# Compaction Characteristics and Mechanical Response of Gravel-Glass-Rubber Mixtures +
## 4 Experimental Results and Discussions
### Strength Characteristics of Compacted GGRM from Direct Shear Tests
Alternatively, if \(c^{\prime}\) = 0 is imposed, then the strength is underestimated for \(\sigma_{n}{{}^{\prime}}\) < 80 kPa and overestimated for \(\sigma_{n}{{}^{\prime}}\) > 80 kPa. On the other hand, the nonlinear approach (i.e., Equation (6)) better captures the stress dependency of the strength to the normal stress. The values of the \(a\) and \(b\) coefficients obtained for all GGRMs tested in this study are reported in Figure 14 for completeness. In this study, the evolution of the secant friction angle (\(\phi_{\text{sec}}\) = \(\tan^{-1}\left(\tau/\sigma_{n}{{}^{\prime}}\right)\)) during shearing was also evaluated for the different \(\sigma_{n}{{}^{\prime}}\) levels. From Figures 15 and 16, it is evident that \(\phi_{\text{sec}}\) is stress-dependent and decreases with increasing \(\sigma_{n}{{}^{\prime}}\). Specifically, \(\phi_{\text{sec(peak)}}\) decreases from 40-48\({}^{\circ}\) at \(\sigma_{n}{{}^{\prime}}\) = 30 kPa to 33-37\({}^{\circ}\) at \(\sigma_{n}{{}^{\prime}}\) = 100 kPa for \(R_{\text{B}}\) = 0.4, and from 40-44\({}^{\circ}\) at \(\sigma_{n}{{}^{\prime}}\) = 30 kPa to 30-34\({}^{\circ}\) at \(\sigma_{n}{{}^{\prime}}\) = 100 kPa for \(R_{\text{B}}\) = 0.55. Figure 13: Direct shear strength of GRMs evaluated by (a) Mohr–Coulomb failure criterion and (b) nonlinear failure approach. Combining the definition of \(\phi_{\text{sec}}\) and Equation (6), then \(\phi_{\text{sec(peak)}}\) can be expressed by the nonlinear function shown in Equation (7):  
\[\phi_{\text{sec(peak)}}=\tan^{-1}\!\left(\frac{\tau_{\text{peak}}}{\sigma_{n}^{ \prime}}\right)=\tan^{-1}\!\left[a\!\left(\sigma_{n}^{\prime}\right)^{b-1}\right] \tag{7}\]  
The values of \(\phi_{\text{sec(peak)}}\) experimentally evaluated and those estimated by Equation (7) are reported in Table 3 for all the GGRM and the three different \(\alpha_{n}{}^{\prime}\) levels. The \(\phi_{\text{peak}}\) values obtained by the MC method with and without \(c_{a}{}^{\prime}\) are also reported in Table 3 for comprehensive. Figure 16: Secant friction angle for GGRM (\(R_{\text{B}}=0.55\)) obtained from direct tests at the various normal stress levels of (**a**) 30 kPa, (**b**) 60 kPa, and (**c**) 100 kPa. Figure 14: Example of strength parameters evaluation for GGRM using MC (\(c^{\prime}=c_{a}{}^{\prime}\)), MC (\(c^{\prime}=0\)), and the nonlinear failure approach (Equation (5)). Figure 10:0 Secant friction angle for GGRM (\(R_{\text{B}}=0.4\)) obtained from direct tests at the various normal stress levels of (**a**) 30 kPa, (**b**) 60 kPa, and (**c**) 100 kPa. For the purpose of validation of the nonlinear power-law model in Equations (6) and (7), secant friction angle values obtained by using the well-known nonlinear strength model of [PERSON] (2016) are also provided in Table 3 for all GGRM and the three levels of \(\sigma_{\mathrm{n}}{}^{\prime}\) = 30, 60, and 100 kPa. The [PERSON] model is described by Equation (8):  
Figure 10:1  
where \(\Delta\phi\) and \(\phi_{0}\) are fitting parameters; the values obtained for GGRM are reported in Figure 10:2 There is a very good agreement between the estimates of the two methods (i.e., the maximum difference is 0.2\({}^{\circ}\)), indicating the suitability of the nonlinear power-law model for the evaluation of GGRM strength. Based on the direct shear test results and analyses reported above, the \(\phi_{\mathrm{peak}}\) values of GGRM with \(R_{\mathrm{B}}\) = 0.4 and 0.55 are typically higher than 25-30\({}^{\circ}\), making GGRM suitable structural fills ([PERSON] et al., 2017) for typical geotechnical applications (e.g., embankments, foundations, and backfills for retaining structures).