## 4 Calculation Model and Parameter Selection
### Calculation Parameter Values  
The parameters to be determined in the calculation of the large-strain consolidation theory include initial mud cake thickness \(h\), initial void ratio \(e_{0}\), initial effective stress \(\sigma_{0}^{\prime}\), initial permeability coefficient \(k_{0}\), soil compression index \(C_{C}\), and permeability index \(C_{k}\).  
Figure 5: Mud deformation model under pressure filtration: (**a**) initial filtration stage; (**b**) soil skeleton formation stage; (**c**) continuous dewatering stage.  
The initial void ratio can be calculated from Equation (5), where the relative density of particle ds is known and the saturation \(S_{r}\) is 100%, and only the water content \(w\) needs to be obtained.  
\[e=\frac{wd_{s}}{S_{r}} \tag{5}\]  
Since the mud slurry used in the previous test has a high water content (up to 250% after adding flocculant), it can be assumed to be saturated. The relative density of soil particles is 2.70, and the initial void ratio of the mixed mud slurry is calculated to be 6.75. Assuming that after the first stage of dewatering, the mud slurry reaches the state shown in Figure 5b with a water content of 150%, and then the corresponding initial void ratio of the mud cake is 4.05, according to the initial thickness \(h_{01}\) and the initial void ratio \(e_{0}\) of the mixed mud slurry before pressure filtration, the initial thickness \(h_{0}\) of the mud cake when the pressure filtration process reaches the state shown in Figure 5b can be calculated from Equation (6).  
\[h_{0}=h_{01}\cdot\frac{1+e_{0}}{1+e_{01}} \tag{6}\]  
The initial effective stress of the mud cake is low, generally around 0\(\sim\)1 KPa [39], and 1 KPa is taken in this paper. The compression index \(C_{C}\) can be obtained using a one-dimensional consolidation test in a laboratory. In this paper, \(C_{C}\) is set to 1.2 by summarizing the previous research results of the consolidation characteristics of mud slurry after flocculation conditioning and considering the high compressibility of a mud cake. The permeability index \(C_{k}\) can be taken as 0.5\(\sim\)2.0 times of \(C_{C}\)[40], and in this paper, \(C_{k}\) is set as 0.9 times of \(C_{C}\) with reference to the values taken in the related literature [41], i.e., \(C_{k}=0.9C_{C}=1.08\). The initial permeability coefficient \(k\) of the mud cake is calculated by referring to the empirical equations in the relevant literature [42; 43; 44], which is suitable for the clay in Wenzhou, as shown in Equation (7).  
\[\lg(k_{0})=-8.89+4.89\lg_{0}-5.12\lg w_{L} \tag{7}\]  
where \(w_{L}\) is the liquid limit of the mud slurry.  
Notably, the \(k_{0}\) calculated by Equation (7) is 1.82 \(\times\) 10\({}^{-5}\) cm/s for the mud slurry without flocculation conditioning. In order to reflect the improvement of the mud slurry dewatering performance due to flocculation conditioning, the permeability coefficient of the flocculation-conditioned mud cake was enlarged 1000 times for the calculation in this paper with reference to the measured permeability coefficient of a flocculation-conditioned mud cake in the literature [45]. The calculation parameters for different working conditions are shown in Table 3.