## 1 Introduction  
Coastal slopes are often subject to wave erosion, leading to landslides into marine environments. Wave erosion not only exposes the slope and causes soil loss but also severely threatens the ecology, human activities, and the safety of public facilities. A \"marine geohazard\" is defined as geological features and processes in coastal and offshore environments that lead to loss of life and assets [1; 2; 3; 4; 5; 6]. The fundamental problems of marine geohazards are highlighted, such as coastal erosion, beach erosion, and retreat, among others. To develop corresponding mitigation measures, it is crucial to monitor and investigate the failure mechanisms of slopes under wave erosion. The investigation into geomorphological changes in slope profiles caused by wave erosion has been a focus of numerous studies, each contributing to our understanding of coastal dynamics, erosion processes, and the mechanisms behind bluff and cliff retreat. [PERSON] [7] examined how unconsolidated coastal bluffs along the Great Lakes in the USA respond to wave action, uncovering patterns of bluff retreat and incorporating these findings into slope evolution models. These models provide insights into recession rates and the impact of wave action on bluff stability. Similarly, [PERSON] [8] focused on coastal bluffs and sea cliffs on Puget Sound, Washington, USA, identifying wave action as a key driver of erosion. [PERSON]'s work highlighted the vulnerability of sedimentary layers to erosion and the importance of beach and berm geometry in protecting bluffs from wave-induced erosion in shielding the bluff toe from direct wave contact. [PERSON] et al. [9] provided comprehensive overviews of coastal cliff formation, evolution, stability, and the dual influence of terrestrial processes and wave action. They noted the episodic nature of wave impact and cliff retreat, influenced by the wave climate, and identified wave action at the base of landslides and high groundwater levels as key triggers for large coastal landslides. [PERSON] and [PERSON] [10] and [PERSON] et al. [11] contributed to understanding the mechanisms behind wave-induced erosion and its impact on coastal geology. [PERSON] and [PERSON]'s physical model tests shed light on the failure mechanism of coastal cliffs, while [PERSON] et al. [11] explored the geometric evolution of reservoir banks due to wave erosion, demonstrating the formation of a stepped topography influenced by wave actions. [PERSON] et al. [12] and [PERSON] et al. [13] investigated erosion processes in specific coastal environments, with [PERSON] et al. focusing on riverside slope failure due to wind wave erosion and [PERSON] et al. examining wave-impacted embankment slopes. Both studies emphasized the correlation between wave characteristics and the erosion process. [PERSON] et al. [14] and [PERSON] et al. [15] studied the dynamics of coastal cliffs and platforms, noting the significant influence of wave processes on coastal morphology and the triggering of landslide activity by a combination of wave-induced erosion and substantial rainfall. These studies highlight the differential erosion along coastlines and the importance of geological and climatic factors in coastal stability and erosion rates. The retreat of coastal slopes due to erosion is a critical concern for coastal management and environmental sustainability. [PERSON] et al. [16] discussed the recession rates of soft cliffs. They indicated that the rate of sea level rise and strength of the costal materials control the cliff retreat and shore profile. [PERSON] et al. [17] investigated wave erosion on clay coasts. They concluded that bluff crest recession rates are highest during high water levels, and the bluff slopes failed in rotational slides and topples. The volume and morphology of the beach significantly influence the frequency and intensity of run-up reaching the bluff face, thus impacting the rates of bluff recession. [PERSON] et al.