Study on the Mix Ratios of Early-Strength High-Permeability Cement-Based Grouting Materials for Seepage Control in Water-Sealed Underground Caverns

Abstract

To meet the demanding requirements of high permeability and early strength in seepage control grouting for water-sealed underground caverns, a series of cement-based grouts was developed via novel polymer modification techniques. A systematic orthogonal experiment was designed to evaluate the influence of five key factors—W/C, CWRA, PS, TEA, and AS—on the workability and mechanical properties of the grouts. Range, variance, and comprehensive analyses were conducted to determine the weight of each factor. Based on these findings, quantitative methods were employed to optimize mix proportions for two specific engineering purposes: sealing permeable fractures and plugging grouting holes. The optimized mixes exhibited enhanced workability and mechanical performance, thereby offering a reliable technical solution for seepage control in water-sealed underground caverns.

1. Introduction

With the rapid development of infrastructure, underground construction activities, including tunnel excavation, mining, and hydropower engineering, have expanded substantially, leading to increasingly complex construction conditions [1,2,3,4,5,6,7,8,9]. A water-sealed underground cavern is a representative type of underground facility that relies on the water-sealing principle, whereby the pore and fracture water pressures in the surrounding rock must remain higher than the internal pressure of the stored medium to prevent leakage. This pressure condition is maintained by the combined effect of natural groundwater and an engineered artificial water curtain system [10]. Under this design concept, limited groundwater seepage through the surrounding rock is allowed, whereas uncontrolled inflow into the cavern is prevented [11,12]. To satisfy the commonly adopted engineering criterion that “the daily infiltration volume should be less than 0.02% of the total storage capacity,” the permeability of the surrounding rock must be controlled below 0.1 Lu (approximately 1 × 10⁻³ m/d). This limit is an order of magnitude stricter than the seepage control requirement of 1 Lu for the Three Gorges Dam foundation [13]. Therefore, effective control of water infiltration remains a key technical issue in the design and construction of water-sealed underground caverns.

Grouting is widely recognized as one of the most effective methods for controlling seepage in water-sealed underground caverns [14,15,16,17]. By selecting appropriate grouting materials and optimizing the mix design, groundwater flow through fractured rock masses can be effectively sealed, thereby reducing permeability, enhancing strength, and improving the stability of the treated zone [18,19]. The effectiveness of infiltration control is primarily determined by two key factors: the grout diffusion range and the completeness of its filling within the rock mass [20,21,22,23,24]. In contrast to curtain grouting commonly used in hydraulic engineering, grouting in this context focuses on relatively closed, low-permeability fractures, which often contain pressurized water, presenting significant challenges to the penetration of conventional grouts [25]. Moreover, the excavation of water-sealed caverns typically involves smooth blasting techniques, which generate high-frequency vibrations that can disturb and reopen weak structural planes. If the grout’s early-age strength is insufficient, these disturbances may lead to recurrent water ingress, undermining the long-term sealing performance.

The water-to-cement ratio (W/C) is a critical parameter in the mix design of cement-based grouts, as it significantly influences both their workability and mechanical properties [26,27]. A higher W/C ratio improves grout penetrability, but it simultaneously reduces the ultimate strength of the hardened grout [28,29,30]. Research has shown that the incorporation of chemical admixtures is an effective approach to enhancing the performance of cement-based grouts [31,32,33,34,35,36,37,38]. For example, early-strength agents accelerate the cement hydration process and heat release, thereby increasing the early-age strength. However, this improvement often comes at the expense of reduced flowability, which negatively impacts workability [39,40,41,42]. On the other hand, polycarboxylate-based superplasticizers can significantly enhance the flowability of grouts. Their high water-reducing capacity effectively lowers the actual W/C ratio, resulting in a notable increase in compressive strength [43,44,45].

In recent years, various grouting materials have been widely used in engineering applications. These include ordinary cement-based grouts, cement-clay mixtures, chemical solutions, and synthetic foams. They are applied in areas such as seepage control in water-sealed underground caverns, foundation treatment, and tunnel seepage mitigation [46,47,48,49]. Among these, cement-based grouts are the most commonly used. However, their practical application is often limited by inherent drawbacks, including poor stability, low early-age strength, and inferior flowability when compared to chemical solutions. As a result, performance modification to meet specific engineering requirements is frequently necessary [50].

Shu et al. [51] used a fiber-polymer-modified cement-based grout to repair voids beneath concrete pavements. The addition of fibers and an early-strength agent significantly improved both the bending and early-age strength of the grout. However, its relatively low flowability limited its application primarily to large cracks in pavements, reducing its effectiveness in sealing smaller fissures. In another study, Zhang et al. [52] developed a polymer-modified cement-based grout for loose sediments by incorporating polyethylene glycol, polycarboxylate superplasticizer, and sodium silicate. This formulation notably enhanced the material’s penetrability, although its early-age strength remained relatively low.

Despite considerable research on modifying cement-based grouting materials, studies focused on their specific application in water-sealed underground caverns remain limited [53]. The unique operational requirements of these structures demand grouts that combine high penetrability with early-age strength. Additionally, due to the large scale and complex geological conditions typical of such caverns, a single grout mix design is unlikely to fulfill all grouting objectives. As a result, there is a clear need for the systematic and targeted development of multiple grout formulations. These formulations should be designed to address diverse requirements under varying conditions, including hole sealing and grouting in fractured rock masses with high (Lu ≥ 10), medium (3 ≤ Lu < 10), and low (Lu < 3) permeability.

During the construction of an underground oil storage facility in Japan, low-pressure clay injection grouting was employed to reduce the permeability of the surrounding rock. However, the low early-age strength of the clay grout resulted in recurrent seepage problems, particularly in the frequently blasted excavation environment [54]. A similar issue was encountered during the construction of an underground oil storage cavern in South Korea. Despite the use of ordinary cement-based grouts for remediation, seepage reoccurred following repeated blasting activities [55]. Sun et al. [56] developed a high-permeability cement-based grouting material suitable for fractured rock mass grouting. By employing an inorganic-organic composite modification technology, the material effectively addressed the excessive brittleness commonly found in conventional cement grouts. However, the early-age compressive strength of the developed grout remains insufficient. Aboulayt et al. [57] introduced a geopolymer-based grouting material. Through systematic experimentation, they explored the regulatory effects of fly ash and stabilizers on the rheological properties of the material, thus developing a mix with superior fluidity. Although the high-permeability grouting materials developed in these studies have demonstrated satisfactory performance in groundwater-sealed cavern engineering, their long-term durability in complex environments, particularly those subject to frequent blasting and other dynamic loads, requires further improvement. Therefore, focusing solely on material permeability is clearly inadequate to meet the comprehensive performance requirements of such engineering applications.

Wei et al. [58] investigated the use of modified calcium aluminate cement grouts for seepage control in water-sealed underground caverns. The material exhibited favorable early-age strength and slight expansion, with positive results obtained from field grouting trials. Liu et al. [59] developed an early-strength cement-based grouting material to improve the mechanical properties of fractured rock masses. By integrating a particle swarm optimization–radial basis function coupling model with the entropy weight method, they performed multi-objective optimization of the material’s mix proportion, providing a scientific and intelligent framework for the design and application of grouting materials. Fang et al. [60] systematically explored the effects of polycarboxylate superplasticizer (PS) and silica fume (SF) on the rheological properties of early-strength cement-based grouting materials. They elucidated the synergistic mechanisms of PS and SF from both macro- and micro-scale perspectives and developed a corresponding physical model. This work not only optimized the mix proportions of early-strength cement-based grouts, but also offered a theoretical basis and scientific guidance for designing mix proportions to meet diverse engineering requirements. However, to ensure the early strength of cement-based grouting materials, the studies mentioned above often employ a low water-to-cement ratio. This results in reduced grout penetrability, limiting its application in low-permeability fractures. Alternatively, excessively high grouting pressures used to enhance penetration may induce the propagation of micro-fractures within seepage channels. Therefore, for groundwater-sealed cavern projects with complex geological conditions, focusing solely on the early strength of grouting materials is inadequate.

Ouyang et al. [61] applied epoxy resin-based composite grouts in water-sealed underground caverns. These composites offer good penetrability and controllable properties, such as setting time and strength. However, their application is mainly limited to low-permeability fractures. For high-permeability fractures, controlling the grout volume becomes challenging, and the material cost is significantly higher compared to conventional cement-based grouts. Jiang et al. [62] used industrial by-products, namely fly ash and limestone powder, as supplementary cementitious materials to partially replace cement. They examined the synergistic effects of these materials on the performance of cement-based materials and determined the optimal substitution ratio. Additionally, the underlying mechanisms were explored from both macroscopic and microscopic perspectives. The optimal mix proportion identified in their study demonstrates relatively high early strength and favorable fluidity. While the grouting material mix proposed in these studies is suitable for groundwater-sealed cavern projects, a single formulation is often inadequate to meet the diverse grouting requirements imposed by different geological conditions. Therefore, when addressing grouting projects in complex geological settings, greater attention must be paid to the geological adaptability and tunability of the designed mix proportions. It is clear that a gap remains in the development of grouting materials with the following comprehensive performance characteristics for seepage control in groundwater-sealed caverns: high early strength to withstand frequent blasting disturbances during the initial strength development phase; excellent permeability to effectively seal low-permeability fractures; and broad applicability, enabling adaptation to various engineering conditions through simple mix proportion adjustments while maintaining low cost. This study is specifically aimed at addressing this gap.

This study developed an early-strength, high-permeability cement-based grout (EHCG) through innovative polymer modification techniques. An orthogonal experimental design was used to systematically examine the effects of W/C, a composite water-reducing agent (CWRA), PS, triethanolamine (TEA), and an acrylate salt (AS) on the workability and mechanical properties of the cement paste. Through range, variance, comprehensive, and quantitative analyses of the experimental data, optimal EHCG mix proportions were determined under various conditions, all meeting the specified grouting design requirements. This formulation effectively overcomes the high viscosity and poor flowability typically associated with conventional cement pastes, thus enhancing injectability in complex geological settings. Furthermore, compared to traditional grouts, the EHCG exhibited significantly improved early-age strength while maintaining similar permeability.

2. Raw Materials

2.1. Cement

The cement used in this study was Ordinary Portland Cement (OPC, strength grade 42.5 MPa) produced by Anqing Jigang Baqi Dolphin Cement Co., Ltd., Anqing City, Anhui Province, China, conforming to the Chinese National Standard GB 8076-2008 [63]. The particle size distribution of the cement was characterized using a laser particle size analyzer, which indicated a specific surface area of 300.6 m²/kg (Figure 1). Its mineral composition was determined by X-ray diffraction (XRD), with the corresponding diffraction pattern and quantitative phase distribution presented in Figure 2 and Figure 3, respectively. The physical and mechanical properties, along with the chemical composition of the cement, are summarized in

Table 1. Physical and mechanical properties of the cement.

Sample Name	Water Requirement for Standard Consistency (%)	Initial Setting Time (min)	Final Setting Time (min)	Flexural Strength (MPa)		Compressive Strength (MPa)
				3 d	28 d	3 d	28 d
OPC	28.7	217	284	5.2	8.6	28.4	51.7

and

Table 2. Chemical composition of the cement.

Oxides	Na2O	MgO	Al2O3	SiO2	SO3	K2O	CaO	TiO2	Fe2O3	Other
Content (%)	0.4240	2.994	10.19	33.73	3.296	1.082	38.80	0.479	2.558	0.6800

.

2.2. Superplasticizer

Superplasticizers, as high-performance water-reducing admixtures for cementitious systems, effectively lower water demand while enhancing the fluidity, strength, and stability of the paste. In this study, two types were employed: a polycarboxylate superplasticizer (PS) and a composite water-reducing agent (CWRA). Both PS and its corresponding mother liquor were supplied by Hebei Sidong Environmental Protection Technology Co., Ltd., Tangshan City, Hebei Province, China, in compliance with the Chinese National Standard GB 8076-2008 [63]. The physical and mechanical properties, as well as the chemical composition of PS, are detailed in

Table 3. Physical and mechanical properties of the polycarboxylate superplasticizer.

Sample Name	Density (g/cm3)	Water Reduction Rate (%)	28-Day Shrinkage Ratio (%)	Condensation Time Difference (min)		Compressive Strength (%)
				Initial Setting	Final Setting	1 d	3 d	7 d	28 d
PS	1.039	19.0	105	+15	+10	144	132	133	131

and

Table 4. Chemical composition of the polycarboxylate superplasticizer.

Sample Name	Total Alkalinity (%)	pH Value	Formaldehyde (%)	Chloride Ion (%)	Sodium Sulfate (%)	Air Content (%)	Solid Content (%)
PS	2.60	2.6	0.02	0.05	0.80	2.00	14.0

, respectively.

CWRA was prepared by uniformly mixing PS mother liquor with sodium lignosulfonate (SL) at a mass ratio of 25:1, followed by the addition of an air-entraining agent (0.05% by total mass of the mixture). The resulting blend was stirred thoroughly, sealed, and cured in an oven at 40 °C for 24 h. The sodium lignosulfonate used was supplied by Nanyang Longxiang Chemical Technology Co., Ltd., Nanyang City, Henan Province, China, and conformed to the relevant enterprise standards. Its physical properties and chemical composition are summarized in

Table 5. Physical properties and chemical composition of sodium lignosulfonate.

Sample Name	Water Reduction Rate (%)	pH Value	Fineness (Mesh)	Purity (%)	Calcium and Magnesium Content (%)	Insoluble Content (%)	Water Content (%)
SL	14.0	8.6	120	65.0	0.60	0.70	5.00

.

The air-entraining agent (AA) was supplied by Jiangsu Bote New Materials Co., Ltd., Nanjing City, Jiangsu Province, China, and complies with the relevant specifications of the Chinese National Standard GB 8076-2008 [63]. Its physical and mechanical properties and chemical characteristics are detailed in

Table 6. Physical and mechanical properties of air-entraining agents.

Sample Name	Shrinkage Ratio (%)	Water Reduction Rate (%)	Bleeding Rate (%)	Condensation Time Difference (min)		Compressive Strength (%)
				Initial Setting	Final Setting	1 d	3 d	7 d	28 d
AA	115	7.50	25.0	+10	+15	-	101	99.0	95.0

and

Table 7. Chemical composition of air-entraining agents.

Sample Name	Total Alkalinity (%)	pH Value	Formaldehyde (%)	Chloride Ion (%)	Sodium Sulfate (%)	Air Content (%)	Solid Content (%)
AA	2.11	6.5	-	0.05	-	4.50	5.00

, respectively.

PS offers significant advantages, including excellent slump retention, high water-reduction rates, effective cement dispersion, and good adaptability to varying temperatures. Their primary limitations are higher cost and selective compatibility with air-entraining agents during formulation. In contrast, SL is more economical and benefits from well-established application technology. However, they provide lower water-reduction efficiency and, at higher dosages, can lead to undesirable retardation and segregation of the cement paste [64]. To address the inherent low water-reduction efficiency of SL, it can be compounded with other agents to enhance overall performance and thereby improve paste fluidity. In mix design, the careful adjustment of CWRA and PS dosages can effectively mitigate the retardation and segregation risks associated with lignosulfonate, while maintaining the desired workability of the mixture.

2.3. Triethanolamine (TEA)

The triethanolamine (TEA) employed in this study was an industrial-grade product (85% purity) supplied by Shanghai Fujia Fine Chemicals Co., Ltd., Shanghai City, China. As a common surfactant, TEA contains both nitrogen atoms and hydroxyl (-OH) groups in its molecular structure, imparting properties characteristic of both alcohols and amines. It acts as a hydration promoter and strength enhancer in cementitious systems, leading to its frequent use as an early-strength agent in engineering applications [65]. Research has shown that TEA extends the induction period of tricalcium silicate (C₃S) hydration, thereby retarding the strength development of the silicate phase. Conversely, it accelerates the hydration of tricalcium aluminate (C₃A) and the formation of ettringite. Furthermore, in high-pH environments, TEA promotes the formation of amine–iron complexes, which contribute to increased early-age strength of the cement paste [66].

TEA exhibits a significant dosage-dependent influence on cement performance. At dosages of 0.02% to 0.05% (by mass of cement), it typically enhances the 3-day strength of ordinary Portland cement by approximately 10%. Increasing the dosage to 0.06–0.1% yields a more pronounced early-strength gain but may lead to a reduction in compressive strength beyond 3 days. When the TEA content exceeds 0.1%, the inhibition of C₃S hydration further delays early-strength development, while the accelerated hydration of C₃A can significantly shorten the setting time, potentially inducing false set. At a dosage as high as 1%, TEA acts as a strong set accelerator but results in a drastic decrease in 28-day strength [67]. These effects demonstrate that the efficacy of TEA is highly dosage-sensitive, and its optimal effective range can vary depending on the type and proportion of other admixtures present in the cement system.

2.4. Acrylate Salt (AS)

The acrylate salt (AS) solution used in this experiment was prepared by dissolving solid calcium acrylate powder (supplied by Henan Hongfa Chemical Products Co., Ltd., Zhengzhou City, Henan Province, China.) to a concentration of 0.3 g/mL. In cementitious systems, AS can be incorporated through both physical and chemical adsorption. Through physical adsorption, the large polar groups in AS molecules form numerous hydrogen bonds with inorganic ions, such as calcium and silicate ions, present in the cement paste, thereby promoting the adhesion of AS gel to cement particles. Concurrently, chemical adsorption enables AS to chelate with calcium and aluminum ions in the paste, improving interfacial interactions and ultimately enhancing the permeability and corrosion resistance of the hardened cement matrix [68].

3. Sample Preparation

The sample preparation procedure was conducted as follows (see Figure 4 for the workflow). First, predetermined quantities of cement, water (maintained at 20 ± 2 °C), and chemical admixtures were weighed according to the target mix proportion, with the weighing accuracy controlled within ±1%. The admixtures were then dissolved in the measured water under stirring for 30 s. Subsequently, cement was gradually added to the solution over a period of 1 min under continuous agitation. After complete addition, the mixture was stirred at low speed for 90 s using a mechanical mixer. Following mixing, the slurry was allowed to rest for 1 min before being poured into pre-oiled cubic molds (70.7 mm side length). Each mold was lightly tapped 10 times to remove entrapped air. The filled molds were then stored in a controlled environment (20 ± 2 °C) to ensure normal setting. After 6 h, the surface was leveled, and demolding was carried out after 24 h. The specimens were subsequently transferred to a standard curing chamber (20 ± 2 °C, relative humidity > 95%) and maintained until the required curing age before testing.

The mixing process was performed using a JJ-5 380V cement mortar mixer (Maifang Instrument Equipment Co., Ltd., Wuxi City, Jiangsu Province, China.). Weighing was conducted with a JA5001 multifunctional electronic balance (Shanghai Puchun Measuring Instrument Co., Ltd., Shanghai City, China.), and curing was carried out in an HBY-40 standard constant temperature and humidity curing chamber (Tianjin Changji Test Instrument Technology Co., Ltd., Tianjin City, China).

4. Experimental Methods

4.1. Operational Performance Testing

4.1.1. Density, Water Permeability, and Stone Formation Rate

Density, bleeding rate, and stone ratio are key parameters for evaluating the workability of cement-based grouts. These tests provide critical insights into the quality characteristics of the fresh slurry and its volumetric stability during hardening [69]. The bleeding rate represents the proportion of water that separates from the cement slurry under static conditions due to particle settlement; a lower value indicates better stability. The stone ratio reflects the volumetric loss of the slurry during solidification; a higher value suggests more complete filling of rock fractures by the grout.

This experiment employs a 100 mL graduated cylinder for testing density, water permeability, and stone formation rate, following the industry standard “Test Method for Water Permeability of Cement” (JC/T2153-2012) [70]. The procedure is as follows (Figure 5): After preparing the slurry, measure the mass of the graduated cylinder (m₀), then pour 100 mL of slurry into the cylinder and measure the mass again (m). Seal the top of the container with a water-retaining membrane and allow it to stand for 1 min before recording the slurry height (h₁). After 24 h of resting at a constant temperature of 20 °C, measure the height of the separated water (h₂) and the height of the stone formation (h₃). The bleeding rate is calculated using Equation 1, the stone rate using Equation (2), the slurry density ${\rho }_1$ (g/cm³) using Equation (3), and the specimen density ${\rho }_2$ (g/cm³) using Equation (4).

$$\mathrm{Bleeding}\mathrm{rate}(\%)={\displaystyle \frac{{\mathrm{h}}_2{-\mathrm{h}}_3}{{\mathrm{h}}_1}}\times 100\%$$

(1)

$$\mathrm{Stone}\mathrm{rate}(\%)={\displaystyle \frac{{\mathrm{h}}_3}{{\mathrm{h}}_1}}\times 100\%$$

(2)

$${\rho }_1={\displaystyle \frac{{\mathrm{m}-\mathrm{m}}_0}{100}}$$

(3)

$${\rho }_2=1+({\rho }_1-1)\cdot {\displaystyle \frac{{\mathrm{h}}_1}{{\mathrm{h}}_3}}$$

(4)

4.1.2. Flowability

The flowability test is a key method for evaluating the flow characteristics of cement-based grouts. In the specific test protocol adopted in this study, a lower flow time corresponds to better fluidity and injectability of the slurry. Flowability has a direct influence on the grout diffusion radius; under otherwise identical conditions, a slurry with lower flowability (shorter flow time) achieves a larger diffusion radius. By varying the water-to-cement ratio or admixture dosage and monitoring the resulting changes in flowability, the mix design can be optimized. This approach assists in determining the minimum water content required to meet specified construction performance criteria [71].

The fluidity test in this experiment was conducted using a Model 1006 mud viscometer manufactured by Cangzhou Kanxin Instrument Equipment Co., Ltd., Cangzhou City, Hebei Province, China. (Figure 6). The testing procedure followed the industry standard “Standard Test Methods for Basic Performance of Masonry Mortar” (JGJ/T70-2009) [72].

The test shall be conducted under ambient laboratory conditions at 20 °C ± 2 °C. First, moisten the inner wall of the flow cone and close its bottom outlet. Using the two standard measuring cups (deep and shallow) provided with the apparatus, fill each separately with clean water and pour the water into the cone. Open the bottom outlet to allow the water to flow out freely, and record the time (in seconds) required to fill the deep cup. An efflux time between 14.5 and 15.5 s indicates that the apparatus meets the accuracy requirements, and subsequent testing may proceed. Replace the water with the grout slurry to be tested, repeat the above procedure, and record the time taken for the slurry to fill the deep cup—this value represents the fluidity (flow time) of the slurry. For each mix proportion, at least two independent tests shall be performed, each using freshly prepared slurry. Testing shall commence within 3 min after slurry preparation. The result shall be taken as the average of the two measurements. The mean experimental error was 0.1 s, and the two results shall not differ by more than ±1.8 s.

4.2. Mechanical Performance Testing

4.2.1. Viscosity Test

The viscosity of cement-based grouts is a key rheological property. Viscosity measurements were performed using an SNB-1 digital viscometer (Shanghai Sunyu Hengping Scientific Instrument Co., Ltd., Shanghai City, China.; see Figure 7).

The testing procedure was as follows. Under ambient conditions of 20 ± 2 °C, select an appropriate rotor based on the estimated viscosity range of the slurry according to the trial mix proportion. Prepare the cement paste following the method illustrated in Figure 4, and immediately transfer it into a beaker placed on the measuring platform of the rotational viscometer. Add additional paste until the liquid level aligns with the marking line on the rotor. Set the instrument to automatic measurement mode and record the reading once it stabilizes. The entire testing process must be completed within 3 min after paste preparation. For each mix proportion, repeat the test three times using freshly prepared paste, and report the average of the three measurements as the viscosity value for that group.

4.2.2. Strength Test

To evaluate the compressive and splitting tensile strength of cementitious specimens at 3, 7, and 28 days, mechanical tests were carried out after standard curing (Figure 8). In accordance with the Chinese National Standard “Test Method for Mechanical Properties of Ordinary Concrete” (GB/T 50081-2019) [73], splitting tensile strength was determined using a fully automatic cement flexural-compressive testing machine (model HYZ-300-10, Hebei Jingwei Testing Instrument Co., Ltd., Shijiazhuang City, Hebei Province, China.). Two parallel molded side faces of the specimen were selected as the test surfaces. A cross-mark was drawn on each surface to locate its midpoint. A line parallel to the molded face and passing through the midpoint was defined as the central line of that surface. Thin metal strips were placed along the central lines on both the upper and lower test surfaces. The length of each strip exceeded the side length of the test face, and its width was kept below 5 mm. The testing machine was set to a stress rate of 0.03 MPa/s, and loading was applied gradually until failure occurred. The splitting tensile strength was then recorded.

The unconfined compressive strength of the specimens was determined using a microcomputer-controlled electro-hydraulic servo universal testing machine (model WAW-1000B, Wuxi Jiasenqi Monitoring Equipment Co., Ltd., Wuxi City, Jiangsu Province, China.). The two parallel molded side faces of the specimen were selected as bearing surfaces and placed on the bearing plates of the testing machine. The loading rate of the machine was set to 0.5 kN/s. Force was then applied gradually until failure occurred, and the compressive strength was recorded.

Owing to the inherent anisotropy of cementitious materials, strength results typically exhibit scatter. To ensure data reliability, three replicates were tested for each mix proportion, and the average value was reported.

5. Orthogonal Experimental Design

Based on experiences in grouting engineering and actual field needs, as well as prior research and preliminary tests, this orthogonal experiment considers five factors: water-cement ratio (W/C), composite water-reducing agent (CWRA) dosage, polycarboxylate water-reducing agent (PS) dosage, triethanolamine (TEA) dosage, and acrylate (AS) dosage. To ensure that the early strength of the cement stone meets design requirements, the W/C should not exceed 0.6. To maintain the fluidity of the cement slurry, the W/C should not be less than 0.35; thus, the orthogonal experiment is designed with W/C in the range of 0.35~0.6 [26,27]. Preliminary tests indicate that when CWRA dosage exceeds 0.5%, severe segregation occurs, leading to a rapid decrease in cement fluidity; therefore, CWRA dosage is set between 0.0%~0.4%. Research shows that excessive PS dosage can cause cement slurry to retard, so the orthogonal experiment is designed with PS dosage in the range of 0.0%~0.8%, referring to manufacturer recommendations [44]. As a commonly used early-strength agent, TEA exhibits strong dosage dependence, significantly enhancing early strength at low dosages of 0.01%~0.05%, but causing severe retardation at dosages between 0.1%~1.0%; hence, TEA dosage is set at 0.00%~0.08% [67]. A small addition of AS can improve slurry workability with minimal impact on the strength and flowability of the slurry, so AS dosage is designed in the range of 0.00%~0.16% [70]. According to the orthogonal test method, each factor is set at five levels, as shown in

Table 8. Factor level table.

Level	Factors
	W/C	CWRA (%)	PS (%)	TEA (%)	AS (%)
L1	0.40:1	0.0	0.8	0.00	0.00
L2	0.45:1	0.1	0.6	0.02	0.04
L3	0.50:1	0.2	0.4	0.04	0.08
L4	0.55:1	0.3	0.2	0.06	0.12
L5	0.60:1	0.4	0.0	0.08	0.16

.

The orthogonal experiment focuses on six indicators: viscosity, early (3 d) splitting tensile strength (ESTS), standard (28 d) splitting tensile strength (SSTS), early (3 d) compressive strength (ECS), standard (28 d) compressive strength (SCS), and water bleeding rate. A total of 25 orthogonal test groups are designed as presented in

Table 9. Orthogonal experimental table.

Number	W/C	CWRA (%)	PS (%)	TEA (%)	AS (%)
T1	0.40:1	0.0	0.8	0.00	0.00
T2	0.40:1	0.1	0.6	0.02	0.04
T3	0.40:1	0.2	0.4	0.04	0.08
T4	0.40:1	0.3	0.2	0.06	0.12
T5	0.40:1	0.4	0.0	0.08	0.16
T6	0.45:1	0.0	0.6	0.04	0.12
T7	0.45:1	0.1	0.4	0.06	0.16
T8	0.45:1	0.2	0.2	0.08	0.00
T9	0.45:1	0.3	0.0	0.00	0.04
T10	0.45:1	0.4	0.8	0.02	0.08
T11	0.50:1	0.0	0.4	0.08	0.04
T12	0.50:1	0.1	0.2	0.00	0.08
T13	0.50:1	0.2	0.0	0.02	0.12
T14	0.50:1	0.3	0.8	0.04	0.16
T15	0.50:1	0.4	0.6	0.06	0.00
T16	0.55:1	0.0	0.2	0.02	0.16
T17	0.55:1	0.1	0.0	0.04	0.00
T18	0.55:1	0.2	0.8	0.06	0.04
T19	0.55:1	0.3	0.6	0.08	0.08
T20	0.55:1	0.4	0.4	0.00	0.12
T21	0.60:1	0.0	0.0	0.06	0.08
T22	0.60:1	0.1	0.8	0.08	0.12
T23	0.60:1	0.2	0.6	0.00	0.16
T24	0.60:1	0.3	0.4	0.02	0.00
T25	0.60:1	0.4	0.2	0.04	0.04

.

6. Results of the Orthogonal Experiment and Mix Design

6.1. Results of the Orthogonal Experiment

The results of the orthogonal experiment reflect the strength characteristics of the cement paste body at different ages (Figure 9). At 3 days, the splitting tensile strength ranged from 1.13 MPa to 2.53 MPa, and the compressive strength varied from 13.87 MPa to 41.42 MPa. At 7 days, the splitting tensile strength was between 1.33 MPa and 3.00 MPa, with compressive strength ranging from 20.30 MPa to 48.48 MPa. At 28 days, the splitting tensile strength increased to between 1.50 MPa and 3.93 MPa, while compressive strength ranged from 30.68 MPa to 72.73 MPa. Most specimens demonstrated an increase in both splitting tensile strength and compressive strength with age, consistent with the strength development trends observed in cement-based materials.

Figure 10 illustrates the relationship between the density of the cementitious matrix and its 28-day compressive strength. The 28-day compressive strength, due to the completion of hydration by this age, provides a stable and reliable indicator of the long-term strength of the material, being less susceptible to experimental variability. The density of the matrix is strongly influenced by the water-to-cement ratio (W/C), with lower W/C values yielding higher densities. Under a constant W/C, density shows a positive correlation with the 28-day compressive strength. This indicates that a denser structure with fewer internal voids contributes to greater strength over time, a finding consistent with established empirical principles. Furthermore, it was observed during testing that specimens with a higher bleeding rate exhibited relatively greater densities. This is attributed to the fact that water separation reduces the effective W/C of the consolidated paste. Consequently, for pastes with the same initial W/C, a higher bleeding rate leads to a lower effective W/C and a correspondingly significant increase in the density of the hardened matrix.

Figure 11 illustrates the relationship between the fluidity and viscosity of the cement slurry. A positive correlation was generally observed; however, several specimens (T7, T11, T16, T17, T21) exhibited disproportionately high viscosity relative to their fluidity. As listed in Table 7, these samples contained lower dosages of superplasticizers, specifically with the composite water-reducing agent (CWRA) content below 0.1%. Cement slurry behaves as a Bingham fluid, requiring a finite yield stress to be exceeded before flow initiates. When the superplasticizer dosage is insufficient, the adsorption sites on cement particle surfaces remain incompletely covered, leaving residual surface charges. This promotes the formation of flocculated structures via van der Waals forces and electrostatic attraction, which generate considerable yield stress and exhibit pronounced shear-thinning behavior [74]. The fluidity test essentially measures the flow of the slurry under its own weight at a relatively fixed, low shear rate, reflecting its capacity to overcome the yield stress. In contrast, viscosity is measured over a wider range of shear rates, and the recorded value is highly dependent on the selected shear rate. At low superplasticizer dosages, viscosity can vary significantly across different shear rates, leading to measurement instability. Consequently, the correlation between the rheological parameter (viscosity) and the macroscopic empirical parameter (fluidity) becomes weak under such conditions.

6.2. Range Analysis

Range analysis is a fundamental analytical approach in orthogonal experimental design. It involves calculating the average response and the range of experimental results at different levels for each factor, thereby enabling a rapid assessment of the relative significance of factors and the identification of optimal level combinations. In this method, the average value reflects the overall effect of a specific factor level on the target index, while the range value indicates the magnitude of the factor’s influence. A larger range signifies that the factor is of primary importance, whereas a smaller range suggests a secondary influence.

6.2.1. Viscosity

Figure 12 demonstrates that the viscosity of cement paste decreases with an increasing W/C. A higher W/C corresponds to a greater proportion of free water in the mixture. This free water envelops the cement particles, forming a lubricating film on their surfaces that significantly reduces interparticle friction. The reduced friction facilitates particle sliding, resulting in a lower macroscopic viscosity of the paste [28].

The viscosity of cement paste decreases with increasing dosage of the CWRA. This reduction occurs because the water-reducing agent acts as a surfactant, disrupting the flocculated structure of cement particles. This dispersion releases entrapped water, increasing the amount of free water in the system and thereby reducing viscosity [43]. In contrast, the polycarboxylate superplasticizer (PS) exhibits a different influence pattern: viscosity initially increases followed by a decrease as the PS content rises. This is attributed to the relatively lower water-reducing efficiency of PS compared to W/C and CWRA, making its effect on viscosity less pronounced. In mix design, PS is primarily utilized for its functional properties—such as air-entrainment and retardation—to enhance slurry stability, rather than for viscosity reduction.

Based on the range analysis results, the relative importance of the influencing factors on viscosity is ranked as follows: CWRA (range = 303.8) > W/C (range = 287.0) > PS (range = 154.7) > triethanolamine (TEA) (range = 92.7) > acrylate salt (AS) (range = 91.9). The results indicate that the dosage of CWRA and W/C exerts the most pronounced influence on viscosity, thereby serving as the key control factors. Although PS also shows a considerable effect, its impact is secondary to that of CWRA and W/C. The contributions of TEA and AS to viscosity are relatively minor. To minimize the viscosity of the cement paste, the optimal combination of factor levels—selected from those exerting the greatest influence and yielding the highest mean values—is determined as follows: W/C = 0.6, CWRA = 0.4%, PS = 0.2%, TEA = 0.08%, and AS = 0.08%.

6.2.2. Splitting Tensile Strength

Figure 13 illustrates that the early splitting tensile strength (ESTS) of cement paste demonstrates a reduction with an increasing W/C. The role of water in the cement hydration process can be categorized into two distinct components: (1) chemically bound water, which participates directly in the hydration reactions, and (2) capillary water, which is incorporated primarily to achieve the required workability of the fresh mixture. Unlike chemically bound water, capillary water does not engage in hydration; instead, it occupies space within the cementitious matrix during hardening. This ultimately evaporates or remains as voids, contributing to the formation of a capillary pore network. Consequently, W/C governs the initial porosity and pore structure of the hardened cement paste, which is a critical determinant of its early-age mechanical properties [30].

The ESTS of cement paste shows a general increasing trend with higher dosages of water-reducing agents (CWRA and PS). This enhancement is attributed to the dispersing effect of these admixtures, which promotes a more uniform distribution of cement particles. The improved dispersion leads to more complete hydration and a homogeneous microstructure of hydration products. Additionally, the enhanced fluidity facilitates the removal of entrapped air bubbles. Consequently, the incorporation of water-reducing agents contributes to a denser and more uniform hardened matrix with significantly reduced porosity, thereby effectively improving the ESTS.

TEA has a significant impact on the ESTS of cement paste. The ESTS initially increases with the addition of TEA, reaching a peak before declining. It can be observed that at low dosages ranging from 0.02% to 0.05%, TEA markedly enhances the ESTS of the cement. This represents a typical critical dosage effect. The mechanism of action of TEA in the cement hydration process differs from that of water-reducing agents; it primarily acts as a chemical catalyst by influencing the hydration rates of different minerals in cement. At an appropriate dosage, TEA can catalyze the hydration of tricalcium aluminate (C₃A) in the early stage and subsequently promote the hydration of tricalcium silicate (C₃S). This combined effect leads to a significant increase in early strength with minimal reduction in standard strength. However, it is important to precisely control the dosage of TEA. Excessive TEA molecules can excessively and durably adsorb onto the surface of C₃S particles, forming an overly stable protective film that severely hinders the hydration process of C₃S. This negative effect can outweigh the previously mentioned positive catalytic effects, leading to significant retardation and a sharp decrease in both early and standard strengths [65,66,67].

Based on the range analysis, the relative importance of the influencing factors on the early splitting tensile strength (ESTS) is ranked as follows: W/C (range = 0.820) > TEA (range = 0.420) > CWRA (range = 0.288) > PS (range = 0.278) > AS (range = 0.172). The results indicate that the W/C exerts the most significant influence on ESTS, followed by TEA, establishing these two factors as the primary controls. The effects of the water-reducing agents (CWRA and PS) are slightly less pronounced than those of W/C and TEA, while AS exhibits the smallest impact. To maximize ESTS, the optimal combination of factor levels was determined as: W/C = 0.35, TEA = 0.04%, CWRA = 0.4%, PS = 0.8%, and AS = 0.16%.

Figure 14 demonstrates that the standard splitting tensile strength (SSTS) of cement paste decreases with an increasing W/C, while it increases with higher dosages of the water-reducing agents (CWRA and PS). This trend is consistent with that observed for the early splitting tensile strength (ESTS). Based on the range analysis, the relative importance of the influencing factors is ranked as: W/C (range = 1.618) > CWRA (range = 0.894) > PS (range = 0.772) > AS (range = 0.282) > TEA (range = 0.228). The results clearly indicate that W/C exerts the most significant influence on SSTS, followed by the water-reducing agents, establishing these as the critical control factors. The effects of AS and TEA are comparatively minor. To optimize SSTS, the determined optimal factor levels are: W/C = 0.35, CWRA = 0.4%, PS = 0.8%, TEA = 0.06%, and AS = 0.04%.

6.2.3. Compressive Strength

Figure 15 illustrates that the early compressive strength (ECS) of cement paste decreases with an increasing W/C, a trend consistent with that observed for splitting tensile strength. This reduction is attributed to the higher initial porosity and more porous microstructure resulting from an elevated W/C, which fundamentally undermines all macroscopic mechanical properties. The ECS generally increases with higher dosages of the water-reducing agents (CWRA and PS). In contrast, the influence of TEA on ECS is non-monotonic, showing an initial increase followed by a decrease with rising dosage, which aligns with its effect on splitting tensile strength.

Based on the range analysis, the relative importance of the influencing factors on early compressive strength (ECS) is ranked as follows: CWRA (range = 12.396) > W/C (range = 11.488) > PS (range = 7.300) > TEA (range = 4.172) > AS (range = 1.474). The results demonstrate that CWRA and W/C exert the most pronounced influence on ECS. The effects of PS and TEA are secondary, while AS exhibits the least impact. To maximize ECS, the optimal combination of factor levels is determined as: W/C = 0.35, TEA = 0.02%, CWRA = 0.4%, PS = 0.8%, and AS = 0.04%.

Figure 16 illustrates that the standard compressive strength (SCS) of cement paste decreases with an increasing W/C. Conversely, SCS demonstrates a clear improvement with higher dosages of the water-reducing agents (CWRA and PS). Furthermore, the influence of both TEA and AS on SCS is non-monotonic, characterized by an initial increase followed by a decrease as their respective contents rise.

Figure 14 and Figure 16 indicate that AS affects both SSTS and SCS of cement paste, exhibiting a trend of initial increase followed by a decrease with increasing AS content, demonstrating a significant critical dosage effect. This is attributed to the filling and film-forming roles of AS within the cement system [68]. During hydration, AS and the polymers it generates can fill the capillary and gel pores within the hardened matrix, reducing porosity and enhancing structural uniformity and density. Additionally, the resulting polymers encapsulate the surfaces of the cement hydration products and create a composite structure that combines the rigidity of inorganic hydration products with the toughness of organic polymers. This leads to a more even stress distribution under load, thereby improving the mechanical properties of the hardened matrix. However, when the AS content exceeds a certain critical threshold, an excess of polymers forms an overly thick membrane that separates the hydration products. This can lead to a decrease in the strength of the hardened matrix, as the thick membrane obstructs the contact between cement particles and water molecules, thereby causing a delay in the cement hydration process [35,38].

Figure 13 and Figure 15 indicate that the early effects of AS in cement-based materials are not significant, with its reinforcing properties becoming fully realized in later stages. This delay is attributed to the time required for AS to fill and form a membrane, as well as the competitive and sequential nature of the cement hydration process [38]. Cement hydration is the primary factor influencing early strength, while the membrane formation process of AS is relatively delayed. In the later stages of hydration, when the structure of the hardened matrix stabilizes and pore morphology is largely established, the reinforcing effects of AS become more pronounced.

Based on the range analysis, the relative importance of the influencing factors on SCS is ranked as follows: CWRA (range = 19.472) > PS (range = 11.458) > W/C (range = 9.782) > AS (range = 8.326) > TEA (range = 6.118). To maximize SCS, the optimal factor levels were determined as: W/C = 0.35, CWRA = 0.4%, PS = 0.6%, TEA = 0.02%, and AS = 0.12%.

It is evident that the water-reducing agents (CWRA, PS) have a more significant impact on the SCS than W/C. This is because tensile strength is more sensitive to micro-defects, which are determined by the weakest links in the microstructure of the cement paste. While W/C directly affects the porosity of the cement framework, leading to localized defects that can result in permanent deficiencies over time, compressive strength reflects the overall structural integrity of the cement matrix. Water-reducing agents enhance the fluidity of the paste, facilitating the release of air bubbles and promoting more uniform dispersion of hydration products. Thus, it is reasonable that the influence of water-reducing agents on compressive strength is greater than that of W/C.

The incorporation of PS reveals a critical dosage phenomenon for ESTS, SSTS, ECS, and SCS. Ultimately, this reflects the interplay between the positive and negative effects of PS at varying dosages. The addition of PS includes retarding agents, air-entraining agents, and slump-retaining additives, which do not contribute to water reduction. At lower dosages of PS, the strength of the hardened matrix is negatively correlated with the amount of PS used. At this stage, the retarding effect dominates, delaying the hydration reaction. The negative impact of this retardation significantly outweighs the density benefits gained from a lower water-cement ratio. Additionally, the air-entraining agents in PS introduce a substantial number of bubbles, leading to poorer workability at low PS dosages. Consequently, the bubbles cannot be discharged promptly, resulting in increased porosity of the hardened matrix. As the dosage of PS increases, the strength is positively correlated with the amount of PS. In this range, the dispersion effect of PS is fully realized, significantly reducing the mixing water content. This leads to a more uniform distribution of hydration products, enhancing the microstructure of the hardened matrix. Improved workability of the paste allows the positive effects of air-entrainment to outweigh the negative effects. As the dosage of PS continues to increase, the strength becomes negatively correlated with the amount of PS. Excessive PS can form a thick adsorption layer on the surface of cement particles, severely hindering hydration. This not only affects early strength but may also prevent normal strength development. Excessive PS dosage can also lead to bleeding and segregation, severely disrupting the uniformity of the cement system and creating weak zones and areas of high porosity. Additionally, it may trigger re-flocculation of cement particles, known as oversaturation flocculation, resulting in decreased fluidity of the paste, increased viscosity, uneven distribution of cement particles, and a significant decline in strength [43,44,45].

6.2.4. Bleeding Rate

Figure 17 illustrates that the bleeding rate of cement paste increases with a higher W/C. This occurs because an elevated W/C disrupts the equilibrium between the supportive capacity of the solid particle network and the volume of interstitial water. As a result, cement particles are more prone to settle under gravity, leading to water separation, i.e., bleeding.

The bleeding rate of cement paste increases with a higher dosage of the CWRA. This is attributed to the fact that the free water released by the dispersing action of CWRA, when present in excess, tends to migrate upward under gravity, thereby enhancing water separation. In contrast, the effect of PS dosage on the bleeding rate displays a critical dosage phenomenon. This behavior reflects the synergistic and antagonistic interactions among the various functional components of PS, such as its water-reducing, air-entraining, and retarding properties, whereas CWRA, as a pure water-reducing agent, does not exhibit such complex interactions.

The bleeding rate of cement paste initially increases and then decreases with the increasing dosage of TEA. This behavior is attributed to TEA’s modification of the types, generation rates, and microstructure of early hydration products, which subsequently influences the paste’s ability to retain moisture and thereby affects the bleeding rate at a macroscopic level.

The bleeding rate of cement paste shows a trend of initially decreasing and then increasing with the increasing dosage of AS. As a water-retaining agent, AS can form a hydrophilic polymer network through cross-linking polymerization in the high-alkali environment of the cement system when used within an appropriate dosage range. This network effectively hinders the settling of solid particles and the rising of water molecules.

Based on the range analysis, the relative importance of the influencing factors on the bleeding rate is ranked as follows: W/C (range = 0.134) > CWRA (range = 0.115) > TEA (range = 0.046) > PS (range = 0.045) > AS (range = 0.041). The results indicate that the W/C exerts the most significant influence on the bleeding rate, followed by CWRA, establishing these two as the critical control factors. While PS, TEA, and AS also exhibit measurable effects, their impacts are comparatively lower. To minimize the bleeding rate, the optimal factor levels were determined as: W/C = 0.35, CWRA = 0.0%, PS = 0.6%, TEA = 0.08%, and AS = 0.08%.

In general, an elevated bleeding rate is typically attributed to either an excessive dosage of water-reducing agents or a high W/C, which compromises the stability of the paste and reduces its void-filling capacity. It should be noted, however, that during actual grouting operations, the presence of injection pressure can cause free water in the paste to stratify under pressure rather than solely under gravity. Consequently, a paste with a high bleeding rate may retain a certain degree of void-filling capability. Based on engineering practice, the bleeding rate of grouting materials is generally required to be below 25%.

6.3. Analysis of Variance (ANOVA)

Range analysis, which assesses the independent effect of a single factor based only on its extreme values, suffers from low efficiency of information utilization and high sensitivity to outliers. Consequently, it offers limited control over experimental error and is generally suitable only for preliminary, rapid, and low-precision screening. Moreover, because range analysis does not consider interactions between factors, the optimal level combinations identified through this method require further verification via ANOVA.

ANOVA evaluates the sources of data variation to determine whether differences between group means exceed random within-group errors. It quantifies the statistical significance of each factor and identifies the key control variables. In ANOVA, an F-test is performed for each factor; the magnitude of the F-value reflects the extent of the factor’s influence on the response. The corresponding calculation formulas for the F-values are given in Equations (5)–(8) [75].

$$\left\{\begin{array}{l}S{S}_T={\displaystyle \sum (y_n^2-\frac{T^2}{N})}(n=1,2,\dots ,25)\\ S{S}_{A^{[i]}}={\displaystyle \frac{1}{N_{A^{[i]}}}}\cdot {\displaystyle \sum [(T_{A_j^{[i]}}^2)-\frac{T^2}{N}](i=1,2,3,4,5;j=1,2,3,4,5)}\\ S{S}_E=S{S}_T-{\displaystyle \sum S{S}_{A^{[i]}}}(i=1,2,3,4,5)\end{array}\right.$$

(5)

$$\left\{\begin{array}{l}d{f}_T=N-1\\ d{f}_{A^{[i]}}=k-1\\ d{f}_E=d{f}_T-{\displaystyle \sum d{f}_{A^{[i]}}}\end{array}\right.(i=1,2,3,4,5)$$

(6)

$$\left\{\begin{array}{l}M{S}_{A^{[i]}}={\displaystyle \frac{S{S}_{A^{[i]}}}{d{f}_{A^{[i]}}}}(i=1,2,3,4,5)\\ M{S}_E={\displaystyle \frac{S{S}_E}{d{f}_E}}\end{array}\right.$$

(7)

$$F={\displaystyle \frac{M{S}_{A^{[i]}}}{M{S}_E}}(i=1,2,3,4,5)$$

(8)

In the equation, $S{S}_T$ represents the total sum of squares; $y_n$ denotes the experimental result of the nth trial; $T$ is the sum of all experimental results; $N$ indicates the total number of trials; $S{S}_A$ signifies the sum of squares for the factors; $A_j^{[i]}$ corresponds to the experimental result for the ith factor at the jth level; $N_{A^{[i]}}$ denotes the total number of trials for the corresponding factor; $T_{A_j^{[i]}}$ represents the experimental result at the jth level of the ith factor; $S{S}_E$ indicates the sum of squares for error; $d{f}_T$ is the total degrees of freedom; $d{f}_{A^{[i]}}$ represents the degrees of freedom for the ith factor; $k$ denotes the number of levels; $d{f}_E$ indicates the degrees of freedom for error; and $F$ represents the ANOVA statistic.

6.3.1. Viscosity

Figure 18 demonstrates that the relative importance of the factors influencing viscosity follows the order: CWRA > W/C > PS > AS > TEA, which is consistent with the ranking obtained from range analysis.

CWRA and W/C are significant at the $\alpha =0.05$ level, indicating they have a substantial effect on viscosity. PS is significant at the $\alpha =0.1$ level but not at the $\alpha =0.05$ level, suggesting it has a moderate influence on viscosity. TEA and AS are not significant at the $\alpha =0.1$ level, implying they have no considerable impact on viscosity. For mix optimization, viscosity can be reduced by adjusting W/C and CWRA, while PS, TEA, and AS can be flexibly selected based on cost and process requirements without stringent constraints.

6.3.2. Splitting Tensile Strength

Figure 19 illustrates that the relative importance of factors affecting ESTS follows the order: W/C > TEA > PS > CWRA > AS, which aligns with the ranking obtained from range analysis.

According to the results of variance analysis, W/C is significant at the $\alpha =0.05$ level, indicating it has a substantial impact on ESTS. Although TEA, PS, CWRA, and AS are not significant at the $\alpha =0.1$ level, this does not imply that they have no effect on ESTS. ANOVA assesses whether the effect of a factor, across its defined level range, is substantial enough to be distinguished from experimental error. A low F-value may indicate that the factor’s influence on the response does not exhibit a clear, monotonic trend within the tested levels, causing its effect to be obscured by experimental variability and the stronger contributions of other factors. Furthermore, while the orthogonal experimental design assumes no interactions among factors, such interactions are likely present in practice. For example, the early-strength effect of TEA can be modulated by the W/C: under a high W/C, where the inherent strength of the cementitious material is lower, the strengthening effect of TEA tends to be more pronounced than under a low W/C. This type of complex interaction, when analyzing main effects in isolation, may be attributed to the error term, making it more difficult to detect statistically significant main effects for individual factors. Consequently, in mix-design optimization, adjusting the W/C can enhance ESTS, but interactions between W/C and other factors—such as CWRA, PS, and TEA—should also be considered for their combined impact on ESTS.

Figure 20 indicates that the relative importance of factors affecting the SSTS follows the order: W/C > CWRA > PS > AS > TEA, which is fully consistent with the ranking obtained from range analysis. According to the ANOVA results, none of the five experimental factors are significant at the $\alpha =0.1$ A1 level, indicating that their effects on SSTS are not statistically significant.

This observation is not unreasonable. Factors like W/C can significantly affect the initial structure of the stone, while TEA can alter the early hydration kinetics. During the early stages of hydration, when the microstructure is loose and rapidly changing, their impacts are pronounced. However, as hydration approaches completion and the system reaches a relatively stable and balanced state, their influence diminishes. For instance, high W/C can lead to a poor initial structure of the stone, resulting in significantly lower ESTS. Yet, due to larger structural pores, there is more space and moisture available for long-term hydration, potentially leading to greater strength gains, thus narrowing the gap in SSTS compared to lower W/C stones. This reduces the average difference in W/C at various levels, leading to a decrease in the sum of squares of deviations and a decline in significance.

Conversely, factors like water-reducing agents, which have a relatively minor impact on strength, exhibit weak effects by the 28-day mark. Their effect size approaches the level of experimental noise, making it challenging to distinguish their influence clearly.

Based on engineering practice, W/C is considered one of the factors influencing SSTS. Although it is statistically insignificant, adjusting W/C remains essential for optimizing SSTS in mix design. Additionally, attention should be given to the effects of CWRA and PS on SSTS.

6.3.3. Compressive Strength

Figure 21 illustrates that the relative importance of factors affecting ECS follows the order: CWRA > W/C > TEA > PS > AS, which is largely consistent with the ranking derived from range analysis. CWRA and W/C are significant at the $\alpha =0.05$ level, indicating that they have a notable impact on viscosity. While PS, TEA, and AS are not significant at the $\alpha =0.1$ level, the F-values for PS and TEA are close to the critical value at $\alpha =0.1$, suggesting they may have some influence on ECS. In contrast, the F-value for AS is significantly lower than the critical value at $\alpha =0.1$, indicating that AS does not have a significant effect on ECS.

Figure 22 illustrates that the relative importance of factors affecting SCS follows the order: CWRA > W/C > AS > PS > TEA. Compared to the ranking obtained from range analysis, the influence of PS appears substantially lower in this evaluation. According to the variance analysis results, none of the five experimental factors are significant at the $\alpha =0.1$ level, indicating that they do not have a statistically meaningful impact on SCS. Consistent with Figure 19, no single factor is dominant in determining standard strength within the designed levels; the standard strength is a result of the combined effects of all factors. This also suggests that the effect signal strengths of the five experimental factors are close to the experimental noise level, indicating that environmental factors similarly influence the standard strength of the stone body. This underscores the importance of strictly controlling mixing methods, curing temperature, and time during the experimental process.

6.3.4. Bleeding Rate

Figure 23 illustrates that the relative importance of factors affecting the bleeding rate follows the order: W/C > CWRA > AS > PS > TEA. Compared with the ranking obtained from range analysis, the influence of AS appears notably higher in this assessment. According to the variance analysis results, W/C is significant at the $\alpha =0.05$ level, indicating a notable impact on the bleeding rate. While CWRA is not significant at the $\alpha =0.05$ level, it is significant at the $\alpha =0.1$ level, with its F-value approaching the critical value at $\alpha =0.05$, suggesting that CWRA also has a significant effect on the bleeding rate. PS, TEA, and AS are not significant at the $\alpha =0.1$ level, indicating that they do not have a substantial impact on the bleeding rate. In mix design optimization, W/C and CWRA can be adjusted to control the bleeding rate, while PS, TEA, and AS can be flexibly selected based on cost and process requirements without excessive constraints.

6.4. Comprehensive Analysis

While ANOVA addresses the limitation of range analysis by considering the interaction among factors and statistically analyzing the sources of data variability, both methods still provide qualitative insights. In contrast, comprehensive analysis combines subjective weighting of control indicators with objective data analysis, allowing for a quantitative assessment of the overall impact of multiple factors on these indicators. This constructed evaluation system is more specific, flexible, and persuasive compared to range and variance analyses.

To determine the influence weights of different factors at various levels on the control indicators, the Analytic Hierarchy Process (AHP) is employed for a comprehensive analysis of the orthogonal experiment data. According to AHP, the experimental results can be structured into three layers:

• Indicator Layer: This comprises the performance metrics, including viscosity, ESTS, SSTS, ECS, SCS, and bleeding rate;
• Factor Layer: This includes the influencing factors, specifically W/C, CWRA, PS, TEA, and AS;
• Level Layer: The experiment is designed with a total of five levels for each factor.

The average value $K_{ij}$ represents the effect of factor $\mathrm{Ai}$ at level $\mathrm{Lj}$ on the control indicator, calculated as the sum of experimental results at this level. If the analysis of the orthogonal test aims to maximize the control indicator, set $M_{ij}=K_{ij}$; otherwise, set $M_{ij}=1/K_{ij}$. The AHP calculation formulas are presented in Equations (9)–(11) [76].

$$\begin{array}{l}A=\left(\begin{array}{ccc}{P}_1& \dots & 0\\ ⋮& \ddots & ⋮\\ 0& \dots & P_5\end{array}\right)\\ P_i=\left(\begin{array}{l}{M}_{i1}\\ M_{i2}\\ M_{i3}\\ M_{i4}\\ M_{i5}\end{array}\right)(i=1,2,3,4,5)\end{array}$$

(9)

$$\left\{\begin{array}{l}S=\left(\begin{array}{ccc}1/t_1& \dots & 0\\ ⋮& \ddots & ⋮\\ 0& \dots & 1/t_5\end{array}\right)\\ t_j={\displaystyle \sum _{i=1}^5{M}_{ij}}(j=1,2,3,4,5)\end{array}\right.$$

(10)

$$C=\left({\displaystyle \frac{R_1}{{\displaystyle {\sum }_{i=1}^5{R}_i}}}{\displaystyle \frac{R_2}{{\displaystyle {\sum }_{i=1}^5{R}_i}}}{\displaystyle \frac{R_3}{{\displaystyle {\sum }_{i=1}^5{R}_i}}}{\displaystyle \frac{R_4}{{\displaystyle {\sum }_{i=1}^5{R}_i}}}{\displaystyle \frac{R_5}{{\displaystyle {\sum }_{i=1}^5{R}_i}}}\right)$$

(11)

Matrix $A$ is right-multiplied by matrix $S$ to normalize each column of matrix $A$. The range $R_i$ of factor $\mathrm{Ai}$ is referred to as the effect of factor $\mathrm{Ai}$ on the experiment. Matrix $\mathrm{C}$ represents the weight matrix for the influence of factors on the experiment. The influence weights of each factor at various levels can be calculated using Equation (12).

$$\omega =AS{C}^T$$

(12)

The analysis results are shown in Figure 24.

Based on the AHP analysis results of the orthogonal test shown in Figure 25, the optimal level combinations for each indicator can be determined, as illustrated in Figure 24. The optimal level combination for viscosity is (W/C, CWRA, PS, TEA, AS) = [5, 5, 5, 5, 3]; for ESTS, it is [1, 5, 1, 5, 5]; for SSTS, it is [1, 5, 2, 4, 1]; for ECS, it is [1, 5, 1, 2, 5]; for SCS, it is [1, 5, 2, 2, 1]; and for water content rate, it is [1, 1, 4, 3, 2].

The overall influence of each factor on the performance indicators can be quantified by summing its contribution weights across different levels. A greater summed weight signifies a stronger influence of the factor on the respective indicator. As shown in Figure 26, which visualizes the relative influence degree of each factor. The larger the bubble area, the greater the degree of influence. The results align well with the trends identified through both range analysis and ANOVA.

6.5. Quantitative Analysis

According to the AHP analysis results of the orthogonal experiment (Figure 24), a relatively optimal slurry formulation requires the coordinated adjustment of multiple performance indicators. For a given control indicator, a total of 3125 combinations can be generated from the experimental design. The impact weight of each combination on the indicator can be calculated using Equation (13).

$${\omega }_i(k_1,k_2,k_3,k_4,k_5)=P_i(1,k_1)+P_i(2,k_2)+P_i(3,k_3)+P_i(4,k_4)+P_i(5,k_5)$$

(13)

In the equation, ${\omega }_i(i=1,\dots ,6)$ corresponds to the influence weights of the six indicators: viscosity, ESTS, SSTS, ECS, SCS, and bleeding rate. $P_i(j,k_z)$ $(j=1,\dots ,5;z=1,\dots ,5)$ denotes the influence weight of the $z$ level of the $j$ factor on the $i$ indicator, where the $j$ factors correspond to W/C, CWRA, PS, TEA, and AS, respectively.

Based on engineering practice and application requirements, the six performance indicators outlined above must be assigned appropriate weight values. In fractured rock formations, grouting demands high fluidity (low viscosity); in areas subjected to frequent blasting, early strength of the hardened material is critical; and for effective seepage control, the hardened grout must resist cracking, necessitating adequate tensile strength. Accordingly, the weights assigned to viscosity, ESTS, SSTS, ECS, SCS, and bleeding rate are 0.30, 0.20, 0.16, 0.14, 0.12, and 0.08, respectively. The overall performance score of a slurry formulation is obtained by normalizing the influence weights of each indicator and multiplying them by the corresponding assigned weights. The five highest-ranking formulations based on this score are presented in

Table 10. The top five mix proportions with the highest comprehensive rating for slurry performance.

Rating Ranking	Individual Scores					Composite Score
	W/C	CWRA	PS	TEA	AS
1	0.6	0.4	0.0	0.08	0.08	0.2518
2	0.6	0.4	0.0	0.08	0.16	0.2507
3	0.6	0.4	0.0	0.02	0.08	0.2505
4	0.6	0.4	0.0	0.08	0.00	0.2502
5	0.6	0.4	0.0	0.06	0.08	0.2500

, with the calculation method detailed in Equation (14).

$${\omega }_i(k_1,k_2,k_3,k_4,k_5)={\displaystyle \sum {\lambda }_i{\tau }_i{\omega }_i}$$

(14)

In the equation, $\omega$ represents the comprehensive performance score of the slurry based on the mix proportion; ${\lambda }_i$ denotes the weight assigned to the corresponding indicators; ${\tau }_i$ is the normalization coefficient, which can be calculated from ${\tau }_i=1/{\displaystyle \sum a_{jk}}$, where $a_{jk}$ signifies the sum of all elements in the influence weight matrix for the $i$ indicator.

Based on the results of 25 sets of orthogonal experiments, let $\mathrm{F}$ represent the fuzzy set indicating “excellent working performance of cement paste,” and $F(x)$ be the membership function of this set. The performance scores for the 25 sets of orthogonal tests can be calculated under the six indicators: viscosity, ESTS, SSTS, ECS, SCS, and bleeding rate. The calculation formula for $F(x)$ is shown in Equation (15) [76].

$$F(x)={\displaystyle \frac{x-x_{\min }}{x_{\max }-x_{\min }}}$$

(15)

In the equation, $x_{\max }$ and $x_{\min }$ represent the optimal and worst values of the experimental results, respectively.

Weight values are assigned based on actual engineering requirements, with viscosities, ESTS, SSTS, ECS, SCS, and bleeding rate weighted at 0.3, 0.2, 0.16, 0.14, 0.12, and 0.08, respectively. The calculation results are presented in

Table 11. Comprehensive evaluation results of slurry performance in orthogonal experiment set.

Number	Individual Scores						Composite Score
	Viscosity	ESTS	SSTS	ECS	SCS	Bleeding
T1	0.003	0.416	0.501	0.975	0.266	1.000	0.413
T2	0.004	0.909	0.544	0.877	0.443	1.000	0.526
T3	0.395	0.500	0.460	0.605	0.443	1.000	0.510
T4	0.823	0.390	0.370	0.893	0.464	0.857	0.633
T5	0.872	1.000	1.000	0.893	0.807	0.929	0.918
T6	0.000	0.370	0.261	0.535	0.462	1.000	0.326
T7	0.332	0.390	0.284	0.823	0.243	0.929	0.442
T8	0.853	0.584	0.452	0.494	0.289	0.750	0.609
T9	0.883	0.195	0.436	0.535	0.379	0.857	0.563
T10	0.948	0.610	0.966	1.000	1.000	0.750	0.881
T11	0.369	0.221	0.117	0.177	0.035	0.964	0.280
T12	0.822	0.156	0.096	0.082	0.165	0.929	0.399
T13	0.958	0.305	0.365	0.564	0.406	0.679	0.589
T14	0.937	0.500	0.525	0.646	0.132	0.518	0.613
T15	0.985	0.221	0.440	0.852	0.736	0.714	0.675
T16	0.823	0.000	0.023	0.000	0.000	0.964	0.328
T17	0.824	0.175	0.083	0.342	0.338	0.929	0.458
T18	0.887	0.286	0.358	0.235	0.132	0.857	0.498
T19	0.987	0.370	0.299	0.835	0.354	0.714	0.634
T20	0.958	0.156	0.512	0.494	0.435	0.393	0.553
T21	0.822	0.045	0.000	0.053	0.029	0.904	0.339
T22	0.913	0.221	0.151	0.136	0.341	0.643	0.454
T23	0.983	0.11	0.094	0.3	0.414	0.518	0.465
T24	0.973	0.175	0.311	0.082	0.382	0.321	0.46
T25	1	0	0.234	0.342	0.129	0	0.401

.

6.6. Mix Proportion Design

Based on the results presented in Table 10, the W/C and the AS content were fixed at 0.6 and 0.08%, respectively. During testing, it was observed that at a high W/C (exceeding 0.5), a CWRA dosage above 0.3% adversely affected the stability of the cement paste, leading to segregation and a pronounced shortening of its usable workability period. To ensure slurry stability during grouting, the CWRA dosage was therefore reduced to 0.25%. Preliminary tests indicated that the water-reducing efficiency of CWRA is approximately three times that of PS; consequently, to control slurry viscosity, the PS content was increased to 0.5%. Given the strong dosage dependence of TEA, additions exceeding 0.1% may induce excessive retardation and impair long-term strength. Accordingly, its dosage was set at 0.04% in the final design.

According to the comprehensive performance scores listed in Table 11, the top-four ranked experimental groups are T5, T10, T15, and T19, with scores of 0.918, 0.881, 0.675, and 0.634, respectively. The measured viscosity of the T5 group was 82.61 mPa · s, indicating a relatively high value. Although this mix contained 0.4% CWRA, no significant segregation was observed during testing. To further improve workability, an additional 0.4% PS was introduced into the original formulation.

The T10 group satisfied the viscosity requirement and exhibited no segregation; its water-reducing admixture dosage was retained, while the TEA content was increased to 0.04% to enhance early-age strength.

The T15 group met the viscosity criterion, but noticeable segregation occurred during the test. To ensure stability, the CWRA dosage was reduced to 0.3% and the PS dosage was raised to 1%.

The T19 group complied with both viscosity and stability requirements; therefore, no adjustment was made to its mixture proportions. Based on the above evaluations, five optimized cement paste mix designs were selected and are summarized in

Table 12. Cement slurry mix ratio.

Number	Paste Mix Ratio
	W/C	CWRA	PS	TEA	AS
Q1	0.40	0.40	0.4	0.06	0.12
Q2	0.45	0.40	0.8	0.04	0.08
Q3	0.50	0.30	1.0	0.06	0.00
Q4	0.55	0.30	0.6	0.08	0.08
Q5	0.60	0.25	0.5	0.04	0.08
Control group	1.00	0.00	0.0	0.00	0.00

.

According to the experimental methods described in this paper, all control indicators were tested for the five selected cement paste mixes. The comprehensive performance of these mixes is satisfactory, meeting the workability requirements for construction, with mechanical properties reaching the design standards. They comply with the specified technical criteria, demonstrating good feasibility and practicality. The results for each control indicator are presented in

Table 13. Results of various performance indicators of cement paste.

Number	Viscosity	ESTS	SSTS	ECS	SCS	Bleeding	Application Scenarios
	(mPa · s)	(MPa)	(MPa)	(MPa)	(MPa)	(%)
Q1	61.75	2.50	3.72	42.56	67.71	0.03	Sealing of hole
Q2	43.71	2.13	3.91	39.17	72.73	0.06	High-permeability
Q3	22.74	1.74	3.57	29.21	61.64	0.08	Moderate-permeability
Q4	15.17	1.70	3.53	22.12	50.57	0.08	Low-permeability
Q5	11.31	1.42	2.71	20.97	48.18	0.14	Low-permeability
Control group	15.54	0.84	1.67	12.26	35.57	0.24	-

.

7. Conclusions

This study developed an early-strength EHCG using novel polymer modification techniques. The goal was to meet the grouting and seepage control requirements for underground water-sealed cavern storage. An orthogonal experimental design was used to investigate the effects of five key factors: W/C, CWRA, PS, TEA, and AS. These factors were evaluated in terms of their impact on the workability and mechanical properties of the grout. A quantitative analysis was then performed to optimize the material formulation based on field grouting requirements. The main conclusions of this research are as follows:

(1)

The developed polymer-modified cement-based grout consists of cement slurry, water-reducing agents (CWRA and PS), TEA, and AS, tailored for injection into fractured rock media. Each component contributes distinct functional benefits, resulting in a pronounced synergistic effect. CWRA significantly enhances grout flowability due to its high water-reducing efficiency. PS contributes to grout stability while providing supplementary water reduction. TEA notably improves the early-age strength of the hardened material, while AS promotes a more uniform and compact microstructure, enhancing long-term strength.

(2)

The effects of various factors on the workability and mechanical properties of the grout were systematically evaluated through range and variance analyses. The results demonstrate that the W/C ratio has the greatest influence on slurry viscosity, strength, and bleeding rate. CWRA significantly affects viscosity and early compressive strength. PS plays a critical role in enhancing slurry stability and controlling the bleeding rate, but its dosage requires careful optimization. TEA markedly improves early-age strength, although its content needs strict control. AS primarily contributes to long-term strength development without significantly affecting early-age properties.

(3)

A comprehensive analysis using the AHP method quantified the contributions of various factors at different levels to the grout’s performance indicators. This enabled a holistic evaluation and systematic optimization of these performance metrics, providing a quantitative foundation for selecting optimal formulations under various grouting conditions.

(4)

Based on the quantitative analysis, five optimal mix designs for cement-based grouting materials were identified for distinct engineering applications: hole sealing and grouting in fractured rock masses with high, medium, and low permeability. All selected formulations demonstrated excellent workability and mechanical performance, meeting the technical requirements for groundwater sealing in water-sealed underground cavern grouting projects.

(5)

The grouting material formulation design method and process proposed in this study offer clear engineering applicability and operability, providing a theoretical basis and practical reference for the selection and optimization of grouting materials in similar underground projects.