# Sand Rubber Mixtures under Oedometric Loading: Sand-like vs. Rubber-like Behavior
## 4 Conclusions  
The mechanical response of the sand-rubber mixtures under one-dimensional loading was studied in this work. Different parameters, such as the initial void ratio, rubber fraction, and sand/rubber size ratio were varied in order to quantify their effect on the mechanical behavior of the mixtures. The different results obtained are presented, briefly, in the following:  
* The magnitude of the packing deformation increased as the rubber fraction increased. Further, for a given rubber fraction, the mixture with larger sand particles (Sr-D) was more compressible, while the mixture with smaller sand particles (sR-D) was less compressible than the mixture with equal-sized rubber and sand particles. This trend is in accordance with previous observations by [41]. One reason could be that a greater number of rubber (flexible) particles for the same rubber volume fraction increases the displacement/rotation of all particles, including rigid ones, thus, relaxing the particle jamming.
* The concavity of the loading curve in the \(e\)--log (\(\sigma_{v}\)) plane increased for pure sand packing with an increase in the normal stress. However, with the addition of rubber, the curve was found to become more convex at higher values of stress. The observed curvature change can be attributed to the saturation of the voids due to their filling with rubber, thus, indicating the impact of rubber addition on the macroscopic response of the mixture. An estimation of the mean curvature was performed. The mixtures were categorized into \"sand-like\" if the concavity increased and \"rubber-like\" if it decreased with the rubber fraction. This classification is helpful since it gives an objective definition of packing behavior on the basis of vertical stress and rubber fraction.  
Figure 10: Evolution of the swelling index at different levels of unloading vertical stress for the two densities of the packing and different rubber contents.  
* The one-dimensional confined stiffness was found to decrease with an increase in the rubber fraction. A power law decrease of the modulus number, \(m\), with the rubber fraction was observed for both densities. The ratio between the \(m\)-values for loose and dense packings was relatively constant around 75% (standard deviation of 7%) on all the range of rubber fractions. The power law index was relatively constant for all tests, with slightly higher values for looser packings. Moreover, for a given rubber fraction, coarser rubber particle packings (sR-D) showed a stiffer response than the corresponding equal-sized particle mixtures, indicating a stronger sand contact force network.  
This work strengthens the understanding of the mechanical response of sand-rubber mixtures. Such mixtures can be an interesting solution as a composite soil in numerous geotechnical applications. Thus, the results presented here are a step further to better understanding the behaviors of such mixtures. Numerical studies, using DEM, can be the perspective for such experiments, which will help link the micromechanical interactions with the macroscale responses observed.  
Conceptualization, B.C., E.I., P.R.; methodology, B.C., E.I., P.B.; formal analysis, P.B., B.C.; investigation, P.B., E.I.; resources, P.B., E.I., B.C.; writing--original draft preparation, P.B., B.C.; writing--review and editing, E.I., P.R., R.A.; supervision, P.R., B.C., E.I., R.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Data Availability StatementData sharing is not applicable.  
The authors declare no conflict of interest.