## 1 Introduction  
In recent years, urban development has increasingly utilized ultra-deep pits, which present significant challenges to construction safety due to their unstable nature and high risk [1; 2]. Among the various types of foundation-pit-enclosing structures, underground diaphragm walls have become extensively utilized due to their benefits of high rigidity and robust integrity [3; 4]. Circular diaphragm walls, in particular, have been found to be more suitable for ultra-deep foundation pits. The force characteristics of circular diaphragm walls exhibit an arch shape, whereby the ring direction is mainly subjected to axial forces, allowing for the full utilization of the enclosure structure's strength. Nevertheless, it is worth noting that trench walls composing a diaphragm wall often suffer from collapse during construction, particularly when the structure is constructed in a soft and/or unstable soil layer with a sandy interlayer, as reported in prior research [5; 6]. The conventional method of determining trench wall stability involves assuming the shape of the failure surface and developing an instability model based on the limit equilibrium theory [7; 8]. Previous research has employed this approach to analyze various types of trenches. For example, [PERSON] [9; 10; 11] proposed a 3D analytical method based on the limit equilibrium theory, arching theory, and full-scale field tests for slurry-supported trenches in cohesionless soils. [PERSON] utilized the Coulomb-type force balance method to derive analytical solutions for the safety factor and critical failure surface angle of slurry-supported trenches under drained effective stress and undrained total stress [12]. [PERSON] conducted 2D and 3D analyses of the local and overall stability of a slurry trench for cohesive soil using the limit equilibrium theory [13]. [PERSON] [14] proposed a limit equilibrium solution for the stability of slurry-supported trenches and combined the rotational 3D failure mechanism to analyze the stability of narrow trenches. [PERSON] [15] adopted a 3D kinematic approach of limit analysis to analyze the trench stability and deformation law in non-uniform and undrained clay. However, these methods mainly evaluate rectangular trench sections, while circular underground diaphragm walls feature a double-angled design that increases their force characteristics and makes their stability evaluation even more complicated. The application of numerical simulation in investigating the destruction mode of underground diaphragm walls has gained attention due to the development of computer technology. Researchers have delved into various aspects of this field, such as the impact of trench wall construction on surrounding environments, the soil response during the construction process, and factors affecting trench wall stability. Several studies have been conducted by scholars to address these issues. [PERSON] (2016) proposed a design suggestion for the stability of the slurry trench using the elastoplastic finite element method analysis and compared it with a centrifugal test. [PERSON] (2017) analyzed the failure laws of sliding bodies caused by the insufficient slurry support of a corner trench in normally consolidated clay. [PERSON] (2018) used numerical finite element analysis to reveal the stability of 2D and 3D homogeneous and inhomogeneous undrained diaphragm wall trenches. [PERSON] (2019) investigated the stability of slurry-supported trenches by means of a discretization-based kinematic technique and upper-bound analysis. [PERSON] (2019) carried out a stability analysis of slurry-supported trenches in horizontally layered cohesive frictional soils using the kinematical approach of limit analysis. Moreover, scholars have analyzed various approaches to address the stability problem of trench walls. For instance, [PERSON] (2018) studied the global and local stability methods and failure modes of a slurry trench wall through numerical simulation, centrifugal model tests, and theoretical analysis.