## 1 Introduction  
With the continuous development of urban underground space construction in China, particularly in areas with high-water-content soft soils, there has been an increasing number of engineering cases involving deep foundation pits [1; 2; 3; 4]; e.g., approximately 600 deep excavations were reported in the last 15 years in Shanghai [5]. However, the challenging geotechnical conditions of soft soils pose serious risks to excavation stability. These soft soils, characterized by high water content, high compressibility, and low permeability, exhibit pronounced creep behavior due to their elastic viscoplastic nature. The creep characteristics of soft soil can cause considerable deformation in foundation pit retaining structures and ground settlement, gradually increasing over time [6; 7; 8; 9; 10]. If supports are not installed in time or construction is delayed for too long a period, it is highly likely to result in foundation pit engineering accidents [11; 12]: for example, the collapses of the Nicoll highway excavation for the metro circle line in Singapore (2004) [13] and the Xianghu excavation for a subway station in Hangzhou (2008) [14], and excavation instability at Jinxiu Four Seasons Garden in Zhuhai (2011) [15]. Deep excavation in soft soils exhibits significant spatiotemporal effects [16; 17; 18], increasing the risk of geotechnical hazards in the surrounding environment [19; 20; 21]. Therefore, ensuring the safety and stability of deep excavations in soft soil and preventing excessive deformation that may lead to the settlement and cracking of adjacent environments and facilities have become a pressing and critical research focus in engineering. Numerous scholars have conducted extensive research on the spatiotemporal evolution of deformation in deep excavation in soft soil. Based on the three-dimensional failure mode of pit walls, [PERSON] [22] and [PERSON] [23] proposed formulas for the length of the influence area considering spatial effects and calculations for earth pressure. [PERSON] et al. [24] introduced the concept of the equivalent internal friction angle, treating the soil layers around the pit as non-cohesive homogeneous bodies, and using the theory of plastic upper bounds along with the associated flow rule, provided formulas for calculating spatial effect coefficient. [PERSON] [25] performed numerical simulations to analyze the horizontal deformation of retaining structures at different positions and directions during pit excavation; [PERSON] et al. [26] and [PERSON] et al. [27] initially obtained parameters for the soft soil creep model through triaxial rheological tests and then used numerical simulations to analyze the impact of soil creep on the deformation of retaining structures and the surrounding environment. [PERSON] et al. [28] integrated existing creep test curves for soft soils in the Shanghai area to fit the calculation parameters for the soil creep equation and then used the finite element method to analyze the creep deformation and creep strain of soil slopes during the construction process. [PERSON] [29] performed numerical simulations through the secondary development of the viscoelastic-plastic constitutive model to analyze the time-dependent deformation pattern of deep pit retaining structures and the safety of deep pits during a construction process involving timely support and over-excavation. In research on pit deformation in mucky strata, [PERSON] et al. [30] discussed the deformation characteristics of pits in deep mucky strata and systematically analyzed the influence and patterns of factors such as the reinforcement range within the pit, the embedding depth of support piles, and the stiffness of support piles on pit deformation. [PERSON] et al. [31] studied the spatiotemporal evolution pattern of pit retaining structure deformation, ground settlement, and the internal forces of supports in a pit engineering project of Shenzhen Metro Line 11 under marine mucky stratum conditions.