# Effect of Fines Content on the Compression Behavior of Calcareous Sand
## 4 Soil Framework and Compressibility Behavior Analysis  
Building on an intergranular contact state classification method [34], this paper considers calcareous silty sand samples as particle mixtures containing particles of sizes \(D\) (original calcareous sand particles) and \(d\) (added fines) in different proportions. A detailed microstructural analysis of these mixtures is provided, along with an investigation of how varying fines content influences the compressive behavior of calcareous silty sand (Figure 9). Four distinct microstructural configurations were identified as follows: (i) a framework entirely composed of coarse particles (Sample A); (ii) coarse particles mainly in contact, with fine particles filling voids and providing minimal support (Sample B); (iii) coarse particles still in contact, but fine particles begin to contribute to the framework's support (Sample C, E, F); and (iv) fine particles are in contact, completely isolating the coarse particles (Sample G, H). Sample A to H undergo a transition from case (i) to case (iv) at the microstructural level. The transition from Sample A to H reflects a shift from case (i) to (iv), indicating that as fines content increases, the microstructure evolves, with a threshold fines content (\(f_{\text{c+th}}\)) occurring between cases (iii) and (iv). Based on compression test results, the threshold fines content (\(f_{\text{c+th}}\)) for calcareous silty sand is approximately 15-20% (medium-density, \(D_{\text{r}}=50\%\)). When \(f_{\text{c}}\) is less than \(f_{\text{c+th}}\), particularly in Sample B, C, E, and F (\(f_{\text{c}}=5\%\), 10%, 15%, and 20%), the microstructure is dominated by coarse particle contacts, forming the load-bearing skeleton, with fine particles playing a minor role. However, when \(f_{\text{c}}\) exceeds the threshold \(f_{\text{c+th}}\), as seen in Sample G and H (\(f_{\text{c}}=30\%\) and 40%), the microstructure transitions to case (iv), where fine particles dominate the load-bearing structure. The above compression test shows that the addition of 5% fine particles has a minimal effect on compressibility. Furthermore, it is evident that as the fines content increases, the axial deformation first rises and then declines. This behavior can be explained using the classification method based on the inter-particle contact state. Given that the added fines (\(d<75\) um) are much smaller than the diameter of the original calcareous sand particles (\(D\)), and that the fines only partially fill the voids between coarse particles without fully occupying them, the microstructure of Sample B (\(f_{\text{c}}=5\%\)) closely resembles case (i). In Sample B, C, E, and F (\(f_{\text{c}}=5\%\), 10%, 15%, and 20%), the load-bearing skeleton is primarily supported by coarse particles, while fine particles play a secondary role. The interlocking of coarse particles forms a relatively stable skeleton, but with the addition of fines, the fine particles act as lubricants between the coarse particles, reducing the skeleton's stability and promoting particle rearrangement, leading to increased axial deformation under the same load. As the fines content continues to increase, as observed in Sample G and H  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \(f_{\text{c}}\) & \(e_{\text{0}}\) & \(a_{\text{1-2}}\) & \(B_{\text{r}}\) \\ \hline A & 0 & 0.985 & 0.079 & 0.18\% \\ B & 5\% & 0.880 & 0.083 & 0.29\% \\ C &  
(\(f_{\rm c}\) = 30% and 40%), the coarse particles within the load-bearing soil skeleton are progressively replaced by fine particles. This reduces the likelihood of particle rearrangement, consequently lowering axial deformation and compressibility. In the Series II tests, the microstructures of Sample I (low-density, \(D_{\rm r}\) = 30%), A (medium-density, \(D_{\rm r}\) = 50%), and J (high-density, \(D_{\rm r}\) = 70%) all correspond to case (i), where the load-bearing framework is entirely composed of original calcareous sand particles.