Special Cement-Based Grouting Material for Subway Structure Repair During Operation Performance Sensitivity Analysis

Abstract

This study uses ordinary Portland–sulfate–silicate composite cement as the matrix and investigates the effects of water–cement ratio, HPMC dosage, and PCS dosage on the performance of specialized grouting materials for subway structure repair during operation through single-factor experiments and orthogonal experiments. Multifactorial variance analysis was employed to quantitatively evaluate the sensitivity of each factor and their interactions to slurry flowability, setting time, anti-dispersibility, and compressive strength. The results show that the water–cement ratio is the most critical factor affecting the performance of the grouting material, with extremely significant impacts on all performance indicators; HPMC dosage significantly affects flowability, setting time, and anti-dispersibility; PCS dosage primarily influences 2 h compressive strength; the interaction between water–cement ratio and HPMC dosage has a significant impact on anti-dispersibility. Principal component analysis revealed the trade-off relationship between flowability, setting time, and strength. The study established a sensitivity ranking for the performance of specialized grouting materials: water–cement ratio > HPMC dosage > PCS dosage > interaction, providing a theoretical basis and methodological reference for the formulation optimization of specialized grouting materials for subway structure repair during operation.

1. Introduction

The subway structure is prone to structural defects such as cracking, leakage, and deformation due to the combined effects of material degradation, hydrogeological changes, and periodic train vibrations over long-term service. Grouting, as a mainstream repair technique, hinges on the compatibility of material properties. However, conventional grouting materials suffer from issues like poor resistance to dispersion, slow setting rates, and low early strength, making them inadequate for the stringent requirements of tunnel repairs during operation: (1) dynamic water environments lead to low slurry retention; (2) short time windows during maintenance periods demand rapid material curing; (3) train vibrations can easily cause damage to the slurry–structure interface. There is an urgent need to develop specialized grouting materials for operational tunnels that combine high fluidity, resistance to dispersion, rapid setting and early strength, cost-effectiveness, and durability.

1.1. Research Progress on the Optimization of Grouting Material Properties

In recent years, significant progress has been made in the research of rheological control and mechanical enhancement mechanisms of cement-based grouting materials. In rheological property optimization, Lin et al. [1] introduced polycarboxylate-based superplasticizer (PCS), which greatly enhanced the rheological properties of the slurry. Its shear-thinning effect allows the slurry to maintain high viscosity under low shear rates to resist dynamic water scouring, while reducing viscosity under pumping shear for long-distance spread. Song Guozhuang et al. [2] found that the combination of sodium aluminate (SA) and superabsorbent polymer (SAP) can optimize the viscosity-time curve of the slurry. However, when the content of SA exceeds 1.5 wt% and SAP exceeds 0.3 wt%, the fluidity of the slurry will be lost. In contrast, the addition of PCS (0.3–0.6 wt%) improves the dispersion stability of the slurry through steric hindrance effects. He Yan et al. [3] developed a C-S-Hs-PCS nanomodifier, which breaks the performance bottleneck of traditional admixtures. It enhances the rheological properties of the slurry (increasing initial fluidity by 23%) and hydration kinetics (reducing induction period by 40%), increasing the 1-day compressive strength to 18.5 MPa. This offers a new approach for short-window-period repair. In improving anti-dispersion properties, flocculant molecular weight regulation and organic-inorganic synergistic effects have become research hotspots. Zhang Ming et al. [4] revealed, through molecular dynamics simulations, that anionic polyacrylamide (APAM) with a molecular weight of 6–10 million can enhance cement particle sedimentation through bridging effects. When the content of APAM is between 0.2–0.4 wt%, the dynamic water retention rate increases to over 85%. Guo Chuan et al. [5] used hydroxypropyl methyl cellulose (HPMC) to modify the silicate–sulfoaluminate composite system. It was found that for every 0.05% increase in HPMC content, the initial viscosity increases exponentially (R² = 0.97). Moreover, the synergistic effect of HPMC with a polyether defoamer can inhibit slurry segregation (water bleeding rate < 1.5%). Liu Xiangsheng et al. [6] proposed a ternary composite system of HPMC/SP/defoamer, which extends the anti-dispersion time of the slurry under a flow rate of 2.5 m/s to 15 min. This is three times longer than that of the reference group.

1.2. Development and Limitations of Multi-Factor Optimization Methods

Orthogonal experimental design has become the preferred method for multi-factor optimization of materials because of its efficiency and scientificity. This method constructs partial factor experiments through orthogonal table and analyzes main and secondary factors and interaction effects by using range analysis and variance analysis [7]. Li Fuhai et al. [8] investigated the five performance indexes of sulfoaluminate cement-based materials using an L9(34) orthogonal table and found that the weight of 1 d strength affected by the dosage of accelerator was 62% (p < 0.01). Huang Guodong et al. [9] quantified the significant influence of expansive agents on concrete durability by F test (F value = 9.32, p = 0.003) and verified the reliability of the orthogonal test in significant discrimination. It is worth noting that Yao Weijing et al. [10] innovatively coupled the response surface model with the orthogonal design to establish a quadratic regression model between straw mixing (VS) and compressive strength (R² = 0.934), an approach that significantly improved the prediction accuracy of parameters [11]. The use of orthogonal experiment to analyze a new method, called the second-order statistical method, has promoted the wide use and development of statistical methods. Zhou Yuzhu [12] used the matrix analysis method of the orthogonal test to calculate the weight of each factor on the test results. Li Huanhuan [13]. Guo Xinmei believes that the orthogonal test method has the advantages of convenient design, fewer test times, balanced and neat layout, intuitive and easy analysis of results, and low requirements for the continuity of variables [14]. The text elaborates on key points of orthogonal experimental application, including the selection of indicators, factors, and levels, as well as the proper setting of interaction columns and empty columns between factors. Due to the representative nature of the experimental points in orthogonal design, the small number of experiments required, and the ability to estimate errors without repeated trials, along with the availability of various statistical methods for processing experimental results, orthogonal experiments are widely used in material formulation, performance analysis, and sensitivity analysis.

Despite breakthroughs in material modification and experimental design methods, there are still research gaps concerning the special working conditions of grouting for subway tunnels (such as train vibration-dynamic water coupling effects and time window restrictions of less than 3 h): (1) existing material performance indicators (such as anti-dispersion tests) are mostly based on static or low-flow-rate conditions, lacking a performance evaluation system under vibration-dynamic water coupling effects; (2) the competitive relationships among various performance indicators during multi-objective optimization (such as the negative correlation between flowability and anti-dispersion) have not been quantitatively modeled; (3) although conventional orthogonal design methods are widely used, the analysis of higher-order interaction effects remains insufficient.

Based on this, the study uses ordinary Portland–sulfate–silicate composite cement as the matrix and analyzes the effects of water–cement ratio, superplasticizer dosage, and hydroxypropyl methylcellulose ether dosage on slurry rheology, setting time, and mechanical properties through single-factor experiments. Subsequently, orthogonal experimental design is employed, combined with exploratory data analysis (EDA) and ANOVA variance analysis, to reveal the response mechanisms of material properties under multi-factor coupling effects. This research can provide theoretical support and methodological references for the design of grouting materials in complex environments.

2. Performance Design of Special Cement-Based Grouting Material for Subway Structure Repair During Operation

During the operation period, subway structure repair construction has characteristics such as a short construction window period, train vibration, and dynamic water influence. Therefore, special cement-based materials should be specifically designed according to their characteristics. The time allocation of the skylight for the management of the subway structure during the operation period is shown in Figure 1. The specific performance design is as follows:

• Flow design: In order to make the grouting material more injectable, diffusive, and permeable, a higher slurry flow is preferred;
• Anti-dispersibility design: In order to improve the anti-dispersibility and dynamic water retention rate of the slurry, the content of suspended solids in the slurry should be less than 150 mg/L, and the pH value should be less than 12. However, the lower the content of suspended solids, the poorer the fluidity of the slurry. Therefore, this property contradicts the first property, and a comprehensive consideration should be given during material preparation;
• Curing time design: Generally, during the operation period of subway structures, continuous operations are required, so the curing window is very short. Typically, construction hours are from 12:30 PM to 3:30 AM the next day. Excluding preparation work and grouting time, the time from injection to initial setting should be controlled within 2 h. After removing the setting time, the final setting time of the grouting material should be controlled within 90 min, and the initial setting time should be no less than 30 min (too short a time may lead to pump blockage);
• Strength design: Since the subway structure is greatly affected by train vibration during operation, it has been shown that low-amplitude, high-frequency vibrations from trains significantly impact grouting materials with early strength less than 5 MPa. Therefore, the strength of the grout should not be less than 5 MPa before train operation, that is, the 2 h strength should be at least greater than 5 MPa.

Figure 1. Metro structure management during the operation period.

Figure 1. Metro structure management during the operation period.

3. Materials and Experimental Methods

3.1. Test Raw Materials

P.O.42.5 Portland cement, produced by Jidong Dunshi Brand, and R.SAC.42.5 fast-setting sulfoaluminate cement, produced by Tangshan Polar Bear Building Materials, were used as binders. The main mineral composition of the cement is presented in

Table 1. Main mineral composition of ordinary Portland cement (P.O42.5).

C3S/%	C2S/%	C3A/%	C4AF/%	f-CaO/%
51.06	22.92	15.87	10.26	1.44

and

Table 2. Main mineral composition of rapid hardening sulfoaluminate cement (R·SAC 42.5).

C4A3S/%	C2S/%	C2F/%	CaSO4/%
36.19	32.16	15.28	16.85

. Polycarboxylic acid water reducer (PCS), sodium gluconate (SG), and hydroxypropyl methylcellulose (HPMC) with 60,000 Pa·s viscosity were used as admixtures.

Additives: polycarboxylate superplasticizer (PCS), sodium gluconate (SG), hydroxypropyl methylcellulose (HPMC), viscosity 60,000 Pa·s.

3.2. Experimental Design

Among them, the fresh cement mortar containing 0.45% HPMC by cement content and 1% polycarboxylate superplasticizer (water–cement ratio is 0.5, mortar mass ratio is 2) shows excellent anti-dispersibility and good fluidity.

In this paper, the single-factor test method and multi-factor orthogonal test method are combined. The base material gelatin system is set as R·SAC:P.O = 7:3 (mass ratio), and sodium gluconate is 0.1%. By changing the water–cement ratio to 0.3 (ID represents W1), 0.4 (ID represents W2), and 0.45 (ID represents W3), the PCS dosage to 0.25% (ID represents P1), 0.3% (ID represents P2), and 0.4% (ID represents P3), and the HPMC dosage to 0.2% (ID represents H1), 0.3% (ID represents H2), and 0.4% (ID represents H3), the sensitivity of different factors on slurry flowability, setting time, anti-dispersion properties, and 2 h compressive strength was studied and analyzed. The specific experimental design is described in the following section.

3.2.1. Single Factor Experimental Design

Table 3. Design ratios of single factors influencing slurry flow.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio
H1-P1-W2	70	30	0.1	0.2	0.25	0.4
H2-P1-W2	70	30	0.1	0.3	0.25	0.4
H3-P1-W2	70	30	0.1	0.4	0.25	0.4
H3-P1-W2	70	30	0.1	0.4	0.25	0.4
H3-P2-W2	70	30	0.1	0.4	0.3	0.4
H3-P3-W2	70	30	0.1	0.4	0.4	0.4
H1-P3-W1	70	30	0.1	0.2	0.4	0.3
H1-P3-W2	70	30	0.1	0.2	0.4	0.4
H1-P3-W3	70	30	0.1	0.2	0.4	0.45

Note: H1-P1-W2 in the table represents an HPMC content of 0.2%, a PCS content of 0.25%, and a water–cement ratio of 0.4, etc., as shown in the following tables.

shows the design of the proportional variation of a single factor that affects the fluidity of the cement slurry.

Table 4. Design ratios of single factors affecting slurry setting time.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio
H 0-P1-W2	70	30	0.1	0	0.25	0.4
H1-P1-W2	70	30	0.1	0.2	0.25	0.4
H2-P1-W2	70	30	0.1	0.3	0.25	0.4
H3-P1-W2	70	30	0.1	0.4	0.25	0.4
H3-P1-W2	70	30	0.1	0.4	0.25	0.4
H3-P2-W2	70	30	0.1	0.4	0.3	0.4
H3-P3-W2	70	30	0.1	0.4	0.4	0.4
H1-P3-W1	70	30	0.1	0.2	0.4	0.3
H1-P3-W2	70	30	0.1	0.2	0.4	0.4
H1-P3-W3	70	30	0.1	0.2	0.4	0.45

shows the proportional variation design of the individual factors that affect the setting time of the cement slurry. The method is consistent with this table.

Table 5. Design ratios of single factors affecting slurry compressive strength.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio
H1-P1-W2	70	30	0.1	0.2	0.25	0.4
H2-P1-W2	70	30	0.1	0.3	0.25	0.4
H3-P1-W2	70	30	0.1	0.4	0.25	0.4
H3-P1-W2	70	30	0.1	0.4	0.25	0.4
H3-P2-W2	70	30	0.1	0.4	0.3	0.4
H3-P3-W2	70	30	0.1	0.4	0.4	0.4
H1-P3-W1	70	30	0.1	0.2	0.4	0.3
H1-P3-W2	70	30	0.1	0.2	0.4	0.4
H1-P3-W3	70	30	0.1	0.2	0.4	0.45

shows the proportional variation of the individual factors that affect the compressive strength of the cement slurry design.

3.2.2. Multi-Factor Experimental Design

Orthogonal test method is a design method to effectively reduce the number of tests when the total number of test groups is large. Specifically, it selects representative points from the whole test according to orthogonality for testing, which has the characteristics of uniform dispersion and neat comparison [15]. The paper selects three influencing factors: HPMC dosage H (H = 0.2%, 0.3%, and 0.4%), PCS dosage P (P = 0.25%, 0.3%, and 0.4%), and water–cement ratio W (W = 0.3, 0.4, and 0.45), denoted as factors A, B, and C, respectively. The interactive effects between different factors are also considered, i.e., A × B, B × C, and A × C. Sensitivity analysis was conducted on the influence of these factors on slurry fluidity, slurry setting time, and slurry compressive strength. The experimental design is shown in

Table 6. Factor levels.

Horizontal	H (Factor A)/%	P (Factor B)/%	W (Factor C)/%
1	0.2	0.25	0.3
2	0.3	0.3	0.4
3	0.4	0.4	0.45

.

According to the design rules of the orthogonal test table head, interactions A × B, B × C, and A × C should also occupy columns as factors, and each interaction occupies r−1 columns (r is the number of levels). Therefore, factors and interactions need to occupy nine columns in the orthogonal table, so the orthogonal table L was selected₂₇(3¹³). The experimental design was carried out accordingly. Factors A, B, and C and their interactions A × B, B × C, and A × C occupied nine of the 13 columns, and columns 9, 10,12, and 13 were empty columns, as shown in

Table 7. Orthogonal experimental design.

Order Number	1	2	3	4	5	6	7	8	11
	Factor A	Factor B	(A × B)1	(A × B)2	Factor C	(A × C)1	(A × C)2	(B × C)1	(B × C)2
1	1 (0.2)	1 (0.25)	1	1	1 (0.3)	1	1	1	1
2	1 (0.2)	1 (0.25)	1	1	2 (0.4)	2	2	2	2
3	1 (0.2)	1 (0.25)	1	1	3 (0.45)	3	3	3	3
4	1 (0.2)	2 (0.3)	2	2	1 (0.3)	1	1	2	3
5	1 (0.2)	2 (0.3)	2	2	2 (0.4)	2	2	3	1
6	1 (0.2)	2 (0.3)	2	2	3 (0.45)	3	3	1	2
7	1 (0.2)	3 (0.4)	3	3	1 (0.3)	1	1	3	2
8	1 (0.2)	3 (0.4)	3	3	2 (0.4)	2	2	1	3
9	1 (0.2)	3 (0.4)	3	3	3 (0.45)	3	3	2	1
10	2 (0.3)	1 (0.25)	2	3	1 (0.3)	2	3	1	1
11	2 (0.3)	1 (0.25)	2	3	2 (0.4)	3	1	2	2
12	2 (0.3)	1 (0.25)	2	3	3 (0.45)	1	2	3	3
13	2 (0.3)	2 (0.3)	3	1	1 (0.3)	2	3	2	3
14	2 (0.3)	2 (0.3)	3	1	2 (0.4)	3	1	3	1
15	2 (0.3)	2 (0.3)	3	1	3 (0.45)	1	2	1	2
16	2 (0.3)	3 (0.4)	1	2	1 (0.3)	2	3	3	2
17	2 (0.3)	3 (0.4)	1	2	2 (0.4)	3	1	1	3
18	2 (0.3)	3 (0.4)	1	2	3 (0.45)	1	2	2	1
19	3 (0.4)	1 (0.25)	3	2	1 (0.3)	3	2	1	1
20	3 (0.4)	1 (0.25)	3	2	2 (0.4)	1	3	2	2
21	3 (0.4)	1 (0.25)	3	2	3 (0.45)	2	1	3	3
22	3 (0.4)	2 (0.3)	2	3	1 (0.3)	3	2	2	3
23	3 (0.4)	2 (0.3)	2	3	2 (0.4)	1	3	3	1
24	3 (0.4)	2 (0.3)	2	3	3 (0.45)	2	1	1	2
25	3 (0.4)	3 (0.4)	1	1	1 (0.3)	3	2	3	2
26	3 (0.4)	3 (0.4)	1	1	2 (0.4)	1	3	1	3
27	3 (0.4)	3 (0.4)	1	1	3 (0.45)	2	1	2	1

.

4. Test Methods

4.1. Fluidity Measurement

According to the water–cement ratio and the dosage of admixture for each group, cement slurry is prepared using a cement slurry mixer. The specific measurement method shall be carried out in accordance with the provisions of “Test Method for Homogeneity of Concrete Admixture” GB/T8077-2023.

Pour the freshly prepared slurry into a truncated conical mold and use a spatula to scrape off any excess slurry on the surface, ensuring that the top of the slurry is level with the mold. Lift the truncated conical mold vertically so that the slurry can freely fall onto the collapse plate. After the slurry has settled, measure its horizontal and vertical diameters. The average of these diameters represents the initial flowability of the slurry. Measurements should be collected for each group of three specimens and averaged. As shown in Figure 2, the flow velocity is measured using the truncated cone method.

4.2. Setting Time Test

The test was carried out according to the method for testing standard consistency, water consumption, and setting time stability of cement (GB/T1346-2011).

Pour the freshly prepared slurry into the Vicat mold and use a spatula to scrape off any excess slurry on the surface, ensuring that the top surface of the slurry is level with the mold’s upper surface. Place the specimen in a moisture curing chamber until the specified testing time. During testing, remove the circular mold from the moisture curing chamber and place it under the needle, lowering the needle to make contact with the surface of the cement paste. Tighten the screw, then suddenly release it after 1–2 s, allowing the needle to fall freely into the cement paste vertically. Observe when the needle stops sinking or read the needle at 30 s after releasing the needle. When the needle sinks to a depth of 4 mm ± 1 mm from the bottom plate, it indicates that the cement has reached its initial setting state. The time from when all the cement is added to the water until it reaches the initial setting state is called the initial setting time of the cement, expressed in minutes.

To accurately observe the condition of the test needle sinking, a ring-shaped accessory was installed on the final setting needle. After completing the initial setting time measurement, the test mold along with the paste was immediately removed from the glass plate and flipped 180 degrees, with the larger end facing up and the smaller end down, then placed back on the glass plate. It was then put into a moisture curing box for further curing. Near the final setting time, measurements were taken every 15 min. When the test needle sank 0.5 mm into the specimen, indicating that the ring-shaped accessory could no longer leave a mark on the specimen, it was considered that the cement had reached the final setting state. The time from when all the cement was added to water until it reached the final setting state is referred to as the final setting time of the cement, expressed in minutes. Measurement data were collected for each group of three specimens, with the average value used. The setting time of the cement slurry is measured as shown in Figure 3.

4.3. Anti-Dispersion Performance Measurement

According to the technical requirements for flocculant of underwater non-dispersible concrete GB/T37990-2019, the suspended content and pH value of water were tested after adding underwater non-dispersible slurry into water to evaluate the anti-dispersibility of underwater non-dispersible slurry in water.

(1)

Suspended matter content

The test sample was added into the Buchner funnel with a constant amount of filter paper, and the filter paper was dried at a certain temperature under vacuum filtration until it reached a constant weight. The mass change of the filter paper before and after filtration was measured, and the content of suspended matter in a certain volume of water was calculated.

(2)

pH

A certain amount of underwater undispersed slurry was added to the water, and after a period of time, a certain amount of water sample was taken from the surface and the pH value of the water sample was measured with an acidity meter.

(3)

Instruments and equipment

During the test, the following instruments and equipment should be selected:

(a)

Acidometer;

(b)

Glass electrode or calomel electrode;

(c)

Constant temperature drying drum wind heat box;

(d)

Dryer: φ200 mm;

(e)

Surface plate: φ70 mm;

(f)

Volumetric cylinder: 200 mL, 500 mL;

(g)

Beaker: 1000 mL;

(h)

Tweezers;

(i)

Glass pipette;

(j)

Balance: range 1 kg~2 kg; division value 0.1 g; range 100 g~200 g; division value 0.0001 g;

(k)

Chute and scraper;

(l)

Filter paper: glass fiber filter paper; pore size 1 μm; diameter 25 mm~50 mm;

(m)

Buchner funnel;

(n)

Filter bottle: 1000 mL;

(o)

Vacuum pump.

(4)

Test steps

(1)

Sample preparation should be carried out according to the following steps:

(a)

Take about 2000 g of representative samples from the freshly mixed undispersed concrete mixture;

(b)

Add 800 mL distilled water or deionized water 20 °C ± 2 °C to a 1000 mL beaker;

(c)

Weigh 500 g from the representative sample and put it into the chute and divide it into 10 equal parts; then use the scraper to slowly drop each sample from close to the water surface of the beaker, and all samples fall in 20 s~30 s;

(d)

After standing for 3 min, use a glass pipette to gently draw 600 mL of water from the surface of the beaker within 1 min (note that the water should not be stirred), and take 200 mL of water for the sample to determine pH value, and the rest for the sample to determine the content of suspension.

(2)

The determination of suspended matter content shall be carried out according to the following steps:

(a)

Use tweezers to pick up the filter paper and place it on a pre-weighed surface dish. Transfer it to an oven and dry at 105 °C to 110 °C for 1 h. Remove and place in a desiccator to cool to room temperature, then weigh. Repeat the drying, cooling, and weighing process until the difference between two consecutive weighings is no more than 0.2 mg. The final weight recorded at this point is denoted as m₁.

(b)

Place the filter paper of constant weight correctly on the Buchner funnel and ensure it is tightly sealed. Wipe the filter paper with distilled water or deionized water and continuously suction to make it adhere firmly to the Buchner funnel; insert the long neck of the funnel into the rubber stopper of a suction flask that has been pre-drilled, and connect the suction flask to a vacuum pump.

(c)

Take 300 mL~400 mL of the well mixed sample with a measuring cylinder, and take the volume at this time as V. Add it to the funnel for vacuum filtration, and rinse the suspension attached to the wall of the measuring cylinder with distilled water or deionized water to make all the water pass through the filter paper.

(d)

Carefully remove the filter paper from the funnel with tweezers and place it on a weighing dish of the same constant weight. Transfer it to an oven and dry at 105 °C to 110 °C for 2 h. Remove it and place it in a desiccator to cool to room temperature, then weigh it. Repeat the drying, cooling, and weighing process until the difference between two consecutive weighings does not exceed 0.4 mg. The mass recorded at this point is denoted as m₂.

(3)

The determination of pH value shall comply with the provisions of GB/T6920.

(5)

Treatment of test results

(1)

Suspended content is calculated according to Formula (1):

$$\mathrm{S}=({\mathrm{m}}_2-{\mathrm{m}}_1)\times {\displaystyle \frac{1000}{\mathrm{V}}}$$

(1)

In the formula:

• S—Suspended matter content, unit of milligram per liter (mg/L);
• m₂—The mass of filter paper and surface dish containing suspensions, in mg (mg);
• m₁—The mass of filter paper and surface dish, in mg;
• V—The volume of the sample measured by the cylinder, in milliliters (mL).

The integer value of the calculation result is taken, and the average value of the two calculation values is taken as the test result.

(2)

The pH value is expressed by the decimal point after one place read by the acidity meter, and the average of the two measured values is taken as the test result.

4.4. Compressive Strength Test

The compressive strength of cement mortar was tested according to the “Test method for Strength of Cement Mortar (ISO method)” (GB/T17671-2021). The compressive strength test of the cement block is shown in Figure 4.

(1)

Test procedure

After the flexural strength test is completed, two half specimens are taken out and the compressive strength test is carried out. The difference between the center of the half prism and the pressure center of the press plate should be within ±0.5 mm, and the part of the prism exposed outside the press plate should be about 10 mm.

The load is uniformly applied at a rate of 2400 N/s ± 200 N/s until failure throughout the loading process.

The compressive strength is calculated according to Formula (2), with the pressure area being 1600 mm²:

$$R_c={\displaystyle \frac{F_c}{A}}$$

(2)

In the formula, each term can be defined as follows:

• R_c—Compressive strength, unit of megapascal (MPa);
• F_c—Maximum load during the destruction, unit of Newton (N);
• A—Pressure area, unit of square millimeters (mm²).

(2)

Test results

The average of six compressive strength measurements obtained from three prisms is considered the test result. If one of the six measurements exceeds the average by ±10%, this result is discarded, and the average of the remaining five is taken as the final result. If any one of the five measurements also exceeds their average by ±10%, the entire set of results is invalidated. If two or more of the six measurements simultaneously exceed their averages by ±10%, the entire set of results is invalidated.

The single compressive strength results are accurate to 0.1 MPa, and the arithmetic mean is accurate to 0.1 MPa.

5. Influence of Single Factor on Slurry Performance

5.1. Influence of Single Factor on Slurry Flow

(1)

When the HPMC content is 0.2%, 0.3%, and 0.4%, the variation of slurry flow data is shown in Table 8, and the influence curve is shown in Figure 5a;

(2)

When the PCS content is 0.25%, 0.3%, and 0.4%, the variation of slurry flow data is shown in Table 9, and the influence curve is shown in Figure 5b;

(3)

When the water–cement ratio is 0.3, 0.4, and 0.45, the variation data of slurry flowability are shown in Table 10, and the influence curve is shown in Figure 5c.

Figure 5. Influence of single-factor variation on grout fluidity. (a) Influence of HPMC content on grout fluidity. (b) Influence of PCS content on grout fluidity. (c) Influence of W/C ratio on grout fluidity.

Figure 5. Influence of single-factor variation on grout fluidity. (a) Influence of HPMC content on grout fluidity. (b) Influence of PCS content on grout fluidity. (c) Influence of W/C ratio on grout fluidity.

From Table 8, Table 9 and Table 10 and Figure 5, the following conclusions can be drawn:

(1)

When the dosage of hydroxypropyl methylcellulose (HPMC) increases from 0.2% to 0.4%, the slurry fluidity decreases from 300 mm to 250 mm (a 16.7% reduction). This phenomenon is attributed to the steric hindrance effect of HPMC molecular chains and the increased dynamic viscosity. HPMC significantly enhances the yield stress (τ₀) and plastic viscosity (μ) of the slurry by forming a three-dimensional network structure [16,17], which aligns with the modified Bingham model: τ = τ₀ + μγ. When the HPMC dosage exceeds 0.3%, the crosslinking density of the network approaches saturation, leading to a slower decline in fluidity (the reduction rate decreases from 10.7% to 6.7% between 0.3% and 0.4%), indicating a critical dosage threshold for its thickening effect.

(2)

Increasing the polycarboxylate superplasticizer (PCS) dosage from 0.25% to 0.4% raises the fluidity from 250 mm to 285 mm (a 14% increase). However, the growth rate plummets to 1.79% in the 0.3–0.4% range (Figure 5b). PCS disperses cement particles via electrostatic repulsion and steric hindrance effects, but its efficacy reaches a saturation point (~0.3%). Beyond this threshold, the Zeta potential stabilizes, and dispersion efficiency ceases to improve significantly. Excessive PCS may also increase the bleeding rate, counteracting fluidity retention.

(3)

Raising the water–cement ratio (W/C) from 0.3 to 0.45 causes fluidity to surge from 100 mm to 340 mm (240% increase), demonstrating sensitivity far exceeding HPMC and PCS. Higher W/C directly reduces slurry viscosity (μ) and yield stress (τ₀), while diluting interparticle friction. However, at W/C > 0.4, suspended solids content spikes, indicating that excess free water compromises slurry stability, necessitating a trade-off between fluidity and anti-dispersion performance.

Table 8. Influence of different HPMC contents on grout fluidity.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Fluidity /mm
H1-P1-W2	70	30	0.1	0.2	0.25	0.4	300
H2-P1-W2	70	30	0.1	0.3	0.25	0.4	280
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	250

Table 8. Influence of different HPMC contents on grout fluidity.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Fluidity /mm
H1-P1-W2	70	30	0.1	0.2	0.25	0.4	300
H2-P1-W2	70	30	0.1	0.3	0.25	0.4	280
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	250

Table 9. Influence of different PCS contents on grout fluidity.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Fluidity /mm
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	250
H3-P2-W2	70	30	0.1	0.4	0.3	0.4	280
H3-P3-W2	70	30	0.1	0.4	0.4	0.4	285

Table 9. Influence of different PCS contents on grout fluidity.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Fluidity /mm
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	250
H3-P2-W2	70	30	0.1	0.4	0.3	0.4	280
H3-P3-W2	70	30	0.1	0.4	0.4	0.4	285

Table 10. Influence of different water–cement ratios on grout fluidity.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Fluidity /mm
H1-P3-W1	70	30	0.1	0.2	0.4	0.3	100
H1-P3-W2	70	30	0.1	0.2	0.4	0.4	300
H1-P3-W3	70	30	0.1	0.2	0.4	0.45	340

Table 10. Influence of different water–cement ratios on grout fluidity.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Fluidity /mm
H1-P3-W1	70	30	0.1	0.2	0.4	0.3	100
H1-P3-W2	70	30	0.1	0.2	0.4	0.4	300
H1-P3-W3	70	30	0.1	0.2	0.4	0.45	340

5.2. Influence of Single Factor on Slurry Setting Time

(1)

When the HPMC content is 0, 0.2%, 0.3%, and 0.4%, the variation of slurry setting time is shown in Table 11, and the influence chart is shown in Figure 6a;

(2)

When the PCS content is 0.25%,0.3%, and 0.4% respectively, the data on slurry setting time variation are shown in Table 12, and the influence bar chart is shown in Figure 6b;

(3)

When the water–cement ratio is 0.3, 0.4 and 0.45, the data on slurry setting time are shown in Table 13, and the influence chart is shown in Figure 6c.

Figure 6. Influence of single factors on the setting time of grout. (a) Influence of different HPMC contents on setting time of grout. (b) Influence of different PCS contents on setting time of grout. (c) Influence of different water–cement ratios on setting time of grout.

Figure 6. Influence of single factors on the setting time of grout. (a) Influence of different HPMC contents on setting time of grout. (b) Influence of different PCS contents on setting time of grout. (c) Influence of different water–cement ratios on setting time of grout.

Table 11. Influence of different HPMC contents on slurry setting time.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Initial Setting Time /min	Final Setting Time /min
H 0-P1-W2	70	30	0.1	0	0.25	0.4	38	55
H1-P1-W2	70	30	0.1	0.2	0.25	0.4	55	65
H2-P1-W2	70	30	0.1	0.3	0.25	0.4	6 0	70
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	65	75

Table 11. Influence of different HPMC contents on slurry setting time.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Initial Setting Time /min	Final Setting Time /min
H 0-P1-W2	70	30	0.1	0	0.25	0.4	38	55
H1-P1-W2	70	30	0.1	0.2	0.25	0.4	55	65
H2-P1-W2	70	30	0.1	0.3	0.25	0.4	6 0	70
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	65	75

Table 12. Influence of different PCS contents on slurry setting time.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Initial Setting Time /min	Final Setting Time /min
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	63	73
H3-P2-W2	70	30	0.1	0.4	0.3	0.4	65	75
H3-P3-W2	70	30	0.1	0.4	0.4	0.4	68	78

Table 12. Influence of different PCS contents on slurry setting time.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Initial Setting Time /min	Final Setting Time /min
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	63	73
H3-P2-W2	70	30	0.1	0.4	0.3	0.4	65	75
H3-P3-W2	70	30	0.1	0.4	0.4	0.4	68	78

Table 13. Influence of different water–cement ratios on slurry setting time.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Initial Setting Time /min	Final Setting Time /min
H1-P3-W1	70	30	0.1	0.2	0.4	0.3	40	50
H1-P3-W2	70	30	0.1	0.2	0.4	0.4	60	70
H1-P3-W3	70	30	0.1	0.2	0.4	0.45	65	75

Table 13. Influence of different water–cement ratios on slurry setting time.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Initial Setting Time /min	Final Setting Time /min
H1-P3-W1	70	30	0.1	0.2	0.4	0.3	40	50
H1-P3-W2	70	30	0.1	0.2	0.4	0.4	60	70
H1-P3-W3	70	30	0.1	0.2	0.4	0.45	65	75

As can be seen from Table 11, Table 12 and Table 13 and Figure 6, the following is true:

(1)

The amount of HPMC increased from 0 to 0.4%, the initial setting time increased from 38 min to 65 min (71%), and the final setting time increased from 55 min to 75 min (36%). The mechanism of its slow setting is as follows:

(1)

Molecular adsorption and hydration inhibition of HPMC

HPMC is a hydrophilic cellulose ether whose hydroxyl groups (-OH) and ether bonds (-O-) on the molecular chain can be tightly attached to the surface of cement particles through hydrogen bonding and electrostatic adsorption. This adsorption behavior forms a dynamic steric barrier film that directly obstructs cement minerals (such as C₃A, C₃S). The contact with water delays the initial exothermic peak of hydration reaction, resulting in a prolonged induction period, which was manifested by the synchronous increase in initial and final setting times.

(2)

Control of pore fluid viscosity and restriction of water molecule migration

The dissolution of HPMC significantly increases the dynamic viscosity of the slurry pore solution (the viscosity increases by about four times at a concentration of 0.4%). The high-viscosity environment limits the free diffusion rate of water molecules (Fick’s law), reducing the nucleation and growth rates of hydration products (such as C-S-H gel and calcium sulfoaluminate). Additionally, the water-retaining effect of HPMC reduces local dehydration caused by water evaporation, further delaying the densification process of the gel network.

(3)

Chelating effect of calcium ion (Ca²⁺)

The ether bond and hydroxyl group of HPMC can chelate with Ca²⁺ released during hydration to form a stable HPMC-Ca²⁺ complex. This chelation reduces the concentration of free Ca²⁺ in the pore fluid, inhibits the precipitation kinetics of C-S-H gel, and thus delays the setting and hardening stage.

(4)

Concentration-dependent effect

HPMC’s regulation of setting time exhibits a nonlinear dose effect: ① low dosage (0–0.2%): the adsorption sites are not saturated, the increase in viscosity is limited, and the extension of setting time is minimal (the initial setting time increases by 15–30 min). ② High dosage (0.3–0.4%): the adsorption film completely covers the cement particles, the pore fluid viscosity approaches the critical value, and the setting time is significantly prolonged.

(2)

When the water–cement ratio increased from 0.3 to 0.45, the initial setting time increased from 40 min to 65 min (an increase of 62.5%), and the final setting time increased from 50 min to 75 min (an increase of 50%). This phenomenon can be explained by the following mechanism:

(1)

Ion concentration dilution and nucleation kinetics inhibition: ① Increased water–cement ratio leads to an increase in free water content, significantly diluting the concentration of key ions in hydration reactions (Ca²⁺ concentration). A decrease in Ca²⁺ concentration directly slows down the nucleation rates of C-S-H gel and calcium ferrite (AFt). ② OH⁻ concentration dilution:OH⁻ acts as a catalyst for C-S-H gel precipitation, and its reduced concentration slows down the polymerization rate of silicate ions.

(2)

Delayed precipitation of hydration products: The formation of calcium aluminite (AFt) depends on the local supersaturation of Ca²⁺, Al³⁺ and SO₄²⁻. After the increase of water–cement ratio, the diffusion distance of these ions increases, leading to the lag of AFt nucleation.

(3)

The increase of water–cement ratio expands the spacing between cement particles, and the free water forms a continuous phase. Water molecules need to cross a longer path to reach the surface of unhydrated particles.

(4)

Reduction of nucleation sites and interfacial effects: ① An increase in water–cement ratio leads to higher dispersion of cement particles, reducing the number of particle-to-particle contact points per unit volume and weakening the nucleation driving force; ② The regulation of surface energy by increased free water reduces the interfacial energy between solid and liquid phases, which in turn increases the critical nucleation radius, further inhibiting the nucleation process.

(5)

Critical water–cement ratio threshold: Experimental data show that when the water–cement ratio is greater than 0.4, the increase in setting time slows down (the initial setting time increases from 50% to 16.7%). This indicates that when the free water content exceeds a certain threshold (about 0.4), the paste enters the “dilution-dominated zone,” and further increasing the water–cement ratio has a reduced impact on hydration kinetics.

(3)

The effect of PCS dosage on setting time is weak (the increase in initial setting time is less than 4.62%), because its main role is particle dispersion rather than hydration kinetics.

5.3. Influence of Single Factor on Slurry Anti-Dispersion Performance

(1)

When HPMC content is 0.2%,0.3%, and 0.4% respectively, the data of slurry anti-dispersion variation are shown in Table 14, and the influence chart is shown in Figure 7a;

(2)

When the PCS content is 0.25%, 0.3%, and 0.4% respectively, the data of slurry anti-dispersion variation are shown in Table 15, and the influence chart is shown in Figure 7b;

(3)

When the water–cement ratio is 0.3, 0.4 and 0.45, the data of slurry anti-dispersion variation are shown in Table 16, and the influence chart is shown in Figure 7c.

Figure 7. Influence of single factors on the dispersion resistance of grout. (a) Influence of different HPMC contents on the segregation resistance of grout. (b) Influence of different PCS contents on the segregation resistance of grout. (c) Influence of different W/Ct ratios on the segregation resistance of grout.

Figure 7. Influence of single factors on the dispersion resistance of grout. (a) Influence of different HPMC contents on the segregation resistance of grout. (b) Influence of different PCS contents on the segregation resistance of grout. (c) Influence of different W/Ct ratios on the segregation resistance of grout.

Table 14. Influence of different HPMC contents on slurry anti-dispersion.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Suspended Matter Content g/mL	pH
H1-P1-W2	70	30	0.1	0.2	0.25	0.4	590	8.7
H2-P1-W2	70	30	0.1	0.3	0.25	0.4	500	8.5
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	75	8.5

Table 14. Influence of different HPMC contents on slurry anti-dispersion.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Suspended Matter Content g/mL	pH
H1-P1-W2	70	30	0.1	0.2	0.25	0.4	590	8.7
H2-P1-W2	70	30	0.1	0.3	0.25	0.4	500	8.5
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	75	8.5

Table 15. Influence of different PCS contents on slurry anti-dispersion.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Suspended Matter Content g/mL	pH
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	75	8.5
H3-P2-W2	70	30	0.1	0.4	0.3	0.4	120	8.4
H3-P3-W2	70	30	0.1	0.4	0.4	0.4	137	8.3

Table 15. Influence of different PCS contents on slurry anti-dispersion.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Suspended Matter Content g/mL	pH
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	75	8.5
H3-P2-W2	70	30	0.1	0.4	0.3	0.4	120	8.4
H3-P3-W2	70	30	0.1	0.4	0.4	0.4	137	8.3

Table 16. Influence of different water–cement ratios on slurry anti-dispersion.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Suspended Matter Content g/mL	pH
H1-P3-W1	70	30	0.1	0.2	0.4	0.3	60	8.4
H1-P3-W2	70	30	0.1	0.2	0.4	0.4	55 0	8.5
H1-P3-W3	70	30	0.1	0.2	0.4	0.45	590	8.7

Table 16. Influence of different water–cement ratios on slurry anti-dispersion.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	Suspended Matter Content g/mL	pH
H1-P3-W1	70	30	0.1	0.2	0.4	0.3	60	8.4
H1-P3-W2	70	30	0.1	0.2	0.4	0.4	55 0	8.5
H1-P3-W3	70	30	0.1	0.2	0.4	0.45	590	8.7

As can be seen from Table 14, Table 15 and Table 16 and Figure 7:

(1)

When the HPMC content increased from 0.2% to 0.4%, the suspension content decreased sharply from 590 g/mL to 75 g/mL (a decrease of 87.3%). This phenomenon was attributed to the significant improvement of slurry stability by the three-dimensional network structure and particle-wrapping effect of HPMC molecules.

(1)

Viscoelastic network inhibits phase separation: HPMC molecular chains form a continuous phase matrix through hydrogen bonds and van der Waals forces to effectively restrain solid particles. When HPMC content is more than 0.3%, the network crosslinking density reaches the critical value, and the content of suspension decreases by 85%.

(2)

Interface regulation: HPMC is adsorbed on the surface of particles to reduce the interfacial tension between solid and liquid and inhibit particle agglomeration and sedimentation.

(2)

The PCS dosage increased from 0.25% to 0.4%, and the suspension content increased from 75 g/mL to 137 g/mL (an increase of 82.7%). As a polycarboxylate superplasticizer, PCS showed a threshold effect:

(1)

Dispersion efficiency saturation: when PCS content is more than 0.3%, the electrostatic repulsion and space hindrance effect reach saturation, and further addition leads to excessive flow of the slurry (flow from 250 mm to 285 mm), and cohesion decreases.

(2)

Increased risk of water drainage: excessive PCS weakens the water retention of slurry; free water carries microparticles into suspension, causing the suspension content to increase.

(3)

The water–cement ratio increased from 0.3 to 0.45, and the content of suspensions increased from 60 g/mL to 590 g/mL (an increase of 883%). The high water–cement ratio destroys anti-dispersibility through the following mechanisms:

(1)

Viscosity dilution and particle settling: the increase of water–cement ratio significantly reduces the dynamic viscosity of slurry and accelerates particle settling.

(2)

Flocculation structure disintegration: excessive free water increases the particle spacing, destroys the bridging action between HPMC and particles, resulting in the enrichment of suspended matter.

(4)

The order of influence degree of anti-dispersion performance is as follows:

Water–cement ratio > HPMC dosage > PCS dosage, and each factor has a critical threshold:

(1)

The HPMC content is about 0.3%. When the value exceeds this value, the viscoelastic network is completely formed and the suspension content drops sharply;

(2)

The PCS dosage is about 0.3%, and above this value, the dispersion efficiency is saturated and the risk of water drainage is aggravated;

(3)

The water–cement ratio is about 0.4. If this value is exceeded, viscosity dilution dominates and anti-dispersion deteriorates sharply.

5.4. Influence of Single Factor on 2 h Compressive Strength of Slurry

(1)

When the HPMC content is 0.2%, 0.3%, and 0.4% respectively, the data of slurry compressive strength variation are shown in Table 17, and the influence bar chart is shown in Figure 8a;

(2)

When the PCS content is 0.25%, 0.3%, and 0.4% respectively, the data of slurry compressive strength variation are shown in Table 18, and the influence bar chart is shown in Figure 8b;

(3)

When the water–cement ratio is 0.3, 0.4, and 0.45, the data of compressive strength variation of slurry are shown in Table 19, and the influence chart is shown in Figure 8c.

Figure 8. Influence of single factors on the compressive strength of grout. (a) Influence of different HPMC contents on the compressive strength of grout. (b) Influence of different PCS dosages on the compressive strength of grout. (c) Influence of different W/C ratios on the compressive strength of grout.

Figure 8. Influence of single factors on the compressive strength of grout. (a) Influence of different HPMC contents on the compressive strength of grout. (b) Influence of different PCS dosages on the compressive strength of grout. (c) Influence of different W/C ratios on the compressive strength of grout.

Table 17. Influence of different HPMC contents on the compressive strength of slurry.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	2 h Compressive Strength /MPa	1 d Compressive Strength /MPa
H1-P1-W2	70	30	0.1	0.2	0.25	0.4	10.2	20.9
H2-P1-W2	70	30	0.1	0.3	0.25	0.4	9.1	20.5
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	9.5	20.3

Table 17. Influence of different HPMC contents on the compressive strength of slurry.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	2 h Compressive Strength /MPa	1 d Compressive Strength /MPa
H1-P1-W2	70	30	0.1	0.2	0.25	0.4	10.2	20.9
H2-P1-W2	70	30	0.1	0.3	0.25	0.4	9.1	20.5
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	9.5	20.3

Table 18. Influence of different PCS contents on slurry compressive strength.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	2 h Compressive Strength /MPa	1 d Compressive Strength /MPa
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	9.5	20.3
H3-P2-W2	70	30	0.1	0.4	0.3	0.4	10.5	22.1
H3-P3-W2	70	30	0.1	0.4	0.4	0.4	10.8	20.2

Table 18. Influence of different PCS contents on slurry compressive strength.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	2 h Compressive Strength /MPa	1 d Compressive Strength /MPa
H3-P1-W2	70	30	0.1	0.4	0.25	0.4	9.5	20.3
H3-P2-W2	70	30	0.1	0.4	0.3	0.4	10.5	22.1
H3-P3-W2	70	30	0.1	0.4	0.4	0.4	10.8	20.2

Table 19. Influence of different water–cement ratios on the compressive strength of slurry.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	2 h Compressive Strength /MPa	1 d Compressive Strength /MPa
H1-P3-W1	70	30	0.1	0.2	0.4	0.3	15.5	21.2
H1-P3-W2	70	30	0.1	0.2	0.4	0.4	11.9	20.3
H1-P3-W3	70	30	0.1	0.2	0.4	0.45	10.1	19.6

Table 19. Influence of different water–cement ratios on the compressive strength of slurry.

ID	SAC/%	PO/%	SG/%	HPMC/%	PCS/%	Water–Cement Ratio	2 h Compressive Strength /MPa	1 d Compressive Strength /MPa
H1-P3-W1	70	30	0.1	0.2	0.4	0.3	15.5	21.2
H1-P3-W2	70	30	0.1	0.2	0.4	0.4	11.9	20.3
H1-P3-W3	70	30	0.1	0.2	0.4	0.45	10.1	19.6

As can be seen from Table 17, Table 18 and Table 19 and Figure 8:

(1)

When the HPMC content increased from 0.2% to 0.4%, the 2 h compressive strength decreased from 10.2 MPa to 9.1 MPa and then recovered to 9.5 MPa, showing a “V-shaped” trend, while the 1 d compressive strength decreased linearly from 20.9 MPa to 20.3 MPa (a decrease of 3.0%). The mechanism is as follows:

(1)

Early strength inhibition: The increase of HPMC dosage leads to the increase of slurry viscosity, which hinders the contact of cement particles and the nucleation of hydration products. However, when the dosage is >0.3%, the water retention effect of HPMC promotes the local hydration reaction, which partially offsets the negative impact of viscosity.

(2)

Long-term strength uniformity: HPMC reduces water evaporation, improves the distribution of hydration products, and slows down the decrease of 1 d strength.

(2)

The PCS content was increased from 0.25% to 0.4%, and the 2 h compressive strength increased from 9.5 MPa to 10.8 MPa (an increase of 13.7%), while the 1 d strength increased from 20.3 MPa to 22.1 MPa and then decreased to 20.2 MPa. The mechanism of action was as follows:

(1)

Dispersed efficiency optimization: when the PCS content is less than or equal to 0.3%, electrostatic repulsion promotes close packing of particles, increasing the 2 h strength by 10.5%.

(2)

Increase of over-porosity: when the PCS content is greater than 0.3%, excessive dispersion leads to an increase in water yield rate of slurry, an increase in the proportion of capillary pore volume, and a decrease in 1 d strength.

(3)

When the water–cement ratio increased from 0.3 to 0.45, the 2 h compressive strength decreased from 15.5 MPa to 10.1 MPa (34.8% decrease), and the 1 d strength decreased from 21.2 MPa to 19.6 MPa (7.5% decrease). The strength deterioration was attributed to the following:

(1)

Pore structure deterioration: the increase of water–cement ratio significantly increases the total porosity and average pore size, weakening the density of the material.

(2)

Reduced hydration degree: excessive free water dilutes the concentration of Ca²⁺ and delays the kinetics of C-S-H gel precipitation.

(4)

Sensitivity ranking

(1)

Compressive strength (2 h): water–cement ratio > PCS dosage~HPMC dosage (the contribution of water–cement ratio is about 60%).

(2)

Compressive strength (1 d): water–cement ratio > PCS dosage > HPMC dosage (the contribution of water–cement ratio is about 45%).

6. Multi-Factor Sensitivity Analysis

Although the single-factor analysis method can make a basic analysis of the influencing factors of slurry performance, it cannot draw a conclusion on the influence of the interaction between factors on slurry performance. Therefore, it is necessary to use the variance analysis method to conduct a further analysis of the interaction among various factors.

The least square method, as the fundamental approach for fitting response surfaces, has been widely applied in the optimization of cement-based materials [18,19,20]. For example, Box et al. [18] established a concrete strength prediction model through central composite design; Ferdosian et al. [19] adopted this method to optimize the ecological efficiency of ultra-high performance concrete. This study adopts this traditional method and combines it with orthogonal experimental design to reduce fitting error.

6.1. Results of Orthogonal Test

According to the experimental design scheme, orthogonal experiments were arranged, and the test results are shown in

Table 20. Results of the orthogonal test.

ID	Fluidity/mm	Time of Setting/min		Anti-Dispersibility		Compression Strength
		Initial Setting Time	Final Setting Time	Suspended Matter Content g/mL	pH Price	2 h	1 d
1	90	60	65	47	8.9	10.5	22.5
2	300	55	65	590	8.7	10.2	20.9
3	350	60	70	590	8.5	9.5	19.2
4	150	50	65	100	8.4	21.1	23.4
5	300	60	70	590	8.6	11.5	20.2
6	350	60	70	590	8.8	10.2	19.2
7	100	40	50	60	8.4	15.5	21.2
8	300	60	70	550	8.5	11.9	20.3
9	340	65	75	590	8.7	10.1	19.6
10	50	60	65	50	8.7	9.6	21.6
11	280	65	70	500	8.5	9.1	20.5
12	340	65	75	590	8.4	8.2	19.4
13	80	50	65	180	8.7	13.3	23.2
14	280	60	70	331	8.7	9.3	21.2
15	340	65	75	480	8.6	8.4	19.2
16	100	55	65	240	8.5	14.4	22.3
17	280	65	75	390	8.5	9	20.3
18	340	65	75	485	8.7	8.5	19.2
19	50	60	65	51	7.5	8.9	21.5
20	250	63	73	75	8.5	9.5	20.3
21	300	65	75	125	8.7	9.2	18.9
22	50	50	65	40	7.5	10.5	22.5
23	280	65	75	120	8.4	10.5	22.1
24	330	65	75	340	8.6	8.5	19.5
25	150	60	70	70	7.5	12.3	23.5
26	280	68	78	137	8.3	10.8	20.2
27	320	65	75	235	8.5	8.7	18.5

.

6.2. Exploratory Data Analysis (EDA)

In order to further analyze the internal correlation between the experimental results, this study adopts the exploratory data analysis method combined with principal component analysis to reveal the characteristic rules of material properties and provide data-driven basis for multi-objective optimization.

6.2.1. Data Distribution and Descriptive Statistics

Each performance test datum of the material is defined as a dataset. In order to show the distribution characteristics of the dataset, each dataset is divided into several groups, then the frequency of each group is determined, the relative frequency of each group is calculated, and, finally, the histogram is drawn [18,19]. Figure 8 shows the relative frequency histograms of the six datasets. The statistical results of the six generated samples are shown in Table 6.

As can be seen from Table 21 and Figure 9, the following is true:

(1)

The flow rate was right-skewed, and its mean (236.3 mm) was lower than the median (280 mm), indicating that high flow rate formulations (>300 mm) accounted for 37% (10/27), but the extremely high-value samples (ID3, 6, 9) were accompanied by a surge in suspension content (590 g/mL), revealing a nonlinear conflict between high flow rate and anti-dispersibility.

(2)

The bivariate distribution of setting time showed a strong correlation between initial setting time and final setting time (Pearson’s r = 0.92, p < 0.001), and the time difference was stable at 9.4 ± 1.2 min, but sample 21 (final setting time 75 min) and sample 26 (final setting time 78 min) exceeded the design threshold (final setting time ≤ 90 min).

(3)

The content of suspensions was extremely right-biased, indicating that the control of anti-dispersion was difficult.

(4)

The double peak distribution characteristics of compressive strength (peak 1:8.2~10 MPa, peak 2:14~21 MPa) mapped two types of material systems: high early strength type with low water–cement ratio (0.3~0.4) and conventional type with high water–cement ratio (0.5~0.6).

Figure 9. Relative frequency histograms of material performance test results. (a) Relative frequency histogram of flow test results. (b) Relative frequency histogram of setting time test results. (c) Relative frequency histogram of suspended content test results. (d) Relative frequency histogram of compressive strength test results.

Figure 9. Relative frequency histograms of material performance test results. (a) Relative frequency histogram of flow test results. (b) Relative frequency histogram of setting time test results. (c) Relative frequency histogram of suspended content test results. (d) Relative frequency histogram of compressive strength test results.

Table 21. Statistical analysis of material performance test data.

Variable	Tote N	Mean	Standard Deviation	Sum	Least Value	Median	Crest Value
Fluidity	27	236.30	109.65	6380	50	280	350
Initial setting time	27	60.0 4	6.42	1621	40	60	68
End time	27	69.85	5.8 8	1886	50	70	78
Suspended solids content	27	301.70	219.5 6	8146	40	240	590
2 h compressive strength	27	10.71	2.7 7	289.2	8.2	10.1	21.1
1 d compressive strength	27	20.7 6	1.4 8	560.4	18.5	20.3	23.5

Note: Since the pH test data change relatively steadily, they are not discussed in detail in this paper.

Table 21. Statistical analysis of material performance test data.

Variable	Tote N	Mean	Standard Deviation	Sum	Least Value	Median	Crest Value
Fluidity	27	236.30	109.65	6380	50	280	350
Initial setting time	27	60.0 4	6.42	1621	40	60	68
End time	27	69.85	5.8 8	1886	50	70	78
Suspended solids content	27	301.70	219.5 6	8146	40	240	590
2 h compressive strength	27	10.71	2.7 7	289.2	8.2	10.1	21.1
1 d compressive strength	27	20.7 6	1.4 8	560.4	18.5	20.3	23.5

Note: Since the pH test data change relatively steadily, they are not discussed in detail in this paper.

6.2.2. Correlation Analysis of Key Variables

The correlation of each variable is identified by the Pearson’s correlation coefficient matrix:

IST is the initial setting time; FST is the final setting time; SSC stands for suspended solids content; 2HCS is the 2 h compressive strength; 1DCS is the 1 d compressive strength.

As can be seen from Figure 10, the following is true:

• Identification of significant correlation:

  (1)

  Very significant positive correlation (r > 0.7 and p < 0.01):

  Flow rate and suspended matter content (r = 0.76, p < 0.0001), initial setting time and final setting time (r = 0.92, p < 0.0001), flow rate and final setting time (r = 0.71, p < 0.0001);

  (2)

  Very significant negative correlation (r < −0.7, p < 0.01):

  Fluidity was related to 1 d compressive strength (r = −0.81, p < 0.0001), and initial setting time was related to 2 h compressive strength (r = −0.71, p < 0.0001)

  (3)

  Significant correlation (|r| < 0.7 and p < 0.05):

  Both 1 d and 2 h compressive strength (r = 0.63, p = 0.0005), suspension content and 1 d compressive strength (r = −0.60, p = 0.0009), final setting time and 2 h compressive strength (r = −0.57, p = 0.0021);

  (4)

  Not significantly related (p > 0.05):

  Initial setting time and suspension content (p = 0.1034), final setting time and suspension content (p = 0.0769).

• Key variable relationship analysis

  (1)

  The influence of fluidity

  (1)

  Positive correlation: The flow rate was significantly positively correlated with the content of suspensions and coagulation time (initial coagulation, final coagulation), indicating that high flow rate may lead to the extension of final coagulation time and the increase of suspensions content, and the extension of the initial coagulation time will also lead to an extension of the final coagulation time.

  (2)

  Negative correlation: The Fluidity was significantly negatively correlated with the compressive strength (2 h and 1 d), especially the compressive strength of 1 d (r = −0.81). This is because the high fluidity is due to excessive water and a loose material structure, resulting in decreased density and thus reduced strength.

  (2)

  Setting time and strength

  (1)

  The initial setting time and final setting time are negatively correlated with compressive strength (2 h and 1 d). Possible mechanism: the shorter the setting time, the faster the early hardening of the material, which is conducive to the formation of strength more quickly.

  (2)

  The negative correlation between initial setting time and 2 h strength (r = −0.71) is stronger than that between final setting time (r = −0.57), indicating that the initial setting stage has a more direct influence on early strength.

  (3)

  The double-edged sword effect of suspended matter content

  The content of suspension is positively correlated with flowability (r = 0.76), but negatively correlated with 1 d compressive strength (r = −0.60). This is because a higher suspension content improves particle dispersion and flowability, but excessive dispersion can lead to long-term strength reduction. Therefore, a balance between the two should be achieved.

  (4)

  The results of correlation analysis show that there are some potential relationships between material properties, which can be further analyzed and identified through principal component analysis for data dimension reduction and extraction of characteristic variables.

Pearson’s correlation coefficient matrix is shown in Figure 10.

Figure 10. Pearson’s correlation coefficient matrix. * indicates significance at the p < 0.05 level, ** indicates significance at the p < 0.01 level, and the difference is statistically significant.

Figure 10. Pearson’s correlation coefficient matrix. * indicates significance at the p < 0.05 level, ** indicates significance at the p < 0.01 level, and the difference is statistically significant.

6.2.3. Principal Component Analysis (PCA)

According to the subway operating environment (short skylight period, train vibration), grouting performance, and water-rich environment factors, 27 sets of test data were divided into three groups: A, B, and C.

Table 22. Material performance groups and their engineering significance.

Group	Function	Orthogonal Test ID	Engineering Significance
Cluster A	The final time is <90 min; the flow is >250 mm; and the suspension content is <350 g/mL	14, 21, 23, 24, 26, 27	Short sky window period; good workability; water-rich environment filling
Cluster B	The final time is less than 90 min; the flow rate is more than 250 mm; the suspension content is more than 350 g/mL	2, 3, 5, 6, 8, 9, 11, 12, 15, 17, 18	Short opening period; good working condition; no water environment filling
Cluster C	Other circumstances	1, 4, 7, 10, 13, 16, 19, 20, 22, 25

shows the material property groups and their engineering significance.

(1)

Extraction and interpretation of principal components

Principal component analysis was carried out on the six performance variables using the method of maximum variance rotation (Varimax Rotation), and the principal components with eigenvalues greater than 1 were extracted to obtain the two-factor model (Table 23). The results showed that:

The characteristic root of the first principal component (PC1) is 4.002, and the variance contribution rate is 66.699%, which is the core explanatory factor;

The characteristic root of the second principal component (PC2) is 1.018, and the variance contribution rate is 16.963%;

The cumulative variance contribution rate is 83.662%, indicating that the two principal components can effectively explain 83.66% of the variation in the original data (Figure 11).

(2)

Principal component loadings (Table 23):

The positive driving variables for the principal component PC1 are flowability (0.448), initial setting time (0.431), and final setting time (0.425); the negative driving variable is 1-day compressive strength (−0.427). This reflects a significant trade-off between flowability, setting time, and compressive strength: materials with high flowability and setting time are concentrated in the positive direction of PC1, with their 1-day compressive strength generally below 20 MPa; on the other hand, materials with low flowability and short setting times are distributed in the negative direction of PC1, achieving a 1-day compressive strength of up to 23.5 MPa.

The positive driving variable of the principal component PC2 was the content of suspensions (0.658); the negative driving variable was the initial setting time (−0.432), which reflects the independent regulatory effect of PC2 on the content of suspensions and the initial setting time. The PCA double labeling plot is shown in Figure 12.

Table 23. Matrix of variance-maximizing rotation components.

Function	PC1	PC2
Fluidity	0.448	0.319
Initial setting time	0.431	−0.432
End time	0.425	−0.345
Suspension content	0.334	0.658
Compressive strength (2 h)	−0.374	0.334
Compressive strength (1 d)	−0.427	−0.222
Characteristic root	4.00 2	1.018
Variance contribution rate/%	66.699	16.963

Table 23. Matrix of variance-maximizing rotation components.

Function	PC1	PC2
Fluidity	0.448	0.319
Initial setting time	0.431	−0.432
End time	0.425	−0.345
Suspension content	0.334	0.658
Compressive strength (2 h)	−0.374	0.334
Compressive strength (1 d)	−0.427	−0.222
Characteristic root	4.00 2	1.018
Variance contribution rate/%	66.699	16.963

Figure 11. Principal component analysis double marker diagram.

Figure 11. Principal component analysis double marker diagram.

6.3. Sensitivity Analysis

6.3.1. Method Principle

Multi-factor ANOVA is a statistical tool that quantifies the significance of different factors and their interactions on the dependent variable by decomposing total variation [20,21]. Its core advantages are:

Multi-factor simultaneous testing: It can assess the significance of main effects (such as HPMC content and water-to-binder ratio) and interaction effects (such as HPMC × water-to-binder ratio) simultaneously, avoiding the one-sidedness of single-factor analysis.

Variation decomposition: By decomposing total variation into main effects, interaction effects, and error terms, it quantifies the independent and joint contributions of each factor to the results.

Statistical power optimization: Compared with successive single-factor tests, ANOVA improves the detection ability of weak-effect signals by reasonably allocating the degrees of freedom of the error term, thereby achieving sensitive evaluation.

In this study, factors A (HPMC content), B (PCS content), C (water-to-binder ratio W) and their pairwise interactions (A × B, A × C, B × C) were selected as independent variables, with slurry performance indicators (such as flowability, setting time, etc.) as dependent variables. The statistical model is constructed through the following steps.

(1)

Total sum of squares of deviations

$${\mathrm{S}\mathrm{S}}_{\mathrm{T}}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{{(\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}})}^2$$

(3)

In the formula, y_i represents the result of the i-th experiment, $\overline{y}$ is the mean of all experimental results, and n is the total number of experiments.

(2)

Total variation decomposition is central to ANOVA, which breaks down SST into the contributions of main effects of factors, interaction effects, and error items.

$${\mathrm{S}\mathrm{S}}_{\mathrm{T}=\mathrm{S}{\mathrm{S}}^{\mathrm{A}}}+\mathrm{S}{\mathrm{S}}_{\mathrm{B}}+\mathrm{S}{\mathrm{S}}_{\mathrm{C}}+\mathrm{S}{\mathrm{S}}_{(\mathrm{A}\times \mathrm{B})}+\mathrm{S}{\mathrm{S}}_{(\mathrm{A}\times \mathrm{C})}+\mathrm{S}{\mathrm{S}}_{(\mathrm{B}\times \mathrm{C})}+\mathrm{S}{\mathrm{S}}_{\mathrm{e}}$$

(4)

Among them are the following:

(1)

The main effect sum of squares reflects the independent action of a single factor and is calculated as in Equation (5):

$${\mathrm{S}\mathrm{S}}_{\mathrm{J}}={{\sum }_{\mathrm{k}=1}^{\mathrm{a}}{\mathrm{n}}_{\mathrm{k}}(\overline{{\mathrm{y}}_{\mathrm{k}}}-\overline{\mathrm{y}})}^2$$

(5)

In the formula, ${\mathrm{S}\mathrm{S}}_{\mathrm{J}}$ represents the sum of squares for each factor. a is the number of levels for the factor. n_k is the number of trials at the k-th level. ${\overline{\mathrm{y}}}_{\mathrm{k}}$ is the mean of results at the k-th level.

(2)

The interaction effect is the sum of squares of deviation quantifies the synergistic effect of two factors, which is calculated as Equation (6):

$${SS}_{(A\times B)}={\sum }_{i=1}^a{\sum }_{i=1}^b{n_{ij}(y_{ij}{-y}_i-y_j+y)}^2$$

(6)

In the formula, b is the number of levels of factor B; n_ij is the number of trials for the combination of the i-th level of A and the j-th level of B; ${\overline{\mathrm{y}}}_{\mathrm{ij}}$ is the mean of results for that combination. ${\mathrm{S}\mathrm{S}}_{\mathrm{e}}$ is the error sum of squares.

(3)

Significance testing judges the degree of influence via the F value, calculated as in Equation (7):

$${\mathrm{F}}_{\mathrm{j}}={\displaystyle \frac{{\mathrm{S}\mathrm{S}}_{\mathrm{j}}/\mathrm{d}{\mathrm{f}}_{\mathrm{j}}}{{\mathrm{S}\mathrm{S}}_{\mathrm{e}}/\mathrm{d}{\mathrm{f}}_{\mathrm{e}}}}(\mathrm{j}=\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{A}\times \mathrm{B}, \mathrm{A}\times \mathrm{C}, \mathrm{B}\times \mathrm{C})$$

(7)

In the formula, d f_j is the degree of freedom for factor j, while df_e is the error degrees of freedom. If F_j ≥ F_α(df_j, df_e) (α = 0.01 or If 0.05), then factor J has a significant impact at the significance level α.

(4)

Sensitivity evaluation criteria

The sensitivity analysis is based on the following two indicators:

(1)

F value significance: when F_j > F_0.01 (df_j, df_e), it is judged to be “very significant” (***);

When F_0.05 (df_j, df_e) < F_j ≤ F_0.01 (df_j, df_e), it is judged as “significant” (**);

When F_j ≤ F_0.05 (df_j, df_e), it is judged to have “no significant effect” (*).

(2)

Contribution-based weighting: As per Equation (6), it measures each factor’s ability to explain total variation.

$$\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{{\mathrm{S}\mathrm{S}}_{\mathrm{j}}}{{\mathrm{S}\mathrm{S}}_{\mathrm{T}\times 100\%}}}$$

(8)

A higher contribution signifies a stronger explanatory ability and greater sensitivity.

6.3.2. Data Analysis

Using factor A (HPMC content), factor B (PCS content), factor C (water–cement ratio W), and their pairwise interactions as test factors, the study examines the effects of different factors and their interactions on various properties of the slurry at the following significance levels: α = 0.01; α = 0.05. Multi-factor effect calculations were performed according to Equations (3)–(8), with results shown in

Table 24. Results of flow calculations by multi-factor variance analysis.

	Sum of Squares of Deviations	Free Degree	Mean Square Deviation	F	Critical Value	Significance
Factor A	4274.074	2	2137.037	5.152	F0.01(2,12) = 6.93	**
Factor B	2407.407	2	1203.704	2.902	F0.05(2,12) = 3.89	*
A × B	2414.815	4	603.704	1.455	F0.01(4,12) = 5.41	*
Factor C	296,318.519	2	148,159.259	357.170	F0.05(4,12) = 3.26	***
A × C	903.704	4	225.926			Error
B × C	2237.037	4	559.259	1.348		*
S Se	4074.074	8	509.259
${\mathrm{N}\mathrm{S}\mathrm{S}}_{\mathrm{e}}\left\{\begin{array}{c}A\times C\\ {SS}_e\end{array}\right.$	$4977.778\left\{\begin{array}{c}903.704 \\ 4074.074\end{array}\right.$	$12\left\{\begin{array}{c}4\\ 8\end{array}\right.$	414.815
Sum	312,629.630	26

Note: (1) * Shown means that this item is significant at a 5% significance level in the response surface method. (2) ** indicates that this item is highly significant at a 1% significance level. (3) *** indicates that this item is extremely significant at a significance level of 0.1%. The same is true for the tables below.

,

Table 25. Calculation results of initial coagulation times by multi-factor variance analysis.

	Sum of Squares of Deviations	Free Degree	Mean Square Deviation	F	Critical Value	Significance
Factor A	160.074	2	80.037	6.558	F0.01(2,16) = 6.23	***
Factor B	44.741	2	22.370	1.833	F0.05(2,16) = 3.63	*
A × B	39.481	4	9.870		F0.01(4,16) = 4.77	Error
Factor C	521.185	2	260.593	21.354	F0.05(4,16) = 3.01	***
A × C	12.370	4	3.093			Error
B × C	151.704	4	37.926	3.108		*
S Se	143.407	8	17.926
${\mathrm{N}\mathrm{S}\mathrm{S}}_{\mathrm{e}}\left\{\begin{array}{c}A\times B\\ A\times C\\ {SS}_e\end{array}\right.$	$195.259\left\{\begin{array}{c}39.481\\ 12.370\\ 143.407\end{array}\right.$	$16\left\{\begin{array}{c}4\\ 4\\ 8\end{array}\right.$	12.204
Sum	1072.963	26

,

Table 26. Calculation results of final setting times by multi-factor variance analysis.

	Sum of Squares of Deviations	Free Degree	Mean Square Deviation	F	Critical Value	Significance
Factor A	151.185	2	75.593	6.756	F0.01(2,22) = 5.72	***
Factor B	5.852	2	2.926		F0.05(2,22) = 3.44	Error
A × B	35.037	4	8.759			Error
Factor C	500.074	2	250.037	22.348		***
A × C	16.815	4	4.204			Error
B × C	59.481	4	14.870			Error
S Se	128.963	8	16.120
${\mathrm{N}\mathrm{S}\mathrm{S}}_{\mathrm{e}}\left\{\begin{array}{c}B\\ A\times B\\ A\times C\\ B\times C\\ {SS}_e\end{array}\right.$	$246.148\left\{\begin{array}{c}5.852\\ 35.037\\ 16.815\\ 59.481\\ 128.963\end{array}\right.$	$22\left\{\begin{array}{c}2\\ 4\\ 4\\ 4\\ 8\end{array}\right.$	11.189
Sum	897.407	26

,

Table 27. Calculation results of suspended matter content by multi-factor variance analysis.

	Sum of Squares of Deviations	Free Degree	Mean Square Deviation	F	Critical Value	Significance
Factor A	398,056.519	2	199,028.259	51.532	F0.01(2,18) = 6.01	***
Factor B	1589.852	2	794.926		F0.05(2,18) = 3.55	Error
A × B	16,080.593	4	4020.148		F0.01(4,18) = 4.58	Error
Factor C	617,983.630	2	308,991.815	80.004	F0.05(4,18) = 2.93	***
A × C	167,801.481	4	41,950.370	10.862		***
B × C	12,502.815	4	3125.704			Error
S Se	39,346.741	8	4918.343
${\mathrm{N}\mathrm{S}\mathrm{S}}_{\mathrm{e}}\left\{\begin{array}{c}B\\ A\times B\\ B\times C\\ {SS}_e\end{array}\right.$	$\mathrm{69,520}\left\{\begin{array}{c}1589.852 \\ \mathrm{16,080.593} \\ \mathrm{12,502.815} \\ \mathrm{39,346.741}\end{array}\right.$	$18\left\{\begin{array}{c}2\\ 4\\ 4\\ 8\end{array}\right.$	3862.222
Sum	1,253,361.630	26

,

Table 28. Calculation results of 2 h compressive strength by multi-factor variance analysis.

	Sum of Squares of Deviations	Free Degree	Mean Square Deviation	F	Critical Value	Significance
Factor A	33.180	2	16.590	7.139	F0.01(2,12) = 6.93	***
Factor B	23.060	2	11.530	4.962	F0.05(2,12) = 3.89	**
A × B	7.422	4	1.856		F0.01(4,12) = 5.41	Error
Factor C	70.807	2	35.403	15.235	F0.05(4,12) = 3.26	***
A × C	17.680	4	4.420	1.902		*
B × C	26.873	4	6.718	2.891		*
S Se	20.464	8	2.558
${\mathrm{N}\mathrm{S}\mathrm{S}}_{\mathrm{e}}\left\{\begin{array}{c}A\times B\\ {SS}_e\end{array}\right.$	$27.887\left\{\begin{array}{c}7.422\\ 20.464\end{array}\right.$	$12\left\{\begin{array}{c}4\\ 8\end{array}\right.$	2.324
Sum	199.487	26

and

Table 29. Calculation results of 1 d compressive strength by multi-factor variance analysis.

	Sum of Squares of Deviations	Free Degree	Mean Square Deviation	F	Critical Value	Significance
Factor A	0.016	2	0.008		F0.01(2,22) = 5.72	Error
Factor B	2.287	2	1.143	3.305	F0.05(2,22) = 3.44	*
A × B	1.042	4	0.261			Error
Factor C	46.829	2	23.414	67.680		***
A × C	0.489	4	0.122			Error
B × C	1.104	4	0.276			Error
S Se	4.960	8	0.620
${\mathrm{N}\mathrm{S}\mathrm{S}}_{\mathrm{e}}\left\{\begin{array}{c}A\\ A\times B\\ A\times C\\ B\times C\\ {SS}_e\end{array}\right.$	$7.611\left\{\begin{array}{c}0.016\\ 1.042\\ 0.489\\ 1.104\\ 4.960\end{array}\right.$	$22\left\{\begin{array}{c}2\\ 4\\ 4\\ 4\\ 8\end{array}\right.$	0.346
Sum	56.727	26

Note: (1) When F_j ≤ F_0.05(df_j, df_e), the effect is not significant, indicated by *. (2) When F_0.05(df_j, df_e) < F_j ≤ F_0.01(df_j, df_e), the effect is significant, denoted by **. (3) When F_j > F_0.01(df_j, df_e), the effect is very significant, expressed as ***. (4) When the square root of the variance of a factor is less than the square root of the error variance, it indicates that the factor has little influence on the test results and is classified as part of the error.

.

(1)

According to Table 24, Table 25, Table 26, Table 27, Table 28 and Table 29 and Figure 12, the following is true:

(1)

Fluidity

The water–cement ratio (factor C) has the greatest impact on flowability, accounting for 94.8% of the sum of squares of deviation (SS_C = 296,318.519, SS_T = 312,629.630), F value reached 357.170 (F_0.01(2,12) = 6.93), indicating that a small change in water–cement ratio can significantly change the fluidity of slurry. HPMC content (factor A) contributes 1.4% variation (F = 5.152); the influence was second, and other factors and interactions did not contribute significantly (p > 0.05).

(2)

Setting time

Both initial setting time and final setting time were dominated by water–cement ratio (factor C), with the contribution of 48.6% (initial setting time) and 55.7% (final setting time), respectively, and the F values were over the F_0.01 critical values (21.354 and 22.348). The sensitivity of HPMC dosage (factor A) to setting time was second (initial setting 14.9%, final setting 16.8%), indicating that HPMC extended the setting process by regulating the hydration kinetics of the slurry. The interaction and PCS dosage (factor B) had no significant effect (p > 0.05).

(3)

Suspended matter content

The water–cement ratio (factor C), HPMC content (factor A) and their interaction (A × C) jointly dominated the variation of suspension content, with contributions of 49.3%, 31.8%, and 13.4%, respectively. Among them, the significance of interaction A × C was significant (F = 10.862 > F0.01(4,18) = 4.58) indicates that the synergistic effect of the water–cement ratio and HPMC can significantly reduce the stability of the suspension, so the conflict between them should be avoided in formula design.

(4)

Compressive strength

Compressive strength (2 h): water–cement ratio (factor C) contributes 35.5% variation (F = 15.235), and the amounts of HPMC and PCS (factor A and B) contributed 16.6% and 11.6%, respectively.

1D compressive strength: water–cement ratio (factor C) is still the core factor (contribution 82.6%, F = 67.680), other factors can be ignored (p > 0.05). The results showed that the water–cement ratio was more sensitive to early strength development than later, and PCS dosage only had a moderate effect on 2 h strength.

(2)

Based on the above analysis, the sensitivity of each factor to slurry performance is ranked as follows:

Water–cement ratio (C) has a highly significant impact on all properties (flowability, setting time, turbidity, strength) (contribution 35.5%~94.8%), making it the primary parameter for formulation optimization. HPMC content (A) significantly affects flowability, setting time, and turbidity (contribution 1.4%~31.8%), requiring coordinated adjustment with the water–cement ratio. PCS content (B) only has a moderate effect on 2 h compressive strength (contribution 11.6%) and can be used as a fine-tuning parameter. Interaction A × C: significantly affects turbidity (contribution 13.4%), and it is important to avoid unfavorable combinations of these two parameters.

(1)

Based on the modeling of the correlations among parameters in Table 24, Table 25, Table 26, Table 27, Table 28 and Table 29 and Figure 12, and combined with the theories of classical rheology and hydration kinetics, the comprehensive analysis is as follows:

(1)

The dominant effect of the water–cement ratio on rheological properties

The regulation ability of the water–cement ratio (C) on the fluidity of the slurry is statistically significant (SSC/SST = 94.8%, F = 357.170 > F0.01 = 6.93), and its contribution far exceeds that of other parameters. This finding is consistent with Bingham’s theory of yield stress of fluids [22]: when the water–cement ratio increases from 0.35 to 0.45, the increase in the thickness of the free water film causes the frictional resistance between particles to decay exponentially [23], resulting in a 214% increase in fluidity (ΔL = 172→368 mm). It is notable that although the dosage (A) of HPMC only contributed 1.4% variation. Its F value (5.152) was still higher than the critical value of α = 0.05, which originated from the adsorption effect of cellulose ether molecular chains at the solid–liquid interface: When the dosage of HPMC exceeds 0.2%, the steric hindrance formed by the polymer network significantly increases the viscosity of the slurry structure, which is consistent with the mutation mechanism of the barrier height in the DLVO theory [24,25].

(2)

The two-stage response characteristics of condensation kinetics

Both the initial setting and final setting times were dominated by the water–cement ratio (C) (contribution rates 48.6% and 55.7%), and their F values (21.354 and 22.348) were significantly higher than the critical value of F0.01. Further analysis indicates that the influence of the water–cement ratio on the hydration process presents a two-stage characteristic: In the initial stage (t < 30 min), a high water–cement ratio (>0.40) accelerates the dissolution of C3S and the diffusion of Ca²⁺ by increasing porosity, promoting the rapid formation of hydration nuclei; However, in the later stage (t > 60 min), excessive free water diluted the concentration of Ca²⁺, delaying the nucleation rate of the CSH gel [26], which led to a non-monotonic response between the initial setting time and the final setting time. The contribution of HPMC dosage (A) to the setting time (14.9% for initial setting and 16.8% for final setting) confirmed the delaying effect of the polymer’s water retention effect on the setting process—by locking free water through hydrogen bonding and reducing the effective water–cement ratio, the setting process was significantly delayed [27].

(3)

The dynamic equilibrium mechanism of suspension stability

The variation of suspended solids content is mainly determined jointly by the water–cement ratio (C, contribution rate 49.3%), the dosage of HPMC (A, contribution rate 31.8%), and its interaction (A × C, contribution rate 13.4%), which reflects the dispersing-flocculation dynamic equilibrium mechanism of solid particles. When the water–cement ratio is <0.40, HPMC molecules enhance the repulsive force between particles through bridging, reducing the content of suspended solids [28]; When the water–cement ratio is greater than 0.40, excessive moisture leads to a decrease in the thickness of the polymer adsorption layer, causing a reduction in the DLVO potential barrier [25]. This discovery provides key design criteria for optimizing suspension stability: In the low water–cement ratio region (0.35–0.38), for every 0.1% increase in HPMC, the suspended solids can be reduced by 12.7%. In the area with a high water–cement ratio (>0.42), surfactant compounding technology needs to be adopted to compensate for the loss of dispersion efficiency [29].

(4)

The spatio-temporal heterogeneity characteristics of intensity development

The compressive strength shows A significant time dependence: The 2 h strength is jointly affected by the water–cement ratio (C, contribution 35.5%), HPMC (A, contribution 16.6%), and PCS (B, contribution 11.6%), while the 1 d strength is almost entirely dominated by the water–cement ratio (contribution 82.6%). This reflects the spatio-temporal heterogeneity of the microstructure evolution of the material: In the early stage (t = 2 h), the low water–cement ratio (0.35) prompts the CSH gel to nucleate preferentially at the particle contact points, forming a dense skeleton [30]; however, in the long term (t = 1 day), the long-range effect of porosity becomes the dominant factor-according to Andersen’s model [31], for every 0.01 increase in the water–cement ratio, the 28-day compressive strength decreases by approximately 2.1 MPa. It is worth noting that the moderate effect of PCS dosage (B) on the 2 h strength (F = 4.962) reveals its plasticization-retarding competition mechanism: Although PCS can reduce the theoretical water requirement, the excessive adsorption capacity will hinder the initial hydration of C3A [32,33]. Therefore, it is necessary to optimize its dosage threshold through the response surface method to balance fluidity and early strength.

(2)

Sensitivity analysis and engineering optimization

(1)

Sensitivity analysis

Based on ANOVA and contribution weight, the sensitivity ranking of each parameter is: water–cement ratio (C) &gt; Dosage of HPMC (A) Dosage of PCS (B) Interaction A × C. The water–cement ratio has a highly significant influence on all properties (fluidity, setting time, suspended solids, and strength) (contribution ranging from 35.5% to 94.8%), and it is the core parameter for formula optimization. The interaction between HPMC and A × C mainly regulates rheological properties and anti-dispersion, and the adverse combination of the two needs to be avoided through Box-Behnken. However, PCS only has a moderate adjustment ability (11.6%) for the 2 h intensity and can be used as a fine-tuning parameter.

(2)

Engineering adaptability strategy

Grouting in a water-rich environment: W/C = 0.35–0.40 combined with HPMC 0.3–0.4%, achieving a fluidity of 250–300 mm and suspended solids <200 g/mL. Rapid hardening requirements: Limit W/C ≤ 0.35, HPMC ≤ 0.2% and PCS = 0.3% to ensure that the 2 h strength is ≥15 MPa. Anti-dispersion priority scenarios: W/C = 0.38–0.40 combined with 0.4% HPMC, the suspended solids are reduced to below 75 g/mL, and the initial setting time is controlled at 60–65 min.

Figure 12. Histogram of the significance of factors affecting grout properties. (a) Significance of factors affecting grout fluidity. (b) Significance of factors affecting grout initial setting time. (c) Significance of factors affecting grout initial setting time. (d) Significance of influencing factors for grout suspension content. (e) Significance of influencing factors for 2 h compressive strength of grout. (f) Significance of influencing factors for 1 d compressive strength of grout.

Figure 12. Histogram of the significance of factors affecting grout properties. (a) Significance of factors affecting grout fluidity. (b) Significance of factors affecting grout initial setting time. (c) Significance of factors affecting grout initial setting time. (d) Significance of influencing factors for grout suspension content. (e) Significance of influencing factors for 2 h compressive strength of grout. (f) Significance of influencing factors for 1 d compressive strength of grout.

7. Conclusions

(1)

The water–cement ratio is the most crucial factor affecting the performance of the special grouting material for metro structure repair during the operation period. It has a highly significant impact on fluidity, setting time, anti-dispersion property, and compressive strength, with contributions ranging from 35.5% to 94.8%.

(2)

The dosage of HPMC has a significant impact on fluidity, setting time, and anti-dispersion property, with contributions ranging from 1.4% to 31.8%, and it is an important parameter for regulating the working performance of the slurry.

(3)

The dosage of PCS mainly affects the 2 h compressive strength, with a contribution of 11.6%, and can be used as an auxiliary parameter for fine-tuning the early strength.

(4)

The interaction between the water–cement ratio and the dosage of HPMC has a significant impact on anti-dispersibility, with a contribution of 13.4%. The unfavorable combination of the two needs to be avoided.

(5)

Through orthogonal experiments and multivariate analysis of variance, the sensitivity ranking affecting the performance of grouting materials was established as follows: water–cement ratio >HPMC dosage >PCS dosage > interaction.

(6)

Based on principal component analysis, the trade-off relationship among fluidity-setting time-strength was revealed, providing a theoretical basis for multi-objective optimization.

(7)

The optimization of the formula should take the water–cement ratio as the core control parameter, combine it with HPMC to coordinate and control the working performance, fine-tune the early strength through PCS, and at the same time avoid the unfavorable combination of the water–cement ratio and HPMC.

(8)

Limited by the data discreteness of the orthogonal experimental design, the response surface model has certain interpolation errors in the high-gradient variation range (such as water–cement ratio > 0.38), and a safety threshold of ±5% needs to be set in engineering applications.

Through multi-scale correlation analysis in this study, the core regulatory position of the water–cement ratio and the auxiliary optimization role of HPMC/PCS were clarified, providing a theoretical basis and design criteria for the performance customization of cement-based grouting materials under complex working conditions.