## 4 Calculation Model and Parameter Selection
### Validation of the Computational Model  
Up to now, an analytical solution to the consolidation governing equation (Equation (1)) has not be found, and most of the existing methods for solving the one-dimensional large-strain consolidation control equation are simplified by some linear assumptions, and in this paper, \(e-\lg\sigma^{\prime}\) and \(e-\lg k\) are assumed to be linear, and the finite difference \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Calculation Parameters** & **A1** & **A2** & **A3** \\ \hline Initial thickness of mixed mud slurry, \(h_{01}\) (mm) & 102 & 136 & 170 \\ Initial void ratio of mixed mud slurry, \(e_{01}\) & 6.75 & 6.75 & 6.75 \\ Initial mud cake thickness, \(h_{0}\) (mm) & 66.5 & 88.6 & 110.8 \\ Initial void ratio of mud cake, \(e_{0}\) & 4.05 & 4.05 & 4.05 \\ Initial effective stress of mud cake, \(e_{0}^{\prime}\) (KPa) & 1.0 & 1.0 & 1.0 \\ Initial permeability coefficient of mud cake, \(k_{0}\) (cm/s) & 1.82 \(\times\) 10\({}^{-2}\) & 1.82 \(\times\) 10\({}^{-2}\) \\ Compression index, \(C_{c}\) & 1.2 & 1.2 & 1.2 \\ Permeability index, \(C_{k}\) & 1.08 & 1.08 & 1.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculation parameter values for each working condition. computational procedure is adopted for solving the consolidation control equation. After the calculation, the change rule of parameters such as mud cake deformation and excess pore water pressure over time can be obtained. The variation in the average excess pore water pressure inside the mud cake during the pressure filtration process is shown in Figure 6. It can be seen that for conditions A1-A3, the calculated average initial excess pore pressure is around 290 KPa, which is basically consistent with the filtration pressure of 0.3 MPa used in the test. As the pressure filtration process proceeds, the pore water is discharged and the excess pore water pressure decreases, but the figure shows that the excess pore water pressure does not dissipate completely when the dewatering time is 480 s. From the actual situation, there is still pore water flowing out when the filter press is stopped in the test, which shows that there is still excess pore water pressure in the mud cake at this time. The pressure filtration process is usually stopped when the deformation of the mud cake is relatively stable, without considering whether the excess pore water pressure has completely dissipated. At the beginning of the pressure application, the initial excess pore water pressure in the mud cake under each condition is similar, but as the pressure filtration proceeds, the excess pore water pressure under condition A1 dissipates faster, which is attributed to the smaller initial mud cake thickness and shorter drainage path under this condition, resulting in the pore water being discharged more easily. The variation in mud cake deformation over time under different initial cake thicknesses and the comparison between the calculated final cake thicknesses and the measured values of the previous test conditions are shown in Figure 7. Figure 7a shows the variation in the mud cake thickness over time at the second stage of pressure filtration (the process from Figure 5b,c), reflecting the trend of the mud cake thickness decreasing with an increase in the dewatering time. Due to the larger initial mud cake thickness, the trend of thickness reduction over time is basically the same for conditions A2 and A3, while for A1 condition with smaller initial mud cake thickness, the deformation rate of mud cake in the early stage of filter press is faster because of its shorter drainage path. The comparison between the calculated and measured values of the final mud cake thickness is shown in Figure 7b. The theoretical calculated value of the mud cake thickness is slightly larger than the measured value, with a difference of about 2-5 mm, but the overall variation rule is consistent.