# Experimental Study on Mechanical Properties of Mask-Improved Calcareous Sand
## 3 Test Results and Analysis  
### Stress-Strain Characteristics  
Quantification of soil strength under triaxial stress conditions using stress ratios [26; 29]:  
\[\mathrm{q}=\sigma_{1}-\sigma_{3} \tag{1}\]  
\[\mathrm{p}=(\sigma_{1}+2\sigma_{3})/3 \tag{2}\]  
\[\eta=\mathrm{q}/\mathrm{p} \tag{3}\]  
where \(\sigma_{1}\) is axial stress, \(\sigma_{3}\) is confining pressure, \(\mathrm{q}\) is deviatoric stress, \(\mathrm{p}\) is effective mean stress, and \(\eta\) is stress ratio. Figure 3 presents the stress-strain curves of the specimens. The stress ratio initially increases sharply to the peak value, before gradually decreasing and leveling off. As the mask content increases, the peak of the curve is delayed and becomes less pronounced, while the stress-strain relationship transitions from a softening to a hardening behavior. This suggests that the ductility of the mixture improves with increasing mask content. Furthermore, increasing the mask content results in enhanced strength of the specimens, as the mask restricts the rotation of surrounding particles due to its high coefficient of friction, thereby inhibiting their movement [30]. As the confining pressure rises, the stress peak is delayed and eventually vanishes, a phenomenon that is more pronounced in mask-calcareous sand mixtures than in conventional geotechnical materials [31; 32]. The observed phenomenon can be attributed to the significant increase in pore instability around the mask, which is exacerbated by higher particle contact stress [33]. Furthermore, under high-stress conditions, the angularity of the calcareous sand surface undergoes localized fragmentation, resulting in a reduction in the coefficient of friction [26; 34]. Under high confining pressure, the stress-strain curves of samples with varying mask contents exhibit greater similarity, This phenomenon reflects the weakening of the reinforcement effect of masks under high confining pressure, indicating that the mask-calcareous sand mixtures are more suitable for high-confining-pressure conditions [34]. Figure 4 presents the stress-strain curves for various mask sizes with identical mask content at an enclosure pressure of 200 kPa. For the 5 mm \(\times\) 5 mm mask size, the mask-calcareous sand hybrid demonstrates superior shear strength compared to the other mask sizes. This suggests that mask size also influences the mechanical behavior of the mask-calcareous sand mixture. Figure 5 presents the variation in peak stress ratio with mask content, as obtained from triaxial tests of each mask-calcareous sand mixture. Figure 5 illustrates the mean and standard deviation of the peak stress ratios at varying mask contents, providing a clearer correlation between peak stress ratios and mask contents. The stress ratio for each specimen exhibits minimal dispersion. As the mask content increases, the peak stress ratio increases by approximately 4.1% per stage, exhibiting a nearly linear relationship. Conversely, as the confining pressure increases, the stress ratio decreases by approximately 4.7%. The initial modulus (defined as the tangent modulus at 1% strain) was used to assess the effect of mask content on the elastic modulus of the mixture. To minimize the influence of confining pressure, the initial modulus was calculated based on the stress ratio [35]. Figure 4: Stress ratio–strain curves for different mask sizes. Figure 5: Peak stress ratio. Figure 3: Stress ratio–strain curve. As shown in Figure 6, an increase in mask mass content leads to a decrease in the initial modulus. The initial modulus decreased by over 25% as the mask content increased from 0% to 0.3%. Beyond this point, the modulus stabilized before further decreasing to 10% with continued increases in mask content. Meanwhile, an increase in confining pressure leads to an increase in the initial modulus and the standard deviation exhibits greater uniformity. The increase in confining pressure led to a 25% increase in initial stiffness.