# Compaction Characteristics and Mechanical Response of Gravel-Glass-Rubber Mixtures +
## 4 Experimental Results and Discussions
### Strength Characteristics of Compacted GGRM from Direct Shear Tests  
Results of the direct shear tests showing the different shear stress-horizontal strain relationships and volumetric responses for pure gravel, crushed green glass, and granulated tire rubber under 30, 60, and 100 kPa normal stress (\(\sigma_{n}\)\({}^{\prime}\)) are shown in Figure 10.  
The gravel displays stiff behavior typical of dense, hard-grained soils, characterized by a high peak strength (e.g., 137 kPa at \(\sigma_{n}\)\({}^{\prime}\) = 100 kPa) and brittle failure. Its volumetric response is primarily dilative. In contrast, the soft rubber has a ductile response with no clear peak and contractive volumetric behavior; it has a peak strength of 54 kPa at \(\sigma_{n}\)\({}^{\prime}\) = 100 kPa. The green glass strength is in between that of gravel and rubber (i.e., the peak strength is 91 kPa \(\sigma_{n}\)\({}^{\prime}\) = 100 kPa), but its volumetric behavior is similar to that of stiff gravel, although much less dilative. This is because green glass particles, although stiff, are highly crushable under shearing loading, especially when subjected to higher \(\sigma_{n}\)\({}^{\prime}\) levels. The direct shear behavior of GGRM with \(R_{\text{B}}\) = 0.4 and 0.55 is reported in Figures 11 and 12. Due to the presence of softer rubber particles, the mechanical response of the mixtures is more ductile than that observed for pure gravel and pure glass. The variation of \(G_{\text{L}}\) (= 0 - 0.6) in the mixtures does not affect the overall response qualitatively or quantitatively, indicating that \(R_{\text{B}}\) is primarily responsible for the observed ductile behavior. Figure 10: Direct shear response of (**a**) gravel, (**b**) crushed green glass, and (**c**) granulated tire rubber under different normal stress levels. Figure 11: Direct shear response of GGRM (\(R_{\rm B}\) = 0.4) under **(a)** 30 kPa, **(b)** 60 kPa, and **(c)** 100 kPa normal stress. Figure 12: Direct shear response of GGRM (\(R_{\rm B}\) = 0.55) under **(a)** 30 kPa, **(b)** 60 kPa, and **(c)** 100 kPa normal stress. [PERSON] et al. [15] conducted direct shear tests on GRM over a range of \(\sigma_{n}{{}^{\prime}}\) from 6.5 kPa to 100 kPa. Figure 13a reports the peak strength (\(\tau_{\text{peak}}\)) determined for gravel, rubber and GRM (\(R_{\text{B}}\) = 0.4) using the linear Mohr-Coulomb (MC) failure criterion as described by Equation (5):  
\[\tau_{\text{peak}}=c_{a}^{\prime}+\sigma_{n}^{\prime}\text{tan}\left(\phi_{ \text{peak}}\right) \tag{5}\]  
The strength is characterized by friction angles (\(\phi_{\text{peak}}\)) values of 53.2\({}^{\circ}\) (gravel), 34.0\({}^{\circ}\) (GRM, \(R_{\text{B}}\) = 0.4), and 26.0\({}^{\circ}\) (rubber). Moreover, the MC method indicates that GRM may have an apparent cohesion (\(c_{a}{{}^{\prime}}\)), whose values are 3.2 kPa (gravel), 7.2 kPa (GRM, \(R_{\text{B}}\) = 0.4), and 6.1 kPa (rubber). Nevertheless, unbounded materials like gravel, rubber, and GRM are not expected to have interparticle forces leading to cohesion. A similar observation has been reported by [PERSON] et al. [55], who conducted direct shear tests on large rubber particle sizes. Hence, although \(c_{a}{{}^{\prime}}\) may be seen as a convenient strength parameter, it does not provide an accurate representation of the actual strength of cohesionless (\(c^{\prime}\) = 0) materials like GRM, especially at very low-stress levels. As shown in Figure 13b, because of the cohesionless nature of GRM, a nonlinear power form fitting curve can be adopted to better capture the strength dependency of GRM with the normal stress as expressed by Equation (6):  
\[\tau_{\text{peak}}=a\left(\sigma_{n}^{\prime}\right)^{b} \tag{6}\]  
where \(a\) and \(b\) are material fitting parameters. Similarly, as shown in the example in Figure 14, the MC approach considering \(c_{a}{{}^{\prime}}\) overestimates the strength of unbounded GGRM for \(\sigma_{n}{{}^{\prime}}\) < 30 kPa.