## 1 Introduction  
A tailings dam is a large-scale, man-made structure that is constructed worldwide to keep waste tailings away from ongoing mining activities where tailing are mixtures of crushed rocks [1]. Waste tailings pose a potential hazard to communities and ecosystems near mining areas [2]. The upstream construction method is the main method for raising tailings dams [3]. Currently, in China, there are 14,000 tailings dams (in operation, inactive, and abandoned), and more than 90% of these dams are constructed using the upstream method [4]. In the raising method, dikes are sequentially constructed on the previously deposited tailings, which may be present in a saturated and loose state. The saturated tailings uplift the phreatic surface, which is usually called the \"lifeline\" of the tailings dam, and cause an increase in the pore water stresses in the saturated zone [5]. Therefore, the effective stresses are reduced, which could lead to slope instability. Over the past few decades, tailings dams that have undergone failure have caused serious disasters and have drawn public attention regarding the safety of tailings construction and management [6; 7]. Various factors usually contribute to the failure of a tailings dam, such as extreme events, foundation failure, overtopping, poor operational and management practices, or a combination of these factors [8; 9; 10; 11]. Seepage and a rise in the phreatic surface are related to 30%-40% of the failures of tailings ponds [12]. Currently, tighter legislation and regulations on tailings disposal have forced the mining industry to address the disposal of a vast quantity of highly visible waste originating from mining activities [13; 14]. Because suitable land for tailings dams is increasingly rare and expensive in a developing economy, to reduce costs, the mining industry prefers to expand and increase the height of tailings ponds instead of constructing a new tailings dam [15]. Increasing the height of a tailings dam to extend its tailings storage capacity is very common in China's mines [16]. However, this change could lead to an increase in the phreatic surface, causing the original drainage system to no longer meet the requirements of seepage and consolidation after increasing the dam height, thus decreasing the stability of the tailings dams [17; 18]. Hence, a comprehensive analysis of the new drainage system is essential before the structure is applied to increase the height of an existing tailings dam [19]. The drainage facilities of a tailings dam are complex, and the accurate simulation of the drainage behavior is a technical problem in seepage calculations. The research on the seepage capacity of a drainage pipe is mainly divided into theoretical research and numerical simulations. For theoretical research, by analyzing the structure and permeability of the drainage pipe, [PERSON] et al. [20] affirmed the seepage capacity of the embedded drainage pipe. [PERSON] et al. [21] proposed a formulation for calculating the total seepage discharge and obtained the equivalent radius of the filter layer by establishing a theoretical calculation model of the drainage pipe system. For numerical simulations, finite element analysis of a draining pipe remains a challenge [22; 23]. The major cause of this problem can be attributed to two factors. The first factor is the difficulty of generating the finite element mesh with hundreds or even thousands of drainage pipes with small diameters and dense spacing, and the second factor is the strong nonlinearity in the calculation of the phreatic surface. To avoid these difficulties, an equivalent medium producing the same flow rate was proposed to model the drainage pipe. At the same time, many new techniques were developed for simulating the seepage behavior of the drainage system, such as a substructure technique, a point well model, a semianalytical approach, or composite element methods [24; 25; 26].