A tunnel section convergence deformation monitoring device and a monitoring method

Abstract

The application provides a tunnel cross section convergence deformation monitoring device and a monitoring method, the monitoring device comprises a sensing unit and a plurality of fish eye bearing supports; the sensing unit comprises an arc thin-walled rectangular square tube with the same arc length and bending radius as the tunnel cross section and a plurality of groups of strain sensors arranged on the arc thin-walled rectangular square tube in sequence; the plurality of fish eye bearing supports are connected to the arc thin-walled rectangular square tube in sequence, and the fish eye bearing supports are connected and fixed on the inner surface of the tunnel cross section. The monitoring device is consistent with the deformation of the tunnel cross section, the strain sensors obtain the strain information of each measuring point of the sensing unit, and the real-time monitoring of the convergence deformation of the tunnel cross section is realized by combining the monitoring method. The monitoring device and the monitoring method have the advantages of strong adaptability, high calculation efficiency, good real-time performance, small influence of environmental factors and the like.

Description

Technical Field

[0001] This invention belongs to the field of tunnel deformation monitoring technology, specifically a tunnel cross-section convergence deformation monitoring device and monitoring method. Background Technology

[0002] Over the past decade, my country's tunnel construction industry has developed rapidly, with the number and scale of tunnels ranking among the world's top. However, due to changes in geological conditions, geological disasters, vehicles, and other external factors, tunnels are highly susceptible to localized damage during operation, such as lining cracks, water leakage, and concrete block spalling, threatening the operational safety of the tunnel structure. Tunnel cross-sectional convergence deformation, as one of the most direct response parameters of the tunnel structure under the combined effects of various factors, is crucial for accurate monitoring in tunnel safety assessment.

[0003] Currently, tunnel cross-section convergence deformation monitoring technologies can be divided into point-based monitoring technologies and distributed monitoring technologies. Point-based monitoring technologies include convergence meters, levels, fully automatic total stations, and inclinometers. These technologies can accurately measure the convergence deformation of certain key nodes in the tunnel cross-section; however, they struggle to accurately depict the overall deformation shape of the tunnel cross-section and require manual operation, resulting in low measurement efficiency and poor real-time performance. Distributed monitoring technologies include close-range photogrammetry, 3D laser scanning, and machine vision measurement. These technologies solve the problem of limited measurement quantity in point-based monitoring technologies; however, measurement methods based on optical detection principles have poor applicability. In complex underground tunnel environments with low light, confined spaces, and poor visibility, these technologies exhibit significant measurement errors. Summary of the Invention

[0004] To address the shortcomings and deficiencies in the existing technology, this invention provides a tunnel cross-section convergence deformation monitoring device and method, which transforms the tunnel cross-section convergence deformation monitoring problem into a deformation problem of the sensing unit in the tunnel cross-section convergence deformation monitoring device. This method is highly adaptable, computationally efficient, has good real-time performance, and is less affected by environmental factors.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A tunnel section convergence deformation monitoring device includes a sensing unit and several fisheye bearing supports; the sensing unit includes an arc-shaped thin-walled rectangular tube with the same arc length and bending radius as the tunnel section and several sets of strain sensors arranged sequentially and at intervals on the arc-shaped thin-walled rectangular tube; the several fisheye bearing supports are sequentially and at intervals connected to the arc-shaped thin-walled rectangular tube, and the fisheye bearing supports are connected and fixed to the inner surface of the tunnel section.

[0007] Furthermore, each set of strain sensors includes two strain sensors respectively mounted on the upper and lower outer surfaces of the curved thin-walled rectangular square tube.

[0008] Furthermore, it also includes several internally threaded cylindrical pins, and the arc-shaped thin-walled rectangular square tube is connected to the fisheye bearing support through the internally threaded cylindrical pins.

[0009] Furthermore, the internally threaded cylindrical pin extends from one side of the arc-shaped thin-walled rectangular tube to the other side of the arc-shaped thin-walled rectangular tube, and both threaded ends of the pin extend out of the arc-shaped thin-walled rectangular tube.

[0010] Furthermore, the spherical bearing support includes a connecting steel plate and two ball-end spherical bearings disposed on both sides of the connecting steel plate, with each ball-end spherical bearing connected to the threaded end of the corresponding internal thread cylindrical pin.

[0011] The present invention also provides a method for monitoring the convergence deformation of a tunnel cross section, comprising the following steps:

[0012] Step 1: Establish a spatial rectangular coordinate system xyz. Establish the x-axis along the line connecting the left and right end nodes of the sensing unit, establish the y-axis along the direction of the arch of the sensing unit, and determine the z-axis according to the right-hand screw rule. The origin of the coordinate system is located at the center of the cross section of the sensing unit.

[0013] Step 2: Establish arc coordinates s. Establish natural coordinate axes along the arc length of the sensing unit, with the origin located at the left end node of the sensing unit;

[0014] Step 3: According to the theory of non-uniform rational B-splines, the coordinates of any point of the sensing unit in the spatial rectangular coordinate system xyz can be represented as:

[0015]

[0016]

[0017]

[0018] Where, x p y p and z p Let m be the coordinates of control point p; m be the total number of control points; R p (ξ) is the interpolation function;

[0019] Step 4: Set up several strain measurement points at different positions along the arc coordinate direction on the sensing unit. Each strain measurement point includes two strain sensors, which are installed on the upper and lower outer surfaces of the sensing unit, respectively. Based on the measured strain values ​​of the strain sensors, calculate the measured tensile strain ε. i and measured value of curvature k i for:

[0020]

[0021]

[0022] in, and , i and h are the measured strain values ​​of the strain sensors on the upper and lower surfaces, respectively; i is the installation position of the strain sensor in the sensing unit; h is the center-to-center distance between the two strain sensors at the same measuring point; r is the radius of curvature of the sensing unit curve at the strain measuring point.

[0023] Step 5: Establish the solution vector F using the measured values ​​of tensile strain and bending curvature:

[0024] F=[ε1k1ε2k2…ε n k n ] T

[0025] Where n is the number of strain measurement points on the sensing unit; T represents the transpose of the vector; and the dimension of F is 2n×1.

[0026] Step 6: Based on the isoparametric element theory, control point deformation is used to measure the tangential deformation u, radial deformation v, and rotation angle of the sensing element. Represented as:

[0027]

[0028]

[0029]

[0030] Among them, u p ,v p and The tangential deformation, radial deformation, and rotation angle at control point p; m is the total number of control points; R p (ξ) is the interpolation function;

[0031] Step 7: Using the strain-displacement relationship of the curved beam, obtain the theoretical values ​​of tensile strain and bending curvature:

[0032]

[0033]

[0034] Where ε(ξ) and k(ξ) are the theoretical values ​​of tensile strain and bending curvature, respectively; J is the arc differential; u′ and The tangential deformation u of the sensing unit and the rotation angle of the sensing unit Find the first derivative with respect to s; H1 and H2 are derived from R. p (ξ) is a vector formed by its derivative; U is the deformation vector of the control point; r is the radius of curvature of the curve of the sensing unit at the strain measurement point;

[0035] Step 8: Establish the solution matrix M using the theoretical values ​​of tensile strain ε and bending curvature k at different strain measurement points;

[0036]

[0037] Where, ξ i Let ε be the theoretical value of tensile strain and bending curvature k corresponding to strain measurement point i; the M matrix has a dimension of 2n×3m; n is the number of strain measurement points on the sensing unit; m is the total number of control points.

[0038] Step 9: Establish the objective function for deformation solving, and obtain the convergent deformation of the tunnel section:

[0039]

[0040] Where Φ(U) is the objective function for deformation solution; λ is the penalty coefficient;

[0041] Furthermore, in step 7, vectors H1 and H2 are represented as follows:

[0042]

[0043]

[0044] Among them, R i ′(ξ) is R i (ξ) Take the first derivative with respect to ξ; the dimensions of H1 and H2 are 1×3m; m is the total number of control points.

[0045] Furthermore, in step 7, vector U is represented as:

[0046]

[0047] Among them, u i v i and corner These represent the tangential deformation, radial deformation, and rotation angle of the sensing unit at control point i, respectively; m is the total number of control points; T represents the transpose of the vector; and U has a dimension of 3m×1.

[0048] Furthermore, the arc differential J in step 7 is expressed as:

[0049]

[0050] Where x′ and y′ are the first derivatives of x and y with respect to ξ; ξ is a dimensionless curvilinear coordinate system, and the relationship between ξ and s is:

[0051] ds=Jdξ.

[0052] By adopting the above technical solution, the present invention can achieve the following beneficial effects:

[0053] This invention discloses a tunnel cross-section convergence deformation monitoring device and method. The device is installed on the surface of the tunnel cross-section, ensuring that both deform together. The problem of monitoring tunnel cross-section convergence deformation is transformed into a problem of solving the deformation of the sensing unit within the monitoring device. Subsequently, using strain data measured by strain sensors, combined with the tunnel cross-section convergence deformation monitoring method provided by this invention, the tunnel cross-section convergence deformation can be measured through simple linear calculations. This method offers advantages such as strong adaptability, high computational efficiency, good real-time performance, and minimal impact from environmental factors. Based on this, the invention possesses the following advantages:

[0054] 1. This invention can realize automated remote monitoring of tunnel cross-section convergence deformation, with a measurement frequency of over 1 kHz.

[0055] 2. This invention can accurately depict the overall distribution shape of the tunnel cross section at different times, and the measurement accuracy can reach the sub-millimeter level.

[0056] 3. The strain sensor layout method used in the monitoring device of the present invention can effectively reduce the influence of external ambient temperature on deformation measurement.

[0057] 4. The monitoring device and method of the present invention are suitable for harsh underground measurement environments and have low requirements for the environment in which the tunnel structure is located. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the tunnel cross-section convergence deformation monitoring device of the present invention;

[0059] Figure 2 This is a cross-sectional view of the sensing unit of the present invention;

[0060] Figure 3 This is a cross-sectional view of the fisheye bearing support of the present invention;

[0061] In the diagram: 101-sensing unit, 102-internal threaded cylindrical pin, 103-fisheye bearing support, 201-arc thin-walled rectangular tube, 202-strain sensor, 301-ball joint connecting rod fisheye bearing, 302-connecting steel plate. Detailed Implementation

[0062] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0064] Example 1

[0065] A tunnel cross-section convergence deformation monitoring device, such as Figures 1-3 As shown, it includes a sensing unit 101, a plurality of internally threaded cylindrical pins 102 and a plurality of fish-eye bearing supports 103. The plurality of internally threaded cylindrical pins 102 are arranged sequentially and spaced apart on the sensing unit 101, and a fish-eye bearing support 103 is provided at each internally threaded cylindrical pin 102.

[0066] The internally threaded cylindrical pin 102 is fixed to the sensing unit 101 by welding. Both ends of the internally threaded cylindrical pin 102 extend into arc-shaped thin-walled rectangular square tubes 201. The internally threaded cylindrical pin 102 is connected to the fisheye bearing support 103 by bolt mechanical connection.

[0067] The sensing unit 101 consists of an arc-shaped thin-walled rectangular tube 201 and 2n strain sensors 202. The arc-shaped thin-walled rectangular tube 201 has the same arc length and bending radius as the tunnel cross section. The arc-shaped thin-walled rectangular tube 201 is evenly divided into n segments according to the total arc length. A set of strain sensors 202 is installed at the midpoint of each segment by adhesive bonding or welding. The two strain sensors 202 in each set are respectively installed on the upper and lower outer surfaces of the arc-shaped thin-walled rectangular tube 201.

[0068] The fisheye bearing support 103 includes two ball joint connecting rod fisheye bearings 301 and a connecting steel plate 302. The ball joint connecting rod fisheye bearings 301 are mechanically fixed to both sides of the connecting steel plate 302.

[0069] During installation, the arc-shaped thin-walled rectangular tube 201 is first divided into n segments according to the total arc length, and internally threaded cylindrical pins 102 are welded at n+1 nodes. Next, strain sensors 202 are installed on the upper and lower surfaces at the midpoint of each segment. Then, ball-end connecting rod spherical bearings 301 are installed on the left and right sides of each internally threaded cylindrical pin 102. Finally, the ball-end connecting rod spherical bearings 301 are connected to the connecting steel plate 302 by bolt mechanical connection, and the spherical bearing support 103 is fixed to the inner surface of the tunnel section by bonding or mechanical connection.

[0070] like Figure 1 and Figure 2 As shown, the sensing unit 101 is 30mm wide and 20mm high, and includes an arc-shaped thin-walled rectangular tube 201 and a strain sensor 202. Preferably, the strain sensor 202 can be a fiber optic strain sensor.

[0071] like Figure 1 and Figure 3As shown, the ball joint connecting rod spherical bearing 301 has an M6 threaded rod at the top and a 10mm deep M6 threaded hole at the bottom. The connecting steel plate 302 has 6.5mm through holes on both sides along the length direction.

[0072] The monitoring device deforms in sync with the tunnel cross-section. After the tunnel cross-section deforms, the monitoring device deforms along with it. Strain sensors capture strain changes at various measuring points on the surface of the sensing unit and input the measured values ​​into the monitoring method. Combined with the monitoring method, real-time monitoring of the tunnel cross-section's convergence deformation is achieved. The monitoring device and method of this invention have advantages such as strong adaptability, high computational efficiency, good real-time performance, and minimal impact from environmental factors.

[0073] Example 2

[0074] A method for monitoring convergence deformation of a tunnel cross section includes the following steps:

[0075] Step 1: Based on the arc length and radius of curvature of the tunnel section, design and install the tunnel section convergence deformation monitoring device described in Example 1. The fisheye bearing supports 103 at both ends need to be installed in the stable area to ensure that the lateral and longitudinal displacements are 0.

[0076] Step 2: Establish a spatial rectangular coordinate system xyz. Establish the x-axis along the line connecting the left and right end nodes of the sensing unit 101, establish the y-axis along the height direction of the sensing unit 101, and determine the z-axis according to the right-hand screw rule. The origin of the coordinate system is located at the center of the cross section of the sensing unit 101.

[0077] Step 3: Establish arc coordinates s. Establish natural coordinate axes along the arc length direction of sensing unit 101, with the origin located at the left end node of sensing unit 101;

[0078] Step 4: According to the theory of non-uniform rational B-splines, the coordinates of any point of sensing unit 101 in the spatial rectangular coordinate system xyz can be expressed as:

[0079]

[0080]

[0081]

[0082] Where, x p y p and z p Let m be the coordinates of control point p; m be the total number of control points; R p (ξ) is the interpolation function;

[0083] Step 5: Divide the arc-shaped thin-walled rectangular tube 201 into n segments according to the total arc length. At the midpoint of each segment, install a set of strain sensors 202 using adhesive bonding or welding. The two strain sensors 202 in each set are installed on the upper and lower outer surfaces of the arc-shaped thin-walled rectangular tube 201, respectively. Based on the measured strain values ​​from the strain sensors 202, calculate the measured tensile strain ε. i and measured value of curvature k i for:

[0084]

[0085]

[0086] in, and , i and h are the measured strain values ​​of the upper and lower surface strain sensors 202, respectively; i is the installation position of the strain sensor 202 in the sensing unit 101; h is the center distance between the two strain sensors 202 at the same measuring point; r is the radius of curvature of the curve of the sensing unit 101 at the strain measuring point.

[0087] Step 6: Establish the solution vector F using the measured values ​​of tensile strain and bending curvature:

[0088] F=[ε1 k1 ε2 k2…ε n k n ] T

[0089] Where n is the number of strain measurement points on sensing unit 101; the dimension of F is 2n×1;

[0090] Step 7: Based on the isoparametric element theory, control point deformation is used to deform the tangential deformation u, radial deformation v, and rotation angle of the sensing element 101. Represented as:

[0091]

[0092]

[0093]

[0094] Among them, u p ,v p and To control the tangential deformation, radial deformation, and rotation angle at point p;

[0095] Step 8: Using the strain-displacement relationship of the curved beam, obtain the theoretical values ​​of tensile strain and bending curvature:

[0096]

[0097]

[0098] Where ε(ξ) and k(ξ) are the theoretical values ​​of tensile strain and bending curvature; For the arc differential; ξ is a dimensionless curvilinear coordinate system, and the relationship between ξ and s is ds = Jdξ; u′ and For u and Find the first derivative with respect to s; H1 and H2 are derived from the interpolation function R. p The vector consisting of (ξ) and its derivative;

[0099]

[0100]

[0101] The deformation vector of the control point, U, has a dimension of 3m×1;

[0102] Step 9: Establish the solution matrix M using the theoretical values ​​of tensile strain ε and bending curvature k at different strain measurement points:

[0103]

[0104] Where, ξ i Let ε(ξ) be the theoretical value of tensile strain and k(ξ) be the theoretical value of bending curvature corresponding to strain measurement point i; the M matrix has a dimension of 2n×3m.

[0105] Step 10: Establish the objective function for deformation solving, and obtain the convergent deformation of the tunnel section:

[0106]

[0107] Where Φ(U) is the objective function for deformation solution; λ is the penalty coefficient.

[0108] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method of monitoring convergence deformation of a tunnel cross section, the method using a tunnel cross section convergence deformation monitoring device, characterized by, The tunnel cross section convergence deformation monitoring device comprises a sensing unit (101) and a plurality of fish-eye bearing supports (103); the sensing unit (101) comprises an arc-shaped thin-walled rectangular square tube (201) with the same arc length and bending radius as the tunnel cross section and a plurality of groups of strain sensors (202) sequentially and spacedly arranged on the arc-shaped thin-walled rectangular square tube (201); the plurality of fish-eye bearing supports (103) are sequentially and spacedly connected to the arc-shaped thin-walled rectangular square tube (201), and the fish-eye bearing supports (103) are connected and fixed on the inner surface of the tunnel cross section. The tunnel cross section convergence deformation monitoring method comprises the following steps: S1, a space rectangular coordinate system x-y-z is established: the x-axis is established along the connecting line of the left and right end nodes of the sensing unit (101), the y-axis is established in the direction of the vault of the sensing unit (101), the z-axis is determined according to the right-hand screw rule, and the coordinate system origin is located at the cross section center of the sensing unit (101); S2, an arc coordinate s is established: a natural coordinate axis is established along the arc length direction of the sensing unit (101), and the coordinate origin is located at the left end node of the sensing unit (101); S3, the coordinates of any point of the sensing unit (101) in the space rectangular coordinate system x-y-z are expressed as: where x p , y p , and z p are the coordinates of the control points p; m is the total number of control points; R p (ξ) is an interpolation function; S4, a plurality of strain measuring points are arranged at different positions of the sensing unit (101) in the arc coordinate direction, each of the strain measuring points including two strain sensors (202) respectively mounted on the upper and lower outer surfaces of the sensing unit (101), and the tensile strain measured value ε and the bending curvature measured value k are obtained according to the measured strain values of the strain sensors (202) i are as follows: i ​ wherein, and respectively are the measured strain values of the upper and lower surface strain sensors (202); i is the installation position of the strain sensor (202) on the sensing unit (101); h is the center distance of the two strain sensors (202) at the same measuring point; r is the curve radius of curvature of the sensing unit (101) at the strain measuring point; S5, the solving vector F is established by using the measured values of the tensile strain and the bending curvature: F = [ε1 k1 ε2 k2... ε n k n ] T Wherein, n is the number of strain measuring points on the sensing unit (101); the dimension of F is 2n x 1; S6, the sensing unit (101) is tangentially deformed by u, radially deformed by v and rotated by an angle is represented as: where u p , v p and are the tangential deformation, radial deformation and rotation angle at the control point p; m is the total number of control points; R p (ξ) is an interpolation function; S7, the tensile strain theoretical value ε(ξ) and the bending curvature theoretical value k(ξ) are solved by using the strain-displacement relationship of the curved beam: where J is the arc differential; u' and is the tangential deformation of the sensor unit (101) and the rotation angle of the sensor unit (101) is the first derivative of s; H1 and H2 are vectors composed of the interpolation functions R p (ξ) and its derivatives; U is the control point deformation vector; r is the curve radius of curvature of the sensor unit (101) at the strain measurement point; S8, the solving matrix M is established by using the tensile strain theoretical value ε(ξ) and the bending curvature theoretical value k(ξ) at different strain measuring points: wherein ξ i is the theoretical tensile strain value ε(ξ) and the theoretical bending curvature value k(ξ) corresponding to the strain measuring point i; R i ′(ξ i ) is the first-order derivative of the interpolation function R i (ξ i ) with respect to ξ i ; J is the arc differential; r is the curve curvature radius of the sensing unit (101) at the strain measuring point; n is the number of strain measuring points on the sensing unit (101); m is the total number of control points; and M is a matrix with a dimension of 2n x 3m. S9, the deformation solving target function Φ(U) is established, and the tunnel cross section convergence deformation is solved: Wherein, λ is a penalty coefficient.

2. The method of claim 1, wherein, Each group of strain sensors (202) comprises two strain sensors (202) respectively mounted on the upper and lower outer surfaces of the arc-shaped thin-walled rectangular square tube (201).

3. The method of claim 2, wherein the tunnel cross-section convergence deformation monitoring method is characterized by, The tunnel cross section convergence deformation monitoring device further comprises a plurality of internally threaded cylindrical pins (102), and the arc-shaped thin-walled rectangular square tube (201) is connected with the fish-eye bearing support (103) through the internally threaded cylindrical pin (102).

4. The method of claim 3, wherein the tunnel cross-section convergence deformation monitoring method is characterized by, The internally threaded cylindrical pin (102) penetrates from one side surface of the arc-shaped thin-walled rectangular square tube (201) to the other side surface of the arc-shaped thin-walled rectangular square tube (201), and the threaded ends of the two ends thereof extend out of the arc-shaped thin-walled rectangular square tube (201).

5. The method of claim 4, wherein the tunnel cross-section convergence deformation monitoring method is characterized by, The fish-eye bearing support (103) comprises a connecting steel plate (302) and two ball head link fish-eye bearings (301) respectively arranged on the two sides of the connecting steel plate (302), and the two ball head link fish-eye bearings (301) are respectively connected with the threaded ends of the internally threaded cylindrical pins (102) on the corresponding sides.

6. The method of claim 1, wherein, In step S7, the vectors H1 and H2 are expressed as: wherein R i is an interpolation function R i is the first derivative of R i with respect to ξ, ξ is a dimensionless curvilinear coordinate system; J is an arc differential; r is the curvilinear radius of curvature of the sensor unit (101) at the strain measurement point; m is the total number of control points; H1 and H2 have dimensions 1 x 3m.

7. The method of claim 6, wherein the tunnel cross-section convergence deformation monitoring method is characterized by, In step S7, the control point deformation vector U is expressed as: where u i , v i and the rotation angle are the tangential deformation, the radial deformation, the rotation angle of the sensor unit (101) at the control point i, respectively; m is the total number of control points; T denotes the transpose of a vector; the dimension of U is 3m x 1.

8. A method of monitoring convergence deformation of a tunnel cross section according to any one of claims 6-7, characterized in that, The arc differential J is expressed as: Wherein, x' and y' are the first-order derivatives of x and y with respect to ξ; ξ is a dimensionless curve coordinate system, and the relationship between ξ and s is: ds = Jdξ.

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