## 3 Results and Discussion
### Under the Condition of Similar Interfine Void Ratios  
The specimens were prepared at similar initial interfering void ratios ranging between 0.698 and 0.736. Likewise, only the triaxial drained test results obtained under an effective confining pressure of 0.5 MPa are presented, as shown in Figure 5. The peak strength of the specimen increased with an increase in carbonate sand content, and both deviator stress and volumetric strain maintained a steady value around an axial strain of 30%. In addition, the specimen changed from dilative to contractive behaviour with a decrease in carbonate sand content. As the carbonate sand content increased, the specimen became \"denser\" \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Initial State**} & \multicolumn{2}{c}{**Critical State**} \\ \cline{2-6}
**Specimen** & \multicolumn{2}{c}{**Void Ratio**} & \multicolumn{2}{c}{**Void Ratio**} & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Deviator**} \\
**Identity** & **Void Ratio** & \multicolumn{2}{c}{**After Consolidation**} & \multicolumn{2}{c}{**Stress (MPa)**} & \multicolumn{2}{c}{**Stress (MPa)**} & \multicolumn{2}{c}{**Void Ratio**} \\ \hline C5\_V0 & 0.583 & 0.581 & 0.789 & 0.895 & 0.597 \\ C5\_V20 & 0.576 & 0.560 & 0.809 & 0.926 & 0.545 \\ C5\_V40 & 0.573 & 0.531 & 0.804 & 0.913 & 0.492 \\ \hline C10\_V0 & 0.589 & 0.587 & 1.564 & 1.693 & 0.577 \\ C10\_V20 & 0.580 & 0.556 & 1.657 & 1.972 & 0.521 \\ C10\_V40 & 0.575 & 0.513 & 1.624 & 1.873 & 0.460 \\ \hline C30\_V0 & 0.590 & 0.587 & 4.609 & 4.828 & 0.509 \\ C30\_V20 & 0.572 & 0.541 & 4.741 & 5.223 & 0.447 \\ C30\_V40 & 0.570 & 0.510 & 4.682 & 5.046 & 0.412 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Critical state data of triaxial tests under the condition of similar void ratios. Figure 4: Critical state lines of carbonate sand-fine mixtures with similar void ratios in (a) \(p^{\prime}\)–\(q\) and (b) \(e\)–\(\ln p^{\prime}\) planes. despite being under the condition of similar initial interfine void ratios. Compared to the specimens whose density was controlled by the void ratio, the carbonate sand content had the opposite effect on mechanical properties in the specimens controlled by the interfine void ratio. Similarly, the three specimens all exhibited strain-softening behaviour, and the shear strength of the three specimens approached a similar value at large deformation under the same effective confining pressure. Thus, under the condition of similar initial interfine void ratios, all tested specimens presumably reached the critical state at the end of shearing. The critical state data of triaxial tests under the condition of similar interfine void ratios are summarised in Table 3.  
Figure 6a,b show the critical state data of the triaxial drained tests in the \(p^{\prime}\)-\(q\) and \(e_{\ell}\)-\(\ln p^{\prime}\) planes for specimens with similar initial interfine void ratios, respectively. Similar to the previous scenario, the critical state in the \(p^{\prime}\)-\(q\) plane is represented by a linear best-fit line passing through the origin. The CSL of carbonate sand-fine mixtures in the \(p^{\prime}\)-\(q\) plane is unique despite different carbonate sand contents; the potential reason for this was explained previously. In the \(e_{\ell}\)-\(\ln p^{\prime}\) plane, the CSLs of carbonate sand-fine mixtures with 20 and 40% carbonate sand content were parallel to that of fines only (i.e., 0% carbonate sand  
Figure 5: Triaxial test results of carbonate sand-fine mixtures with similar interfine void ratios under a confining pressure of 0.5 MPa: (**a**) stress–strain curves; (**b**) volumetric deformation curves.