Introduction

The technology of large-section quasi-rectangular shield tunnels in urban metro tunnel projects, which enables the formation of dual-line tunnels in one go, effectively increases section utilization, saves urban underground space resources, and minimizes impacts on the surrounding environment, is gradually being widely applied. However, the large dimensions of rectangular tunnel sections often result in sizable building voids, and the low early strength of the synchronous grouting slurry makes it difficult to control ground deformation, leading to significant surface settlement and posing serious challenges to the safety and stability of the surrounding environment.

Currently, there have been numerous studies in China focusing on surface settlement caused by the excavation of rectangular shield tunnels. In terms of field measurements, based on monitoring data from the Ningbo Metro Line 3 construction site, Si et al.1 analyzed the vertical deformation characteristics of the strata caused by the construction of rectangular shield tunnels in soft soil layers. Building upon this analysis, Ji et al.2 constructed a model of surrounding strata deformation induced by rectangular tunnel construction. Cheng et al.3 utilized monitoring data from the Hangzhou Metro to study the impact of rectangular tunnel construction on the surrounding environment in cases where there is no superposition or superposition with existing metro tunnels.

In theoretical calculations, Wei et al.4 studied the vertical displacement of soil caused by rectangular shield tunnel construction based on Mindlin displacement solutions and stochastic medium theory. Chen et al.5 employed elastic mechanics Mindlin solutions to analyze additional stress in soil induced by rectangular shield tunnel construction. Zhang et al.6, based on Mindlin displacement solutions, used numerical integration and superposition principles to analyze surface deformation caused by construction. Zhang et al.7 proposed a method for calculating soil deformation induced by rectangular shield tunnel construction based on the mirror method and the Winkler foundation model. Wei et al.8, based on stochastic medium theory and cumulative probability curves, calculated vertical soil displacement. Xiao et al.9, based on Verruijt solutions and integral methods, derived analytical solutions for soil response.

Regarding model experiments, Wei et al.10,11 investigated longitudinal deformation of surface and deep soil through indoor reduced-scale model tests. Zhang et al.12 established an excavation model test system to analyze the distribution and development of free-field soil displacement induced by rectangular tunnel construction.

In numerical analysis, Ma et al.13 used three-dimensional numerical simulation technology to explore the influence of advance pressure on surface settlement ahead of the excavation face. Chen et al.14, using finite element software, analyzed the influence of construction factors on strata deformation. Deng et al.15 conducted numerical simulations and sensitivity analyses on various construction factors. Tang et al.16 simulated the entire construction process of rectangular shield tunnels and analyzed the effects of advance pressure and grouting materials on strata deformation and surface settlement.

Influenced by the shield construction process, the shield tunnel construction will inevitably cause the loss of the ground layer, which will lead to uneven ground settlement. Scholars in various countries have conducted predictive studies on the ground settlement caused by circular shield tunnel boring construction, and the main methods are as follows: ① empirical method17,18; ② theoretical analysis method19,20; ③ random medium theory21,22; ④ the boundary element method23,24; ⑤ the finite element analysis method25,26; ⑥ model test method27,28. In summary, there are fewer studies on the effect of quasi-rectangular shield tunnel excavation on surface settlement. It is the first time in China to carry out excavation construction in the typical high permeability sand layer in Zhengzhou. Influenced by the characteristics of high permeability, abundant water, and high water pressure in the highly permeable sand layers, phenomena such as water and sand influx may occur during the excavation process, leading to significant strata settlement and subsequent ground collapse, damaging surface structures. Therefore, based on a section of the Zhengzhou Metro Line 8 as the project foundation, this study conducted onsite excavation experiments for quasi-rectangular shield tunnel construction in highly permeable sand layers in Zhengzhou. It analyzed the surface settlement patterns induced by quasi-rectangular shield tunnel construction and proposed corresponding control measures for surface settlement. The research findings can provide construction technical references and data support for similar projects.

Engineering background and geological conditions

Project overview

The actual engineering of a large cross-section rectangular shield tunnel for Zhengzhou Metro Line 8 is shown in Fig. 1. The project is located within the scope of Zhengzhou East Railway Station, with sensitive and complex geological conditions and surrounding environments. The cross-section rectangular shield tunnel segment needs to pass under North Street and South Street of East Station and traverse existing operational subway Line 5 tunnel and other important infrastructure. The construction process of the cross-section rectangular shield tunnel requires a high level of precision control.

Fig. 1
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Satellite image of quasi-rectangular shield tunnel section (Google Map; annotations made by author).

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Geological conditions

The segment of the quasi-rectangular shield tunnel is constructed using one 11.83 m × 7.27 m rectangular earth pressure balance shield tunneling machine. The tunnel section is 87.473 m long, with a maximum longitudinal gradient of -26‰, and the top cover soil is buried at a depth of 17.26 m to 18.17 m. The main geological formations traversed in the section are: layer ②41, consisting of fine sand, and layer ②51, consisting of silty sand. Groundwater mainly exists in the layers of fine sand and silt. Groundwater recharge mainly comes from precipitation infiltration, surface water infiltration, and lateral groundwater flow. There is no surface water within the segment of the rectangular shield tunnel. The stable groundwater level depth ranges from 8.9 m to 12.1 m (absolute elevation 76.59 m to 77.55 m). The segment’s plan axis starts with a gentle curve and ends with a straight line, while the longitudinal axis is a variable gradient segment (-26‰ to 2‰). The longitudinal cross-section of the geological formations in the rectangular shield tunnel section is shown in Fig. 2. The physical and mechanical parameters of each soil layer are listed in Table 1.

Fig. 2
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Longitudinal cross-section diagram of the quasi-rectangular shield tunnel section.

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Table 1 Physical and mechanical parameters of each stratum in the test ring section.
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Monitoring results and analysis

Monitoring plan

To explore the ground settlement pattern induced by the construction of a large-section quasi-rectangular shield tunnel in the Fushui sand layer in Zhengzhou, multiple ground settlement monitoring sections are arranged along the excavation direction of the shield tunnel. The monitoring points are distributed approximately 30 m on each side of the tunnel centerline.

The study selects three ground settlement monitoring sections above the excavation positions of the 40th, 45th, and 50th rings from the North Departure Shaft (I Foundation Pit) to the North Receiving Shaft as research objects, denoted as DBC40, DBC45, and DBC50 respectively. The layout of the monitoring sections is illustrated in Fig. 3. DBC40 and DBC45 are small monitoring sections, each with five measurement points positioned above and 3 m, 6 m to the left and right sides of the tunnel centerline. They are numbered from left to right as 1 to 5. The large monitoring section has 15 measurement points, positioned above and 3 m, 6 m, 11 m, 16.6 m, 19.7 m, 22.8 m, and 27.8 m to the left and right sides of the tunnel centerline, numbered from left to right as 1 to 15. The profile layout of the DBC50 monitoring section is shown in Fig. 4.

Fig. 3
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Layout of monitoring section measurement points. (a) Schematic diagram of monitoring section measurement point layout; (b) Photographs of on-site monitoring points; (c) Schematic diagram of monitoring point layout.

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Fig. 4
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Profile of monitoring section DBC50.

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Surface settlement

According to the law of the time-history curve of measured data, the spatial relationship between the shield machine and the monitoring section is divided into four stages (as shown in Fig. 5; Table 2), namely Stage I: Before the shield machine arrives (as shown in Fig. 5a), Stage II: Shield passing (as shown in Fig. 5b), Stage III: Shield tail exits 14.4 ~ 18 m (as shown in Fig. 5c), and Stage IV: Later settlement (as shown in Fig. 5d). In the text, the notation of “+” for settlement values indicates uplift, and “- ” indicates settlement.

Table 2 Typical construction stages for quasi-rectangular shield tunneling.
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Fig. 5
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Diagram illustrating construction stage division.

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Figures 6 and 7, and 8 respectively depict the time-history curves of surface settlement for monitoring sections DBC40, DBC45, and DBC50. From the figures, it can be observed that the overall trend of surface settlement is similar, showing a pattern of gradual settlement, rapid settlement, and stable settlement. The maximum cumulative settlement of the surface is located at monitoring points DBC40-3, DBC45-3, and DBC50-8, which are above the tunnel centerline. The maximum settlement values are − 41.58 mm, -39.55 mm, and − 44.84 mm respectively.

As shown in Figs. 6 and 7, and 8, during Stage I: Before the shield machine arrives, this stage is characterized by a period of gradual settlement, indicating initial settlement of the surface. The analysis of its cause reveals that the excavation of the shield machine leads to changes in pore water pressure ahead, resulting in consolidation settlement of the soil. The phenomenon of increased surface settlement 6 ~ 7.2 m ahead of the excavation face is caused by disturbance of the soil ahead due to the cutterhead excavation while the face is in a slightly under-pressure state. The variations in surface settlement at monitoring points DBC40-3, DBC45-3, and DBC50-8 during this stage are 4.61 mm, 3.67 mm, and 3.99 mm respectively, accounting for 11.09%, 9.28%, and 8.90% of the final cumulative surface settlement.

Fig. 6
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The time-history curve of ground settlement at monitoring section DBC40.

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Fig. 7
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The time-history curve of ground settlement at monitoring section DBC45.

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Fig. 8
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The time-history curve of ground settlement at monitoring section DBC50.

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Stage II: When the shield passes through, the ground enters a rapid settlement period. This is because there is a hinge gap between the front shield and the middle shield, the diameter of the cutter head is larger than the outer diameter of the shield, resulting in over-excavation clearance, and factors such as shear and compression of the surrounding soil under the friction of the shield cause rapid increase in ground settlement. At this stage, the ground settlement changes at monitoring points DBC40-3, DBC45-3, and DBC50-8 are 19.25 mm, 12.05 mm, and 20.69 mm respectively, accounting for 43.30%, 30.47%, and 46.14% of the final cumulative settlement.

Stage III: When the shield tail exits at 14.4 to 18 m, the ground also enters a rapid settlement period. This is because the diameter of the shield machine is larger than the outer diameter of the lining pipe, causing the construction gap to not be filled with grout in a timely manner, and the low early strength of the grout causes collapse of the surrounding soil around the shield. At this stage, the ground settlement changes at monitoring points DBC40-3, DBC45-3, and DBC50-8 are 11.75 mm, 17.64 mm, and 14.48 mm respectively, accounting for 28.25%, 44.60%, and 32.29% of the final cumulative settlement.

Stage IV: In the later settlement stage, the ground enters a stable settlement period. This is because the disturbance of the shield advancement on the surrounding soil dissipates the pore water pressure generated, causing consolidation settlement and creep settlement of the soil layer, and the ground settlement gradually tends to be stable. At this stage, the ground settlement changes at monitoring points DBC40-3, DBC45-3, and DBC50-8 are 5.97 mm, 6.19 mm, and 5.68 mm respectively, accounting for 14.36%, 15.65%, and 12.67% of the final cumulative settlement.

Lateral ground settlement trough

Figure 9 shows the cumulative surface deformation at various stages of the DBC50 monitoring section, with the shaded area representing the surface range corresponding to the shield outline. Before the shield reached the monitoring section, initial settlement occurred within 6 m, with minimal differences in settlement at each measurement point. As the shield advanced, the depth of the surface settlement trough increased while its width remained relatively constant. The influence range of surface settlement caused by shield excavation was within 20 m on either side of the tunnel centerline (approximately twice the tunnel width). The settlement values on the right side of the tunnel centerline were slightly smaller than those on the left side, with noticeable bulging of the soil above on the right side, preliminarily attributed to the deviation of the shield posture.

Fig. 9
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DBC50 monitoring section surface lateral settlement trough at various stages.

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Figure 10a–c respectively fit the final settlement data of monitoring sections DBC40, DBC45, and DBC50 using the Peck formula. The linear correlation coefficients ( R2 ) for the fitted curve of monitoring section DBC50 are 0.983, with a settlement trough width parameter (K = 0.383) and a ground loss rate (Vl = 1.366%). This indicates that using the Peck formula to predict surface settlements caused by large-section quasi-rectangular shield tunnel construction in the Zhengzhou Fushui sand layer is feasible.

Fig. 10
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The final settlement of each monitoring section and the fitted curve.

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Settlement control measures

According to the surface settlement law during the construction of large-section rectangular shield tunnels crossing through rich water and sand layers as described above, the following surface settlement control measures are proposed:

During over-excavation in the rich water and sand layers, due to the small cohesive force of the soil, the front soil may undergo compression and shear failure, which may lead to pipe jacking and cause greater surface settlement, especially under high water pressure. During under-excavation, there may be an increase in surface settlement within 6 to 7.2 m ahead of the excavation face, as mentioned earlier. Therefore, to control the surface settlement in front of the cutterhead, it is necessary to maintain the balance of soil pressure by controlling the excavation rate reasonably.

To reduce the surface settlement during the passage of the shield tunnel, low-friction slurry can be injected into the surrounding soil layers to reduce the effect of frictional resistance, thereby reducing the shear slip effect on the surrounding soil.

To reduce the surface settlement after the shield tail breakout, the synchronous grouting volume can be appropriately increased to fill the shield tail construction gap adequately, and the grouting pressure can be adjusted appropriately to balance the relationship between filling gaps and grouting-induced shear disturbances, and to match the early strength of the synchronous slurry with the excavation speed.

When the shield machine rotates around the longitudinal axis, it will produce obvious squeezing effect on one side of the soil, causing bulging of the soil on that side. This creates voids in the strata above the shell on the other side, thereby increasing the settlement of the soil on that side. Therefore, to reduce surface settlement, attention should be paid to controlling the attitude of the shield machine.

Conclusions

This paper takes a section of the Zhengzhou Rail Transit Line 8 as the engineering background and conducts on-site excavation tests of a certain type of quasi-rectangular shield tunnel. It investigates the surface settlement law during the construction of large-section quasi-rectangular shield tunnels in rich water and sand layers. The following main conclusions are drawn:

(1) Considering the spatial positioning of shield and monitoring sections, the construction of large-section quasi-rectangular shield tunnels in Zhengzhou’s rich water and sand layers shows distinct settlement stages: slow settlement (Stage I before shield arrival), rapid settlement (Stage II during shield passage, Stage III at shield tail breakout between 14.4 and 18 m), and stable settlement (Stage IV post-settlement). To manage these conditions effectively, it is recommended to balance cutterhead frontal pressure with soil pressure by adjusting excavation rates. Implementing low-friction slurry between the shield shell and sand layer can mitigate soil friction and shear slip. Enhancing synchronous grouting at the shield tail and promptly filling construction gaps, while matching grouting slurry strength with construction speed, and controlling shield machine attitude, are crucial for controlling surface settlement.

(2) The Peck formula was used to fit the lateral surface settlement trough data of the DBC50 monitoring section, resulting in a linear correlation coefficient (R2) of 0.983. The width parameter of the settlement trough (K) was calculated as 0.383, and the stratum loss rate (Vl) was determined to be 1.366%. This indicates that using the Peck formula to predict surface settlement troughs caused by the construction of large-section quasi-rectangular shield tunnels in the rich water and sand layers of Zhengzhou is feasible.