# Damping Ratio of Sand Containing Fine Particles in Cyclic Triaxial Liquefaction Tests
## 1 Introduction  
Subjected to earthquake motions, sand liquefaction [1; 2; 3] can likely occur where an underground water table is pretty shallow. In such a case, the foundation soil might develop a \"flow-type\" behaviour due to the rapid accumulation of excess pore water pressure and experiences a sudden loss of shear resistance. Spectacular examples of engineering failure (e.g., civil buildings and underground lifelines) can be ascribed to the triggering of sand liquefaction, as shown in Figure 1. For instance, Kamisu city (Osaka province in Japan) was severely touched by sand liquefaction during the 2011 Tohoku earthquake (\(M_{w}=9.1\)). According to the follow-up disaster report [4], a series of land cracks and some remains of sand boils associated with large permanent ground deformation were apparent on ground surfaces and walking streets, respectively. Evidence from a number of field surveys has already established that sandy deposits containing a small amount of fine particles (i.e., fines content usually lower than 10.0%) are more likely to liquefy [5]. The similar conclusion has been repeatably drawn by others. For instance, in an experimental study including 17 worldwide earthquakes [6], more than half of the liquefied data fall within a small range of fines content less than 5.0%, as indicated in Figure 2. Hence, the influence of fine particles on the liquefaction potential has become one of the most significant current discussions and received increased attention in geotechnical earthquake engineering. Fruitful studies reported in the literature that concentrate on this topic frequently adopt triaxial tests to assess the possible influence of fine particles in the light of certain physical indicators such as plastic index [7], particle shape [8] and gradation characteristics [9]. In an experimental study carried out by [PERSON] [10], the relationship between the liquefaction potential and different void ratios have been carefully analysed: (i) for the same global void ratio, the liquefaction potential decreased with the addition of non-plastic fines from 0 to 44%; (ii) for the same intergranular void ratio with low fines contents, the increase in the fines content led to a higher liquefaction resistance, whereas a reversed tendency was found for the same interfering void ratio with higher fines contents. These references have mainly concentrated on homogeneous soil being the test specimens. With the purpose of  
Figure 1: Schematic of liquefaction-induced failures under seismic loading. Figure 2: Triangular classification chart for liquefied soil including 17 worldwide earthquakes [6]. embodying soil stratification, [PERSON] [11] performed a series of cyclic triaxial tests directly with stratified sand-silt specimens and found that the increase in the number and thickness of silt layer significantly increased the corresponding liquefaction resistance. Recently, the initial soil fabric given by the specimen preparation method has been proven to be a predominant factor governing the liquefaction response [12]. Regarding sand-silt mixtures, [PERSON] [13] found that the angular nature of fines provided a negative contribution to shear strength since some fines can possibly located between coarse sand grains by breaking the global force chain yielding the shear resistance. In general, deformation characteristics of a soil element vary to a large extent decisively relying on the magnitude of shear strain. While assessing the liquefaction failure with a watchful eye toward large deformation, the effect of cyclic degradation [14] is an essential descriptor to assess the liquefaction process. The evolution of damping ratio in excess of the incipient deformation range [15; 16] has been widely recognised as an intrinsic variable to describe the cyclic degradation.