Eco-Friendly Shield Muck-Incorporated Grouting Materials: Mix Optimization and Property Evaluation for Silty Clay Tunnel Construction

Abstract

As shield tunnels increase, managing shield muck strains construction and the environment. To mitigate this problem, shield muck replaced bentonite in silty clay to improve synchronous grouting slurry. Initially, the physical attributes and microstructural composition of shield muck were obtained, alongside an analysis of the effects of the muck content, particle size, and general influencing factors on the slurry properties through standardized tests and regression models. Subsequently, leveraging three-dimensional response surface methodology, admixture interactions and multiple factor impacts on the slurry were explored. Finally, utilizing the SQP optimization technique, an optimal slurry blend ratio tailored for actual project needs was derived for improved muck slurry. The findings reveal with the decreasing bleeding rates as the muck content rises, the particle size diminishes. An inverse relationship exists between the muck content and slurry fluidity. At soil–binder ratios below 0.6, a decrease in the soil–binder ratio intensifies the influence of the water–binder ratio on the slurry density, bleeding rate, and setting time. The fly flash–cement ratio inversely correlates with the slurry bleeding rate, while the ratio greater than 0.6 is positively correlated. For muck particle sizes under 0.2 mm, the fly flash–cement ratio inversely impacts the density, while over 0.2 mm, it correlates positively. The optimal proportion for silty clay stratum synchronous grouting slurry, substituting muck for bentonite, includes a water–binder ratio of 0.559, binder–sand ratio of 0.684, fly flash–cement ratio of 2.080, soil–binder ratio of 0.253, particle size under 0.075 mm, and water-reducing admixture of 0.06.

1. Introduction

Since the turn of the 21st century, subway construction has undergone rapid expansion, with the global operating mileage exceeding 21,745.16 km by 2023 [1]. Amidst this growth, the shield method has emerged as the preferred construction technique for subways, attributed to its efficiency, safety, and high mechanization levels. During shield tunneling, modifying shield muck is crucial to maintain the tunnel face pressure stability and enhance tunneling efficiency [2,3,4], resulting in substantial amounts of shield tunnel muck. In practical projects, the accumulation and transportation of this regulated muck pose significant environmental hazards and economic burdens [5,6,7,8], potentially triggering disasters like landslides [9]. Hence, proper disposal is imperative. Effective recycling of shield muck can mitigate these issues and promote sustainable resource development [6,10]. However, current utilization rates remain unsatisfactory. For instance, China annually produces approximately 119 million tons of shield muck, yet the actual effective utilization rate falls below 1% [11]. Consequently, exploring efficient utilization strategies for shield muck holds great significance.

The muck generated from shield construction, upon undergoing secondary treatment, can be versatilely applied in various fields, encompassing road base filling [12], structural concrete [13], controlled low-strength material (CLSM) [14,15,16,17], construction materials [18], concrete aggregates [19], unfired bricks [20,21], gardening soil amendment [22], and ceramsite production [23], among others. Although these treatments elevate muck utilization, they necessitate transporting the muck to designated facilities, thereby augmenting transportation expenses and environmental risks. The application potential for the direct utilization of silt in shield construction is extremely broad [8]. During shield tunneling, substantial synchronous grouting is necessary to manage stratum settlement, ensure tunnel structural stability, and improve waterproofing [24,25,26,27]. Notably, the muck discharged can undergo minimal treatment and be directly utilized as the base material for synchronous grouting, particularly in the form of single-phase slurries (typically comprising cement, bentonite, fly flash, sand, water, and additives). This approach streamlines the treatment process, significantly curtailing transportation and treatment costs. Moreover, implementing this scheme onsite negates the need for external muck transportation, offering operational convenience and economic benefits.

The focus of research on slurry performance enhancement through muck primarily revolves around sandy and clay muck. In sandy stratum, the shield excavation generates sandy muck, which often substitutes sand in synchronous grouting processes [28,29,30]. Conversely, when tunneling through clay stratum, clay muck typically replaces bentonite in the grouting mixture [31,32,33,34,35,36]. Several studies have examined the effects of slurry parameters like the ratio, content, injection quality, and diffusion time on slurry characteristics in clay stratum [34,37]. However, most of these studies isolate individual factors, neglecting that the performance of synchronous grouting slurry is a holistic outcome of intricate chemical interactions among mixed raw materials [38]. As a result, a comprehensive evaluation of slurry performance under multiple-factor interactions remains inadequate. Moreover, few practical project instances exist where clay stratum shield tunnel muck is reused in lieu of bentonite. Thus, to bolster the practicality and reliability of this substitution, further investigation is vital.

In this paper, based on a practical project, the project concerning the substitution of bentonite with silty clay and muck generated during shield tunneling as the raw material for simultaneous grouting slurry is investigated. Through homogeneous tests and regression analysis, the impact of individual factors like the muck content and particle size on the slurry performance is explored. Furthermore, response surface methodology is applied to assess the collective influence of multiple factors on the response outcomes. Utilizing the SQP (Sequential Quadratic Programming) optimization method, the study delves into how the muck content and particle size affect the slurry performance, ultimately identifying the optimal residue slurry mixture that fulfills the project specifications.

2. Test Design and Test Method

2.1. Test Material

The Jinan Yellow River Tunnel project, located in Jinan City, China, spans approximately 2.5 km and primarily utilizes the slurry pressure balanced shield tunneling method. The tunnel traverses primarily through silty clay strata with soil thicknesses varying from 11.2 m to 42.3 m, as shown in Figure 1. The tunnel segments feature an outer diameter of 15.20 m, an inner diameter of 13.90 m, a wall thickness of 0.65 m, and a width of 2 m. During construction of the shield tunnel, the excavated muck is conveyed from the shield machine to a pre-screening system via a distributor and muck discharge pump. Here, particles larger than 3 mm are separated. The remaining muck undergoes further processing in a cyclone desander, where muck material is screened and dehydrated before disposal. The finer muck below the screen flows into a slurry tank through a collection tank and undergoes additional two-stage swirl treatment. Subsequently, the slurry–water separation system isolates clay particles greater than 20 µm, which then undergo solid–liquid separation in press filtration equipment, resulting in muck with a moisture content below 30%. The overall muck treatment process is depicted in Figure 2.

2.1.1. Shield Muck

The physical property indices of the muck from the Yellow River Tunnel project are summarized in

Table 1. Physical properties of the shield muck.

Physical Parameter	Water Content	Density	Dry Density	Void Ratio	Saturation	Liquid Limit	Plastic Limit
Value	23.7%	1.95 g/cm3	1.58 g/cm3	41.6%	87.2%	32.5%	19.4%

. Before formulating the slurry, crucial preparatory steps include air-drying, breaking, and screening the shield muck, as illustrated in Figure 3. A comparative analysis of the material and chemical compositions of the shield muck and bentonite was conducted via XRD testing, as shown in Figure 4 and

Table 2. Chemical constituents of the shield muck.

Chemical Constituent	SiO2	Al2O3	Fe2O3	CaO	MgO	Na2O	K2O
Content	67.75%	12.79%	5.34%	6.42%	2.35%	1.74%	2.28%

. It was found that, to ensure tunnel face stability, a significant quantity of bentonite is injected during excavation, leading to a bentonite content in the shield muck comparable to that in the synchronous grouting slurry. Consequently, the shield muck can fully replace bentonite in the synchronous grouting slurry, enhancing its performance. The original slurry composition comprises 110.0 kg/m³ cement, 240.0 kg/m³ fly flash, 80.0 kg/m³ bentonite, 950.0 kg/m³ sand, 350.0 kg/m³ water, and 10.8 kg/m3 water-reducing admixture.

2.1.2. Cement

The P.O42.5 ordinary Portland cement employed in the testing meets the specified standards [39]. Its key properties include an initial setting time of 160 min and a final setting time of 222 min. The compressive strength, measured at 3 days and 28 days, was 27.5 MPa and 51 MPa, respectively. The detailed chemical composition of this cement is outlined in

Table 3. Chemical composition of cement.

Chemical Constituent	CaO	SiO2	Al2O3	Fe2O3	MgO	SO3	LOI
Content	65.81%	18.32%	1.72%	5.41%	3.48%	2.45%	<4%

.

2.1.3. Fly Flash

The fly flash utilized in the testing is of Class F, Grade I [40]. It possesses a density of 2.4 g/cm³, a bulk density of 0.896 g/cm³, and a standard consistency for the raw ash of 47%. Furthermore, its 28-day compressive strength ratio is 61%. The comprehensive chemical composition of this fly flash is documented in

Table 4. Chemical composition of fly flash.

Chemical Constituent	SiO2	Al2O3	Fe2O3	CaO	MgO	SO3	Na2O	K2O	LOI
Content	49.23%	30.17%	3.86%	5.41%	2.46%	3.00%	2.66%	1.28%	1.93%

.

2.1.4. Sand and Water

For the testing, river sand sourced from the fine sand region of Dongping Lake III zone in Tai ’an [41] was utilized, featuring a water content ranging between 15% and 18%. The groundwater served as the test water.

2.2. Test Process

The synchronous grouting slurry necessitates three key properties: fluidity, stability, and strength [42]. However, existing research [34] indicates the substantial impact of factors like the water–binder ratio (w/b), binder–sand ratio (b/s), fly flash–cement ratio (f/c), soil–binder ratio (so/b), water-reducing admixture (SPs), and muck particle size on these properties. Thus, based on 20 uniformity tests [43], the properties of the synchronous grouting slurry were evaluated under varying conditions of the w/b, b/s, f/c, so/b, SPs, and muck particle size. Notably, cementitious material encompasses both fly flash and cement. The water–binder ratio signifies the proportion of water to binding material, while the binder–sand ratio represents the ratio of binding material to sand. The fly flash–cement ratio denotes the proportion of fly flash to cement, and the soil–binder ratio is the ratio of muck to cementitious material. The content of the water-reducing agent is expressed as the ratio of water-reducing admixture to water. Prior to the tests, the ranges of these factors were established according to previous experience in grouting engineering, relevant specifications [44], existing research [32,34], and are presented in

Table 5. Factor-level table.

No.	Ratio Level	w/b	b/s	f/c	so/b	Particle Size	SPs
1	−2	0.6	0.5	1	0.2	0.5 mm–0.3 mm	0
2	−1	0.7	0.55	1.5	0.4	0.3 mm–0.1 mm	1.5%
3	0	0.8	0.6	2	0.6	0.1 mm–0.075 mm	3%
4	1	0.9	0.65	2.5	0.8	0.075 mm–0.0385 mm	4.5%
5	2	1	0.7	3	1.0	0.0385 mm–0 mm	6%

: water–binder ratio from 0.6 to 1.0, binder–sand ratio from 0.5 to 0.7, fly flash–cement ratio from 1.0 to 3.0, soil–binder ratio from 0.2 to 1.0, water-reducing admixture content from 0% to 6%, and muck particle size ranging from 0.5 mm to 0 mm. To guarantee test precision, avoid the effect of incomplete data on the results, and comprehensively capture the response surface, this paper delineates specific test points within these factor ranges, drawing upon existing studies [32,42].

The methods for determining the density, bleeding rate, consistency, fluidity, setting time, and strength of the slurry are as follows:

(1) Density: Pour the prepared slurry into a 250 mL graduated cylinder and allow it to settle, as shown in Figure 5a. Subsequently, measure the weight and volume of the slurry, thereby enabling the calculation of the slurry’s density.

(2) Bleeding rate: In accordance with relevant specifications [44], pour the prepared slurry into a 250 mL measuring cylinder and allow it to stand until all water precipitation from the slurry within the cylinder ceases [45], as depicted in Figure 5b. The bleeding rate is defined as the ratio of the final upper water film volume to the total slurry volume.

(3) Consistency: In accordance with relevant specifications [46], the mortar consistency tester (SC-145) was utilized to determine the slurry consistency, as shown in Figure 5c. Prior to the test, the slide rod was lubricated with oil, and both the conical container and test cone were wiped clean using a damp cloth. The slurry was then poured into the conical container in a single motion, followed by even tamping with the rammer from the center towards the edge for 25 times. The container was shaken 5 to 6 times to ensure a smooth slurry surface and positioned on the base. With the test cone’s tip adjusted to touch the slurry surface, the brake screw was released, and the starting time was noted. After 10 s, the cone’s descent indicated the slurry consistency, and the average of two readings was recorded as the final test result [47].

(4) Fluidity: In accordance with relevant specifications [48], the slurry fluidity was measured utilizing an apparatus of fluidity of cement mortar (NLD-3) employing the reciprocating flow table method, as shown in Figure 5d. Prior to the test, a damp cloth was used to clean the interior of the countertop, rammer, truncated round die, and set die, which were then positioned centrally on the skip table. The slurry was swiftly loaded into the truncated cone mold in two stages. Initially, two-thirds of the mold were filled, and the rammer was pressed 15 times, moving from the edge towards the center. Subsequently, the remaining slurry was added to slightly exceed the height of the test die, and the rammer was pressed another 10 times in the same manner. After removing the sleeve mold and trimming the excess slurry, the truncated cone mold was lifted vertically. The reciprocating flow table was activated for 25 beats, and the diameter of the slurry in two perpendicular directions was recorded. The average of these measurements was taken as the final result of the slurry flow test.

(5) Setting time: According to relevant specifications [46], the mortar setting time measuring instrument (ZKS-100) was utilized, as shown in Figure 5e. Prior to testing, a wet cloth was used to clean the interior of the container, and freshly prepared slurry was poured into the container, maintaining a 10 mm distance from the top. The slurry surface was leveled and covered for proper storage. During measurement, the container was positioned on the pressure gauge base, ensuring the penetration test needle touched the grout surface with a 25 mm depth. The pressure gauge reading was noted, and the setting time, ts (min), of the grout was determined as the time taken for the penetration resistance to reach 0.5 MPa. This test required the simultaneous recording of two samples, with an acceptable error margin of no more than 30 min between the results; exceeding this threshold necessitated a repeat of the determination.

(6) Slurry strength: According to relevant specifications [46], the compressive strength of five 70.7 mm × 70.7 mm × 70.7 mm cement mortar cube test blocks, as shown in Figure 5f, was measured using the compression testing machine (JYE-2000). This test was performed after 28 days of curing. During the test, the application of load progressed at a rate of 0.25 kN per second. When the test pressure data exhibited a downward trend instead of ascending, the peak pressure value recorded signified the failure load of the grout test block.

3. Analysis of Test Results

3.1. Test Results

Table 6. Slurry ratio test results.

No.	w/b	b/s	f/c	so/b	Particle Size	SPs	Sequence Combination	Density (g/cm3)	Setting Time (h)	Bleeding Rate	Fluidity (cm)	Consistency (cm)	Strength (MPa)
1	0.6	0.55	3	0.6	0.5–0.3	0.015	125,312	1.78	3.9	0.60%	12.5	4.78	2.07
2	0.7	0.6	1	0.4	0.0385–0	0.045	231,254	1.85	10.82	1.00%	21.94	11.25	3.54
3	0.8	0.65	2	0.8	0.075–0.0385	0	343,441	1.77	4.56	0.41%	13.23	6.75	2.49
4	0.9	0.7	1.5	0.2	0.3–0.1	0.03	452,123	1.65	22.25	7.45%	30	13.01	2.63
5	1	0.5	1	0.8	0.1–0.075	0.015	511,452	1.71	14.24	1.29%	22.82	12.2	1.66
6	0.6	0.55	2	1	0.3–0.1	0.06	123,525	1.73	1.58	0.00%	10	2.21	3.16
7	0.7	0.6	2.5	0.2	0.075–0.0385	0.015	234,142	1.70	22.28	1.82%	28.93	11.3	1.20
8	0.8	0.7	3	0.8	0.1–0.075	0.045	355,434	1.72	7.05	1.70%	14.41	8.14	1.25
9	0.9	0.5	1.5	0.2	0.1–0.075	0.06	412,135	1.62	34.89	6.48%	30	14.5	0.92
10	1	0.5	3	1	0.0385–0	0.03	515,553	1.72	6.35	0.64%	16.86	9.45	0.99
11	0.6	0.65	2.5	0.4	0.5–0.3	0.06	144,215	1.75	7.81	1.06%	21.75	10.75	1.99
12	0.7	0.7	1	0.6	0.5–0.3	0	251,311	1.79	6.93	0.50%	19.69	9.85	4.79
13	0.8	0.55	1.5	0.4	0.0385–0	0	322,251	1.69	17.13	2.27%	28.63	12.72	2.09
14	0.9	0.55	2.5	0.6	0.075–0.0385	0.045	424,344	1.69	12.09	1.58%	26.48	11.51	0.99
15	1	0.6	2.5	1	0.3–0.1	0	534,521	1.72	5.08	2.52%	16.63	9.52	1.36
16	0.6	0.65	1	1	0.075–0.0385	0.03	141,543	1.93	1.21	0.00%	10	2.32	3.70
17	0.7	0.5	2	0.4	0.3–0.1	0.03	213,223	1.78	12.28	1.29%	23	11.45	1.55
18	0.8	0.6	1.5	0.8	0.5–0.3	0.045	332,414	1.82	5.23	1.80%	19.46	8.05	2.20
19	0.9	0.65	3	0.2	0.1–0.075	0.015	445,132	1.65	28.22	3.18%	30	14.27	0.68
20	1	0.7	2	0.6	0.0385–0	0.06	553,355	1.65	16.04	0.53%	25.1	12.52	1.18

summarizes the uniform test results, where the sequence combination was obtained from Table 5, and the performance of the slurry is jointly governed by six factors: water–binder ratio (x₁), binder–sand ratio (x₂), fly flash–cement ratio (x₃), soil–binder ratio (x₄), particle size (x₅), and water-reducing admixture content (x₆). To analyze these relationships, a regression analysis was performed on the test data in Table 6 using the Scheffe second-order polynomial mix specification in SPSS software (SPSS Statistics 27.0.1), as outlined in Equation (1) through (6), where the particle size (x₅) was input as the average within a specific range. This approach enables an understanding of how the individual and interactive effects of these variables influence the performance of slurry.

$$f_n=B_0+{\sum }_{i=1}^m{B}_i{x}_i+{\sum }_{i=1}^m{B}_{ii}{x}_i^2+{\sum }_{i=1}^m{B}_{ij}{x}_i{x}_j$$

(1)

where f_n represents the response observed, encompassing properties such as the density, setting time, bleeding rate, consistency, fluidity, and strength. The coefficients B_i and B_ij correspond to the regression coefficients. B0 is the constant of the regression equation, while xi and xj denote the experimental factors.

Density:

$$\begin{gathered} f_1=2.268-0.762x_1^2+0.026x_3^2-0.109x_4^2-0.4x_3+0.342x_1{x}_3+ \\ 0.473x_1{x}_4-0.498x_2{x}_5-0.074x_3{x}_4+0.203x_3{x}_5 \end{gathered}$$

(2)

Bleeding rate:

$$\begin{gathered} f_2=-6.768+6.272x_4^2+18.366x_1-14.341x_5-2.434x_1{x}_3-20.317x_1{x}_4+ \\ 50.925x_1{x}_5-12.070x_2{x}_5+3.420x_3{x}_4-18.488x_4{x}_5 \end{gathered}$$

(3)

Fluidity:

$$\begin{gathered} f_3=26.617-1.771x_3^2-150.019x_6-25.359x_2{x}_4-5.55x_3{x}_4+8.929x_1{x}_3 \\ +85.372x_3{x}_6+6.514x_1{x}_4 \end{gathered}$$

(4)

Consistency:

$$\begin{gathered} f_4=16.920-0.926x_3-25.550x_4+23.256x_1{x}_4-1.335x_3{x}_4-99.789x_2{x}_6+ \\ 39.864x_3{x}_6 \end{gathered}$$

(5)

Setting time:

$$\begin{gathered} f_5=-2199.459+2714.710x_2^2+1040.001x_4^2+7119.275x_1- \\ 5283.061x_1{x}_2-3521.543x_1{x}_4 \end{gathered}$$

(6)

Slurry strength:

$$\begin{gathered} f_6=-2.429-3.916x_1^2+0.312x_3^2+14.007x_2+4.212x_4+4.067x_1{x}_2-4.359x_2{x}_3 \\ -8.091x_2{x}_4+0.688x_3{x}_4+0.703x_4{x}_5 \end{gathered}$$

(7)

The regression analysis outcomes are shown in

Table 7. Variance analysis and model validation of slurry regression model.

	Density	Setting Time	Bleeding Rate	Fluidity	Consistency	Strength
MS	0.033	3,235,534.279	24.512	195.477	359.354	14.575
SS	0.296	16,177,671.393	220.612	1172.859	2515.481	131.173
DF	9	5	9	6	7	9
R2	0.920	0.953	0.948	0.964	0.967	0.953
Adjusted R2	0.905	0.948	0.939	0.962	0.963	0.949
F value	63.727	216.872	101.825	416.272	220.845	249.961
p value	<0.0001	<0.0001	<0.0001	<0.0001	<0.0001	<0.0001
Significance	Significant	Significant	Significant	Significant	Significant	Significant

. Key metrics include MS for mean square, SS for sum of squares deviation from the mean, and DF for degree of freedom. An R2 nearing 1 signifies a superior fit, suggesting that the independent variable is better able to elucidate variations in the test results through the regression model [49]. Furthermore, the goodness of fit of the regression equation is assessed by the concordance between R2 and adjusted R2 values. A narrow gap between adjusted R2 and predicted R2 signifies the predictive significance of the model [50]. The F-test evaluates the statistical significance of the regression equation, with higher F-values and p-values below 0.05 indicating greater equation significance.

3.2. Single-Factor Analysis

The average value of each factor level was designated as the initial ratio to investigate the influence of a single-factor alteration on the performance of the slurry. Among them, the significance of each symbol has been provided in Section 2.2.

3.2.1. Density

Based on Equation (2), the relationship curve between each factor and slurry density is shown in Figure 6. It can be observed that among these factors, the binder–sand ratio and muck particle size exert the weakest influence on the slurry density. With the increase in the soil–binder ratio, that is, the increase in the muck content, the slurry density will increase significantly, but the significance will gradually diminish. Likewise, the slurry density escalates with the augmentation of the muck particle size. Conversely, an increase in the water–binder ratio, fly flash–cement ratio, or binder–sand ratio leads to a decrease in the slurry density, among which the water–binder ratio has the most pronounced effect on the slurry density.

3.2.2. Bleeding Rate

The curve depicting the relationship between each factor and the bleeding rate is shown in Figure 7. Notably, the soil–binder ratio and muck particle size significantly influence the bleeding rate, surpassing the impact of the water–binder ratio, binder–sand ratio, and fly flash–cement ratio, with the latter two having negligible effects. Specifically, the higher the ratio of soil–binder ratio, the greater the muck content, the smaller the muck particle size, and the lower the bleeding rate of the slurry. In other words, the stronger the adsorption capacity of the muck particles for water, the larger the specific surface area of the muck particles, the lower the bleeding rate of the slurry. However, when the muck particle size of the slurry is less than 0.075 mm, the bleeding rate of the slurry is no longer affected by the muck particle size. Additionally, as the water–binder ratio increases and the fly flash–cement ratio increases, and the binder–sand ratio decreases, the bleeding rate of the slurry decreases.

3.2.3. Fluidity

Based on Equation (4), the relationship curve between each factor and fluidity is shown in Figure 8. It can be observed that the influence of the muck size on the slurry fluidity is negligible. In contrast, the soil–binder ratio exerts a more substantial influence on the slurry fluidity compared to the water–binder ratio, binder–sand ratio, fly flash–cement ratio, and water-reducing admixture content. As the soil–binder ratio and, consequently, muck content rise, the slurry fluidity diminishes, aligning with the observations by Zhou et al. [28]. In essence, the viscosity of soil in the muck, larger relative surface area of clay particles, and their enhanced water adsorption capacity [31,51], coupled with the angular and rough surface of silty clay particles [52], contribute to reduced slurry fluidity. A decrease in the water–binder ratio and water-reducing admixture content, and an increase in the binder–sand ratio, leads to a decline in the slurry flow rate. Additionally, as the fly flash–cement ratio increases, the slurry fluidity initially improves but subsequently declines.

3.2.4. Consistency

Based on Equation (5), the relationship curve among various factors and the slurry consistency is shown in Figure 9. It should be noted that the absence of the slurry particle size in Equation (5) indicates that its influence on the slurry consistency can be overlooked. The soil–binder ratio exerts a more significant impact on the slurry consistency than the water–binder ratio, water-reducing admixture content, fly flash–cement ratio, and binder–sand ratio. As the soil–binder ratio and muck content increase, the slurry fluidity decreases, directly affecting the consistency, which is tied to the free water content in the slurry. The silty clay in the muck adsorbs substantial water molecules, reducing free water and notably decreasing the slurry consistency. Other factors, such as the water–binder ratio and water-reducing admixture content positively correlate with the slurry consistency, while the binder–sand ratio negatively correlates with the fly flash–cement ratio. Additionally, the slurry consistency enhances as the water-reducing admixture content increases.

3.2.5. Setting Time

Based on Equation (6), the relationship curve among various factors and the slurry setting time is shown in Figure 10. Notably, Equation (6) considers only the water–binder ratio, binder–sand ratio, and soil–binder ratio, suggesting that the influence of other factors on the slurry setting time can be neglected [53,54]. The soil–binder ratio has a more pronounced effect on the slurry setting time compared to the water–binder ratio and binder–sand ratio. As the soil–binder ratio and muck content increase, the slurry setting time significantly decreases due to the clay in the muck’s enhanced ability to bind water molecules [31,51], bringing the slurry closer to a solid state and shortening its setting time. An increase in the water–binder ratio prolongs the slurry setting time, while a slight decrease is observed with an increase in the binder–sand ratio. The larger the water–binder ratio, the better the flowability of the slurry, the more water molecules in the slurry, and the longer the slurry setting time.

3.2.6. Compressive Strength

Based on Equation (7), the relationship curve among various factors and the slurry compressive strength is shown in Figure 11. The fly flash–cement ratio exerts a more significant influence on the slurry compressive strength than the water–binder ratio, soil–binder ratio, binder–sand ratio, and particle size. As the soil–binder ratio, or muck content, increases, so does the slurry compressive strength. On one hand, the increase in the slurry compressive strength can be attributed to the addition of residuum, which provides more fine aggregate for the slurry, thereby increasing the uniformity and segregation degree of the slurry. On the other hand, the silty clay in the muck can offer more cohesion to the slurry mixture than the bentonite [36]. Compared to the muck content, the muck particle size has a relatively minor impact on the compressive strength. Regarding other factors, the slurry compressive strength augments with an increase in the binder–sand ratio but diminishes with higher water–binder and fly flash–cement ratios. Notably, due to the pozzolanic reaction of cement, the increase in the cement ratio can significantly enhance the slurry compressive strength [51].

3.3. Response Surface Analysis

Employing the response surface method, the influence of various factors on the response outcomes within a defined range is mirrored through the deformation of the response surface and contour trends. When multiple factors concurrently affect the test results, and these factors exhibit interactive effects, this methodology effectively obtains their impacts [55]. In this section, the response surface is utilized to visualize the effect of the interplay between two factors on the ultimate outcome amidst multiple influencing factors in the experimental setting. It is necessary to substitute the mean values of the remaining factors’ levels other than the factors to be analyzed into the objective equation, effectively minimizing the independent variables [34,42,56]. For example, Equation (8) is obtained by substituting into Equation (2) the average values from Table 6 for all variables except x₁ and x₄, which are the variables under analysis.

3.3.1. The Interaction Effect of Multiple Factors on Slurry Density

The interplay of multiple factors on the slurry density is shown in Figure 12. Based on the contour line trend in Figure 12a, the sequence of the influence of various factors on the slurry fluidity is as follows: fly flash–cement ratio > water–binder ratio > soil–binder ratio > particle size > binder–sand ratio. As seen in Figure 12b–e, the response surface undergoes distortion, and the fly flash–cement ratio and the soil–binder ratio have a certain interaction effect on the density of grouting slurry. Further, more significant interactive impacts are observed between the fly flash–cement ratio and particle size, soil–binder ratio and water–binder ratio, and fly flash–cement ratio and particle size, respectively. Figure 12b and Equation (8) indicate that as the muck content decreases, the influence of the water–binder on the density intensifies. When the soil–binder ratio falls below 0.6, the water–binder ratio’s effect becomes more pronounced, and its linear relationship with the density strengthens as the soil–binder ratio diminishes. From Figure 12c and Equation (9), it is evident that reduced muck content diminishes the powder-to-ash ratio’s impact on the density. Figure 12d and Equation (10) reveal that for particle sizes below 0.2 mm, the fly flash–cement ratio inversely correlates with the slurry density, following an approximately parabolic curve. Conversely, for sizes exceeding 0.2 mm, a direct proportionality exists, also adhering to a parabolic trend. Lastly, Figure 12e and Equation (11) show that larger particle sizes amplify the influence of the binder–sand ratio on the density, with a linearly inverse proportional relationship.

$$f_{11}=-0.762x_1^2-0.109x_4^2+0.684x_1-0.148x_4+0.473x_1{x}_4+1.581$$

(8)

$$f_{12}=0.026x_3^2-0.109x_4^2-0.109x_3+0.3784x_4-0.074x_3{x}_4+1.754$$

(9)

$$f_{13}=0.026x_3^2-0.171x_3-0.299x_5+0.203x_3{x}_5+1.968$$

(10)

$$f_{14}=0.406x_5-0.498x_2{x}_5+1.809$$

(11)

3.3.2. The Interaction Effect of Multiple Factors on Slurry Bleeding Rate

The interactive effects of multiple factors on the slurry bleeding rate are shown in Figure 13. Following the contour line trend in Figure 13a, the sequence of the influence of various factors on the slurry fluidity is as follows: water–binder ratio > soil–binder ratio > particle size > binder–sand ratio = fly flash–cement ratio. As depicted in Figure 13b–e, significant interactions exist between the water–binder and soil–binder ratios, fly flash–cement and soil–binder ratios, and water–binder and particle size, as well as soil–binder and particle size, all of which modulate the slurry bleeding. It is evident that the muck content and muck particle size exert substantial independent effects on the bleeding rate, while also interacting with each other and other factors. When the soil–binder ratio is high, the impact of the water–binder ratio on the bleeding is minor. However, when the soil–binder ratio falls below 0.6, the water–binder ratio’s impact becomes more significant, displaying a near-linear relationship, as shown in Figure 13b and Equation (12). Additionally, the fly flash–cement ratio inversely correlates with the slurry bleeding rate when the soil–binder ratio is less than 0.6, and directly correlates when it exceeds 0.6, as illustrated in Figure 13c and Equation (13). The water–binder ratio’s influence on the bleeding intensifies with larger particle sizes, exhibiting a linear relationship. Higher water–binder ratios result in higher bleeding rates, as demonstrated in Figure 13d and Equation (14). When the particle size is greater than 0.3 mm and the soil–cement ratio is less than 0.4, the response surface is extremely steep, and the change in the particle size and soil–cement ratio can more significantly affect the slurry bleeding rate. Furthermore, in scenarios where the particle size exceeds 0.3 mm and the soil–cement ratio is below 0.4, the response surface steepens significantly, enhancing the sensitivity of the bleeding rate to changes in the particle size and soil–cement ratio. Smaller particle sizes and larger soil–cement ratios result in lower bleeding rates, as demonstrated in Figure 13e and Equation (15).

$$f_{21}=6.272x_4^2+17.954x_1+5.222x_4-20.317x_1{x}_4-8.657$$

(12)

$$f_{22}=6.272x_4^2-17.871x_4-1.947x_3+3.420x_3{x}_4+9.521$$

(13)

$$f_{23}=1.208x_1-32.676x_5+50.925x_1{x}_5-0.406$$

(14)

$$f_{24}=6.272x_4^2+19.157x_5-9.414x_4-18.488x_4{x}_5+3.95$$

(15)

3.3.3. The Interaction Effect of Multiple Factors on Slurry Fluidity

The interactive effects of multiple factors on the slurry fluidity are shown in Figure 14. Based on the trend of the contour line in Figure 14a, the sequence of the influence of various factors on the slurry fluidity is as follows: soil–binder ratio > water–binder ratio > binder–sand ratio > fly flash–cement ratio = water-reducing admixture. As shown in Figure 14b–e, all the response surfaces are curved. For Figure 14b, the response surfaces are less warped, and the contour curvature is smaller. Regarding Figure 14c and Equation (17), although the contours are curved, the response surface is not distorted. According to the regression model of the powder to ash ratio and fluidity, the contours are curved due to the type of function. The response surface is significantly distorted, and the contour curvature is large, as shown in Figure 14d,e. Thus, it can be observed that the water–binder ratio and fly flash–cement ratio, as well as the fly flash–cement ratio and water-reducing admixture, exhibit a pronounced interactive effect on the slurry fluidity, as shown in Equations (18) and (19). While the soil–binder ratio significantly impacts the slurry fluidity, its interaction with other factors is minimal, as shown in Figure 14b and Equation (16). Additionally, the influence of the muck particle size on the slurry fluidity can be considered negligible.

$$f_{31}=22.116-1.771x_3^2-10.004x_4-5.55x_3{x}_4+9.704x_3$$

(16)

$$f_{32}=25.243-1.771x_3^2-15.215x_2+6.374x_3$$

(17)

$$f_{33}=29.287-1.771x_3^2-150.019x_6+3.813x_3+85.372x_3{x}_6$$

(18)

$$f_{34}=12.987-1.771x_3^2-0.769x_3+8.929x_1{x}_3+3.908x_1$$

(19)

3.3.4. The Interaction Effect of Multiple Factors on Slurry Consistency

The interactive effects of multiple factors on the slurry consistency are shown in Figure 15. In accordance with the trend of the contour line in Figure 15a, the order of influence of multiple factors on the slurry consistency is as follows: soil–cement ratio > water–cement ratio > fly flash–cement ratio = water-reducing admixture > binder–sand ratio. As illustrated in Figure 15b,c, the response surface is distorted, and Figure 15b features greater plane distortion and a larger contour curvature. Notably, the binder–sand ratio and water-reducing admixture exhibit a certain interactive effect on the slurry consistency. The fly flash–cement ratio and water-reducing admixture, however, demonstrate a more significant interactive impact. Analogous to the slurry fluidity, while the soil–cement ratio significantly affects the slurry consistency, its interaction with other factors is minimal. Additionally, the influence of the muck particle size on the slurry consistency can be disregarded.

$$f_{41}=12.753-1.727x_3-59.873x_6+39.864x_3{x}_6$$

(20)

$$f_{42}=9.299-99.789x_2{x}_6+79.728x_6$$

(21)

3.3.5. The Interaction Effect of Multiple Factors on Slurry Setting Time

The interactive effects of multiple factors on the slurry setting time are depicted in Figure 16. As can be observed from the trend of the contour line in Figure 16a, the sequence of the influence of various factors on the slurry setting time is as follows: soil–binder ratio > water–binder ratio > binder–sand ratio. The response surface is distorted, indicating an interaction between the water–binder ratio and soil–binder ratio, as shown in Figure 16b and Equation (23). Specifically, the smaller the slurry content, the more pronounced the influence of the water–binder ratio becomes, as shown in Figure 16b. When the soil–binder ratio dips below 0.6, the water–binder ratio linearly positively correlates with the setting time. Conversely, above a soil–binder ratio of 0.6, the response surface flattens, indicating a reduced influence of the water–binder ratio on the slurry setting time.

$$f_{51}=-1227.163+1040.001x_4^2+3949.438x_1-3521.543x_1{x}_4$$

(22)

$$f_{52}=-1825.059+2714.710x_2^2+5006.3492x_1-5283.061x_1{x}_2$$

(23)

$$f_{53}=3495.961+2714.710x_2^2+1040.001x_4^2-4226.449x_2-2817.234x_4$$

(24)

3.3.6. The Interaction Effect of Multiple Factors on Slurry Compressive Strength

The interactive effects of multiple factors on the slurry compressive strength are presented in Figure 17. According to the trend of the contour line in Figure 17a, the order of influence of multiple factors on the slurry compressive strength is as follows: fly flash–cement ratio > water–binder ratio > binder–sand ratio = soil–binder ratio > particle size. Figure 17b,c exhibit pronounced distortions and curved contours in the response surfaces, indicating a simultaneous interplay between the binder–sand ratio with both the fly flash–cement ratio and soil–binder ratio on the slurry strength. It can be noted that the muck content and the muck particle size not only have a relatively minor influence on the slurry, but also the interaction between them is not prominent.

$$f_{61}=-2.371+0.312x_3^2+12.406x_2-4.359x_2{x}_3+0.413x_3$$

(25)

$$f_{62}=-3.687+8.543x_2+5.650x_4-8.091x_2{x}_4$$

(26)

4. Optimize the Proportion of the Slurry for Synchronous Grouting

Given that the mixing location of synchronous grouting slurry is distant from the actual grouting position in the shield tunnel, the slurry must exhibit exceptional pumpability, characterized by superior flow properties and stability. Additionally, the solidification time of the slurry needs to be commensurate with the tunneling speed of the shield, while maintaining adequate strength as the grouting material. To address the multi-faceted requirements of the slurry, the SQP optimization method from the MATLAB optimization toolbox is utilized to determine the optimal mix ratio for the synchronous grouting slurry.

During the implementation of the SQP optimization approach, firstly, the target range for indices like the slurry density is initially set based on pertinent specifications and practical engineering requirements, functioning as a constraint to bound the output values. Subsequently, Equations (2)–(7) are incorporated into a unified objective function, each weighted appropriately, converting the problem from multi-objective to single-objective optimization. Finally, by entering the constraints on independent variables, grout index constraints, and the resulting objective function into MATLAB’s optimization toolbox, the optimal grout ratio is derived.

4.1. Model Constrained

The constraints of the model are established based on the performance indices of the slurry and the defined range of its influencing factors. Adhering to the relevant specifications [44] and the specific construction demands for the Jinan Yellow River Tunnel, the following provisions are enacted:

(1) To guarantee the pumpability of the slurry, the initial flow of the slurry ought to exceed 16.0 cm. However, since excessive flow would decrease the stability of the slurry, the flow should be considered to be less than 25.0 cm.

(2) The consistency of the slurry is 10.0 cm~13.0 cm.

(3) The slurry setting time should match the speed of the shield tunneling, and the setting time is 360 min~720 min.

(4) The rate of serous fluid bleeding should be no more than 5%.

(5) The 28-day slurry compressive strength is required to exceed 2.5 MPa.

(6) Constraints of influencing factors: 0.6 < x₁ < 1, 0.5 < x₂ < 0.7, 1 < x₃ < 3, 0.2 < x₄ < 1, 0 < x₅ < 0.5, 0 < x₆ < 0.06.

4.2. Objective Function

Given the constraints imposed by the performance indicators and influencing factors of the synchronous grouting slurry, considerations include the minimum slurry density, the minimum bleeding rate, the maximum flow performance, the shortest setting time, and the maximum 28-day compressive strength. To achieve the optimal balance, Equations (2)–(7) are formulated to attain their extreme values within these constraints, specifically f_1min, f_2min, f_3max, f_4max, f_5max, and f_6max.

4.3. Solving Model

Utilizing the SQP optimization method from the MATLAB optimization toolbox, the optimal mix ratio of the slurry was determined based on the model constraints and objective functions outlined in Section 4.1 and Section 4.2. It should be noted that considering the difficulty of reducing the muck particle size to the optimal particle size of 0 mm in actual engineering, along with the particle size standard of bentonite [57] and the test results, it can be observed that the slurry bleeding rate stabilizes when the muck particle size is less than 0.075 mm. Consequently, the optimized parameters are as follows: water–binder ratio of 0.559, binder–sand ratio of 0.684, fly flash–cement ratio of 2.08, soil–binder ratio of 0.253, particle size < 0.075 mm, and water-reducing admixture of 0.06. The actual optimal dosages for the raw materials of slurry in this project are as follows: cement 176.52 kg/m³, fly flash 367.16 kg/m³, muck 137.55 kg/m³, sand 794.85 kg/m³, water 303.92 kg/m³, and water-reducing admixture 18.24 kg/m³, with the muck particle size kept below 0.075 mm. Drawing on relevant research [36,56,58], the actual optimal dosages for the raw materials of slurry in this project align with the typical ranges observed in synchronous grouting operations within silty clay environments, suggesting the applicability of the methodology presented herein to a wide range of conditions encountered in silty clay shield tunneling projects.

4.4. Result Verification

The optimal slurry ratio obtained by the model was experimentally verified and compared with the predicted value, as shown in

Table 8. The optimal proportion slurry performance.

	Density (g/cm3)	Setting Time (h)	Bleeding Rate	Fluidity (cm)	Consistency (cm)
Model results	1.73	600.00	0	24.61	12.00
Test results	1.70	534.07	1.2	25.23	13.12

. Additionally, the slurry properties can satisfy the construction requirements of the relevant specifications [44] and actual projects.

5. Discussion

During shield tunnel construction, muck accumulation and disposal inevitably lead to land occupation and environmental pollution. On the other hand, bentonite, a vital raw material for synchronous grouting slurry, entails significant costs in preparation and transportation. By replacing bentonite with the muck from shield construction, resource recycling is achieved, minimizing waste, and substantially lowering the cost of synchronous grouting. This approach fosters environmental protection and sustainable development. The present study investigates the influence of the soil content, particle size, and various other factors on the slurry properties of the new grouting material, used in lieu of bentonite, in silty clay strata shield tunnels. An optimal grout ratio that meets practical engineering demands has been identified, demonstrating its clear practical applicability.

In this study, XRD analysis revealed the physical attributes and microstructural composition of the muck. The impact of multiple variables on the slurry performance was systematically evaluated through standardized tests and regression models, and three-dimensional response surface methodology, achieving an optimal slurry mix ratio via the SQP optimization approach. However, the derived slurry optimal ratio is project-specific and not directly transferable to other similar endeavors without first conducting field tests adhering to the methodology herein. Moreover, this method is tailored for synchronous grouting in the construction of general silty clay tunnels to control shield tunnel segment floating. For distinct deformation control demands in actual projects, the optimal slurry proportion necessitates re-evaluation. For instance, proximity to existing pipelines necessitates tighter control over segment floating and subsequent formation deformation. Additionally, the applicability of this method may be limited in certain strata or under special engineering constraints. For example, in strata where synchronous grouting material fails to readily harden around the tunnel lining, a shorter setting time and early-stage strength slurry may be required [42]. Thus, in scenarios involving intricate geological conditions or precise formation deformation control demands, conducting tests adhering to the present methodology becomes imperative to ascertain the optimal slurry ratio.

6. Conclusions

In silty clay, the feasibility of substituting slurry pressure balanced shield muck for bentonite in single slurry synchronous grouting was explored via uniform tests, regression, and 3D response surface analysis. The effects of the water–binder, fly flash–cement, binder–sand, soil–binder ratios, and water-reducing admixture content on the slurry performance were systematically analyzed. The optimal slurry ratio for a slurry pressure balanced shield in silty clay formation was determined. The conclusions are as follows:

(1) Considering the chemical similarity between shield muck and bentonite, refined shield muck particles can substitute bentonite in silty clay synchronous grouting, reducing transportation needs, maximizing resource utilization, and saving costs. The optimized slurry mixture ratio comprises water–binder (0.559), binder–sand (0.684), fly flash–cement (2.080), soil–binder (0.253) ratios, a particle size < 0.075 mm, and water-reducing admixture (0.06).

(2) The muck content and particle size significantly affect the slurry properties. A higher muck content reduces the bleeding rate, fluidity, and consistency. A smaller particle size also decreases the bleeding rate. When the muck particle size is less than 0.075 mm, it tends to stabilize slurry gradually.

(3) Below a soil–binder ratio of 0.6, the water–binder ratio’s impact on the slurry density, bleeding rate, and setting time intensifies inversely. The fly flash–cement ratio inversely correlates with a bleeding rate below 0.6, shifting to a positive correlation above. Larger muck particles amplify the water–binder ratio’s effect on the bleeding and the binder–sand ratio’s on the density. The fly flash–cement ratio inversely correlates with the density for a <0.2 mm particle size, directly for >0.2 mm.