## 1 Introduction  
As urbanization accelerates, the construction of large and complex underground infrastructure has necessitated launching a series of excavations [1, 2]. Within the excavation depth, when encountering an aquifer, it is commonly required to set up a seepage barrier curtain to drain the underground water preliminarily, then to brace and excavate, and a staged construction is also necessary. During this process, the increased effective stress in the soil within the groundwater depression cone contributes to soil compression, manifested as a soil settlement [3]. It typically leads to a series of safety threats to the surrounding buildings, thus affecting the urban economy and human safety significantly. To some extent, under the premise of ensuring its stability, the deformation control of pits and the influence on the surrounding environment have become crucial issues of excavations [4]. Hence, it has become a priority of geotechnical engineers to accurately evaluate the patterns of ground settlement variations during staged excavation, which is of great engineering significance and research value. Traditionally, settlement induced by soil consolidation has been one of the most classic problems explored in geotechnics [5], and there has been a dramatic increase in simple theoretical solutions [6, 7]. The settlement caused by excavation is a comprehensive geotechnicalengineering challenge involving a series of problems in soil mechanics such as strength, stability, deformation, groundwater seepage, etc. Simple theoretical solutions often fail to comprehensively express the effects of numerous parameters, thus having limited applications [8]. For the above reasons, numerous studies have investigated the deformation caused by excavation construction based on the empirical method with statistical analysis of a significant amount of measured data [9; 10; 11; 12; 13]. However, it has the shortcoming of disregarding the discrepancies between different stratigraphic conditions and soil mechanical properties. Thus the findings are not convincing. The numerical analysis solutions represented by the finite element method (FEM), comparatively, enable to consider not only the coupling effect of a variety of factors but also the sophisticated nonlinear mechanical properties of the soil, thus becoming an effective way to address the problem and being applied extensively in practical engineering [14; 15; 16; 17; 18]. It confirmed the critical role played by the constitution model of the geotechnical material employed in numerical simulation [19; 20]. The modified Cam-clay (MCC) model can reproduce the consolidation process of the soil under a complex stress path of repeated loading and unloading [21; 22; 23]. It is recognized by many studies as particularly applicable to deformation problems such as excavation [24] and has developed productive results [25; 26; 27; 28; 29; 30]. However, the deterministic approach treats geotechnical materials as homogeneous and employs invariant geotechnical parameters obtained by limited time-consuming tests or analogy methods, which is inconsistent with the actual situation. While the geotechnical parameters, including MCC model parameters, are characterized by spatial variability due to depositional conditions, stress history, weathering, and other geological effects [31; 32; 33]. Relatively, the probabilistic analysis of the excavation provides a solution that considers the uncertainty of geotechnical parameters [34; 35]. [PERSON] et al. [36] evaluated the stability of basement uplift in clay pits using a reliability index-based approach. [PERSON] and [PERSON] [37] proposed a simplified framework system for assessing the probability of surface displacement failure due to foundation excavation. [PERSON] et al.