## 3 Test Results and Discussion
### Grain Breakage  
Bearing in mind that the calcareous sand is susceptible to being crushed under compression loads, it is interesting to consider whether the presence of rubber chips affects the crushability of calcareous sand. To address this issue, the grain crushing needs evaluating by adopting a quantitative approach, for example, using the grain crushing index. Among a list of indices, a parameter proposed by [PERSON] [28], namely, the relative breakage (B\({}_{\text{r}}\)), appears to be more versatile and is often referred to in other research [10; 29]. The above index is derived based on changes in the cumulative distribution of grains before and after the test and it can be simply expressed as in Equation (4):  
\[\text{B}_{\text{r}}=\text{B}_{\text{t}}/\text{B}_{\text{p}} \tag{4}\]  
where B\({}_{\text{t}}\) is the total breakage represented by the area between the initial grading curve of sand and the final one, and B\({}_{\text{p}}\) is represented by the area between the vertical line of d = 74 \(\mu\)m and the initial grading curve.  
The particle size distribution curves of the test materials are presented in a semi-logarithmic format in Figure 5. It needs to be clarified that each test specimen was sieved by hand three times,  
Figure 4: Comparison of the compression curves for mixtures with different rubber contents.  
and the average values were adopted to determine the particle size distribution curves. This was not because of large discrepancies in each sieving test; rather, little difference was found in terms of the grading curves for the same mixture, implying that the potential problem of particle breakage during sieving was negligible. Hence, the shift of the distribution curves was due to the grain breakage in the compression test. Moreover, it needs to be clarified that the overall particle size of the calcareous sands after the compression test was in a range greater than 2 \(\upmu\)m. Hence, no cohesive soils (i.e., a particle size less than 2 \(\upmu\)m) were obtained.  
In Figure 6, the B\({}_{\text{r}}\) value of the mixtures with different rubber contents were compared, along with the results of the Fujian sand. A clear difference between the Fujian sand and the calcareous sand was observed. More interestingly, a marked trend was found in that the B\({}_{\text{r}}\) value tended to decrease with the rubber content. For example, the B\({}_{\text{r}}\) value of the specimen with a 10% rubber content reduced by approximately 77% as compared with the pure calcareous sand--i.e., sieved (0). Moreover, little difference in the B\({}_{\text{r}}\) value was found between the Fujian sand and the mixture with a 10% rubber content. Considering that the compressibility of the soils measured in the oedometer cell resulted from the deformation and possible reorientation of the grains, the above observations in Figures 3-6 provide solid evidence that a part of the external loads was shared by the soft plastic interparticle contacts between the rubber and the calcareous sand in the mixtures. As a consequence, the deformation of calcareous sands under external loads was well reduced.  
Figure 5: Particle size distribution curves of the test materials before and after the compression tests.  
Figure 6: Breakage index of the rubber–calcareous sand mixtures and the Fujian sand.