# Damping Ratio of Sand Containing Fine Particles in Cyclic Triaxial Liquefaction Tests
## 4 Discussion  
On the question of liquefaction potential with fine particles, one interesting issue that emerges from the experimental results is that the fine particles provided a quite negative contribution to the global soil skeleton since the undrained shear strength of the HN31-C500 mixtures continuously decreased with the increase in fines content \(F_{\rm c}\). By keeping the quantity of the main sand matrix constant, the gradual introduction of fine particles (i.e., \(F_{\rm c}\) from 5.0% to 15.0%) indeed densified the triaxial specimens. Corresponding to this densification effect, the basic soil mechanics regularly suggests an enhanced mechanical response contrary to our experimental outcomes. The other unanticipated result from the experimental results is the independence of the damping ratio \(D\) with the variation in \(F_{\rm c}\). In the following sections, these two phenomena will be further discussed from a microscopic point of view. As for granular assemblies, previous studies [33; 34; 35; 36; 37; 38] have already underlined the close relationship between the microscopic soil fabric and the macroscopic mechanical response in laboratory tests. For instance, a thin section of a sand specimen containing 20.0% silica fines was examined through the scanning electron microscopy (SEM) [38]. Based on the observation of the relative positions of coarse sand grains and fine particles on the microscale, it was thus inferred that three kinds of force chains might exist in a sand-fines mixture, including (i) sand-to-sand force chain, (ii) fine-to-fine force chain and (iii) fine-to-sand force chain. Regarding the clean sand specimen shown in Figure 10a, the straight line represents the strong force chain constructed by two coarse sand grains in contact with each other. Due to the influence of confining pressure, strong force chains can form an interlocking system and thus prevent the sand grains from displacing each other. Upon shearing, these force chains sustain the main stress transfer and yield the overall soil resistance to deformation. Regarding the sand-fines specimen shown in Figure 10b, two other force chains can then be defined according to the location of fine particles. Since  
Figure 9: Relationships between the damping ratio and amplitude of shear strain of HN31-C500 mixtures with (**a**) \(F_{\rm c}\) = 5.0%, (**b**) \(F_{\rm c}\) = 10.0% and (**c**) \(F_{\rm c}\) = 15.0%. the fine particles are much smaller than the coarse sand, they certainly have a greater level of mobility. A large proportion of them is thus accommodated into the coarse sand matrix, forming the fine-to-fine force chain (highlighted by the red crosses in the graph). Subjected to external loading, these fines are almost free to shift and move without truly participating in the global stress transfer. As a result, these inactive fine particles might be assumed to behave as \"voids\" and make no actual contribution to the overall resistance. The other part of fine particles is located nearby the sand-to-sand contact points by separating coarse grains in contact, which forms the fine-to-sand force chain (highlighted by the discontinuous red lines in the graph). In this case, some strong force chains (sand-to-sand) yielding the global soil resistance disappear, further substituted by unstable fine-to-sand force chains. Moreover, this kind of fines can serve as minor ball bearings during shearing and thus facilitate the relative sliding between coarse sand grains. As a consequence, the contractiveness of the global soil matrix might be essentially favoured. With the increase in fines content \(F_{c}\), the added fines are more likely to destroy the strong force chains. This rationale behind can explain why the decrease in the liquefaction resistance is interestingly accompanied with the densification process. Provided that the presence of these fine particles in a sand matrix is capable of facilitating the relative sliding between coarse sand grains, more macroscopic deformation can then be imagined in triaxial tests.