# Experimental Study on Mechanical Properties of Mask-Improved Calcareous Sand
## 3 Test Results and Analysis
### Volume Change Characteristics  
In granular materials, particles slide and rotate under shear, leading to a change in sample volume. The volumetric strain, denoted as \(\epsilon_{\text{V}}\), is calculated using the following equation:  
\[\epsilon_{\text{V}}=(\text{V}_{0}-\text{V})/\text{V}_{0} \tag{5}\]  
where V\({}_{0}\) and V are the pre-shear (post-consolidation) and present sample volumes, respectively. Figure 8 illustrates the volumetric strain of each specimen under varying pressures. Positive values correspond to shear contraction, while negative values indicate dilatancy. Initially, all specimens undergo volumetric shrinkage, followed by a rapid dilatancy, and ultimately stabilize gradually [37]. The shear shrinkage tendency of calcium sand mixed with mask is more pronounced than that of plain calcium sand. Furthermore, an increase in mask content leads to greater shear shrinkage of the specimens. This suggests that the mask effectively inhibits the dilatancy of calcium sand, thereby improving the material's service performance. The confining pressure also has a significant effect on the mixture. At confining pressure of 80 kPa and 200 kPa, the specimens initially exhibit shear shrinkage followed by dilatancy [38; 39]. Specifically, while the shear expansion phenomenon remains unclear at an enclosure pressure of 500 kPa, the increase in both enclosure pressure and mask content leads to a corresponding increase in axial strain at the phase transition point (the state where the specimen reaches zero dilatancy rate). When the confining pressure reaches 500 kPa, the phase transition is substantially delayed, and the specimen exhibits shear contraction within a 20% axial strain range [39]. Figure 9 illustrates the shear deformation of mask-calcareous sand mixtures with different mask sizes, all at the same content and under identical confining pressure. The specimen with a 5 mm \(\times\) 5 mm mask size appears to exhibit greater shear shrinkage during shearing, which aligns with the observed stress-strain curve. Figure 8: Volumetric strain curve. Figure 9: Volumetric strain curves for different mask sizes. The accuracy of the traditional constitutive model in describing the mechanical behavior of soft-rigid mixtures largely depends on the stress dilatancy relationship [40]. This relationship can be characterized by the dilatancy coefficient \(d\); dilatancy coefficient \(d\) can be quantified as \(de_{y}^{p}/de_{q}^{p}\); \(de_{v}^{p}\) and \(de_{q}^{p}\) denote incremental plastic volumetric strain and incremental plastic distortional strain, respectively [41]. From the characteristics of the stress-strain curves, the elastic strain of the mask-calcareous sand mixture is small; therefore, it is assumed that the \(de_{v}^{p}\) and \(de_{q}^{p}\) is equal to the incremental volumetric strain and the incremental distortional strain [42; 43; 44]. Figure 10a illustrates the relationship between stress ratio and dilatancy for the specimens at 200 kPa. With the increase in stress ratio, the curve first decreases, and then turns back and decreases after the peak stress. This phenomenon suggests that the stress ratio at the peak state is greater than that at the critical state, likely due to the specimens being prepared in a relatively dense state. The dilatancy rate serves as a critical parameter for evaluating shear strength. As the mask content increases, the dilatancy curve exhibits an upward trend. This observation suggests that the enhanced interaction between particles within the sample leads to an increase in shear strength. To quantify the impact of mask addition on the dilatancy of calcareous sand, Figure 10b shows the variation in the maximum dilatancy angle with respect to mask content under different confining pressures. It is evident that the maximum dilatancy angle decreases as both mask content and confining pressure increase, indicating that the addition of masks reduces the dilatancy degree of the samples. The standard deviation also exhibits reduced dispersion as the confining pressure increases.