Introduction

The unloading due to pit excavation can lead to redistribution of the surrounding soil stresses, causing additional displacements in the underlying tunnels and the degradation of soil engineering properties due to the construction disturbances, which also affects the structural safety of the tunnels1,2,3,4. Since metro tunnels are extremely sensitive to deformations, excessive deformations can cause the lining segments to crack. Therefore, employing tunnel protection measures to limit tunnel displacements during nearby pit excavations is crucial. In metro deep excavation projects within soft soil regions, soil reinforcement technique at the base of the pit has been widely adopted as an effective measure to enhance the strength of the soft soil foundations5,6. However, the construction of such protection measures can also disturb the surrounding soil, impacting the tunnel. Previous studies have indicated that a primary cause of engineering problems in pits and tunnels is the inadequate recognition of the changes in soil properties due to construction disturbances7. Thus, research on soil reinforcement protection measures for metro tunnels considering construction disturbances holds significant engineering value.

The construction of pit excavation and bored cast-in-place piles induces significant disturbance through multiple mechanisms. The processes of pit excavation and drilling lead to stress release, resulting in changes in the effective stress within the soil. The relieved stress is replaced by the tension in the soil’s pore water, resulting in negative pressure in the pore water, which causes the gas dissolved in the water to escape, further altering the effective stress in the soil. During the construction of pit excavation and bored cast-in-place piles, construction disturbances cause extensive soil remodeling, disrupting the original soil structure and leading to particle rearrangement, fundamentally altering the natural soil structure. During the concrete pouring process of bored cast-in-place piles, the injection of fresh concrete significantly alters the stress state of the surrounding soil, causing changes in pore water pressure and effective stress distribution. These combined effects create a complex disturbance zone around the piles, significantly affecting the engineering behavior of the soil8,9.

Zhejiang province is located in a developed coastal region, where coastal soft soils exhibit widespread sedimentation, high moisture content, high compressibility, low strength, and pronounced structure. The structural integrity of these soils is highly susceptible to disturbances, leading to irreversible structural damage and significant changes in mechanical properties. Numerous domestic and international scholars have studied the construction-induced disturbance through laboratory tests and field monitoring. Hardin and Drnevich10 found through resonant column tests that even minimal disturbances could alter the soil’s initial modulus. Wang et al.11, based on the Wenzhou coal yard project, discovered through vane tests that the installation of drainage boards disturbed the soft soil, reducing its strength by approximately 50%. Chen et al.12 conducted field tests and laboratory experiments on the disturbed soils at the bottom of the Hangzhou Xianghu Station pit, which collapsed, finding that the soil strength reduced by 40–80%. Zuo et al.13 installed earth pressure sensors on bored piles to study the disturbance range during pile construction, noting significant effects on the soil within three diameters horizontally and vertically from the pile. Li et al.14, based on multifunctional cone penetration tests (CPTU), determined the range of disturbance caused by pit excavation unloading and proposed that the depth of disturbance could be defined as the ___location where cone resistance decreases to 20% of its original value.

While existing research primarily focuses on the impacts of construction disturbances on pit or tunnel engineering, there is limited research on the effects of pit construction disturbances on nearby tunnels. Wang et al.15 considered construction disturbances and proposed equations for the stability against heave of deep excavations. Lu et al.16, combining finite element numerical analysis, analyzed the effects of disturbances on the heave at the bottom of pits. Zhang et al.17, based on the Terzaghi-Rendulic consolidation theory, studied the effects of shield tunnel disturbances on soil pore water pressures and surface subsidence. Zhu et al.18 used three-dimensional finite element analysis to study the impacts of diaphragm wall construction on disturbances and adjacent buildings. In research considering the impacts of pit excavation construction disturbances on existing tunnels, Hu et al.19 set the disturbed area at the bottom of the pit and analyzed the effects on adjacent tunnels through numerical simulation. Wang et al.20, through numerical simulation, set the entire area as a disturbance zone and studied the effects of pit excavation on adjacent tunnels. From the research conducted by these scholars, studies on the impacts of deep pit excavation considering construction disturbances on nearby underlying tunnels are scarce, and existing research has not detailed the division of disturbed soil areas according to actual disturbance levels, nor considered the impact of disturbances from soil reinforcement construction on the protective effectiveness for metro tunnels.

This paper verifies the methods of adding small amounts of cement and salt grains to silty clay in Zhejiang Province, simulating artificially disturbed structured soils, and obtains the parameters of different disturbance degrees of soil bodies based on uniaxial compression tests and triaxial tests. Disturbance zones are delineated based on the unloading ratio and field disturbance tests conducted at the Gaotangqiao metro station excavation site in Ningbo. Relying on a practical engineering project in Zhejiang province, this paper primarily investigates the impacts of disturbances caused by pit excavation on tunnel displacement using the finite element software Plaxis3D, with particular emphasis on the degradation of soil engineering properties due to the construction-induced disturbance. Additionally, the impact of disturbances from soil reinforcement construction on the protective efficacy for metro tunnels was systematically evaluated. The protective performance of three distinct foundation reinforcement methods on the metro tunnel are also compared.

Engineering overview

As shown in Fig. 1, a practical pit engineering project in Zhejiang province consists of two blocks, north and south (with an interconnected basement), covering an excavation area of approximately 34,000 m2 and a perimeter of about 960 m. Except for a single basement layer set up in the southernmost 40 m range, the remaining areas are constructed with two basement layers. The bottom slab of the two-layer basement is at an elevation of − 11.1 m, and the bottom slab of the single-layer basement is at − 6.7 m. A dual-line metro shield tunnel passes beneath the pit. The tunnel has an outer diameter of 6.2 m and an inner diameter of 5.5 m, with the lining made of assembled segments of C50 concrete, and a cover depth of about 22.7 m.

Fig. 1
figure 1

Plan view of the foundation pit and underlying dual-line tunnel.

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The primary support system employs large-diameter bored cast-in-place piles (ϕ1000@1400) in combination with two reinforced concrete braces, with the exception of the intersection area between the metro shield tunnel and retaining structures, extending approximately 30 m on either side. Triple-axis cement mixing piles are implemented externally to the bored piles for effective water and soil retention.

The bored cast-in-place piles of this engineering project are only 2 m away from the tunnel at the closest point, making the construction of the retaining structure and engineering piles challenging. In soft soil foundations, methods such as high-pressure jet grouting or cement mixing piles are commonly used to reinforce the foundation to reduce deformations in the underlying tunnel caused by excavation. After foundation reinforcement, the compressibility of the soil is reduced, and its strength is enhanced, ensuring the stability of the pit during excavation and the safety of surrounding infrastructure and buildings.

As shown in Fig. 2, for situations where excavation occurs above the tunnel, the main methods include full-scale reinforcement, where the entire bottom of the pit is reinforced, and portal reinforcement, where the soil around the tunnel is reinforced. In addition to foundation reinforcement, grouting reinforcement around the tunnel is also widely used. By enhancing the engineering properties of the soil around the tunnel, the additional deformation caused by pit excavation unloading is reduced.

Fig. 2
figure 2

Schematic of foundation reinforcement (units: mm).

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During the construction of the enclosure piles and pit excavation, the soil is disturbed, and the tunnel, located in highly sensitive soft soil, experiences a decrease in bearing capacity, leading to continuous deformation. During soil reinforcement, the construction process of concrete mixing piles causes disturbances to the soil near the tunnel; high-pressure jet grouting exerts radial pressure on the surrounding soil, also causing deformation due to grouting disturbances. Before the strength of the soil is enhanced during the reinforcement process, large machinery continuously operates above, leading to ongoing settlement and convergence deformation of the tunnel.

This paper mainly analyzes the impacts of pit excavation and the aforementioned three types of foundation reinforcement methods on tunnel displacement, considering the degradation of soil properties due to the disturbances caused by construction. The protective performance of these three foundation reinforcement methods on the metro tunnel are also compared.

Construction disturbance delineation

To study the impact of construction disturbances on the underlying tunnel, the disturbed soil zones caused by pit excavation were delineated based on existing research results and field tests. The unloading due to pit excavation leads to the release of soil stresses at the bottom of the pit, reducing the soil strength and causing rebound deformation. The maximum depth of soil affected by the engineering property changes due to pit excavation is called the unloading influence depth14.

Pan et al.21 used the unloading ratio R to measure the change in stress levels at the bottom of the pit (Eq. 1). Through direct shear tests, the strength curves under loading and unloading states were obtained. The strength retention rate \(f_{s}\) was obtained (Eq. 2)

$$R = \frac{{p_{\max } - p_{i} }}{{p_{\max } }}$$
(1)
$$f_{s} = \frac{{S_{0} - S_{i} }}{{S_{0} }}$$
(2)

where \(p_{max}\) is the initial overburden load, \(p_{i}\) is the remaining overburden load after i stages of unloading. \(S_{0}\) and \(S_{i}\) are the shear strengths at the consolidation point and unloading point, respectively.

The depth of the disturbance zone \(H_{{u\left( {cr} \right)}}\) can be determined using Eq. 321, where H is the depth of the pit excavation:

$$H_{u(cr)} = \frac{(1 - R)H}{R}$$
(3)

Several studies on the disturbance depth of excavation areas are shown in Table 1:

Table 1 Excavation disturbance depth.
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It is reasonable to divide the bottom of the pit into strong and weak disturbance zones. Since many field measurements and laboratory tests determine the strong disturbance zone to be about 0.25H, this paper sets the depth of the strong disturbance zone as 0.25H; the depth of the weak disturbance zone is set as 1.3H according to Pan et al.21.

Pit excavation not only disturbs the soil at the bottom of the pit but also affects the soil behind the retaining walls. This paper also divides the disturbance zones based on the field disturbance tests conducted at the Gaotangqiao metro station pit in Ningbo, located in Zhejiang Province. The project obtained the degree of construction disturbance through CPT, vane shear, and shear wave velocity tests. As shown in Fig. 3:

Fig. 3
figure 3

Disturbance zones of the Ningbo metro pit.

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Zone 1 is the connection area between the outer surface of the pit from 0.8 to 1H and the diaphragm wall from 1.37 to 1.45H. After the pit excavation, this area experiences significant unloading of horizontal stress, large deformations, and severe structural disturbance of the soil. Vane shear tests in this area showed a decrease in vane shear strength of about 14–16%, shear wave velocity tests showed a reduction in soil shear modulus by about 15.9–20.3%, and CPT tests showed a decrease in cone tip resistance by about 10%. Various test methods confirm severe disturbance in this area.

Zone 2 is the connection area between the bottom of the diaphragm wall and the ground settlement point from 1.8 to 2.0H. After pit excavation, vane shear tests showed a decrease in soil vane shear strength by about 4–6%, shear wave velocity tests showed a reduction in soil shear modulus by about 6.2–21.9%. CPT tests showed a decrease in cone tip resistance by about 5%. Various testing methods verify significant disturbance in this area.

Zone 3 is the bottom disturbance zone, determined by the influence depth of 1.8–2.0H from CPT tests at the bottom of the pit and the excavation face position H. After pit excavation, the vertical stress in this area is unloaded, and the soil inside the pit will experience significant upheaval, causing severe structural disturbance. CPT tests show a decrease in cone tip resistance by about 10–30% in this area, with the reduction in cone tip resistance decreasing with depth. Vane shear tests show a decrease in soil vane shear strength by about 22% in this area. Various test methods confirm severe construction disturbance in this zone.

This paper divides the disturbance zones behind the retaining walls according to the field disturbance tests of the Ningbo metro pit project. Zone 1 is delineated as a strong disturbance zone, and Zone 2 as a weak disturbance zone. The division of the disturbance zones caused by pit excavation is shown in Fig. 4. The disturbance is divided into bottom disturbance and outside wall disturbance: the bottom disturbance is divided into two areas, from the bottom of the pit to 1.25 H excavation depth as a strong disturbance zone, and from 1.25 to 2.3 H as a weak disturbance zone. The construction disturbance outside the diaphragm wall is divided into two areas, with the connection area between the buried depth of the underground continuous wall at 1.4H and outside the pit at 1H delineated as a strong disturbance zone, and the connection area between the buried depth of 2.0H and outside 2.0H as a weak disturbance zone.

Fig. 4
figure 4

Diagram of disturbance zones.

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Preparation of artificially disturbed soil and evaluation of disturbance degree

Due to the complex conditions of actual engineering projects, it is difficult to obtain soil with the same disturbance degree, and secondary disturbances to the soil can occur during sampling, transportation, and sample preparation. Regarding the indoor preparation of disturbed soil, Meng24, Li25 and Hu et al.19 used methods such as artificial squeezing, ring knife, and kneading to prepare disturbed soil; Liu26 used a vibration table to disturb the soil, controlling the vibration time to obtain soil samples with different degrees of disturbance. The soil samples produced through squeezing and vibration methods are unevenly disturbed, and the operations are challenging. These methods make it difficult to quantitatively control the disturbance degree, difficult to obtain completely consistent disturbed soil samples, have poor repeatability, and are not conducive to application in indoor geotechnical tests.

Carter and Liu27 proposed that the difference between disturbed soil and undisturbed soil lies in the change in its structure. When coastal soft soils are disturbed, the equilibrium system composed of cementitious substances between soil particles, water molecules, and soil particles is disrupted, leading to changes in the internal structure and stress state of the soil. The reduction in strength and increase in compressibility of disturbed coastal soft soils originate from these structural changes. The soil structure encompasses the spatial arrangement of soil particles, the condition of pores, and the characteristics of particle contacts and connections. Given that the structure of soft soils is influenced by their cementation and fabric features, scholars have simulated the cementing action between soil particles by adding cementitious materials to soil in laboratory experiments. Additionally, the simulation of large pore structures has been attempted using salt grains or ice grains. Jiang and Shen28 has added cement to soil powder to simulate the cementing action of structured soils and used ice grains to replicate large pore spaces. Researchers such as Liu and Shen29, Li et al.30, and Ling et al.31 have transformed undisturbed soil into remolded soil powder and created artificial structured soils by incorporating cement and salt grains into the soil powder. This method of sample preparation is relatively simple and effective in simulating both the cementing characteristics and large pore structures of structured soils.

Wang et al.20 verified the reliability and rationality of simulating disturbed soil using artificially structured soil. Based on the research results of Wang et al.20, this paper uses artificially structured soil with salt grains and different cement contents to simulate disturbed soil with different degrees of disturbance.

Preparation of artificially disturbed soil

The soil strata at the project site in “Engineering Overview” Section are characteristic of the typical soft soil layers found in Zhejiang Province. Apart from the mixed fill soil of Layer ①-0–1, the plain fill soil of Layer ①-0–2, and the clayey silt of Layer ②-1, the remaining strata consist primarily of silty clay.

To facilitate the investigation of construction disturbance effects on tunnel displacement and the protective efficacy of soil reinforcement, subsequent analyses are conducted under the assumption that the foundation pit enclosure, tunnel structure, and concrete mixing piles are situated within a homogeneous silty clay stratum. The soil samples used in this experimental study were extracted from the ④-2 silty clay layer at an approximate depth of 33 m. These samples exhibit a dark gray coloration, which is typical of deep soft soil formations in the coastal regions of Zhejiang. The basic physical properties of the soil are comprehensively presented in Table 2.

Table 2 Basic physical property indices of the ④-2 silty clay layer.
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The preparation of artificially structured soil was strictly conducted according to the standard “Geotechnical Test Method Standard GBT50123-1999.” After drying the original soil material, it was crushed and passed through a 0.5 mm sieve, with different amounts of 525# Portland cement and a small amount of salt grains added (the salt content was 8% relative to the total weight of silty clay and cement). The salt grains were made by crushing large-grain edible salt and passing it through a 0.5 mm sieve. After thoroughly mixing the required mass of the mixture, it was compacted in five layers using a standard compactor. After compaction, the saturator containing the soil sample was placed in a saturation infiltration system for vacuum saturation. After saturation, the saturator was placed in flowing water, ensuring the soil sample was completely immersed in water. The flow of water helped flush away the dissolved salt grains, forming a structured soil sample with a cementing effect and large pores.

The cement content calculation is shown in the following equation:

$$\varphi_{c} = \frac{{m_{c} }}{{m_{c} + m_{s} }} \times 100\%$$
(4)

where \(\varphi_{c}\) is the percentage of cement content, \(m_{c}\) is the mass of cement, and \(m_{s}\) is the mass of the original soil material.

Since Wang et al.20 utilized the ④-2 silty clay layer from Zhejiang Province, which is identical to the soil stratum adopted in our investigation, to simulate soils with varying degrees of disturbance, their study adopts the well-established conclusions regarding cement content parameters. Specifically, the experimental protocol maintains a cement content range of 0–2%, where the soil specimen with 2% cement content accurately represents the engineering properties of undisturbed soil. This paper adopts their well-established conclusions regarding cement content parameters to ensure consistency and reliability.

Uniaxial compression tests and triaxial consolidated undrained tests were conducted for six types of soil samples: natural soil, artificially structured soil 1 (cement 2.0%), artificially structured soil 2 (cement 1.5%), artificially structured soil 3 (cement 1.0%), artificially structured soil 4 (cement 0.5%), and remolded soil (Fig. 5).

Fig. 5
figure 5

Test equipment.

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The uniaxial compression tests were conducted using a triple consolidation apparatus, with applied pressure levels of 12.5, 25, 50, 100, 200, and 400 kPa. The deformation measurements were systematically recorded using an automated data acquisition system to ensure accuracy and consistency. For the triaxial testing program, consolidated undrained (CU) tests were performed using a GDS triaxial testing system under confining pressures of 25, 50, 100, and 200 kPa. The deviator stress and axial strain were continuously monitored and recorded through a computerized data acquisition system, enabling precise measurement of the stress–strain behavior and pore pressure development throughout the testing process.

Compression indices

Based on the results of uniaxial compression tests, the compression indices of different structured soils were obtained, and the fitting curves of the compression indices and cement content were drawn, as shown in Fig. 6. It was found that as the cement content increased, the compression modulus of the artificially structured soil increased, reducing its compressibility. The hydration reaction of cement can build bonds between clay particles, effectively enhancing the cementing action between soil particles. These results indicate that using artificially prepared structured soil can restore the compressibility of remolded soil to its natural state.

Fig. 6
figure 6

Fitting curves of compression indices and cement content.

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Effective shear strength index

The stress–strain curves from the triaxial consolidated undrained tests are depicted in Fig. 7. It can be observed that under the same confining pressure, as the cement content increases, the deviatoric stress rises more rapidly with the strain rate, and the peak deviatoric stress progressively increases while the corresponding axial strain tends to decrease. When the cement content reaches 2%, the stress–strain curve of the soil closely resembles that of the natural soil, both exhibiting strain-softening behavior. Additionally, the peak deviatoric stress and strain at this cement content are relatively similar to those of the natural soil.

Fig. 7
figure 7

Triaxial Test Stress–Strain Curve.

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Figure 8 shows the relationship curves between the shear strength indices of different structured soils and cement content. It can be seen from the figure that as the cement content in the remolded soil increases, its cohesion \(c\) and \(c^{\prime }\) both show exponential growth; when the cement content reaches 2%, the sample’s cohesion is nearly consistent with that of the natural soil; the internal friction angles \(\varphi\) and \(\varphi^{\prime }\) do not change significantly with increasing cement content, remaining essentially consistent with the natural soil’s internal friction angle. The results of uniaxial compression tests and triaxial tests indicate that as the cement content increases, the structural integrity of the soil is enhanced, allowing artificially prepared structured soil to restore the natural soil, and the deformation and strength characteristics of the natural soil after disturbance can be simulated by controlling the cement content.

Fig. 8
figure 8

Relationship between effective shear strength index and cement content.

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Evaluation of disturbance degree of artificially disturbed soil

Many scholars32,33,34 have conducted some research on the disturbance degree of structured soft soils, proposing their own methods for determining the disturbance degree of soil based on changes in soil pore water pressure, e-lgp curves, and soil strength. Based on the research results of Wang et al.20, this paper adopts the evaluation method proposed by Nagaraj35, evaluating the disturbance degree of artificially disturbed soil with different cement contents based on the structural yield stress obtained from uniaxial compression consolidation tests, as shown in Table 3. The disturbance degree is defined as shown in Eq. 5:

$$SD = \frac{{P_{c} - P_{c}^{\prime } }}{{P_{c} }} \times 100\%$$
(5)

where SD is the disturbance degree defined according to yield stress; \(P_{c}\) is the yield stress of the natural soil, \(P_{c}{\prime}\) is the yield stress of the disturbed soil, and the structural yield stress corresponds to the axial pressure at the turning point of the e-lgp curve.

Table 3 Evaluation of disturbance degree of different structured soils.
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Based on Table 3, the fitting curve of disturbance degree and cement content is drawn. As shown in Fig. 9, the disturbance degree of the soil decreases linearly with increasing cement content, reaching nearly 0% when the cement content is 2%. This also verifies the rationality and reliability of simulating the disturbance degree of natural soil by controlling the cement content.

Fig. 9
figure 9

Fitting curve of disturbance degree and cement content.

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Numerical analysis of the impact of construction disturbance on the tunnel

Parameter settings

Soil parameter settings

In this paper, the soil is modeled using the Hardening Soil Small (HSS) model. The HSS model parameters include 11 HS model parameters and 2 small strain parameters. This paper obtained the soil’s reference tangent modulus \(E_{oed}^{ref}\) from one-dimensional compression consolidation tests; the reference secant modulus \(E_{50}^{ref}\), failure ratio \(R_{f}\), and dilation angle \(\psi\) from triaxial consolidation drained shear tests; effective cohesion \(c^{\prime }\) and effective internal friction angle \(\varphi^{\prime }\) from triaxial consolidation undrained shear tests; and the reference unloading–reloading modulus \(E_{ur}^{ref}\) from triaxial consolidation drained unloading–reloading tests. The other HS model parameters \({\text{m}}\), \({ }\upsilon_{ur}\), \({ }p^{ref}\) and \(K_{0}\) can refer to existing research results for specific values and literature sources as shown in Table 4. The small strain parameter \(G_{0}^{ref}\) can be determined based on the conclusion by Wang et al.36, taking \(G_{0}^{ref} = 3.5\sim 5.0E_{ur}^{ref}\), and \(\gamma_{0.7}\) can be calculated according to the introduction by Brinkgreve and Broere37 using Eq. 6;

$$\gamma_{0.7} = \frac{1}{{9G_{0} }}[2c^{\prime } (1 + \cos (2\varphi^{\prime } )) + \sigma_{1}^{\prime } (1 + K_{0} )\sin (2\varphi^{\prime } )]$$
(6)

where

$$G_{0} = G_{0}^{{{\text{ref}}}} \left( {\frac{{c^{\prime } \cos \varphi^{\prime } + \sigma_{3}^{\prime } \sin \varphi^{\prime } }}{{c^{\prime } \cos \varphi^{\prime } + p^{ref} \sin \varphi^{\prime } }}} \right)^{m}$$
(7)
Table 4 Partial parameters of the HSS model.
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In the equation: \(\sigma_{1}^{\prime }\) is the vertical effective stress of the soil, which can be taken as the vertical effective stress at the middle point of the corresponding soil layer during calculation; \(\sigma_{3}^{\prime }\) is the lateral stress of the soil.

Lu et al.16 measured a disturbance degree of about 60% in the strong disturbance zone through field CPTU tests, with the disturbance degree of the soil in the weak disturbance zone gradually decreasing from 60 to 0% with increasing distance from the pit. Based on the parameters of disturbed soil measured in “Preparation of Artificially Disturbed Soil and Evaluation of Disturbance Degree” Section, the disturbance degree of the strong disturbance zone is set at 62%, and the weak disturbance zone at 40% for numerical analysis.

The main parameters of the HSS model are detailed in Table 5.

Table 5 Main Parameters of Different Disturbed Soils.
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Reinforcement area parameters

After using concrete mixing piles to reinforce the foundation, the foundation of the reinforced area is considered a composite foundation. There are various ways to determine the parameters of a composite foundation. This paper simulates foundation reinforcement by improving the soil parameters. Zheng et al.40 considered the soil of the tunnel grouting reinforcement area as a linear elastic material, with an elastic modulus of 300 MPa. Huang et al.41 studied the protective effect of foundation reinforcement on metro tunnels through numerical simulation. When considering the parameters of the reinforced soil in the reinforced area, the stiffness parameters of the HS model were increased by three times, while the effective cohesion \(c^{\prime }\) was set at 170 kPa and the effective internal friction angle \(\varphi^{\prime }\) at 40°. The numerical simulation results were compared with field measurements, showing good consistency. This paper adopts Huang Hongwei’s method, increasing the stiffness parameters of the soil in the reinforced area by three times, and the strength parameters are determined according to the comprehensive strength method of the composite foundation:

$$c_{sp} = mc_{p} + (1 - m)c_{s}$$
(8)
$$\tan \varphi_{sp} = m\tan \varphi_{p} + (1 - m)\tan \varphi_{s}$$
(9)

In the equation, \(c_{sp}\) is the total cohesion of the reinforced area, \(c_{p}\) is the cohesion of the concrete mixing pile, \(c_{s}\) is the cohesion of the foundation soil, \(\varphi_{sp}\) is the comprehensive internal friction angle of the reinforced area, \(\varphi_{p}\) is the internal friction angle of the concrete mixing pile, \(\varphi_{s}\) is the internal friction angle of the foundation soil, and m is the foundation replacement rate.

Tao42 determined from laboratory test results that the cohesion \(c_{p}\) of the granite residual soil reinforced by high-pressure rotary jet piles can be taken as 500 kPa after 28 days, and the internal friction angle \(\varphi_{p}\) can be taken as 40°. The small strain parameters are obtained through empirical equations according to “Soil Parameter Settings” Section. As such, the HSS model parameters of the soil in the reinforced area in this paper are shown in Table 6.

Table 6 HSS Model Parameters of the Reinforced Area Soil.
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Pit and tunnel parameter settings

The concrete strength grade of the retaining piles is C30, and the piles are simulated using plate elements, with the thickness determined according to Eq. 10, where D is the pile diameter, t is the pile spacing, and h is the equivalent thickness of the plate element. The three-dimensional calculation parameters of the retaining structure plate element are shown in Table 7.

$$\frac{1}{12}(D + t)h^{3} = \frac{1}{64}\pi D^{4}$$
(10)
Table 7 Equivalent Parameters of Retaining Piles.
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The northern block of the project is equipped with two supports, consisting of 0.7 m × 0.9 m reinforced concrete supports, using C30 concrete, and simulated using beam elements in the finite element model. The calculation parameters of the internal supports are shown in Table 8:

Table 8 Internal Support Parameters.
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The metro tunnel constructed by the shield method has longitudinal joints between the segments, leading to reduced lateral bending stiffness of the lining. Ye43 used the modified customary method from the Japanese tunnel standards to account for the reduction in bending stiffness caused by longitudinal joints. This method considers the reduction in bending stiffness caused by longitudinal joints as an effective reduction in the overall bending stiffness of the lining, introducing an effective lateral bending stiffness ratio η to account for the impact of longitudinal joints on the tunnel lining, taking the lateral bending stiffness of the tunnel as ηEI. Huang et al.41,44 determined through tunnel model tests that the effective lateral bending stiffness ratio of shield tunnel misaligned joints can be taken as about 0.75, and the longitudinal bending stiffness can be taken as 1/6. The tunnel has an inner diameter of 5.5 m and an outer diameter of 6.2 m. The strength grade of the concrete for the tunnel lining structure is C50, with a weight of 15.5kN/m3, and Poisson’s ratio is taken as 0.15. The tunnel lining parameters are shown in Table 9:

Table 9 Tunnel Lining Parameters.
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Analysis model

This paper primarily analyzes the impact of construction disturbances on the underlying tunnel, so only the northern pit is modeled for analysis. Based on the actual engineering project, the numerical simulation model used is shown in Fig. 10. The pit area is 238 × 110 m, excavated in four steps to the bottom of the pit, with excavation depths of 2.5 m, 4.9 m, 8.1 m, and 10.6 m, and supports placed at − 1.9 m and − 4.9 m. The tunnel diameter is 6 m, a dual-line tunnel, with a burial depth of − 22.7 m. To consider the influence of boundary effects, the model dimensions are set at 305 × 190 m. In the numerical analysis, both the disturbances caused by pit excavation and tunnel protection measures are considered. According to the disturbance zones in “Construction Disturbance Delineation” Section, the disturbance zones in the three-dimensional model are set as shown in Fig. 11.

Fig. 10
figure 10

Model Schematic (created using Plaxis3D, version 2024.2.0.1144, www.seequent.com/products-solutions/plaxis-3d/).

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Fig. 11
figure 11

Schematic of the disturbance profile caused by pit excavation (created using Plaxis3D, version 2024.2.0.1144, www.seequent.com/products-solutions/plaxis-3d/).

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In the Plaxis3D model, the boundary condition at the top surface of the soil body is set to be free and unconstrained. The boundary conditions along the lateral sides are configured to restrict horizontal displacement, while the bottom boundary condition is designed to constrain vertical displacement.

The numerical analysis process for the model is outlined as follows:

  1. 1.

    Generation of the Initial Geostress Field.

  2. 2.

    Resetting Initial Displacements, Excavation within the Tunnel and Tunnel Lining Activation.

  3. 3.

    Resetting Initial Displacements and Activation of the Retaining Structure’s Plate Elements.

  4. 4.

    Excavation to 2.5 Meters Below Ground Surface, Degradation of Soil Properties within Disturbance Zone and Construction of Corresponding Supports.

  5. 5.

    Excavation to 4.9 Meters Below Ground Surface, Degradation of Soil Properties within Disturbance Zone and Construction of Corresponding Supports.

  6. 6.

    Excavation to 8.1 Meters Below Ground Surface and Degradation of Soil Properties within Disturbance Zone.

  7. 7.

    Excavation to the Bottom of the Pit at 10.6 Meters Below Ground Surface and Degradation of Soil Properties within Disturbance Zone.

Analysis results

Impact of disturbance on the tunnel

Since the two tunnels are closely spaced, their deformations and displacements are similar, so only the left line tunnel is analyzed. The tunnel crown beneath the pit is most affected by excavation unloading, and the following analysis focuses on the deformation of the tunnel crown. As shown in Fig. 12, the tunnel experiences uplift displacement within the range of pit excavation, and subsidence occurs outside the range of pit excavation due to dewatering. When the tunnel is near the boundary of the pit, it experiences significant horizontal displacement, while in the middle of the pit, the horizontal displacement of the tunnel is close to zero. Due to the small angle of intersection between the tunnel and the pit at the tunnel length of 223 m, the impact of pit unloading is greater, leading to larger horizontal displacement. Figure 12 shows the tunnel displacements under two conditions: with and without considering construction disturbance. When considering disturbance, the maximum horizontal displacement of the tunnel is 4.08 mm, and the maximum vertical displacement is 9.74 mm. Without considering disturbance, the tunnel’s maximum horizontal displacement is 3.92 mm, and the maximum vertical displacement is 8.23 mm. It is evident that considering construction disturbance has a significant impact on the vertical displacement of the tunnel, increasing the maximum vertical displacement by 18%; however, the change in horizontal displacement is minimal, with a maximum increase of 4.1%. The results considering disturbances are used for analysis in the following sections. In the text below, “unmitigated excavation” refers to considering only the disturbances caused by pit construction, and “strength not enhanced” refers to considering both the disturbances caused by pit construction and foundation reinforcement.

Fig. 12
figure 12

Tunnel displacement considering disturbance.

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Impact of foundation reinforcement construction disturbance on the tunnel

Deng et al.45 pointed out that cement mixing pile construction causes noticeable disturbances to the soil around the piles, and the disturbance degree decreases with depth and distance from the pile. For simplicity in analysis, the disturbance degree is set at 62%. Deng and Wang46 arranged grouting holes near the tunnel grouting holes and found that tunnel grouting causes certain disturbances to the surrounding soil, and the soil strength does not recover in a short period, with the disturbance degree also set at 62%.

Cement mixing pile construction causes noticeable disturbances to the soil. In actual engineering projects, due to constraints such as construction schedules, there may be situations where pit construction is carried out before the foundation reinforcement material fully reacts with the soil, which can increase tunnel displacement to some extent. This section analyzes the three reinforcement measures, i.e., full-scale reinforcement, portal reinforcement, and tunnel grouting reinforcement (Fig. 2), to study the impact of soil strength recovery and enhancement on the tunnel after different excavation steps.

Figure 13 shows the calculation results for tunnel horizontal and vertical displacements for portal reinforcement under five conditions, i.e., soil strength enhanced at excavation depths of − 2.5 m, − 4.9 m, and − 8.1 m, strength not enhanced, and unmitigated excavation. It is evident that the disturbance caused by portal reinforcement construction significantly impacts the tunnel. When soil strength is not enhanced, the maximum vertical displacement of the tunnel increases by 35% compared to unmitigated excavation, and the maximum horizontal displacement increases by 36.5%, which is significantly higher than the condition where soil strength is enhanced. When excavation reaches − 2.5 m and soil strength is enhanced, there is a protective effect on the tunnel, with the maximum vertical and horizontal displacements decreasing by 16.6% and 5.4%, respectively, compared to unmitigated excavation. When excavation reaches − 4.9 m with soil strength enhancement, tunnel displacement is roughly the same as in the unprotected scenario.

Fig. 13
figure 13

Impact of portal reinforcement disturbance on tunnel displacement.

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Figure 14 shows the computation results for tunnel horizontal and vertical displacements for tunnel grouting reinforcement under five conditions, i.e., soil strength enhanced at excavation depths of − 2.5 m, − 4.9 m, and − 8.1 m, strength not enhanced, and unmitigated excavation. It is clear that tunnel grouting reinforcement causes more significant disturbance to the tunnel compared to portal reinforcement, with maximum vertical and horizontal displacements increasing by 45% and 48%, respectively, compared to unmitigated excavation when soil strength is not formed. When excavation reaches − 2.5 m and soil strength is enhanced, there is a protective effect on the tunnel, reducing maximum vertical and horizontal displacements by 11% and 28%, respectively, compared to unmitigated excavation. The later the soil strength recovery, the greater the tunnel displacement.

Fig. 14
figure 14

Impact of tunnel grouting reinforcement disturbance on tunnel displacement.

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Figure 15 shows the calculation results for tunnel vertical and horizontal displacements for full-scale reinforcement under five conditions, i.e., soil strength enhanced at excavation depths of − 2.5 m, − 4.9 m, and − 8.1 m, strength not enhanced, and unmitigated excavation. When soil strength is not enhanced and excavation reaches the bottom, the vertical and horizontal displacements of the tunnel increase by 8% and 18%, respectively, compared to unmitigated excavation. Full-scale reinforcement causes less disturbance to the tunnel compared to tunnel grouting reinforcement and portal reinforcement. When excavation reaches − 2.5 m and − 4.9 m with soil strength enhancement, there is a protective effect on the tunnel. Excavation reaching − 8.1 m with increased soil strength will increase tunnel displacement, but the increase is not significant.

Fig. 15
figure 15

Impact of full-scale reinforcement disturbance on tunnel displacement.

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In summary, the disturbance caused by foundation reinforcement construction significantly affects tunnel displacement, and the greater the delay in soil strength recovery, the larger the increase in tunnel displacement. Among the three measures, tunnel grouting reinforcement, due to its direct reinforcement of the soil around the tunnel, causes the largest tunnel displacement due to the disturbance it creates. Portal reinforcement, by working on the soil on both sides of the tunnel, significantly increases the tunnel’s horizontal displacement. Full-scale reinforcement only reinforces the soil at the bottom of the pit and causes minimal disturbance to the tunnel, with the smallest increase in tunnel displacement.

Protective effect of foundation reinforcement construction on the tunnel

The disturbance caused by foundation reinforcement construction significantly affects the tunnel, and it is necessary to allow sufficient time before pit construction for the reinforcement material to fully react with the soil and for soil strength to recover and increase. This section studies the protective effects of the three foundation reinforcement measures on the tunnel when soil strength has fully increased before pit excavation.

Figure 16 shows the vertical displacement of the tunnel crown under different foundation reinforcement methods. In the full-scale reinforcement mode, the maximum vertical displacement of the tunnel is 7.76 mm, while without reinforcement measures, the maximum vertical displacement of the tunnel is 9.70 mm, with full-scale reinforcement reducing vertical displacement by about 20%. Using portal reinforcement, the maximum vertical displacement of the tunnel is 6.77 mm, reducing vertical displacement by about 30% compared to no reinforcement. Using tunnel grouting reinforcement, the maximum vertical displacement of the tunnel is 5.44 mm, reducing vertical displacement by about 44% compared to no reinforcement.

Fig. 16
figure 16

Vertical displacement of the tunnel under different foundation reinforcement measures.

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Figure 17 shows the horizontal displacement of the tunnel crown under different foundation reinforcement methods. It can be seen that without foundation reinforcement measures, the maximum horizontal displacement of the tunnel is 4.0 mm. With full-scale reinforcement, the maximum horizontal displacement of the tunnel is 3.4 mm, reducing it by 15%; with portal reinforcement, the maximum horizontal displacement is 2.5 mm, reducing it by 37.5%; with tunnel grouting reinforcement, the maximum horizontal displacement is 1.6 mm, reducing it by 60%. It is evident that full-scale reinforcement has a poorer effect on controlling horizontal displacement of the tunnel, while portal reinforcement and tunnel grouting reinforcement, by reinforcing the soil horizontally around the tunnel, can significantly reduce the tunnel’s horizontal displacement.

Fig. 17
figure 17

Horizontal displacement of the tunnel under different foundation reinforcement measures.

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Full-scale reinforcement, due to the need to reinforce the entire bottom of the pit, involves a large amount of construction work and only reinforces the soil at the bottom of the pit, making its control of tunnel deformation less effective than the other two methods. Portal reinforcement provides good control over both vertical and horizontal displacements of the tunnel, with a smaller area of reinforcement and easier implementation. Tunnel grouting reinforcement, by directly reinforcing the soil around the tunnel, provides the best control over tunnel deformation, but the disturbance it causes to the tunnel is also the most significant. In actual engineering, the range and uniformity of tunnel grouting outside the tunnel are difficult to guarantee, and tunnel grouting may cause tunnel misalignment and damage to the segments47.

In summary, among the three tunnel protection measures discussed, portal reinforcement provides the best protection against tunnel deformation and is easier to implement, making it suitable as the main method of reinforcement. Tunnel grouting reinforcement, due to the significant tunnel displacement it causes, is more suitable as an auxiliary reinforcement measure. After foundation reinforcement construction, it is important to wait for soil strength to recover and increase before proceeding with pit excavation.

Conclusion

Based on a practical engineering project in Zhejiang province, this paper studied the effectiveness of soil reinforcement protection measures for metro tunnels considering construction disturbances using Plaxis3D. The main conclusions are as follows:

  1. (1)

    For the silty clay in Zhejiang province, mixing 2% cement into remolded soil results in compression and strength characteristics that are essentially similar to those of undisturbed soil. Within the range of 0% to 2% cement content, as the cement content increases, the compression index of the artificially structured soil decreases linearly, the compression modulus increases linearly, cohesion c’ rises exponentially, and the internal friction angle φ’ remains largely unchanged. The artificially structured soil’s disturbance degree decreases linearly with increasing cement content, reaching nearly 0% when the cement content reaches 2%.

  2. (2)

    The tunnel experiences uplift displacement within the range of pit excavation; near the boundary of the pit, the tunnel exhibits significant horizontal displacement, while at the center of the pit, the horizontal displacement of the tunnel is close to zero. Considering the construction disturbances caused by pit excavation significantly affects the vertical displacement of the tunnel, increasing the maximum vertical displacement by 18.3%; however, the change in horizontal displacement is minimal, with a maximum increase of 4.1%.

  3. (3)

    During foundation reinforcement construction, concrete mixing piles and tunnel grouting cause disturbances in the foundation soil, resulting in certain additional displacements of the tunnel, with tunnel grouting showing the most significant disturbance-induced displacement. When excavation reaches the bottom without formed soil strength, the vertical deformation of the tunnel increases by about 45%, and the horizontal deformation by about 48%. Portal reinforcement and full-scale reinforcement also affect the tunnel, and the later the soil strength recovery, the greater the impact on the tunnel. It is necessary to ensure that the reinforcement material fully reacts with the soil before construction in actual engineering projects.

  4. (4)

    After soil strength has formed before pit excavation, the three foundation reinforcement methods analyzed in this paper all provide some protective effects on the tunnel compared to direct pit excavation. Among them, portal reinforcement is easy to implement, reduces vertical displacement of the tunnel by 30%, and horizontal displacement by 37.5%, providing good protection, making it suitable as the main reinforcement method. Tunnel grouting reinforcement, by reinforcing the soil around the tunnel, provides the best control over tunnel deformation, but because it causes significant disturbance to the tunnel, it is more suitable as an auxiliary reinforcement method.