## 3 Numerical Example
### Example 3  
The Yinchaojiliao Project is currently the largest water-conservancy project in Inner Mongolia, China. As an important part of the project, the Wendegen water control project is an ultra-long asphalt-concrete core dam under construction in the cold region. The maximum dam height is 48 m, and the total length of the dam is 1358 m. Due to the large scale of the project and the limited time available for construction, the dam was constructed in sections. However, large day and night temperature differences or long overwintering low-temperature conditions can easily lead to unhealable cracks between the core wall sections or the construction layers. In order to guarantee the quality of the asphalt-concrete core wall from the temperature control point of view, it is necessary to firstly simulate the temperature field for the whole construction process of the asphalt-concrete core wall and then use this as a basis for calculating the temperature stress in each part. The project was designed and built a large scale on-site solid model to facilitate the study of the laws governing the construction quality of core wall. The model was selected from an actual 80 m long dam with the height of the dam as the scaled dimension, and the scale of the model was 1:10. As shown in Figures 10 and 11, the length of the model is 19.6 m, the width is 16.8 m, and the height is 4.8 m. The slope ratio of upstream and downstream is 1:1.5, and that on the left and right banks is 1:1. The core wall in the model has a length of 8.0 m, a width of 0.6 m, and a height of 4.8 m. The core wall and rockfill material are constructed with 0.3 m as a layer, with a total of 16 layers. The FEM model, which is shown in Figure 12, is established based on the on-site solid model. The FEM model includes the initial coarse mesh and the refined computational mesh based on the coarse mesh. The coarse mesh provides the basic information of the FEM model, but it does not have the ability to simulate the whole process dynamically. Compared with the coarse mesh, the refined mesh can simulate the construction process and has higher accuracy, but its computational cost is large. It is assumed that the initial temperatures of each layer of asphalt concrete and rockfill material are \(T_{a0}=150\)\({}^{\circ}\)C and \(T_{r0}=20\)\({}^{\circ}\)C, respectively, and the temperature of the air outside is \(T_{a}=20\)\({}^{\circ}\)C. The thermal parameters of asphalt concrete are the same as in Example 2. The parameters of the rockfill material are as follows: the heat-conduction coefficient of the rockfill material \(k=1.45\) W/(m \(\cdot\)\({}^{\circ}\) C), the density of the rockfill material \(\rho=2010\) kg/m\({}^{3}\), the specific heat \(c_{\rho}=900\) J/(kg \(\cdot\)\({}^{\circ}\) C), and the surface heat-transfer coefficient between the asphalt concrete and the air outside \(h=9.70\) W/\(\left(\text{m}^{2}\cdot{}^{\circ}\text{C}\right)\). The boundary conditions of Example 3 are as follows: the bottom surface is the adiabatic boundary, and the other outer surfaces are the heat dissipation  
Figure 9: The change of the number of DOFs and computational time in Example 2.  
temperature field of asphalt-concrete core wall construction. Since the FEM calculation results are basically the same as the ADOF-FEM calculation results, only the ADOF-FEM results are included in Figure 13 as a demonstration. At the same time, four typical point positions, which are shown in Figure 11, are selected to compare the results with and without adaptive DOFs. Points A, B, and C are located in the center of the core wall, respectively, at the bottom of the 1 st layer, the middle of the 8 th layer, and the top of the 16 th layer. Point D is located at the contact position between the core wall and the rockfill material at the same elevation as Point B.