# Effect of Fines Content on the Compression Behavior of Calcareous Sand
## 3 Results of Compression Tests
### Effects of Fines Content on the Particle Breakage Characteristics of Calcareous Sand  
For mixed soils containing calcareous sand, particle breakage leads to significant volumetric reduction [29; 30; 31]. [PERSON] et al. found that for Persian Gulf calcareous sand under pressures below 1000 kPa, up to 20% of the total axial strain is attributed to particle breakage [32]. This volumetric change is driven by two factors: the re-arrangement of particles following breakage, which reduces the overall void ratio of the sand skeleton [33], and the release of intra-particle voids after breakage, which provides additional space for fine sand particles. Therefore, the volumetric reduction associated with particle breakage also contributes to the compressive deformation of calcareous sand.  
Through Equation (4), it is evident that the relative breakage (\(B_{\text{r}}\)) ranges between 0 and 1, where a value closer to 1 indicates a more severe degree of particle breakage. Using the aforementioned calculation method and the particle size distribution curves before and after compression testing, the relative breakage for Sample A-H were calculated, with results presented in Table 4. It can be observed that in the initial stage of adding fines, the relative breakage of calcareous sand increases, especially the Br value of calcareous silty sand Sample C is 2.44 times that of Sample A. This phenomenon indicates that under the same loading path, the stress required for significant breakage occurs earlier with the addition of fine particles. Furthermore, when the stress levels are equal, the amounts of breakage for Sample B, C, E, and F significantly increase with the addition of fines. It can be explained by the particle shape characteristics and the development of internal voids in calcareous sand. On one hand, during compression, the average contact area between the irregularly shaped coarse particles of calcareous sand is relatively small, making it easier to form high localized stress at these contact points or surfaces, which causes particle breakage. With the addition of fines, the number of particles in contact around each coarse particle decreases, increasing the average stress acting on that coarse particle, thus making breakage more likely. On the other hand, the addition of fine particles causes point contacts between coarse particles to deviate from the centroid, generating additional bending moments on the particles, and making stress concentration more likely to occur at their smaller size directions and irregular contact points (corner contact points), thereby exacerbating breakage (\(B_{\text{r-C}}>B_{\text{r-B}}>B_{\text{r-A}}\)). The small particles formed from the breakage of coarse particles fill the voids between them, reducing the void ratio while releasing internal voids, which further increases the compressive deformation of the samples. However, as the fines content increases further, the load-bearing soil framework gradually transitions to being supported by both coarse and fine particles. As a result, the aforementioned two effects of  
Figure 8: The variation of the coefficient of volumetric compressibility of clean sand and mixed sand samples with axial load under different initial relative densities.  
particle breakage caused by fines weaken, leading to a reduction in the relative breakage of the samples (\(B_{\text{r-H}}<B_{\text{r-F}}<B_{\text{r-C}}\)). The phenomenon of particle breakage of calcareous sand further clarifies the results of the compression tests mentioned above. At higher stress levels, in the initial stage of adding fines (Sample B-F), the degree of particle breakage increased, which contributed to the compressive deformation of the samples. However, as the fines content increased further (Sample G and H), the degree of particle breakage relatively decreased, thereby playing a mitigating role in the compression deformation of the samples.