1. Introduction
Shield excavation is a widely used technique in tunneling, which involves the use of a shield or a tunnel boring machine (TBM) to excavate the soil and create the tunnel [1]. In shield excavation, the TBM is equipped with a shield that supports the tunnel walls as the soil is excavated, providing temporary stability until the final support system is installed. It has been an increasingly popular technique for constructing tunnels in urban areas due to its minimal disruption to surface infrastructure and buildings. However, the application of conventional large curvature shield tunnels in densely populated cities has been limited by large tunnel diameters and high construction costs [2]. In recent years, the small curvature shield tunnel has emerged as a promising solution to this problem as it requires a smaller excavation area and reduces the impact on the surrounding environment. With its unique advantages, the small curvature shield tunnel has become an essential tool for urban tunnel construction, enabling the development of subway systems, sewage pipelines, and other urban infrastructure projects with minimum surface disruption and high efficiency [3].
Face stability refers to the ability of the tunnel’s walls to maintain their structural integrity and prevent collapse during the excavation process [4]. The stability of the shield face is essential for the safe and efficient operation of the TBM, whilst the stability of the excavation face is a critical issue during the construction of tunnels and other underground structures [5]. Face stability is particularly important as it has a direct impact on the safety of the workers and the surrounding environment [6]. Therefore, it is important to analyze and understand the factors that affect face stability during shield excavation. Despite the increasing use of shield tunneling in urban areas, where small curvature shield tunnels are frequently employed, research on this type of tunnel is limited. Much of the existing literature on shield tunneling focuses on straight shield tunnels. Given that the uncertainties of small curvature tunnel excavation remain, it is critical to understand face stability of small curvature shield tunnels to optimize their performance and ensure the safety and efficiency of underground construction projects. Therefore, further research is necessary to fill this gap and support the continued development of shield tunneling in urban areas.
In this study, the effects of different excavation parameters on the face stability of small curvature tunnels were investigated. The scope of works focused on the mechanisms of different excavation parameters such as jacking force, cutting speed, and soil conditioning that can affect face stability in small curvature shield tunnels. The significance of this research lies in its ability to provide valuable insights into optimizing the performance of small curvature shield tunnels, improving the safety and efficiency of underground construction projects, and supporting the continuous development of shield tunneling in urban areas. The methodology used in the study involved numerical simulations to analyze the impact of the excavation parameters on face stability, providing a comprehensive and specific approach to studying this critical issue.
2. Literature Review
The factors that affect face stability during shield excavation are complex and depend on various geological, environmental, and construction-related factors. These factors include the type of soil or rock being excavated, the groundwater level and pressure, the depth and angle of the excavation, the size and type of the TBM, and the design and quality of the support system. Li et al. [7] examined the face stability of large slurry shield-driven tunnels, considering non-uniform slurry pressure and different gradients of support pressure. Zou et al. [8] discussed the face stability of a tunnel excavated in saturated non-homogeneous soils. Huang et al. [9] provided a comprehensive overview of the mechanism where shield tunnels can be affected by high fluid pressures in confined aquifers. Their study presented a method to compute the limit of face pressures in layered ground with confined aquifers. Do et al. [10] investigated the effect of four main parameters (face pressure, grouting pressure at the shield tail, length and weight of the shield, and conicity of the shield) on tunnel linings and surface settlements. In conclusion, studying the factors that affect the stability of shield tunnels is essential to improve our understanding of this complex process and to develop effective strategies to ensure the safety and efficiency of tunnel construction projects.
The stability of the excavation face during shield tunnel construction is a critical aspect that requires close monitoring and analysis. To ensure the safety and efficiency of the construction process, various methods have been developed to analyze the stability of the excavation face. These methods can be broadly categorized into three groups: theoretical methods, experimental methods, and numerical simulations [7,11,12,13]. The limit equilibrium method (LEM) is a widely used theoretical approach to analyze tunnel face stability, which has been extensively studied by innovative researchers. The wedge model was utilized by Anagnostou and Kovári [14,15] to determine the limit of support face pressure in a homogeneous stratum. The wedge model has maintained its popularity to this day, with numerous researchers expanding and applying it in subsequent studies. Chen et al. [16] presented a novel three-dimensional (3D) wedge-prism model based on previous works, offering an enhanced approach to analyze the stability of tunnel faces. Liu et al. [17] introduced an upgraded model to analyze face stability, utilizing a dual-failure mechanism approach based on the limit equilibrium method. Another theoretical method is the limit analysis, which includes the kinematic approach and an upper bound analysis [18]. Leca and Mormieux [19] established a lower and upper limit analysis and then derived the closed expressions for the evaluation of the stability of an excavated soil surface. Using a three-dimensional multi-block failure mechanism, Mollon et al. [20] conducted a kinematic analysis to investigate the face limit support pressure in a circular tunnel.
In recent years, the development of experimental methods for face stability analyses has enabled researchers to gain a better understanding of the complex behavior of tunnel face stability. Chambon and Corté [4] filled the gap of limited experimental data for a model in cohesionless soils using a centrifugal model test. Kirsch [21] performed two series of small-scale model experiments to further assess the quality of the proposed models for a face stability analysis. Lü et al. [22] conducted nine physical model tests to understand the failure mechanism and limit support pressure of a shield tunnel face under seepage conditions.
Numerical simulations have emerged as a critical tool to analyze the stability of tunnel faces as they allow for more realistic and detailed modeling of complex conditions. With advances in computing power and software capabilities, numerical simulations have become increasingly popular in recent years and are now widely used to investigate various aspects of tunnel face stability [23]. Li et al. [7] carried out more comprehensive three-dimensional numerical modeling to compare critical slurry pressures with on-site data. Yin et al. [24] used the finite difference method (FDM) to investigate the effect of permeability anisotropy on the tunnel face support pressure. Mallı et al. [25] illustrated a numerical simulation model for the Bayındır lead–zinc mine, which evaluated the stresses that occurred in the pillars at different stages of excavation. The results of the model demonstrated the effectiveness of the numerical simulation to analyze the stability. Using numerical simulations, Sazid et al. [26,27] examined the influence of the rock class on the blasting performance and focused on the stability of shallow-depth tunnels in weak rock masses. Both studies highlighted the crucial role of rock properties in determining the safety and efficiency of tunnel construction and excavation.
Although the LEM and experimental methods are commonly used to evaluate face stability, there are certain limitations associated with these two methods. The LEM, despite providing an analytical solution for limit support pressure, heavily relies on the accuracy of the adopted failure mode [28]. Its reliability may be compromised if the preliminary assumption of the failure mode cannot accurately represent the actual conditions during tunnel excavations. The experimental methods, which are valuable to understand the physical behavior of tunnel face stability, are constrained by the scalability of the model, the costs, and the difficulty in replicating in situ conditions in a controlled laboratory environment [22,29]. In contrast, numerical methods allow for a more comprehensive and realistic representation of complex geological conditions, offering greater flexibility in simulating different excavation scenarios and parameter variations. As a result, numerical methods have been widely accepted to solve geotechnical problems.
Despite the critical role of face stability in tunneling, the existing literature on shield tunneling primarily focuses on straight shield tunnels; the effect of different excavation parameters on the face stability of small curvature shield tunnels is still unclear. Without a clear understanding of the factors that affect face stability during small curvature shield excavation, there is a risk of tunnel collapse, which can lead to significant safety risks, construction delays, and increased project costs. Filling this research gap will not only improve our understanding of the face stability of small curvature shield tunnels but also contribute to the continued development of shield tunneling in urban areas.
3. Numerical Modeling
3.1. Project Overview
The Tianjin City subway is a significant engineering project that involves the construction of a new subway connecting line. The project aims to link Line 7 and Line 8, both of which will converge at Liulitai Station for efficient metro train dispatching (Figure 1). The subway line will construct a tunnel with a small radius of 180 m, which is the first of its type in China. The small curvature radius refers to the distance from the center of the circle, of which the tunnel forms a part, to the tunnel’s centerline. Generally, the radius of this type of tunnel is around 300 m to 500 m [3,30,31]. A smaller radius represents a tighter curvature, which can present challenges in tunneling and face stability. The tunnel’s construction poses a significant challenge due to its unique design and the complexity of the excavation process. Additionally, the project’s location is in close proximity to numerous infrastructures and residential areas, further complicating the construction process.
3.2. Soil Profile and Position of the Tunnel
The engineering survey report for the project identified that the foundation soil within the exploration scope can be divided into 10 different categories (see Table 1 for a simplified soil profile and material parameters). The top layer of the soil is a man-made plain fill material, which has been deposited by human activity. The main soil layer is silty clay, which is a type of cohesive soil that is composed of fine-grained particles with a high water content. The groundwater level within the site has been determined to be at an elevation of 1.47 m from the ground surface. The depth of the overburden soil above the tunnel is approximately 21 m. The project involves the construction of a tunnel with an outer diameter of 6.6 m and an inner diameter of 5.9 m. In order to facilitate the numerical modeling and analysis of the soil and tunnel behavior, the soil profile has been simplified into three layers: plain fill, clay, and silty clay. Figure 2 shows the soil profile and position of the tunnel. This simplification allows for the accurate and efficient calculation of the stresses and deformations that will occur during the construction and operation of the tunnel.
3.3. Model Description
The simulation model utilized a shield machine that was 9.0 m in length, with a conical shape that tapered from the face to the tail. The first 7.5 m of the shield experienced a gradual decline in diameter, whilst the final 1.5 m maintained a constant diameter. The volume loss alongside the tunnel lining during excavation was modeled where the surface contracted using Plaxis 3D to simulate this effect. Specifically, a 0.5% reduction in volume was assumed from the face to the tail. To account for this axial contraction, an increment of −0.0667% was applied. To capture the construction process, the excavation was divided into separate construction stages, with each tunnel ring being 1.5 m in length. This meant that the shield machine advanced 1.5 m within each stage. This helped to accurately simulate the behavior of the shield machine and its impact on the surrounding soil and ground surface. The schematic of the shape of shield and advance phase can be seen in Figure 3.
In order to accurately simulate the conditions of the tunnel excavation site, the following pressure types were taken into consideration. The support pressure, for instance, is the lateral earth pressure that acts on the excavation face of the tunnel [32]. This pressure increased in intensity with depth, gradually increasing at a rate of 14 kPa as the excavation continued. Meanwhile, the grouting pressure applied to the surrounding rock was also taken into account and it followed a similar trend of increasing with depth, with a value of 100 kPa at the top of the tunnel and an increase of 19 kPa per unit depth [33]. The final pressure considered in the model was the jack thrust, which was a uniform load applied to the ring area of the tunnel segment in the opposite direction of the excavation [31]. For a more detailed illustration of the application of the jack thrust, please refer to Figure 4. By incorporating these varied and dynamic pressure types into the model, a highly accurate and realistic simulation of the tunnel excavation site was created.
In the numerical model, the tunnel excavation area was represented using Plaxis 3D with a finite element to analyze the effect of different excavation parameters on face stability. The model domain was extended (dimensions of the model domain) to ensure the minimal influence of the boundaries on the results. The boundary conditions applied included a free surface, normal constraints applied at the lateral boundaries, and zero displacements at the bottom. Figure 5 provides a schematic representation of the numerical model and its boundary conditions for a better visualization and understanding.
3.4. Simulation Cases
Table 2 presents the simulation cases in our study. Case I and Case II represent the two tunnel configurations analyzed in the study, which were a straight tunnel and a small curvature tunnel, respectively.
To investigate the impact of supporting pressure on ground surface settlement, three different levels of supporting pressure for the straight tunnel (Case I) and small curvature tunnel (Case II) were simulated using Plaxis 3D. The simulations were represented in subcases, denoted as Case I-I to Case I-III and Case II-I to Case II-III, respectively. The supporting pressure was varied in steps of 50 kPa, with a range from 50 kPa to 150 kPa.
4. Results and Discussion
In this section, the results of our study are presented. The numerical analyses results were analyzed with respect to their significance to address the research questions of this study. First, the ground surface settlement induced by three different types of supporting pressures was investigated, specifically with respect to the effect of gradients of 50 kPa. A detailed analysis of the findings was then provided, with a particular focus on the impact of an uneven distribution of the jacking load. Finally, the results were compared with those of a control group, enabling us to quantify the specific effects of constructing a small curvature tunnel.
4.1. Stress Development
The stress distributions in the soil around the straight tunnel (Case I-I to Case I-III) are illustrated in Figure 6. The results in Figure 6 provide visual representations of the stress patterns in this scenario. The changes in the stress distribution patterns and stress magnitudes were helpful to better understand the impact of supporting pressures on the tunnel stability.
Figure 6 indicates that the stress concentrations near the tunnel face and the surrounding soil increased with an increase in supporting pressure. It suggests that higher supporting pressures led to a greater concentration of stress in localized areas, which could potentially increase the risk of soil failure.
The stress distributions in the soil around the small curvature tunnel are illustrated in Figure 7. The results in Figure 7 show that the stress distributions in the soil around the small curvature tunnel were different from those around the straight tunnel, as shown in Figure 6.
The stress distributions in the soil around the small curvature tunnel, as shown in Figure 7, had similar trends to those around the straight tunnel, as shown in Figure 6. Both results indicated that the stress concentration near the tunnel face increased with an increase in supporting pressure. However, because of the turning angle, the stress concentrations in the small curvature tunnel were more significant compared to the straight tunnel. It indicated that the curvature of the tunnel had a notable influence on stress development during excavation. The results in Figure 6 and Figure 7 suggested that careful consideration should be given to supporting pressure and the curvature of the tunnel in order to ensure adequate stability and minimize potential issues related to stress concentrations.
4.2. Ground Surface Settlement
Figure 8 shows the ground surface settlement of the simulations. The ground surface settlement induced by the tunnel excavation was simulated under three different supporting pressures (50 kPa, 100 kPa, and 150 kPa) for both the straight and curved tunnel configurations. The results showed that an increase in supporting pressure led to a decrease in ground surface settlement, regardless of the tunnel configuration.
For the straight tunnel, the ground surface settlement decreased from 16.5 mm at 50 kPa to 4.5 mm at 150 kPa. Similarly, for the curved tunnel, the ground surface settlement decreased from 18.0 mm at 50 kPa to 10.0 mm at 150 kPa. These results indicated that the ground surface settlement was strongly influenced by the supporting pressure, with a higher pressure resulting in a smaller settlement.
The results of this study suggested that supporting pressure played a critical role in controlling surface stability induced by the tunnel excavation. The finding that the ground surface settlement decreased with an increase in supporting pressure was consistent with the basic principles of soil mechanics, which suggest that an increase in pressure leads to a reduction in soil deformation.
4.3. The Impact of Small Curvature Tunnels
To investigate the impact of tunnel curvature on ground surface settlement, we compared the settlement profiles of small curvature and straight tunnels under the same supporting pressures (50 kPa, 100 kPa, and 150 kPa). Figure 9 shows the ground surface settlement profile for both tunnel configurations. We found that, under the same supporting pressure, the maximum ground settlement induced by the small curvature tunnel was larger than that of the straight tunnel.
The results of the study suggested that tunnel curvature could have a significant impact on ground surface settlement. The finding that the maximum settlement for the small curvature tunnel was larger than the straight tunnel was consistent with previous studies on the topic. This was due to the fact that an uneven distribution jacking load generated more deformation and the inner overcut area resulted in a larger ground surface settlement.
It is important to note that the effect of tunnel curvature on ground surface settlement is complex and depends on several factors such as the radius of the curvature and the depth of the tunnel. Nevertheless, our results provide valuable insights into the behavior of soil during the construction of small curvature tunnels.
Figure 10 illustrates the trend of maximum ground surface settlement in response to an increase in supporting pressure for both the straight and small curvature tunnel configurations. The results in Figure 10 reveal a clear pattern of decreasing maximum ground surface settlement as the supporting pressure increased for both tunnel configurations. The trend suggested that higher supporting pressures effectively mitigated ground surface settlement by providing better stress redistribution in the soil, thereby enhancing the overall stability of the excavation.
5. Conclusions
In conclusion, this study provides valuable insights into the behavior of soil during tunnel construction and the factors that influence ground surface settlement. Through the use of numerical simulations, the impact of different supporting pressures and tunnel configurations on ground surface settlement was analyzed.
The results of the study indicated that an increase in supporting pressure could effectively reduce ground surface settlement induced by tunnel excavations, regardless of the tunnel configuration. It was also observed that small curvature tunnels could cause larger ground surface settlement than straight tunnels under the same supporting pressure. Additionally, our findings on stress distribution revealed that higher supporting pressures led to greater stress concentrations near the tunnel face and surrounding soil, which could potentially increase the risk of soil failure.
The findings of this study have practical implications for the design and construction of tunnels as they can be used to optimize the design and minimize the environmental impact of small curvature tunnels. Moreover, the results of this study can serve as a reference for future research in the field of tunnel engineering.
However, this study has a few limitations that should be acknowledged. First, factors such as heterogeneity in soil properties, variable groundwater conditions, and the presence of existing underground infrastructures can significantly influence tunnel stability and ground surface settlement. Second, this study focused on the effects of supporting pressure and tunnel curvature, but other factors such as TBM type, cutterhead design, and grouting techniques can also impact the face stability of small curvature shield tunnels. Future research should consider these factors and potentially integrate field data from actual tunnel construction projects to validate and refine the findings of this study.
Conceptualization, Y.N.; methodology, T.R.; software, K.X.; validation, Q.Z. (Qiang Zhou), X.J. and J.S.; formal analysis, X.J.; investigation, J.S.; resources, Y.N.; data curation, T.R.; writing—original draft preparation, K.X.; writing—review and editing, J.T., Q.Z. (Qian Zhai) and A.S.; visualization, K.X.; supervision, Q.Z. (Qian Zhai); project administration, Y.N., T.R., Q.Z. (Qiang Zhou), X.J. and J.S.; funding acquisition, Y.N., T.R., Q.Z. (Qiang Zhou), X.J. and J.S. All authors have read and agreed to the published version of the manuscript.
Not applicable.
Not applicable.
The data presented in this study are available within the article.
The authors declare no conflict of interest.
Footnotes
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Enlarge this image.Figure 5. Schematic representation of the numerical model and its boundary condition.
Enlarge this image.Figure 7. Stress development of small curvature tunnel from Case II-I to Case II-III.
Enlarge this image.Figure 8. Ground surface settlement: (a) straight tunnel; (b) small curvature tunnel.
Enlarge this image.Figure 9. Comparison between straight tunnel and small curvature tunnel: (a) 50 kPa supporting pressure applied; (b) 100 kPa supporting pressure applied; (c) 150 kPa supporting pressure applied.
Enlarge this image.Figure 9. Comparison between straight tunnel and small curvature tunnel: (a) 50 kPa supporting pressure applied; (b) 100 kPa supporting pressure applied; (c) 150 kPa supporting pressure applied.
Simplified soil profile and material parameters.
| Soil | Thickness (m) | Unit Weight (kN/m3) | Young’s Modulus (kN/m2) | Poisson’s |
Cohesion |
Friction Angle |
|---|---|---|---|---|---|---|
| Plain fill | 3.5 | 19.0 | 3.81 | 0.35 | 8 | 13 |
| Clay | 16.9 | 19.5 | 8.60 | 0.35 | 46.5 | 14 |
| Silty clay | 5.1 | 20.4 | 7.30 | 0.30 | 24.4 | 26 |
| Lining | \ | 27.0 | 3.1 × 107 | 0.10 | \ | \ |
| Shield shell | 0.17 | 247 | 200 × 106 | 0 | \ | \ |
Simulation cases.
| Condition | Supporting Pressures | |
|---|---|---|
| Case I | Case I-I | 50 kPa |
| Case I-II | 100 kPa | |
| Case I-III | 150 kPa | |
| Case II | Case II-I | 50 kPa |
| Case II-II | 100 kPa | |
| Case II-III | 150 kPa | |
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Details
; Satyanaga, Alfrendo 4
1 China Construction Eighth Bureau Rail Transit Construction Co., Ltd., Nanjing 210046, China;
2 China Construction Infrastructure Co., Ltd., Beijing 100029, China;
3 Bridge Engineering Research Center, Southeast University, Nanjing 210096, China;
4 Department of Civil and Environmental Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Kabanbay Batyr Ave., 53, Nur-Sultan 010000, Kazakhstan;