## 3 Introduction of One-Dimensional Large Strain Consolidation Theory  
The conventional one-dimensional consolidation theory considers the permeability coefficient \(k\) and the compression coefficient a of the soil body as invariant constants in infiltration consolidation and assumes that only minor deformation occurs in the soil, which is obviously not applicable to calculating the compression and filtration deformation of the mud slurry after flocculation conditioning in this paper.  
The basic assumption of soft dredged soil's self-weight consolidation is basically the same as that in [PERSON]'s large deformation consolidation theory [36], and its basic assumptions are as follows:  
* The soil is homogeneous and completely saturated, the soil particles and pore water are incompressible, and the self-weight of the soil is considered;
* The seepage in the soil obeys [PERSON]'s law;
* Only the vertical deformation of water and soil particles is considered;
* The external load is applied instantaneously and held constant
* The thickness of the soil layer changes with the consolidation process
* The permeability coefficient and compressibility coefficient change nonlinearly  
According to the above assumptions, the governing equation is derived as shown in Equation (1) [37].  
\[\pm(\frac{\gamma_{s}}{\gamma_{w}}-1)\frac{d}{de}[\frac{k}{1+e^{t}}]\frac{ \partial e}{\partial z}+\frac{\partial}{\partial z}[\frac{k}{\gamma_{w}(1+e) }\cdot\frac{d\sigma^{\prime}}{de}\cdot\frac{\partial e}{\partial z}]+\frac{ \partial e}{\partial t}=0 \tag{1}\]  
where \(\gamma_{s}\) and \(\gamma_{w}\) are the specific gravity of soil particles and water, respectively, \(k\) is the permeability coefficient of the soil, \(e\) is the void ratio, \(z\) is the reduced coordinate, \(t\) is the consolidation time, and \(\sigma^{\prime}\) is the effective stress in the soil, respectively. However, it is still difficult to obtain the analytical solution to Equation (1). In this paper, the finite difference program is used for numerical calculation to obtain an approximate solution.  
The change in the void ratio and permeability coefficient during compression should be taken into account in the calculation of the mud cake deformation during the pressure filtration process. Referring to [PERSON] et al. [38], the nonlinear consolidation equation for the soil is established by using linear-relationship \(e-\lg\sigma^{\prime}\) and \(e-\lg k\) formulas. In this paper, the change in the void ratio and permeability coefficient in the consolidation process is also considered by this relationship. The functional relationship is shown in Equations (2) and (3).  
\[e=e_{0}-C_{C}\lg\frac{\sigma^{\prime}}{\sigma^{\prime}_{0}} \tag{2}\]  
\[e=e_{0}-C_{k}\lg\frac{k_{0}}{k} \tag{3}\]  
where \(e_{0}\), \(\sigma^{\prime}_{0}\), and \(k_{0}\) are the initial void ratio, initial effective stress, and initial permeability coefficient of the soil, respectively; \(e\), \(\sigma^{\prime}\), and \(k\) represent the void ratio, effective stress, and permeability coefficient of the soil at a certain moment; \(C_{C}\) is the compression index of the soil (slope of the \(e-\lg\sigma^{\prime}\) curve); and \(C_{k}\) is the permeability index (the slope of the \(e-\lg k\) curve).  
Equations (1) and (2) both involve effective stress \(\sigma^{\prime}\). If the continuous pressure applied to the mixed mud slurry is \(p\), the effective stress at a certain moment can be obtained from Equation (4).  
\[\sigma^{\prime}=\sigma^{\prime}_{0}+p-u \tag{4}\]where \(u\) is the excess pore water pressure at the corresponding time.