#### Abstract

This paper presents the ground deformation induced by the large slurry shield tunnelling with a diameter of about 12 m in urban areas, which may challenge the safety of the existing nearby constructions and infrastructures. In this study, the ground deformation is analyzed by a three-dimensional finite difference model, involving the simulation of tunnelling advance, grouting, and grouting hardening. The transverse settlement, longitudinal settlement, and horizontal displacement of the ground are analyzed by comparing the simulation results with the field measurements in the Rapid Transit Line Project from Beijing Railway station to West Beijing Railway station in China. The numerical model proposed in this paper could well predict the ground deformation induced by large slurry shield tunnelling. The results show that the main transverse settlement occurs within the zone about 1.5 times of the excavation diameter, and the settlement during the passage of the shield and the tail void plays a most important role in the excavation process.

#### 1. Introduction

At present, lots of tunnels are constructed or being planned to relieve the traffic pressure in metropolis. The application of the slurry shield method to urban tunnel construction in sandy cobble ground is more and more popular for its comfortable work environment [1]. Ground deformation is inevitably induced by the excavation of the slurry shield tunnel in urban areas, which is negative to the existing structures and pipelines. As a result, a great deal of attention has been attracted all over the world [2, 3]. Several approaches, such as the empirical method, model test, numerical simulation, and field monitoring, have been used to estimate the ground deformation during the shield tunnelling.

The empirical method is based on the regression analysis of the recorded ground surface settlement and then used to predict the ground surface settlement [4, 5]. Based on the ground surface settlement measured in the field of a mine roadway, the empirical method was first put forward by Martos [6], and the error function was suggested to present the surface settlement through profile approximately. A description of the green-field settlement was proposed by collecting field observations from many case histories over the years by Peck [7], and O’Reilly and New [8, 9] summarized plenty of empirical equations and pointed out that Peck’s empirical method is unable to provide a reasonable prediction for soils other than normally consolidated clays, as the empirical model is based on limited scope of the database. With the assumption that the ground loss is uniformly distributed along the longitudinal direction, the settlement profile can be expressed by Gaussian distribution. Attewell and Woodman [10] suggested that the longitudinal settlement at any longitudinal coordinate can be described by cumulative Gaussian probability.

Model test is also a common way to investigate the evolution law of the ground deformation, including the centrifuge model test and physical model test [11]. Based on a series of plane-strain centrifuge model tests on the single tunnels in moderately stiff clay, Grant and Taylor [12] found that the high-quality data can be used to improve the predictions of both surface and subsurface movements in the plane transverse to the tunnel. And a procedure for predicting horizontal movements as a function of the vertical settlement profile was also suggested. Kuwahara et al. [13] investigated the mechanism of ground settlement in the process of tail void by the centrifuge model test and found that the ground deformation mechanism in the field had a close similarity with the results observed in the physical models. Atkinson and Potts [14] investigated the influence of the depth of burial and crown settlement on the surface subsidence above shallow tunnels in soft ground. Compared with the observations of settlements above some existed tunnels, the model’s behaviour matches with the field records well, and an empirical relationship is given between the buried depth, the trough width, the crown, and surface settlements for tunnels in sands and in clays.

With the development of the computer technique and numerical software, the numerical simulation method has become more and more effective to solve the problem in tunnel construction [15, 16]. Finno and Clough [17] simulated the entire EPB tunnelling process in five stages by the finite element program and obtained the lateral displacement. Do et al. [18] proposed a finite element method to study the failure mechanisms of deep excavations in soft clay. Besides, Melis et al. [19] assessed the accuracy of each analytical or empirical predictive method with reference to the soil movements using a numerical model of shield tunnel excavation.

Field monitoring is also widely used in the tunnel construction [1]. Chen et al. [20] mainly focused on the field measurements of parallel tunnels using EPB shields in silty soils. This research revealed the changes of pore pressure in the soils and ground deformation during EPB shield tunnelling. Generally, field measurement can be used in combination with other methods. Sugiyama et al. [21] compared the field measurement of ground deformation due to slurry shield tunnelling with the model test and numerical simulation, and two kinds of practical design charts were proposed to appropriately predict the transverse surface settlement troughs in the clays or sands and gravels. Ocak [22] proposed a new empirical formula for estimating the surface transverse settlement trough of twin tunnels. Moreover, the comparison with field measurement validated the reasonability of an empirical formula.

However, it should be pointed out that the studies above mainly focused on the influences of small diameter shield excavation on the ground deformation. The research on the large-diameter shield excavation in sands and gravels is still limited up to now. In this study, a three-dimensional numerical model is carried out to investigate the ground deformation due to large-diameter slurry shield tunnelling in sandy cobble stratum. The reliability of the numerical model is validated by comparing with the field measurement in the Rapid Transit Line Project from Beijing Railway Station to West Beijing Railway Station in Beijing, China (hereinafter referred to as RTLP).

#### 2. Project Description and Monitoring

In order to alleviate traffic congestion and improve the ground surface environment of Beijing, the capital city in China with a population of around 30,000,000, the RTLP was started in 2005, which begins at Beijing West Railway Station in the west and ends at Beijing Railway Station in the east as shown in Figure 1. The total length of the RTLP is 9,151 m. The tunnel takes up about 7,230 m in the whole project, with a buried depth varying from 16 to 22 m. 5,227 m of the tunnel is constructed by the slurry shield, while other parts are built by the open-cut method and mining method. It should be pointed out that there are several historical buildings with traditional Chinese style above the tunnel including Jianlou and Zhengyangmen, which are particularly sensitive to the subsidence induced by excavation. Considering the historical, cultural, and communal value of these buildings, the evaluation of the ground surface settlement is the key ingredient in the design stage and during the whole construction process. Thus, a monitoring system was set along the tunnel to investigate the effects of excavation on the ground deformation. The monitoring portion considered in this study is the first 509 m of the shield tunnel which begins at the north of Tianningsi Bridge.

In this project, results of extensive in situ and laboratory tests provided a description of the different geological formations. A typical geological profile of the shield tunnel is shown in Figure 2. The profile reveals that the monitoring portion of the shield tunnel is mainly located in gravel environment. Figure 3 shows the typical in situ soil of this project. Figure 4 shows the distribution of the grain size obtained by the indoor screening test. The results indicate that the maximum grain diameter is about 300 mm. The elliptical gravel with strong compression capacity accounts for 12%. It can also be found that about 1/3 of the sands are in the size from 0.25 mm to 0.5 mm. According to the available documents about the water table in the excavation area, the influence of the underground water level can be negligible.

The slurry shield used in this project with a total length of about 11.52 m is characterized by an outer diameter of 11.97 m at the face and 11.95 m at the tail. However, in some special circumstances, the maximum excavation diameter at the face can reach up to 12.04 m.

The tunnel lining is fabricated by concrete with the maximum compressive strength of 50 MPa based on the experimental tests on the cubic specimens with the dimensions of 150 mm × 150 mm × 150 mm. The tunnel lining is set in place inside the shield tail to support the surrounding rock as the machine moves forward. The outer and inner diameters of the lining ring are equal to 11.6 m and 10.5 m, respectively. The thickness of the tunnel lining is 550 mm. The width of each segment is 1.8 m. Stagger-jointed segmental linings are applied in this tunnel. As shown in Figure 5, each lining ring is composed of 9 segments.

In order to validate the prediction results of numerical simulation, a monitoring system was set in the monitoring section, as shown in Figure 6. The monitoring system is comprised of a total of 13 monitoring points on the ground surface, and the monitoring zone ranges to 41 m from the tunnel center. 2 bore inclinometers are set about 2 m away from the tunnel. The buried depth of the tunnel crown at the monitoring section is about 17 m.

#### 3. Numerical Model

The numerical test was carried out based on a three-dimensional explicit finite difference program, FLAC^{3D}. A three-dimensional model with small-strain formulation was applied to simulate the performance of the ground surrounded by a mechanized tunnelling. The tunnel construction process is modelled by a step-by-step approach. Each excavation step corresponds to an advancement of the tunnel face of 1.8 m, which is equal to the width of a lining ring. In this numerical model, the tunnelling process consists of three main phases: (1) excavating the ground at the tunnel face and applying a face pressure to ensure the tunnel face stability simultaneously; (2) installing the tunnel lining, applying the jacking force, and injecting the grout behind the segments to fill the voids created at the shield tail; and (3) as the slurry shield machine continues to advance, the grout becomes stabilized gradually.

About the three main phases referred above, some key points are required to be clarified. The face pressure is supposed to be in trapezoidal distribution on the excavation face by taking into account the slurry density. In order to simplify the simulation processes, the 9 segmental joints are ignored and the lining is installed as a ring. The ring joint is simulated by using double connections. The jacking force is assumed to be in linear distribution which is set on each segment with a total value of about 40,000 kN. A simplified geometry is assumed, with the original cone-shaped shield replaced by a cylindrical shape. Lambrughi et al. [23] simulated the grout hardening by the law, in which the Young’s modulus increases with time, as follows:where is the Young’s modulus of grout at time *t*, is the Young’s modulus of grout corresponding to complete hardening, and *t* is the time interval from the grout injection. An initial value (*E*_{initial}, for *t* = 0) must also be estimated for Young’s modulus. Lambrughi et al. [23] assumed that the grout is completely hardened beyond 12 h. In this project, the excavation speed is about 1.8 m/d. Considering the actual construction condition, the complete hardening of grout is 24 h. As a result, two different Young’s modules are adopted: and represent the Young’s modules of fresh grout and hardened grout, respectively. The parameters for the modelling of grout mechanical behaviour are summarized in Table 1. The detailed layout of the proposed slurry shield model is shown in Figure 7.

In this project, the actual values of the pressure applied at the cutterhead and the grouting pressure are about 0.18 MPa and 0.3 MPa at the monitoring section. The same values are applied to the numerical model. In the numerical model, a trapezoid pressure is applied at the cutterhead with a consideration of the slurry’s density of about 1.05 g/cm^{3}, and the pressure value at the center of the cutterhead is 0.18 MPa.

The soil behaviour was described using an elastic-plastic constitutive model based on the Mohr–Coulomb criterion. According to the extensive in situ and laboratory tests, the project data and average geotechnical characteristics of different layers are summarized in Table 2. These parameters are also adopted in the numerical analysis.

In order to balance the boundary effect and the computational efficiency, the model was built with dimensions of 99 m (length) × 100 m (width) × 60 m (depth). The bottom boundary was fixed in the *x*, *y*, and *z* directions, and the four vertical boundaries were fixed in the *x*- and *y*-directions. The typical cross section of the tunnel is illustrated in Figure 8. The perspective view of the numerical model, which is composed of around 141,960 grid points and 134,200 zones, is presented in Figure 9. The displacements are set to be zero in three directions before the excavation.

**(a)**

**(b)**

#### 4. Definitions of Ground Movements

##### 4.1. Transverse Settlement

Construction of a tunnel inevitably results in the ground movements with a ground surface settlement trough above and ahead of the tunnel. Field observations [7–9] collected from a considerable number of case histories have demonstrated that the ground surface transverse settlement trough can be described by a Gaussian distribution as follows:where is the settlement, is the maximum settlement on the tunnel centerline, *x* is the horizontal distance from the centerline, *i* is the horizontal distance from the tunnel centerline to the point of inflection on the settlement trough, is the ground loss, and *R* is the radius of the tunnel.

Based on a survey of the tunnelling monitoring data in London, O’Reilly and New [8] showed that the point of inflection *i* as shown in Figure 10 is an approximately linear function of the depth of the tunnel centerline, *z*_{0}. A simple relationship was proposed as follows:where is a parameter depending solely on the soil nature. Field data during tunnelling collected all over the world indicate that varies between 0.2 and 0.45 for sands and gravels, between 0.4 and 0.6 for stiff clays, and between 0.6 and 0.75 for soft clays [24], regardless of the tunnel size and tunnelling method.

Mair and Taylor [24] also pointed out that the transverse settlement trough below the ground surface can be described by Gaussian distribution, and the function of inflection *i* was proposed as follows:where the parameter is a function of depth . According to the field data, Mair and Taylor [24] found that decreases with the depth and the parameter can be deduced by

##### 4.2. Longitudinal Settlement

According to Sugiyama et al. [21], the ground displacement caused by shield tunnelling can be divided into five types:

*Step 1. *Preceding settlement occurs far ahead of the shield tunnel’s arrival, which does not occur in all the shield tunnellings.

*Step 2. *Ground deformation at the front of the tunnel face that occurs immediately before the shield tunnel’s arrival is due to the imbalance of the support pressure at the tunnel face.

*Step 3. *Settlement during passage of the shield is sensitive to the thickness of the over-cutting edge and the steering problems in maintaining the alignment of the shield.

*Step 4. *Settlement due to the tail void is induced by the interval time between excavation and grouting.

*Step 5. *Succeeding settlement is caused by the disturbance of the ground due to the shield driving.

#### 5. Numerical Results and Discussion

In this section, a detailed analysis on the evolution laws of ground settlement caused by shield tunnelling is made by comparing the field measurement with the numerical results. The field measurement is conducted to verify and evaluate the accuracy of numerical results. Transverse and longitudinal settlement troughs and horizontal displacements were obtained on the basis of measurements recorded during the excavation process, and the displacement results at the corresponding positions are extracted from the numerical model.

##### 5.1. Transverse Settlement

The eventual transverse ground surface settlement trough is highlighted. Figure 11 shows the transverse settlement trough of the ground surface at Step 5. Both the numerical results and the monitoring results match well with the Gauss distribution. From the numerical results, it can be found that the maximum surface settlement, , occurs at the tunnel axis *x*, and the final value of is 17.25 mm. The maximum settlement in the monitoring section of the project is 14.44 mm, about 84% of the corresponding numerical result.

In the area close to the tunnel axis (−18 < *x* < 18 m), about 1.5 times of the excavation diameter, the numerical result is larger than the measured result with an average value of about 4.00 mm, which means the numerical prediction slightly overestimates the eventual surface settlement. The overestimation of numerical results could be treated as the safety margin in a reasonable way. In the area far away from the tunnel axis (*x* < −18 m and *x* > 18 m), the numerical result is smaller than the measured result, which means the numerical prediction slightly underestimates the eventual surface settlement. As all the measured results are smaller than 2.30 mm, the influence of the underestimation could be well accepted in the construction project.

The ground surface settlement predicted by the Peck formula is also shown in Figure 11. Before using the Peck formula, two experiential parameters *K* and *V*_{L} are needed. Based on the parameter statics of the Peck formula in the Beijing area [25] and the actual condition of the project, the experiential parameters *K* = 0.4 and *V*_{L} = 0.5% are adopted in this project. The ground surface settlement predicted by the Peck formula is carried out by using formulas (2)–(4). In the area close to the tunnel axis (−18 < *x* < 18 m), Peck formula overestimates the ground surface settlement, which is at least 1.6 times of the settlement monitored in situ. It is obvious that the prediction results deduced by the Peck formula are much more conservative than that of the proposed model in this paper.

From the overall perspective, the numerical ground surface settlement trough is symmetrical. However, influenced by the existed structures and the nonuniform excavation, the measured transverse settlement profile is not perfectly symmetrical. In general, the numerical model can predict the ground surface settlement very well. According to the Peck formula’s prediction, the numerical and field measurement results, the main settlement in the transverse section occurs within 18 m of the centerline.

It is possible to get the ground loss by integrating the ground surface settlement curve, and the ground loss of the numerical simulation and the monitoring are 0.33% and 0.27%, respectively. Compared with the experiential value *V*_{L} = 0.5%, the ground loss of the simulation is closer to the monitoring result, which means the numerical simulation is more reasonable.

Moreover, the measured surface settlement data of two typical sections in Beijing [26] and Changsha [27] metro construction are included in Figure 12. The geological conditions of these two constructions are similar to the project investigated in this paper. The diameters of these two shield tunnels are 6.0 m, and the depths of two tunnels are 15.0 m in the Beijing metro and 12.5 m in the Changsha metro, respectively. Obviously, both the settlement and the main influenced range induced by the small shield tunnel with a diameter of 6 m are smaller than the large shield tunnel with the diameter of 12 m. The maximum settlement of the two metro tunnels is smaller than 6.7 mm. However, the main influence ranges of two small metro tunnels are about 9 m, about 1.5 times of the excavation diameter, which is the same to that of the large shield tunnel investigated in this project.

The development of the transverse ground surface settlement trough obtained by the finite difference method (FDM) during the face advancement is shown in Figure 13. This figure shows that the settlement is close to Gaussian distribution. The excavation causes an increase in the surface settlement, which could be explained by the accumulated loss of the ground during tunnelling. Both the settlement and the width of the transverse ground surface settlement trough get increased during the excavation process.

The transverse ground settlement troughs of different subsurfaces are shown in Figure 14. According to Figure 14, the maximum settlement magnitude increases as the depth. With the distance decreasing from the tunnel, the ground is strongly influenced by the excavation. Thus, the maximum settlement of the ground near the tunnel is much larger than that of the ground surface. It can also be observed that the settlement area of the ground gets increased gradually with the depth. Compared to the maximum settlement, the area with the ground deformation induced by the excavation expands with the distance between the tunnel and ground in *z*-axis. Similar results are also found by Mair and Taylor [24], as described in equation (4).

##### 5.2. Longitudinal Settlement

The longitudinal ground surface settlement troughs (*x* = 0) calculated by FLAC^{3D} and measured in site are presented in Figure 15. It is obvious that the performance of the longitudinal settlement troughs is similar. Before the tunnel face’s arrival, the ground settlements are almost zero. The main settlement occurs in Step 3 and Step 4, which means that the tunnel passage and tail void disturb the ground seriously. From both the numerical and monitoring results of this project, the settlement induced by the excavation (in Step 3) is larger than that induced by the tail void (in Step 4), and similar conclusions were found by Melis et al. [19] and Lambrughi et al. [23]. In other words, the passage of the shield is the most dangerous stage for the structures above the tunnel. Compared with the other curves in Figure 14, a similar conclusion can be obtained that the maximum settlement increases as the depth.

Table 3 represents the maximum settlements at different subsurfaces of each step during tunnelling both in the numerical model and field measurement. is the cumulated settlement at the tunnel center (*x* = 0) at the end of Step *i *. is the settlement at the tunnel center that occurred in Step *i* and equals to .

In Step 1 of the numerical results, the settlement decreases with the depth of the measured section, which is due to the slight influence of the excavation in this step on the ground far away from the tunnel face. The monitoring results influenced by many unexpected factors in Step 1 do not have such features, and the values are much larger than those of the numerical method. However, in Steps 2 to 4, the ground is strongly influenced by the excavation of the tunnel, the ground near the tunnel has a significant movement, and the settlements both in numerical results and monitoring results increase with the distance from the ground surface. This model magnifies the impact of tail void, the settlements in Steps 1 and 2 are underestimated, and the settlements in Steps 3 to 5 are overestimated by this numerical model, especially in Step 4.

From Table 3, it also can be found that the cumulated settlements of different subsurfaces both in the numerical method and monitoring method are more than 81.8% of the total settlements before the succeeding settlement, and the settlements in Steps 3 and 4 are about 66.2∼78.8% in the numerical method and 48.1∼63.9% in the monitoring method. Hence, the driving speed and lining construction time are of great importance for controlling the settlement in slurry shield tunnelling.

Table 4 compares the numerical results and the measured results at the tunnel centerline of different subsurfaces. The settlements predicted by this model during the first three steps are much smaller than the measured settlements, especially in Step 1 and Step 2. And the predicted settlements in the last two steps are 15∼30% larger than the measured settlements. However, 15∼30% overestimation of the final settlement in the numerical model can be regarded as a safety margin for the unpredictable factors during the construction progress. Thus, this numerical model can predict the longitudinal settlement in a more reasonable way.

##### 5.3. Settlement of the Tunnel Vault

In general, the maximum deformation at the tunnel vault may influence the normal operation of the tunnel and threaten the traffic safety. As it is impossible to construct the segmental lining immediately after the shield tail, there is a construction time lag which has great influence on the settlement of the tunnel vault, as shown in Figure 16. The point A is the moment when the shield tail has been passed, and the point B is the moment when the ring segmental lining has been formed. It is evident that the settlement of the tunnel vault between points A and B is significant, , AB = 9.00 mm which is 27.0% of the total settlement. Thus, reduction of the construction time lag after the shield tail is of great importance.

##### 5.4. Horizontal Displacement along the Depth

Figure 17 shows the computed and monitored horizontal displacements of the ground along the depth, corresponding to the tunnel face 5 m away from the measured section and 5 m and 10 m past the measured section, which locates at the distance from the tunnel side wall of 2 m, as shown in Figure 6. The three curves belong to the excavation procedure Step 2 and Step 3, respectively. Before the arrival of the shield, a tiny outward displacement with the value smaller than 1.00 mm is occurred at the measured section. As the shield moves forward, the outward displacement increases gradually. And the maximum outward displacements of the numerical model and monitoring result are = 2.68 mm and 1.57 mm, respectively, both of which appear at the tunnel centerline when the shield passes.

#### 6. Conclusions

A three-dimensional finite difference model for the large-diameter slurry shield tunnelling is built to predict the ground deformation. The finite difference model comprehensively takes into account the entire shield tunnelling components, such as face pressure, grouting pressure, structure void, and hardening of grout and realistically simulates the step-by-step tunnel excavation. The numerical model is validated by the field measurements in the Rapid Transit Line Project from Beijing Railway Station to West Beijing Railway Station in China (RTLP), which means the numerical model in this paper can predict the ground deformation induced by large slurry shield tunnelling very well. Some conclusions are summarized as follows:(1)The transverse settlement reaches the peak at the center and gets decreased with the distance from the center. The main settlement in the transverse section occurs within the zone about 1.5 times of the excavation diameter. In the main range of ground surface settlement, the numerical prediction is larger than the measured result with an average value of about 4.00 mm.(2)The main longitudinal settlement occurs when the shield is passing and the tail has passed the measured section. The settlements during these two steps are more than 50% of the eventual settlement. Hence, the driving speed and lining construction time are of great importance for controlling the settlement during the tunnelling process.(3)The settlement of the tunnel vault accounts for 27% of the total settlement. Therefore, accomplishing the first ring segmental lining after the tunnel tail is also very important.(4)The outward vertical deformation mainly happens to the ground layer where the tunnel exists. Besides, the maximum vertical deformation is located at the tunnel centerline.

#### Data Availability

The data used to support the findings of this study are included within the article.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

The authors acknowledge the financial support provided by the Beijing Municipal Natural Science Foundation of China (Grant no. 8172037) and the National Natural Science Foundation of China (Grant no. 51378002).