# Analysis of the Dynamic Stability of Tailing Dams:
## 1 Introduction  
Tailings are artificial soil particles discharged from ores after they are crushed, ground, and beneficiated. The particle composition, based on the particle size, is as follows: sand particles (>0.075 mm), powder particles (0.005-0.075 mm), and clay particles (<0.005 mm). According to the difference in the particle composition content and plasticity index, tailings can be classified as sand tailings, powder tailings, and viscous tailings. Tailing silt refers to powder tailings with a particle size greater than 0.074 mm, a particle mass less than 50% of the total mass, and a plasticity index less than 10. Owing to improvements in the mining-grade requirements and beneficiation process of tailings, the average particle size of tailing materials is expected to reduce. The primary components of many tailing ponds have been transformed from coarse-grained soil to fine-grained soil. Tailings discharged from the ore dressing plant are gradually deposited upstream of the tailings under hydraulic filling. After sorting, tailing silt forms the primary component of several dam structures. Compared with other tailing materials, tailing silt has poorer consolidation and drainage, lower permeability, and an uneven discharge. With an increase in the dam height, the infiltration line of the dam rises, which increases the susceptibility to liquefaction duringan earthquake [1; 2]. Data from various sources show that earthquakes are the second major cause of tailing dam accidents [3], and the dynamic instability of many fine-grained tailing dams during an earthquake has become an unavoidable issue for various mining corporations [4; 5; 6]. Scholars worldwide have conducted extensive research on the stability of rock and soil and the vibration liquefaction of soil particles and have achieved a lot of results. [PERSON] et al. [7] summarized the law of stress-strain development and proposed the Hardin-Drnevich hyperbolic model through the dynamic triaxial test of sand, which can reflect the dynamic stress-strain relationship of different types of sand with a high fitting degree. [PERSON] et al. [8] summarized the pore pressure generation and diffusion mechanism of soil in the process of vibration liquefaction and put forward the corresponding liquefaction possibility evaluation criteria. [PERSON] et al. [9] carried out dynamic triaxial testing on silt with different dynamic stress amplitudes, summarized the trend of excess pore pressure in the process of vibration liquefaction, and analyzed the influencing factors and causes of pore pressure changes. [PERSON] et al. [10] proposed a polygon approximation method to calculate the damping ratio of soil. This method can be directly used to calculate experimental data, and the algorithm can be reused, which considerably simplifies the calculation of the damping ratio. [PERSON] et al. [11] compared the dynamic strength curves of offshore silt under different failure criteria, discussed the existence of the critical value of the dynamic strength of the sample, and proposed a pore pressure development model suitable for offshore silt. [PERSON] et al. [12] conducted dynamic tests on samples from a gold mine located in western Quebec and found that the CRR (which reflects the liquefaction resistance) of the samples was not significantly affected by the effective consolidation stress. [PERSON] et al. [13] studied the influence of multiple factors on the dynamic strength of gravel soil through dynamic triaxial tests and explored the influence of various factors on the deformation of the dynamic strength of the sample. They found that the plastic strain increases with an increase in the initial static deviatoric stress and dynamic stress and decreases with an increase in the confining pressure, load frequency, and consolidation ratio. [PERSON] et al.