Optimization of synchronous grout properties and construction parameters for shield tunnels in soft soil

Abstract

Improper synchronous grouting materials and construction parameters may cause the shield segments to float, resulting in tunnel dislocation, open joints, uneven deformation, and water leakage. This paper conducts tests on shield synchronous grout performance and presents a multi-objective optimization method for grout performance. This method considers initial setting time, shear yield strength, early compressive strength, and density as optimization performance indicators. An optimized grouting ratio suitable for tunnel anti-floating is recommended and verified. The corresponding construction parameters matching the grout performance are also discussed using numerical simulation methods. Results indicate that the performance of synchronous grout and grouting pressure, distribution, and shield advancing speed have the most significant impact on tunnel stability. A synchronous grout with ratios of water-cement, glue-sand, bentonite-water, cement-fly ash, and additive-glue of 0.602, 0.613, 0.267, 0.733, and 0.010 can obtain a shorter initial setting time and higher shear and compressive strength. Accordingly, the shield tunneling speed should not exceed 83.28 min/ring, ensuring the liquid grout length is regulated at 5 rings. Alternatively, grouting should be limited to the top portion of the segment, or additional grouting holes at high positions should be installed. The related studies can offer recommendations for shield tunnel construction in soft strata.

Introduction

In the Yangtze River Delta, Pearl River Delta, Bohai Bay, and other riverbank and coastal locations in China, there are widely distributed soft soils with high water content, high rheology, high compressibility, low strength, and easy thixotropy, such as silt and muddy silty clay^1–3. Shield construction faces significant challenges in these soils, particularly the uplift of the shield segment during construction. This is primarily because the shield tunnel is more buoyant in water-rich environments, and the soft strata cannot provide enough stratum restriction to the tunnel, resulting in the tunnel becoming unrestrained after it exits the shield tail. Excessive segment uplift can lead to construction quality problems, such as misalignment, open joints, uneven deformation, and water leakage in the shield tunnel. These issues increase the risk of settlement and deformation of the shield tunnel during both construction and long-term periods^4–12.

Synchronous grouting is a crucial process in shield construction and a key technology for controlling the shield tunnel axis. The grout materials and grouting quality greatly influence tunnel buoyancy^13–18. On one hand, synchronous grouting materials can fill gaps during tunnel construction and stabilize the tunnel position. However, if the materials and parameters are not properly chosen, the grout’s hardening strength and setting time will be inappropriate, and the tunnel may not be restrained effectively. Additionally, the grouting process can generate dynamic buoyancy, which worsens deviations in the tunnel axis. There are two main types of synchronous grout: double liquid grout (which consists of cement and water glass) and single liquid grout (which includes cement-based hard grout and slaked lime-based inert grout). Depending on the initial setting time, double liquid grout can be categorized into three types: plastic, slow-setting, and instantaneous. While double liquid grout offers quick setting times and strong early strength, it is expensive, involves a complex construction process, and can clog pipes. In contrast, single liquid inert grout does not clog pipes, but it takes a long time to set and develops strength slowly. The most popular choice among these is single liquid hard grout, which is favored for its high stone strength and customizable setting times.

Scholars have conducted many studies on synchronous grout performance, including double-liquid and single-liquid grouts^19–24. Related research mainly focuses on using electron microscopy or indoor tests to study the influence of cement, sand, and other components and their contents on the performance of synchronous grout and their mechanisms. The relevant results guide optimizing one or more indicators. In addition, some scholars have concentrated on creating new materials to enhance grout performance, such as water-soluble epoxy resin-modified cement grout^25,26desulfurized gypsum-modified grout²⁷shield slag-modified grout^28–30and CO₂-foamed lightweight grout³¹. These novel materials perform better in terms of density, strength, initial setting time, and other attributes, but further practical verification is still required. Furthermore, in addition to grout performance, appropriate grouting settings and construction parameters also play a role in tunnel buoyancy management^32,33. For example, controlling the buoyancy of the shield tunnel will also be challenging if factors such as grouting pressure, grouting location, grouting volume, and shield advancement speed are not well synchronized with the grout properties. However, previous research mainly focuses on the impact of proportions on grout performance; less research comprehensively considers grout properties and construction parameters according to the soil characteristics. Nevertheless, optimizing the grout performance and proposing the corresponding construction parameters, such as grout pressure and shield tunneling speed, that match the grout performance are both important for tunnel anti-floating, especially for soft soil. Currently, there aren’t many published studies on this topic.

This paper conducts shield synchronous grout performance tests and analyzes the mechanical properties of cement-based grouts with different proportions based on tunnel engineering. Taking initial setting time, shear yield strength, early compressive strength, and density as optimization performance indicators, a multi-objective optimization method for grouting performance is established, along with an ideal grouting ratio for tunnel anti-floating. The construction parameters that match the grout performance used in soft soil are also discussed using numerical simulation methods. The relevant research has reference significance for guiding the construction of shield tunnels in similar strata.

Suzhou metro tunnel-line 11 project

The Suzhou Metro Line 11 in Kunshan is situated on the eastern outskirts of Suzhou and adjacent to Shanghai. This metro system consists of twin tunnels with a combined length of 41.36 km and encompasses a total of 28 stations spaced at an average interval of 1.523 km along the line. The outer and inner diameters of each tunnel are 6.6 m and 5.9 m, respectively. Earth Pressure Balance (EPB) shield machines were employed for the excavation of the tunnel section. The shield excavation diameter measures 6.86 m, resulting in a building gap of 0.13 m. The shield excavation passed through muddy silty clay, silty clay, and sandy soil. Typical soil profiles and properties are illustrated in Fig. 1; Table 1. Managing the shield tunnel axis presents significant challenges when dealing with muddy silty clay. This type of soil has high water content and compressibility, along with low permeability and shear strength. These characteristics make controlling the tunnel axis particularly difficult, necessitating careful planning and engineering considerations.

Fig. 1.

Typical soil profile along Suzhou Metro Line 11.

Table 1.

Typical soil parameters between section of Zhanlan center station ~ xihuan road Station.

Layer	Moisture content w (%)	Weight γ kN/m3)	Compression modulus Es (MPa)	Cohesion ccq (kPa)	Internal friction angle φcq (°)	Poisson’s ratioµ	Horizontal foundation coefficient kh (MN/m2)	Vertical foundation coefficient kv (MN/m2)
Fill①1		21		5	15		6	5
Silty clay②1	32.8	18.8	4.54	24.2	14.4	0.35	10	8
Muddy silty clay ②y	43.2	17.7	3.01	12.7	18.5	0.45	5.0	4.0
Silty clay ③2	27.2	19.6	8.28	35.0	14.0	0.3	22.0	19.0
Silt with silty sand ③3	28.4	19.4	8.94	6.3	19.1	0.25	22.0	20.0
Silty clay⑤1	37.0	18.2	4.21	15.2	16	0.35	14.0	12.0
Silt with silty sand⑦2	28.9	19.3	9.66	10.2	19.6	0.25	32.0	28.0

During construction, both single-liquid inert grout and cement-based hard grout are utilized for synchronous grouting. Single-liquid cement-based hard grout is employed in areas with significant tunnel uplift, such as muddy soft soils. During the construction process, it was observed that although cement-based grout was used, the uplift of the segment was still quite significant. For example, in the muddy silty clay, the maximum uplift displacement of the segment reached 150 mm, as shown in Fig. 2. Monitoring data indicate that the segment floating in the soft clay layer is considerably larger than that in the sandy soil layer. Furthermore, the performance of the synchronous grout has a significant impact on tube segment uplift, which means it is essential to optimize the synchronous grout performance.

Fig. 2.

Segment floating in Zhanlan Center Station ~ Xihuan Road Station.

Materials and experimental method

Experiment materials

This experiment investigates the mix proportions of simultaneous grouting materials, which include water, bentonite, cement, fly ash, fine sand, and the SJJ^®-M (I) type water-reducing agent. All materials were sourced from the designated supplier of synchronous grouting materials for Suzhou Metro Line 11 to ensure consistency with actual engineering practices. The detailed mix composition is presented in Table 2.

Table 2.

Raw materials of synchronous grout.

Materials	Material introduction
Water	Tap water, pH value 7.0 ~ 7.5, obtained from Jiangsu Jiada Concrete Products Co., Ltd.
Cement	Ordinary Portland cement, P.O42.5, produced by Changzhou Pangu Cement Factory
Fly ash	Class F II, produced by Changshu Suyutianrun Fly Ash Co., Ltd.
Bentonite	Sodium bentonite (yellow-white appearance), produced by Guangde Shengchang New Materials Co., Ltd.
Fine sand	Natural sand, produced in Ganjiang, Jiangxi, has a fineness modulus of 1.8, an apparent density of 2560 kg·m−3, and a bulk density of 1540 kg·m−3.
Admixture	SJJⓇ-M (I) (reinforced, water-retaining) cement mortar plasticizer, produced by Jiangsu Subote New Materials Co., Ltd.

Experimental scheme

An orthogonal experimental design with five variables and five levels was carried out following T/CECS 563–2018, “Technical Regulations for the Application of Synchronous Grouting Materials in Shield Tunnels,” as well as real engineering experience. The test comprised five factors: water-cement ratio, glue-sand ratio (cementing material to fine sand), bentonite-water ratio (bentonite to water), cement-fly ash ratio (cement to fly ash), and additive-glue ratio (external additive to cementing material). Cement and fly ash were the cementing materials utilized in this test. Table 3 lists the level values for each design component. Table 4 lists the orthogonal experimental design of synchronous grout. It was determined that the total weight of the grout created for each test would be about 36 kg, considering the laboratory mixing apparatus and the volume necessary for grout physical index testing.

Table 3.

Orthogonal test with five variables and five levels.

Levels	Level values
	Water-cement ratio	Glue-sand ratio	Bentonite-water ratio	Cement-fly ash ratio	Additive-glue ratio
1	0.60	0.50	0.10	0.60	0.007
2	0.70	0.55	0.15	0.65	0.008
3	0.80	0.60	0.20	0.70	0.009
4	0.90	0.65	0.25	0.75	0.010
5	1.00	0.70	0.30	0.80	0.011

Table 4.

Orthogonal experimental design of synchronous grout.

Test number	Factors
	Water-cement ratio	Glue-sand ratio	Bentonite-water ratio	Cement-fly ash ratio	Additive-glue ratio
1	1	1	1	1	1
2	1	2	2	2	2
3	1	3	3	3	3
4	1	4	4	4	4
5	1	5	5	5	5
6	2	1	2	3	4
7	2	2	3	4	5
8	2	3	4	5	1
9	2	4	5	1	2
10	2	5	1	2	3
11	3	1	3	5	2
12	3	2	4	1	3
13	3	3	5	2	4
14	3	4	1	3	5
15	3	5	2	4	1
16	4	1	4	2	5
17	4	2	5	3	1
18	4	3	1	4	2
19	4	4	3	5	3
20	4	5	2	1	4
21	5	1	5	4	3
22	5	2	1	5	4
23	5	3	2	1	5
24	5	4	3	2	1
25	5	5	4	3	2

Test methods

Mechanical stirring is employed to thoroughly mix the components of the synchronous grout. To ensure proper mixing efficiency and material consistency, the grout mixture should occupy between 30% and 70% of the mixer’s total capacity, with a minimum mixing duration of 180 s. After achieving a uniform mixture, the grout’s performance characteristics are evaluated following standard testing procedures.

Particular attention is given to the compressive strength of the grout, as water-rich environments may adversely affect the strength development of the hardened material. Therefore, compressive strength tests are conducted on grout cube specimens cured under both standard (air) and water-curing conditions to simulate different field environments. The test equipment and procedures are illustrated in Fig. 3.

Fig. 3.

Grout testing process and equipment: (a) raw materials for grout; (b) grout mixing and mixer; (c) clotting time test sample; (d) cube compressive strength test specimen; (e) density test; (f) consistency test; (g) bleeding rate and stone rate test; (h) shear yield strength test; (l) clotting time test and clotting time meter; (m) cube compressive strength testing and compression testing machine.

(1) Density test: The grout density is determined by measuring the mass difference of a 1 L metal container before and after it is filled with the grout. The final density value is taken as the arithmetic mean of two measurements, with a precision of kg·m⁻³. 

1

where ρ is the mass density of the grout mixture (kg·m⁻³); m₁ is the mass of the empty container (kg); m₂ is the mass of the container with the sample (kg); V is the volume of the container (L).

(2) Consistency test: The grout consistency is measured using a mortar consistency tester. A small amount of lubricating oil is applied to the metal rod to ensure free movement. The container and test cone are cleaned, then filled with grout to about 10 mm below the rim. The grout is compacted and leveled by gentle vibration. The container is placed on the tester base, and the test cone is adjusted to just touch the grout surface. The initial dial reading (accurate to 1 mm) is recorded. After releasing the brake screw, the cone is allowed to sink freely, and the dial reading at 10 s is taken. The difference between the two readings gives the consistency value. Each mix is tested twice, and the average is reported. If the difference exceeds 10 mm, the test is repeated with a new sample. In addition, the consistency of each mix is also measured after 5 h to assess its ability to retain flowability over time.

(3) Setting time test: A Setting time tester was used in laboratories to test grout setting times. The prepared synchronous grout is poured into the test container until the surface is approximately 10 mm below the rim. The container is gently tapped to compact the grout and level the surface without removing bleed water. The container is then placed on the testing platform, and the penetration needle (cross-sectional area: 30 mm²) is positioned at the grout surface. The pressure gauge is set to zero.

To measure the penetration resistance, the needle is slowly and evenly pressed 25 mm into the grout over 10 s, and the pressure reading Np is recorded. Penetration resistance testing begins 2 h after mixing, and measurements are taken every 30 min. Once the resistance reaches 0.3 MPa, the interval is reduced to 15 min, and testing continues until it reaches 0.7 MPa. The resistance Np is calculated as shown in Eq. (2), with a precision of 0.01 MPa.

2

Where f_p is the penetration resistance (MPa), N_p is the static pressure at 25 mm penetration depth (N), and A_p is the cross-sectional area of the penetration needle, equal to 30 mm².

Based on the test data, a curve of penetration resistance versus time is plotted. The time corresponding to 0.5 MPa on the curve is defined as the setting time of the grout. Each grout mix is tested twice, and if the difference between the two results exceeds 30 min, the test must be repeated.

(4) Bleeding rate test: An appropriate volume of grout is placed in a 250 mL graduated cylinder, which is set on a level surface for 1 min before recording the initial grout surface reading  . The cylinder is then sealed with a rubber stopper to prevent moisture evaporation. After standing for 3 h, the readings corresponding to the bleed water surface and the grout surface are recorded. The bleeding rate after 3 h is calculated by Eq. (3):

3

Where BR_3h is bleeding rate after 3 h (%), accurate to 0.1%; 

is initial grout surface reading (mL);  is bleed water surface reading after 3 h (mL); is grout surface reading after 3 h (mL).

(5) Shear yield strength test: The shear yield strength of the grout was measured using a touch screen digital rotational viscometer model N DJ-8T produced by Shanghai Fangrui Instrument Co., Ltd. Unlike consolidated soils, freshly prepared grout behaves as a Bingham or non-Newtonian fluid before setting. Its rheological properties, including yield stress and plastic viscosity, can be effectively characterized using rotational viscometers under controlled shear conditions. This method provides a practical and repeatable approach for assessing early-age flow resistance and shear strength of slurry-type materials, which is critical for engineering applications such as synchronous grouting in shield tunneling^34,35.

For the test, the grout sample was placed in a glass beaker and gently vibrated on a foam pad to level the surface. The viscometer was powered on and leveled, and a suitable rotor was selected and installed. The rotor was then immersed into the sample to the designated depth using the adjustment knob. The sample was allowed to stand for 2 min to stabilize. Before measurement, relevant test information, such as the test ID and rotor number, was entered into the device.

(6) Cube compressive strength test: Use a pressure testing machine model TYA300BI to measure the grout cube compressive strength at different ages and curing conditions (water and steam). Cube specimens with dimensions of 70.7 mm × 70.7 mm × 70.7 mm are prepared using bottomed molds, with three specimens per group. Before casting, butter is applied to the mold joints, and a release agent is brushed inside the mold. The grout is then poured into the mold in a single step and compacted. Once the surface moisture slightly dries, the excess grout above the mold is scraped off and leveled. Each specimen is labeled and cured in a water tank or curing chamber. After reaching the specified curing age, the specimens are demolded for testing.

For compressive strength testing, the demolded specimen is placed on the lower platen of the testing machine, ensuring that the loading surface is perpendicular to the top surface formed during casting and that the specimen is centered. As the upper platen approaches the specimen, the spherical seat is adjusted to ensure uniform contact. The loading rate should be between 0.25 kN/s and 1.5 kN/s; the lower limit is recommended when the expected strength is ≤ 5 MPa, and the upper limit when > 5 MPa. Loading continues until failure occurs, and the peak load is recorded. The cube compressive strength f_{m, cu} is calculated using Eq. (4):

4

Where f_{m, cu} is compressive strength of the cube specimen (MPa); N_u is failure load (N); A is loading area of the specimen (mm²).

The compressive strength should be accurate to 0.1 MPa. The cube compressive strength of the group is taken as 1.3 times the average of the three specimens.

Test results

Grout density

The grout density affects the buoyancy force that the shield tunnel encounters during excavation. This test determined the density values of 25 distinct synchronous grouts with various ratios. Figure 4 displays the specific results. The test results show that the grout density value varies from 1815 to 2077 kg·m⁻³ within the design test range.

Fig. 4.

Grout density measurement results.

Figure 5 shows the correlation between grout density and different variables. As depicted in Fig. 5, the grout density ranges from 14.5 kg·m⁻³ under the cement-cement ratio factor to a maximum of 190.5 kg·m⁻³ under the water-cement ratio factor. Among the 5 factors affecting density, the water-cement ratio has the most significant impact. The degree of influence gradually decreases in the following order: glue-sand ratio, bentonite-water ratio, additive-glue ratio, and cement-fly ash ratio. Therefore, adjusting the ratio of water to cementitious material is the quickest and most effective way to change the density value of the grout. Additionally, grout density experiences a linear decrease as water-cement and glue-sand ratios increase. This is because increasing the water proportion in the grout, which has a lower density than ordinary Portland cement, leads to a rapid decline in grout density. Similarly, ordinary Portland cement has a lower density than fine sand, so increasing the cement-to-sand ratio in the grout decreases its density. However, the ratios of bentonite to water, cement to fly ash, and additive to glue do not significantly affect grout density because the density of ordinary Portland cement is only slightly higher than that of fly ash. The amount of additives in the grout is relatively low compared to the grout itself, so it won’t significantly change the grout density. However, increasing the amount of additives to a certain level may decrease grout density due to physical and chemical reactions. Consequently, if the grout density is the only designed indicator from the perspective of anti-floating during shield tunnel construction, the optimal ratio can be determined as follows: water-cement ratio of 1.0, cement-sand ratio of 0.7, bentonite-water ratio of 0.1, cement-fly ash ratio of 0.75, and additive-glue ratio of 0.011. Both the density of the grout and the static buoyancy value produced by synchronous grout during construction are currently at their lowest points.

Fig. 5.

Relationship between grout density and various factors.

Grout consistency

The process of synchronous grouting involves filling the gap between a segment and the formation through a grouting pipeline promptly. To ensure this process is successful, the grout must possess good fluidity and pumpability. The consistency value of the grout is an indicator of its fluidity. The higher the consistency value, the better the fluidity of the grout. In engineering, it is generally required that the grout consistency value is 10 ~ 12 cm. Figure 6 shows the initial consistency value and the consistency value after 5 h of synchronous grout with 25 ratios.

Fig. 6.

Measurement results of consistency of grout.

Figure 7 displays the correlation between the initial consistency of the grout and influencing factors. Figure 5 shows that the range value has a maximum of 3.0 cm under the cement-cement ratio factor and a minimum of 0.5 cm under the additive-glue ratio factor. The water-cement plays a decisive role in the initial consistency value of the synchronous grout. The effects of the water-cement ratio, bentonite-water ratio, cement-fly ash ratio, additive-glue ratio, and glue-sand ratio on the initial consistency value of the grout are gradually weakened. Additionally, within the research range, the initial consistency value of the grout raised with an increased water-cement ratio. This is because a higher water-cement ratio results in the grout containing more free water, enhancing its flow performance. However, while cement mortar plasticizers can save water usage and improve grout fluidity, a higher bentonite content lowers the quantity of free water in the grout, resulting in poor flow qualities. Research indicates an optimal range (0.8 ~ 0.9) for this additive. An increased amount of additives may increase the initial consistency value within a certain range. However, when the additive content is high, it has the opposite effect. Additionally, the research results show that the initial consistency value of the grout decreases and then increases as the cement-fly ash ratio and glue-sand ratio increase. The flow performance of the grout is at its worst when the cement-fly ash ratio is 0.75 and the glue-sand ratio is 0.6.

Fig. 7.

Relationship between the initial consistency value of grout and various factors.

There will frequently be a gradual decrease in fluidity after the simultaneous grout mixing is finished. The consistency loss range of those 25 grouts after 5 h was examined. Figure 8 depicts the correlation between grout consistency loss and factors. Figure 8 displays the lowest range value is 4.04% under the cement-fly ash ratio factor and the largest is 18.12% under the bentonite-water ratio factor. The effects of the bentonite-water ratio, water-cement ratio, additive-glue ratio, glue-sand ratio, and cement-fly ash ratio on the grout consistency loss are gradually weakened, among which the first three factors play a major role. Further, the consistency loss of the grout grows gradually as the bentonite-water ratio rises, and it decreases when the water-cement ratio raises.

Fig. 8.

Relationship between grout consistency loss and various factors.

Grout initial setting time

Synchronous grouting materials will gradually set and harden in the presence of cement and other cementing materials, losing their fluid properties and providing some compressive and shear strength. The time required for hardening is the initial setting time of the grout. Early hardening of the grout helps limit segment displacement and prevent excessive formation deformation during shield construction. Figure 9 displays the initial setting times of those 25 synchronous grouts. According to the test results, the grout initial setting time ranges from a minimum of 431 min to a maximum of 1052 min.

Fig. 9.

Measurement results of grout initial setting time.

Figure 10 plots the relationship between grout’s initial setting time and factors. The largest range value among the five factors is 451 min under the water-cement ratio factor, while the smallest range value is 72 min under the cement-fly ash ratio factor. The impact of the water-cement ratio, bentonite-water ratio, glue-sand ratio, additive-glue ratio, and cement-fly ash ratio on the initial setting time of the grout diminishes gradually. This indicates that the most effective way to decrease the setting time of the grout is by increasing the amount of cementitious material. Furthermore, the initial setting time increases following an approximately exponential function as the water-cement ratio rises. This is because the coagulation and hardening of synchronous grout primarily depend on the complex hydration reaction between cementitious materials and water. An increased water-cement ratio causes the grout’s cementitious material content to decrease, which postpones the grout’s coagulation process. Besides, as the glue-sand ratio rises, the grout’s initial setting time generally increases. On the other hand, when the cement-fly ash and additive-glue ratios increase, the grout initial setting time initially decreases and then increases. The shortest initial setting time occurs when the cement-fly ash ratio is 0.75 and the additive-glue ratio is 0.009. Additionally, as the bentonite-water ratio increases, the initial setting time first increases and then decreases. This phenomenon may be because when bentonite reaches a certain proportion, its hygroscopicity causes the grout water-glue ratio to decrease, which in turn causes the setting time to drop.

Fig. 10.

Relationship between grout initial setting time and various factors.

Grout bleeding rate

A layer of free water forms on the top of the grout due to some water escaping the grout particles during the synchronous grout hardening process. The bleeding rate is defined as the volume of free water divided by the initial volume of the grout. The bleeding rate can describe the water-holding capacity of the grout and reflect the grout volume loss after hardening. A higher grout bleeding rate corresponds to a higher volume loss upon hardening and more noticeable grout volume shrinking, which will cause a poorer filling effect. It is typically advised that the bleeding rate of the grout should be less than 5%.

Figure 11 shows the bleeding rates of synchronous grouts with 25 ratios and Fig. 12 illustrates the correlation between the grout bleeding rate and various factors. It was found that the maximum range value is 4.36% under the bentonite-water ratio factor, while the minimum is 1.08% under the cement-fly ash ratio factor. The effects of the bentonite-water ratio, water-cement ratio, additive-glue ratio, glue-sand ratio, and cement-fly ash ratio on the grout bleeding rate are gradually weakened. However, the additives in the grout have excellent water retention effects, which means that the upper bleeding rate value is not too high. Furthermore, there is a proportional increase in grout bleeding as the water-cement ratio increases. This is because the mixing process of the grout involves a series of physical and chemical reactions between cementitious materials and water. This reaction consumes the free water in the grout, and the excess water overflows the grout and accumulates on the surface of the hardened grout, forming a layer of free water. An increase in the water-cement ratio leads to an increased excess free moisture, resulting in severe bleeding. Strong hygroscopicity allows bentonite to absorb water up to multiple times its capacity. As the bentonite-water ratio increases, both the relative proportion of bentonite and its content in the mixture increase. This results in more free water being adsorbed around the bentonite particles, which helps alleviate the bleeding phenomenon. In addition, as the cement-fly ash and additive-glue ratios increase, the bleeding rate of the grout decreases at first and then increases. Similarly, when the glue-sand ratio increases, the bleeding rate increases first and then decreases. The lowest grout bleeding rate is achieved when the glue-sand ratio is 0.6, the cement-fly ash ratio is 0.65, and the additive-glue ratio is 0.008.

Fig. 11.

Test results of grout bleeding rate.

Fig. 12.

Relationship between grout bleeding rate and various factors.

Shear yield strength of grout

The shear yield strength of grout in its fluid state greatly influences its ability to resist flotation. This property is an important physical indicator of the grout’s anti-floating performance. Figure 13 plots the shear yield strength of 25 different proportions of simultaneous grouts. In the test range, the maximum shear yield strength of the grout is 15.33 Pa, and the minimum is only 0.79 Pa. The grout proportion significantly affects its shear yield strength.

Fig. 13.

Test results of shear yield strength of grout.

Figure 14 depicts the correlation between the shear yield strength of the grout and various factors. The grout shear yield strength has a maximum range value of 8.84 Pa under the water-cement ratio factor and a minimum of 1.53 Pa under the additive-glue ratio factor. The influence of the water-cement ratio, bentonite-water ratio, glue-sand ratio, cement-fly ash ratio, and additive-glue ratio on the grout shear yield strength decreases in that order. It is evident that cementitious material and bentonite significantly impact the shear yield strength of the grout. Additionally, as illustrated in Fig. 14, the shear yield strength of the grout shows a general rising tendency when the water-cement ratio drops. This is because the grout viscosity increases as the silicate cement reacts with water during mixing, producing a series of reaction products and consuming water. As the reaction progresses, a fibrous arrangement forms around the cement particles. The overlap of these fibers causes the shear yield strength of the grout to continue to increase. Therefore, decreasing the water-cement ratio increases the cement content in the grout, enhances the cement hydration reaction, and increases the shear yield strength of the grout. Notably, as the bentonite-water ratio of the grout increases, the hygroscopicity of bentonite indirectly results in a relative increase in the cement content, thereby raising the shear yield strength of the grout. However, bentonite particles also have a lubricating effect. When the bentonite content in the grout reaches a certain level, it will have the opposite effect. In addition, the study revealed that as the additive-glue ratio increases, the shear yield strength of the grout remains relatively unchanged at first and then increases. The glue-sand and cement-fly ash ratios do not seem to influence the shear performance of the grout.

Fig. 14.

Relationship between shear yield strength of grout and various factors.

Cube compressive strength of grout

After the synchronous grout fills the gap at the shield tail, its strength will continue to increase as it hardens. This will allow it to resist deformation better and eventually stabilize the position of the segments. The grout needs appropriate strength at different stages of hardening for this process to be successful. Additionally, since the water-rich environment can weaken the strength of the hardened grout, unlike standard curing conditions, this paper uses the compressive strength of the grout specimen cube under water curing conditions to assess the strength of the hardened grout.

Figure 15 shows the measured cubic compressive strength of synchronized grouts for 25 different ratios after being cured in water for 1 day and 28 days. The test results indicate that after 1 day of curing, the maximum cube compressive strength is 1.3 MPa, and the minimum is 0.2 MPa. After 28 days of curing, the maximum cube compressive strength is 18.4 MPa, and the minimum is 5.2 MPa. It indicates that there are significant differences in grout compressive strength and growth ability under different mixing ratio conditions.

Fig. 15.

Test results of cube compressive strength (water curing) of grout at each age.

Figure 16 illustrates the relationship between the early compressive strength of the hardened grout (1 day) and various factors. The maximum range value for the compressive strength of the hardened grout after 1 day is 0.7 MPa under the water-cement ratio factor, while the minimum range value is 0.1 MPa under the glue-sand ratio factor. The water-cement ratio, cement-fly ash ratio, bentonite-water ratio, additive-glue ratio, and glue-sand ratio all have a decreasing effect on the early compressive strength of the hardened grout. Additionally, the early compressive strength of the hardened grout shows a decreasing tendency with an increased water-cement ratio and an overall increasing trend with a raised cement-fly ash ratio. This is because water reacts chemically with silicate cement, tricalcium aluminate, calcium silicate, and other elements to progressively harden the grout and cement fine sand, creating a strong overall structure. However, it is also evident that an optimal range exists for the ratio of cementitious materials and fine sand. The early compressive strength of the hardened grout declines with an increased glue-sand ratio once it is above a particular threshold. Furthermore, the research indicates that the addictive-glue ratio does not significantly impact the grout’s early compressive strength. Rather, the grout’s early strength rises initially before decreasing as the bentonite-water ratio increases.

Fig. 16.

Relationship between early strength (1 day) and various factors after grout hardening.

Figure 17 illustrates the correlation between the ultimate compressive strength of the solidified grout (28 days) and different variables. The maximum range of the final compressive strength of the hardened grout is 10.1 MPa under the water-cement ratio factor, and the minimum range is 0.9 MPa under the glue-sand ratio factor. Consistent with the early compressive strength, the water-cement ratio, cement-fly ash ratio, bentonite-water ratio, additive-glue ratio, and glue-sand ratio all decrease the final compressive strength of the hardened grout. Similar to the early compressive strength progression, the ultimate compressive strength of the solidified grout declines as the water-cement ratio increases. Conversely, the ultimate compressive strength generally rises with an increased cement-fly ash ratio. However, the impact of the glue-sand, additive-glue, and bentonite-water ratios is not evident.

Fig. 17.

Relationship between final compressive strength and various factors after grout hardening.

The grout’s compressive strength under normal curing circumstances divided by its strength after 28 days of underwater curing is known as the water-land compressive strength ratio. This ratio shows the grout’s ability to resist water dispersion and maintain its strength in a watery environment. Synchronous grouts with 25 ratios have water-land strength ratios ranging from 0.69 to 0.98. Specific results are shown in Fig. 18.

Fig. 18.

Water-land compressive strength ratio of the grout.

The relationship between the grout water-land compressive strength ratio and factors is shown in Fig. 19. The water-land compressive strength ratio of the grout has a maximum range of 0.14 under the water-cement ratio factor and a minimum of 0.03 under the bentonite-water ratio factor. In that order, the water-land compressive strength ratio is weakened by the water-cement ratio, cement-fly ash ratio, glue-sand ratio, additive-glue ratio, and bentonite-water ratio. Furthermore, Fig. 19 shows that the water-to-land compressive strength ratio of the grout initially declines and subsequently increases as the ratios of bentonite to water and cement to fly ash rise. The water-cement ratio has a greater impact on the grout water-land compressive strength ratio than the above two ratios, but it does not clearly show an influence pattern. The glue-sand and the additive-glue ratios have less of an effect.

Fig. 19.

Relationship between water-land strength ratio of grout and various factors.

Optimal design and verification of the synchronous grout ratio

Previous studies have examined the sensitivity of grout mix proportions to several physical performance indicators. The effects of each factor in order of importance are listed in Table 5. Factors A through E represent the water-cement ratio, glue-sand ratio, bentonite-water ratio, cement-fly ash ratio, and additive-glue ratio. Based on the test results, it is clear that the water-cement ratio (A) has the most significant influence on the grout performance indices. Among the six evaluated indices, factor A consistently emerges as the dominant influencing factor. The optimal mix ratios for individual performance indicators can be identified through multilevel testing specific to each indicator. However, relying on single-indicator optimization fails to meet the comprehensive anti-floating requirements of the grout. Therefore, it is essential to investigate multi-objective optimization methods that balance multiple performance criteria.

Table 5.

Factor importance order.

Grout physical properties	Factor importance order
Density	A-B-C-E-D
Setting time	A-C-B-E-D
Shear yield strength	A-C-B-D-E
Early compressive strength	A-D-C-E-B
Bleeding rate	C-A-E-B-D
Consistency	A-C-D-B-E
Water-land compressive ratio	A-D-B-E-C

Bleeding rate, consistency, and water-land compressive ratio mainly affect the operability and filling effect of the grout, while a long setting time, slow compressive strength growth, low shear yield strength, and high density of the grout significantly impact tunnel floating during shield construction. Therefore, the initial setting time, early compressive strength, density, and shear yield strength of the synchronous grout are used as anti-floating indicators in the design and adjustment of the grout mix ratio. These parameters are selected due to their direct relevance to the grout’s ability to resist segment uplift during shield tunneling. Specifically, the initial setting time affects the grout’s rapid gelation capability, the early compressive strength ensures structural integrity shortly after injection, the density contributes to resisting buoyant forces through its self-weight, and the shear yield strength reflects the grout’s resistance to deformation under buoyancy and shear stresses. Previous studies have also emphasized similar criteria, finding that physical properties such as setting time, strength, and density significantly influence the control of segment uplift and ground stability during shield tunneling^11,36,37.

These 25 experimental factors and response data were input into the Design Expert software for multivariate regression analysis. Equations (5–8) shows the corresponding multi-factor regression formula. Figure 20 shows the response surface of initial setting time, shear yield strength, early compressive strength, and density, with the two factors that have the most effect on each response designated as independent variables. The most influential factor is the water-cement ratio, followed by the bentonite-water ratio, glue-sand ratio, and cement-fly ash ratio. Additionally, Fig. 21 illustrates the predicted values compared to the actual values for the full responses. A nearly 45-degree straight line is visible in the plot, indicating a satisfactory agreement between the predicted and observed values.

Fig. 20.

Response surface: (a) density with C = 0.2, D = 0.7, E = 0.009; (b) shear yield strength with B = 0.6, D = 0.7, E = 0.009; (c) early compressive strength with B = 0.6, C = 0.2, E = 0.009; (d) initial setting time with B = 0.6, D = 0.7, E = 0.009.

Fig. 21.

Predicted vs. actual values plots: (a) density; (b) shear yield strength; (c) early compressive strength; (d) initial setting time.

(R²=0.9557)

5

(R²=0.9878)

6

 (R²=0.9318)

7

(R² = 0.8922)

8

Where, is the initial setting time, is the early compressive strength, is the grout density, and is the shear yield strength of the grout.

The need for controlling tunnel anti-floating throughout the construction period cannot be fulfilled by optimizing grout using a single criterion. Therefore, a multi-objective optimization design of grout performance is essential to achieve the best construction control impact. Based on the regression analysis of the four target responses, we optimized the grout ratio to achieve the shortest setting time, maximum shear yield strength, maximum early compressive strength, and a specific density range. Notably, Other indicators are optimized first since the density fluctuation range is narrow, and the following text will demonstrate that their effect on buoyancy is comparatively limited. The optimization results are depicted in Fig. 22. As shown in Fig. 22, when the conditions are C = 0.267, D = 0.733, and E = 0.010, the water-cement ratio between 0.6 and 0.7 can better achieve the optimization goal. Among them, the density can reach 1970–2080 kg·m⁻³, the shear yield strength can reach 0–50 Pa, the early compressive strength can reach 0.75-1.75 MPa, and the setting time can reach 380–550 min.

Fig. 22.

Multi-objective optimization design curve of synchronous grout.

According to the optimal design of the software, we selected the ratios of water-cement, glue-sand, bentonite-water, cement-fly ash, and additive-glue as 0.602, 0.613, 0.267, 0.733, and 0.010, respectively. As shown in Fig. 22, the predicted grout density is 2033.74 kg·m⁻³, the shear yield strength is 21.944 Pa, the early compressive strength is 1.338 MPa, and the setting time is 416.388 min. According to the optimized ratio, the synchronous grout was prepared, and the performance of the optimized grout was physically tested. The results were presented in Table 6. The test results closely match the predicted values. The approximately 17% deviation between the predicted and measured shear yield strength is due to the simplified assumptions of the regression model, which may not fully capture the nonlinear interactions among mix components affecting rheological behavior. In addition, shear yield strength is sensitive to variations in experimental conditions such as mixing uniformity, temperature, and equipment calibration. Furthermore, it is necessary to clarify that the regression equations developed in this study are based on grout mix designs intended for use in soft clay, such as muddy silty clay, which characterizes the project area. As such, their applicability is most appropriate for similar strata and may require recalibration when applied to significantly different geological environments such as sand.

Table 6.

Predicted and experimental values of optimized synchronous grout.

Classification	Density (kg·m−3)	Shear yield strength (Pa)	Compressive strength(1 day) (MPa)	Setting time (min)
Predicted	2033.74	21.944	1.338	416.388
Tested	2047.5	18.23	1.2	422.04
Error	0.68%	16.92%	10.31%	1.36%

Discussions on construction parameters matching synchronous Grout

Numerical model

Optimizing the proper grouting volume, grouting pressure, and shield tunneling speed to match grout performance is also required to enhance the anti-floating effect. This paper develops a floating tunnel model based on the section of Zhanlan Center station ~ Xihuan Road Station using Abques software. Figure 23 illustrates the numerical model, which has dimensions of 120 m in length, 60 m in width, and 40 m in height. From top to bottom, the soil layers consist of 3 m of silty clay ②₁, 20 m of muddy silty clay ②_y, and 17 m of silty clay ⑤₁. The shield tunnel has a total length of 120 m and comprises 100 rings. It is buried at a depth of 14.4 m and has an outer diameter of 6.6 m and an inner diameter of 5.9 m for the segment, with an additional grout layer of 0.13 m. The soil, grout layer, and tunnel consist of three-dimensional solid units (C3D8), totaling 173,600 soil units and 19,200 tunnel and grout units. The soil is modeled using linear elastic and Mohr-Coulomb plastic constitutive models. The specific soil parameters can be found in Table 1. The tunnel and grouting layer utilize the elastic constitutive model. The tunnel elastic modulus is 27.6 MPa and the Poisson’s ratio is 0.2. The elastic modulus of synchronous grout increases linearly, from 15 MPa to 69 MPa, and the Poisson’s ratio is 0.35. The sides of the model are subject to displacement restrictions in both the x and y directions, its bottom surface is subject to fixed constraints, and its upper surface is subject to free displacement bounds.

Fig. 23.

Simulation model.

This paper simulates tunnel excavation by presetting convergent displacement. The shield excavation diameter is 6.86 m, and the convergence boundary is outside the tunnel, with the displacement of the arch soil being 0.26 m and the bottom being 0. The shield excavation step is 1.2 m long. In each excavation step, the soil units are invalid, and the corresponding position of the segment and grout layer units are activated. Meanwhile, binding constraints are imposed between the segment and the grouting layer, and between the soil and the grouting layer.

This paper conducts sensitivity analysis of tunnel floating by considering the liquid grout length L_liq, upward grouting pressure p_up, density, and grouting filling rate G_f. Table 7 displays the simulation conditions.

Table 7.

Simulation conditions.

Parameters	Values
Liquid grout length Lg (Ring)	20(5; 10; 20; 30)
Upward grouting pressure pup (MPa)	0.2(0.1; 0.2; 0.3; 0.4)
Density ρ (kg·m−3)	2000(1400; 1700; 2000; 2300)
Grouting filling rate Gf (%)	100(100; 120; 140; 160)

Note: The values outside brackets are the basic simulation values of the corresponding parameters and the values in brackets correspond to the values of parameter sensitivity analysis.

Discussions of construction parameters on tunnel floating

Figure 24 (a) shows the floating displacement of the tunnel when Lg is 5, 10, 20, and 30 rings. The development pattern of the floating tunnel is the same under different L_g. The floating displacement of the tunnel steadily rises and then stabilizes as it gets farther away from the shield tail. As the Lg rises, so does the maximum floating development of the tunnel. For instance, the floating displacement of the tunnel is 22 mm when L_g is 5 rings long, and it rises to 65 mm when L_g is 30 rings long. Additionally, for each additional ring of the unsolidified zone, the maximum floating displacement of the tunnel increases by 1.75 mm. It is noted that, under constant excavation speed of the shield and grouting volume, a shorter grout initial setting time is more favorable for controlling the tunnel floating.

Fig. 24.

Tunnel floating displacement under different influencing factors: (a) liquid grout length; (b) density; (c) upward grouting pressure; (d) grouting filling rate.

Figure 24(b) shows the floating displacement of the tunnel with 4 grout densities of 1400 kg·m⁻³, 1700 kg·m⁻³, 2000 kg·m⁻³, and 2300 kg·m⁻³. The longitudinal floating mode of the tunnel remains constant, and the maximum floating displacement increases as the grout density increases. A 100 kg·m⁻³ increase in the average grout density causes a 0.36 mm increase in the maximum floating displacement of the tunnel. Grout density has a negligible impact on the tunnel floating. Consequently, as mentioned above, the least density may be chosen as much as feasible during grout optimization by prioritizing other attributes.

After the segment has been separated from the shield tail, grouting pressure is applied, with more pressure on the bottom surface and less on the top surface. The combined force produces upward grouting pressure, which affects the tunnel deviation. Figure 24 (c) shows the floating displacement of the tunnel when the grouting pressure difference is 0.1 MPa, 0.2 MPa, 0.3 MPa, and 0.4 MPa. The grouting pressure difference has a significant effect on the maximum floating displacement of the tunnel. As the upward grouting pressure increases, the peak value of the floating displacement rises and shifts toward the shield tail. Specifically, for every 0.1 MPa increase in the upward grouting pressure, the maximum floating displacement of the tunnel increases by 16.55 mm. This indicates that the upward grouting pressure significantly affects the floating of the shield tunnel.

The grouting filling rate is the ratio of the volume of slurry injected into each ring of the segment to the volume of the void at the shield tail. Figure 24 (d) illustrates the floating displacement of the tunnels at grouting filling rates of 100%, 120%, 140%, and 160%. It is noted that the segment floating displacement shows a similar development pattern under varying grouting filling rates, with the segment floating displacement increasing as the grouting filling rate increases. The maximum floating displacement of the segment rises by 1.03 mm for every 10% increase in the average grouting filling rate. It is observed that the grouting filling rate has a negligible effect on tunnel floating.

The normalization of the computation results is displayed in Fig. 25. The vertical axis displays the ratio of the segment’s maximum floating displacement to its maximum floating displacement under the minimum variable , while the horizontal axis displays the ratio of each factor value  to the minimum value  . The normalized curve approximates a straight line, and the slope of the curve indicates how much each component affects the maximum floating displacement of the segment. The most significant factors influencing the tunnel floating are the upward grouting pressure and the liquid grout length. Upward grouting pressure can increase the floating displacement of the tunnel by 2.5 times, while the liquid grout length can increase it by 3 times. On the other hand, the grout density and filling rate have a smaller impact, increasing the maximum tunnel floating displacement by less than 1.2 times. Therefore, controlling the floating of shield tunnels requires careful consideration of grouting pressure values, distribution, and the initial setting time of synchronous grout. Here are some recommendations: (1) The grout’s initial setting time and the shield advancing speed should coincide. The simulation findings suggest that the liquid grout length should be regulated at 5 rings. The shield tunneling speed should be regulated to be more than 83.28 min/ring if a grout with a setting time of 416.4 min is utilized. (2) To ensure proper grouting, it is recommended to either increase the number of higher grouting holes, decrease the lower grouting pipe pressure value, or grout only on the upper portion of the segment.

Fig. 25.

Normalized displacement results.

Notably, when the soil is abnormally soft and the single-liquid grout cannot meet the anti-floating requirements of the tunnel, it is recommended to use double-liquid grout or novel grout, including adding steel fiber or organic fiber. In addition, it should be noted that in addition to grout properties and basic construction parameters, mechanical control factors such as propulsion cylinder thrust and shield attitude may also influence the final position of the segment lining. These factors were not within the scope of this study and will be addressed in future research.

Conclusions

This paper carried out a shield synchronous grout performance test and analyzed the mechanical properties of cement grouts with different proportions. Aiming at the problems of tunnel floating in water-rich soft strata, a multi-objective optimization method for grout performance was established with initial setting time, shear yield strength, early compressive strength, and density as optimization performance indicators. Based on this test, an optimized proportion was suggested and verified in combination with experimental tests. In addition, the construction parameters matching the grout properties were discussed using numerical simulation methods. Results indicate that the performance of synchronous grouting, grouting pressure values, distribution, and shield advancing speed has the most significant impact on tunnel stability. A synchronous grout with ratios of water-cement, glue-sand, bentonite-water, cement-fly ash, and additive-glue of 0.602, 0.613, 0.267, 0.733, and 0.010 can obtain a shorter setting time and higher shear and compressive strength. Accordingly, the shield tunneling speed should not exceed 83.28 min/ring, ensuring the liquid grout length is regulated at 5 rings. Alternatively, grouting should be limited to the top portion of the segment, or additional grouting holes at high positions should be installed.

Author contributions

1. Hui Jin (Corresponding Author)Conceptualization; Formal Analysis; Investigation; Methodology; Software; Writing – Original Draft; Writing - Review & Editing; Funding Acquisition.2. Enzhi WangConceptualization; Funding Acquisition.3. Dajun YuanConceptualization; Resources; Funding Acquisition4. Xiaoli LiuResources; Validation.5. Shangkun WuData Curation; Investigation; Methodology; Software.

Data availability

Data generated or analyzed during this study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.