## 1 Introduction  
The safety and stability of the open-pit slope (OP-slope) is the lifeline of open-pit mining [1; 2; 3; 4; 5; 6]. Underground goals are a major factor affecting the stability of the OP-slope [7; 8; 9; 10; 11]. In recent years, open-pit landslides caused by goafs have frequently occurred. The Yanqiangshan iron mine in China, Palabora mine in South Africa, and Shanxi Anjialing coal mine in China have suffered different degrees of surface collapse and landslide accidents under the influence of underground goafs and mining disturbances [12; 13]. The existence of underground goafs poses a serious threat to the safe operation of open pits [14]. Considering this issue, numerous studies have examined slope stability under the influence of underground goafs. [PERSON] et al. [15] revealed the deformation and damage law and evolution characteristics of the rocks around goafs during the transition from open-pit to underground mining through physical modeling. As a result, it was found that the fracture of the overlying strata showed a clear layer structure. [PERSON] et al. [16] performed modeling to investigate the effects of underground mining process parameters on the deformation evolution of the OP-slope. The risk of slope destabilization gradually increased with the increase in mining volume. [PERSON] et al. [17] used physical modeling experiments to investigate the deformation and damage process and evolution of the fractured rock and found that the overburdened rock in the mining area contained a high fracture angle of 30\({}^{\circ}\)-90\({}^{\circ}\). Owing to the size effect of the experimental model and the material properties, there is inevitably a certain error between modeling experiments and the actual open-pit mine. Numerical simulation is an efficient and flexible research method [18; 19; 20; 21; 22], which has been used to study slope stability. [PERSON] et al. [13] used finite element modeling/discrete element modeling to analyze the development of step-path failure caused by the collapse of large OP-slope blocks. The analysis indicated that there is a threshold or critical intact rock bridge percentage along step-path failure planes that determines the stability of an open-pit mine during caving operations. [PERSON] [23] investigated the influence of pit wall stability on underground planning during the transition from open-pit to underground mining. [PERSON] et al. [24] proposed a mining scheme for the hanging wall based on the induced caving method during the transition from open-pit to underground mining. The numerical simulation results show that a gentler inclination of the predominant joint set indicates a higher possibility of the collapsed rock mass rushing out to the bottom of the open pit. [PERSON] et al. [25] used the strength reduction method and limit equilibrium method to study the hazard classification and stability of steep slopes under different load conditions. [PERSON] et al. [26] demonstrated that the maximum displacement occurs at the slope face at the foot of the slope and reaches 10 cm. [PERSON] [27] combined ABAQUS software and field monitoring and found that stress redistribution due to underground excavation is the main cause of slope damage. Rock damage is essentially the result of being subjected to loads that exceed their bearing limits [28]. Moreover, the presence of faults can change the stress distribution and increase the magnitude of changes in local stress concentrations [29]. Research shows that the slope failure process can be divided into three stages in chronological order, namely, collapse pit, small landslide, and large landslide [12]. To summarize, the current study mainly focuses on the effect of underground goals on slope stability from open-pit to underground mines. There is fewer research on the effect of pre-existing concealed goals underneath OP-slopes (PCO-goafs).