## 1 Introduction  
The curtain is an impermeable structure used for dam foundation containment in hydraulic engineering. Calcium hydroxide (CH) and calcium silicate hydrate (C-S-H) are the main components of the solid-phase calcium in the curtain. CH partly determines the decay process of the curtain's impermeability. At the same time, C-S-H affects the physical and mechanical properties of the curtain. The precipitation of the solid-phase calcium in cement-based materials occurs in weakly alkaline or basic solutions. During operation, the cyclic action of ambient water causes the solid-phase calcium in the curtain to decompose and precipitate out, increasing the permeability of the curtain and affecting the operation of the hydraulic project [1]. For example, after nearly twenty years of operation, the Daheiding dam had a significant calcium precipitation problem, deteriorating year by year. The impervious curtain was found to be seriously damaged by sampling the curtain bore-hole and underwater television observation [2]. The permeability coefficient of cement-based materials is generally defined as a function of porosity, influenced by pore structure, degree of dissolution, and physical damage [3]. [PERSON] [4] proposed an exponential equation between permeability and porosity for simulating the permeability coefficient of cement-based materials during leaching. This equation works effectively in accelerated mortar electrochemical tests and has been adopted by [PERSON] [5, 6]. Based on this, [PERSON] and [PERSON] further considered the evolution of microstructural parameters by introducing pore shape, specific surface area, and degree of distortion. This evolution provides a more accurate characterization of the hydraulic properties and has been extensively used in species of cement-based materials [7; 8; 9; 10]. Significantly, the permeability coefficient of cement-based materials is similarly influenced by the process and rate of solid-phase calcium decomposition. For diffusion-driven leaching, [PERSON] et al. [11], [PERSON] et al. [12], and [PERSON] et al. [13; 14] have proposed different solid-liquid phase equilibrium equations based on thermodynamic equilibrium relations. Regarding advection-diffusion-driven leaching, [PERSON] [15] adopted the discrete element method to simulate the dissolution process at the rock-mortar contact, which provided a new strategy for solving the calcium leaching problem. [PERSON] et al. [16] considered the calcium leaching effect and presented the calcium hydroxide content and initial infiltration flow rate as the durability control index of the impervious curtain. A great deal of research has been conducted on the calcium leaching effect. However, one primary problem with calcium leaching is that those calculation parameters are not efficiently and accurately determined. This problem is accentuated by the little research on calcium leaching parameters during the construction period. An alternative approach to the problem is inversion analysis. The inversion method has been proven to be an efficient way for obtaining rational seepage parameters [17; 18; 19; 20; 21; 22; 23; 24]. Nevertheless, little research has been carried out specifically for the permeability coefficient of the impervious curtain. Furthermore, the existing studies simply considered the role of the seepage field without applying the coupling model of the chemical and seepage fields [25; 26], which is unable to determine the parameters accurately for the calcium leaching problem. The essence of inversion analysis is to determine the calculation parameters based on observations. The inversion analysis exists relative to the forward computation. An artificial neural network is required to construct the data mapping in the forward research, while an optimization algorithm is selected to minimize the objective function in the back process. The optimal parameters are found by iterative computation while minimizing the defined objective function.