# Spatiotemporal Monitoring and Evaluation Method for Sand-Filling of Immersed Tube Tunnel Foundation
## 4 Application of Spatiotemporal Monitoring Model  
### Spatiotemporal Monitoring for Sand-Filling  
To realize the spatiotemporal monitoring of the state of the sand deposit, the sand-filling holes were divided into two types: side and middle holes. A side hole is a hole at the edge of the pipe section, where both ends of the sand deposit are free boundaries. A middle hole is a hole in the middle of the pipe section. The sand deposit of middle holes have one free boundary and the constrained boundary is affected by the adjacent sand deposit. For the side holes, the formation mechanism of the sand deposit is that the sand gradually accumulates along the direction of the diffusion radius. As shown in Figure 12, for the sand-filled hole W8, elastic wave data collection was performed every hour, and the sand-filling state was predicted by the trained neural network model. With the progress of sand-filling, along the direction of the diffusion radius, the state of each monitoring point gradually changed from the unfilled state to the filled state, and the sand deposit gradually formed. At the 13 th hour, the diffusion radius reached design diffusion radius R\({}_{\text{d}}\). For the middle holes, monitoring lines were arranged on both the constrained boundary and the free boundary. The diffusion mechanism on both boundaries of the sand-filling hole takes different forms. As shown in Figure 13a, for the free boundary, it can be found that the state of the monitoring points within the diffusion radius gradually changes from state 1 (unfilled) to state 2 (filled) with the progress of sand-filling, indicating the expansion of the sand deposit. The speed of sand deposit formation is low at first, and then it is gradually accelerated. Finally, the diffusion radius reached R\({}_{\text{d}}\) at the 11 th hour. However, for the constrained boundary, the speed of sand deposit formation is much higher than that  
Figure 11: Test results of BP neural network. Figure 12: Spatiotemporal monitoring results of sand-filling hole W8. at the free boundary. The formation mechanism at the constrained boundary is obviously different from that at the free boundary. The state of several monitoring points outside the diffusion radius is in the state 2 because of the sand spreading during the previous sand-filling process at adjacent holes. Therefore, for different categories of boundaries at the sand-filling hole, the formation mechanism of sand deposits could exhibit different forms. At the free boundary, the formation of sand deposits is accompanied by the diffusion and accumulation of filling sand, like the sand-filling hole W8 in Figure 12. At the constrained boundary, under the influence of adjacent sand-filling holes, there are partially filled sand deposits or unfilled sand within the diffusion radius. The sand-filling process at the constrained boundary requires less filling time and exhibits the docking form of the sand deposit formation. According to the obtained spatiotemporal model of sand-filling hole W6, the change in the sand-deposit diffusion radius of sand-filling hole W6 over time can be evaluated. For each sand-filling time, the distance between the sand-filling hole and the monitoring point, which is in state 2 and closest to the sand-filling hole, is considered as the diffusion radius at that moment. As the sand-filling progresses, the relationship between the diffusion radius and sand-filling time can be obtained. When the diffusion radius reaches the design value R\({}_{\text{d}}\), the sand-filling process can be stopped. The diffusion radius with the time of sand-filling hole W6 is shown in Figure 14. At the free end, the sand deposit required a long sand-filling time, and it was gradually filled at the 11 th hour. At the constrained end, the sand deposit was well connected to the adjacent sand deposit at the 8 th hour, and the connection was stable. Since the adjacent sand deposits have been formed, the amount of sand required on the constrained end is less than that of the free end.