# Limit Equilibrium Analysis of Landfill Instability Based on Actual Failure Surface
## 1 Introduction  
A landfill is a commonly used method for municipal solid waste disposal, and the stability of the landfill slope is crucial during the entire life cycle of construction, operation, and closure [1, 2, 3, 4]. In the past few decades, several serious landfill failures and landslides in urban solid waste have evolved into significant disasters and led to severe environmental pollution. The failure of the Payatas solid waste landfill in Manila, Philippines is one of the most catastrophic landfill failure and landslide cases, causing massive casualties and property losses. Many scholars have conducted theoretical research on the stability analysis of solid waste landfills since the 1990s. The instability modes of the landfill can be categorized into six types, and the stability analysis can be performed based on the traditional limit equilibrium method [5, 6, 7]. [PERSON] et al. [8, 9] analyzed the stability of the landfill slope system by the two-wedge limit equilibrium method. On this basis, the three-wedge limit equilibrium method is also used to evaluate the stability of landfills and their engineering terms [10, 11, 12, 13]. In these methods, it is assumed that the solid waste landfill slides along the surface of the liner system or the engineered term, the sliding blocks are divided into active wedges and passive wedges, and the limit equilibrium method is used to calculate the \(FS\). The advantage of these methods is their ease of use in engineering; however, matching the failure process of the slope can be difficult. In addition, these theoretical models do not consider the influence of the water level on slope stability due to (1) rainfall [14]; (2) a large amount of leachate generation [15, 16]; and (3) leachate recirculation in the bioreactor landfill [17, 18], resulting in the elevation of pore pressure in the slope and the accumulation of a large amount of leachate inside the waste body. Similarly, this is also a defect of the traditional slope limit equilibrium analysis method in the application of landfill stability analysis [19]. According to on-site investigation and research, it appears that the landfill's instability may be caused by excessive pore water pressure due to continuous rainstorms [20]. Survey and monitoring data from ten large landfills indicate that high leachate levels and excessivewater content are major or significant triggers for landfill instability [14]. Research [21] shows that landfill instability is often related to the accumulation of water levels at the bottom of the landfill. [PERSON] [22] provides a detailed review of six serious MSW landfill failures between 1977 and 2005, pointing out that continuous heavy rainfall or poorly controlled leachate recirculation may have contributed to the failures through increased water levels. [PERSON] et al. [23] analyzed 62 historical cases of slope instability in landfill sites, and the high water level was the main cause in 25 of them. The presence of high water levels can also soften the bedrock at the bottom of the landfill [24]. Therefore, it is crucial to understand the triggering mechanism and evolution of MSW landfill failure caused by the increase in water level. During a slope failure process, the interface between the active wedge, the passive wedge, and the block wedge is not vertical, as traditionally assumed in the wedge limit equilibrium analysis. In fact, the face between the wedges has a certain angle with the horizontal plane. The factors influencing this angle are very complex, such as slope geometry, waste characteristics, water level, and so on. Figure 1 shows the failure at Payatas landfill in the Philippines, in which about 30 m failure took place. It is not difficult to observe that the failure surface is a sector rather than perpendicular to the ground. A similar phenomenon occurred at the Meetotamulla landfill in Sri Lanka in 2017 [25].