Shield tunnel segment relative displacement monitoring system and calculation method

Abstract

The invention discloses a shield tunnel segment relative displacement monitoring system and a calculation method, and relates to the technical field of civil engineering. The system comprises an optical fiber fixing point, a zigzag optical fiber, an optical fiber demodulator and a computer, the optical fiber fixing point is used for fixing an optical fiber at a set position on the tunnel segment; the zigzag optical fibers are arranged in three optical fiber arrangement modes to form an optical fiber monitoring network of two parallel optical fibers at the upper part and the lower part of the segment and a V-shaped optical fiber in the middle; the optical fiber demodulator is respectively connected with the zigzag optical fibers in the three layout forms and the computer, and is used for acquiring the strain magnitude of the three zigzag optical fibers in the tunnel deformation process, obtaining the length variation of the optical fibers among the optical fiber fixing points, and calculating the opening amount, the slab staggering amount and the corner deformation among the segments. According to the invention, opening, slab staggering and corner deformation of tunnel segments can be comprehensively monitored in real time, so that tunnel risks and hidden dangers can be monitored more comprehensively, and the safety and stability of a tunnel are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering, and particularly to a relative displacement monitoring system and calculation method for shield tunnel segments. Background Art

[0002] With the rapid development of cities, the construction of urban rail transit shows a rapid upward trend. As an important part of urban rail transit, how to efficiently monitor tunnels has become a top priority. Due to the complex environment inside shield tunnels, high requirements are placed on monitoring technologies. Traditional monitoring methods, such as surveying and mapping measurement methods, GPS methods, laser scanning methods, etc., are all susceptible to environmental influences and cannot meet the requirements of high precision and high efficiency. Among fiber optic monitoring technologies, fiber optic sensors have the characteristics of small volume, light weight, corrosion resistance, and electromagnetic interference resistance, and can well adapt to the environment of shield tunnels. However, many current fiber optic laying methods cannot achieve the monitoring of segment rotation while monitoring tunnel settlement. Summary of the Invention

[0003] The purpose of the present invention is to provide a relative displacement monitoring system and calculation method for shield tunnel segments, which can comprehensively and real-time monitor the opening, dislocation, and rotational deformation of tunnel segments, so as to more comprehensively monitor the risk hazards of tunnels and ensure the safety and stability of tunnels.

[0004] To achieve the above purpose, the present invention provides the following solutions:

[0005] A relative displacement monitoring system for shield tunnel segments includes: fiber optic fixed points, zigzag optical fibers, a fiber optic demodulator, and a computer;

[0006] The fiber optic fixed points are used to fix optical fibers at set positions on tunnel segments; the set positions are at the transverse center of the segments, and the distance between fixed points of adjacent segments is equal to the segment width;

[0007] The zigzag optical fibers are arranged in three fiber laying methods, and finally form an optical fiber monitoring network with two parallel optical fibers above and below the segment and a "V"-shaped optical fiber in the middle;

[0008] The fiber optic demodulator is respectively connected to the zigzag optical fibers in three laying forms and the computer, and is used to obtain the strain magnitudes that occur in the three zigzag optical fibers during tunnel deformation, obtain the length change amounts of the optical fibers between each fiber optic fixed point, and calculate the relative displacement between segments; the relative displacement includes the opening amount, dislocation amount, and rotational deformation.

[0009] Optionally, two fiber optic fixed points are arranged for each ring of segments, symmetrically distributed with respect to the tunnel central axis, and avoiding segment joints.

[0010] Optionally, the three fiber laying methods of the zigzag optical fibers specifically include:

[0011] The first fiber - laying method is to connect the upper fiber fixing points of the first three segments respectively, then connect the lower fiber fixing point of the fourth segment with an inclined fiber, then connect the lower fiber fixing points of the fourth, fifth, and sixth segments, and then connect the upper fiber fixing point of the seventh segment with an inclined fiber. The subsequent segments are all connected according to the rule, forming the first zigzag - shaped fiber - laying method;

[0012] The second fiber - laying method is to connect the lower fiber fixing points of the first two segments, then connect the upper fiber fixing point of the third segment with an inclined fiber, and then connect the upper fiber fixing points of the third, fourth, and fifth segments. After that, the fiber - laying follows the rule of connecting the upper or lower fiber fixing points of three segments and then connecting the fiber fixing point at another height of the next segment with an inclined fiber, forming the second zigzag - shaped fiber - laying;

[0013] The third fiber - laying method is to connect the upper fiber fixing point of the first segment with the lower fiber fixing point of the second segment. After that, the fiber - laying follows the rule of connecting the lower or upper fiber fixing points of three segments and then connecting the fiber fixing point at another height of the next segment with an inclined fiber, forming the third zigzag - shaped fiber - laying.

[0014] The present invention also provides a method for monitoring and calculating the relative displacement of shield - tunnel segments. Based on the above - mentioned system, it includes:

[0015] Construct a fiber - optic monitoring network and obtain the fiber - optic strain data between each fiber fixing point;

[0016] Calculate the length of the fiber between each fixing point after deformation according to each fiber - optic strain data, obtain the included - angle value between the fibers through the cosine formula, and finally obtain the rotation angle between any two adjacent rings of segments from the sum of the interior angles of a triangle;

[0017] Establish a coordinate system with two adjacent segments. Determine the coordinates of each fiber fixing point from the fiber included - angle, and finally compare the coordinates of the centroid points of the two segments to calculate the opening amount and offset amount between any two adjacent rings of segments.

[0018] Optionally, the calculation formula for the length of the fiber after deformation is:

[0019]

[0020] where the fiber - optic strain data ε is measured by a fiber - optic demodulator, L0 is the initial length of the fiber, and L is the length of the fiber after deformation;

[0021] Taking the first segment as a reference, the rotation - deformation formula of the second segment relative to the first segment is:

[0022]

[0023] Taking the second segment of the segment lining as the reference, the formula for the angular deformation between the second segment of the segment lining and the third segment of the segment lining is as follows:

[0024]

[0025] Wherein, a represents the length value of the optical fiber after deformation in the BD section, b represents the length value of the optical fiber after deformation in the AC section, c1 represents the length value of the optical fiber after deformation in the BC section, c2 represents the length value of the optical fiber after deformation in the AD section, and d represents the distance between the two optical fiber fixing points on the segment lining.

[0026] Optionally, the calculation formulas for the opening amount and the stagger amount between any two adjacent rings of segment linings are as follows:

[0027] Taking the first segment of the segment lining as the reference, the formula for calculating the stagger amount of the second segment of the segment lining relative to the first segment of the segment lining is as follows: The formula for calculating the opening amount of the second segment of the segment lining relative to the first segment of the segment lining is as follows:

[0028] Wherein:

[0029] Taking the second segment of the segment lining as the reference, the formula for calculating the stagger amount of the third segment of the segment lining relative to the second segment of the segment lining is The formula for calculating the opening amount of the third segment of the segment lining relative to the second segment of the segment lining is

[0030] Wherein:

[0031] In the formula, a represents the length value of the optical fiber after deformation in the BD section, b represents the length value of the optical fiber after deformation in the AC section, c1 represents the length value of the optical fiber after deformation in the BC section, c2 represents the length value of the optical fiber after deformation in the AD section, and d represents the distance between the two optical fiber fixing points on the segment lining.

[0032] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0033] The present invention discloses a shield tunnel segment relative displacement monitoring system and a calculation method. The system includes an optical fiber fixing point, a zigzag optical fiber, an optical fiber demodulator, and a computer. The optical fiber fixing point is used to fix the optical fiber at a set position on the tunnel segment. The zigzag optical fiber is arranged in three optical fiber laying methods to form an optical fiber monitoring network with two parallel optical fibers on the upper and lower parts of the segment and a "V"-shaped optical fiber in the middle. The optical fiber demodulator is respectively connected to the zigzag optical fibers in the three laying forms and the computer, and is used to obtain the strain magnitudes generated by the three zigzag optical fibers during the tunnel deformation, obtain the length change amounts of the optical fiber between the optical fiber fixing points, and calculate the opening amount, dislocation amount, and angular deformation between the segments. The present invention can comprehensively and real-time monitor the opening, dislocation, and angular deformation of the tunnel segment, so as to more comprehensively monitor the tunnel risk hazards and ensure the safety and stability of the tunnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0035] Figure 1 It is the final schematic diagram of the optical fiber network in this embodiment;

[0036] Figure 2 It is the schematic diagram of the laying methods of the three rectangular optical fibers in this embodiment;

[0037] Figure 3 It is the schematic diagram of the coordinate selection after the deformation of the first segment and the second segment in this embodiment;

[0038] Figure 4 It is the schematic diagram of the coordinate selection after the deformation of the second segment and the third segment in this embodiment.

[0039] Reference numerals: 1, zigzag optical fiber; 2, tunnel segment; 3, optical fiber fixing point; 4, optical fiber demodulator; 5, computer. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present invention.

[0041] The object of the present invention is to provide a relative displacement monitoring system and calculation method for shield tunnel segments, which can comprehensively and real-time monitor the opening, dislocation and angular deformation of tunnel segments, so as to more comprehensively monitor the risk hazards of the tunnel and ensure the safety and stability of the tunnel.

[0042] In order to make the above objects, features and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] The present invention provides a relative displacement monitoring system and calculation method for shield tunnel segments 2, which is used to monitor the opening, dislocation and angular deformation of shield tunnel segments 2. The method includes the following steps:

[0044] Step 1: Determine the tunnel monitoring range. In the tunnel monitoring range, determine the positions of the optical fiber fixing points 3 on each ring of tunnel segments 2, and install the optical fiber fixing points 3. The optical fiber fixing points 3 are selected at the transverse midpoint positions of the tunnel segments 2, and two optical fiber fixing points 3 are arranged on each ring of segments, symmetrically distributed with respect to the tunnel central axis and avoiding the segment joints. As Figure 1 shown.

[0045] Step 2: On the basis of the arranged optical fiber fixing points 3, perform the layout of the three zigzag optical fibers 1 as shown in Figure 2 . The final layout result is as shown in Figure 1 , forming an overall layout method of two parallel optical fibers on the upper and lower parts of the segment and a "V"-shaped optical fiber in the middle.

[0046] Step 3: Connect the three zigzag optical fibers 1 to the optical fiber demodulator 4 respectively, monitor the optical fiber strain between each optical fiber fixing point 3, calculate the length of the optical fiber after deformation between each fixing point according to the monitoring results, obtain the included angle value between the optical fibers through the cosine formula, and finally obtain the rotation angle between any two adjacent rings of segments from the sum of the interior angles of the triangle.

[0047] Step 4: Measure the optical fiber strain values between each optical fiber fixing point 3 by the optical fiber demodulator 4, and combine with the strain formula (where the strain ε is measured by the optical fiber demodulator 4, L0 is the initial length of the optical fiber, and L is the length of the optical fiber after deformation), calculate the length of the optical fiber after deformation between each fixing point, and then obtain the included angle value between the optical fibers through the cosine formula. Taking Figure 3 as an example, taking the first segment as the reference, the rotation angle deformation formula between the second segment and the first segment is:

[0048]

[0049] Taking Figure 4 as an example, taking the second segment as the reference, the rotation angle deformation formula between the second segment and the third segment is:

[0050] Step 5: As shown in Figure 3 and Figure 4 , establish a coordinate system with two adjacent segments. Determine the coordinates of each optical fiber fixing point 3 based on the included angle of the optical fibers. Finally, compare the coordinates of the centroid points of the two segments to calculate the opening and offset amounts between any two adjacent rings of segments. Taking Figure 3 as an example, with the first segment as the reference, the formula for calculating the offset amount of the second segment relative to the first segment is The formula for calculating the opening amount of the second segment relative to the first segment is where Similarly, taking Figure 4 as an example, with the second segment as the reference, the formula for calculating the offset amount of the third segment relative to the second segment is The formula for calculating the opening amount of the third segment relative to the second segment is where

[0051] In the formula, a represents the length value of the optical fiber after deformation in the BD section, b represents the length value of the optical fiber after deformation in the AC section, c1 represents the length value of the optical fiber after deformation in the BC section, c2 represents the length value of the optical fiber after deformation in the AD section, and d represents the distance between the two optical fiber fixing points on the upper and lower sides of the segment.

[0052] Except that the displacement calculation methods for the first segment and the second segment are different, the calculation methods for the angular deformation amount, opening amount, and offset amount of the segments after the second segment can all apply the calculation methods for the angular deformation amount, opening amount, and offset amount of the third segment relative to the second segment.

[0053] Based on the above technical solution, the following specific embodiments are provided.

[0054] As shown in Figure 1 , the present invention provides a relative displacement monitoring network for shield tunnel segments 2 based on optical fiber sensors and its monitoring and calculation method. The optical fiber network includes a zigzag optical fiber 1, an optical fiber fixing point 3, an optical fiber demodulator 4, and a computer 5. The optical fiber fixing point 3 is used to fix the optical fiber on the tunnel segment 2. Its position is selected at the transverse center of the segment to ensure that the distance between the fixing points of adjacent segments is equal to the segment width; and two optical fiber fixing points 3 are arranged on each ring of segments, symmetrically distributed with respect to the tunnel central axis and avoiding the segment joints. Then, the three types of zigzag optical fibers 1 shown in Figure 2 are respectively arranged on the segments, and finally form as shown in Figure 1As shown, there is a fiber optic layout method in which the upper and lower segments of the segment are connected by two horizontal optical fibers and the middle part is composed of adjacent diagonal optical fibers to form a "V" shape. Three zigzag optical fibers 1 are respectively connected to an optical fiber demodulator 4 to measure the strain magnitudes generated in the three optical fibers during the tunnel deformation, and obtain the length change amounts between the optical fiber fixed points 3 of each optical fiber. Then, the included angle value between the optical fibers is obtained through the cosine formula, and finally the angular deformation between any two adjacent segments is obtained from the sum of the interior angles of a triangle. As Figure 3 and Figure 4 shown, a coordinate system is established with two adjacent segments. The coordinates of each optical fiber fixed point 3 are determined by the included angle of the optical fibers. Finally, the coordinates of the centroid points of the two segments are compared, and the opening amount and offset amount between any two adjacent segments are calculated.

[0055] For the above implementation method, specific data is used here for calculation demonstration. The angular deformation calculation between the tunnel segments 2 is as follows:

[0056] Taking Figure 3 the first segment and the second segment as an example, calculate the angular deformation of the second segment relative to the first segment. Assume that the deformed lengths a and b of the optical fibers BD and AC are 802 mm and 801 mm respectively. The deformed length c1 of the optical fiber BC is 1281 mm. d is the distance between the upper and lower fixed points of the segment, which is a fixed value determined when the fixed points are initially set. Here, it is selected as 1000 mm. The ∠ABD and ∠BDC can be calculated through the cosine formula. The calculation process is as follows:

[0057]

[0058] Finally, the angular deformation of the segment is calculated as follows:

[0059] ∠α = π - ∠ABD - ∠BDC = 180° - 90.02° - 89.92° = 0.06°

[0060] Taking Figure 4 the second segment and the third segment as an example, calculate the angular deformation of the third segment relative to the second segment. Assume that the deformed lengths a and b of the optical fibers BD and AC are also 802 mm and 801 mm. The deformed length c2 of the optical fiber AD is 1281 mm, and the distance d between the upper and lower fixed points of the segment is 1000 mm. The ∠ABD and ∠BDC can be calculated through the cosine formula. The calculation process is as follows:

[0061]

[0062] The angular deformation of the third segment relative to the second segment is calculated as follows:

[0063] ∠β = 180° - ∠ABD - ∠BDC = 180° - 89.92° - 90.02° = 0.06°

[0064] Combined with specific data, the opening amount and offset amount between two tunnel segments 2 are calculated as follows:

[0065] Taking Figure 3 as an example, find the offset amount and opening amount of the second segment relative to the first segment. Take the midpoint E of the line segment AB connecting the two optical fiber fixing points 3 on the first segment as the coordinate origin to establish a coordinate system, where F is the midpoint of CD. Similarly, assume that the lengths a and b of the deformed optical fibers BD and AC are measured to be 802 mm and 801 mm respectively, the length c1 of the deformed optical fiber BC is 1281 mm, and the distance d between the optical fiber fixing points 3 on the same segment is 1000 mm. Combining the angles between the optical fibers, the coordinates of each point on the optical fiber can be obtained, and the specific coordinates are as follows:

[0066] E(0, 0)

[0067] A(0, -500)

[0068] B(0, 500)

[0069] D(802×sin∠ABD, 500 - 802×cos∠ABD)

[0070] C(801×sin∠BAC, -500 + 801×cos∠BAC)

[0071]

[0072] Among them:

[0073] Finally, compare the centroids of the two segments to obtain the offset amount ω and opening amount S of the second segment relative to the first segment. The calculation process is as follows:

[0074]

[0075] Taking Figure 4 as an example, find the offset amount of the third segment relative to the second segment. Take the midpoint E of the line segment AB connecting the two optical fiber fixing points 3 on the second segment as the coordinate origin to establish a coordinate system, where F is the midpoint of CD. Similarly, assume that the lengths a and b of the deformed optical fibers BD and AC are measured to be 802 mm and 801 mm respectively, the length c2 of the deformed optical fiber AD is 1281 mm, and the distance d between the optical fiber fixing points 3 on the same segment is 1000 mm. Combining the angles between the optical fibers, the coordinates of each point on the optical fiber can be obtained, and the specific coordinates are as follows:

[0076] E(0, 0)

[0077] A(-500×sin∠α, -500×cos∠α)

[0078] B(500×sin∠α, 500×cos∠α)

[0079] C(-500×sin∠α + 801×cos∠CAA', -500×cos∠α + 801×sin∠CAA')

[0080] D(500×sin∠α + 802×cos∠DBB', 500×cos∠α + 802×sin∠DBB')

[0081]

[0082] Wherein:

[0083] Finally, compare the centroids of the two segments, and obtain the stagger amount ω and the opening amount S of the third segment relative to the second segment. The calculation process is as follows:

[0084]

[0085] By taking the first segment as the reference point, the opening amount, stagger amount and angular deformation amount of the second segment relative to the first segment can be obtained through the above calculation method. Similarly, by taking the second segment as the reference, the opening amount, stagger amount and angular deformation amount of the third segment relative to the second segment can be obtained. Similarly, the opening amount, stagger amount and angular deformation amount of the subsequent segments can be calculated using this method, and the displacements of each segment relative to the previous reference segment can be calculated in turn. In summary, the above technical means and research methods can provide reference for practical engineering.

[0086] Therefore, the present solution has the following beneficial effects:

[0087] The fiber optic network and its monitoring and calculation method for relative displacement monitoring of shield tunnel segments 2 based on fiber optic sensors of the present invention can not only detect the stagger amount and opening amount of tunnel segments 2, but also monitor the angular deformation amount of the segments. Its calculation steps are clear and the calculation method is simple, which can provide more guarantees for tunnel safety in practical engineering and has good popularization and application value.

[0088] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other.

[0089] In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A monitoring system for the relative displacement of segment linings in a shield tunnel, characterized in that Including: Optical fiber fixing points, zigzag optical fibers, an optical fiber demodulator, and a computer; The optical fiber fixing points are used to fix optical fibers at set positions on tunnel segments; The set positions are at the transverse center of the segments, and the spacing between the fixing points of adjacent segments is equal to the segment width; The zigzag optical fibers are arranged in three optical fiber laying methods to finally form an optical fiber monitoring network with two parallel optical fibers on the upper and lower parts of the segment and a "V"-shaped optical fiber in the middle; The optical fiber demodulator is respectively connected to the zigzag optical fibers in three laying forms and the computer, and is used to obtain the strain magnitudes that occur to the three zigzag optical fibers during tunnel deformation, obtain the length change amounts of the optical fibers between the respective optical fiber fixing points, and calculate the relative displacement between segments; the relative displacement includes the opening amount, the stagger amount, and the angular deformation.

2. The shield tunnel segment relative displacement monitoring system according to claim 1, characterized in that Two optical fiber fixing points are arranged on each ring of segments, symmetrically distributed with respect to the tunnel central axis, and avoiding the segment joints.

3. The shield tunnel segment relative displacement monitoring system according to claim 1, characterized in that The three optical fiber laying methods of the zigzag optical fibers specifically include: The first optical fiber laying method is to connect the upper optical fiber fixing points of the first three segments respectively, then connect the lower optical fiber fixing point of the fourth segment with an oblique optical fiber, then connect the lower optical fiber fixing points of the fourth, fifth, and sixth segments, and then connect the upper optical fiber fixing point of the seventh segment with an oblique optical fiber. The subsequent segments are all connected according to the rule to form the first zigzag optical fiber laying method; The second optical fiber laying method is to connect the lower optical fiber fixing points of the first two segments, then connect the upper optical fiber fixing point of the third segment with an oblique optical fiber, and then connect the upper optical fiber fixing points of the third, fourth, and fifth segments. The subsequent optical fiber laying all follows the rule of connecting the upper or lower optical fiber fixing points of three segments and then connecting the optical fiber fixing point at the other height of the next segment with an oblique optical fiber to form the second zigzag optical fiber laying; The third optical fiber laying method is to connect the upper optical fiber fixing point of the first segment with the lower optical fiber fixing point of the second segment. The subsequent optical fiber laying all follows the rule of connecting the lower or upper optical fiber fixing points of three segments and then connecting the optical fiber fixing point at the other height of the next segment with an oblique optical fiber to form the third zigzag optical fiber laying.

4. A monitoring and calculation method for the relative displacement of segments in a shield tunnel, based on the system described in any one of claims 1-3, characterized in that, Including: Constructing an optical fiber monitoring network and obtaining the optical fiber strain data between the respective optical fiber fixing points; Calculating the lengths of the optical fibers between the respective fixing points after deformation according to the respective optical fiber strain data, obtaining the included angle values between the optical fibers through the cosine formula, and finally obtaining the rotation angle between any two adjacent rings of segments from the sum of the interior angles of a triangle; Establishing a coordinate system with two adjacent segments, determining the coordinates of the respective optical fiber fixing points from the included angle of the optical fibers, and finally comparing the coordinates of the centroid points of the two segments to calculate the opening amount and the stagger amount between any two adjacent rings of segments.

5. The method for calculating the relative displacement monitoring of the shield tunnel segment according to claim 4, wherein, The calculation formula for the length of the optical fiber after deformation is: Among them, the optical fiber strain data ε is measured by the optical fiber demodulator, L0 is the initial length of the optical fiber, and L is the length of the optical fiber after deformation; Taking the first segment as the reference, the angular deformation formula between the second segment and the first segment is as follows: Taking the second segment as the reference, the rotation angle deformation formula between the second segment and the third segment is: Among them, a represents the length value of the optical fiber after deformation in the BD section, b represents the length value of the optical fiber after deformation in the AC section, c1 represents the length value of the optical fiber after deformation in the BC section, c2 represents the length value of the optical fiber after deformation in the AD section, and d represents the distance between the two optical fiber fixing points on the upper and lower segments of the segment.

6. The shield tunnel segment relative displacement monitoring and calculation method according to claim 1, wherein The calculation formulas for the opening amount and the stagger amount between any two adjacent segments are as follows: Taking the first segment as the reference, the calculation formula for the stagger amount of the second segment relative to the first segment is as follows: The calculation formula for the opening amount of the second segment relative to the first segment is as follows: Wherein: Taking the second segment as the reference, the calculation formula for the stagger amount of the third segment relative to the second segment is The calculation formula for the opening amount of the third segment relative to the second segment is Wherein: In the formula, a represents the length value of the optical fiber after deformation in the BD section, b represents the length value of the optical fiber after deformation in the AC section, c1 represents the length value of the optical fiber after deformation in the BC section, c2 represents the length value of the optical fiber after deformation in the AD section, and d represents the distance between the two optical fiber fixing points on the upper and lower segments of the segment.

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