## 1 Introduction  
With the fast urbanization in many countries, a large number of underground infrastructures are constructed in central areas of cities [1, 2, 3, 4, 5]. During the construction of these underground infrastructures, foundation excavation is a complex process and requires special attention. Engineers should not only pay attention to the safety of adjacent buildings during excavation, but also need to appropriately pump out groundwater [6, 7, 8, 9]. In recent years, as the excavation becomes deeper, the number of accidents related to foundation pit excavation is rising rapidly [10, 11, 12]. Particularly, it is reported that accidents caused by groundwater account for around 60% of total accidents [13, 14, 15, 16]. Excavation usually adopts the dewatering scheme which pumps groundwater inside the foundation pit to work in dry conditions [17, 18, 19, 20]. This process can improve the safety of the foundation pit and increase stability of the soil around it, preventing flowing stand, piping effect and other related accident from happening. Foundation pit dewatering relies on the system of pumping wells and the waterproof curtain, and pumping wells can further be divided into two types: wells in the confined aquifer and wells in the phreatic aquifer [21; 22]. In the past decades, most of research focus on wells in the confined aquifer, and mathematical models of a well in a confined aquifer were established based on the assumptions [23; 24]. Wells in the confined aquifer lower the piezometric head of the confined aquifer to prevent water-inrush damage in the foundation pit [25; 26; 27]. On the other hand, wells in the phreatic aquifer need to consider more conditions when establishing mathematical models, which has always been a difficult problem [28; 29]. Some scholars equate the mathematical model of a well in the confined aquifer to the model of a well in the phreatic aquifer [30; 31]. However, the dewatering scheme is generally composed of several wells, forming a huge drawdown curve centered on the foundation pit, and the whole dewatering system is even more complex [32]. The dewatering scheme requires one to pump a large amount of groundwater to maintain the groundwater drawdown below the bottom of the pit with waterproof curtain [33]. At present, model tests about pumping groundwater are used to carry out the process of dewatering and investigate the mechanism of waterproof curtain, but these tests take more factors into consideration, which is likely to cause inaccurate results and this makes it difficult to acquire quantitative conclusions [34; 35; 36]. The finite-element method (FEM) has been used to simulate the dewatering process in foundation pits with waterproof curtains, which is convenient to directly simulate different dewatering conditions and to calculate groundwater drawdown [7; 37; 38]. However, this method cannot be directly applied for engineering design and construction. To save groundwater resources and protect adjacent buildings, it is essential to reasonably pump groundwater without affecting the surrounding environment [39; 40; 41; 42]. Therefore, the prediction of the groundwater level around the pit during dewatering is an urgent problem to solve. Particularly, in soils with thick phreatic aquifers, the groundwater is constantly recharged into the foundation pit, so the foundation pit needs to pump more than the expected amount of groundwater to maintain the groundwater level below the bottom of the pit. Most of the scholars focus on numerical analysis and model tests, but few of them investigate the mechanism of foundation pit dewatering from the analytical solution. In this study, an analytical solution to unsteady flow around a foundation pit located in a thick phreatic aquifer with the suspended waterproof curtain was derived by using Boltzmann transformation, and the formula of groundwater drawdown difference between the inside and outside of the pit was obtained.