## 1 Introduction  
Recently, to meet the demands of food security and urban development, the underground grain silos have received more and more attention due to their advantages of low energy consumption and safety compared to the traditional aboveground grain silos [1; 2; 3; 4]. Therefore, the PRSS is proposed for the excavations of the underground grain silos, which consists of supporting piles, walings, steel plates, and flexible waterproof polymers, and is characterized by high construction efficiency and reusability [5; 6; 7]. The underground grain silo is generally designed to have a cylindrical body and conical bottom for the purposes of convenience of grain transportation and excellent load bearing capacity [8; 9; 10], which is different from other underground structures [11; 12; 13]. As a result, it is common to find the PRSS being supported by earth berms in the circular excavations for the underground grain silos. Utilizing earth berms is a cost-effective and efficient method of stabilizing embedded retaining walls and minimizing their displacement [14; 15; 16; 17]. Studies by [PERSON] and [PERSON] [18; 19] have showed that enlarging the size of the berm had a more significant impact on improving short-term wall stability compared to deepening the embedment of a wall supported by a smaller berm. For a wall with specific embedment in particular soil conditions, the extent of support provided by a berm is related to the bench width, the slope, and the height [20; 21; 22]. The maximum slope is determined by the soil and groundwater conditions, whereas the height and bench width are constrained by factors such as space availability, accessibility, and the characteristics of the underground structure. Current research on earth berms has mainly been conducted under plane strain conditions, assuming that the earth berms were uniform along the perimeter of the retaining wall. The stability and deformations of retaining walls have been investigated using the 2D finite element method to examine the effects of changes in berm geometry and soil properties [23; 24; 25; 26; 27; 28; 29]. In terms of theoretical studies, earth berms are considered in limit equilibrium analyses in the following ways: as an equivalent surcharge [30; 31; 32], by means of raised effective formation level in drained [33] or undrained [29; 34] conditions, and by performing a single [35; 36] or multiple [18] Coulomb wedge analysis. However, [PERSON] and [PERSON]'s [19] plane stain centrifuge model tests showed that these approaches were to some extent conservative. The main reason is the berm's lateral resistance being either disregarded or dealt with empirically and/or incorrectly [33]. Another reason is that these methods only considered plane strain conditions, assuming that the berm remained intact along the entire length of the wall during the period of excavation or installation. Notably, in many practical excavations stabilized with earth berms, the assumption of plane strain may not accurately represent field conditions. For instance, it is often necessary to remove berms in sections to install permanent support systems, such as in the case of road cuttings or formation level props. In such cases, the berms are discontinuous along the longitudinal length of the wall, requiring a comprehensive consideration of the three-dimensional (3D) effects [37; 38]. Moreover, owing to the soil arching effect that causes the soil to be compressed in the tangential direction [39; 40], earth berms placed in a circular excavation are more appropriately analyzed as an axisymmetric problem rather than plane strain [41]. Furthermore, discontinuous supporting structures (e.g., row piles wall and the PRSS) are usually simplified to continuous supporting structures and analyzed by equivalence, but such a simplification is insufficient for understanding the actual behavior of the supporting structures, especially in the case of berms.