CN111680383A - A prediction method for the change of the additional confining pressure of the shield tunnel below caused by the excavation of the foundation pit - Google Patents

Abstract

The invention discloses a method for predicting the change of the additional confining pressure of the lower shield tunnel caused by the excavation of the foundation pit. The method calculates the distribution of the additional load on the cross section of the tunnel according to the unloading model of the excavation of the foundation pit; Variation model of lateral additional confining pressure of shield tunnel based on the force between deformation rings, and the calculation method of additional confining pressure is obtained. The method of the invention can predict the change of the lining confining pressure of the shield tunnel below caused by the excavation of the foundation pit, and is suitable for the operating conditions of the shield tunnel over the foundation pit with different excavation sizes; Force, full-size shield segment loading test and subway tunnel operation safety provide theoretical support; early warning of the possibility of excessive confining pressure and force changes, preventing safety accidents, preventing and guiding the project, and saving construction costs.

Description

A prediction method for the change of the additional confining pressure of the shield tunnel below caused by the excavation of the foundation pit

technical field

The invention belongs to the technical field of underground engineering, and in particular relates to a method for predicting the change of the additional confining pressure of a shield tunnel below caused by excavation of a foundation pit.

Background technique

With the development of urban rail transit and the development and utilization of underground space, there will be more and more cases of shield tunnels operating across foundation pit projects. When the foundation pit is excavated, the excavation unloading effect will be directly transmitted from the excavation surface to the shield tunnel below through the soil. The tunnel is uplifted with the soil layer, and at the same time, a large additional load is generated on the tunnel structure. Due to the large amount of unloading in the excavation of the foundation pit, the unloading effect on the structure will destroy the force balance of the segment structure, resulting in deformation or even damage, which has a great impact on the safety of shield tunnels in operation. In order to ensure the safe operation of rail transit lines, subway tunnels have relatively strict deformation control requirements. Therefore, it is of great application value to study the influence of foundation pit excavation on the deformation of shield tunnels below. Therefore, the theoretical calculation method of the confining pressure change of the shield tunnel below caused by the excavation of the foundation pit needs to be further studied, so as to provide theoretical support for the operation safety of the subway tunnel and related full-size structural loading tests.

This kind of engineering problem has received attention at home and abroad. At present, the main research methods are: statistical analysis of measured data, numerical simulation, theoretical calculation and centrifugal model test. At present, the research results of the confining pressure changes of shield tunnels caused by foundation pit excavation are mainly obtained by finite element simulation and centrifugal model. result. Refined numerical simulation has higher requirements for computing models and computing equipment, and requires higher computing costs. Centrifugal model tests require experimental equipment such as large-scale hypergravity centrifuges, high-precision sensors, and model experimental boxes, and the cost of experimental research is relatively high. The theoretical calculation method of shield tunnel confining pressure change caused by foundation pit is seldom studied, especially the theoretical calculation method of additional confining pressure of shield tunnel below caused by foundation pit excavation has not been reported.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for predicting the change of the additional confining pressure of the shield tunnel below caused by the excavation of the foundation pit, aiming at the deficiencies of the prior art. The tunnel confining pressure obtained by this method is superimposed on the normal working condition load combination, which can effectively evaluate the influence of foundation pit excavation on the shield tunnel below.

The purpose of this invention is to realize through the following technical scheme: a kind of bottom shield tunnel additional confining pressure change prediction method caused by foundation pit excavation, comprises the steps:

(1) A coordinate system is established at the center o of the foundation pit, the x-axis is perpendicular to the axis of the tunnel, the y-axis is parallel to the axis of the tunnel, and the z-axis takes the vertical downward direction as the positive direction.

(2) According to the coordinate system established in step 1, calculate the unloading of the excavation surface at the bottom of the foundation pit caused by the excavation of the upper foundation pit, and obtain the vertical additional on the cross section of the shield tunnel below caused by the unloading of the excavation surface at the bottom of the foundation pit. Stress and horizontal additional stress distribution, including the following sub-steps:

(2.1) The unloading of the excavation surface at the bottom of the foundation pit is the uniformly distributed load vertically upward at the bottom of the foundation pit. Calculate the unloading p at the bottom of the foundation pit:

p=(1-α ₀ )γd (1)

Among them: γ is the soil weight, which is the weighted average of the excavated soil layers above the foundation pit bottom; d is the excavation depth of the foundation pit; α ₀ is the residual stress coefficient.

(2.2) According to the Mindlin stress solution, taking the excavation surface at the bottom of the foundation pit as the integral area, calculate the vertical additional stress σ _az (θ, l ) and the additional horizontal stress σ _ax (θ,l) are:

Among them: θ is the position angle of the calculated point on the cross section of the shield tunnel below, the upper vertex is 0°, and the angle increases clockwise; B is the excavation size of the foundation pit along the x-axis direction; L is the foundation pit along the y-axis direction d is the excavation depth of the foundation pit; h is the buried depth of the tunnel; D is the outer diameter of the shield tunnel below; a is the horizontal distance between the center of the foundation pit and the tunnel axis, and l is any point on the tunnel axis in the The corresponding y coordinate value in the coordinate system; x ₁ is the first integral variable, y ₁ is the second integral variable, σ _zz is the Mindlin vertical stress solution, and σ _xz is the Mindlin horizontal stress solution.

(3) According to the on-site monitoring data of the longitudinal deformation of the tunnel, combined with the vertical displacement of the tunnel, the distribution of the resultant force acting between the vertical rings of the segment is obtained, which specifically includes the following sub-steps:

(3.1) Measure the total vertical displacement w(l) of the tunnel along the longitudinal direction, measure the displacement caused by the rotation angle between the segment rings, and calculate the vertical inter-ring shear between the segment ring at l and the previous segment ring Shear force Q _L (l) and vertical inter-ring shear force Q _R (l) between the succeeding segment rings:

Q _L (l)=(1-j)[w(lD _t )-w(l)]×k _sl (4)

Q _R (l)=(1-j)[w(l)-w(lD _t )]×k _sl (5)

Among them, j is the ratio of the displacement caused by the rotation angle between adjacent segment rings to the total vertical displacement, D _t is the width of the segment rings, k _sl is the inter-ring shear stiffness of the tunnel, and Q _L (l) is given by The direction of action is upward as positive, and Q _R (l) is positive when the direction of action is downward.

(3.2) According to Q _L (l) and Q _R (l), the resultant force F _sz (l) acting on the vertical ring of the segment on the segment ring at position l is obtained:

F _sz (l) = Q _R (l) - Q _L (l) (6)

(4) According to the vertical additional stress σ _az (θ,l) and the horizontal additional stress σ _ax (θ,l) on the cross section of the shield tunnel below obtained in step (2.2), calculate the different linings of the shield tunnel below. Additional load distribution in all directions of the section:

Among them, p _az (θ,l) is the vertical additional load of the lining of the upper half of the shield tunnel below, p′ _ax (θ,l) is the horizontal additional load of the left lining of the shield tunnel below, p″ _ax ( θ,l) is the horizontal additional load of the lining on the right side of the shield tunnel below.

Then, according to the distribution of additional loads in all directions on different parts of the shield tunnel lining below, a variation model of the additional confining pressure of the shield tunnel lining below is established:

Among them, F _sx is the resultant force between the rings in the horizontal direction, F _sz is the resultant force between the rings in the vertical direction, and Δq _R is the unloading amount of the vertical reaction force at the bottom of the arch.

(5) Select the calculated cross section of the shield tunnel below to be analyzed according to the evaluation requirements, add the additional load on the tunnel lining at the position of the calculated cross section obtained in step (4) and the vertical ring of the segment at the position of the calculated cross section obtained in step (3). The resultant force is introduced into the additional confining pressure variation model of the lower shield tunnel lining established in step (4), and the resultant force F _sx acting between the horizontal rings at the calculated section and the unloading amount Δq _R of the vertical reaction force at the bottom of the arch are obtained.

(6) According to the distribution of additional loads in all directions on different parts of the shield tunnel lining below and the unloading amount Δq _R of the vertical reaction force at the bottom of the arch, the additional confining pressure _par (θ) of the shield tunnel lining below after the deformation is stabilized is obtained. ,l):

Compared with the prior art, the beneficial effects of the present invention are:

(1) The present invention can be applied to the operating conditions of shield tunnels spanning the operation of foundation pits with different excavation sizes of foundation pits and different positional relationships;

(2) The present invention adopts the engineering geological and hydrological information and design parameters necessary for the corresponding project in the process of predicting the change of the confining pressure of the shield tunnel below before the excavation of the foundation pit construction, and does not need to increase the investment of additional survey and design costs.

(3) The invention can predict the confining pressure change of the shield tunnel below caused by the excavation of the foundation pit, and provide the theory for the stress of the tunnel structure, the loading test of the full-size shield segment and the operation safety of the subway tunnel under the corresponding working conditions Support; early warning of the possibility of excessive changes in confining pressure and force, preventing safety accidents, preventing and guiding the project, and saving construction costs.

Description of drawings

Figure 1 is a schematic diagram of the impact of foundation pit excavation on the shield tunnel below;

Figure 2 is a diagram showing the positional relationship between the foundation pit and the shield tunnel;

Figure 3 is a schematic diagram of the redistribution of the confining pressure of the tunnel under the additional load of the excavation of the foundation pit, wherein (a) is a schematic diagram of the first stage, (b) is a schematic diagram of the second stage, and (c) is a schematic diagram of the third stage;

Figure 4 is a schematic diagram of the initial load combination and the additional load combination, in which (a) is a schematic diagram of the load combination under the initial working condition of the tunnel, and (b) is a schematic diagram of the additional confining pressure of the tunnel lining after the tunnel is deformed and stabilized;

Figure 5 is a comparison diagram of the confining pressure before and after excavation of the foundation pit;

Figure 6 is a comparison diagram of the additional confining pressure of the shield tunnel caused by the excavation of the upper foundation pit;

Figure 7 is a comparison diagram of the measured and calculated values of the additional horizontal convergence deformation of the tunnel below caused by the excavation of the foundation pit.

Detailed ways

The present invention will be further described below through embodiments and accompanying drawings.

Figure 1 is a schematic diagram of the influence of foundation pit excavation on the shield tunnel below. As shown in Figure 1, the shield tunnel below the foundation pit project will not only cause longitudinal uplift and deformation of the axis of the shield tunnel below, but also affect the tunnel within the scope of influence. The lining section also produces global displacement and elliptical deformation. Fig. 2 is the positional relationship diagram of the foundation pit and the shield tunnel in the applicable working conditions of the present invention. As shown in Fig. 2, the upper foundation pit spans the lower shield tunnel, d is the excavation depth of the foundation pit, h is the buried depth of the tunnel, and D is the The outer diameter of the shield tunnel below, a is the horizontal distance between the center of the foundation pit and the tunnel axis.

A method for predicting the change of the additional confining pressure of the lower shield tunnel caused by the excavation of the foundation pit of the present invention comprises the following steps:

(1) According to the design data, as shown in Figures 1-2, a coordinate system is established at the center o of the foundation pit, the x-axis is perpendicular to the axis of the tunnel, the y-axis is parallel to the axis of the tunnel, and the z-axis is vertical Straight down is the positive direction.

(2) According to the coordinate system established in step 1, calculate the unloading of the excavation surface at the bottom of the foundation pit caused by the excavation of the foundation pit above, and obtain the vertical additional on the cross section of the shield tunnel below caused by the unloading of the excavation surface at the bottom of the foundation pit. Stress and horizontal additional stress distribution, including the following sub-steps:

(2.1) The unloading of the excavation surface at the bottom of the foundation pit is the uniformly distributed load vertically upward at the bottom of the foundation pit. Calculate the unloading p at the bottom of the foundation pit:

p=(1-α ₀ )γd (1)

Among them: γ is the soil weight, which is the weighted average value of the excavated soil layer above the foundation pit bottom; d is the foundation pit excavation depth; α ₀ is the residual stress coefficient, which can be used to consider the incomplete stress release at the foundation pit bottom Case.

(2.2) According to the Mindlin stress solution, taking the excavation surface at the bottom of the foundation pit as the integral area, calculate the vertical additional stress σ _az (θ, l ) and the additional horizontal stress σ _ax (θ,l) are:

Among them: θ is the position angle of the calculated point on the cross section of the shield tunnel below, the upper vertex is 0°, and the angle increases clockwise; B is the excavation size of the foundation pit along the x-axis direction; L is the foundation pit along the y-axis direction As shown in Figure 2, d is the excavation depth of the foundation pit, h is the buried depth of the tunnel, D is the outer diameter of the shield tunnel below, a is the horizontal distance between the center of the foundation pit and the tunnel axis; l is the tunnel axis The y-coordinate value corresponding to any point above in the coordinate system; x ₁ is the first integral variable, y ₁ is the second integral variable, σ _zz is the Mindlin vertical stress solution, and σ _xz is the Mindlin horizontal stress solution.

(3) According to the on-site monitoring data of the longitudinal deformation of the tunnel, combined with the vertical displacement of the tunnel, the distribution of the resultant force acting between the vertical rings of the segment is obtained, which specifically includes the following sub-steps:

(3.1) Measure the total vertical displacement w(l) of the tunnel along the longitudinal direction, measure the displacement caused by the rotation angle between the segment rings, and calculate the vertical inter-ring shear between the segment ring at l and the previous segment ring Shear force Q _L (l) and vertical inter-ring shear force Q _R (l) between the succeeding segment rings:

Q _L (l)=(1-j)[w(lD _t )-w(l)]×k _sl (4)

Q _R (l)=(1-j)[w(l)-w(lD _t )]×k _sl (5)

Among them, j is the ratio of the displacement caused by the rotation angle between adjacent segment rings to the total vertical displacement, D _t is the width of the segment rings, k _sl is the inter-ring shear stiffness of the tunnel, and Q _L (l) is given by The direction of action is upward as positive, and Q _R (l) is positive when the direction of action is downward.

(3.2) According to Q _L (l) and Q _R (l), the resultant force F _sz (l) acting on the vertical ring of the segment on the segment ring at position l is obtained:

F _sz (l) = Q _R (l) - Q _L (l) (6)

(4) Figure 3 is a schematic diagram of the tunnel confining pressure redistribution under the additional load of foundation pit excavation. The tunnel confining pressure redistribution is divided into three stages. The first stage is shown in Figure 3(a). The foundation pit excavation will cause the tunnel below. The vertical additional load p _az of the upper half of the lining and the horizontal additional loads p′ _ax and p″ _ax of the lining on the left and right sides, the vertical additional stress σ _az on the cross section of the shield tunnel below is obtained according to step (2.2). (θ,l) and the horizontal additional stress σ _ax (θ,l), calculate the additional load distribution in all directions on different parts of the shield tunnel lining below:

Among them, p _az (θ,l) is the vertical additional load of the lining of the upper half of the shield tunnel below, p′ _ax (θ,l) is the horizontal additional load of the left lining of the shield tunnel below, p″ _ax ( θ,l) is the horizontal additional load of the lining on the right side of the shield tunnel below.

In the second stage, as shown in Figure 3(b), the additional load destroys the confining pressure balance of the tunnel, the overall cross-section of the tunnel is displaced, and the longitudinal axis is deformed. Relative displacement occurs between adjacent segment rings due to uneven deformation in the longitudinal direction of the tunnel. Adjacent segment rings connected by longitudinal bolts restrain each other and generate inter-ring forces.

In the third stage, as shown in Figure 3(c), the unloading of the upper part of the tunnel will eventually be transmitted to the bottom through the structure, and the vertical reaction force of the arch bottom at the bottom of the tunnel will be partially unloaded. Acting on the lining in the straight direction, according to the additional load distribution in all directions of different parts of the shield tunnel lining below, establish the additional confining pressure variation model of the shield tunnel lining below:

Among them, F _sx is the resultant force between the rings in the horizontal direction, F _sz is the resultant force between the rings in the vertical direction, and Δq _R is the unloading amount of the vertical reaction force at the bottom of the arch.

(5) The horizontal displacement of the tunnel under the foundation pit and the horizontal force between the rings are mainly caused by the asymmetric unloading of the confining pressure of the entire ring of the tunnel in the horizontal direction, and considering the mutual influence of the longitudinal and lateral forces, the research The key to the change of the confining pressure of the tunnel below is to combine the longitudinal inter-ring force on the basis of the lateral force of the tunnel. Therefore, according to the evaluation requirements, select the calculated cross-section of the shield tunnel below to be analyzed, and use the calculated cross-section obtained in step (4) at the position of the tunnel. The additional load on the lining and the resultant force acting between the vertical rings of the segment at the calculated cross-section position obtained in step (3) are imported into the additional confining pressure variation model of the shield tunnel lining below established in step (4) to obtain the horizontal ring at the calculated cross-section. The resultant force F _sx and the unloading amount Δq _R of the vertical reaction force of the arch bottom.

(6) According to the distribution of additional loads in all directions on different parts of the shield tunnel lining below and the unloading amount Δq _R of the vertical reaction force at the bottom of the arch, the additional confining pressure _par (θ) of the shield tunnel lining below after the deformation is stabilized is obtained. ,l):

It should be noted that the invention obtains the additional confining pressure of the tunnel lining, and the initial confining pressure can be obtained from the load combination under the initial working condition of the tunnel. The load combination under the initial working condition of the tunnel considered in the present invention is shown in Fig. 4(a). The initial load combination in the figure includes: (1) the dead weight g of the lining; (2) the vertical earth pressure q of the overlying soil; (3) the lateral active earth pressure p _e ; (4) the hydrostatic pressure p _w ; (5) the arch bottom reaction force q _R ; (6) lateral soil resistance p _k after the segment ring is deformed under various loads. After the excavation of the foundation pit is completed, the additional confining pressure of the tunnel lining after the tunnel deformation is stabilized calculated according to the method of the present invention is shown in Figure 4(b). The initial confining pressure and the additional confining pressure are superimposed to obtain the final confining pressure value of the tunnel lining, which can be used to study the internal force and deformation response of the tunnel lining by applying the commonly used correction method or finite element analysis model.

Example

Taking the tunnel on the left line of Metro Line 1 on the first phase of the Yan'an Road-Renhe Road crossing in Hangzhou as an example: the excavation size of the foundation pit is L=11.4m, B=14.83m, and the excavation depth d=8.2m. The axial buried depth of the shield tunnel below is h=15.3m, the outer diameter of the shield tunnel lining is D=6.2m, and the ring width _Dt =1.2m; the segment rings are connected by 16 M30 longitudinal bolts. The buried depth of the groundwater level is about 1m, and the fluctuation of the water level during the construction process is small, and the change of the groundwater level is not considered in the calculation. The soil layer distribution and corresponding parameters are shown in Table 1. When calculating the excavation and unloading of the foundation pit, the residual stress coefficient is taken as α ₀ =0.3.

Table 1: Soil layer distribution and physical and mechanical parameters

The weighted average method is used to obtain the calculation parameters related to the soil: soil gravity γ(kN/m ³ ); cohesion C(kPa); internal friction angle Φ(°); soil Poisson's ratio μ. The horizontal distance l between the tunnel section and the excavation center of the foundation pit along the y-axis direction to be calculated.

According to the method of the present invention, the additional confining pressure _par (θ,l) of the tunnel lining after the deformation is stabilized is obtained.

Figure 5 is a comparison chart of the confining pressure before and after excavation of the foundation pit. According to the working conditions of this embodiment, the method of the present invention can be used to calculate the confining pressure of the tunnel before and after the excavation of the foundation pit, taking the section at l=0m below the excavation center as an example, as shown in Figure 5. Before the excavation of the foundation pit, since the water and soil pressure increases with the depth, the calculated confining pressure of the shield tunnel is small in the upper part and larger in the lower part, and is symmetrically distributed on the left and right. The vertex above is 0° and the angle increases clockwise. The change of confining pressure in the range of 0°～90° is small, between 218.46kPa～234.56kPa. The confining pressure increases gradually between 90° and 150°, and the confining pressure is the largest near 150°, about 272.45kPa. Since the foundation pit is located directly above the tunnel in this implementation, the confining pressure of the tunnel lining calculated according to the theoretical method of the present invention is still distributed symmetrically. As shown in Figure 5, after the excavation of the foundation pit, the confining pressure of the tunnel below the excavation center (at l=0m) is significantly reduced. The confining pressure unloading effect caused by the excavation of the foundation pit mainly acts near the vault and vault bottom of the tunnel lining below. Among them, the unloading effect of the tunnel vault (at 0°) is the most obvious, and the confining pressure is reduced from 218.46kPa before excavation to 161.92kPa, a decrease of 25.88%.

Figure 6 shows the additional confining pressure acting on the segment lining ring at different distances from the excavation center along the shield tunnel direction. As shown in the figure, the additional confining pressures are all negative values, that is, the excavation of the foundation pit mainly causes the confining pressure of the tunnel lining below to decrease. The area affected by the additional confining pressure is mainly near the top and bottom of the vault, and the absolute value of the additional confining pressure at the arch waist is small. The absolute value of the additional confining pressure at the tunnel lining vault below the excavation center of the foundation pit (l=0m) is the largest, which is 56.54kPa. As the horizontal distance from the excavation center increases, the absolute value of the additional confining pressure acting on the shield tunnel lining below decreases. Near the bottom of the excavation area, the absolute value of the additional confining pressure acting on the upper half of the shield tunnel lining is greater than that on the lower half. As the distance from the excavation area increases, the difference in the additional confining pressure between the upper and lower parts of the lining gradually decreases until it is located 7.2m away from the excavation center (l=7.2m), and the additional confining pressure at the top and bottom of the vault is basically Equivalent, -22.42kPa and -21.12kPa respectively. With the further increase of the distance from the excavation center, the absolute value of the additional load on the tunnel lining will change to the distribution of the lower large and the upper small.

It is difficult to obtain the confining pressure change data on the shield tunnel lining in the actual project. In order to verify the reliability of the method of the present invention, the initial confining pressure calculated by the theoretical method of the present invention and the additional confining pressure caused by the excavation of the foundation pit above and the inter-ring Forces are used as load combinations for structural force analysis in finite element models. The deformation of the segment ring at different positions can be obtained by calculation, and the measured values of the additional convergent deformation in the horizontal direction of each ring segment are compared. Figure 7 shows the comparison between the measured value and the calculated result of the additional horizontal convergence deformation of the lower tunnel caused by the excavation of the foundation pit in this case. A positive value indicates that the shield tunnel segment ring is compressed horizontally, and the arch waist radially converges and deforms, and the unit is mm. As shown in Fig. 7 , the horizontal convergence deformation values at various positions of the tunnel below calculated by the method of the present invention and its variation law along the longitudinal direction of the tunnel are basically consistent with the measured values, which verifies the reliability of the calculation results of the method of the present invention.

Claims (1)

1. a method for predicting the additional confining pressure variation of the shield tunnel below caused by excavation of foundation pit, is characterized in that, comprises the steps: (1) A coordinate system is established at the center o of the foundation pit, the x-axis is perpendicular to the axis of the tunnel, the y-axis is parallel to the axis of the tunnel, and the z-axis is vertically downward as the positive direction. (2) According to the coordinate system established in step 1, calculate the unloading of the excavation surface at the bottom of the foundation pit caused by the excavation of the upper foundation pit, and obtain the vertical additional on the cross section of the shield tunnel below caused by the unloading of the excavation surface at the bottom of the foundation pit. Stress and horizontal additional stress distribution, including the following sub-steps: (2.1) The unloading of the excavation surface at the bottom of the foundation pit is the uniformly distributed load vertically upward at the bottom of the foundation pit. Calculate the unloading p at the bottom of the foundation pit: p=(1-α ₀ )γd (1) Among them: γ is the soil weight, which is the weighted average of the excavated soil layers above the foundation pit bottom; d is the excavation depth of the foundation pit; α ₀ is the residual stress coefficient. (2.2) According to the Mindlin stress solution, taking the excavation surface at the bottom of the foundation pit as the integral area, calculate the vertical additional stress σ _az (θ, l ) and the additional horizontal stress σ _ax (θ,l) are:

Among them: θ is the position angle of the calculated point on the cross section of the shield tunnel below, the upper vertex is 0°, and the angle increases clockwise; B is the excavation size of the foundation pit along the x-axis direction; L is the foundation pit along the y-axis direction d is the excavation depth of the foundation pit; h is the buried depth of the tunnel; D is the outer diameter of the shield tunnel below; a is the horizontal distance between the center of the foundation pit and the tunnel axis, and l is any point on the tunnel axis in the The corresponding y coordinate value in the coordinate system; x ₁ is the first integral variable, y ₁ is the second integral variable, σ _zz is the Mindlin vertical stress solution, and σ _xz is the Mindlin horizontal stress solution. (3) According to the on-site monitoring data of the longitudinal deformation of the tunnel, combined with the vertical displacement of the tunnel, the distribution of the resultant force acting between the vertical rings of the segment is obtained, which specifically includes the following sub-steps: (3.1) Measure the total vertical displacement w(l) of the tunnel along the longitudinal direction, measure the displacement caused by the rotation angle between the segment rings, and calculate the vertical inter-ring shear between the segment ring at l and the previous segment ring Shear force Q _L (l) and vertical inter-ring shear force Q _R (l) between the succeeding segment rings: Q _L (l)=(1-j)[w(lD _t )-w(l)]×k _sl (4) Q _R (l)=(1-j)[w(l)-w(lD _t )]×k _sl (5) Among them, j is the ratio of the displacement caused by the rotation angle between adjacent segment rings to the total vertical displacement, D _t is the width of the segment rings, k _sl is the inter-ring shear stiffness of the tunnel, and Q _L (l) is given by The upward direction of action is positive, and Q _R (l) is positive when the action direction is downward. (3.2) According to Q _L (l) and Q _R (l), the resultant force F _sz (l) acting on the vertical ring of the segment on the segment ring at position l is obtained: F _sz (l) = Q _R (l) - Q _L (l) (6) (4) According to the vertical additional stress σ _az (θ,l) and the horizontal additional stress σ _ax (θ,l) on the cross section of the shield tunnel below obtained in step (2.2), calculate the different linings of the shield tunnel below. Additional load distribution in all directions of the section:

Among them, p _az (θ,l) is the vertical additional load of the lining of the upper half of the shield tunnel below, p′ _ax (θ,l) is the horizontal additional load of the left lining of the shield tunnel below, p″ _ax ( θ,l) is the horizontal additional load of the lining on the right side of the shield tunnel below. Then, according to the additional load distribution in all directions on different parts of the shield tunnel lining below, the additional confining pressure variation model of the shield tunnel lining below is established:

Among them, F _sx is the resultant force between the rings in the horizontal direction, F _sz is the resultant force between the rings in the vertical direction, and Δq _R is the unloading amount of the vertical reaction force at the bottom of the arch. (5) Select the calculated cross section of the shield tunnel below to be analyzed according to the evaluation requirements, add the additional load on the tunnel lining at the position of the calculated cross section obtained in step (4) and the vertical ring of the segment at the position of the calculated cross section obtained in step (3). The resultant force is introduced into the additional confining pressure variation model of the lower shield tunnel lining established in step (4), and the resultant force F _sx acting between the horizontal rings at the calculated section and the unloading amount Δq _R of the vertical reaction force at the bottom of the arch are obtained.

(6) According to the distribution of additional loads in all directions on different parts of the shield tunnel lining below and the unloading amount Δq _R of the vertical reaction force at the bottom of the arch, the additional confining pressure _par (θ) of the shield tunnel lining below after the deformation is stabilized is obtained. ,l):

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