Calculation method for predicting subway tunnel operation deformation caused by stacked line shield construction

Abstract

The invention discloses a calculation method for predicting operation subway tunnel deformation caused by overlapped line shield construction, and the method comprises the following steps: obtaining soil body real source deformation caused by a shield tunnel based on a two-dimensional plane strain model and a mirror image source sink principle; performing superposition correction on the real source and the mirror image source to obtain a plane strain correction formula of any point; solving the soil displacement of an operation tunnel node during the lower hole construction period of the stacked line tunnel; the soil body displacement is converted into an additional load to act on the operation tunnel structure, and a first operation subway tunnel predicted deformation value caused by lower tunnel construction is obtained; solving the soil body displacement of the operation tunnel node during the upper hole construction period of the stacked line tunnel; and converting the soil body displacement into an additional load to act on a calculation result of the upper stage, and obtaining a predicted deformation value of the operating subway tunnel caused by upper hole construction. The invention provides an important calculation method for deformation prediction in the design construction process. The method is safe, efficient and rapid in calculation.

Description

Technical Field

[0001] The present invention belongs to the field of tunnel engineering, and particularly relates to a calculation method for predicting the deformation of an operating subway tunnel caused by the construction of overlapping shield tunnels. Background Art

[0002] The long-distance proximity of overlapping shield tunnels to an operating subway tunnel is a very complex engineering problem. During the engineering implementation process, a practical method is needed to predict the deformation amount of the operating subway tunnel caused by the construction of the overlapping tunnels, so as to adjust the construction parameters in a timely manner and ensure the safety of the operating subway. Existing research mainly focuses on the soil deformation caused by shield construction, including empirical methods (Peck formula and improved formulas), theoretical calculation methods, numerical calculation methods, experimental methods, field measurement methods, etc., but there is no deformation prediction method for operating subway tunnels. The deficiencies of existing research are as follows: Firstly, the Peck formula is an empirical formula that can only calculate the surface settlement and cannot calculate the deep soil displacement; Secondly, most of the existing relevant theoretical formulas are extremely complex and cannot calculate the deep soil displacement; Thirdly, the numerical method requires re-modeling and calculation for each construction step, and the workload and calculation amount are extremely large. In reality, no relevant project continuously uses it for prediction; Fourthly, the experimental method targets few working conditions, costs a high amount of money, and takes a long time, and cannot meet the engineering needs; Fifthly, the field measurement method cannot predict in advance. It takes emergency measures afterwards and cannot meet the purpose of advance prediction.

[0003] In view of the blank in the existing technical field and the actual needs of existing projects, therefore, it is urgent and necessary to solve such practical difficulties. Summary of the Invention

[0004] The present invention is proposed to solve the problems existing in the prior art, and its purpose is to provide a calculation method for predicting the deformation of an operating subway tunnel caused by the construction of overlapping shield tunnels.

[0005] The technical solution of the present invention is: a calculation method for predicting the deformation of an operating subway tunnel caused by the construction of overlapping shield tunnels, including the following steps: A. Based on the two-dimensional plane strain model and the principle of mirror sources and sinks, obtain the true source deformation of the soil caused by the shield tunnel; B. Superimpose and correct the true source and the mirror source to obtain the plane strain correction formula for any point; C. According to the plane strain correction formula, solve the soil displacement of the operating tunnel nodes during the construction period of the lower tunnel of the overlapping tunnels; D. Convert the soil displacement obtained in step C into an additional load acting on the operating tunnel structure to obtain the predicted deformation value of the operating subway tunnel caused by the construction of the lower tunnel; E. Solve for the soil displacement of the nodes of the operating tunnel during the construction of the upper tunnel of the overlapping tunnels according to the plane strain correction formula; F. Convert the soil displacement obtained in step E into an additional load and apply it to the calculation result of step D to obtain the predicted deformation value of the operating subway tunnel caused by the construction of the upper tunnel.

[0006] Furthermore, step A is based on the two-dimensional plane strain model and the principle of mirror sources and sinks to obtain the true source deformation of the soil caused by the shield tunnel. The specific process is as follows: First, the ground loss caused by shield construction is equivalent to a three-dimensional point source; Then, according to the theory of elasticity, establish a displacement field model caused by a point source in an infinite elastic body; Next, in the project of overlapping tunnels with a long distance adjacent to the operating subway tunnel, the overlapping tunnels are long line sources and are equivalent to a two-dimensional plane strain model; Finally, convert the three-dimensional point source formula into a two-dimensional line source to obtain the true source deformation of the soil.

[0007] Furthermore, step B superimposes and corrects the true source and the mirror source to obtain the plane strain correction formula for any point. The specific process is as follows: First, obtain the soil mirror source deformation according to the true source deformation of the soil obtained in step A; Then, superimpose the true source deformation of the soil and the mirror source deformation of the soil; Finally, obtain the plane strain correction formula for any point after superposition.

[0008] Furthermore, step C solves for the soil displacement of the nodes of the operating tunnel during the construction of the lower tunnel of the overlapping tunnels according to the plane strain correction formula. The specific process is as follows: First, divide the segment lining of the operating subway tunnel to obtain unit linings; Then, obtain the intersection points of the unit linings and confirm the intersection points as nodes; Next, confirm the relative distance coordinates of the nodes; Finally, according to the relative distance coordinates and the plane strain correction formula, obtain the soil displacement of the nodes of the operating tunnel during the construction of the lower tunnel of the overlapping tunnels.

[0009] Furthermore, divide the segment lining of the operating subway tunnel to obtain unit linings. The specific process is as follows: Divide the segment lining of the operating subway tunnel every 1 m to obtain a number of unit linings.

[0010] Furthermore, confirm the relative distance coordinates of the nodes. The specific process is as follows: The intersection point of the unit lining is node i, and the relative distance coordinates of node i are (D i, L i ).

[0011] Furthermore, step D converts the soil displacement obtained in step C into an additional load acting on the operating tunnel structure, and obtains the predicted deformation value of the first operating subway tunnel caused by the lower tunnel construction. The specific process is as follows: First, based on the soil displacement obtained in step C, the first additional load acting on the operating tunnel structure is obtained; Then, the water and soil load model is obtained; Finally, the first additional load is superimposed with the water and soil load model, and the load - structure model calculation is carried out to obtain the predicted deformation value of the first operating subway tunnel.

[0012] Furthermore, step E solves the soil displacement of the operating tunnel nodes during the upper tunnel construction period of the overlapping tunnels according to the plane strain correction formula. The specific process is as follows: First, the relative distance coordinates of node i after the lower tunnel construction are (D ii , L ii ); Then, based on the plane strain correction formula, the soil displacement of the operating tunnel nodes during the upper tunnel construction period of the overlapping tunnels is obtained.

[0013] Furthermore, step F converts the soil displacement obtained in step E into an additional load acting on the calculation result of step D, and obtains the predicted deformation value of the operating subway tunnel caused by the lower tunnel construction. The specific process is as follows: First, based on the soil displacement of the operating tunnel nodes during the upper tunnel construction period of the overlapping tunnels, the second additional load is obtained; Then, the second additional load is applied to the calculation result of step D to obtain the final predicted deformation value of the operating subway tunnel.

[0014] The beneficial effects of the present invention are as follows: Aiming at the blank of the existing technology, the present invention solves the problem of deformation prediction of long - distance adjacent operating subway tunnels, and provides an important tool for deformation prediction in the design and construction process. At the same time, this method is safe, efficient, and fast in calculation, can be widely used in engineering, and solves the problems of complex calculation, long time consumption, and unsatisfactory results of the existing theoretical formulas. Description of the Drawings

[0015] Figure 1 is the flow chart of the method of the present invention; Figure 2 is the coordinate schematic diagram of the two - dimensional overlapping tunnels with long - distance adjacent operating subway tunnels in the present invention; Figure 3 is the relative distance coordinate schematic diagram of the operating subway tunnel in the present invention; Figure 4It is a schematic diagram of the additional load on the operating subway tunnel during the construction of the lower tunnel in the present invention; Figure 5 It is a superposition schematic diagram during the construction of the lower tunnel in the present invention; Figure 6 It is a schematic diagram of the additional load on the operating subway tunnel during the construction of the upper tunnel in the present invention; Figure 7 It is a superposition schematic diagram during the construction of the upper tunnel in the present invention. Specific embodiments

[0016] Hereinafter, the present invention will be described in detail with reference to the drawings and embodiments: As Figures 1 to 7 shown, a calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling includes the following steps: A. Based on the two-dimensional plane strain model and the principle of mirror sources and sinks, obtain the true source deformation of the soil mass caused by the shield tunnel; B. Superpose and correct the true source and the mirror source to obtain the plane strain correction formula for any point; C. According to the plane strain correction formula, solve the soil displacement of the nodes of the operating tunnel during the construction period of the lower tunnel of the overlapping tunnel; D. Convert the soil displacement obtained in step C into an additional load acting on the operating tunnel structure to obtain the predicted deformation value of the operating subway tunnel caused by the construction of the lower tunnel; E. According to the plane strain correction formula, solve the soil displacement of the nodes of the operating tunnel during the construction period of the upper tunnel of the overlapping tunnel; F. Convert the soil displacement obtained in step E into an additional load acting on the calculation result of step D to obtain the predicted deformation value of the operating subway tunnel caused by the construction of the upper tunnel.

[0017] Step A is based on the two-dimensional plane strain model and the principle of mirror sources and sinks to obtain the true source deformation of the soil mass caused by the shield tunnel. The specific process is as follows: First, the ground loss caused by shield construction is equivalent to a three-dimensional point source; Then, according to the theory of elasticity, establish a displacement field model caused by a point source in an infinite elastic body; Furthermore, in the project of the overlapping tunnel being close to the operating subway tunnel over a long distance, the overlapping tunnel is a long line source and is equivalent to a two-dimensional plane strain model; Finally, convert the three-dimensional point source formula into a two-dimensional line source to obtain the true source deformation of the soil mass.

[0018] Step B superposes and corrects the true source and the mirror source to obtain the plane strain correction formula for any point. The specific process is as follows: First, according to the true source deformation of the soil mass obtained in step A, obtain the mirror source deformation of the soil mass; Then, the true source deformation of the soil mass and the mirror source deformation of the soil mass are superimposed; Finally, the plane strain correction formula for any point is obtained after superposition.

[0019] In step C, according to the plane strain correction formula, the soil displacement of the nodes of the operating tunnel during the construction period of the lower tunnel of the overlapping tunnels is solved. The specific process is as follows: First, the segment lining of the operating subway tunnel is divided to obtain unit linings; Then, the intersection points of the unit linings are obtained, and the intersection points are confirmed as nodes; Next, the relative distance coordinates of the nodes are confirmed; Finally, according to the relative distance coordinates and the plane strain correction formula, the soil displacement of the nodes of the operating tunnel during the construction period of the lower tunnel of the overlapping tunnels is obtained.

[0020] The segment lining of the operating subway tunnel is divided to obtain unit linings. The specific process is as follows: The segment lining of the operating subway tunnel is divided every 1 m to obtain a number of unit linings.

[0021] The relative distance coordinates of the nodes are confirmed. The specific process is as follows: The intersection point of the unit lining is node i, and the relative distance coordinates of node i are (D i , L i ).

[0022] In step D, the soil displacement obtained in step C is converted into an additional load acting on the operating tunnel structure, and the predicted deformation value of the first operating subway tunnel caused by the construction of the lower tunnel is obtained. The specific process is as follows: First, based on the soil displacement obtained in step C, the first additional load acting on the operating tunnel structure is obtained; Then, the water and soil load model is obtained; Finally, the first additional load is superimposed with the water and soil load model, and the load - structure model calculation is carried out to obtain the predicted deformation value of the first operating subway tunnel.

[0023] In step E, according to the plane strain correction formula, the soil displacement of the nodes of the operating tunnel during the construction period of the upper tunnel of the overlapping tunnels is solved. The specific process is as follows: First, the relative distance coordinates of node i after the construction of the lower tunnel are (D ii , L ii ); Then, based on the plane strain correction formula, the soil displacement of the nodes of the operating tunnel during the construction period of the upper tunnel of the overlapping tunnels is obtained.

[0024] Step F converts the soil displacement obtained in Step E into an additional load and applies it to the calculation result of Step D to obtain the predicted deformation value of the operating subway tunnel caused by the lower tunnel construction. The specific process is as follows: First, based on the soil displacement of the operating tunnel nodes during the upper tunnel construction period of the overlapping tunnels, a second additional load is obtained; Then, the second additional load is applied to the calculation result of Step D to obtain the final predicted deformation value of the operating subway tunnel. Embodiment

[0025] A calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling, comprising the following steps: A. Based on the two-dimensional plane strain model and the principle of mirror sources and sinks, the true source deformation of the soil caused by the shield tunnel is obtained; B. The true source and the mirror source are superimposed and corrected to obtain the plane strain correction formula for any point; C. According to the plane strain correction formula, the soil displacement of the operating tunnel nodes during the lower tunnel construction period of the overlapping tunnels is solved; D. The soil displacement obtained in Step C is converted into an additional load and applied to the operating tunnel structure to obtain the first predicted deformation value of the operating subway tunnel caused by the lower tunnel construction; E. According to the plane strain correction formula, the soil displacement of the operating tunnel nodes during the upper tunnel construction period of the overlapping tunnels is solved; F. The soil displacement obtained in Step E is converted into an additional load and applied to the calculation result of Step D to obtain the predicted deformation value of the operating subway tunnel caused by the lower tunnel construction.

[0026] Specifically, Step A is based on the two-dimensional plane strain model and the principle of mirror sources and sinks to obtain the true source deformation of the soil caused by the shield tunnel, as follows: In a semi-infinite elastic space, the ground surface is a free boundary, that is, the normal stress is zero. The ground loss caused by shield construction is equivalent to a three-dimensional point source, and its volume is , located at a depth of H, with coordinates (0, H, 0), as Figure 2 shown.

[0027] The equivalent of ground loss simplifies the ground loss caused by shield construction into a uniformly shrinking virtual volume source.

[0028] Then the volume of ground loss per unit length is:

[0029] where A is the ground loss area, is the outer diameter of the overlapping tunnels, is the inner diameter of the overlapping tunnels, and η is the ground loss rate.

[0030]

[0031] Among them, M is the physical gap after considering grouting filling, and U is the equivalent three-dimensional radial displacement. is a parameter related to the construction quality and can be taken as .

[0032]

[0033] Among them, is the thickness of the shield tail wall, about 0.1 m, is the space of the assembled lining.

[0034]

[0035] Among them, R is the tunnel radius, is the elastic modulus of the soil at the tunnel axis; is the original soil pressure and cutting pressure at the tunnel axis, is the dimensionless displacement factor and can be taken as 1.12.

[0036] According to the theory of elasticity, the displacement field caused by a point source in an infinite elastic body is:

[0037] Among them, G = E / 2(1 + ν) is the shear modulus, r is the distance from the observation point (D, L, y) to the point source, E is the elastic modulus of the soil, and ν is the Poisson's ratio.

[0038] For the project of long-distance adjacent operating subway tunnels with overlapping tunnels, it can be known that the overlapping tunnels are long line sources and can be simplified into a two-dimensional plane strain model.

[0039] Convert the three-dimensional point source formula into a two-dimensional line source integral:

[0040] The integral result is:

[0041] Among them, is the displacement of the point source in the x direction, is the displacement of the point source in the z direction.

[0042] Specifically, in step B, the real source and the image source are superimposed and corrected to obtain the plane strain correction formula for any point, as follows: The displacement of the image source Z = -H. According to step A, its displacement field is:

[0043] Among them, is the displacement of the image source in the x direction, is the displacement of the image source in the z direction.

[0044] Superpose the displacements of the real source and the mirror source to obtain the plane strain correction formula:

[0045] Among them, is the displacement in the x direction after superposition, is the displacement in the z direction after superposition.

[0046] is the average elastic modulus of the soil mass:

[0047] Among them, is the elastic model of soil layer i, is the thickness of soil layer i.

[0048] Specifically, step C solves the soil displacement of the operation tunnel nodes during the construction period of the lower tunnel of the superimposed line tunnel according to the plane strain correction formula, as follows: Divide the segment lining of the operating subway tunnel into several unit linings every 1 m. The intersection points of the unit linings are node i, and the relative distance coordinates of node i are (D i , L i ). As shown in Figure 3 , it can be seen from step B that the soil displacement at each node is:

[0049] Among them, is the displacement in the x direction during the construction of the lower tunnel at node i, is the displacement in the z direction during the construction of the lower tunnel at node i.

[0050] Specifically, step D converts the soil displacement obtained in step C into an additional load acting on the operating tunnel structure to obtain the predicted deformation value of the first operating subway tunnel caused by the construction of the lower tunnel, as follows: It can be seen from step C that the displacement of each node is , then the additional load acting on the operating tunnel structure is:

[0051] Among them, is the coefficient of subgrade reaction in the x direction within the length of the soil element, is the coefficient of subgrade reaction in the z direction within the length of the soil element, is the additional load in the x direction during the construction of the lower tunnel at node i, is the additional load in the z direction during the construction of the lower tunnel at node i.

[0052] When it is a tensile force, its value is set to 0, as Figure 4 shown.

[0053] Superimpose the soil and water loads to conduct the load - structure model calculation, and obtain the predicted deformation value of the operating subway tunnel , as Figure 5 shown.

[0054] Specifically, step E solves the soil displacement of the nodes of the operating tunnel during the construction period of the upper - hole of the overlapping tunnels according to the plane - strain correction formula, as follows: According to step C, it can be known that the soil displacement at each node caused during the construction of the upper - hole is:

[0055] Among them, is the displacement in the x - direction during the construction of the upper - hole of the i - node, is the displacement in the z - direction during the construction of the upper - hole of the i - node.

[0056] Specifically, step F converts the soil displacement obtained in step E into additional loads and applies them to the calculation result of step D to obtain the predicted deformation value of the operating subway tunnel caused by the construction of the lower - hole, as follows: It can be known from step E that the displacement of each node is , then the additional load acting on the operating tunnel structure is:

[0057] Among them, is the subgrade coefficient in the x - direction within the soil element length, is the subgrade coefficient in the z - direction within the soil element length, is the additional load in the x - direction during the construction of the upper - hole of the i - node, is the additional load in the z - direction during the construction of the upper - hole of the i - node.

[0058] Specifically, when and are tensile forces, their values are set to 0, as Figure 6 shown.

[0059] Apply and to the calculation result of step D to obtain the predicted deformation value of the operating subway tunnel, as Figure 7 shown.

[0060] Aiming at the blank in the prior art, the present invention solves the problem of deformation prediction of adjacent operating subway tunnels over long distances, and provides an important tool for deformation prediction in the design and construction process. At the same time, this method is safe, efficient, and fast in calculation, can be widely used in engineering applications, and solves the problems of complex calculation, long time consumption, and unsatisfactory results of existing theoretical formulas.

Claims

1. A calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling, characterized in that: It includes the following steps: A. Based on the two-dimensional plane strain model and the principle of mirror source and sink, obtain the true source deformation of the soil caused by the shield tunnel; B. Superpose and correct the true source and the mirror source to obtain the plane strain correction formula for any point; C. According to the plane strain correction formula, solve the soil displacement of the operation tunnel node during the construction period of the lower tunnel of the overlapping tunnels; D. Convert the soil displacement obtained in step C into an additional load acting on the operation tunnel structure to obtain the predicted deformation value of the first operation subway tunnel caused by the construction of the lower tunnel; E. According to the plane strain correction formula, solve the soil displacement of the operation tunnel node during the construction period of the upper tunnel of the overlapping tunnels; F. Convert the soil displacement obtained in step E into an additional load acting on the calculation result of step D to obtain the predicted deformation value of the operation subway tunnel caused by the construction of the upper tunnel.

2. The calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling according to claim 1, characterized in that: Step A, based on the two-dimensional plane strain model and the principle of mirror source and sink, obtains the true source deformation of the soil caused by the shield tunnel. The specific process is as follows: First, equivalent the ground loss caused by shield construction to a three-dimensional point source; Then, according to the theory of elasticity, establish a displacement field model caused by the point source in an infinite elastic body; Next, in the project of the overlapping tunnels with a long distance adjacent to the operation subway tunnel, the overlapping tunnels are long line sources and are equivalent to a two-dimensional plane strain model; Finally, convert the three-dimensional point source formula into a two-dimensional line source to obtain the true source deformation of the soil.

3. A calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling according to claim 1, characterized in that: Step B superposes and corrects the true source and the mirror source to obtain the plane strain correction formula for any point. The specific process is as follows: First, according to the true source deformation of the soil obtained in step A, obtain the mirror source deformation of the soil; Then, superpose the true source deformation of the soil and the mirror source deformation of the soil; Finally, the plane strain correction formula for any point is obtained after superposition.

4. The calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling according to claim 1, characterized in that: Step C, according to the plane strain correction formula, solves the soil displacement of the operation tunnel node during the construction period of the lower tunnel of the overlapping tunnels. The specific process is as follows: First, divide the segment lining of the operation subway tunnel to obtain the unit lining; Then, obtain the intersection points of the unit lining and confirm the intersection points as nodes; Next, confirm the relative distance coordinates of the nodes; Finally, according to the relative distance coordinates and the plane strain correction formula, obtain the soil displacement of the operation tunnel node during the construction period of the lower tunnel of the overlapping tunnels.

5. A calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling according to claim 4, characterized in that: The process of dividing the segment lining of the operation subway tunnel to obtain the unit lining is as follows: Divide the segment lining of the operation subway tunnel every 1m to obtain several unit linings.

6. The calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling according to claim 1, characterized in that: The process of confirming the relative distance coordinates of the nodes is as follows: The intersection point of the unit linings is node i, and the relative distance coordinates of node i are (D i , L i ).

7. A calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling according to claim 1, characterized in that: Step D converts the soil displacement obtained in step C into an additional load acting on the operation tunnel structure to obtain the predicted deformation value of the operation subway tunnel caused by the construction of the lower tunnel. The specific process is as follows: First, based on the soil displacement obtained in step C, obtain the first additional load acting on the operation tunnel structure; Then, obtain the water and soil load model; Finally, superpose the first additional load and the water and soil load model and perform load-structure model calculation to obtain the predicted deformation value of the first operation subway tunnel.

8. A calculation method for predicting the deformation of an operating subway tunnel caused by the construction of an overlapping shield according to claim 7, characterized in that: Step E, according to the plane strain correction formula, solves the soil displacement of the operation tunnel node during the construction period of the upper tunnel of the overlapping tunnels. The specific process is as follows: First, the relative distance coordinates of node i after the lower tunnel construction are (D ii , L ii ); Then, based on the plane strain correction formula, the soil displacement of the operation tunnel nodes during the construction period of the upper tunnel of the overlapping tunnels is obtained.

9. The calculation method for predicting the deformation of an operating subway tunnel caused by overlapping shield tunneling according to claim 1, characterized in that: In step F, the soil displacement obtained in step E is converted into an additional load and applied to the calculation result in step D to obtain the predicted deformation value of the operation subway tunnel caused by the construction of the lower tunnel. The specific process is as follows: First, based on the soil displacement of the operation tunnel nodes during the construction period of the upper tunnel of the overlapping tunnels, a second additional load is obtained. Then, the second additional load is applied to the calculation result in step D to obtain the final predicted deformation value of the operation subway tunnel.

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