# Experimental Study on Torsional Shear Testing of
## 7 Analyses of the Torsional Shear Test  
### Cohesion  
The cohesion \(c\) and the angle of internal friction \(\varphi\) can be determined from the intercept and slope of the Mohr's failure envelope, respectively. The cohesion \(c\) is the shear strength obtained by the pure shear test. The cohesion \(c\) analysis is performed based on the torsional shear test in unconfined compression, as an independent strength parameter. The form of the shear strength \(\tau_{f}\) represents the relationship with the temperature \(T\) and the relationship  
Figure 10: Time dependency of the shear stress at six normal stress levels. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Specimen** & \(\sigma\) & \(\tau_{max}\) & **Specimen** & \(\sigma\) & \(\tau_{max}\) & **Specimen** & \(\sigma\) & \(\tau_{max}\) \\
**No.** & **(MPa)** & **(MPa)** & **No.** & **(MPa)** & **(MPa)** & **No.** & **(MPa)** & **(MPa)** \\ \hline
0-1 & 0.002 & 0.507 & 1-1 & 0.125 & 0.721 & 2-1 & 0.203 & 0.816 \\
0-2 & 0.006 & 0.530 & 1-2 & 0.125 & 0.719 & 2-2 & 0.200 & 0.784 \\
0-3 & 0.003 & 0.521 & 1-3 & 0.125 & 0.699 & 2-3 & 0.200 & 0.800 \\
3-1 & 0.357 & 0.746 & 4-1 & 0.468 & 1.081 & 5-1 & 0.583 & 1.091 \\
3-2 & 0.355 & 0.746 & 4-2 & 0.463 & 1.058 & 5-2 & 0.576 & 1.121 \\
3-3 & 0.358 & 0.704 & 4-3 & 0.465 & 1.108 & 5-3 & 0.562 & 1.097 \\ \hline \end{tabular}
\end{table} 
Table 5: The maximum shear stress of various specimens at different normal stress levels. with the loading speed \(\
u\). The shear strength \(\tau_{f}\) is the function described in Equations (11) and (12). \[\log\tau_{f}(T)=aT+b \tag{11}\]  
\[\tau_{f}(\
u)=av^{b} \tag{12}\]  
By inserting the test data from Tables 3 and 4 into Equations (11) and (12), respectively, the fitting results of the maximum shear stress were obtained and are shown in Figures 11 and 12. The linear regression functions, showing a good agreement with the temperature \(T\) or loading speed \(\
u\), are illustrated in Table 6. The mean of the maximum shear stress was obtained by the torsional shear test in unconfined compression under a constant loading speed (2.4 rad/min) at 40 \({}^{\circ}\)C. The cohesion \(c\) for the shear strength by the type I test was measured as 0.519 MPa. Comparing the earlier test to assess the shear failure envelope of the asphalt mixture AC-13, the triaxial compression test conducted by [PERSON] et al. [19] at two temperatures (40 \({}^{\circ}\)C and 60 \({}^{\circ}\)C) and a loading speed of 50.8 mm/min obtained a cohesion \(c\) of 0.50 MPa and 0.18 MPa, respectively, and an angle of internal friction \(\varphi\) of 44\({}^{\circ}\) and 43\({}^{\circ}\), respectively. The uniaxial penetration test conducted by [PERSON] et al. [20] at a temperature of 60 \({}^{\circ}\)C and a loading speed of 1 mm/s obtained a cohesion of 0.1543 MPa and an angle of internal friction of 39.75\({}^{\circ}\). The cohesion \(c\) was dependent on the temperature and/or loading speed. The cohesion \(c\) and the angle of internal friction \(\varphi\) measured in the torsional shear test were in agreement with the triaxial compression test and the uniaxial penetration test of Figure 14.  
Earlier tests were conducted at high confinement and obtained the shear parameter; however, this test was conducted at both high confinement and low confinement and indicated that the coefficient of determination was less than that of earlier tests. Based on the test data at three normal stress levels (0, 0.125 and 0.200) of the Mohr-Coulomb failure criterion from Table 5, the fitting results of the maximum shear stress are illustrated in Figure 13. The cohesion \(c\) was taken from the mean of the maximum shear stress of three specimens as 0.519 MPa. The linear regression function was obtained from Equation (14):  
\[\tau_{f}=1.4396\sigma+0.5193 \tag{14}\]  
It is apparent from the above results that the cohesion \(c\) was 0.519 MPa, the angle of internal friction \(\varphi\) was 55.21\({}^{\circ}\) (tan \(\varphi\) = 1.4396), and the coefficient of determination \(R^{2}\) was equal to 0.9843.