Experimental Study on the Characteristics and Formation Mechanism of Dynamic Filter Cake for Slurry Shield Tunneling

Abstract

The key to guaranteeing excavation face stability in slurry shield tunneling is the formation of an impermeable dynamic filter cake. At the same time, the effect of the cutter head and rotation speed should be taken into account. We studied the characteristics and formation mechanism of the dynamic filter cake using a newly developed experimental apparatus. The experiment results show that the hysteretic infiltration zone appeared in the curves of stepped loading filtration while the cutter head was rotating, and the volume of water filtration increased by 11.2% compared to when the cutter head stopped. The higher the rotation speed was, the lower the conversion rate of the effective stress was. Under the same rotation speed, the formation time of the 6-cutter arm was almost 5 s slower than that of the 5-cutter arm. As the cutter arms and the rotation speed increased, the stratum’s electrical conductivity increased and stabilized at a distance of 20 cm from the cutter head. The filter cake transited from ‘filter cake plus an infiltration zone’ to ‘an infiltration zone without a filter cake’ with the increase of the rotation speed. The thickness of the dynamic filter cake was smaller than that of the static filter cake, the thickness of 10 groups decreased significantly, and the average thickness decreased by 76.15% at 1.0 rpm. The mesoscopic formation process of the dynamic filter cake can be divided into six stages. This study revealed the slurry penetration mechanism and filter cake characteristics present under cyclic damage by the shield cutter head to the filter cake and soil and provided theoretical support on how to maintain the stability of the excavation face during slurry shield tunneling.

1. Introduction

In the past few years, due to their extensive range of geological applications, low disturbance to surrounding rock, and high excavation face stability, slurry pressure balance shield (SPB) technology has been widely used in shield tunnels [1,2,3,4], such as the fourth tunnel of the Elbe River in Germany, the Westerschelde tunnel in The Netherlands, the Eurasia tunnel in Turkey, the Tokyo Bay submerged highway tunnel in Japan, and the Nanjing Yangtze River and Hangzhou Qianjiang tunnels in China [5,6,7,8]. However, when slurry shield tunnels are constructed in a stratum in which the water pressure is more than 0.5 Mpa and the permeability coefficient is more than 10⁻³ cm/s, the excavation face will become unstable, causing seawater backflow and slurry spillover if special measures are not taken. This can lead to major accidents, such as tunnel collapse [9,10].

During slurry shield tunneling, the balance between the stratum’s initial stress field and the underwater seepage field is broken, so the tunnel’s excavation surface is prone to large deformation or instability failure [11,12,13,14,15]. Therefore, it is especially crucial to guarantee the stability of the slurry shield’s excavation face. Based on Horn’s theory [16], Anagnostou et al. [17] proposed a wedge failure model for slurry shield tunnels and studied the complicated relationships among the slurry shear strength, permeability, suspension parameters, slurry pressure, tunnel alignment, and safety factors. Regarding slurry permeation, Broere et al. [18] established a mechanical model for excavation face stabilization. He also compared the calculated pore-pressure distribution with the actual results of the slurry shield in the sand stratum, indicating that the excess pore pressure had an important impact on the tunnel face stability. Zizka et al. [19] applied a method for predicting an increase in pore water pressure in front of the tunnel face and concluded that the permeation of slurry is related to time and the pore water pressure transfer follows Darcy’s law.

Zumsteg et al. [20] found that increasing the slurry strength can guarantee the excavation face’s stability, while the cutter head can be easily clogged. Considering the permeable filter cake, Chen et al. [21] established a two-dimensional numerical model and obtained the pore water pressure’s maximum value through a transient seepage analysis. It was found that the efficiency of tunnel face stabilization deteriorated when the slurry pressure increased. Liu et al. [22] studied the failure mechanism of slurry shields through a series of model tests and the vertical displacement of the ground surface and the earth pressure distribution in strata with different covering depths. It was found that the vertical displacement was mainly distributed in a triangular region bounded by the fracture surface above the cutter head, and the horizontal displacement was mainly distributed in the excavation face. The above studies did not consider the influence of the cutter head on the excavation face, and this effect needs to be discussed.

In highly permeable stratum, the underwater environment is complex [23,24,25]. The timely formation of a safe and effective filter cake is the key to guaranteeing the stability of the excavation face in slurry balance shield tunnels and reducing the project risks [26,27,28]. Through designing the slurry filtration column test, Fritz [29] confirmed that the addition of certain proportions of bentonite, polymer, sand, and vermiculite could improve the stability of the excavation face for the high-permeability stratum (the maximum permeability value is 10⁻³ m/s). Zdenek et al. [30] investigated the pressure transfer mechanism interaction with cutting tools for the transfer of pressure in areas of deep penetration exceeding the cutting tool depth. They proposed that a linear pore pressure distribution can deliver more efficient support pressure transfer due to the lower slurry penetration depth with increased stagnation. Min et al. [10] used a self-made slurry filtration device to investigate filter cake formation under conditions with different slurry characteristics and stratum combinations and categorized the slurry particle accumulating form into three types, as shown in Figure 1: an intact filter cake, filter cake plus a permeation, and an infiltration zone without a filter cake.

Through the slurry filtration model test, Liu et al. [31] studied the influence of the pore parameters of the stratum on the characteristics of the filter cake and established a two-parameter model for formation fluid loss. They proposed that the average pore volume per particle (v) of the formation soil significantly affected the filter cake formation. Xu et al. [32] conducted an experimental study on the penetration process of bentonite slurry in saturated sand and found that the filter cake was only formed in front of the cutter head. The slurry proportion was shown to have a remarkable effect on the stability of the excavation face—the greater the bentonite concentration was, the lower the permeability of the sand and filter cake were. Lin et al. [33] considered the clogging behavior of the slurry particles and the filtering ability of the ground, and the particle retention rate was proposed to evaluate the degree of matching between the slurry and the ground. Mao et al. [34] established a constant pressure slurry permeation cake model of a slurry shield excavation face in sandy stratum and analyzed the effects of the permeation time, slurry concentration, slurry pressure, and initial stratum porosity on filter cake formation. He summarized the variation law of soil porosity at the excavation face during periodic slurry permeation. Obviously, the cutting effect of the cutter head has a negative effect on the formation of the filter cake. Few studies have investigated the formation mechanism and characteristics of the filter cake constructed under the influence of the ‘machine–soil’ relationship using experimental methods. Therefore, it is necessary to carry out an experiment of dynamic filter cake formation.

The filter cake formation process is complicated. The slurry proportion, slurry pressure, stratum conditions, cutter head structure, rotation speed, and cutter layout all affect the penetration process and the filter cake quality. However, previous studies all focused on the static filter cake, ignoring the effects of periodic cutting and slurry pressure fluctuation on the surrounding soil, as well as the dynamic filter cake formation process [14,17,18,35]. Therefore, a self-made test apparatus was developed to establish a dynamic infiltration model in the saturated sand stratum. The features of this apparatus are as follows: Dynamic filter cake experiments of the slurry shield can be carried out. A replaceable cutter head type experiment apparatus can be designed. As the cutter head of the shield machine used in each shield tunnel is designed uniquely, the apparatus can be used for relevant experiments for each shield machine by making and replacing the experiment cutter head. By applying TDR equipment (TDR is a time-domain reflection technique that can measure the conductivity of soil), the slurry penetration distance can be tracked more accurately through the change in soil conductivity. It is an experimental apparatus system that can be used for future shield machine selection. The apparatus can also be used for filter cake-formation experiments in the cutter head-selection stage, and the characteristics of the cutter head can be selected from the perspective of filter cake formation, including the number of cutter arms, opening rate, and other key parameters.

In this study, a new dynamic filter cake test device was designed to investigate the dynamic filter cake characteristics and formation mechanism of the slurry shield. Through experimental research, the characteristics of the dynamic filter cake (water filtration, maximum penetration distance, formation time, and final state) were studied, as shown in Figure 2. The dynamic filter cake formation process is divided into six stages. The rotating speed of the cutter head is reduced in the process of shield tunneling, and the number of cutter arms and opening rate of the cutter head, are decreased in the shield selection stage to form a high-quality filter cake.

2. Experimental Apparatus and Methods

2.1. Test Slurry and Stratum

In this test, clay from the middle and lower reaches of the Yangtze River was selected and immersed to make the base slurry. Referring to the slurry parameters commonly used in slurry shields, it was made with a bentonite to water ratio of 1:12 [36,37]. The mixture included bentonite, CMC (carboxymethyl cellulose), and Na₂CO₃ (sodium carbonate) in certain proportions and had a hydration time of about 24 h. As the main pulping material, bentonite has good water absorption, expansibility, and cohesiveness. CMC was used as the tackifier of the slurry, and Na₂CO₃ played roles in dispersion and uniformity in the slurry. To reduce the test error and ensure test repeatability and comparability among data, 10 groups of slurry (SL1–SL10) were tested, as shown in Figure 3. In physical shield tunneling, the values of slurry density and viscosity are strictly controlled within certain ranges. The density of the slurry shield should be 1.05–1.30 g/cm³, and the viscosity should be 20–35 s. Thus, as shown in

Table 1. Physical parameters of the testing slurry.

Test No.	Bentonite Content	Slurry Relative Density	Slurry Viscosity	Clay Content	CMC Content	d85/μm
SL1	62 g	1.05	28 s	60 g	5 g	170
SL2	62 g	1.10	30 s	80 g	6 g	168
SL3	62 g	1.15	30 s	100 g	6 g	173
SL4	83 g	1.20	32 s	120 g	8 g	212
SL5	83 g	1.25	32 s	140 g	8 g	206
SL6	62 g	1.12	22 s	50 g	5 g	140
SL7	62 g	1.15	25 s	100 g	5 g	138
SL8	83 g	1.20	30 s	120 g	5 g	136
SL9	100 g	1.25	30 s	130 g	5 g	135
SL10	100 g	1.28	32 s	150 g	5 g	128

, the physical–mechanical parameters of the test slurry were selected. The properties of the slurry samples were measured in the laboratory. Specifically, a 1002 type slurry-specific gravity scale and a Russian funnel viscometer were used to measure the slurry’s density and viscosity. The relative density error was within 0.01 g/cm³, the error in the slurry viscosity was within ±1 s, the 10 groups of slurry samples had good physical stability, and the 2 h bleeding rate was less than 2%. The grain size distribution of the 10 groups of slurry measured by the MS2000 laser particle size analyzer is shown in Figure 4.

Silty–fine and medium–coarse sands, which have difficulty forming a filter cake in the middle and lower reaches of the Yangtze River, were collected as the main standard sample and used to prepare the test sand. To control the grain size and gradation, the stratum was divided into two types of sand with different particle dimensions. As determined by the geological investigation, the basic parameters of the test soil are shown in

Table 2. Basic properties of the strata.

Sand No.	Name of Sand	Density	Permeability Coefficient	Internal Friction Angle	Void Ratio
S1	Silty–fine sand	1.45 g/cm3	5.7 × 10−3	31.8°	0.54
S2	Medium–coarse sand	1.86 g/cm3	1.08 × 10−2	33.5°	0.62

. The dry density of the stratum and the parameters of the saturated sand sample were strictly controlled using the layered compaction method. The test stratum was divided into layers by the rectangular open funnel. The initial dry density was 1.61 g/cm³, the effective weight was 9.98 KN/m³, and the stratum porosity was 0.41. After a layer of the sand sample had been prepared, the water was slowly immersed until all layers were saturated, and the permeation column was sealed with a top cover. According to ASTM (American Society of Testing Materials) D2432–06 (ASTM,2006) [38], the permeability coefficient of the stratum was measured as 6.5 × 10⁻³ m/s through the long-head permeation test.

2.2. Experiment System

The previously developed device can only simulate the static filter cake [29,32,36,39]. This was based on the slurry infiltration principle of the slurry shield machine, the balance between compressed air, slurry in the slurry chamber, and the water and earth pressure, as shown in Figure 5. A dynamic filter cake test system, as shown in Figure 6, was independently developed. The slurry chamber and cutter head of the slurry shield machine are key components in the simulation of dynamic filter cake formation. This apparatus reflects the interaction between the slurry chamber, cutter head, and stratum of the physical shield machine well. The test system consists of a slurry filtration column, slurry mixing tank, air pressure source, connecting shaft, motor and cutter head, controller, and measuring devices. The top of the filtration column is fixed with a specific low-speed motor. The motor is equipped with a cutter head governor to adjust the rotation speed and direction, and the speed range is 0–9 rpm with an accuracy level of 0.1 rpm. The dimensions of the test apparatus and measurement devices are shown in Figure 7.

The filtration column has a height of 80 cm and an outer diameter of 42 cm. Time-domain reflectometries (TDR) were placed in 6 holes on the sidewall to measure the electrical conductivity after the penetration of the stratum by slurry so as to determine the penetration distance and diffusion scope of the slurry under the influence of the cutter head’s rotation. The conductivity range of the TDR is 0–20,000 μs/cm, and the accuracy level is ±3%. Simultaneously, 4 vibrating wire-type pore pressure transducers were installed on the other sidewall to measure the slurry pressure and pore pressure in the filtration column. The measurable range is 0˜600 Kpa, and the accuracy is 1.0 Kpa. Cutter heads with a large opening rate are widely selected during slurry shield tunneling in underwater sandy soil [36,37]. Two types of cutter head were designed in this test, as shown in Figure 8. The CH1 type is characterized by 5 cutter arms with an opening rate of 36%, and the CH2 type is characterized by 6 cutter arms with an opening rate of 28%. The outer diameter of the cutter head (400 mm) is made of alloy steel and has a thickness of 15 mm. In addition, the upper part of the cutter is covered with a large number of grid-like alloys.

2.3. Experiment Conditions and Production Procedure

Once the test instrument had been assembled and debugged, the prepared slurry was injected into the mixing tank and continuously stirred for more than 1 h. The basic parameters of the TDR were calibrated, and ECp (the conductivity of the initial sample) was calculated. After turning the motor on, the rotation speed was adjusted to 1.0 rpm to observe the rotation of the cutter head. Simultaneously, the motor rotation was measured for more than 3 min, and the number of rotations was recorded per minute until the frequency converter’s indication was consistent with the rotation number of the cutter head.

After setting the air pressure, the valve was opened to slowly infiltrate the stratum with slurry, and the starting time was recorded. Considering the unfavorable situation of slurry shield tunneling [1,2,3,4,37], the pressure was loaded to 0.5 MPa, with each step being 0.1 Mpa to facilitate the observation of the slurry infiltration process. At the same time, the water filtration volume under each level of pressure was recorded at 10-s intervals. It should be noted that the parameters used in the experiment (rotating speed, slurry pressure, and experiment duration) were chosen according to physical engineering records. With the water filtration becoming stable, the next level of air pressure was applied under the same rotation speed and cutter head direction. Statistics for the rotation speed of the cutter head [37] show that, for the medium–coarse sand stratum, the rotation speed is generally controlled within the range of 0.5 to 1.0 rpm. Therefore, three typical rotation speeds were chosen to investigate the formation of the dynamic filter cake. The typical rotation speeds were 0 rpm for the segment assembly state, 0.5 rpm, and 1.0 rpm for the slurry shield tunneling state.

3. Results and Discussion

3.1. Water Filtration

In the slurry permeation test, the water filtration volume at a certain time can reflect the quality of the filter cake: the less water filtration, the better the quality of the filter cake and the greater the stability of the excavation face [32,36]. The water filtration time curves considering the effects of the cutter head structure and rotation are shown in Figure 9. We found that the SL1–SL10 slurry sample curves had a stepped frame distribution with the two cutter head types and three different speeds; that is, the permeation speed increased rapidly and then gradually decreased within 10 s for each loading pressure when the cutter head stopped. As shown in Figure 9A,B, as the slurry pressure increased, the slurry particles penetrated into the soil to form a filter cake, and the stress was transmitted to the soil particles through the filter cake.

The water in the slurry penetrated through the pores, and the pressure increased until reaching stability. Through the continuous accumulation of slurry particles, the water filtration volume increased and then gradually became stable. Therefore, the curve has a stepped distribution. As shown in Figure 9C–F, as the rotation speed increased, the final water filtration volume per unit of area slowly increased. For the shaded area, the slurry permeation time was longer than the working duration of the cutter head, showing a hysteretic infiltration zone and indicating that there was a delay of about 10–20 s while the cutter head stopped. The cutter head rotation decreased the water permeation speed during cutting, and there were slurry particles, and water stuck on the cutter head when the slurry passed through the opening of the rotating cutter head. As the rotation speed increased, the hysteretic infiltration zone gradually shortened, suggesting that the delayed effect of water filtration became weaker over a longer time scale.

The cutter head structure (the number of cutter arms and opening ratio) and rotation speed were found to have essential impacts on the volume of water filtration. The final water filtration volume produced with different cutter heads and rotation speeds for the SL5 slurry sample (SL5 slurry is also selected as the final state) is shown in Figure 10A. When the cutter head stopped, the differences in the water filtration volume were minute. As the cyclic damage to soil and filter cake increased with the cutter head speed, the final water filtration volume continued to increase. When the cutter head rotated, the water filtration volume of the 6-cutter arm was more than that of the 5-cutter arm. The more cutter arms there were, the greater the soil destruction was, increasing water filtration and reducing the quality of the filter cake.

Taking SL4 and SL10, for example, the viscosity of the two slurries was 32 s, and the density of SL4 was less than that of SL10. The experiment’s results revealed that the greater the relative density and viscosity of the slurry were, the lower the water filtration was and the better the quality of the filter cake was, as shown in Figure 10B. When the cutter head speed was 0, 0.5, or 1.0 rpm, the infiltration volume of SL4 was greater than that of SL10. The main reason for this is that the slurry density represents the content of solid particles in the slurry. When the slurry density is high, there are many solid particles in the slurry, which makes it easier to accumulate and block the soil and form a high-quality filter cake. Therefore, the volume of water filtration in high-density soil is relatively low. Taking SL3 and SL7, for example, the density of the two slurries was found to be 1.15 g/cm³. The viscosity of SL3 was greater than that of SL7. As is shown in Figure 10C, when the cutter head speed was 0, 0.5, or 1.0 rpm, the water filtration volume of SL3 was less than that of SL7. This can be attributed to the viscosity, which represents the physical stability of the slurry: the higher the viscosity of the slurry is, the stronger the binding forces between particles and water are. Once the particles in the slurry clog the pores during filter cake formation, it is difficult for the water in the slurry to penetrate the soil and reduce the water filtration volume.

3.2. Effective Stress

Referring to the actual slurry shield construction experience, a slurry pressure of 0.2 Mpa was selected. According to research by Wei et al. [37], the conversion rate of effective stress ω can be used to represent the formation time and the characteristics of the filter cake. The time that the filter cake takes to reach a stable state from the beginning of the experiment is defined as the formation time: the shorter the formation time, the more compact the filter cake. ω can be calculated as follows:

$$\omega =\frac{P_s-P_w-P_e}{P_s-P_w}\times 100\%$$

(1)

where $P_s$ is the slurry pressure, $P_w$ is the stratum hydrostatic pressure, and $P_e$ is the excess pore water pressure. $P_w$ can be calculated according to the depth that the pressure transducers are buried. $P_e$ represents the data measured by the pore transducer minus the corresponding $P_w$. As shown in Figure 6, pressure transducer 2# was the closest to the filter cake. Thus, the effective stress conversion rate in this region was selected to determine the filter cake formation time.

Under a pressure of 0.2 Mpa, the value of ω at pressure transducer 1# increased rapidly and then achieved stability when the maximum effective stress conversion rate ${\omega }_{\max }$ was reached. As shown in Figure 11A,B, with the same slurry parameters and rotation speed, ${\omega }_{\max }$ and the formation time of different cutter heads were similar when the cutter head stopped. However, as the rotation speed increased, ${\omega }_{\max }$ and the formation time varied for different cutter arms. As shown in Figure 11C–F, when the rotation speed was 0.5 and 1.0 rpm, the average ${\omega }_{\max }$ values of the 5-cutter arm were 79.1% and 77%, respectively, higher than the values of 76.7% and 73.2% achieved by the 6-cutter arm. The average formation time occurred about 5 s earlier than that of the 6-cutter arm.

For the same cutter head, the ${\omega }_{\max }$ decreased continuously as the rotation speed increased. As shown in Figure 11, when the rotation speed was 0, 0.5, and 1.0 rpm, the average ${\omega }_{\max }$ of the 5-cutter arm was 91%, 82%, and 80%, respectively, while the average ${\omega }_{\max }$ of the 6-cutter arm was 90%, 81%, and 77%, respectively. The formation time increased as the rotation speed increased. For the 6-cutter arm cutter head, the filter cake formation time was about 25 s at a rotation speed of 1.0 rpm, about 5 s slower than with a rotation speed of 0.5 rpm.

3.3. Electrical Conductivity

As the main component used in the slurry shield tunneling, the pulping agent bentonite is a layered aluminosilicate clay mineral with montmorillonite. The unsaturated interlayer electrovalence makes the bentonite slurry particles negatively charged [21]. The conductivity of slurry particles infiltrating the sand with pressure was greater than that of the original stratum. Based on this principle, the slurry infiltrating range and distance were estimated to evaluate the quality of the filter cake. At the beginning of the test, the conductivity of the stratum (ECp) in the standard state was measured. To avoid the influence of the boundary effect, the six TDR probes were placed under the center of the cutter head. Setting the interface between the cutter head and the stratum as the origin and the vertical direction as the infiltration direction, the TDR1–TDR6 probes were buried at 5, 10, 15, 20, 25, and 35 cm below the slurry–sand interface, as shown in Figure 7. Based on the data acquisition system, the variation law of the stratum conductivity of SL1–SL10 slurries under different types of cutter heads and speeds was studied.

It was found that when the cutter head rotated and stopped, the variation trend for the electrical conductivity of the stratum was basically unchanged. As shown in Figure 12, the variation curves of the electrical conductivity can be divided into two parts: the descent stage and the stable stage. The first part is the descent stage, which includes the zone ranging from 0 to 20 cm below the cutter head–stratum interface. The negative charge of the slurry particles was shown to penetrate the stratum through the cutter opening, and the electrical conductivity of sand near the cutter head–stratum interface decreased obviously, mainly due to the cutter head’s rotation. The electrical conductivity at 5 cm below the cutter head–stratum interface was three to four times the initial value. As the penetration distance increased, under the function of the permeation force, the slurry particles penetrated the stratum pores, making the electrical conductivity in this area steadily decrease, indicating that the slurry particles continued to decrease as the penetration distance increased. The average electrical conductivity dropped to two to three times that of the original stratum. The second part was the stable stage, and this included zones ranging from 20 to 35 cm below the cutter head–stratum interface, where the stratum was minimally affected by the cutter head rotation. Under the function of the permeation force, most of the particles penetrated into the front stratum pores, and only the water filtration passed through this stratum. Due to the small slurry particles in this area, the electrical conductivity was basically the same as that of the original stratum.

For the same type of cutter head, the rotation speed affected the electrical conductivity remarkably. As the rotation speed increased, the electrical conductivity in the descent stage of the curves increased obviously. As shown in Figure 12A–F, when the speed was 1.0 rpm, the electrical conductivity increased by an average of about 21% compared to that of the stopped cutter head, and the greater the rotation speed was, the more quickly the electrical conductivity. When the rotation speed was 1.0 rpm, the ratio of the electrical conductivity to the initial value approached 4–5, probably due because the cutter head’s cutting enlarged the size and number of stratum pores, leading to more slurry particles becoming clogged and adsorbed.

As shown in Figure 12A,B, when the cutter head stopped, the variation laws of electrical conductivity for the two cutter heads were consistent, and the electrical conductivity at the same measuring site was similar. When the cutter head rotated for a given slurry type and rotation speed, the variation law of electrical conductivity of different cutter heads appeared different. As shown in Figure 12C–F, in the descent stage, at a given measurement point, the conductivity of the 6-cutter arm was about 4% higher than that of the 5-cutter arm. This trend became more obvious as the rotation speed increased. The more cutter arms there were, the more frequently the stratum was cut within a certain period, and the more severely the internal structure of the stratum was damaged, leading to an increase in pores and penetration of the stratum by more slurry particles so that the electrical conductivity was raised.

As shown in Figure 12, the bentonite in the slurry sample appeared to have no effect on the slurry’s maximum permeation distance. On the other hand, at the measurement site closer to the cutter head, the electrical conductivity of slurry sample SL10, which had more bentonite, had a maximum permeation distance of 16% greater than that of slurry sample SL1, which had less bentonite. This is because bentonite, with its negative charge, enhanced the electrical conductivity of the stratum.

3.4. The Final State of the Filter Cake

The filter cake formation penetration ×tests were carried out on 10 groups of slurry samples with different cutter head structures and rotation speeds. By analyzing the final slurry cake morphologies, it was found that the 10 groups formed similar slurry cake morphologies. In front of the center of the cutter head, the filter cake produced by the representative SL5 slurry was selected as the representative case.

As shown in Figure 13, when the cutter head stopped or rotated, a ‘filter cake plus an infiltration zone’ was formed with a clear boundary between the accumulation layer of the slurry particles and the stratum. As shown in Figure 13A,B, it is evident that when the CH1 and CH2 cutter heads stopped, the thickness of the filter cake was consistent—about 8 mm. As shown in Figure 13C–F, as the rotation speed increased continuously, the shapes of filter cakes constructed with two types of cutter head gradually transited from ‘filter cake plus a permeation zone’ to ‘a permeation zone without filter cake’, and the thickness of the filter cakes decreased gradually. Specifically, when the rotation speed increased to 0.5 rpm, the surface of the filter cake formed by the 5-cutter arm was smoother with a thickness of about 4 mm, while the 6-cutter arm cutter head formed a rougher filter cake surface with a thickness of about 3 mm, because the more cutter arms there were, the more times the stratum was cut within a certain time period and the thinner the filter cake became. As shown in Figure 13E,F, as the rotation speed increased, the thickness of the filter cake continued to decrease. The thicknesses of the filter cakes generated by the 5-cutter and 6-cutter arm were about 3 and 1 mm, respectively, because, under the combined functions of the cutter head cutting, slurry permeation, and air pressure, sand particles on the stratum surface were redistributed. The rotation of the cutter head destroyed the structure of the sand at the surface of the stratum, the thickness of the filter cake was thin, and the slurry particles completely penetrated the stratum pores. Based on the characteristics of the formed filter cake, it appears that the fewer cutter arms there were, the lower the permeability of the slurry film was, and the slower the speed of the cutter head was, making the set up more conducive to maintaining the stability of the shield excavation face.

As shown in

Table 3. Thickness of the Filter Cake (mm).

Slurry No.	Type of Cutter Head	Rotation Speed of the Cutter Head
		0 rpm	0.5 rpm	1.0 rpm
SL1	5 cutter arms	6	2	1
	6 cutter arms	6	2	1
SL2	5 cutter arms	6	3	2
	6 cutter arms	6	2	1
SL3	5 cutter arms	6	3	2
	6 cutter arms	6	2	1
SL4	5 cutter arms	7	3	3
	6 cutter arms	7	3	1
SL5	5 cutter arms	8	4	3
	6 cutter arms	8	3	1
SL6	5 cutter arms	5	2	1
	6 cutter arms	5	1	1
SL7	5 cutter arms	6	2	1
	6 cutter arms	6	2	1
SL8	5 cutter arms	6	3	2
	6 cutter arms	6	3	1
SL9	5 cutter arms	6	4	2
	6 cutter arms	6	3	1
SL10	5 cutter arms	9	5	3
	6 cutter arms	9	5	2

, as the rotating speed of the cutter head increased, the thickness of the filter cake decreased. The cutter arms of the cutter head increased, and the damage frequency of the filter cake increased, leading to a decrease in the filter cake thickness. After rotation of the cutter head, the average thickness of the static filter cake among the 10 groups of samples was 6.5 mm. The average thickness at 0.5 rpm was 2.85 mm, and the average thickness at 1.0 rpm was 1.55 mm. The filter cake thickness at 0.5 rpm was 56.15% lower than that at static speed. Moreover, the thickness at 1.0 rpm was 76.15% lower than that at static speed; that is, the thickness of the static filter cake was significantly lower than that of the static filter cake.

As shown in Figure 14, the cutter head was removed after the test. By observing the filter cake on the cutter head, a thin filter cake attached to the surface of the cutter head was identified. This occurred because the mixture of slurry and bentonite particles has a certain viscosity. This filter cake can be considered to be firmly adhered to the cutter head and is not affected by the cutting of the cutter head. The filter cake attached to the center of the cutter head was found to be thicker than that at other sites, as the center of the cutter head is relatively static relative to the soil, meaning there is less damage to the formed filter cake, and the filter cake formed at the center of the cutter head is more compact. While the filter cake at the edge of the cutter head is relatively thin due to the high linear speed, when the edge rotates, this greatly disturbs the formed filter cake.

The filter cake formed from the test was dried and scanned by an electron microscope. The filter cake was observed at the same position at different magnifications. It can be seen from Figure 15A (magnified 500 times) that the particles in the filter cake accumulated in a disorderly manner, the particles of the filter cake differed in size, the particles were neither spherical nor smooth, and the maximum particle size reached 35.54 μm. Various contact modes were observed, mostly edge to surface and surface to surface, with good connectivity between particles. Slurry particles filled the formation pores under water pressure, and the pores between large particles were gradually filled and compacted, with the maximum pore size being 12.51–16.35 μm. The fine particles in the slurry gradually accumulated into a thin, small particle layer. Although there were pores between the particles, most formed a dense filter cake structure, achieving the effect of impermeability. At high magnification, as shown in Figure 15B (magnified 10,000 times), the filter cake particles were established in a squamous structure, and the maximum pore size of the adjacent squamous structure was 1.38 μm. This was an open pore with discontinuity and poor connectivity.

4. Discussion

The experiment’s results show that the dynamic filter cake formation time is longer than that of the static filter cake (when the rotating speed of the cutter head is 0 rpm), which indicates the process of regeneration after the destruction of the filter cake. With an increase in the rotating speed of the cutter head, the conductivity of the soil increases, which indicates that the cutter head destroys the newly formed filter cake and soil, and the slurry particles penetrate a larger area. The filter cake is thinner than the static filter cake, which means that the newly formed filter cake is destroyed repeatedly, resulting in a reduction in thickness. Above all, the mesoscopic formation process of the dynamic filter cake can be divided into six stages, as shown in Figure 16: initial slurry permeation, large-scale permeation of slurry, the initial formation of the filter cake, the failure of the filter cake, deep permeation of slurry, and final formation of the filter cake.

Stage I: The initial porosity of the sand was relatively high when the cutter head stopped. Under the function of the effective slurry pressure, the slurry particles passed through the cutter head opening and continuously penetrated the stratum pores, as shown in Figure 16A.

Stage II: The cutter head started to rotate and cut sand particles from the stratum surface. The original sand structure was destroyed, and the pores increased and enlarged, resulting in a large number of slurry particles infiltrating and filling in the stratum, as shown in Figure 16B.

Stage III: With the continuous permeation of slurry particles, a large number were accumulated in the pores of the sand. Then, they aggregated and settled down gradually on the surface of the stratum to form a micro-permeable cake (filter cake Ⅰ), as shown in Figure 16C.

Stage Ⅳ: The cutter head rotated, and the newly formed filter cake structure was destroyed. Meanwhile, as the cutter head cut the sand particles, the structure of the sand was further destroyed, and the slurry particles in the stratum surface were mixed with sand particles, as shown in Figure 16D.

Stage V: The cutting of sand particles by the cutter head increased and enlarged the particle pores. Under the function of the effective slurry pressure, most of the slurry particles deeply penetrated the sand stratum in a larger area, and a small number of slurry particles stuck to the surface of the cutter head to form the inner filter cake (Figure 13). It should be noted that the new filter cake structure was not completely formed, as shown in Figure 16E.

Stage VI: As the slurry particles continuously penetrated the sand pores, when a large number of slurry particles accumulated in the pores of the damaged sand structure, slurry particles continued to settle on the surface, and the thickness of the slurry particles increased continuously, resulting in the formation of the outside of the filter cake (external filter cake). Then, the final filter cake (filter cake II) was formed together with the slurry particles, which initially attached to the cutter head panel (inner filter cake), as shown in Figure 16F.

With the continuous rotation of the cutter head, the ‘destruction–formation’ of the filter cake was repeated cyclically. From the perspective of the formation quality of the filter cake and the stability of the excavation face, a panel-type cutter head should be used to increase the area of a single cutter arm to reduce the damage done to the filter cake.

5. Conclusions

In this study, a series of pressure filtration tests were carried out with 10 different slurries and 2 types of cutter head, using a self-made dynamic filter cake permeation test device. The characteristics of the filter cakes of the slurry shield tunnels were studied. Previous studies ignored the impact of cutter head cutting on the filter cake and soil [40,41]. Through the test, it was found that this impact will increase the permeability and forming time of filter cake expand the slurry penetration distance. The rotation speed and structure of the cutter head significantly impact the characteristics and quality of the filter cake and can easily cause instability of the tunnel excavation surface. Therefore, in practical engineering, the cutter head speed should be adjusted reasonably, and the cutter head selection should be carried out in combination with the influence of filter cake formation. The following conclusions were obtained by conducting the dynamic slurry penetration test:

(1)

Considering the effect of the cutter head structure and rotation, the time curve of water filtration showed a stepped frame distribution, and the filtration volume increased rapidly in the early stage and gradually stabilized in the later stage of the test. The more cutter arms there were and the higher the rotation speed was, the greater the water filtration volume was, decreasing the impermeability of the filter cake.

(2)

The variation curve of electric conductivity can be divided into two parts: the descent stage and the stable stage. When the cutter head rotated at 1.0 rpm, the penetration distance of the slurry was 1.5 times that when the cutter head stopped. Moreover, the formation of filter cake with a 6-cutter arm occurred about 5 s later than with the 5-cutter arm.

(3)

As the rotation speed of the cutter head increased in saturated sand, the final form of the filter cake transited from a filter cake plus an infiltration zone to an infiltration zone without a filter cake, the thickness of the filter cake decreased continuously, and the filter cake’s permeability increased, which decreased the stability of the excavation face.

(4)

At the mesoscopic level, the dynamic formation process of the filter cake can be divided into six stages: the initial permeation of slurry particles, large-scale permeation after rotation of the cutter head, the initial formation of the filter cake, the failure of the filter cake, deep permeation of slurry, and the final formation of the filter cake.