# Experimental Study on Mechanical Properties of Mask-Improved Calcareous Sand
## 3 Test Results and Analysis
### Particle Breakage Characteristics  
Calcareous sand is prone to fragmentation, making it essential to investigate the effect of mask particles on sand particle breaking. The concept of particle breaking rate, introduced by [PERSON], was employed to quantify particle fragmentation. It is assumed that particles smaller than 0.074 mm no longer undergo crushing [45]. The area bounded by the initial particle gradation curve and the vertical line at particle size S = 0.074 mm is termed the initial crushing potential \(B_{po}\). The area enclosed by the gradation curve of the sheared specimen, the initial gradation curve, and the vertical line at S = 0.074 mm are defined as the total crushing potential \(B_{t}\). The relative breaking rate at this point, denoted as \(B_{r}\) is:  
\[B_{r}=B_{t}/B_{po} \tag{6}\]  
Figure 12 illustrates the relative breakage rate \(B_{r}\) of particles under varying confining pressures for mixtures with different mask contents. As depicted in Figure 12a, the values of \(B_{r}\) generally increase both with higher mask content and increased confining pressure. Specifically, the average increase in \(B_{r}\) is approximately 21% as the confining pressure rises from 80 kPa to 200 kPa, whereas the increase is around 36% when the confining pressure increases from 200 kPa to 500 kPa. This suggests a significant rise in the breaking rate of calcareous sand when the confining pressure exceeds 200 kPa, which is consistent with the observations researched by [PERSON] [44; 46].  
At varying stress levels, the inflection point of \(B_{r}\) was observed at 0.3% mask content, beyond which \(B_{r}\) exhibited a positive correlation with mask content. Figure 12b illustrates the relationship between the relative fragmentation rate \(Br\) and the peak internal friction angle \(\varphi\). A linear and positive correlation was found between \(\varphi\) and mask content. Notably,  
Figure 11: Phase transformation state line.  
Figure 12: (**a**) Relationship between relative breakage rate and mask content and (**b**) relationship between relative breakage rate and internal friction angle.  
the relative fragmentation rate of particles was minimized at 0.3% mask content, indicating that the mask exerts a protective effect on the calcareous sand particles.  
At different stress levels, the inflection point of \(Br\) occurred at 0.3% of mask content, after which \(B_{r}\) was positively correlated with mask content. Figure 12b shows the relationship curve between the relative fragmentation rate \(B_{r}\) and the peak internal friction angle \(\varphi\). \(\varphi\) and the mask content are linearly and positively correlated, but the relative fragmentation rate of the particles is the smallest when the mask content is 0.3%, which suggests that the mask has a protective effect on the calcareous sand particles [46].  
When the mask content exceeds 0.3%, \(Br\) increases with increasing \(\varphi\), suggesting that while mask blending can reduce the fragmentation of calcareous sand particles, there is limited benefit in using a high mask content to further mitigate particle fragmentation.