# Cnoidal Wave-Induced Residual Liquefaction in Loosely Deposited Seabed under Coastal Shallow Water
## 1 Introduction  
In the shallow water environment, offshore structures, such as breakwater, offshore turbines, and oil platforms, generally are directly constructed on the seabed foundation. However, there is an inescapable truth that the seabed soil layers newly deposited in the Quaternary are widely distributed in offshore areas. Under the application of cyclic loadings, such as ocean waves and seismic waves, these loose seabed soil layers are easily liquefied or softened under cyclic loading, such as ocean waves and seismic waves, which poses an enormous threat to the stability of offshore structures constructed on it. After a comprehensive analysis of the failure reasons for some typical breakwater projects that occurred since the 1930s, [PERSON] (1994) [1] pointed out that the ocean wave-induced liquefaction in seabed foundations is one of the factors causing the failure of offshore breakwaters. [PERSON] et al. (2018) [2] and [PERSON] et al. (2004) [3] investigated the liquefaction phenomena on seismic waves by laboratory tests and numerical simulations of saturated cohesive soils. Therefore, it has important research significance in science and engineering to study the dynamic characteristics and the liquefaction process of a loosely deposited seabed floor under the loading of extreme waves in a shallow water environment. About the ocean wave-induced dynamics of a seabed floor, there have been a great number of works done previously. Before 2000, analytical derivation was the main researchmethod. According to [PERSON]'s consolidation theory, a series of analytical solutions are proposed, in which the seabed can be finite [4; 5] or infinite [6; 7] in depth; the seabed can also be isotropic or anisotropic. After 2000, the analytical derivation was further developed. Some new analytical solutions were proposed either considering the stratification of the seabed or adopting the 'u-p' form/'u-w' form of [PERSON]'s equation as the governing equation; a detailed brief review can be found in [PERSON] and [PERSON] (2017) [8]. However, these analytical solutions are only applicable to the very dense seabed soil, which can be described by the poroelastic soil model. For loosely deposited seabed soil, a poro-elastoplastic soil model must be utilized. As a result, numerical modeling would be the only reliable way to study the dynamics. On this aspect, typical works were conducted by [PERSON] (1994) [9] and [PERSON] et al. (2006) [10] before 2010. Several works have been conducted in the past decade. [PERSON] et al. (2015) [11] and [PERSON] and [PERSON] (2011) [12] numerically studied the accumulation of pore pressure in a loose seabed floor by extending [PERSON]'s model [13] from 1D to 2D under the action of a random wave. Recently, [PERSON] and [PERSON] (2017, 2018) [8; 14] comprehensively studied the dynamics of a loose seabed floor as well as the progressive liquefaction process by utilizing the integrated model FSSI-CAS 2D. However, the Stokes wave theory is used in their works. Actually, the Stokes wave theory is not applicable in offshore shallow water. The cnoidal wave should be used. On the aspect of cnoidal wave-induced dynamics of the seabed floor, there are also a few works available in the recent decade. For example, [PERSON] et al. (2014) [15] numerically investigated the dynamics of a dense seabed floor under the action of the cnoidal wave, taking a COMSOL-based numerical model. [PERSON] et al. (2013) [16] and [PERSON] et al. (2019, 2021) [17; 18] analytically investigated the cnoidal wave-induced dynamics of the dense seabed and the momentary liquefaction. However, the above studies are all limited to the poroelastic soil model, which is only applicable to very dense seabed soil. Currently, there is still a lack of research work on the cnoidal wave-induced dynamics of a loosely deposited seabed floor and on the residual liquefaction in it in a shallow water environment.