## 1 Introduction  
Food security directly determines the stability of the country and society at large. In the grain storage process, the distribution of temperature and humidity in the grain pile changes because of environmental changes, grain respiration, and the presence of microorganisms [1]. Large differences in the grain storage pressure at different depths of a grain pile lead to an uneven distribution of porosity in the grain pile. Further, the change in grain contact area affects heat transfer. Heat accumulation in grain pile results in high local temperature that can cause grain fever, mildew, and the infestation of pests. If not handled in time, it will hamper the quality of large grain piles [2, 3]. Therefore, it is very important to study the effect of vertical pressure on the temperature distribution in grain piles for their safe storage. At present, field measurement and numerical simulation are the main research methods for investigating the pressure field and temperature field distributions of grain piles. To access the pressure field distribution, [PERSON] [4] proposed a formula for the calculation of the vertical and horizontal pressures of barrel storage materials through experimentation. This formula has been obtained under the assumption that the vertical pressure at any given depth is uniformly distributed along the horizontal plane and that the external friction coefficient along the vertical direction is constant Therefore, the spatial pressure inside the grain pile cannot be calculated. Considering the uneven vertical pressure along the same horizontal plane inside the grain pile, [PERSON] et al. [5,6] simulated and measured the spatial pressure field of a bulk grain pile in silos. They obtained the influencing mechanism of the grain pile pressure at the bottom of the storage structure along the radial direction. The researchers also proposed the relationship between the depth of the grain pile and its porosity [7, 8, 9, 10]. The porosity of a grain pile varies significantly with the pressure and depth of the grain pile. The influence of the change of physical parameters caused by the height of the grain pile on heat transfer should be considered when analyzing the grain storage safety in large storage structures [11, 12, 13]. There are many studies on the distribution of the temperature field in grain piles. [PERSON] [14] established a mathematical model that considers the effect of solar radiation on the heat transfer during grain storage. However, the air temperature between the grain piles and the grain temperature were considered separately, and the changes in latent heat and the momentum in the process of air flow were ignored. The energy balance equation was simplified to an enthalpy equilibrium equation that considered only one-dimensional cases and was, therefore, not applicable to complex conditions. Some authors [15, 16, 17, 18, 19, 20] studied the variation of temperature and moisture content of stored wheat and paddy with change in external environment through theoretical analysis and numerical simulation. However, the adsorption and desorption characteristics of grain were ignored, and the influence of the change in moisture content of the grain pile on the temperature field distribution was not considered. Considering the effect of grain respiration, [PERSON] et al. [21] and [PERSON] et al. [22] established a two-dimensional finite element model and a three-dimensional transient heat, mass, and momentum coupling model, respectively, to predict the temperature transfer of grain piles stored in cylindrical plastic bag warehouses with changes in the external environment. The predicted results of the model were in good agreement with the measured data. [PERSON] et al. [23,24] conducted the long-term monitoring of the temperature and moisture distribution of a bulk wheat grain pile and analyzed the its moisture and heat transfer characteristics in different seasons.