## 4 Discussion  
### Influence of Diatoms on Attterberg Limits from a Microstructural Perspective  
The diatom and kaolin structures are shown schematically in Figure 11. A disk-shaped diatom is a spheroid cell with two symmetrical porous shells connected by a girdle band. The shells have a regular and centrosymmetric arrangement of skeletal pores on their surfaces. Inside the spheroid cell is a large inner chamber that stores the biological protoplasm of the diatom; this chamber becomes a typical intra-skeletal pore in a frustule after the diatom dies. Furthermore, [PERSON] et al. [38] showed that the disk-shaped diatom frustule comprises three membranes at the nanoscale--namely the areola, cribium, and cribellum--containing large, small, and tiny nanoholes, respectively. Figure 11b shows the distribution of nanoholes in cribellum and cribium corresponding to a large nanohole in the areola membrane. Notably, the pores in the cribellum were observed in the TEM images (Figure 4c,d) from the vertical direction of a frustule, as shown by the arrow in Figure 11b. As described above, the microstructure of the diatom frustule is porous and water is stored in the skeletal and intra-skeletal pores. These pores are connected through the nanoholes inside the frustule so that the \(w_{\rm L}\) and \(w_{\rm P}\) values and water content of DS are measured high. Figure 11c shows the crystal structure of kaolinite with two tetrahedral and octahedral sheets. The structure of kaolin clays is a layered stacking with limited space inside, and the water in kaolin is adsorbed in the surface of kaolinite platelets in the form of a double layer, which is different from the case of the diatom. However, although the higher consistency limits of diatomaceous samples compared to kaolin caused by the water inside the diatom frustules were measured, the kaolin and diatomaceous samples have similar \(I_{\rm P}\) values. This is because the water inside the diatoms contributes little to the plasticity of the soil. Furthermore, it is observed that the diatoms with \(I_{\rm P}=22\) are non-plastic, whereas the kaolin with \(I_{\rm P}=17\) is plastic; therefore, the applicability of \(I_{\rm P}\) as a parameter for soil plasticity evaluation and soil classification for DS should be assessed carefully, especially when the DS contains 20% or more diatom microfossils (by weight).  
Figure 10: Values of \(w_{\rm P}\), \(w_{\rm L}\), and \(I_{\rm P}\) for DKM samples with different NaCl concentrations.  
Apart from the diatom content, the Atterberg limits of DS are also related to diatom crushing. The crushed DKM samples have lower \(w_{\rm L}\) and \(w_{\rm p}\) values than uncrushed ones. This is because the hollow intra-skeletal and skeletal pores collapsed, thereby reducing water retention capacity, and the higher crushing degree of diatoms leads to the lower Atterberg limits. Moreover, the presence of diatoms affects the response of the Atterberg limits of the soil to the NaCl concentration. The \(w_{\rm L}\), \(w_{\rm p}\), and \(I_{\rm P}\) values of the DS hardly changed upon changing the NaCl concentration, whereas those of the kaolin did (Figure 10). For pure kaolin, different values of NaCl concentration lead to various particle associations among kaolinites and further changes in the forces among clay particles [36]. For pure diatoms, the double layer is thin because of the low surface charge density of a frustule and does not change with NaCl concentration [20; 39]. The water that significantly affects the consistency limits of the diatoms is stored mainly in the intra-skeletal pores instead of in the double layer. Interestingly, the effects of NaCl concentration on the kaolin sample almost disappear with the addition of diatoms (Figure 10), which may be because of the unique interactions between kaolin and diatom particles of the diatom-kaolin aggregates.  
Figure 11: Schematics of (**a**) disk-shaped diatom frustule, (**b**) profile structure of frustule, and (**c**) crystal structure of kaolinite.