# Stability Analysis of the Landfill Slope with an Engineered Berm Under Composite Failure Mode
## 1 Introduction  
The engineered berm is frequently built at the front slope of landfills, which can not only increase the storage capacity of the landfill but also improve the stability of the landfill slope [1, 2, 3]. Theoretically, it can be said that maintaining the stable operation of this type of landfill inevitably requires reliable design of berms. The specific design of a berm needs to consider which failure mode this type of landfill slopes may resist. From a practical perspective, the failure of landfill slopes is mainly dominated by translational failure along the liner system [4]. Considering the existence of the berm, however, the failure of landfill slopes can be divided into two types, namely over-berm and under-berm failure modes [5, 6]. Furthermore, the limit equilibrium method is commonly used to establish a stability assessment model for landfill slopes based on specific failure modes [7, 8, 9], and it is also used to analyze the structural stability in tunnels and deep excavations [10]. Meanwhile, due to the existence of the berm, the evaluation model is strongly correlated with the geometric shape of this structure. From the perspective of the cross-sectional shape of berms, they can be thus divided into two categories, namely triangular and trapezoidal berms [11]. Regardless of the geometric shape of the berm constructed in the landfill, the three-wedge method is often used to analyze the stability of such landfill slopes. This method was developed from the two-wedge method proposed by [PERSON] et al. [12, 13] and further extended to consider the effects of leachate level and seismic load on the slope stability [14, 15]. [PERSON] et al. [16, 17, 18] divided the sliding body with a triangular berm into three parts, i.e.,active, passive and block wedges, and then proposed the three-wedge method based on the principle of limit equilibrium when that type of landfill slopes occurred the under-perm failure. Considering the effect of earthquakes on structural stability, [PERSON] and [PERSON] [19] used the pseudo-static method to introduce horizontal seismic loads to construct an assessment model for seismic stability of landfill slopes, and further [PERSON] and [PERSON] [11] extended the above-mentioned model by increasing the effect of vertical seismic loads. For the failure mode of the over berm, [PERSON] et al. [20] used the three-wedge method to build up a stability analysis model for this type of landfill slopes. When conducting seismic design of this structure in earthquake prone areas, [PERSON] et al. [21] extended the above analysis model based on the Newmark method to carry out engineering design considering permanent seismic displacement. When designing the landfill slope with an engineering berm, considering only the over-berm or under-berm failure mode may lead to unreliable design results. Therefore, it is necessary to analyze the stability of the landfill slope simultaneously under both failure modes. For the landfill slope with a trapezoidal berm, [PERSON] and [PERSON] [6], respectively, established safety factor calculation models to resist the two types of failure modes mentioned above and conducted slope stability analysis using the three-wedge method. Subsequently, [PERSON] and [PERSON] [22] developed these calculation models by introducing seismic loads using the pseudo-static method, and furthermore, considering the dynamic characteristics of seismic loads, [PERSON] et al. [23; 24] investigated the pseudo-dynamic stability of this type of landfill slopes. Apart from seismic loads, blasting vibration loads may also affect the stability of landfill slopes for dynamic loads due to the rapid development of transportation infrastructure construction. Considering the above practical situation, [PERSON] et al. [25] studied the influence of this type of loads on the stability of the landfill slope with a trapezoidal berm. Currently, reinforced soil retaining walls are used as berms, and the cross-sectional shape of the structure is generally rectangular.