Study on the Factors Affecting the Performance of a Pressure Filtration–Flocculation–Solidification Combined Method for Mud Slurry Treatment

Abstract

A pressure filtration–flocculation–solidification combined treatment possesses great potential for the reutilization of the waste mud slurry generated from diverse construction projects as filling material due to its versatility and high efficiency. However, very limited existing studies have focused on the factors affecting pressure filtration’s efficiency. In this paper, a calculation model for compression filtration is established based on laboratory pressure filtration model tests and one-dimensional large-strain consolidation theory. The influence of various parameters on pressure filtration’s efficiency is analyzed, and favorable values for these parameters are recommended. The results show that an increased initial mud cake thickness significantly increases the dewatering time and reduces the treatment’s efficiency. A lower dewatering time and higher efficiency can be achieved by increasing the filtration pressure, but the efficiency improvements become limited after reaching the critical pressure threshold. For the mud slurry used in this study, the optimal values for the initial mud slurry bag thickness, filtration pressure, and dewatering time are 240 mm, 1.0 MPa, and 30 min, respectively, yielding a final mud cake water content of 58.7% after filtration.

1. Introduction

As an important auxiliary material in engineering construction, mud slurry is widely used in a large number of underground engineering construction projects such as cast-in-place piles, underground diaphragm walls, and trenchless construction [1,2] due to its important functions of lubrication and cooling, hole cleaning and slag discharge, mud slurry wall protection, etc. However, the mud slurry will be mixed with a large amount of drilling cuttings and other debris produced in the construction process [3], resulting in a change in its properties after a few cycles of recycling, rendering it unusable and thus inevitably generating huge quantities of waste engineering mud slurry, which are huge in volume, complex in composition, and extremely high in water content [4], and, as a typical construction waste product, pose a great threat to the environment if not handled properly [5,6,7].

Due to an improvement in environmental awareness and limited natural sand resources, it is objectively required that backfill materials should make use of solid waste as much as possible to turn waste into wealth [8]. If huge quantities of waste mud slurry can be processed to obtain good mechanical properties for use as backfill material, the resource utilization of solid waste can be achieved. Currently, the treatment methods of waste-engineering mud slurry mainly include transport discharge, chemical curing, mechanical dewatering, etc. [9,10,11,12], for which the transport discharge landfill treatment takes up a large area of land, but the mechanical properties of the treated mud slurry are not obvious improved [13]. The chemical solidification method has a good effect on sludge treatment [14,15,16], but the effectiveness of solidification treatment on waste mud slurry with a high water content is greatly reduced [17,18]. As for the mechanical dewatering method, flocculants and other additives are often added to the mud slurry to improve the dewatering efficiency [19,20,21,22,23], resulting in a high pH value and poor engineering mechanical properties of the dewatered mud cake, which cannot be directly utilized as a resource, and most of it can only end up in landfill [24]. In the context of extremely scarce land resources, the stacking treatment of waste mud slurry after being transported and discharged is greatly limited [25], and due to the high water content of the actual mud slurry, direct chemical solidification treatment is not effective. To overcome these shortcomings, scholars have promoted the development of efficient mud treatment technology from being unitary to composite, and have successively put forward diversified treatment methods such as a flocculation–solidification combined method [26,27,28,29], vacuum preloading combined with the flocculant method [30,31], and a pressure filtration method modified with flocculants [32] for the treatment of mud slurry. Combining the advantages of the above-mentioned methods, we also proposed the vacuum preloading–flocculation–solidification combined method (VP-FSCM) in our previous study for the treatment of mud slurry with a high water content [33]. This method improves the dewatering performance of mud slurry within minutes through the addition of flocculants, then filters out the water from the mud slurry by applying pressure during the window period before the curing agent fully reacts, and finally allows the curing agent to fully react in the dewatered and denser medium, which greatly improves the mechanical properties of the treated slurry, and overcomes the various shortcomings existing in the previous single-treatment methods. At present, plate-and-frame pressure filtration using lime for conditioning after flocculation is widely employed to treat large volumes of waste mud slurry [34], with a mechanism similar to the above-mentioned mechanism. However, there are many existing demands for waste mud slurry treatment involving highways, railways, and other traffic engineering, which are characterized by “scattered output sites and small mud slurry output”, and the traditional plate-and-frame filter press dewatering treatment method is not applicable due to its many drawbacks such as multiple equipment modules, large footprint, and poor mobility. Therefore, the treatment process for this type of waste mud slurry urgently needs to be improved to provide high mobility and efficiency so as to realize the efficient treatment of mud slurry at each work site.

To address the above problems, on the basis of VP-FSCM, the vacuum preloading method is replaced by mechanical pressure filtration, and the pressure filtration–flocculation–solidification combined method (PF-FSCM) is proposed for the development of vehicle-mounted integrated high-efficiency drying equipment for the treatment of engineering mud slurry. This method can offer both the mobility not available with the plate-and-frame filter press method and the potential for extensive resource utilization of the treated mud slurry cake, which is particularly suitable for the treatment of mud slurry produced by road, railway, and other traffic engineering and needs to be further investigated.

In the above integrated treatment equipment, the mechanical pressure filtration is a very important part which will directly affect the effect of slurry treatment, including the water content of the mud cake after press filtration as well as its strength. However, most of the existing research results only focus on the effect of flocculation conditioning on the dewatering of mud slurry in the pressure filtration process [21,22,23], and lack further exploration of the influencing factors, such as the dewatering time, filtration pressure, and initial mud cake thickness, which undoubtedly affect the efficiency of the pressure filtration of the PF-FSCM, and play an important role in the application of the PF-FSCM to the treatment of the mud slurry generated in traffic engineering.

Therefore, in order to clarify the influence law of the influencing factors on a pressure filtration effect and to provide a reference for the selection of pressure filtration parameters in the proposed method for the treatment of mud slurry with an ultra-high water content, this paper firstly determines the calculation parameters by integrating the results of the previous laboratory pressure filtration model test, then establishing the pressure filtration calculation model based on the one-dimensional large-strain consolidation theory, and verifying it by comparing the calculated mud cake deformation with measurements obtained from laboratory tests. Moreover, the pressure filtration parameters are extended to an engineering scale for calculation, and the influences of the pressure filtration parameters on mud cake compression deformation are further explored. Finally, suggestions are given for the values of pressure filtration parameters in practical applications.

2. Laboratory Pressure Filtration Model Test

2.1. Materials and Methods

This paper focuses on the application of the above-mentioned PF-FSCM to mud slurry treatment in traffic engineering. The vehicle-mounted integrated high-efficiency drying treatment equipment includes a mud slurry pumping module, an additive (flocculant and curing agent, etc.) delivery and mud slurry conditioning module, a high-pressure filtration module, and a geotechnical mud bag output module, which has the remarkable advantages of strong mobility, high efficiency, and quick treatment, and can directly obtain geotechnical mud bags that can be used as resources after treatment. The principle of the PF-FSCM is shown in Figure 1.

In a laboratory pressure filtration model test, the mud slurry used is taken from a coastal landfill project in Wenzhou, China, where the properties of the mud slurry are generally similar to those found in the area covered by this research. The basic physical property indexes of the mud slurry were measured according to the GB/T 50123-2019 [35], as shown in

Table 1. Physical properties of fluid mud slurry.

Specific Gravity Gs	Liquid Limit wL/%	Plastic Limit wp/%	Sand Content/%	Silt Content/%	Clay Content/%
2.70	53.7	26.5	14.9	79.5	5.6

. The optimum dosage of flocculant and curing agent that can make the treated mud slurry samples have lower water content and higher strength was obtained through preliminary tests. On the basis of the optimal dosage, two working conditions were set for the pressure filtration parameters, in which Group A fixed the dewatering time to study the influence of the initial mud cake thickness (which was linearly related to the dry mud mass) on the pressure filtration effect, and Group B studied the influence of the dewatering time on the pressure filtration effect under the premise of fixing the initial thickness of the mud slurry bag, and the filtration pressure was fixed to 0.3 MPa for both working conditions. The specific working conditions for the laboratory pressure filtration test are shown in

Table 2. Mud pressure filtration model test working conditions.

Working Condition	Dewatering Time (min)	Mass of Dry Mud Slurry (kg)	Calculated Initial Thickness (mm)	Pressure Filtration Press (MPa)	Equivalent Initial Water Content
A1	10	3	102	0.3	250%
A2	10	4	136
A3	10	5	170
B1	6	3	102
B2	8	3	102
B3	10	3	102
B4	12	3	102

, and a flow chart of the laboratory pressure filtration test is shown in Figure 2.

2.2. Results of Pressure Filtration Model Test

2.2.1. Influence of Initial Mud Cake Thickness on the Pressure Filtration Effect

Figure 3 shows the influence of the initial mud cake thickness on the water content and mud cake thickness after pressure filtration (A1~A3 test group). It can be seen that an increased initial mud cake thickness (dry mud mass) increases the water content of the mud cake after pressure filtration; this is because an increased mud cake thickness will result in longer drainage paths for the pore water in the floc during the pressure filtration process, which makes it more difficult to dewater. At the same time, the inner side of the geotechnical bag will be covered with a dense mud skin due to early mud slurry dewatering, which is manifested as a lower permeability coefficient. The pore water is then difficult to discharge, leading to the difficulty of internal mud slurry dewatering at a later stage, which has a negative impact on the dewatering process of a mud cake with a larger thickness.

In addition, the square dot solid line in Figure 3 shows the change curve of mud cake thickness after actual filter pressing, and the dotted line represents the ideal thickness of the mud cake under pressure filtration when the dewatering effect under various working conditions is completely consistent with the minimum initial mud bag thickness. It can be seen that the difference between the actual mud cake thickness and ideal thickness becomes larger when the dry mud mass increases from 4 kg to 5 kg, which is similar to the change law of water content given by the polka-dot solid line in the figure, indicating that a change in the mud cake thickness is closely related to the change in the pore water volume.

2.2.2. Influence of the Dewatering Time on the Pressure Filtration Effect

Figure 4 shows the trend of the mud cake water content with the dewatering time (B1~B4 test group); it can be seen that when the dewatering time increases from 6 to 12 min, the water content of the mud cake decreases from 101% to 74%, and the thickness of the mud cake decreases from 41.8 mm to 37.9 mm, which indicates that the increase in the dewatering time can greatly reduce the water content of the mud cake, i.e., greatly increase the drainage volume in the process of filtration. This indicates that the increase in the dewatering time can greatly reduce the water content of the mud cake; in other words, the drainage capacity during the filtration process can be greatly increased, and thus a mud cake with a higher consolidation degree and better mechanical properties can be obtained.

The effects of the initial cake thickness and dewatering time on the pressure filtration effect were obtained by analyzing the results of the above pressure filtration model test. In the following, an attempt is made to introduce the one-dimensional large-strain consolidation theory to establish a calculation model to simulate the laboratory pressure filtration model test, and the accuracy of the calculation model is verified with the help of the above-mentioned laboratory test results.

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 Gibson’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 Darcy’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].

$$\pm (\frac{{\gamma }_s}{{\gamma }_w}-1)\frac{d}{de}[\frac{k}{1+e}]\frac{\partial e}{\partial z}+\frac{\partial }{\partial z}[\frac{k}{{\gamma }_w(1+e)}\cdot \frac{d{\sigma }^{\prime }}{de}\cdot \frac{\partial e}{\partial z}]+\frac{\partial e}{\partial t}=0$$

(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 Li 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).

$$e=e_0-C_C\lg \frac{{\sigma }^{\prime }}{{{\sigma }_0}^{\prime }}$$

(2)

$$e=e_0-C_k\lg \frac{k_0}{k}$$

(3)

where $e_0$, ${{\sigma }_0}^{\prime }$, 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).

$${\sigma }^{\prime }={{\sigma }_0}^{\prime }+p-u$$

(4)

where u is the excess pore water pressure at the corresponding time.

4. Calculation Model and Parameter Selection

4.1. Pressure Filtration Calculation Model

The simplified mud slurry compression and filtration model is shown in Figure 5, and the mud slurry can be regarded as one-dimensionally compressed under pressure, with deformation occurring only in the horizontal direction. On both sides of the mud slurry are permeable plates, which allow the pore water in the mud slurry to seep out freely. In fact, the pressure filtration dewatering process of the mud slurry includes two stages. The first stage is the preliminary dewatering stage of the fluid-mixed mud slurry (the mixture of mud slurry, flocculant, and curing agent), and the interaction between the soil particles begins to form a soil skeleton, as shown in Figure 5a,b. At the second stage, the mud cake with a soil skeleton continues to be dewatered under pressure to form a mud cake with a low water content, as shown in Figure 5b,c.

At the first stage, the mixed mud slurry is a suspended system due to the incompletely formed soil skeleton, and the consolidation theory is not applicable to the deformation calculation at this stage, but this stage can be completed quickly for the flocculated conditioned mud slurry with a better dewatering performance, so the second stage of pressure filtration can be regarded as the deformation of the mud cake by draining and consolidating it under the external force, which is an important stage in the determination of the time required for pressure filtration; therefore, the one-dimensional large-strain consolidation calculation introduced in this paper is limited to the second stage of pressure filtration.

4.2. 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.

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.

$$e=\frac{w{d}_s}{S_r}$$

(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 h₀₁ and the initial void ratio e₀ of the mixed mud slurry before pressure filtration, the initial thickness h₀ of the mud cake when the pressure filtration process reaches the state shown in Figure 5b can be calculated from Equation (6).

$$h_0=h_0{}_1\cdot \frac{1+e_0}{1+e_{01}}$$

(6)

The initial effective stress of the mud cake is low, generally around 0~1 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 0.5~2.0 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).

$$\lg (k_0)=-8.89+4.89\lg e_0-5.12\lg w_L$$

(7)

where w_L is the liquid limit of the mud slurry.

Notably, the k₀ calculated by Equation (7) is 1.82 × 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. Calculation parameter values for each working condition.

Calculation Parameters	A1	A2	A3
Initial thickness of mixed mud slurry, h01 (mm)	102	136	170
Initial void ratio of mixed mud slurry, $e_{01}$	6.75	6.75	6.75
Initial mud cake thickness, h0 (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, ${{\sigma }_0}^{\prime }$ (KPa)	1.0	1.0	1.0
Initial permeability coefficient of mud cake, $k_0$ (cm/s)	1.82 × 10−2	1.82 × 10−2	1.82 × 10−2
Compression index, Cc	1.2	1.2	1.2
Permeability index, Ck	1.08	1.08	1.08

.

4.3. 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 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. Among the calculation parameters, the values of compression index C_C and permeability index C_k greatly affect the deformation, and the parameter values derived from the previous research results and relevant empirical formulas may differ from the actual situation, which ultimately leads to the difference between the calculated values and the measured values.

In addition, the influence of the change in the dewatering time on the filtration effect (characterized by changes in mud cake thickness) is explored by varying only the dewatering time under the Group A1 test condition, and the comparison between the calculated and measured mud cake thicknesses is shown in Figure 8.

Obviously, with an increase in the dewatering time, the thickness of the mud cake becomes smaller, from the theoretical calculation results, the mud cake permeability coefficient is larger in the early stage of pressure filtration, and the pore water is discharged more quickly, reflecting the rapid reduction in the mud cake thickness, but the trend of the change slows down with the growth of time, and the thickness of the mud cake is basically stable after a certain dewatering time. Figure 8 also indicates that the calculated and measured cake thicknesses after pressure filtration are close to each other, with the measured values slightly larger than the calculated values in the early stage of filtration and slightly smaller than the calculated values in the late stage of filtration.

By comparing the mud cake thickness shown in Figure 8, it is found that there is a slight difference between the calculated and measured mud cake thickness, but the variation is basically the same. On the one hand, the values of the parameters in a theoretical calculation are not exactly the same as those in practice, and on the other hand, there are some errors in actual measurements. In general, according to the parameter values mentioned above, it is feasible to use the one-dimensional large-strain nonlinear consolidation theory to calculate and analyze the mud cake deformation against the time, and the results obtained from the calculations are of reference value.

5. Influence of Pressure Filtration Parameters on Mud Cake Deformation

In order to make up for the insufficiency of the laboratory test conditions and to extend the calculation parameters on an actual engineering scale, based on the above validated calculation model, the relationship between the deformation of the mud cake and the dewatering time under different filtration pressures and initial cake thicknesses will be further calculated in this section, so as to take into account the influences of the dewatering time, the filtration pressure, and the initial thickness of the mud cake on the filtration effect.

5.1. Effect of Initial Cake Thickness and Dewatering Time on Cake Deformation

Figure 9 illustrates the variation in the calculated compression deformation of the mud cake with the dewatering time for different initial cake thicknesses at filtration pressures of 0.8 MPa and 1.2 MPa. Comparing Figure 9a,b, it can be seen that the deformation pattern of a mud cake with the dewatering time under different filtration pressures is basically the same, only differing in values; therefore, only working conditions with filtration pressures of 0.8 MPa and 1.2 MPa are shown here.

As can be seen from Figure 9, the compression deformation of the mud cake at the beginning of pressure filtration is very similar under different initial cake thicknesses, and the rate of compression deformation gradually slows down over time. When the compression deformation of the mud cake changes less with the dewatering time, in other words, when the deformation–time curve tends to flatten, the filtration can be considered to have been completed completely. According to the trend of the curves in Figure 9, the time needed to complete the pressure filtration process is shorter when the initial mud cake thickness is smaller, and a longer time is needed as the initial mud cake thickness increases. Obviously, the increase in the mud cake thickness increases the drainage path of the pore water, resulting in a longer time being required to complete pressure filtration.

According to Equation (6) mentioned above, the void ratio e of the mud cake can be calculated using the compression deformation of the mud cake, and then the water content of the mud cake after pressure filtration can be obtained by substituting e into Equation (5), which is one of the important indexes that needs to be considered in the process of mud slurry dewatering using pressure filtration. In this paper, the water content of the mud cake after pressure filtration is also used as the basis for evaluating the effect of pressure filtration. Combined with the previous laboratory tests, the lowest water content of a mud cake obtained after the pressure filtration process in a coastal landfill in Wenzhou, China, is about 70%, which is used as a control index in this paper, and the relationship between the initial mud cake thickness and the dewatering time when the water content is reduced to 70% under different filtration pressures is shown in Figure 10.

As shown in Figure 10, the dewatering time increases nonlinearly with an increase in the initial mud cake thickness, and referring to the linear trend line, such a nonlinear characteristic is more obvious with a smaller filtration pressure. In terms of the processing efficiency, an increase in the initial cake thickness leads to a multiplied increase in the dewatering time and the reduction in the processing efficiency. Meanwhile, in terms of the pressure filtration processing time, most of the working conditions are below 40 min, and the shortest can be up to 10 min or less. When the initial cake thickness is 420 mm, the dewatering time is below 40 min only when the pressure reaches 1.4 MPa. Therefore, in order to shorten the processing time, one should consider reducing the initial cake thickness appropriately.

5.2. The Effect of Filtration Pressure on Mud Cake Deformation and Dewatering Time

An increase in filter pressure is helpful for the rapid discharge of pore water, which can accelerate completion and reduce the required time to a certain extent. The influence of the filtration pressure on mud cake deformation and the dewatering time is analyzed below. In addition, the variation in the compression deformation of a mud cake over time under different filtration pressures is minimal, and the corresponding dewatering time is also similar as the deformation–time curve tends to flatten. In addition, the filtration pressure has some influence on the final mud cake thickness, but has little influence on the time required for the compression deformation to be stabilized, which is usually around 60 min.

It can also be seen from Figure 11 that it takes a long time until the thickness of mud cake is basically unchanged under pressure, and the thickness of mud cake changes less at a later stage. The variation in the dewatering time with the filtration pressure obtained by taking a 70% water content in the mud cake after pressure filtration as a control index is shown in Figure 12. For each working condition under different initial cake thicknesses, the increase in pressure can effectively shorten the dewatering time when the filtration pressure is small, and when the filtration pressure is increased to the critical value, thereafter, the influence of the filtration pressure on the dewatering time is small, which is reflected in the gradual slowing down of the change trend of the curve of the filtration pressure–dewatering time. This law is similar to that given by theoretical calculations in reference [46]. This is because when the pressure increases, the excess pore pressure in the mud cake also increases, the discharge rate for the pore water increases, and the decrease rate of the void ratio accelerates, leading to a decrease in the pressure time. But at the same time, an increase in filter pressure also shortens the time when the void ratio of the mud cake decreases to the lowest, which results in a decrease in the filter pressure time.

After the filtration pressure reaches the critical value, a continuous increase in pressure has less influence on a reduction in the dewatering time; therefore, considering the comprehensive processing efficiency and the increase in processing energy consumption brought about by the pressure increase, it is more economical to adopt the critical filtration pressure for the pressure filtration process in engineering. It can be seen from Figure 12 that when the initial cake thickness reaches more than 300 mm, the dewatering time decreases greatly when the filtration pressure increases from 0.6 MPa to 1.0 MPa, whereas the dewatering time decreases greatly when the filtration pressure is increased from 0.4 MPa to 0.8 MPa for initial cake thicknesses below 300 mm. When the initial cake thickness increases, the corresponding critical filtration pressure also increases.

5.3. Optimization of the Pressure Filtration Parameters

The parameters involved in the pressure filtration treatment of waste mud slurry include the dewatering time, initial mud cake thickness, and filtration pressure, all of which have mutual constraints on the improvement of treatment efficiency. Treatment efficiency can be regarded as the amount of mud slurry treated per unit of time, and for this paper, the mud cake only changes in thickness, and the ratio v between the initial mud cake thickness and dewatering time can be used as the basis for judging the construction efficiency according to Equation (8).

$$v=\frac{h_0}{t}$$

(8)

According to the data in Figure 12, the treatment efficiency v corresponding to different initial thicknesses and filtration pressures when the mud cake is pressed to 70% water content is calculated, as shown in

Table 4. Treatment efficiency v at different initial cake thicknesses and filtration pressures.

Initial Thickness (mm)	Filtration Pressure (MPa)
	0.4	0.6	0.8	1.0	1.2	1.4
180	8.61	12.14	15.10	17.28	18.23	19.30
240	6.40	9.61	12.05	14.12	15.09	16.29
300	-	7.73	10.06	11.56	12.84	13.73
360	-	6.71	8.77	9.97	11.07	11.98
420	-	5.91	7.51	8.88	9.89	10.82

.

Figure 10 and Figure 12 and Table 4 together reflect the effects of the dewatering time, filtration pressure, and initial cake thickness on the pressure filtration effect:

• An increased initial cake thickness will lead to a non-linear increase in the dewatering time, resulting in a reduction in the processing efficiency; the initial cake thickness should be appropriately reduced.
• Under the same initial mud cake thickness, a continuous increase in filtration pressure after the pressure is increased to the critical value has less effect on the dewatering time.

Combined with the above analyses, when the initial cake thickness exceeded 240 mm, the processing efficiency decreased significantly at all filtration pressures, and the reduced thickness increased the treatment efficiency. Meanwhile, the efficiency increase with filtration pressure was no longer significant beyond 1.0 MPa for each initial thickness. Therefore, in order to improve the efficiency of pressure filtration while maintaining low energy consumption, an initial cake thickness of 180 mm~240 mm and a filtration pressure of 1.0 MPa are recommended. Under these pressure filtration parameters, the time to achieve deformation stability for the initial cake thicknesses of 180 mm and 240 mm is calculated to be 21.3 min and 28.2 min, respectively, and the corresponding efficiencies v are 8.45 and 8.51, respectively. For the mud slurry used in this study, the optimal values for the initial mud slurry bag thickness, filtration pressure, and dewatering time are 240 mm, 1.0 MPa, and 30 min, respectively, yielding a final mud cake water content of 58.7% after filtration.

The above pressure filtration parameter values take into account the impact of processing energy consumption and processing efficiency, which can provide a reference for the parameter values in the pressure filtration part of the PF-FSCM for waste mud slurry treatment.

6. Conclusions

In this paper, a pressure filtration calculation model for mud slurry after flocculation consolidation was established based on the one-dimensional large strain consolidation theory and was verified with the help of a laboratory pressure filtration model test. The pressure filtration parameters were extended on an engineering scale to further analyze the influence of the pressure filtration parameters on the compression deformation of a mud cake, and the recommended values of the filtration parameters for practical application were given. The main conclusions are as follows.

• The mud cake thickness after pressure filtration obtained by the calculation model proposed in this paper combined with the one-dimensional large-strain consolidation theory is only slightly larger than the measured mud cake thickness, and the trend of the mud cake thickness against the dewatering time is basically the same. It is feasible to use the calculation model proposed in this paper to analyze the relationship between mud cake deformation and dewatering time.
• An increased initial cake thickness greatly affects the pressure filtration efficiency. In order to achieve the same dewatering effect, doubling the initial cake thickness will lead to an increase several times over in the dewatering time. Reducing the initial cake thickness within a certain range can improve the pressure filtration efficiency.
• An increased filtration pressure increases the final compression deformation of the mud cake. In order to treat the mud cake to the same water content, an increase in pressure when the filtration pressure is small effectively reduces the dewatering time, but a continuous increase in the filtration pressure after the pressure has been increased to the critical value had less effect on the dewatering time.
• Considering the processing efficiency and energy consumption, the initial mud cake thickness of 240 mm, filtration pressure of 1.0 MPa, and dewatering time of 30 min obtained from the calculation model in this paper are recommended for slurry treatment.

Although this study provides a comprehensive study on the factors affecting the performance of mud treatment using the PF-FSCM, there still are some limitations in this paper, such as a single slurry type and no consideration of mud viscosity, which need to be further investigated to improve the applicability of the PF-FSCM to practical engineering.