Characterization of Clay Shock Slurry and Its Safety Risk Control in Shield Crossing Project

Abstract

To investigate the mechanism by which clay shock slurry fills excavation gaps and reduces ground layer deformation during shield tunneling, we conducted a study using the project example of Beijing Metro Line 19 from Youanmenwai Station to Niujie Station, which passes through Guang’anmennei Station to CaiShiKou Station of Beijing Metro Line 7 at a close distance. We employed physical and mechanical testing, numerical simulation calculations, and other methods to examine the deformation law and mechanism of the clay shock method in shield tunneling construction. Our results indicate that (1) as the mass concentration of clay shock slurry increases, its permeability decreases significantly; at a mass concentration of 400 kg/m³, clay shock slurry can prevent synchronous grouting slurry from flowing forward, providing optimal filling and support for excavation gaps. (2) Clay shock slurry can reduce friction between the shield shell and soil body by 50%, avoiding super-consolidation, shear damage, and volumetric expansion of the surrounding soil body. (3) Radial grouting with a two-fluid slurry of cement–water glass at a 1:1 ratio within 15 rings after shield tail removal effectively reduces settlement of the existing tunnel. (4) Numerical simulations demonstrate that using clay shock slurry to fill shield tunnel gaps not only significantly reduces construction settlement but also effectively inhibits strata displacement along the tunnel axis.

1. Introduction

As social development accelerates, the conflict between ground transportation and urban development layout has become increasingly pronounced. Transportation, considered the lifeblood of a city, can have a significant positive impact on urban development when it is convenient and efficient. Consequently, subway transportation, represented by the subway, is being constructed in an increasing number of cities [1]. The shield method has emerged as the predominant approach to subway tunnel construction due to its high degree of mechanization, adaptability to ground conditions, and safety during construction. However, the rapid expansion of underground transportation networks inevitably results in new tunnels intersecting with existing tunnels or underground structures in parallel, overlapping, or crossing configurations. This necessitates the implementation of effective settlement control measures during shield construction. Fatemeh Eskandari [2] put forth the proposition that the surface settlement diminishes as the equilibrium pressure of the earth’s pressure increases. The research conducted by Yoo, C [3] revealed that the most significant influence on the tube sheet of the pre-existing tunnel occurs when the angle formed between the newly constructed tunnel and the traversed tunnel is acute.

Currently, international scholars primarily address the issue of settlement control during shield tunnel crossings through theoretical derivation and numerical simulation. Dalong Jin [4] collected and analyzed extensive monitoring data from shield tunnel underpass construction, examining the influence of spatial location, support pressure, and stiffness, and proposed new empirical formulas for estimating settlement caused by existing tunnels due to shield tunnels. Ahn, CY [5] has proposed the utilization of fitting techniques involving symmetrically shifted Gaussian functions and the superposition of asymmetric functions as a means to preliminarily estimate the cohesive ground surface settlement resulting from the construction of double-layer shield tunnels. Rongzhu Liang [6] proposed a new empirical formula for estimating the settlement of existing tunnels caused by shield tunnels based on the commonly used “Euler-Bernoulli beam + Winkler foundation” tunnel traversal analysis model. This formula incorporates calculations of unloading stresses above the tunnel using the Mindlin method and accounts for tunnel-soil interactions resulting from these stresses, providing a new simplified algorithm for calculating tunnel settlement during traversal. Hongpeng Lai [7] analyzed the effect of settlement and deformation of a diagonally intersecting shield tunnel on an existing tunnel using monitoring data and the finite difference method. Peng Fei [8] analyzed ground settlement during the successive superposition of two parallel shield tunnels to bypass an existing masonry structure and the effect of this process on masonry structure settlement. Bousbia Nawel [9] analyzed twin parallel tunnels, taking into account tunnel size, depth, relative position, and lining thickness.

The settlement effect of shield construction on overlying strata can be divided into five stages, as shown in Figure 1. Settlement generated by the fourth stage (the shield tail gap) accounts for the largest proportion, and settlement control measures are primarily focused on this stage. These measures include grouting control, synchronized grouting to fill the shield tail gap in a timely manner, and second grouting to fill any remaining voids. Fine control of grouting volume, pressure, and speed is used to achieve resistance to settlement and deformation. Zhang, D.-M [10] elaborated on the effectiveness of grouting in controlling tunnel settlement. Grouting can effectively reduce the tunnel settlement rate, and the maximum settlement can be controlled to reach 50%.The research results of Huang, H.-W [11] showed that as the amount of grouting increases, the settlement decreases linearly. However, during the grouting process, the horizontal deformation will increase, and the maximum deformation is approximately 63% of the settlement. The research of Chunmei Xu [12] demonstrated that by reasonably selecting the synchronous grouting slurry and shield tunneling parameters, the settlement of ground buildings can be controlled within the range of +3 to −5 mm, and the ground settlement can be controlled within the range of +5 to −10 mm. When shield tunnels are constructed in shallow strata, surface collapse may occur. Qi Zhang [13] proposed a numerical simulation method to model changes in grouting material during tunnel excavation and consolidation, revealing the relationship between grouting material type and surface deformation. Minglun Yin [14] used a finite element method to study the impacts of grouting material on the surface deformation of downward tunneling shield tunnels under excavation loads, examining the different responses of elastic modulus to existing shield tunnels. Xiao-Xue Liu [15] proposed a nonlinear spring model to simulate backfill grouting consolidation behind the wall, obtaining two parameters for slurry pressure attenuation and consolidation thickness due to consolidation. Slurry diffusion in the formation is uncontrollable and accompanied by certain losses [16]. Jie Yang [17] developed a hydrodynamic model based on a hybrid theory of grouting losses in sandy soils, demonstrating that a coupled hydrodynamic modeling method based on mixing theory can qualitatively simulate slurry transport in soil around tunnel tail voids and predict ground deformation caused by tunnel excavation and backfill grouting. Y. Liu proposed a new model to characterize the spatial–temporal distribution of slurry pressure in rock section voids based on group diffusion and consolidation theories. Xiao-Xue Liu [18] put forth an analytical model of backfill slurry diffusion after tunnel tube sheet lining using Bingham fluid as the medium, emphasizing time-dependent slurry diffusion pressure and distance, with results in good agreement with actual measurements. He, S. [19] formulated a theoretical framework encompassing the constant velocity diffusion of grout within diagonal cracks of rock formations, drawing upon the principles of fluid mechanics. This model takes into account the influence of the slurry’s self-weight and the non-uniform spatial distribution of viscosity in the fast-curing grout.

Commonly used engineering grouting materials are typically composed of cement, fly ash, lime, fine aggregate, and bentonite mixed with chemical additives [20]. These materials can be classified as lime-based grouting, cement-based grouting, or bi-liquid grouting according to their ratios [21]. However, they all have shortcomings, such as long solidification time, large volume shrinkage, and weak resistance to water dispersion [22]. Various new materials and ratios of grouting materials have been developed to address these issues, including cement–water glass [23], polyurethane/water glass [24], epoxy resin, and the reuse of shield drain soil [25].

The clay shock method represents an emerging technique employed in the construction of shield structures aimed at mitigating risks. Its fundamental principle entails the injection of a special slurry composed of clay shock outside the shield shell at precise positions within the shield machine. This slurry possesses remarkable attributes, such as resistance to water dilution, supportive characteristics, and resistance to solidification. Its timely injection enables the effective filling of gaps between the shield shell and the surrounding soil layer, thereby achieving meticulous settlement control. However, currently, most of the research on clay shock has focused on its application process. For instance, in a certain project, clay shock was employed, and it successfully controlled the settlement. Nevertheless, there is still a lack of systematic experimental analysis regarding the physical and mechanical properties and material proportioning of clay shock slurry, as well as its functional mechanism in settlement control during shield tunneling. In this paper, taking clay shock slurry as the research object and combined with the engineering example of shield tunneling passing through an in-service tunnel at an ultra-close distance, the physical and mechanical properties and proportioning of clay shock slurry were systematically tested. Moreover, the functional mechanism and effect of the clay shock construction method were investigated by means of numerical simulation. This research examined clay shock from two perspectives: material properties and engineering applications.

2. Background of the Study

The Beijing Subway Line 19, extending from Right Anmenwai Station to Niujie Station, adheres to a preconceived route and is constructed utilizing the shield tunneling technique. The line spans approximately 2.23 km in length, with a tunnel diameter of 6.4 m, a tube sheet thickness of 300 mm, a tube sheet width of 1.2 m, a tunnel spacing ranging from 10.88 to 58.15 m, and an interval structure depth of 12.07–28.3 m. The crossing strata primarily consist of pebbles and fine sand, with a portion of the line situated entirely below the water table. The tunneling process intersects with the pre-existing Beijing Metro Line 7, as depicted in Figure 2.

The intersecting line, Beijing Metro Line 7, extends from Guang’anmennei Station to Caishikou Jim and is situated directly beneath the main road. It was completed utilizing the shield method and has a tunnel diameter of 6 m, a tube sheet thickness of 0.3 m, a line spacing of 15 m, and a line depth of approximately 21.8 m. The ground layer at this location predominantly consists of cobble, as shown in

Table 1. Physical and mechanical property parameters of each soil layer.

Stratum	Thicknesses (m)	γ (kN/m3)	Es (MPa)	ν	Static Earth Pressure Coefficient (K0)	c (kPa)	φ (°)
Plain fill	6.14	18.4	8	0.3	-	8	10
Silty clay	5	20.1	15	0.3	0.38	30	15
Silty fine clay	3.8	20.5	16	0.32	0.39	31	16
Pebble①&②	30.2	22.5	70	0.25	0.38	0	40

.

As depicted in Figure 3, the section where the tunnel crosses is located below the main road at ground level. Traffic on these roads is dense, and high-rise buildings, primarily residential, are densely packed in the surrounding area. The intersection is located 35 m from Niujie station, and the new tunnel intersects vertically with the existing tunnel, with an arch only 2.3 m away from it. The underpass area spans 20 m in length and has an impact area of approximately 50 m. The strata of the crossing section is a pebble layer. During the crossing process, the newly built tunnel is below the groundwater level. The strata of the crossing section is a pebble layer. During the crossing process, the newly built tunnel is below the groundwater level. When constructing shield tunnels in water-rich pebble strata, the disturbance generated may cause excess pore water pressure and increase the risk of settlement and deformation of the tunnel and the strata. Therefore, when the shield tunnels pass closely beneath the existing tunnel at this location, it is necessary to adopt necessary reinforcement measures to address the potential ground settlement in the water-rich sandy pebble strata. Figure 3 shows a cross-section of the geology of the crossing.

The pre-existing line is operational, and the crossing section coincides with an acceleration/deceleration section of the subway. Tunnel excavation can only be conducted at night when the subway is out of service, and construction is prohibited at other times. The underpass section has a considerable burial depth, complex ground conditions, and abundant groundwater, necessitating stringent settlement and deformation control measures for the project. In addition to reinforcing the existing line and improving fine control of the shield tunneling parameters, grouting reinforcement measures must be implemented for tunnel boring to reduce ground disturbance and strictly control settlement. Clay shock is proposed as the material for grouting reinforcement.

3. Clay Shock Slurry Physical and Mechanical Properties Test

3.1. Clay Shock Method

Clay shock is a grouting material composed of two groups of materials, a specialized clay and a potent plasticizer (water glass), mixed in a specific ratio. It rapidly forms a high viscosity (300~500 dPa·s), non-hardening plasticized clay, which is then pumped to the grouting position. The specialized clay group primarily consists of calcium-based clay minerals, cellulose derivatives, colloidal stabilizers, and dispersants.

The viscosity of clay shock can be altered by adjusting the ratio of the two groups of ingredients. Although it lacks strength, it provides excellent support. The mixed slurry is insoluble in water and exhibits exceptional water-blocking capabilities, good fluidity, and high lubrication ability.

The cutter plate of the shield is typically slightly larger than the shield body, and the shield body is conical. During excavation, a gap is produced between the shield shell and the soil body. Clay shock is primarily used to fill this gap, synchronously injected at the shield position in the middle of the shield during excavation to support the soil above in a timely manner, effectively inhibiting and mitigating subsidence. Simultaneously, it envelops the shield shell, reducing friction between the shield shell and the soil body and minimizing disturbance to the soil body. Additionally, due to its high viscosity, clay shock is not easily dispersed, and the clay shock ring formed after injection effectively prevents synchronized grouting at the shield tail from flowing back, preventing the shield from being held by the slurry.

In this study, different ratios of clay shock solution mixed with a water glass solution were used to prepare clay shock slurry for testing. The test was conducted using clay shock ratios (clay shock material (kg): water (m³)) of 350 kg/m³, 400 kg/m³, 450 kg/m³, and 500 kg/m³ for on-site proportioning and mixing, as shown in Figure 4.

3.2. Viscosity Test

The viscosity of the clay shock slurry with different proportions was tested using an NDJ-8S digital display viscometer (manufacturer: Shanghai Yi’xin instrument. Shanghai; China). The experimental process is presented as follows:

(1)

Get a straight cylindrical container. Its diameter should be at least 70 mm and its height at least 120 mm. Put the liquid to be measured in it. Keep the inner wall clean;

(2)

Control the temperature of the measured liquid accurately;

(3)

Adjust the leveling device of the instrument to position the leveling bubble in the middle. If not, the result will be inaccurate;

(4)

Look at the odometer. Choose a proper rotor and screw it into the connector. For high-viscosity liquids, pick a small rotor (a high rotor number). Set a slow rotational speed. If the measured viscosity is much lower than the range, speed up. For low-viscosity liquids, use a large rotor (a low rotor number) and a fast rotational speed. Keep the range percentage reading between 10% and 90% during measurement;

(5)

Slowly adjust the lifting button. Change the depth of the rotor in the liquid. When you look horizontally, make sure the liquid level mark of the rotor (the middle of the groove) is at the same level as the liquid surface. Then, start the measurement.

Figure 5 shows the actual experimental situation.

Table 2. Test results of clay shock effective viscosity of different proportions.

Proportion (kg/m3)	η/(MPa·s)	M1/%
350	24,300	47%
400	33,100	53%
450	45,400	67%
500	51,900	52%

Note: M₁ value is the ratio of the measured fluid viscosity to the maximum range value of the rotary head; close to 50% of the test results are relatively accurate; and η is the viscosity value of the fluid.

presents the test results.

In order to evaluate the shear stress between the shield shell and the clay shock slurry during construction and thus assess the “drag reduction” effect of the clay shock slurry, we opted for a simpler Newtonian viscosity calculation method for estimation. The internal friction parallel to the friction surface in the shear rheology of the fluid microelement is as follows in Formula (1):

$$dF=\eta DdS$$

(1)

where η represents the viscosity of the fluid; D denotes the shear rate per instant of bending along the radius of rotation; and D = dr/dv; dS signifies the micro-area of the friction surface in rotation. This translates to Formula (2):

$${\displaystyle \frac{F}{A}}=\eta {\displaystyle \frac{dv}{dr}}$$

(2)

The formula represents the internal friction parallel to the friction surface in the shear rheology of a fluid microelement for a pair of parallel plates with an area of A, separated by a distance dr and filled with a viscous material. A thrust F is applied to the upper plate, producing a change in velocity dv. Due to the viscosity of the fluid, force is transferred layer by layer, causing corresponding movement in the layers of liquid and forming a velocity gradient dv/dr—the shear rate.

To determine the shear rate of the clay shock slurry during shield advancement, we considered its force characteristics. The pressure at the tail shield is higher than that at the front shield, forming a pressure difference pointing from the tail of the shield toward the cutter plate. Due to forward advancement of the shield, the direction of shear velocity v_x is the same as that of the pressure difference (the pressure difference ΔP = P_b − P_a, where P_b is the pressure of tail slurry and P_a is that of front shield slurry), producing a flow velocity that follows a parabolic distribution law. The two flow velocity vectors are added together to synthesize the overall flow velocity of clay shock slurry.

According to fluid continuum assumptions, under high soil pressure and high shear rate conditions during shield operation, clay shock slurry flows in the excavation gap along the advancement direction of the shield (v_y ≈ 0, and v_z ≈ 0, where v_y and v_z are components of slurry flow velocity in y and z directions, respectively). The force per unit mass Z = −g can be transformed into a force per unit mass Z = −g, according to equations of motion from fluid dynamics that describe the conservation of momentum for viscous incompressible fluids (Navier–Stokes equations). These equations can be translated into the system of Equation (3) as follows:

$$\left\{\begin{array}{l}{\displaystyle \frac{d^2{v}_x}{d{z}^2}}={\displaystyle \frac{1}{\eta }}{\displaystyle \frac{dp}{dx}}\\ -{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{dp}{dy}}=0\\ -g-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{dp}{dz}}=0\end{array}\right.$$

(3)

where ρ is the clay shock slurry density, p is the pressure, and z is used as a variable to integrate the equation to obtain the velocity (Equation (4)) at any point in the gap:

$$v={\displaystyle \frac{1}{2\eta }}{\displaystyle \frac{dp}{dx}}{z}^2+C_{1}z+C_2$$

(4)

where C₁ and C₂ are constant term passes, and substituting the z and v values for the boundary case—v = 0 for z = 0, and v = v_x for z = δ—yields the velocity distribution (Equation (5)) as:

$$v={\displaystyle \frac{1}{2\eta }}{\displaystyle \frac{dp}{dx}}(z-\delta )\cdot z+{\displaystyle \frac{v_x}{\delta }}\cdot z$$

(5)

where δ is the average size of the excavation gap between the soil and the shield shell, which takes the value of δ = 20 mm. If dp/dx is the gradient of change of the pressure difference along the excavation gap, then:

$${\displaystyle \frac{dv}{dz}}={\displaystyle \frac{1}{\eta }}{\displaystyle \frac{dp}{dx}}z-{\displaystyle \frac{\delta }{2\eta }}{\displaystyle \frac{dp}{dx}}+{\displaystyle \frac{v_x}{\delta }}$$

(6)

The shear stress between the shield shell and the clay shock slurry can be obtained as τ = 25 kPa. The average friction stress between the shield shell and the soil layer is calculated as follows:

$$f_1=2\pi RLc+uW=9005.86\mathrm{kN}$$

(7)

$$P_2=f_1/2\pi RL=47.99\mathrm{kPa}$$

(8)

where f₁ represents the average friction between the shield shell and soil layer, R denotes the excavation radius, L signifies the length of the shield shell, u is the friction coefficient between the shield shell and pebble (taken as 0.3), W is the self-weight of the shield (approximately 500 t), c is the value of clay cohesion, and P₂ is the average value of friction stress between the shield shell and ground layer. After calculation, it was determined that filling the excavation gap with clay shock slurry reduces friction between the shield shell and soil by approximately 50%. It should be noted that using Newton’s law of viscosity to estimate the “drag reduction” effect of clay shock slurry is a conservative assessment method. The clay shock slurry exhibits a “shear thinning” phenomenon, and its actual effect in reducing frictional resistance will be more pronounced. The effect of friction resistance reduction in practical application will be more evident.

3.3. Variable-Head Permeability Test

The TST-55 (Figure 6) variable-head permeameter (manufacturer: Changzhou ying’an instrument; Changzhou; China) can be used to measure the permeability coefficient of cohesive soil under variable-head conditions. The specific experimental steps are as follows:

(1) Place the permeable stone and sealing ring into the base. Coat the inner wall of the sleeve with a layer of petrolatum. Use a soil sample cutting ring to obtain saturated clay shock. Then, place the soil sample cutting ring inside the sleeve and put the extra petrolatum on the base (Figure 7);

(2) Firstly, place the permeable stone. Then, install the sealing ring. Insert the cutting ring with the specimen. Put on the upper cover and tighten it with a screw rod to compress the specimen to prevent water and air leakage. Connect the water supply pipe to the water tank and link the permeameter through the water pressure device (Figure 8). Let it stand still for a period of time under a certain water pressure. The test can be carried out when water begins to flow out from the water outlet;

(3) At the beginning of the test, fill the water pressure device to a certain height and close the inlet valve. Meanwhile, record the initial water head (h_1). After time (t), measure the final water head (h_2). Then, make the water level in the water head pipe rise back to the required height. Repeat the measurement 2–3 times and then terminate the test.

Table 3. Test results of mud removal efficiency and permeability of different proportions.

Proportion (kg/m3)	Δh1/mm	Δh2/mm	t/h	k/(cm/s)
350	220	187	46	1.03 × 10−⁷
400	214	211	115	5.69 × 10−⁹
450	215	213	-	-
500	218	217	-	-

shows the experimental results. According to indoor variable-head permeability tests, it can be observed that the permeability coefficient of clay shock slurry ranges from 1.00 × 10⁻⁹ cm·s⁻¹ to 1.00 × 10⁻⁷ cm·s⁻¹, exhibiting low permeability. As the concentration of clay shock slurry increases, its permeability is significantly reduced. Therefore, when the ratio of clay shock slurry reaches or exceeds 400 kg/m³, it can prevent slurry from flowing into the soil bin, enabling it to effectively fill, support, and reinforce.

3.4. Triaxial Compression Test

Conduct the experiment according to the following steps:

(1) Prepare standard test specimens with a cross-sectional radius of ϕ = 50 mm and a height of 100 mm;

(2) After the specimen preparation is completed, place the sample on the test bench. Prepare a rubber membrane, make it adsorb and wrap around the specimen, and fix it with a strong rubber ring and the test bench (Figure 9);

(3) Place the glass cover onto the test bench, open the valve, and inject air-free water. Meanwhile, manually operate the loading system and lift the pressure chamber until it contacts the pressure sensor (Figure 10).

According to the calculations, each ring of the existing tunnel weighs approximately 16.5 t, with 64.3 t of soil replaced at the same location, resulting in a difference in consolidation stress of approximately 478 kN. The consolidation stress on the soil beneath the tunnel is reduced by approximately 60 kPa. Therefore, in this test, the initial consolidation pressure was set to be the overburden pressure of 200 kPa, and the peripheral pressure was subsequently reduced to 140 kPa, reducing the consolidation pressure of the soil beneath the existing tunnel. The soil was then sheared under this peripheral pressure. The over-consolidation ratio (OCR) of the clay was 1.43, and Figure 11 shows the change in the pore water pressure of clay and clay shock slurry during the comparison experiment. The total volume of the specimen remained constant during undrained shear, with continuous adjustments made to the pore water pressure and effective stress. An increase in pore water pressure indicates shear shrinkage of the specimen at the beginning of the shear process, with pore water pressure peaking and then decreasing, indicating a slight shear expansion trend of the specimen.

When shield excavating below the existing tunnel, cutter excavation causes soil stress beneath the existing tunnel to be greater than that above it. Additionally, due to the downward slanting of the tunnel during excavation, a large amount of earth is excavated in the upper tunnel. This results in a super-consolidated state in the soil body beneath the existing tunnel. Shear damage to this state of the soil body produces significant volume expansion, which is unfavorable for the structural stability of the existing tunnel above it. Therefore, injecting clay shock slurry into the outer gap of the shield shell can prevent super-consolidation of the surrounding clay during shield crossing construction, which would otherwise cause large shear damage and volume expansion, impacting the structural stability of the existing line.

3.5. Consolidation Test

In order to obtain the stress path and the consolidation mechanical properties of the clay shock slurry, a single-lever consolidometer was used for consolidation tests. The specimen was subjected to gradually increasing pressure in a vessel with side constraints and allowable axial drainage, allowing the determination of the relationship between pressure and specimen deformation or pore ratio, as well as the relationship between deformation and time. The compression stabilization standard specifies 24 h of compression at each load level, or a change in gauge readings per hour of no more than 0.005 mm is considered stable. Upon measuring the compression stabilization readings, the second load level was applied, with loads sequentially applied in stages until the end of the test. Figure 12 shows the results of the consolidation tests on clay shock slurry specimens of the same proportion.

When the consolidation pressure is within 100 kPa, the pore ratio of clay shock slurry with different ratios varies significantly. After the consolidation pressure exceeds 100 kPa, changes in the pore ratio tend to become consistent, exhibiting an overall slow decrease with increasing consolidation pressure. The consolidation coefficient is the slope of a section of the cut line on the e-p curve. As such, the compression coefficient of clay shock with different ratios varies greatly and decays rapidly. After consolidation pressure exceeds 100 kPa, changes in the compression coefficient tend to become consistent, exhibiting an overall slow decrease with increasing consolidation pressure.

4. Numerical Simulation Calculation

4.1. Establishment of Numerical Model

A three-dimensional numerical simulation model with dimensions of 100 m × 120 m × 50 m was constructed using the finite-difference numerical simulation program FLAC^3D, comprising a total of 390,132 meshes. According to the actual tunnel dimensions, the existing tunnel group has a burial depth of 15 m, an inner tunnel diameter of 5.4 m, a tube sheet thickness of 0.3 m, and a tunnel spacing of 13 m. The new tunnel has a burial depth of 18 m, an inner tunnel diameter of 5.8 m, and a tube sheet thickness of 0.3 m. The distance between the new tunnel’s vault and the existing tunnel’s bottom is 2.96 m. Figure 13 depicts the numerical simulation calculation model and the relative positions of the tunnels. Fixed constraints were applied at the bottom of the model, and vertical sliding constraints were applied around the model. The top surface is the ground surface and is taken as a free boundary.

4.2. Model Parameters

The physical and mechanical parameters of the soil layers given in Table 1 can be used to assign the required parameters to the M-C principal model for noncohesive soils, while the modified Cambridge model was used for cohesive soils. In addition to the soil materials, materials such as pipe sheets, shield shells, and grouting layers during construction were simulated using an isotropic elastic principal model with the parameters shown in Table 3 and

Table 4. Clay and clay shock mechanical parameters.

	Parameters	M	Λ	κ	p1	νλ	OCR
Stratum
Silty clay		1.13	0.049	0.0059	1	2.31	0.87
Silty fine clay		1.07	0.051	0.0058	1	2.18	1.15
Clay shock (400 kg/m3)		1.07	0.05	0.0044	1	1.25	1

.

The clayey soil and clay shock slurry were modeled by the modified Cambridge principal model, which can reflect soil-specific properties such as elastic nonlinearity, hardening/softening, and yield characteristics of the soil, and is more suitable for describing the soft and weak clayey soil with a high water content. The parameters input in Flac3D for the modified Cambridge model were mainly six parameters, such as M, λ, κ, v_λ, p₁, p_c0, and so on:

(1)

Friction Constant M

$$M={\displaystyle \frac{6\mathit{sin}\phi }{3-\mathit{sin}\phi }}$$

(9)

Based on the results of the field clay consolidation undrained shear test, the shear strength, angle of internal friction (φ), cohesion (c) and other indexes were calculated by plotting the limiting molar circle metric tangent of the soil under different principal stresses, as shown in Figure 14;

(2)

Initial Isocompression Consolidation Curve

In order to determine the isotropic compression coefficient λ and isotropic rebound coefficient κ, it is necessary to determine the initial calculation point on the normal consolidation line (ν_λ, P₁). This requires determining parameter values based on the results of compression consolidation tests, using the following calculation formula:

$$\lambda =C_c/\mathit{ln}(10)$$

(10)

$$\kappa \approx C_s/\mathit{ln}(10)$$

(11)

where Cc and Cs are the compression and expansion indices of the soil, respectively, which can be obtained from the normal consolidation line and isobaric expansion line of the soil:

$$c_u={\displaystyle \frac{M{p}_1}{2}}\mathit{exp}({\displaystyle \frac{\Gamma -v_{cr}}{\lambda }})$$

(12)

$$\Gamma =v_{\lambda }-(\lambda -\kappa )\mathit{ln}(2)$$

(13)

In the formula, p₁ represents the base stress; c_u denotes the undrained shear strength of the soil; Γ signifies the critical specific volume of the soil; and ν_cr is the critical shear strain of the soil. The initial normal isobaric consolidation curve parameters of the soil, p₁ and ν_λ, can be obtained using coupling Formulas (11) and (12);

(3)

Prior Consolidation Stress P_c0

The prior consolidation stress can be calculated according to the critical state line in space, using the yield equation as follows:

$$q^2=M^2\left[p(p_{\mathrm{c}0}-p)\right]$$

(14)

q is the yield stress of the soil, and P_c0 is the prior consolidation stress with:

$$p_{co}=p_0[1+({\displaystyle \frac{q_0}{M{p}_0}}{)}^2]OCR$$

(15)

where OCR is the over-consolidation ratio, and p_o and q₀ are the existing stress state of the soil (Figure 15). Table 4 shows the relevant parameters of clay shock obtained, and

Table 5. Shield construction material parameters.

Structure	ρ/(kg/m3)	E/MPa	v
Tube sheet	2487	34,400	0.2
Shield	7850	205,000	0.3
Clay shock slurry (400 kg/m3)	1230	590	0.4
Grouting layer	2290	7200	0.22

lists the material parameters required for subsequent numerical simulations.

4.3. Simulation of Shield Excavation Process

A key issue addressed in this study is the filling of the excavation gap with clay shock slurry during shield tunneling and its mechanism for reducing ground deformation. As such, the excavation gap between the shield shell and strata was considered in a refined manner during modeling, with the clay shock slurry filling area assigned a value in the simulation process for comparative study. The shield excavation process was simulated, as depicted in Figure 16, with support force applied to the excavation surface to maintain ground stability. The shield shell was simplified to an integer multiple of the tube sheet ring width (seven rings, i.e., 8.4 m) based on its actual length, with the shell structural unit used for the simulation, and the pipe sheet, synchronous grouting, and secondary grouting (radial grouting) all simulated using solid units. The action mechanism of clay shock was investigated by setting two calculation conditions: whether or not to inject clay shock slurry to fill the excavation gap. In addition to its filling effect, the friction of the shield shell was applied to simulate the damping effect of clay shock slurry according to the viscosity test results.

The area where this project is located is not a seismic-prone area. During the research process, we did not consider the dynamic response of the structure, nor did we take into account the influence of structural damping and earthquakes on the crossing process [26].

4.4. Calculations

In order to study the effect of filling the excavation gap with clay shock slurry during shield tunnel construction, the deformation of the existing tunnel was compared under two numerical calculation conditions: with and without clay shock slurry filling the excavation gap. The results are shown in Figure 17. Prior to the cutter plate reaching the bottom of the existing tunnel, the tunnel deformation curves for both conditions develop similarly. However, from the cutter plate to the shield exit, the development trend of the two curves diverges significantly. When clay shock slurry is used to fill the excavation gap, the deformation of the existing tunnel is suppressed, with deformation at this stage reduced by 57% compared to conditions without clay shock slurry filling. When the shield tail was released, the deformation of the existing tunnel was 50% smaller in the clay shock slurry-filled condition than in the non-clay shock slurry-filled condition. The final deformation of the existing tunnel with clay shock slurry filling was 55% smaller than that without clay shock slurry filling, demonstrating that using clay shock slurry to fill excavation gaps during shield crossing construction can significantly reduce the deformation of existing structures. This effect is primarily reflected in the suppression of the deformation of the soil around the shield during shield crossing construction through the existing structures.

Comparing the calculation results for different radial grouting sequences reveals that the final settlement for 15 rings of radial grouting at the shield end is approximately 1.3 mm, while the final settlement for the 20th and 25th rings of radial grouting at the shield end is 1.8 mm and 2.7 mm, respectively. This renders control of the soil body disturbance less effective and subsequent settlement difficult to control. Therefore, the timeliness of radial grouting is crucial, and the radial grouting position should be advanced to within 15 rings of the shield tail as much as possible under shield tunnel construction conditions.

5. Deformation Analysis of Existing Tunnels

Numerical calculation results were obtained to verify the reliability of the proposed measures, such as using clay shock grouting, synchronous grouting, and radial grouting, to reduce the structural deformation of the existing tunnel during new tunnel crossing. In order to further study the deformation law of the existing tunnel during actual construction, the deformation of the tunnel tube sheet and track structure within the scope of construction influence was monitored. Vertical deformation automation monitoring points were established on the track structure of the existing subway airport line from Dongzhimen Station to Sanyuanqiao Station, with specific locations of the vertical deformation automation monitoring points for the track structure shown in Figure 18. SJC-01-01~SJC-01-08 are monitoring points for the deformation of the existing tunnel segments within the underpass scope, while JLC-01-01~JLC-01-08 are track deformation measurement points for the existing tunnel within that scope.

5.1. Deformation of Existing Tunnels

As depicted in Figure 19, the maximum settlement of the existing upline tunnel following left line shield penetration occurs at monitoring point SJC-01-04, with a settlement of −1.3 mm (control value: −2 mm). The maximum settlement of the existing downline tunnel occurs at monitoring point SJC-03-03, with a settlement of −1.0 mm (control value: −2 mm), representing a significant reduction compared to the settlement of the existing upline tunnel.

The maximum settlement of the existing upstream tunnel following right line shield tunnel penetration occurs at monitoring point SJC-01-07, with a settlement of −1.3 mm (control value: −2 mm). The maximum settlement of the existing downstream tunnel occurs at monitoring point SJC-03-07, with a settlement of −1.2 mm (control value: −2 mm). These results indicate that during the shield tunnel crossing through the existing tunnel, the overall settlement of the existing tunnel is well-controlled and does not exceed the control value.

In addition, a comparison between the measured results and the numerical simulation results was carried out. Both the actual construction and the simulation process used clay shock. The measuring points SJC-01-01 to SJC-01-08 were selected, with a total of eight points. The final settlement data after the segment was removed from the shield tail were chosen as the result, and Figure 20 was drawn. According to the results, the simulation results are basically consistent with the measured results. The maximum settlement position in the simulation results was on the tunnel centerline, and the maximum settlement was approximately −1.05 mm. However, the maximum settlement point of the measured data was located outside the existing tunnel, and the settlement at the centerline position was relatively small. From this, it can also be reflected that when clay shock is used during the shield tunneling process, it can fill the gap between the shield shell and the soil in a timely manner and significantly control the settlement deformation of the soil above the shield body.

5.2. Deformation of Existing Tracks

As depicted in Figure 21, the track deformation of the existing line can be divided into five stages:

• Before shield entry into the crossing area, there is a slight bulge in the soil in front of the shield, with a generally smooth settlement curve. During this stage, shield thrust is the primary cause of ground deformation;
• Shield arrival stage: The existing tunnel experiences a gradual increase in load in the direction of excavation, with additional frontal thrust and sidewall friction impacting the crossing influence area of the existing tunnel. This phase is brief but important for the transformation of influencing factors. The influence of pressure on soil at the face of the palm reaches its maximum and then gradually decreases, while the influence of sidewall friction increases. At this stage, settlement of the existing tunnel is not yet complete, and the self-stability of the soil body decreases, but settlement remains steady;
• Shield passage stage: Injection of clay shock slurry into the shield shell effectively reduces the effect of sidewall drag, while synchronized grouting at the shield tail compensates for part of the soil loss. Change in settlement of the existing line is controlled within 0.5 mm during this stage;
• Shield tail disengagement stage: Deformation of the existing tunnel is no longer significantly impacted by frontal pressure and sidewall resistance. The impact of shield tail release on the existing tunnel primarily depends on the quality of synchronized grouting and the degree of filling at the shield tail gap. The longer the shield tail gap exists, the greater the deformation of the soil body becomes. The amount of change in the settlement of the existing line is largest during this stage, with cumulative settlement reaching approximately 1.1 mm;
• Replenishment and late settlement stage: Superporous water pressure in the soil beneath the tunnel continuously dissipates, causing deformation of the existing tunnel due to the consolidation or sub-consolidation of soil. In order to control the late settlement of the existing tunnel, secondary grout replenishment and radial grouting are used to compensate for the loss of soil due to soil consolidation.

6. Discussion

In this paper, an in-depth exploration was carried out on the physical and mechanical properties of clay shock slurry and its application in controlling settlement during shield tunneling beneath existing structures.

(1) The penetration property test results indicate a significant inverse relationship between the permeability of clay shock slurry and its concentration. Notably, when the ratio of clay shock slurry reached 400 kg/m³, it effectively impeded the forward flow of synchronous grouting slurry, thereby optimizing the filling, supporting, and reinforcing capabilities of the slurry at the excavation boundary. The viscosity test demonstrates that clay shock slurry could halve the friction between the shield shell and the soil body, while the triaxial compression test results show its capacity to prevent super-consolidation, large shear damage, and volume expansion within the soil. These findings collectively highlight the crucial role of clay shock slurry in minimizing the impact on the structural stability of existing lines when filling the shield excavation gap;

(2) Regarding the grouting strategy, the employment of a 1:1 cement–water glass two-fluid slurry in the shield close-through area, combined with 180° radial grouting at the top of the tunnel, proved effective in curbing the settlement of existing tunnels. The timeliness of radial grouting was also a determining factor, with more pronounced settlement reduction typically observed when it was implemented within 15 rings of the shield tail;

(3) Through numerical simulations of different working conditions, it was evident that injecting clay shock slurry outside the shield to fill the excavation gap during construction substantially mitigated ground settlement and axial deformation of the tunnel. The filling and damping characteristics of clay shock slurry ensured that the deformation of existing structures remained within a safe threshold;

(4) Nevertheless, this study also has certain limitations. Although extensive experiments were conducted to examine the physical and mechanical properties of various ratios of clay shock slurry and clay, further research is warranted to fully understand the rheological properties of the slurry. Additionally, the influence of grouting pressure on the deformation of existing junction structures during traversing construction remains an area that requires more detailed investigation.

7. Conclusions

In conclusion, the research in this paper demonstrates how clay shock slurry controls settlement during shield tunnel construction. The research results can provide a certain reference value for similar projects and offer some theoretical support for the efficient and safe tunneling of shields.