A computational method for predicting deformation of operating subway tunnels caused by stacked shield construction

Abstract

The present invention discloses a calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction, comprising the following steps: based on a two-dimensional plane strain model and the mirror source-sink principle, deriving the true source deformation of the soil caused by the shield tunnel; superimposing and correcting the true source and the mirror source to derive a plane strain correction formula for any point; solving the soil displacement of the operating tunnel node during the stacked tunnel lower hole construction period; converting the soil displacement into an additional load acting on the operating tunnel structure to derive the predicted deformation value of the first operating subway tunnel caused by the lower hole construction; solving the soil displacement of the operating tunnel node during the stacked tunnel upper hole construction period; converting the soil displacement into an additional load acting on the calculation result of the previous stage to derive the predicted deformation value of the operating subway tunnel caused by the upper hole construction. The present invention provides an important calculation method for deformation prediction during the design and construction process. The present invention is safe, efficient, and fast in calculation.

Description

Technical Field

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

[0002] The construction of a stacked shield tunnel over long distances adjacent to an operating subway tunnel is a complex engineering problem. During project implementation, practical methods are needed to predict the deformation of the operating subway tunnel caused by the stacked tunnel construction, allowing for timely adjustment of construction parameters to ensure the safety of the operating subway. Existing research primarily focuses on soil deformation caused by shield construction, using empirical methods (Peck's formula and its improved formula), theoretical calculations, numerical calculations, experiments, and field measurements. However, there is no method for predicting deformation of operating subway tunnels. However, the shortcomings of existing research include the following:

[0003] First, the Peck formula is an empirical formula that can only calculate surface settlement but not deep soil displacement;

[0004] Second, the existing theoretical formulas are mostly complex and cannot calculate the displacement of deep soil.

[0005] Third, numerical methods require re-modeling and calculation at each construction step, which is extremely labor-intensive and computationally intensive. In reality, no relevant projects have consistently adopted prediction methods.

[0006] Fourth, the experimental method targets few working conditions, is expensive and time-consuming, and cannot meet engineering needs;

[0007] Fifth, the on-site measurement method cannot make predictions in advance and requires emergency measures to be taken after the fact, which cannot meet the purpose of making predictions in advance.

[0008] In view of the gaps in existing technical fields and the actual needs of existing projects, it is urgent and necessary to solve such practical difficulties. Summary of the Invention

[0009] 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 stacked shield construction.

[0010] The technical solution of the present invention is: a calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction, comprising the following steps:

[0011] A. Based on the two-dimensional plane strain model and the mirror source-sink principle, the true source deformation of the soil caused by the shield tunnel is obtained;

[0012] B. Superimpose and correct the real source and the mirror image source to obtain the plane strain correction formula for any point;

[0013] C. Using the plane strain correction formula, calculate the soil displacement of the operational tunnel nodes during the construction period of the superimposed tunnel;

[0014] D. Convert the soil displacement obtained in step C into an additional load and apply it to the operating tunnel structure to obtain the predicted deformation value of the operating subway tunnel caused by the tunnel construction;

[0015] E. Using the plane strain correction formula, calculate the soil displacement of the operational tunnel nodes during the construction period of the upper tunnel of the superimposed tunnel;

[0016] F. Convert the soil displacement obtained in step E into an additional load and apply it to the calculation result in step D to obtain the predicted deformation value of the operating subway tunnel caused by the upper hole construction.

[0017] Furthermore, step A is based on the two-dimensional plane strain model and the mirror source-sink principle to obtain the true source deformation of the soil caused by the shield tunnel. The specific process is as follows:

[0018] First, the ground loss caused by shield construction is equivalent to a three-dimensional point source;

[0019] Then, based on the theory of elasticity, a displacement field model caused by a point source in an infinite elastic body is established;

[0020] Later, in the long-distance adjacent operation subway tunnel project, the superimposed tunnel is a long-line source, which is equivalent to a two-dimensional plane strain model;

[0021] Finally, the three-dimensional point source formula is converted into a two-dimensional line source to obtain the true source deformation of the soil.

[0022] Furthermore, step B superimposes and corrects the real source and the mirror source to obtain the plane strain correction formula of any point. The specific process is as follows:

[0023] First, the soil image source deformation is obtained based on the real source deformation of the soil obtained in step A;

[0024] Then, the soil real source deformation and soil mirror source deformation are superimposed;

[0025] Finally, the plane strain correction formula of any point is obtained after superposition.

[0026] Furthermore, in step C, the soil displacement of the operating tunnel node during the construction period of the superimposed tunnel is solved based on the plane strain correction formula. The specific process is as follows:

[0027] First, the segmental lining of the operating subway tunnel is divided into unit linings.

[0028] Then, the intersection points of the unit linings are obtained and confirmed as nodes;

[0029] Then, confirm the relative distance coordinates of the nodes;

[0030] Finally, based on the relative distance coordinates and plane strain correction formula, the soil displacement of the operating tunnel node during the construction period of the superimposed tunnel is obtained.

[0031] Furthermore, the segmental lining of the operating subway tunnel is divided into unit linings. The specific process is as follows:

[0032] The segmental lining of an operating subway tunnel is divided into sections of 1m each to obtain several unit linings.

[0033] Furthermore, to confirm the relative distance coordinates of the nodes, the specific process is as follows:

[0034] The intersection point of the unit lining is node i, and the relative distance coordinate of node i is (D i , L i ).

[0035] Furthermore, 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 tunnel construction. The specific process is as follows:

[0036] First, based on the soil displacement obtained in step C, the first additional load acting on the operating tunnel structure is obtained;

[0037] Then, the water and soil load model is obtained;

[0038] Finally, the first additional load is superimposed on the water-soil load model, and the load-structure model calculation is performed to obtain the predicted deformation value of the first operating subway tunnel.

[0039] Furthermore, in step E, the soil displacement of the operating tunnel node during the construction period of the upper tunnel of the superimposed tunnel is solved according to the plane strain correction formula. The specific process is as follows:

[0040] First, the relative distance coordinate of node i after the tunnel construction is obtained as (D ii , L ii );

[0041] Then, based on the plane strain correction formula, the soil displacement of the operating tunnel node during the construction period of the upper tunnel of the superimposed tunnel is obtained.

[0042] Furthermore, 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 tunnel construction. The specific process is as follows:

[0043] First, the second additional load is obtained based on the soil displacement of the operating tunnel node during the construction period of the superimposed tunnel upper hole.

[0044] 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.

[0045] The beneficial effects of the present invention are as follows:

[0046] This invention addresses the existing technical gap by solving the challenge of deformation prediction for long-distance adjacent subway tunnels, providing an important tool for deformation prediction during design and construction. Furthermore, this method is computationally secure, efficient, and rapid, enabling widespread application in engineering projects. It addresses the complex, time-consuming, and unsatisfactory results inherent in existing theoretical formulas. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flow chart of the method of the present invention;

[0048] Figure 2 This is a coordinate diagram of a two-dimensional superimposed tunnel in the present invention that is close to an operating subway tunnel over a long distance;

[0049] Figure 3 This is a schematic diagram of relative distance coordinates of operating subway tunnels in the present invention;

[0050] Figure 4 This is a schematic diagram of the additional load on an operating subway tunnel during lower tunnel construction in the present invention;

[0051] Figure 5 This is a schematic diagram of the superposition of the lower tunnel construction in the present invention;

[0052] Figure 6 This is a schematic diagram of the additional load on an operating subway tunnel during upper tunnel construction in the present invention;

[0053] Figure 7 It is a superimposed schematic diagram during the upper hole construction in the present invention. DETAILED DESCRIPTION

[0054] Hereinafter, the present invention will be described in detail with reference to the accompanying drawings and embodiments:

[0055] like Figures 1 to 7 As shown, a calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction includes the following steps:

[0056] A. Based on the two-dimensional plane strain model and the mirror source-sink principle, the true source deformation of the soil caused by the shield tunnel is obtained;

[0057] B. Superimpose and correct the real source and the mirror image source to obtain the plane strain correction formula for any point;

[0058] C. Using the plane strain correction formula, calculate the soil displacement of the operational tunnel nodes during the construction period of the superimposed tunnel;

[0059] D. Convert the soil displacement obtained in step C into an additional load and apply it to the operating tunnel structure to obtain the predicted deformation value of the operating subway tunnel caused by the tunnel construction;

[0060] E. Using the plane strain correction formula, calculate the soil displacement of the operational tunnel nodes during the construction period of the upper tunnel of the superimposed tunnel;

[0061] F. Convert the soil displacement obtained in step E into an additional load and apply it to the calculation result in step D to obtain the predicted deformation value of the operating subway tunnel caused by the upper hole construction.

[0062] Step A is based on a two-dimensional plane strain model and the mirror source-sink principle to derive the true source deformation of the soil caused by the shield tunnel. The specific process is as follows:

[0063] First, the stratum loss caused by shield construction is equivalent to a three-dimensional point source;

[0064] Then, based on the theory of elasticity, a displacement field model caused by a point source in an infinite elastic body is established;

[0065] Later, in the long-distance adjacent operation subway tunnel project, the superimposed tunnel is a long-line source, which is equivalent to a two-dimensional plane strain model;

[0066] Finally, the three-dimensional point source formula is converted into a two-dimensional line source to obtain the true source deformation of the soil.

[0067] Step B superimposes and corrects the real source and the mirror image source to obtain the plane strain correction formula for any point. The specific process is as follows:

[0068] First, the soil image source deformation is obtained based on the real source deformation of the soil obtained in step A;

[0069] Then, the soil real source deformation and soil mirror source deformation are superimposed;

[0070] Finally, the plane strain correction formula of any point is obtained after superposition.

[0071] In step C, the soil displacement of the operational tunnel nodes during the construction period of the superimposed tunnel is calculated based on the plane strain correction formula. The specific process is as follows:

[0072] First, the segmental lining of the operating subway tunnel is divided into unit linings;

[0073] Then, the intersection points of the unit linings are obtained and confirmed as nodes;

[0074] Then, confirm the relative distance coordinates of the nodes;

[0075] Finally, based on the relative distance coordinates and plane strain correction formula, the soil displacement of the operating tunnel node during the construction period of the superimposed tunnel is obtained.

[0076] The segmental lining of an operating subway tunnel is divided into unit linings. The specific process is as follows:

[0077] The segmental lining of an operating subway tunnel is divided into sections of 1m each to obtain several unit linings.

[0078] Confirm the relative distance coordinates of the nodes. The specific process is as follows:

[0079] The intersection point of the unit lining is node i, and the relative distance coordinate of node i is (D i , L i ).

[0080] 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 tunnel construction. The specific process is as follows:

[0081] First, based on the soil displacement obtained in step C, the first additional load acting on the operating tunnel structure is obtained;

[0082] Then, the water and soil load model is obtained;

[0083] Finally, the first additional load is superimposed on the water-soil load model, and the load-structure model calculation is performed to obtain the predicted deformation value of the first operating subway tunnel.

[0084] In step E, the soil displacement of the operational tunnel node during the construction period of the upper tunnel of the superimposed tunnel is calculated based on the plane strain correction formula. The specific process is as follows:

[0085] First, the relative distance coordinate of node i after the tunnel construction is obtained as (D ii , L ii );

[0086] Then, based on the plane strain correction formula, the soil displacement of the operating tunnel node during the construction period of the upper tunnel of the superimposed tunnel is obtained.

[0087] 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 tunnel construction. The specific process is as follows:

[0088] First, the second additional load is obtained based on the soil displacement of the operating tunnel node during the construction period of the superimposed tunnel upper hole.

[0089] 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. Example

[0090] A calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction includes the following steps:

[0091] A. Based on the two-dimensional plane strain model and the mirror source-sink principle, the true source deformation of the soil caused by the shield tunnel is obtained;

[0092] B. Superimpose and correct the real source and the mirror image source to obtain the plane strain correction formula for any point;

[0093] C. Using the plane strain correction formula, calculate the soil displacement of the operational tunnel nodes during the construction period of the superimposed tunnel;

[0094] D. Converting the soil displacement obtained in step C into an additional load and applying it to the operating tunnel structure to obtain the predicted deformation value of the first operating subway tunnel caused by tunnel construction;

[0095] E. Using the plane strain correction formula, calculate the soil displacement of the operational tunnel nodes during the construction period of the upper tunnel of the superimposed tunnel;

[0096] F. Convert the soil displacement obtained in step E into an additional load and apply it to the calculation result in step D to obtain the predicted deformation value of the operating subway tunnel caused by the tunnel construction.

[0097] Specifically, step A is based on the two-dimensional plane strain model and the mirror source-sink principle to obtain the true source deformation of the soil caused by the shield tunnel, as follows:

[0098] 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 depth H, coordinates (0, H, 0), such as Figure 2 shown.

[0099] The stratum loss equivalence simplifies the stratum loss caused by shield construction into a uniformly shrinking virtual volume source.

[0100] The formation loss volume per unit length is:

[0101]

[0102] Where A is the formation loss area, is the outer diameter of the stacked tunnel, is the inner diameter of the stacked tunnel, and η is the formation loss rate.

[0103]

[0104] Where M is the physical gap after grouting filling, U is the equivalent three-dimensional radial displacement, For parameters related to construction quality, .

[0105]

[0106] in, The thickness of the shield tail wall is about 0.1m. Create space for assembly lining.

[0107]

[0108] Where R is the tunnel radius, is the elastic modulus of the soil at the tunnel axis; is the original earth pressure and cut pressure on the tunnel axis, is the dimensionless displacement factor and can be taken as 1.12.

[0109] According to the theory of elasticity, the displacement field caused by a point source in an infinite elastic body is:

[0110]

[0111] Where 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.

[0112] The superimposed tunnel is close to the operating subway tunnel project at a long distance. It can be seen that the superimposed tunnel is a long-line source and can be simplified into a two-dimensional plane strain model.

[0113] Convert the 3D point source formula to a 2D line source integral:

[0114]

[0115] Points earned:

[0116]

[0117] in, is the displacement of the point source in the x direction, is the displacement of the point source in the z direction.

[0118] Specifically, step B superimposes and corrects the real source and the mirror image source to obtain the plane strain correction formula of any point, which is as follows:

[0119] The image source displacement Z=-H. According to step A, its displacement field is:

[0120]

[0121] in, is the displacement of the mirror source in the x direction, is the displacement of the mirror source in the z direction.

[0122] By superimposing the displacements of the real source and the mirror image source, we can obtain the plane strain correction formula:

[0123]

[0124] in, is the displacement in the x direction after superposition, is the displacement in the z direction after superposition.

[0125] is the average elastic modulus of soil:

[0126]

[0127] in, is the elastic model of soil layer i, is the thickness of soil layer i.

[0128] Specifically, step C solves the soil displacement of the operating tunnel node during the construction period of the superimposed tunnel using the plane strain correction formula, as follows:

[0129] The operating subway tunnel segment lining is divided into several unit linings at every 1m. The intersection of the unit linings is node i, and the relative distance coordinate of node i is (D i , L i ),like Figure 3 As shown in step B, the soil displacement at each node is:

[0130]

[0131] in, is the displacement in the x direction during the construction of the hole under node i, is the displacement in the z direction during the construction of the tunnel under node i.

[0132] 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 tunnel construction. , as follows:

[0133] From step C, we can see that the displacement of each node is , then the additional load acting on the operating tunnel structure is:

[0134]

[0135] in, is the base bed coefficient in the x direction within the length of the soil unit, is the base bed coefficient in the z direction within the length of the soil unit, is the additional load in the x direction during the construction of the hole under node i, It is the additional load in the z direction during the construction of the tunnel under node i.

[0136] When it is tension, its value is set to 0, such as Figure 4 shown.

[0137] Superimpose water and soil loads to calculate the load structure model and obtain the predicted deformation value of the operating subway tunnel ,like Figure 5 shown.

[0138] Specifically, step E solves the soil displacement of the operating tunnel node during the construction period of the upper tunnel of the superimposed tunnel according to the plane strain correction formula, as follows:

[0139] According to step C, the soil displacement at each node caused by the construction of the upper hole is:

[0140]

[0141] in, is the displacement in the x direction during the construction of the hole on node i, is the displacement in the z direction during the construction of the hole on node i.

[0142] Specifically, 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 tunnel construction. , as follows:

[0143] From step E, we can see that the displacement of each node is , then the additional load acting on the operating tunnel structure is:

[0144]

[0145] in, is the base bed coefficient in the x direction within the length of the soil unit, is the base bed coefficient in the z direction within the length of the soil unit, is the additional load in the x direction during the construction of the hole on node i, is the additional load in the z direction during the construction of the hole on node i.

[0146] Specifically, when and When it is tension, its value is set to 0, such as Figure 6 shown.

[0147] Will and Acting on the calculation results of step D, the predicted deformation value of the operating subway tunnel is obtained ,like Figure 7shown.

[0148] This invention addresses the existing technical gap by solving the challenge of deformation prediction for long-distance adjacent operational subway tunnels, providing an important tool for deformation prediction during design and construction. Furthermore, this method offers safe, efficient, and rapid computational security, enabling widespread application in engineering projects. It addresses the complex, time-consuming, and unsatisfactory results inherent in existing theoretical formulas.

Claims

1. A calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction, characterized by: The following steps are involved: A. Based on the two-dimensional plane strain model and the mirror source-sink principle, the true source deformation of the soil caused by the shield tunnel is obtained; B. Superimpose and correct the real source and the mirror image source to obtain the plane strain correction formula for any point; C. Using the plane strain correction formula, calculate the soil displacement of the operational tunnel nodes during the construction period of the superimposed tunnel; D. Converting the soil displacement obtained in step C into an additional load and applying it to the operating tunnel structure to obtain the predicted deformation value of the first operating subway tunnel caused by tunnel construction; E. Using the plane strain correction formula, calculate the soil displacement of the operational tunnel nodes during the construction period of the upper tunnel of the superimposed tunnel; F. Convert the soil displacement obtained in step E into an additional load and apply it to the calculation result in step D to obtain the predicted deformation value of the operating subway tunnel caused by the upper tunnel construction; Step A is based on a two-dimensional plane strain model and the mirror source-sink principle to derive 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, based on the theory of elasticity, a displacement field model caused by a point source in an infinite elastic body is established; Finally, the three-dimensional point source formula is converted into a two-dimensional line source to obtain the true source deformation of the soil.

2. The calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction according to claim 1 is characterized by: Step B superimposes and corrects the real source and the mirror image source to obtain the plane strain correction formula for any point. The specific process is as follows: First, the soil image source deformation is obtained based on the real source deformation of the soil obtained in step A; Then, the soil real source deformation and soil mirror source deformation are superimposed; Finally, the plane strain correction formula of any point is obtained after superposition.

3. The calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction according to claim 1 is characterized by: In step C, the soil displacement of the operational tunnel nodes during the construction period of the superimposed tunnel is calculated based on the plane strain correction formula. The specific process is as follows: First, the segmental lining of the operating subway tunnel is divided into unit linings. Then, the intersection points of the unit linings are obtained and confirmed as nodes; Then, confirm the relative distance coordinates of the nodes; Finally, based on the relative distance coordinates and plane strain correction formula, the soil displacement of the operating tunnel node during the construction period of the superimposed tunnel is obtained.

4. The calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction according to claim 3 is characterized by: The segmental lining of an operating subway tunnel is divided into unit linings. The specific process is as follows: The segmental lining of an operating subway tunnel is divided into sections of 1m each to obtain several unit linings.

5. The calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction according to claim 1 is characterized by: 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 coordinate of node i is (D i , L i ).

6. The calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction according to claim 1 is characterized by: 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 operating subway tunnel caused by the 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 on the water-soil load model, and the load-structure model calculation is performed to obtain the predicted deformation value of the first operating subway tunnel.

7. The calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction according to claim 6 is characterized by: In step E, the soil displacement of the operational tunnel node during the construction period of the upper tunnel of the superimposed tunnel is calculated based on the plane strain correction formula. The specific process is as follows: First, the relative distance coordinate of node i after the tunnel construction is obtained as (D ii , L ii ); Then, based on the plane strain correction formula, the soil displacement of the operating tunnel node during the construction period of the upper tunnel of the superimposed tunnel is obtained.

8. The calculation method for predicting deformation of an operating subway tunnel caused by stacked shield construction according to claim 1 is characterized by: 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 tunnel construction. The specific process is as follows: First, the second additional load is obtained based on the soil displacement of the operating tunnel node during the construction period of the superimposed tunnel upper hole. 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.

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