## 1 Introduction  
Over 70% of dams worldwide are constructed using soil; consequently, they are vulnerable to leakage and internal erosion due to heavy rain and other factors [1; 2]. Climate variability has exacerbated these vulnerabilities, increasing the frequency of dam failures [3]. The aging of dams is affected by various factors, such as structural conditions, soil properties, infiltration control, and drainage performance, causing dams to degrade over time, thereby limiting their ability to withstand heavy rainfall [4; 5; 6; 7]. In South Korea, most agricultural reservoirs are earth-filled dams, referred to hereafter as earth dams. Of the 17,080 reservoirs, 99% are earnthen dams, with 87% constructed over 50 years ago [8]. The historical context, including the agricultural infrastructure focus of the Japanese colonial period and the Korean War, promoted the economical and rapid construction of earnthen dams [9]. Most of these dams were constructed to low design standards in the 1900s, without considering their service life [10]. In 2020, 22 reservoirs failed during the rainy season, and the primary failure factor was age. Although existing evidence is insufficient to conclusively attribute failures to dam aging, there are perspectives suggesting that the challenges in explaining the phenomenon as solely due to rainfall may be linked to older dams constructed in an era without modern designs or mechanical equipment. These older dams were more prone to exhibiting inhomogeneous zones. When water levels in a dam increase owing to rainfall, seepage water accumulates in the path of least resistance in the uneven fill zone, indicating potential susceptibility to failure under such conditions [11; 12; 13]. From 2010 to 2020, failures in 104 reservoirs in Korea occurred most frequently during the monsoon period between July and October and were mainly attributed to aging and heavy rainfall. Failures at 11 locations (10.5%) of water leaks and piping were attributed to dam aging, whereas those at 90 locations (86.5%) were associated with spillway-boundary failure, overtopping, and slope failure [8]. Global statistics on earthem dam failures have identified the primary causes of failure as overtopping (35.9%) and piping (30.5%) [1,14]. However, in Korea, reservoir dam failures caused by heavy rainfall were dominant in 2010 [8]. Figure 1 illustrates the number of dam failures according to dam type and failure cause. The failure rate was not significantly influenced by the type of dam, such as zone, core, and homogeneous dams (See Figure 1). Zoned-type dams, generally considered the most stable, exhibited the highest failure rate (53%). These findings suggest that design approaches focusing on controlling seepage within the dam body may be insufficient regardless of the dam type. The results highlight the vulnerability of all earthem dams to slope erosion and overtopping during intense rainfall, thereby posing a potential failure risk. The failure of an earthem dam owing to overtopping is a multifaceted process influenced by several factors, including dam compaction, material, crest width, and slope. Several studies have highlighted this complexity, suggesting that more dam failures are due to overtopping than to internal erosion [15, 16, 17, 18]. To mitigate the risks associated with overtopping, several different slope protection methods have been used on downstream slopes, including rirpaps, gabions, vegetative cover, roller-compacted concrete, and biopolymers [19, 20, 21]. In some cases, the dam crest is constructed with a parapet and a flat concrete foundation for support [10,22]. However, these methods cannot guarantee the continued safety of dams in small earth reservoirs with frequent water level fluctuations, as there is a high possibility of differential settlement between the dam body and its foundation. Since dam crest railing installations and slope protection methods do not fundamentally prevent overtopping, there is a need for a more comprehensive solution from a methodological perspective [23,24].