# Analysis of the Dynamic Stability of Tailing Dams:
## 3 Analysis of the Test Results
### Model of Pore Pressure Growth for Typical Tailing Silt  
For the cumulative pore pressure growth model of saturated soil, several scholars have performed extensive research and suggested corresponding dynamic pore pressure rise models. Among these, the inverse sine function model suggested by [PERSON] et al. [23] is one of the more typical models. However, [PERSON]'s proposed development model is only applicable to the cumulative pore pressure growth model in a single development stage, and the description of the cumulative pore pressure growth in the multiple stages of tailing silt is not ideal. In addition, [PERSON] and others have generally used the vibration ratio as an independent variable to study the cumulative pore pressure development law, which cannot better reflect the difference in pore pressure curves. Therefore, this paper used the vibration number N as an independent variable to summarize the development law of pore pressure and found that its growth trend is consistent with the h\({}_{1}\)-A\({}_{2}\) segment in the BiDoseResp function (as shown in Figure 7 and Formula (3)).  
\[y=\frac{\mu}{\sigma_{0}^{\prime}}=A_{1}+\left(A_{2}-A_{1}\right)\times\left[ \frac{c}{1+10^{(v_{1}-x)h_{1}}}+\frac{1-c}{1+10^{(v_{2}-x)h_{2}}}\right] \tag{3}\]  
In Formula (3), \(A_{1}\), \(A_{2}\), \(c\), \(v_{1}\), \(v_{2}\), \(h_{1}\), and \(h_{2}\) are the model parameters, where \(A_{1}\) represents the initial value of the function development, \(A_{2}\) represents the final value of the function, \(h_{1}\) represents the slope of the rapid growth stage of pore pressure, \(h_{2}\) represents the slope of the instantaneous failure stage, and \(c\), \(v_{1}\), and \(v_{2}\) represent other parameters of the fitting function. To fit the pore pressure ratio-vibration number curves of saturated silty soil at different densities, the BiDoseResp function was used. Owing to space limitation, Figure 8 only shows the pore pressure ratio-vibration number curves at \(\rho=1.62\) g/cm\({}^{3}\) and \(\sigma_{o}^{\prime}=250\) kPa, \(\rho=1.67\) g/cm\({}^{3}\) and \(\sigma_{o}^{\prime}=150\) kPa, and \(\rho=1.70\) g/cm\({}^{3}\) and \(\sigma_{o}^{\prime}=100\) kPa. The specific fitting parameters under other test conditions are shown in Table 2. The fluctuation ranges of the test parameters \(v_{1}\) and \(v_{2}\) in each group were large, the other parameters' fluctuation range was quite limited, and R\({}^{2}\) surpassed 0.990. The fitting effect achieved was good. As a result, the model may be deemed applicable to the cumulative pore pressure development of tailing silt at different densities. In addition, as shown in Table 2, at \(\rho=1.67\) g/cm\({}^{3}\) and \(\rho=1.70\) g/cm\({}^{3}\), the parameter \(h_{1}\) was greater than that at \(\rho=1.62\) g/cm\({}^{3}\), indicating that the pore pressure development rate increases with an increase in sample density when the cyclic load begins to be applicable; this is because the particle connection is relatively stronger and the pore is small at high density. When cyclic load is applied, the volume of pore pressure dissipation is limited, causing the pore pressure to rise fast at first.  
Figure 7: Characteristics of the BiDoseResp function.