## 1 Introduction  
Foundation pits are significant structures utilized in large-scale underground space construction [1; 2; 3]. As urban development progresses, the continuous expansion of excavation area and depth could pose environmental impacts. In particular, excavations in multi-aquifier-aquifract strata, abundant in groundwater, present considerable risks [4]. Groundwater control is thus imperative to prevent water inrush accidents and ensure the safety of underground construction [5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. However, inappropriate dewatering can lead to undesirable consequences such as soil deformation, differential settlement, and sand flow or piping [15; 16; 17; 18]. To mitigate these adverse effects, waterproof curtains such as diaphragm walls, bored piles, and mixing piles are established before excavation [19; 20]. By preventing water seepage and extending the seepage path, these curtains help minimize groundwater extraction and ground settlement. Depending on the relative position of the excavation depth of the foundation pit and the confined aquifer, foundation pits can be classified into three categories. In the case of shallow foundation pit excavation, diaphragm wallsdo not intrude into the aquifer. This method, however, is unsuitable for further urban underground space development. Diaphragm walls are employed to completely sever the aquifer. While effective when dealing with thin and shallow aquifers, this method becomes cost-prohibitive and technically challenging when the pit intersects deep aquifers. The third method uses an unclosed waterproof curtain (Figure 1). This technique is applied when a deep excavation pit is situated over a deep aquifer, offering economic, technical, safety, and environmental advantages. The unclosed waterproof curtain method has been extensively used in foundation pit dewatering, evident in various projects such as the Shanghai Metro station [21], Shanghai Metro Line 4 [22; 23], Shanghai Metro Line 9 [24], Hangzhou Metro Line 1 [25], and Hangzhou Yangtze River Crossing Tunnel, among others [26; 27; 28; 29; 30; 31]. Numerous simulations have been performed to study the effect of unclosed waterproof curtains on dewatering [32; 33]. The seepage mechanism associated with an unclosed waterproof curtain is more complex than that of a closed waterproof curtain. Combining partially penetrating wells with curtains results in a complex 3D seepage field, where coupled non-Darcy flow phenomena significantly contribute to seepage energy dissipation [34; 35]. The anisotropy of aquifer permeability also enhances the effectiveness of dewatering methods [31]. The evolution of experimental methods has enabled a more in-depth examination of the coupled wall-well effect, facilitating a more comprehensive understanding of its attributes. Due to the hydraulic connection between the groundwater inside and outside of the unclosed waterproof curtain, a rapid drop in the water level inside the pit leads to the outside groundwater bypassing the curtain bottom. This water then enters the foundation pit directly due to pressure differences on both sides of the curtain. Moreover, the flow mode of the unclosed waterproof curtain can be analyzed in three dimensions due to the anisotropy of the curtain geometry and soil characteristics. [PERSON] (1995) [34] conducted a field case study for Metro station dewatering engineering, where he examined the characteristics of groundwater seepage along diaphragm walls and proposed a mathematical model for 3D seepage flow in a viscoelastic leaky aquifer. More recent studies have explored the 3D seepage flow mechanism using numerical modeling [36; 37; 38; 39; 40; 41; 42]. For instance, a finite element numerical model was utilized to assess and quantify the impact of significant dewatering on fault-controlled regional groundwater flow in the Acque Albule basin [43].