# Mechanical Behavior of Sand Mixed with Rubber Aggregates
## 3 Results and Discussion
### Effect of Rubber Content on Maximum Shear Strength of Sand  
Figure 12 shows the variation of the maximum shear stress as a function of the rubber content of the crushed tires ranging from 0 to 30%. It's clear that the maximum shear strength of these two sands increased significantly with the addition of rubber content. Indeed, with a rubber content of 20%, the shear strength of Hostun sand and Dune sand has increased from 34.39 \(\pm\) 2.89 kPa to 72.92 \(\pm\) 3.02 kPa and from 23.28 \(\pm\) 2.86 kPa to 51.72 \(\pm\) 2.95 kPa, respectively, under normal stress of 100 kPa. Beyond this value, the maximum shear strength for these two sands decreased for a rubber content of 30% but it always remains superior to that of pure sand. In fact, the shear strength Hostun sand and Dune sand increased from 34.39 \(\pm\) 2.89 kPa to 68.75 \(\pm\) 3.01 kPa and from 23.28 \(\pm\) 2.86 kPa to 48,194 \(\pm\) 2.94 kPa, respectively, for a rubber content of 30% under a stress of 100 kPa. The shear strength of these two sands is totally dependent on the friction between the particles. The presence of the aggregate rubber material affects the friction between the sand and rubber particles. The increase in maximum shear strength associated with 20%  
Figure 11: Maximum shear stress in terms of rubber content for Hostun sand. is related to the filling of the voids between the sand particles by the rubber aggregates, which will subsequently prevent the sand particles from moving or sliding easily during the direct shear test; and therefore, sand/aggregate rubber mixtures exhibit higher strength values. Note that the 20% aggregate rubber content is likely to be the optimum content. However, the decrease in maximum shear strength which has occurred in sand when the rubber content is greater than equal to 30% is attributed to the fact that the rubber material can be deformed significantly under the applied normal stress. In addition, the particles in the high rubber content mixtures can move and slide easily during the shear test; and therefore, the blends exhibit lower values of shear strength. This variation in maximum shear strength as a function of the rubber content of the tires can be explained by the variation of the void ratio of the sand/rubber mixtures as a function of the rubber content. Figure 13 shows the variation of the friction angle as a function of the rubber content for a medium relative density (\(D_{r}\) = 55%). It is observed that the addition of aggregate rubber up to 20% can increase the initial friction angle of Hostun sand from 27.57 \(\pm\) 1.02\({}^{\circ}\) to 31.94 \(\pm\) 0.62\({}^{\circ}\) and Dune sand from 18.75 \(\pm\) 1.02\({}^{\circ}\) to 26.18 \(\pm\)0.83\({}^{\circ}\). However, for a content of 30% aggregate rubber which is added to sand decreases the friction angle from 27.57 \(\pm\) 1.02\({}^{\circ}\) to 29.36 \(\pm\) 0.65\({}^{\circ}\) for Hostun sand and from 18.75 \(\pm\) 1.02\({}^{\circ}\) to 25.38 \(\pm\) 0.85\({}^{\circ}\) for Dune sand. This is explained since in the shear zone by rubber particles surrounding the sand grains and creating more voids. Therefore, the rubber grains mainly control the friction between the particles. These results agree with the results obtained in previous work, in particular that of [PERSON] et al. [12]. This difference in the friction angle of Hostun sand and Dune sand mixed with aggregate rubber may also be attributed to the effect of particle shape of the sand. Since the angularity of particles causes more antiparticle locking that restrains relative sliding and rotation between particles. A greater shear stress is required for Hostun sand than for Dune sand to break the interlocking owing to particle angularity before  
Figure 12: Maximum shear stress in terms of rubber content for dune sand. relative particle movement associated with dilation can take place, which also implies that the mobilized shear strength is a combination of dilation and interparticle locking.