Method for determining ground stress of shallow-buried unequal-span bifurcated tunnel

Abstract

The application discloses a method for determining stratum stress of a shallow-buried unequal-span bifurcated tunnel, which mainly comprises the following steps: establishing a mechanical model of the shallow-buried unequal-span bifurcated tunnel; performing a conformal transformation on the shallow-buried bifurcated tunnel hole 1 to map a semi-infinite plane domain into a circular ring; calculating the stress caused by the excavation of the shallow-buried bifurcated tunnel hole 1 in the mapping plane; obtaining the stress of any position of the shallow-buried bifurcated tunnel hole 1 through the inverse mapping; converting the stress under different coordinates, and converting the stress function into a function under the coordinate system of hole 2; determining the excess surface force generated by the shallow-buried bifurcated tunnel hole 1 around hole 2; calculating the excess surface force by using a series method; applying a reverse surface force to calculate the stress caused by the excavation of the shallow-buried bifurcated tunnel hole 2; converting the stress under different coordinates, and converting the stress function into a function under the coordinate system of hole 1; iteratively solving the final stress function according to the accuracy requirement; and solving the stress components of any point around hole 1 and hole 2 of the shallow-buried unequal-span bifurcated tunnel. The application provides a calculation method for determining the stratum stress of the shallow-buried unequal-span bifurcated tunnel, and can consider the influence of the relative size and relative position of the two bifurcated tunnels, so as to make up for the deficiency of the current railway tunnel / highway tunnel / underground railway design specification which does not have a stratum stress method for the unequal-span bifurcated tunnel, and can provide a theoretical method basis for the design construction and safety evaluation of the unequal-span bifurcated tunnel and the underground overpass tunnel.

Description

Technical Field

[0001] This invention relates to the field of tunnel design and construction, specifically to a method for determining the stratum stress in shallow-buried bifurcated tunnels with unequal spans. Background Technology

[0002] Unequal span bifurcation tunnels are a new and special type of tunnel structure. In terms of route layout, this type of tunnel structure can be regarded as a combination of tunnels with large spans, continuous arches, and small spacing. However, its stress characteristics, stability analysis, design and construction methods are not simply superimposed single tunnel forms. Due to the special nature of its structure, most existing research and analysis on bifurcation tunnels are conducted by combining actual engineering data with numerical software.

[0003] Unequal-span bifurcation tunnels experience asymmetrical stress and deformation, and the construction process involves disturbances from the sequential construction of two unequal-span tunnels, as well as interactions with the larger span bifurcation sections. This results in extremely complex stress variations in the surrounding rock and support, making design and construction extremely difficult. The distribution of ground stress is a fundamental parameter for the design and construction of unequal-span bifurcation tunnels and a crucial factor affecting tunnel stability. The current "Railway Tunnel Design Code" lacks provisions specifically addressing bifurcation tunnels; the current "Highway Tunnel Design Code, Volume 1: Civil Engineering" only provides a brief overview of equal-span bifurcation tunnels and lacks theoretical calculations for ground stress in unequal-span bifurcation tunnels. This is inconsistent with the increasing trend of constructing underground interchange tunnels. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned technical problems in the prior art by providing a method for determining the stratum stress of shallow-buried bifurcation tunnels with unequal spans.

[0005] The above-mentioned objective of the present invention is achieved through the following technical solution: The method for determining the ground stress in shallow-buried bifurcated tunnels with unequal spans according to the present invention includes the following sequential steps: (1) Establish a mechanical model for shallow-buried bifurcation tunnels with unequal spans. This mechanical model can consider the case where the two tunnels of a bifurcation tunnel have unequal spans and unequal burial depths, that is, tunnel 1 and tunnel 2 have different spans and different burial depths; (2) Perform conformal transformation on the shallow-buried bifurcated tunnel 1, mapping the planar domain of the shallow-buried semi-infinite tunnel 1 into a ring, which is determined by the following formula: ; In the formula, z1 is the coordinate of the O1X1Y1 coordinate system of hole 1; Mapping function for bifurcation tunnel 1; h1 represents the coordinates on the mapping plane; i is the unit imaginary number; h1 is the burial depth of tunnel 1 in the bifurcation tunnel. Map the inner diameter of the annulus to hole 1. Where r1 is the radius of tunnel 1 at the bifurcation point; (3) Within the mapping plane, calculate the stress caused by the excavation of shallow-buried unequal-span bifurcation tunnel 1, which is determined by the following formula: ; ; In the formula, To map the stress function under the excavation of tunnel 1 in the plane; To map the stress function under the excavation of tunnel 1 in the plane; , where t is the support force of tunnel 1; (4) By inverse mapping, the stress at any position of the shallow-buried bifurcated tunnel 1 is obtained, where the inverse mapping is determined by the following formula: ; In the formula, ; (5) The stress under different coordinate systems is converted. The converted stress function in the coordinate system of Tunnel 2 is determined by the following formula: ; In the formula, Let O2X2Y2 be the stress function in the coordinate system O2X2Y2 of hole 2; Let z2 be the stress function in the coordinate system O2X2Y2 of tunnel 2; z2 be the coordinates in the coordinate system O2X2Y2 of tunnel 2; c be the relative position between tunnel 1 and tunnel 2, which is represented by a complex number here. Let c be the conjugate complex number; for The first derivative; (6) Determine the redundant surface forces generated by tunnel 1 around tunnel 2, which are determined by the following formula: ; In the formula, t1 represents the excess surface force generated by tunnel 1 around tunnel 2; t2 represents the coordinates of points around tunnel 2 in the tunnel 2 coordinate system; for The first derivative; for The conjugate of complex numbers; for The conjugate of complex numbers; (7) The redundant surface forces are calculated using the series method and are determined by the following formula: ; In the formula, D k The complex coefficients of each power term can be obtained by solving the orthogonality of trigonometric functions; L is the number of terms; k is the power. (8) Apply a reverse surface force and calculate the stress caused by the excavation of the bifurcation tunnel 2, which is determined by the following formula: ; In the formula, Let O2X2Y2 be the stress function in the coordinate system O2X2Y2 under the excavation of Tunnel 2; Map the inner diameter of the circular ring to tunnel 2 at the bifurcation point. Where h2 is the burial depth of the bifurcation tunnel 2; r2 is the radius of the bifurcation tunnel 2; For the mapping function of bifurcation tunnel 2, ; The stress function in coordinate system O2X2Y2 is given for the excavation of Tunnel 2. for The first derivative of ; F is the supporting force of hole 2; (9) Convert the stress under different coordinates, and convert the stress function to the function in the coordinate system of Tunnel 1. ; In the formula: Let O1X1Y1 be the stress function in the coordinate system O1X1Y1 under the excavation of Tunnel 2; The stress function under coordinate system O1X1Y1 during the excavation of Tunnel 2; (10) Based on the accuracy requirements, the final stress function is solved iteratively, and it is determined by the following formula: ; ; In the formula, Let O1X1Y1 be the stress function of coordinate system O1X1Y1; Let O1X1Y1 be the stress function of coordinate system O1X1Y1; The stress function is obtained through n iterations. The stress function is obtained through n iterations. (11) Solve for the stress components at any point around the surrounding rock of shallow buried unequal span bifurcation tunnels 1 and 2, which are determined by the following formula: ; ; ; In the formula, The stress in the x-direction of coordinate system O1X1Y1; Let O1X1Y1 be the y-direction stress; Let Re represent the shear stress in coordinate system O1X1Y1; Re denotes the real part; Im denotes the imaginary part. for The first derivative; for The second derivative; for The first derivative; Let z be the conjugate complex number of z1.

[0006] Compared with existing technologies and research methods, this invention has the following advantages: Existing research mainly focuses on analyzing tunnels with equal spans and small clearances, or conducting numerical simulation analysis on tunnels with equal spans and bifurcations. However, there is very little research on shallow-buried tunnels with unequal spans and bifurcations. A few studies have focused on the surrounding rock pressure, but there is a lack of theoretical basis for analyzing the ground stress in shallow-buried tunnels with unequal spans and bifurcations.

[0007] This invention provides a theoretical calculation method for determining the ground stress in shallow-buried bifurcated tunnels with unequal spans. By changing the relative burial depth and relative size of the two tunnels, the ground stress in shallow-buried bifurcated tunnels with unequal spans under different burial depths and relative sizes can be obtained, thus providing a theoretical basis for the design and construction of such tunnels. The method of this invention can be applied to the calculation and safety assessment of ground stress in shallow-buried underground engineering projects with unequal spans and small spacing, such as adjacent roadways in mining, adjacent tunnels in hydraulic engineering, and adjacent sections of subway tunnels. Attached Figure Description

[0008] Figure 1 This is a schematic model of the ground stress in the shallow-buried bifurcation tunnel with unequal spans according to the present invention.

[0009] In the diagram, O1X1Y1 is the coordinate system of tunnel 1; r1 is the radius of tunnel 1; h1 is the burial depth of tunnel 1; O2X2Y2 is the coordinate system of tunnel 2; r2 is the radius of tunnel 2; h2 is the burial depth of tunnel 2; c is the relative position between tunnel 1 and tunnel 2, which is represented by a complex number here.

[0010] Figure 2 Analysis diagram of shallow-buried bifurcated tunnel 1.

[0011] Figure 3 This is a conformal transformation diagram for shallow-buried bifurcated tunnel 1.

[0012] Figure 4 This is a stress distribution diagram of the arch path around the bifurcation tunnel 1, which is an example of the implementation of this invention.

[0013] Figure 5 This is a stress distribution diagram of the perimeter wall path of the bifurcation tunnel 1, which is an example of the implementation of this invention. Detailed Implementation

[0014] The present invention will now be further described with reference to the accompanying drawings and embodiments.

[0015] The specific data of this embodiment of the project are as follows: a shallow buried bifurcation tunnel with unequal spans, the tunnel diameter is replaced by an equivalent circle geometric replacement, the equivalent circle radii of the two holes are 5m and 8m respectively, the bifurcation tunnel 1 is buried at a depth of 10m, the tunnel 2 is buried at a depth of 15m, the distance between the two holes is 4m, and the tunnel 1 of the bifurcation tunnel is subjected to a uniformly distributed stress t=10kPa.

[0016] See Figure 1 , Figure 2 and Figure 3 The method for determining the stratum stress of a shallow-buried bifurcation tunnel with unequal spans in this embodiment is as follows: (1) Establish a mechanical model for shallow-buried bifurcation tunnels with unequal spans. This mechanical model can consider the case where the two tunnels of a bifurcation tunnel have unequal spans and unequal burial depths, that is, tunnel 1 and tunnel 2 have different spans and different burial depths; (2) Perform conformal transformation on the shallow-buried bifurcated tunnel 1, mapping the planar domain of the shallow-buried semi-infinite tunnel 1 into a ring, which is determined by the following formula: ; In the formula, z1 is the coordinate of the O1X1Y1 coordinate system of hole 1; Mapping function for bifurcation tunnel 1; h1 represents the coordinates on the mapping plane; i is the unit imaginary number; h1 is the burial depth of tunnel 1 in the bifurcation tunnel. Map the inner diameter of the annulus to hole 1. Where r1 is the radius of tunnel 1 at the bifurcation point; (3) Within the mapping plane, calculate the stress caused by the excavation of shallow-buried unequal-span bifurcation tunnel 1, which is determined by the following formula: ; ; In the formula, To map the stress function under the excavation of tunnel 1 in the plane; To map the stress function under the excavation of tunnel 1 in the plane; , where t is the support force of tunnel 1; (4) By inverse mapping, the stress at any position of the shallow-buried bifurcated tunnel 1 is obtained, where the inverse mapping is determined by the following formula: ; In the formula, ; (5) The stress under different coordinate systems is converted. The converted stress function in the coordinate system of Tunnel 2 is determined by the following formula: ; In the formula, Let O2X2Y2 be the stress function in the coordinate system O2X2Y2 of hole 2; Let z2 be the stress function in the coordinate system O2X2Y2 of tunnel 2; z2 be the coordinates in the coordinate system O2X2Y2 of tunnel 2; c be the relative position between tunnel 1 and tunnel 2, which is represented by a complex number here. Let c be the conjugate complex number; for The first derivative; (6) Determine the redundant surface forces generated by tunnel 1 around tunnel 2, which are determined by the following formula: ; In the formula, t1 represents the excess surface force generated by tunnel 1 around tunnel 2; t2 represents the coordinates of points around tunnel 2 in the tunnel 2 coordinate system; for The first derivative; for The conjugate of complex numbers; for The conjugate of complex numbers; (7) The redundant surface forces are calculated using the series method and are determined by the following formula: ; In the formula, D k The complex coefficients of each power term can be obtained by solving the orthogonality of trigonometric functions; L is the number of terms; k is the power. (8) Apply a reverse surface force and calculate the stress caused by the excavation of the bifurcation tunnel 2, which is determined by the following formula: ; In the formula, Let O2X2Y2 be the stress function in the coordinate system O2X2Y2 under the excavation of Tunnel 2; Map the inner diameter of the circular ring to tunnel 2 at the bifurcation point. Where h2 is the burial depth of the bifurcation tunnel 2; r2 is the radius of the bifurcation tunnel 2; For the mapping function of bifurcation tunnel 2, ; The stress function in coordinate system O2X2Y2 is given for the excavation of Tunnel 2. for The first derivative of ; F is the supporting force of hole 2; (9) Convert the stress under different coordinates, and convert the stress function to the function in the coordinate system of Tunnel 1. ; In the formula: Let O1X1Y1 be the stress function in the coordinate system O1X1Y1 under the excavation of Tunnel 2; The stress function under coordinate system O1X1Y1 during the excavation of Tunnel 2; (10) Based on the accuracy requirements, the final stress function is solved iteratively, and it is determined by the following formula: ; ; In the formula, Let O1X1Y1 be the stress function of coordinate system O1X1Y1; Let O1X1Y1 be the stress function of coordinate system O1X1Y1; The stress function is obtained through n iterations. The stress function is obtained through n iterations. (11) Solve for the stress components at any point around the surrounding rock of shallow buried unequal span bifurcation tunnels 1 and 2, which are determined by the following formula: ; ; ; In the formula, The stress in the x-direction of coordinate system O1X1Y1; Let O1X1Y1 be the y-direction stress; Let Re represent the shear stress in coordinate system O1X1Y1; Re denotes the real part; Im denotes the imaginary part. for The first derivative; for The second derivative; for The first derivative; Let z be the conjugate complex number of z1.

[0017] Based on the above method and steps, the stress in the strata surrounding tunnel 1 of the unequal-span bifurcation tunnel can be obtained, see... Figure 4 and Figure 5 As shown in the figure, after being subjected to the reverse force applied by the support, the vertical stress on the surrounding rock at the arch crown is close to 20 kPa, and the horizontal stress is close to 10 kPa. Along the path of the arch crown, the closer to the ground surface, the closer the vertical stress of the surrounding rock is to zero, and the horizontal stress is close to 15 kPa. On the path on the same horizontal line as the tunnel center, the vertical stress at the contact position with the tunnel is 0, and the horizontal stress is close to 1.5t. Along the path, the vertical stress gradually increases and the horizontal stress gradually decreases. When the distance from the edge of the hole is close to r, the vertical stress exceeds the horizontal stress.

Claims

1. A method for determining the stratum stress of a shallow-buried bifurcated tunnel with unequal spans, characterized in that... The steps include the following sequence: (1) Establish a mechanical model for shallow-buried bifurcation tunnels with unequal spans. This mechanical model can consider the case where the two tunnels of a bifurcation tunnel have unequal spans and unequal burial depths, i.e., tunnel 1 and tunnel 2 have different spans and different burial depths; (2) Perform conformal transformation on the shallow-buried bifurcated tunnel 1, mapping the planar domain of the shallow-buried semi-infinite tunnel 1 into a ring, which is determined by the following formula: ； In the formula, z1 is the coordinate of the O1X1Y1 coordinate system of hole 1; Mapping function for bifurcation tunnel 1; h1 represents the coordinates on the mapping plane; i is the unit imaginary number; h1 is the burial depth of tunnel 1 in the bifurcation tunnel. Map the inner diameter of the annulus to hole 1. Where r1 is the radius of tunnel 1 at the bifurcation point; (3) Within the mapping plane, calculate the stress caused by the excavation of shallow-buried unequal-span bifurcation tunnel 1, which is determined by the following formula: ； ； In the formula, To map the stress function under the excavation of tunnel 1 in the plane; To map the stress function under the excavation of tunnel 1 in the plane; , where t is the support force of tunnel 1; (4) By inverse mapping, the stress at any position of the shallow-buried bifurcated tunnel 1 is obtained, where the inverse mapping is determined by the following formula: ； In the formula, ; (5) The stress under different coordinate systems is converted. The converted stress function in the coordinate system of Tunnel 2 is determined by the following formula: ； In the formula, Let O2X2Y2 be the stress function in the coordinate system O2X2Y2 of hole 2; Let z2 be the stress function in the coordinate system O2X2Y2 of tunnel 2; z2 be the coordinates in the coordinate system O2X2Y2 of tunnel 2; c be the relative position between tunnel 1 and tunnel 2, which is represented by a complex number here. Let c be the conjugate complex number; for The first derivative; (6) Determine the redundant surface forces generated by tunnel 1 around tunnel 2, which are determined by the following formula: ； In the formula, t1 represents the excess surface force generated by tunnel 1 around tunnel 2; t2 represents the coordinates of points around tunnel 2 in the tunnel 2 coordinate system; for The first derivative; for The conjugate of complex numbers; for The conjugate of complex numbers; (7) The redundant surface forces are calculated using the series method and are determined by the following formula: ； In the formula, D k The complex coefficients of each power term can be obtained by solving the orthogonality of trigonometric functions; L is the number of terms; k is the power. (8) Apply a reverse surface force and calculate the stress caused by the excavation of the bifurcation tunnel 2, which is determined by the following formula: ； In the formula, Let O2X2Y2 be the stress function in the coordinate system O2X2Y2 under the excavation of Tunnel 2; Map the inner diameter of the circular ring to tunnel 2 at the bifurcation point. Where h2 is the burial depth of the bifurcation tunnel 2; r2 is the radius of the bifurcation tunnel 2; For the mapping function of bifurcation tunnel 2, ; The stress function in coordinate system O2X2Y2 is given for the excavation of Tunnel 2. for The first derivative of ; F is the supporting force of hole 2; (9) Convert the stress under different coordinates, and convert the stress function to the function in the coordinate system of Tunnel 1. ； In the formula: Let O1X1Y1 be the stress function in the coordinate system O1X1Y1 under the excavation of Tunnel 2; The stress function under coordinate system O1X1Y1 during the excavation of Tunnel 2; (10) Based on the accuracy requirements, the final stress function is solved iteratively, and it is determined by the following formula: ； ； In the formula, Let O1X1Y1 be the stress function of coordinate system O1X1Y1; Let O1X1Y1 be the stress function of coordinate system O1X1Y1; The stress function is obtained through n iterations. The stress function is obtained through n iterations. (11) Solve for the stress components at any point around the surrounding rock of shallow buried unequal span bifurcation tunnels 1 and 2, which are determined by the following formula: ； ； ； In the formula, The stress in the x-direction of coordinate system O1X1Y1; Let O1X1Y1 be the y-direction stress; Let Re represent the shear stress in coordinate system O1X1Y1; Re denotes the real part; Im denotes the imaginary part. for The first derivative; for The second derivative; for The first derivative; Let z be the conjugate complex number of z1.

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