## 1 Introduction  
Seismic liquefaction is a primary cause of earthquake-induced structural and infrastructural damage. Major seismic events, such as the 2011 Tohoku earthquake (\(M_{W}\) 9.0) and the 1976 Tangshan earthquake (\(M_{W}\) 7.5), have precipitated extensive liquefaction phenomena. These occurrences resulted in differential settlement, foundation failures, and sand boils, rendering numerous structures inoperative and presenting substantial challenges to post-disaster reconstruction initiatives [1; 2; 3]. The precise prediction of liquefaction is paramount for mitigating related disasters and implementing appropriate countermeasures. As a result, liquefaction assessment continues to be a central concern in geotechnical engineering. The parameters frequently employed in liquefaction assessment encompass the Standard Penetration Test (SPT) [4; 5], Cone Penetration Test (CPT) [6; 7], Dynamic Penetration Test (DPT) [8], and Shear Wave Velocity Test (\(V_{s}\)) [9], as well as methodologies integrating multiple parameters [10]. \(V_{s}\) is pivotal in evaluating the site liquefaction probability, being directly correlated with soil relative density [11]. In the realm of geotechnical engineering, \(V_{s}\) offers numerous dynamic elastic mechanical parameters. Owing to its cost-effectiveness and simplicity, \(V_{s}\)-based liquefaction assessment methodologies have witnessed rapid advancements in recent years. Compared to the SPT and CPT, \(V_{s}\) testing exhibits a superior performance in gravelly soils and irregular sites where the SPT and CPT are challenging to implement [12]. In recent years, \(V_{s}\) testing has gained widespread adoption in geotechnical engineering, leading to the accumulation of substantial data. The \(V_{s}\) of soil layers reflects the soil's dynamic properties and is extensively utilized in diverse engineering practices. The principal methodologies of \(V_{s}\) testing encompass borehole techniques and surface wave techniques. Borehole techniques are categorized into single-hole and cross-hole methods, whereas surface wave techniques comprise transient surface wave and steady-state surface wave methods. Table 1 lists the characteristics of each method. Extensive research has been conducted on liquefaction assessment methods based on \(V_{s}\). In 1981, [PERSON] et al. (1981) first studied the soil liquefaction evaluation method based on \(V_{s}\). Through indoor cyclic loading tests, they defined the threshold shear strain that generates the pore water pressure and used [PERSON] et al. 's \(CSR\) (cyclic stress ratio) calculation formula to convert it into the \(V_{s}\) threshold value ([PERSON] et al., 1981). When the field-measured \(V_{s}\) is less than the \(V_{s}\) threshold value, the soil will liquefy. [PERSON] et al. (1981), [PERSON] et al. (1981), and [PERSON] et al. (2019) proposed the critical relationships of liquefaction triggering based on the effective stress-normalized shear wave velocity (\(V_{s1}\)) using different field liquefaction data. Due to the limitations of deterministic methods, researchers have recently begun to adopt probabilistic liquefaction assessment methods. [PERSON] et al. (2018) used logistic regression and Bayesian methods for probabilistic analysis and proposed a liquefaction probability evaluation formula based on \(V_{s}\). [PERSON] et al. (2018) proposed a similar formula based on a logistic regression model, while [PERSON] et al. (2018) proposed a corresponding assessment method based on the Bayesian updating model. In recent years, as human activities have expanded, liquefaction has been observed in lower magnitude earthquakes at deeper depths and in more diverse soil types. For example, the 2018 Songyuan earthquake (\(M_{s}\) 5.7) caused widespread liquefaction ([PERSON] et al., 2018); the 2011 Christchurch earthquake in New Zealand (\(M_{W}\) 6.3) saw significant liquefaction at