A method for calculating relative displacement of tunnel segments across active faults

Abstract

The invention relates to the technical field of tunnel dislocation calculation, in particular to a method for calculating the relative dislocation of a segment ring of a tunnel across an active fault, comprising the following steps: S1: selecting two adjacent segment rings to establish a spatial rectangular coordinate system, pairing corresponding points on the two segment rings in pairs and arranging wire displacement sensors to form eight groups of mutually corresponding coordinate points; S2: obtaining the coordinate formulas of the eight points arranged after the relative motion segment ring A moves, and obtaining the coordinate function of the point P1′ after the relative dislocation; S3: obtaining the relative elongation d; S4: establishing eight nonlinear equation groups based on the linear displacement and relative elongation values ​​measured by the wire displacement sensor after the relative motion segment ring A moves, using an optimization solution program to obtain the optimal solutions of six spatial motion unknowns, and obtaining the final relative motion; the invention has a simple basic principle and convenient displacement sensor arrangement, and can provide a theoretical basis for disaster prevention and mitigation of tunnels across active faults.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel displacement calculation, in particular to a method for calculating the relative displacement of a tunnel segment ring across an active fault. Background Art

[0002] With the continuous advancement of my country's strategy of building a strong transportation country, tunnel construction in the western and southwestern regions has ushered in rapid development. However, most of these areas are located in fault zone concentration areas and have frequent seismic activities. Tunnel projects will inevitably cross these complex fault zones and seismically active areas during construction. Fault activity and geological deformation and stress release caused by earthquakes may have a significant impact on tunnel structures. In recent years, with the advancement of technology, methods such as numerical simulation and scaled model tests have been widely used and have become effective tools for studying the impact of faults when tunnels cross broken zones. The scaled model test analyzes the similarity between the prototype and the model and uses similarity constants to reduce the tunnel model. Although the model size is small, it can still simulate the mechanical response of the real tunnel under earthquake action to a certain extent. This test method not only saves costs, but also effectively reduces the interference factors in the prototype test, providing important support for tunnel seismic research.

[0003] Although the scaled model experiment has achieved certain results in studying the stress and deformation behavior of tunnels, it is still impossible to achieve accurate and effective measurement of the relative displacement of segmental tunnels. In actual engineering, measuring relative displacement faces multiple challenges. First, if the measurement is carried out after the surrounding rock is removed, this method will inevitably destroy the structural integrity of the tunnel, resulting in changes in the stress state of the tunnel, thereby affecting the accuracy and reliability of the measurement. Secondly, if the measuring equipment is placed directly in the tunnel for detection, although the disturbance of the surrounding rock is avoided, human errors may be introduced due to factors such as the installation location of the equipment, sensor accuracy, and environmental conditions, further affecting the accuracy of the direct observation results. In addition, the complex environment inside the tunnel, such as high humidity and temperature changes, will also interfere with the normal operation of the measuring equipment and increase the uncertainty of the measurement. How to obtain accurate relative displacement data without affecting the tunnel structure and environment is still a difficult problem that needs to be solved urgently. Summary of the invention

[0004] The purpose of the present application is to provide a method for calculating the relative displacement of a tunnel segment ring across an active fault, aiming to solve the problems in the prior art.

[0005] The present application provides a method for calculating the relative displacement of a tunnel segment ring across an active fault, comprising the following steps:

[0006] S1: Select two adjacent segment rings to establish a spatial rectangular coordinate system. The two segment rings are the relative motion ring A and the fixed segment ring B. Select two coordinate points at the arch top, the arch waists on both sides and the arch bottom of each segment ring and measure the coordinate values. Pair the corresponding points on the two segment rings and arrange the wire displacement sensors to form eight groups of corresponding coordinate points: any coordinate of the relative motion ring A is P1(x A ,y A , z A ), the coordinates of the point where the immovable segment ring B is paired with it are P2(x B ,y B , z B );

[0007] S2: Through the six basic unknown quantities in space, according to the three-dimensional Euler rotation formula, the rotation matrices Rx, Ry, Rz and the total rotation matrix R and translation vector T are constructed in the order of rotating around the X axis, then around the Y axis and finally around the Z axis, and the coordinate formulas of the eight points arranged after the relative motion segment ring A are obtained, and the coordinate function of the point P1′ after the relative displacement is obtained;

[0008] S3: Obtain the relative elongation d by the difference between the initial distance d1 of the eight paired points and the distance d2 between the points after the movement, that is, d=d2-d1;

[0009] S4: Based on the linear displacement and relative elongation values ​​measured by the wire-type displacement sensor after the relative motion segment ring A moves, eight nonlinear equations are established, and the optimal solution of the six unknown motion quantities in space is obtained using the optimization solution program to obtain the final relative motion quantity.

[0010] Furthermore, in the spatial rectangular coordinate system in S1, the centroid of the relatively moving segment ring A is at the origin of the coordinate system, the centroid of the stationary segment ring B is on the X-axis, the height direction of the segment ring is on the Z-axis, and the Y-axis is perpendicular to the XZ plane.

[0011] Furthermore, the draw-wire displacement sensors at six groups of paired points of the two segment rings in S1 are arranged in a cross-type arrangement, and the draw-wire displacement sensors at the remaining two groups of adjacent paired points are arranged in parallel.

[0012] Furthermore, the six unknown quantities of spatial motion in S2 are: α is the rotation around the X-axis, β is the rotation around the Y-axis, γ is the rotation around the Z-axis, x is the translation along the X-axis, y is the translation along the Y-axis, and z is the translation around the Z-axis.

[0013] Furthermore, the rotation matrix R in S2 X Calculate according to formula 1:

[0014]

[0015] The rotation matrix R Y Calculate according to formula 2:

[0016]

[0017] The rotation matrix R Z Calculate according to formula 3:

[0018]

[0019] The total rotation matrix is ​​calculated according to Formula 4:

[0020] R=R z ×R y ×R x (Formula 4)

[0021] The coordinate formulas of the eight points after the relative motion are shown in Formula 5:

[0022] P1′=R×P1+T (Formula 5)

[0023] P1 is any one of the eight points arranged on the relative motion segment ring A; T = (x, y, z) T is the translation vector;

[0024] The coordinate function of P1′ can be expressed as Formula 6 through Formula 1-5:

[0025] z A1 =[-sin(β)x A +cos(β)sin(α)y A +cos(β)cos(α)z A ]+z (Formula 6).

[0026] Furthermore, the initial distance d1 in S3 is calculated according to Formula 7:

[0027]

[0028] The distance after relative motion occurs is d2 and is calculated according to formula 8:

[0029]

[0030] The beneficial effect of the present invention is that the relative displacement between segment rings that occurs after simulating fault movement in the calculation method provided by the present invention can be determined by the relative elongation obtained by the Euler rotation formula, the distance formula between points, and the linear displacement value of the wire-type displacement sensor. The basic principle of this method is simple, and the displacement sensor is easy to deploy, which can provide a theoretical basis for disaster prevention and mitigation in tunnels across active faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of an example of a segment ring in the tunnel experiment across an active fault of the present invention.

[0032] Figure 2 Schematic diagram of selecting pairing points in the cross-active fault tunnel experiment of the present invention.

[0033] Figure 3 This is a schematic diagram of the layout of displacement sensors in the cross-active fault tunnel experiment of the present invention.

[0034] In the figure:

[0035] 1. Relative motion ring A; 2. Immovable segment ring B; 3. Pull-wire displacement sensor; 4. Any point P1 of relative motion ring A; 5. P2, a point paired with immovable segment ring B. DETAILED DESCRIPTION

[0036] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] The present invention provides a method for calculating the relative displacement of a tunnel segment ring across an active fault, comprising the following steps:

[0038] S1: Select two adjacent segment rings to establish a spatial rectangular coordinate system. The two segment rings are the relative motion ring A and the fixed segment ring B. Select two coordinate points at the arch top, the arch waists on both sides and the arch bottom of each segment ring and measure the coordinate values. Pair the corresponding points on the two segment rings and arrange the wire displacement sensors 3 to form eight groups of corresponding coordinate points: any coordinate of the relative motion ring A is P1(x A ,y A , z A ), the coordinates of the point where the immovable segment ring B is paired with it are P2(x B ,y B , z B );

[0039] S2: Through the six basic unknown quantities in space, according to the three-dimensional Euler rotation formula, the rotation matrices Rx, Ry, Rz and the total rotation matrix R and translation vector T are constructed in the order of rotating around the X axis, then around the Y axis and finally around the Z axis, and the coordinate formulas of the eight points arranged after the relative motion segment ring A are obtained, and the coordinate function of the point P1′ after the relative displacement is obtained;

[0040] S3: Obtain the relative elongation d by the difference between the initial distance d1 of the eight paired points and the distance d2 between the points after the movement, that is, d=d2-d1;

[0041] S4: Based on the linear displacement and relative elongation values ​​measured by the wire-type displacement sensor after the relative motion segment ring A moves, eight nonlinear equations are established, and the optimal solution of the six unknown motion quantities in space is obtained using the optimization solution program to obtain the final relative motion quantity.

[0042] In the spatial rectangular coordinate system of S1, the centroid of the relatively moving segment ring A is at the origin of the coordinates, the centroid of the stationary segment ring B is on the X-axis, the height direction of the segment ring is on the Z-axis, and the Y-axis is perpendicular to the XZ plane.

[0043] like Figure 1 to Figure 2 As shown, the centroid of the relatively moving segment ring A in the two segment rings is at the origin of the coordinates, the centroid of the stationary segment ring B is on the X-axis, the height direction of the segment ring is on the Z-axis, and the Y-axis is perpendicular to the XZ plane, so as to establish a spatial rectangular coordinate system; eight points are selected from each of the two segment rings to form eight groups of paired points corresponding to each other, and the pull-wire displacement sensors 3 are arranged, of which six groups of paired points are arranged in a cross-type arrangement and two groups of paired points are arranged in a parallel type, and the coordinate values ​​of the spatial rectangular coordinate system of the sixteen points are measured at the same time, and the initial distance d1 between the paired points is calculated;

[0044] Assume that any point in the relative motion segment ring A is P1(x A ,y A , z A ), the paired point in the immovable segment ring B is p2(x B ,y B , z B ); Assume that the six basic relative motion components in space are α, β, γ, x, y, and z, and establish the coordinate expression of any point of the relative motion ring A after relative motion through the Euler rotation formula of the three-dimensional rigid body in space, and calculate the relative distance d2 of the eight pairs of paired points after relative motion; finally, establish eight nonlinear equations through the linear displacement value measured by the pull-wire displacement sensor and the relative elongation d, and obtain the optimal solution of the six basic relative motion components in space through the optimization algorithm.

[0045] In the two segment rings of S1, six groups of pull-wire displacement sensors at paired points are arranged in a cross-type arrangement, and the remaining two groups of pull-wire displacement sensors 3 at adjacent paired points are arranged in parallel. For the specific arrangement of the pull-wire displacement sensors 3, see Figure 3 , select any six adjacent pairs of paired points for cross arrangement, and select the remaining two adjacent pairs of paired points for parallel arrangement.

[0046] The six unknown quantities of spatial motion in S2 are: α is the rotation around the X-axis, β is the rotation around the Y-axis, γ is the rotation around the Z-axis, x is the translation along the X-axis, y is the translation along the Y-axis, and z is the translation around the Z-axis.

[0047] The rotation matrix R in S2 X Calculate according to formula 1:

[0048]

[0049] The rotation matrix R Y Calculate according to formula 2:

[0050]

[0051] The rotation matrix R Z Calculate according to formula 3:

[0052]

[0053] The total rotation matrix is ​​calculated according to Formula 4:

[0054] R=R z ×R y ×R x (Formula 4)

[0055] The coordinate formulas of the eight points after the relative motion are shown in Formula 5:

[0056] P1′=R×P1+T (Formula 5)

[0057] P1 is any one of the eight points arranged on the relative motion segment ring A; T = (x, y, z) T is the translation vector;

[0058] The coordinate function of P1′ can be expressed as Formula 6 through Formula 1-5:

[0059] z A1 =[-sin(β)x A +cos(β)sin(α)y A +cos(β)cos(α)z A ]+z (Formula 6).

[0060] The initial distance d1 in S3 is calculated according to Formula 7:

[0061]

[0062] The distance after relative motion occurs is d2 and is calculated according to formula 8:

[0063]

[0064] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

Claims

1. A method for calculating the relative displacement of a tunnel segment ring across an active fault, characterized in that: The following steps are involved: S1: Select two adjacent segment rings to establish a spatial rectangular coordinate system. The two segment rings are the relative motion ring A and the fixed segment ring B. Select two coordinate points at the arch top, the arch waists on both sides and the arch bottom of each segment ring and measure the coordinate values. Pair the corresponding points on the two segment rings and arrange the wire displacement sensors to form eight groups of corresponding coordinate points: any coordinate of the relative motion ring A is P1 (x A ,y A , z A ), the coordinates of the point where the immobile segment ring B is paired with it are P2 (x B ,y B , z B ); S2: Through the six basic unknown quantities in space, according to the three-dimensional Euler rotation formula, the rotation matrices Rx, Ry, Rz and the total rotation matrix R and translation vector T are constructed in the order of rotating around the X axis, then around the Y axis and finally around the Z axis, and the coordinate formulas of the eight points arranged after the relative motion segment ring A are obtained, and the coordinate function of the point P1′ after the relative displacement is obtained; S3: Obtain the relative elongation d by the difference between the initial distance d1 of the eight paired points and the distance d2 between the points after the movement, that is, d=d2-d1; S4: Based on the linear displacement and relative elongation values ​​measured by the wire-type displacement sensor after the relative motion segment ring A moves, eight nonlinear equations are established, and the optimal solution of the six unknown motion quantities in space is obtained using the optimization solution program to obtain the final relative motion quantity.

2. The method for calculating the relative displacement of a tunnel segment ring across an active fault according to claim 1 is characterized in that: In the spatial rectangular coordinate system of S1, the centroid of the relatively moving segment ring A is at the origin of the coordinates, the centroid of the stationary segment ring B is on the X-axis, the height direction of the segment ring is on the Z-axis, and the Y-axis is perpendicular to the XZ plane.

3. The method for calculating the relative displacement of tunnel segments across active faults according to claim 1 is characterized in that: The draw-wire displacement sensors of six groups of paired points in the two segment rings in S1 are arranged in a cross-type arrangement, and the draw-wire displacement sensors of the remaining two groups of adjacent paired points are arranged in parallel.

4. The method for calculating the relative displacement of tunnel segments across active faults according to claim 1 is characterized in that: The six basic spatial unknowns in S2 are: is the rotation around the X axis, is the rotation around the Y axis, is the rotation around the Z axis, x is the translation along the X axis, y is the translation along the Y axis, and z is the translation around the Z axis.

5. The method for calculating the relative displacement of tunnel segments across active faults according to claim 4 is characterized in that: The rotation matrix R in S2 X Calculate according to formula 1: (Formula 1) The rotation matrix R Y Calculate according to formula 2: (Formula 2) The rotation matrix R Z Calculate according to formula 3: (Formula 3) The total rotation matrix is ​​calculated according to Formula 4: R=R z ×R y ×R x (Formula 4) The coordinate formulas of the eight points after the relative motion are shown in Formula 5: P1′=R×P1+T (Formula 5) P1 is any one of the eight points arranged on the relative motion segment ring A; T = (x, y, z) T is the translation vector; The coordinate function of P1′ can be expressed as Formula 6 through Formula 1-5: (Formula 6).

6. The method for calculating the relative displacement of tunnel segments across active faults according to claim 5 is characterized in that: The initial distance d1 in S3 is calculated according to Formula 7: (Formula 7) The distance after relative motion occurs is d2 and is calculated according to formula 8: (Formula 8).

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