# Sand Rubber Mixtures under Oedometric Loading: Sand-like vs. Rubber-like Behavior
## 3 Results and Discussion  
### General One-Dimensional Response  
The vertical strain, \(\varepsilon_{v}\), and stress, \(\sigma_{v}\), during an oedometer test are represented in Figure 2 by a conventional semi-logarithmic scale for the different rubber fractions at the two initial densities, SR-D and SR-L tests. As expected, the magnitude of the packing deformation increases with the rubber fraction, while for a given rubber fraction, the deformation of the dense packing is smaller than that of the loose packing. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Sand-Rubber Mixture Type** & \begin{tabular}{c} **Sand Particle** \\ **Mean Size,** \\ **D\({}_{50}\) (mm)** \\ \end{tabular} & \begin{tabular}{c} **Rubber Particle** \\ **Mean Size,** \\ **D\({}_{50}\) (mm)** \\ \end{tabular} & \begin{tabular}{c} **Sand/Rubber** \\ **Mean Size,** \\ **Size Ratio** \\ \end{tabular} & \
\begin{tabular}{c} **Rubber Fraction,** \\ **\(\mathbf{x_{r}}\) (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Sample Void Ratio at** \\ **the Beginning of Test,** \\ **e\({}_{\mathbf{o}}\)** \\ \end{tabular} \\ \hline SR-D & 1.8 & 1.8 & 1.0 & 1.0 & 25 & 0.643 \\  & & & & 30 & 0.642 \\  & & & & 40 & 0.641 \\  & & & & 50 & 0.640 \\ \hline SR-L & 1.8 & 1.8 & 1.0 & 10 & 0 & 0.748 \\  & & & & 10 & 0.746 \\  & & & & 20 & 0.744 \\  & & & & 25 & 0.744 \\  & & & & 30 & 0.742 \\  & & & & 40 & 0.742 \\  & & & & 50 & 0.740 \\ \hline sr-D & 1.4 & 1.4 & 1.0 & 10 & 25 & 0.644 \\  & & & & 30 & 0.643 \\  & & & & 40 & 0.642 \\  & & & & 50 & 0.642 \\ \hline sR-D-10 & 0.7 & 1.4 & 0.5 & 10 & 0.646 \\  & & & & 50 & 0.645 \\ \hline Sr-D-10 & 2.1 & 1.4 & 1.5 & 10 & 0.642 \\ Sr-D-50 & & & & 50 & 0.642 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the testing series and sample characteristics. The evolutions of the maximum vertical strain \(\varepsilon_{max}\), obtained at the maximum applied vertical stress, \(\sigma_{max}\), of 2.3 MPa, and unrecovered vertical strain, \(\varepsilon_{o}\), after complete unloading with the rubber fraction, x\({}_{r}\), for SR-D, SR-L, and sr-D series tests, and Sr-D-10, Sr-D-50, sR-D-10, and sR-D-50 tests are given in Figure 3. As can be observed, independent of the rubber content, the effect of the particle size for the SR-D and sr-D tests in the measured maximum or unrecovered strain appears negligible (the non-null difference is smaller than 5% of the reference strain). The standard deviations of the strain range differences for the maximum and unrecovered vertical strain at each rubber fraction for these two series are around 0.7% and 0.4%, respectively. For both strain limits, the looser packing of SR-L tests induced, on average, 0.9% more vertical strain compared with the denser SR-D and sr-D samples. Figure 3 also plots the corresponding values of the strain limits for tests on samples made by non-equal sand and rubber particle sizes. For the 10% rubber fractions, while the volume of sand is nine times bigger than the volume of rubber, the behavior is dominated by the sand phase and very close to the SR or sr cases. When x\({}_{r}\) = 50%, the volume of sand equals the volume of rubber, yet the number of sand particles is about eight times larger than the number of rubber particles when the sand/rubber mean size ratio is 0.5 (sR-D tests), while the number of rubber particles is three times bigger than the sand particles when the sand/rubber mean size ratio is 1.5 (Sr-D tests). As a consequence, the response is more compressible for the latter Sr-D case and less compressible for the former sR-D case, when compared with equal sand and rubber particle sizes tests. A similar observation for the effect of the smaller-sized rubber particles on the one-dimensional compression was  
Figure 3: Evolution of (**a**) the maximum vertical strain and (**b**) the unrecovered strain after complete unloading with the rubber fraction for SR-D, SR-L, and sr-D series tests, and Sr-D-10, Sr-D-50, sR-D-10, and sR-D-50 tests (see Table 1).