J. Cent. South Univ. (2021) 28: 2556-2573

DOI: https://doi.org/10.1007/s11771-021-4786-7

Analysis model for deformation mechanism of strip foundation of building: Considering shear effect of down-crossing tunnel under excavation

WU Ting-yao(吴廷尧), JIANG Nan(蒋楠), ZHOU Chuan-bo(周传波),XIA Yu-qing(夏宇磬), ZHANG Yu-qi(张玉琦), ZHU Bin(朱斌)

Faculty of Engineering, China University of Geosciences, Wuhan 430074, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2021

Abstract: When the tunnel underpasses through the building, it will cause deformation and even damage to the buildings above, and the deformation of building foundation is the key to building safety. Based on the engineering case, the theoretical analysis was employed to evaluate the influence of shield tunnel underpass construction on the stability of the building, and the optimal tunneling parameters in the field construction have been obtained through the verified theoretical model and parameter analysis. First, the strip foundation of the building was simplified to the Timoshenko beam, which was taken into account the shear effect, and then the deformation displacement of the soil at the same place of strip foundation was applied to the simplified Timoshenko beam. Finally, the numerical solution of the displacement of the strip foundation was obtained by using the finite element method and verified its reliability using Euler-Bernoulli beam theoretical model, field monitoring data, and numerical simulation. Parameters analysis for the deformation and internal force of strip foundation under different types of shield machine tunneling parameters showed that the influence of the pressure of shield excavation chamber, thrust of shield, and driving speed played an important role in the deformation of the building’s strip foundation and internal force.

Key words: down-crossing tunnel; Timoshenko beam; strip foundation; finite element method; parameters analysis

Cite this article as: WU Ting-yao, JIANG Nan, ZHOU Chuan-bo, XIA Yu-qing, ZHANG Yu-qi, ZHU Bin. Analysis model for deformation mechanism of strip foundation of building: Considering shear effect of down-crossing tunnel under excavation [J]. Journal of Central South University, 2021, 28(8): 2556-2573. DOI: https://doi.org/10.1007/s11771-021-4786-7.

1 Introduction

In recent years, with the development of cities, traffic has become more and more crowded, major cities through the construction of the subway to alleviate traffic pressure. Due to the limitation of urban underground space, new tunnels will inevitably approach or cross existing buildings. The construction of new tunnels will have adverse effects on existing buildings, such as uneven settlement,

inclination, and cracking, which will seriously affect the safety of existing buildings. Therefore, to minimize these problems, it is important to have a reliable damage assessment of the adjacent structures as well as an appropriate protection measure prior to tunnel excavation. Reasonable damage assessments require a better understanding of the complex soil-structure interactions among the tunnel, structure, ground, and construction conditions. A failure to understand these interactions can lead to the implementation of unnecessary protection measures, unnecessary cost and unsatisfactory results.

Scholars have mainly studied the influence of underpass tunnels on existing operating tunnels by means of in-situ monitoring [1, 2], model test [3], finite element analysis [4-7], and simplified analytical theory [8-11]. At the same time, centrifuge model test, numerical model and Winkler foundation model theory are employed to evaluate the relationship between shield tunnel characteristics and surface and stratum deformation [12-15]. At present, most of the research results on tunnel passing under buildings were analyzed by combining numerical simulation and field measurement data [16-18], however, the contact relationship between the building and soil is difficult to determine, which has a great influence on the deformation of the building [19-21]. At the same time, the numerical simulation neglects the influence of shear and vertical deformation caused by shield excavation on the stress and deformation of the strip foundation itself under shallow foundation conditions, which has a significant impact on the overall safety and bearing capacity of buildings [22-24].

Although there are some paper models of building Timoshenko beam and Euler-Bernoulli beam have been published in terms of computational methods and applications for building deformation analysis, most of the studies in this paper are not focused on the deformation of buildings, these studies mainly include three types: 1) an equivalent Timoshenko beam was used for analyzing the influence of relative shear flexibility and offset between the beam axis and ground level on the structural response. Within this context, structural deformations, internal forces and tensile strains within the beam models are investigated [25, 26]; 2) an analytical model is used to investigate the influence of the ground and the building’s mechanical properties, the building load and the initial value of the free-field ground curvature (hogging or sagging) [27]; 3) the study about the effects of tunneling-induced ground movements on the nearby structures in sandy soils considering the soil-structure interactions of different type of tunnels, structures, ground, and construction conditions, while the focus of investigation relates the level of structural distortion and damage to different tunnel field conditions [28]. Through the above analysis, it can be seen that there are few types of research focus on the deformation of the strip foundation of the building above in the tunnel construction, and more researches on the influence of the change of the tunnel’s own structure on the adjacent structures. Moreover, there are also few studies on the use of two different types of shield machines in the left line and right line of the same subway tunnel at the same time, which also pass through the same existing building.

As for the research method, it has been employed many times to interpret the effects of tunnel-structure interaction through greenfield ground movements and the modification factor approach [29, 30]. However, these methods may neglect the shearing deformation of the beam and can only consider the flexural deformation. Apparently, the adoption of an Euler-Bernoulli beam for simulating a strip foundation of building can only take into account the bending mode, and the dislocation mode is ignored. The Timoshenko beam theory as proposed by TIMOSHENKO [31, 32], which allows both bending and shearing deformations of beam, is perhaps a suitable beam model for simulating the strip foundation of building longitudinal behaviors subjected to excavations. Therefore, a better method is that the analysis method generally was divided the interaction problem into two individuals but connected stages. First, the effect of construction on structures is estimated by ignoring the existence of structures. And second, the responses of existing structures subjected to the corresponding construction effect are predicted. Due to its simple mathematical treatment and clear concept of mechanical interactions, also, it is widely accepted by researchers and gives reasonable predictions in real interaction problems [33-36]. Based on the above-mentioned special conditions, it is meaningful and innovative to use a reasonable theoretical analysis method to analyze the deformation of the existing building and verified its reliability using field monitoring data and numerical simulation. More importantly, the research on the influence of different types of shield machines on the same building also plays an important role in the selection of shield machine types during tunnel excavation in the future.

There are two types of shield tunneling machines commonly used in China, including the slurry balance shield machine (SBS) and the earth pressure balance shield (EPBS). On the one hand, the EPBS is to use the front of the shield cutting tool to cut down the front soil, and then the soil goes into the storage sealed bin behind the cutter, where the cabin shall be provided with an appropriate pressure to balance the water and soil pressure on the excavation surface. At the same time, the disturbance to the stratum soil caused by shield propelling can be reduced, so as to control the surface settlement. Moreover, the soil in front of the cutter plate of the shield machine is continuously discharged to the drainage hole by a spiral conveyer mounted on the lower part of the sealed bin. On the other hand, the SBS is to support the soil in the front of the shield machine using the sealed silo installed in front of the shield machine, where the sealed silo is filled with mud at an appropriate pressure to form a mud film on the excavation face. What’s more, the large knife plate installed in the front cuts the surface mud film of the soil and mixes with the mud and water to form the high-density mud, which is transported to the ground for treatment by the slurry discharge pump and pipeline. Specially, the whole process is managed by an automatic control system of mud-water balance established in the central control room on the ground.

The traditional construction process of shield tunneling is to continuously adjust the parameters on site, so as to obtain a relatively appropriate construction parameters to ensure the safety of the site project and carry out the excavation on site. However, in order to ensure the safety of the adjacent buildings during construction, it is necessary to continuously adjust the construction parameters through field tests. But due to the time and cost of construction, the number of field tests is often very limited, so the construction parameters obtained are relatively unreasonable. Therefore, in order to better control the construction period and cost on site, how to obtain the optimal construction tunneling parameters is an important research topic. In this study, a new analytical model for the deformation mechanism of the strip foundation of the existing building was proposed through Timoshenko beams with two generalized displacements. Then, the shear effect of the self-weight load of upper building and influence of lower down-crossing tunnel under excavation were taken into consideration to calculate the equilibrium differential equation of the strip foundation deformation. Based on the finite element method, an analytical solution to reveal the internal force and displacement of the strip foundation was derived in Section 2. The accuracy of the analytical formulation was verified by comparison with the measured data and numerical simulation in Section 3. The deformation data of the strip foundation calculated in different stages of the double-line tunnel by the above theoretical models were compared with the field monitoring data and the monitoring data calculated by numerical simulation, and the theoretical models include Timoshenko beam theoretical model and Euler-Bernoulli beam theoretical model, and then the calculation results of the parameter analysis of different types of shield machines tunneling parameters were illustrated to show the longitudinal variation of the strip foundation, including the SBS and the EPBS underpass existing buildings (Section 4). By analyzing the variation of internal force and displacement of strip foundation, the optimal tunneling parameters of different types of shield tunneling machines are obtained. Meanwhile, the method in this paper to determine the optimal construction parameters can also be used in other similar projects to provide a reference for on-site construction.

2 Establishment of analysis model for deformation mechanism of strip foundation of building

2.1 Longitudinal deformation theory of tunnel considering shear effect

The excavation of a new tunnel will cause ground loss and free displacement of the soil. The strip foundation of a building will undergo settlement deformation under the action of soil displacement [37, 38]. Figure 1 shows the sketch of the influence of the underpass of a new tunnel on the deformation of the strip foundation of an existing building. In order to simplify the calculation and obtain the response formula of strip foundation of existing buildings under the construction of the lower tunnel, the following assumptions are made in the calculation model in this paper: 1) The strip foundation of existing buildings was considered as the Timoshenko beam with shear effect. 2) The interaction between stratum and strip foundation of existing buildings was studied by the Winkler foundation model, and the strip foundation was always connected with the foundation spring, and there was no separation. 3) The time effect of deformation and interaction between layers of strip foundations of existing buildings was not considered, such as creep or consolidation.

Figure 1 Diagram of influence of new tunnel underpass on strip foundation of existing buildings

In this paper, the deformation characteristics of the strip foundation were deduced and solved by a two-stage analysis method. According to its basic principle, the first step was that a 3D numerical calculation model was established to analyze the deformation displacement of the soil at the corresponding horizontal position of the building foundation, and the reliability of the model was verified using the field monitoring data, and then the deformation displacement was applied to the simplified Timoshenko beam. The second step was that the self-weight load of upper buildings was applied to the strip foundation of buildings as a uniform load. Finally, the third step was that under the action of an additional uniform load, the longitudinal differential governing equation of stratum displacement-deformation of the strip foundation of the building was established, and then the internal force and displacement of the strip foundation of the building were obtained by the finite difference method.

2.2 Derivation of longitudinal deformation theory of tunnel

The model sketch of the influence of new tunnel excavation on the strip foundation of building is shown in Figure 2. The equivalent self-weight load of the building above the foundation and the free soil settlement u_z(x) caused by stratum loss are acted on the strip foundation of the existing building, thus the longitudinal deformation and internal force of the strip foundation of the existing building are changed.

To obtain the governing equation of strip foundation deformation of existing buildings under the action of free soil settlement u_z(x), a micro-element at any position in Figure 2 is used for force analysis, as shown in Figure 3. The force and moment balance equation of strip foundation of existing buildings is obtained, as shown in Eqs. (1) and (2):

  (1)

                  (2)

where Q is the additional shear force of the strip foundation of the existing buildings; M is the additional bending moment of strip foundation of existing buildings; k is the reaction coefficient of foundation; D_t is the width of strip foundation of existing buildings; q is the equivalent self-weight load of the building above the foundation; and w(x) is the vertical displacement of the strip foundation of the existing buildings. According to the Timoshenko beam theory, the shear force and bending moment have the following relationship with the vertical displacement and rotation angle θ of the strip foundation of the existing building, as shown in Eqs. (3) and (4) [39-41]:

                          (3)

                    (4)

where (EI)_eq is the longitudinal equivalent bending stiffness of strip foundation of existing buildings; (kGA)_eq is the equivalent shear stiffness of strip foundation of existing buildings. Equations (1) and (2) are further simplified to omit higher order trace elements. Combined with Eqs. (3) and (4), the equilibrium differential equation of vertical displacement w(x) and rotation angle θ on the Timoshenko beam can be obtained, as shown in Eqs. (5) and (6).

(5)

           (6)

By decoupling Eqs. (5) and (6), we can obtain the differential Eq. (7) only for vertical displacement w(x):

        (7)

The longitudinal deformation of the strip foundation of existing buildings under the influence of tunnel excavation can be obtained by Eq. (7). As Eq. (7) is a fourth-order ordinary differential equation, it is difficult to solve mathematically. In order to simplify the calculation and facilitate programming, the finite difference method is used to solve numerically. The strip foundation of existing buildings is discretized into n+5 nodes, and two virtual nodes are added at both ends of the strip foundation of existing buildings. The distance between every two nodes is 1. The discretization sketch of the strip foundation of existing buildings is shown in Figure 4, where l represents the length of each unit. To simplify Figure 4, the dotted line in the middle part of Figure 4 represents the part of the solid unit that is not drawn, and the dashed boxes on each side of Figure 4 represent 2 dummy node units at each end of the building strip foundation. According to the standard finite difference principle, the finite difference form of the differential Eq. (7) is adopted.

(8)

In the formulas, w_i, w_i-1, w_i+1, w_i+2 and w_i-2 are the vertical displacements of node elements i, i-1, i+1, i+2 and i-2, respectively; u_z,i+1, u_z,i, and u_z,i-1 are the vertical displacements of strata caused by tunnel construction at node elements i, i+1 and i-1, respectively.

Figure 2 Computational model of influence of new tunnel excavation on strip foundation of building

Figure 3 Force analysis of microelement

Combining Eqs. (3)-(6), the expression of the shear force Q and bending moment M of the strip foundation of existing buildings under free soil settlement can be obtained, as shown in Eqs. (9) and (10):

                       (9)

(10)

For the finite-difference calculations of Eqs. (9) and (10), the shear force Q_i and the bending moment M_i expression of any node i are obtained.

 (11)

Figure 4 Discrete sketch of strip foundation of existing buildings

                        (12)

where both the strip bases of the building are free, then Eqs. (13) and (14) are obtained:

                            (13)

                             (14)

Combining the Eqs. (11) to (14), the limit difference form of the additional shear force and bending moment at both ends of the strip foundation of the building can be obtained, and the displacement expressions of the additional four virtual nodes in Figure 4 are obtained, as shown in Eqs. (15) to (18):

  (15)

(16)

 (17)

               (18)

Combining the four virtual displacement expressions, Eq. (8) can be rewritten into a matrix expression, as shown in Eq. (19):

              (19)

where K₁ is the displacement stiffness matrix of the strip foundation of the existing building; K₂ is the shear stiffness matrix of the strip foundation of the existing building; and K₃ is the bending stiffness matrix of the strip foundation of the existing building; w(x) is the vertical displacement column vector of the strip foundation of the existing building; U₁ is the column vector of the vertical displacement of the stratum caused by the tunnel construction; U₂ is the column vector corrected by the vertical displacement caused by the tunnel construction; and U₃ is a vertical displacement supplemental column vector, which is caused by tunnel construction. After combining Eqs. (15) to (18), the equations of the matrix and column vectors in Eq. (19) are obtained, as shown in the following Eqs. (20) to (25):

(20)

(21)

    (22)

                         (23)

   (24)

             (25)

where

.

Equation (19) is split into Eqs. (26) and (27):

                          (26)

                         (27)

By multiplying K^-1 on both sides of Eq. (19), the expression of the tunnel vertical displacement column vector w can be obtained:

                              (28)

where K^-1 is the inverse matrix of the matrix K.

It is worth noting that when the equivalent shear stiffness of the strip foundation of the building is infinite, the shear deformation of the strip foundation tends to zero. Moreover, the longitudinal deformation of the strip foundation of existing buildings under the influence of tunnel excavation (Eq. (7)) is reduced to the differential equation of the Euler-Bernoulli infinite beam [42, 43].

3 Validation with history cases

It was noteworthy that the published field test data would be used to validate the analytic method. There were two relatively detailed case studies presented to verify the reliability of the proposed analytical solution of the strip foundation of the building. The proposed analytical model considered the shear effect of self-weight load of upper building and influence of lower shield machine in this paper, which revealed the displacement change and stress condition of the strip foundation of existing buildings when different types of shield machines under passed through the existing building.

3.1 General information of engineering

The Dongge Road Station-Binhu Road Station section of Nanning Metro Line 3 was constructed by the different types of shield method with a total length of 957 m. The tunnel is mainly through gravel layer, silty clay layer, and part of the tunnel through silty sand layer and silty sand layer. The line spacing between the sections was 8.0-14.0 m. The main physical parameters of the soil layer were shown in Table 1. The diameter of cutter head of SBS and EPBS are both 6280 mm, and the thrust of shield of SBS is from 7900 to 12000 kN with a torque of cutter head of 500 kN·m, and a pressure of synchronous grouting of 0.35 MPa. The pressure of shield excavation chamber of SBS is from 0.18 to 0.2 MPa with a driving speed of 35 mm/min. At the same time,the thrust of shield of SBS is from 15000 to12000 kN with the torque of cutter head of 1500 kN·m, and a pressure of synchronous grouting of 0.35 MPa. The pressure of shield excavation chamber of SBS is from 0.18 to 0.23 MPa with a driving speed of 28 mm/min. Nanning Metro Line 3 underpasses existing buildings. The spatial relationship between buildings and shield tunnels was shown in Figure 5. The SBS on the left line of the tunnel interval was excavated first, while the EPBS on the right line was excavated behind.

Table 1 Main physical parameters of soil layer

Figure 5 Diagram of spatial relationship between buildings and shield tunnel

In order to analyze the influence of the different types of shield machines tunneling parameters on the longitudinal deformation of the strip foundation, when the SBS and EPBS were used to underpasses through the existing building, the following two cases were analyzed, which was shown in Table 2.

Table 2 Design table for analysis of different shield types

3.2 Establishment of numerical model and verification of numerical models

In the process of tunnel shield construction, the ground loss caused by shield construction can be directly reflected through the monitoring data of surface settlement. In this paper, FLAC3D software was used for numerical simulation analysis. According to the changes of field monitoring data, the numerical simulation was simplified as follows: when the tail of two types of the shield was separated from the segment, different stress release percentages were used to simulate the formation deformation caused by disturbance of surrounding soil and non-timely grouting. The soil layer in the model was modeled according to the actual overlying layer. The buried depth of the tunnel was 19.5 m; the depth below the bottom of the tunnel was 19.5 m; the distance between the axes of the horizontal tunnel was 32 m; the distance between the axes of the two parallel tunnels was 11 m; and the longitudinal length of the model was 72 m. The dimension of the three-dimensional FLAC3D numerical model was 72 m×81 m×45 m (length×width× height). Among them, the size of the building was 12 m×32 m×11.8 m (length×width× height), and the size of the strip foundation was 0.5 m×32 m×0.6 m. The boundary conditions were as follows: the boundary of the building and the upper surface was free; the lateral boundary restricted the horizontal displacement; and the bottom boundary restricted the vertical displacement. Shell elements were used for shield shell and lining segment, and solid elements were used for soil and grouting layer. The three-dimensional numerical models were shown in Figure 6.

In this paper, the Mohr-Coulomb elastic-plastic model was used for the soil, and elastic materials were used for shield shell, lining segment, and grouting layer. The mechanical parameters used in the model calculation are shown in Table 1. The left line of the tunnel was excavated first, and then the right line of the tunnel was excavated. According to the field monitoring data, when the tail of two shield tunnels was separated from the segment, different calculation time steps were used to make the formation deform. The comparison of ground settlement changes in different stages of double-line tunnel excavation, including numerical simulation and field monitoring data was shown in Figure 7, in which Condition 1 represents data of surface monitoring point after left line excavation; Condition 2 represents data of surface monitoring point when the head of the right line shield machine is directly under the building; Condition 3 represents data of surface monitoring point after right line excavation. From Figure 7, it can be seen that the width and depth of the settlement trough were basically the same as the measured values, which verified that the numerical model can be used to study the change of ground settlement caused by tunnel construction.

Figure 6 Three-dimensional numerical model:

Figure 7 Comparison of ground settlement changes in different stages of double-line tunnel

3.3 Verification of theoretical model

According to in Figure 6(a), the displacement of soil mass at the same horizontal plane as the strip foundation of existing buildings can be obtained. And then under the condition that the additional soil displacement distribution was known, the numerical solution of the vertical displacement w_x of the strip foundation of the existing building caused by tunnel underpass construction can be obtained from Eq. (28). Among them, the shear stiffness and bending stiffness and the foundation coefficient were obtained from the ground-based specifications and the current test, as shown in Table 3.

Table 3 Theoretical calculation parameter table

The deformation data of the strip foundation calculated in different stages of double-line tunnel by the above theoretical models were compared with the field monitoring data and the monitoring data calculated by numerical simulation, and the theoretical models include the Timoshenko beam theoretical model and the Euler-Bernoulli beam theoretical model, in which the numerical calculation data were obtained by the numerical model in Figure 6(b). The comparative analysis was shown in Figure 8.

From Figure 8, it can be seen that the width and depth of the settlement tank were basically consistent with the measured values and the theoretical data obtained in this paper. At the same time, the calculated results in this paper were more in line with the measured results, which verified the feasibility of the theoretical method in this paper. At the same time, compared with the width of longitudinal settlement trough of strip foundation of existing buildings, the numerical simulation data was smaller than the data obtained by the method in this paper. The reason was that the numerical simulation simplified the stratum and ignored the role of Timoshenko beam in the prediction theory of longitudinal deformation of strip foundation of buildings due to stratum absence. Moreover, the maximum settlement value obtained by the method in this paper (Timoshenko beam theoretical model) is slightly larger than that obtained by the Euler-Bernoulli beam theoretical model, but on the whole, the curve trend of the two is basically the same. The calculated results of the method in this paper are in good agreement with the measured longitudinal settlement of the strip foundations of building. Calculation results obtained by the Euler-Bernoulli beam theoretical model are far less than measured values. If this method is used to predict the longitudinal deformation of the strip foundations of the buildings, taking too few protection measures will increase the settlement of strip foundations of the building and cause unnecessary economic losses.

Figure 8 Comparison of field measurements and numerical simulations with theoretical model results:

4 Analysis of construction parameters under different working conditions

4.1 Parameter analysis of strip foundation when tunnels excavated by SBS

4.1.1 Deformation analysis of strip foundation of existing building

Case study 1 was studied using the validated numerical model in Figure 6(a). It meant that the left and right lines of the tunnel were both excavated by SBS. The deformation of the strip foundation was analyzed, and the orthogonal table of tunneling parameters of the SBS was shown in Table 4 [44-46], where k₁ to k₅ represent 5 levels of each influence factor, and the vertical deformation data of the strip foundation of the existing buildings under different tunneling parameters were obtained. Then, the theoretical calculation model in this paper was used to calculate the deformation of the strip foundation under different tunneling parameters of the shield. The deformation of the strip foundation of existing buildings under different tunneling parameters was shown in Figure 9.

Table 4 Orthogonal experiment level and factor design table

Based on the orthogonal test data in Figure 9, the variance analysis was conducted, and the order of contribution rate of shield tunneling parameters to the maximum settlement of buildings can be obtained, which shows that the driving speed, the pressure of shield excavation chamber, torque of cutter head, thrust of shield, and pressure of synchronous grouting have the first to fifth influence on the deformation of the bar foundation respectively. It shows that special attention should be paid to driving speed and the pressure of shield excavation chamber when the tunnel excavated by SBS passes through the existing building. At the same time, the contribution of the pressure of synchronous grouting to the maximum settlement of the strip foundation of buildings is relatively small. When adjusting the parameters of shield tunneling, special attention should be paid to the influence of the driving speed and the pressure of shield excavation chamber on building safety.

When the pressure of synchronous grounding is equal to 0.6 MPa, the thrust of shield is equal to 14000 kN, and the torque of cutter head is equal to 900 kN·m, the maximum settlement of the strip foundation is both less than 20 mm. And when the corresponding factor value is reduced to half, compared with the current level of each shield tunneling parameters, the percentage change in maximum settlement of the strip foundation is only reduced by about 30%, which shows that combined with the construction parameters mentioned above, it is not difficult to find that the shield tunneling parameters in practice are too conservative to accelerate the progress of tunneling. In order to ensure the construction progress and reduce the construction cost, the pressure of synchronous growing and driving speed can be appropriately increased.

Figure 9 Deformation of strip foundation of buildings under different tunneling parameters:

Although the maximum displacement of the strip foundation of the building increases with the increase of thrust of the shield, the change in thrust of the shield has little effect on the deformation value of the foundation. Moreover, the change of the whole graph curve is relatively steep, indicating that the thrust of the shield only has a great influence on the soil directly above the shield, but has little influence on the other parts. With the increase of torque of cutter head of shield machine, the settlement of strip foundation gradually increased. However, when the torque of cutter head is no more than 500 kN·m, the deformation value of the foundation does not change significantly, and when the torque of cutter head is greater than 500 kN·m, the deformation value of the foundation changes significantly, which indicates that the torque of cutter head at a lower level can make the strip foundation have a small deformation, so the torque of cutter head can be appropriately reduced to the deformation caused by shield construction on the strip foundation. When the pressure of synchronous grouting is less than 0.3 MPa, it is found that the settlement of strip foundation changes little with the increase of pressure of synchronous grouting. While after the pressure of synchronous grouting is greater than 0.3 MPa, the settlement of strip foundation decreases slightly. It indicates that the synchronous slurry is in a fluid state and does not have sufficient strength to support soil stress. The synchronous grouting system enables the slurry to have a certain pressure to make up for the instantaneous loss of stress caused by the release of the shield tail, and balance the stress release caused by shield excavation unloading, and form support for surrounding soil to ensure the stability of soil structure. However, due to the limitation of shield machinery’s own equipment, the grouting pressure is difficult to reach a large pressure value.

4.1.2 Inter force analysis of strip foundation of existing building

Combined with the above mentioned, when the tunnel excavated by SBS passes through the existing building, driving speed and the pressure of shield excavation chamber have a great impact on building safety, so the internal force changes of the striped foundation of the building under different driving speed and the pressure of shield excavation chamber are analyzed, as shown in Figure 10. When the pressure of shield excavation chamber is equal to 0.4 MPa, the deformation of the strip foundation of the building is small, while the shear force of the strip foundation of the building is relatively large. At the same time, when the pressure of shield excavation chamber is too large, the requirements for shield machine itself are too high. Especially, when the pressure of the excavation bin is 0.2 MPa, the construction cost of the shield machine is effectively controlled. On the other hand, it not only reduces the deformation of the strip foundation of the building, but also reduces the shear force of the strip foundation. Therefore, it is appropriate to select the pressure of shield excavation chamber of about 0.2 MPa. Also, driving speed has the greatest impact on the deformation of the strip foundation, which indicates that the excavation speed should be slowed down, while it can be seen from Figure 10 that when the driving speed is the minimum, the shear force on the strip foundation of the building is not the minimum, meanwhile, too low driving speed cannot meet the economic requirements of the site construction. Therefore, combined with the data in Figures 9 and 10, it can be seen that when passing through the building below, 30 mm/min is the appropriate driving speed to ensure the safety of the building.

Figure 10 Internal force changes of striped foundation of building under different tunneling parameters:

4.2 Parameter analysis of strip foundation when tunnels excavated by EPBS

4.2.1 Deformation analysis of strip foundation of existing building

The research methods of case study 2 and case study 1 were the same. It means that the left and right lines of the tunnel were excavated by EPBS, and the orthogonal table of the parameters of the EPBS was shown in Table 5 [47, 48]. The deformation of strip foundation of existing buildings under different tunneling parameters was shown in Figure 11.

Table 5 Orthogonal experiment level and factor design table

Based on the orthogonal test data in Figure 11, the variance analysis was conducted, the order of contribution rate of shield parameters to the maximum settlement of buildings can be obtained, which shows that the pressure of shield excavation chamber, thrust of shield, pressure of synchronous grouting, torque of cutter head, and driving speed has the first to fifth influence on the deformation of the bar foundation respectively. It shows that special attention should be paid to the pressure of shield excavation chamber when the tunnel excavated by EPBS passes through the existing building. When adjusting the parameters of shield tunneling, special attention should be paid to the influence of the pressure of shield excavation chamber and thrust of shield on building safety. When the pressure of synchronous drilling is less than or equal to 0.3 MPa, and the torque of cutter head is less than or equal to 1680 kN·m, the deformation of the strip foundation of the building is less than 30 mm, and the deformation is within the safety allowable range.

Although the deformation of the strip foundation of the building increases with the increase of thrust of shield, the change of thrust of shield has little impact on the deformation of the foundation when thrust of shield is less than 14500 kN. Moreover, the change of the whole graph curve is relatively steep, indicating that the thrust of the shield only has a great influence on the soil directly above the shield, but has little influence on other parts. With the increase of torque of cutter head of shield machine, the settlement of the strip foundation gradually increases, and the maximum value increases uniformly with the increase of torque of cutter head, indicating that the settlement of strip foundation is sensitive to the change of torque of cutter head. Therefore, the torque of cutter head can be appropriately reduced, so as to reduce the deformation caused by shield construction on the strip foundation. When the pressure of synchronous grouting is less than 0.3 MPa, it is found that the settlement of strip foundation changes little with the increase of pressure of synchronous grouting, while after the pressure of synchronous grouting is greater than 0.3 MPa, the settlement of the strip foundation decreases slightly. It shows that the pressure of synchronous grouting has a great influence on the EPBS, so the grouting pressure should be appropriately increased to ensure the safety of the building.

When the driving speed is 45.5 mm/min, the deformation value is greater than 30 mm, and when the pressure of shield excavation chamber is equal to 0.4 MPa, the uplift value of the strip foundation of the building is greater than 5 mm. Therefore, the driving speed should be appropriately reduced to ensure the safety of the strip foundation. At the same time, the influence of EPBS on soil loss is obviously greater than SBS, and a low driving speed will also cause the building to deform greatly, so it is considered that the driving speed of 25.5 mm/min is reasonable in actual construction.

4.2.2 Inter force analysis of strip foundation of existing building

Combined with the above mentioned, when the tunnel excavated by EPBS passes through the existing building, pressure of shield excavation chamber and thrust of shield have a great impact on building safety, so the internal force changes of the striped foundation of the building under different pressure of shield excavation chamber and thrust of shield are analyzed, as shown in Figure 12. With the increase of the thrust of shield, the maximum shear force of the strip foundation of the building increases gradually. This is because the thrust of the shield directly affects the internal force of the soil in front of the tunnel face, which directly increases the internal force of the strip foundation of the building. However, when the pressure of shield excavation chamber increases, the shear force of the strip foundation first decreases and then increases. This is because the lower pressure of shield excavation chamber is easy to cause ground loss, and the subsidence caused by ground loss makes the shear force of the strip foundation increase, while when the pressure of shield excavation chamber is large, the deformation of the strip foundation of the building produces uplift deformation, which makes the shear direction of the strip foundation of the building changes in the opposite direction. Also, if the pressure of shield excavation chamber is too large, it will not only cause the ground uplift but also make the shield excavation chamber in a more dangerous state. Therefore, it is considered that the pressure of shield excavation chamber of 0.2 MPa is reasonable in actual construction to ensure the safety of the building.

Figure 11 Deformation of strip foundation of buildings under different tunneling parameters:

Figure 12 Internal force changes of striped foundation of building under different tunneling parameters:

5 Conclusions

1) Analysis model for the deformation mechanism of the strip foundation of the building based on the Timoshenko beam theory was verified by numerical simulation and field monitoring data. At the same time, the theoretical analysis results were closer to the field measured values. It showed that it was necessary to consider the effect of shear action caused by stratum absence on building settlements. The analysis model can be used to predict and analyze the deformation of the strip foundation of the existing buildings in this paper. Meanwhile, the theoretical model verified by field experimental data can study the construction parameters in more detail. Then, the optimal tunneling parameters of different types of shield tunneling machines are obtained by analyzing the changes of internal forces and dislocations of strip foundations of buildings.

2) According to the orthogonal test results, different shield tunneling parameters had different effects on the maximum settlement of the strip foundation of the existing buildings, but for SBS, special attention should be paid to the pressure of shield excavation chamber and driving speed when the tunnel excavated by SBS passes through the existing building. At the same time, the contribution of the pressure of synchronous grouting to the maximum settlement of buildings was relatively small. For EPBS, special attention should be paid to the pressure of shield excavation chamber and torque of cutter head, when the tunnel excavated by EPBS passed through the existing building. At the same time, the contribution of driving speed to the settlement of buildings was relatively small.

3) When the tunnel was excavated by SBS, the pressure of shield excavation chamber of 0.2 MPa and the driving speed of 30 mm/min were reasonable in practice to ensure the safety of the building, and the pressure of synchronous growing and driving speed can be appropriately increased to ensure the construction progress and reduce the construction cost. Also, when the tunnel was excavated by EPBS, the driving speed of 25.5 mm/min and the pressure of shield excavation chamber of 0.2 MPa were reasonable in actual construction to ensure the safety of the building.

Contributors

The overarching research goals were developed by WU Ting-yao, JIANG Nan, and ZHOU Chuan-bo. XIA Yu-qing and WU Ting-yao provided the measured displacement data, and analyzed the measured data. ZHANG Yu-qi, and WU Ting-yao established the models and calculated the predicted displacement. ZHU Bin and WU Ting-yao analyzed the calculated results of theoretical model. The initial draft of the manuscript was written by WU Ting-yao, JIANG Nan, ZHOU Chuan-bo, XIA Yu-qing, ZHANG Yu-qi, and ZHU Bin. All authors replied to reviewers’comments and revised the final version.

Conflict of interest

WU Ting-yao, JIANG Nan, ZHOU Chuan-bo, XIA Yu-qing, ZHANG Yu-qi, and ZHU Bin declare that they have no conflict of interest.

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(Edited by ZHENG Yu-tong)

中文导读

考虑剪切效应的隧道下穿对既有建筑物条形基础的变形规律

摘要：地铁隧道开挖常采用盾构工法，盾构隧道下穿建筑物施工时，将引起地层以及上方建筑物的变形破坏，本文依托实际工程背景，采用现场实测、理论分析和三维数值模拟软件FLAC3D，研究了盾构隧道下穿施工对既有建筑物稳定性的影响。首先将隧道上方的建筑物的条形基础简化为考虑了剪切效应的Timoshenko梁，其次将数值模拟得到的盾构上方建筑物条形基础位置处的位移分布，施加到既有的条形基础上，建立考虑隧道剪切效应的控制微分方程，并通过有限差分的方法求解得到条形基础的内力与位移的数值解，并将其与数值模拟分析结果和欧拉-伯努利梁理论结果进行对比，验证了理论模型的可靠性，最终对不同盾构掘进参数下条形基础的变形和内力进行参数分析，得到了不同类型盾构机的最佳掘进参数。

关键词：下穿隧道；Timoshenko梁；条形基础；有限元法；参数分析

Foundation item: Projects(41807265, 41972286, 42072309) supported by the National Natural Science Foundation of China; Projects (HKLBEF202001, HKLBEF202002) supported by the Hubei Key Laboratory of Blasting Engineering Foundation, China

Received date: 2020-07-24; Accepted date: 2021-03-01

Corresponding author: ZHOU Chuan-bo, PhD, Professor; Tel: +86-13707175382; E-mail: cbzhou@cug.edu.cn; ORCID: https://orcid.org/ 0000-0003-3056-9946