# Dynamic Stability Finite Difference Time Domain Analysis of Landfill Based on Hypergravity Test
## 3 Establishment of Computational Model  
### Model  
The analysis is based on the centrifugal model shaking table tests conducted by the Geotechnical Institute of Zhejiang University. The test was completed on the ZJU-400 centrifuge shaking table at Zhejiang University. The size of the model box is 770 mm \(\times\) 400 mm \(\times\) 530 mm (length \(\times\) width \(\times\) height). In order to study the dynamic response of landfill slopes under different water levels, the test was conducted under a gravity acceleration of 50 g. The acceleration, pore pressure, and slope displacement response of the landfill under different water levels and seismic intensities were obtained [11]. The layout of the test model and sensors can be seen in Figure 2a. Among them, P1-P8 are pore pressure gauges and A1-A8 are accelerometers.  
Figure 1: Flow chart of landfill dynamic calculation method.  
Figure 2: _Cont._The height of the test model heap is 160 mm, the bottom width is 610 mm, and artificial MSW is used [11; 31; 32]. It is composed of peat: kaolin: quartz sand in a ratio of 1:0.2:0.8. The initial dry density is 633 kg/m\({}^{3}\), the initial void ratio is 1.6, and the initial moisture content is 45%. Its physical and mechanical properties are similar to real MSW. The bedrock is made of clay, quartz sand, cement, and water, and the cement content is 37.5%. A HDPE geotextile with a thickness of 0.1 mm is arranged on the top surface of the bedrock, with a single-width tensile stiffness of 7.74 kN/m and a strength of 0.96 kN/m.  
The overall process of the experiment is as follows: Set the centrifuge to 50 g. After the displacement value of the slope stabilizes, start applying the water level. After the water level stabilizes to the predetermined height, apply the Taft wave. Input in four levels in ascending order of acceleration amplitude, monitor the response and stability of the slope, and apply the next level of earthquake after the pore pressure and settlement stabilize after each shaking. Then, apply the next level of water level in the same way, wait for the water level to stabilize, and sequentially apply the earthquake to observe the response and stability of the landfill.  
In accordance with the specified test model, a computational model is delineated in Figure 2b. This model incorporates the bedrock, which is specified as follows: a length of 730 mm, a width of 400 mm, and a height (measured from the base of the bedrock to the lower boundary of the landfill) of 170 mm. The maximum height of the solid waste landfill is 160 mm. The lateral slopes of the landfill are designed with a ratio of 1:2, featuring a top width (along the length direction) of 50 mm. Furthermore, the ratio of the landfill slope, the ratio of the demarcating slope between the solid waste landfill and the bedrock, is established at 1:1, with a height of 20 mm.  
In the analysis of the solution to the dynamic problem, the accuracy of the background grid needs to meet [33]  
\[\Delta l\leq(\frac{1}{10}\sim\frac{1}{8})\lambda \tag{7}\]  
where \(\Delta l\) is the maximum size of the grid along the direction of wave propagation, and \(\lambda\) is the wavelength corresponding to the maximum frequency. Correspondingly, the model is discretized using hexahedral or tetrahedral grid elements, and the background grid plane diagram is shown in Figure 3.  
Figure 3: Landfill calculation model background grid (xoz plane).  
Figure 2: Landfill centrifuge test model and computational model: (a) centrifuge test model, and (b) computational model.