick Unit** & **Brick Prism (1)** & **Brick Unit** & **Brick Prism (1)** & **Brick Prism (1)** \\  & **(N/mm2)** & **(N/mm2)** & **(N/mm2)** & **(N/mm2)** & **(N/mm2)** \\ \hline Test 1 & 37.3 & 15.7 & 46.4 & 18.4 & 39.5 \\ \hline Test 2 & 35.4 & 15.5 & 45.6 & 20.8 & 43.6 \\ \hline Test 3 & 35.3 & 15.4 & 45.6 & 16.7 & 52.1 \\ \hline Average & 36.0 & 15.4 & 45.9 & 18.6 & 45.1 \\ \hline \end{tabular} \({}^{(1)}\)3-layered specimen, \({}^{(2)}\) cylinder type.  
\end{table} 
Table 1: Compressive strengths of each brick and joint mortar. Figure 3: Elevations of the specimens: (**a**) Specimen M-N; (**b**) Specimen M-W; and (**c**) Specimen M-D (unit: mm). Table 2 and Figure 6 show the test results and the relationship between the shear stress and the axial stress, respectively. Consequently, the friction coefficient and adhesive strength of the cement and red bricks were obtained from the linear regression analysis on the experimental data, as shown in Figure 6. As shown in the figure, it was found that the friction coefficient and adhesive strength of the cement and red bricks were almost the same. \[\tau=\mu\cdot\sigma_{0}+\tau_{0} \tag{1}\]  
where \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Brick Type** & **Target Axial Stress, \(\sigma_{0}\) (N/mm\({}^{2}\))** & **Target Strain, \(\epsilon\) (\(\mu\)/bar)** & **Specimen No.** & **Achieved Axial Stress, \(\sigma\) (N/mm\({}^{2}\))** & **Maximum Shear Stress, \(\tau\) (N/mm\({}^{2}\))** \\ \hline \multirow{4}{*}{C Cement brick} & \multirow{2}{*}{0.3} & \multirow{2}{*}{34.5} & Test 1 & 0.31 & 1.29 \\ \cline{3-5}  & & & Test 2 & 0.32 & 1.35 \\ \cline{3-5}  & & & Test 3 & 0.31 & 1.38 \\ \cline{3-5}  & & & Test 1 & 0.57 & 1.49 \\ \cline{3-5}  & & & Test 2 & 0.53 & 1.62 \\ \cline{3-5}  & & & Test 1 & 0.70 & 1.80 \\ \cline{3-5}  & & & Test 2 & 0.69 & 2.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The results of bed joint sliding failure tests.