## 1 Introduction  
The moisture migration and drying shrinkage cracking of concrete have always been one of the main concerns in the engineering field [1, 2]. The internal humidity gradient and uneven distribution of concrete are the main reasons for dry shrinkage deformation and surface cracking [3], which have a great impact on the durability of concrete [4, 5]. At the same time, moisture is the main medium for concrete deterioration, and a variety of deterioration mechanisms of concrete materials are closely related to its permeability and moisture migration process. Studies show that almost all corrosive media (chloride,sulfate, etc.) enter the concrete mainly through moisture migration [6; 7; 8], so water and water migration are the core of concrete durability problems. Previous studies have shown that concrete is a typical non-uniform multi-phase material, which is composed of cement mortar, aggregate, and the interfacial transition zone (ITZ) between them [9]. Each phase material has obvious pore characteristics and is a typical porous medium, and moisture migration is inseparable from its internal micro-structure [10]. Moisture migration also has significant non-uniformity, multi-scale characteristics, and variability during drying and wetting processes [11]. At present, it is difficult to reveal the relation between the microstructure and humidity migration characteristics of concrete by means of experimental testing. Therefore, it is necessary to establish a theoretical model and numerical method of multi-scale moisture migration based on the microstructure of concrete, and to study the moisture migration of concrete from a multi-scale and multi-component perspective (mortar, ITZ, and aggregate). In recent years, due to the shrinkage and expansion induced by the moisture transfer in concrete, scholars have done a lot of research on the problem of moisture migration of concrete from theoretical, experimental, and numerical aspects, which indicates that the moisture diffusion coefficient of concrete is greatly influenced by the porosity and pore size distribution and the effect mechanism is complicated [12; 13; 14; 15; 16]. Studies have shown that the migration of water in concrete pores at the micro scale is closely related to the average pore size and the average free path of water molecules. There are two forms of free diffusion (molecular diffusion) and Knudsen diffusion [17], and, affected by the tortuosity and connectivity of the pore structure, the migration path of humidity is curved and blocked [18]. Macroscopically, it is mainly manifested that the water-cement ratio has a great influence on the moisture diffusion coefficient [19]. At the meso scale, the moisture migration inside the concrete is also affected by the difference in the moisture diffusion coefficients of mortar, aggregate, and ITZ [11]; the \"fortuous\" and \"dilution\" effects of aggregates [20] and the loose pore structure of ITZ [9] change the local moisture migration path, resulting in the non-uniformity of moisture migration in concrete. At the same time, the drying and wetting processes of concrete are also quite different [21]. Some scholars suggest adopting two kinds of moisture diffusion coefficients to simulate the moisture migration process in drying and wetting problems, respectively [22; 23]. In addition, due to the capillary water absorption of concrete pores at high humidity, a variety of existing concrete moisture diffusion coefficient models [24] (exponential, hyperbolic, \"S\", etc.) show that the moisture diffusion coefficient increases with the increase in the relative humidity inside the concrete [25], which makes the moisture migration in the concrete more complicated. It can be seen that the moisture migration of concrete is affected by many factors, such as gel structure, ITZ, pore structure, aggregate, and other microscopic properties, as well as its internal relative humidity.