# Spatiotemporal Monitoring and Evaluation Method for Sand-Filling of Immersed Tube Tunnel Foundation
## 3 Evaluation Model of Foundation Cushion Filling Effect Based on Elastic Wave Monitoring  
### Monitoring Data Analysis  
Taking monitoring point R6 of sand-filled hole W6 as an example, the collected elastic wave data were analyzed in the time, frequency, and time-frequency domains. The waveforms of the monitoring point R6 of the sand-filled hole W6 changing with time are shown in Figure 5(a). The attenuation of the elastic wave was completed within 0.03 s, and the attenuation characteristics of the elastic wave were not obvious during sand-filling. Analyzing the waveform reveals that the attenuation of the elastic wave can be divided into three stages: 0-0.005 s is the main response time of the elastic wave, 0.005-0.015 s is the elastic wave attenuation time, and, during 0.015-0.03 s, the elastic wave is basically attenuated. Therefore, the feature parameters, \(PP_{1}\), \(PP_{2}\), and \(PP_{3}\) are defined as follows:  
\[ \begin{array}{l}PP_{1}=\frac{\int_{0}^{0.005}|f(t)|dt}{\max\limits_{0:c\in \Omega^{\prime}}f(t)^{2}},\\ PP_{2}=\frac{\int_{0}^{0.005}|f(t)|dt}{\max\limits_{0:c\in\Omega^{\prime}}f(t) ^{2}},\\ PP_{3}=\frac{\int_{0}^{0.005}|f(t)|dt}{\max\limits_{0:c\in\Omega^{\prime}}f(t) ^{2}},\\ \end{array}  \tag{3}\]  
In Figure 5(b), \(PP_{1}\), \(PP_{2}\), and \(PP_{3}\) changing with time are shown. There is a downward trend for \(PP_{1}\) with sand-filling time, but it is dynamic. Both \(PP_{2}\) and \(PP_{3}\) have small changes with sand-filling time. The results of the spectrum analysis of the monitoring point R6 of sand-filling hole W6 during the sand-filling process are shown in Figure 7. The spectrum of the received elastic wave had two predominant peaks. The frequency and amplitude corresponding to the frequency peaks varied with the sand-filling process. Therefore, the spectrum characteristic parameters \(F_{1}\) (primary frequency), \(F_{2}\) (secondary frequency), \(A_{1}\) (primary frequency amplitude), and \(A_{2}\) (secondary frequency amplitude) were extracted as feature parameters reflecting the waveform. As shown in Figure 6(b), \(A_{1}\) reduced significantly with the sand-filling processing. With the formation of the sand deposit, the lower part of the bottom concrete layer changes from water and soil mixture to denser sand deposit. The wave impedance between the two layers (the sand deposit layer and the concrete tunnel layer) decreases, and the energy propagation characteristics change. More energy is  
Figure 6: Elastic wave data in the time domain. transmitted, resulting in a decrease in the reflected elastic wave energy. \(F_{1}\) and \(F_{2}\) are the primary frequency and the secondary frequency, related to the change of the propagation medium of the elastic wave. Since the diffusion of the sand deposit is a dynamic process, \(F_{1}\) and \(F_{2}\) show dynamic characteristic. The waveform time-frequency analysis results of the monitoring point R6 of sand-filling hole W6 are shown in Figure 8. In the time-frequency domain, the parameter \(T\) is defined as the characteristic parameter reflecting the characteristics of the elastic wave in the time-frequency domain. As shown in Figure 8, the response time \(T\) decreases overall with the sand-filling processing, but it is also dynamic. The feature parameters \(PP_{1}\), \(PP_{2}\), \(PP_{3}\), \(F_{1}\), \(F_{2}\), \(A_{1}\), \(A_{2}\) and \(T\) of the elastic wave response waveform were analyzed. With the bottom of the plate filling, the wave impedance at the interface of the bottom plate is correspondingly smaller when it is installed. Therefore, the response waveform amplitude, spectral energy, and reverberation time value of the response waveform measured at the same measuring point after sand-filling are also correspondingly smaller. However, because of the complex construction environment, and because the sand-filling process is affected by many factors, the feature parameters show obvious characteristics of nonlinearity and randomness. Figure 8: Time–frequency analysis results. Figure 7: Results of the spectrum analysis.