## 2 Materials and Methods
### Microscopic Investigation  
For a carbonate sand-fine mixture, there are two types of pores: internal pores of carbonate sand grains and intergranular pores between soil particles. In this study, internal pores refer to all the pores within the solid boundary range of the carbonate sand grains, and the intergranular pores refer to the pore spaces existing between sand-sand particles, sand-fine particles, and fine-fine particles. If carbonate sand grains do not contribute to the force chains of the fine matrix, the internal pores of carbonate sand grains will be inactive. Hence, the volume change in the soil mixture is only the result of the volume change in intergranular pores between soil particles, and the volume of internal pores of carbonate sand grains should be neglected in evaluating the \"actual\" void ratio or porosity of the carbonate sand-fine mixture. In this study, computer tomography (CT) was adopted to measure the internal porosity of carbonate sand grains and investigate the microscopic structure of carbonate sand-fine mixtures.  
A total of one hundred grains were randomly selected from the carbonate sand of all tested specimens to measure their internal porosities. A laboratory \(\mu\)CT system, equipped with a high-resolution X-ray tube (XTH225/320 LC \(\mu\)CT scan from Nikon, Tokyo, Japan), was used to scan the high-resolution images of the specimen. In order to conduct \(\mu\)CT scanning, the sand grains were loosely deposited layer by layer into a cylindrical container 5 mm in diameter and 10 mm in height. A plastic sheet was used to cover the top of a layer of sand grains before depositing a subsequent layer of sand grains. This specimen preparation procedure enables the separation of sand grains, thus facilitating the identification of the internal pores of each sand grain from the CT image. Through image processing, a resolution of approximately 5 \(\mu\)m could be achieved for each CT image produced in this study. This is favourably smaller than the diameter of the tested carbonate sand grains which ranges between 500 and 1000 \(\mu\)m, ensuring the accuracy of measurement results. In addition, two carbonate sand-fine mixture specimens with 20 and 40% carbonate sand contents were also prepared using the same sample preparation method with triaxial tests to ensure the consistency of the specimens. Then, the specimens were scanned to investigate the microscopic structure.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen** & **Specimen** & **Initial Void** & **Initial Interfine** & **Effective Confining** & **Carbonate Sand** \\
**Category** & **Identity** & **Ratio** & **Void Ratio** & **Pressure (MPa)** & **Content (\%)** \\ \hline  & C5\_V0 & 0.583 & 0.583 & 0.5 & 0 \\  & C5\_V20 & 0.576 & 0.720 & 0.5 & 20 \\  & C5\_V40 & 0.573 & 0.955 & 0.5 & 40 \\ Similar & C10\_V0 & 0.589 & 0.589 & 1 & 0 \\ initial void & C10\_V20 & 0.580 & 0.725 & 1 & 20 \\ ratio & C10\_V40 & 0.575 & 0.958 & 1 & 40 \\  & C30\_V0 & 0.590 & 0.590 & 3 & 0 \\  & C30\_V20 & 0.572 & 0.715 & 3 & 20 \\  & C30\_V40 & 0.570 & 0.950 & 3 & 40 \\ \hline  & C5\_I0 & 0.698 & 0.698 & 0.5 & 0 \\ Similar & C5\_I40 & 0.442 & 0.736 & 0.5 & 40 \\ initial & C10\_I0 & 0.695 & 0.695 & 1 & 0 \\ interfine & C10\_I40 & 0.443 & 0.738 & 1 & 40 \\ void ratio & C30\_I0 & 0.704 & 0.704 & 3 & 0 \\  & C30\_I40 & 0.444 & 0.740 & 3 & 40 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Testing conditions of drained triaxial tests for carbonate sand-fine mixtures.