Method for detecting relative displacement on a concrete surface
Patent Information
- Application Number
- JP2023019209
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2023-02-10
- Publication Date
- 2026-09-25
- Estimated Expiration
- 2043-02-10
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Figure 0007924881000002 
Figure 0007924881000003 
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Abstract
Description
[Technical Field]
[0001] This invention relates to a method for detecting relative displacement on a concrete surface. [Background technology]
[0002] Techniques have been proposed to detect the width of cracks, for example, as a relative displacement on the surface of concrete. For example, Patent Document 1 describes laying an optical fiber along the longitudinal direction of the tunnel on the inner wall so as to straddle a crack in the inner wall of the tunnel, and determining the current width of the crack from the strain of the optical fiber. [Prior art documents] [Patent Documents]
[0003] [Patent Document 1] Japanese Patent Publication No. 2001-66117 [Overview of the project] [Problems that the invention aims to solve]
[0004] When installing optical fibers on a concrete surface, if the optical fiber is simply spot-fixed with adhesive or the like, with its extension direction aligned with the laying direction, the tension acting on the fixing point of the optical fiber in response to the relative displacement along the optical fiber on the concrete surface may cause the optical fiber to shift relative to the surface. As a result, the relative displacement may be calculated based on a strain smaller than the strain that actually occurs in the optical fiber, which can lead to inaccurate calculations of the relative displacement.
[0005] The present invention aims to provide a method for detecting relative displacement on a concrete surface that can detect relative displacement along an optical fiber on the concrete surface with greater accuracy. [Means for solving the problem]
[0006] One aspect of the present invention is a method for detecting relative displacement on a concrete surface, which detects relative displacement along an optical fiber on the concrete surface based on strain generated in an optical fiber installed on the concrete surface, comprising: an optical fiber installation step of installing an optical fiber on the concrete surface such that the optical fiber alternates between a fixed portion fixed to the concrete surface and an unfixed portion not fixed to the concrete surface; and a detection step of detecting relative displacement along the optical fiber on the concrete surface based on strain generated in the optical fiber in each of the unfixed portions, wherein in the optical fiber installation step, a fixing jig including a columnar optical fiber winding portion is fixed to the concrete surface, and the optical fiber is wound along the side surface of the optical fiber winding portion with one or more turns to constitute the fixed portion.
[0007] In this configuration, a fixing jig including a columnar optical fiber winding section is fixed to the surface of the concrete. The optical fiber is wound along the side of the optical fiber winding section with one or more turns. Therefore, compared to, for example, a case where the optical fiber is simply spot-fixed with adhesive or the like with the optical fiber's extension direction aligned with the laying direction, the fixing section is configured so that the optical fiber is less likely to shift relative to the concrete surface. As a result, it is possible to suppress the occurrence of strain in the unfixed optical fiber that is smaller than the strain corresponding to the relative displacement along the optical fiber on the concrete surface, and thus the relative displacement along the optical fiber on the concrete surface can be detected with greater accuracy.
[0008] In one embodiment, pretension may be applied to the optical fiber in the non-fixed portion adjacent to the fixed portion during the optical fiber installation process. In this case, slippage of the optical fiber between the optical fiber and the optical fiber winding portion becomes less likely.
[0009] In one embodiment, during the optical fiber installation process, the magnitude of the pretension and the number of turns of the optical fiber in the fixed section may be calculated using the elastic modulus of the optical fiber, the cross-sectional area of the optical fiber, the coefficient of friction between the optical fiber and the optical fiber winding section, the assumed strain expected in the unfixed section of the optical fiber, and the capstan equation. In this case, the magnitude of the pretension and the number of turns can be determined so that slippage of the optical fiber does not occur between the optical fiber and the optical fiber winding section, even if the assumed strain expected in the unfixed section of the optical fiber occurs.
[0010] In one embodiment, the optical fiber installation process may be set to a pretension magnitude greater than or equal to the assumed compressive strain that is expected to occur when the concrete is compressed under predetermined conditions, and in the detection process, the compressive strain of the concrete may be measured based on the amount of relaxation of the pretension caused by the compression of the concrete. In this case, the compressive strain of the concrete can be measured within the range of the pretension magnitude.
[0011] In one embodiment, the fixing jig has a side displacement section that displaces the side surface of the optical fiber winding section relative to the concrete surface, and in the optical fiber installation process, pretension may be applied to the optical fiber in the non-fixed section adjacent to the fixed section by displacing the side surface relative to the concrete surface using the side displacement section. In this case, the pretension can be easily adjusted by adjusting the amount by which the side surface is displaced relative to the concrete surface by the side displacement section. [Effects of the Invention]
[0012] According to the method for detecting relative displacement on a concrete surface of the present invention, relative displacement along an optical fiber on the concrete surface can be detected with greater accuracy. [Brief explanation of the drawing]
[0013] [Figure 1] (a) is a side view illustrating a conceptual method for detecting relative displacement of a concrete surface according to one embodiment. (b) is a bottom view of (a). [Figure 2] It is a flowchart illustrating a method for detecting relative displacement of a concrete surface according to an embodiment. [Figure 3] It is a diagram illustrating the concept of spatial resolution of an optical fiber and measurement intervals. [Figure 4] (a) is a perspective view showing an example of a fixing portion. (b) is an enlarged perspective view showing the fixing portion of (a). [Figure 5] (a) is a perspective view showing an example of a fixing jig. (b) is a perspective view showing another example of the fixing jig. [Figure 6] (a) is a perspective view showing an end portion of a separator protruding from concrete. (b) is a cross-sectional view showing a configuration example of a fixing portion using the end portion of the separator of (a). (c) is a perspective view showing an end portion of a separator protruding at the bottom of a cone hole recessed from the formwork surface of concrete. (d) is a cross-sectional view showing a configuration example of a fixing portion using the end portion of the separator of (c). [Figure 7] It is a diagram for explaining calculation using the capstan equation. [Figure 8] (a) is a plan view showing a first example of a fixing jig having a side surface displacement portion. (b) is a plan view showing an example of side surface displacement caused by the side surface displacement portion of (a). (c) is a cross-sectional view taken along line c-c of (b). [Figure 9] (a) is a plan view showing a second example of a fixing jig having a side surface displacement portion. (b) is a plan view showing an example of side surface displacement caused by the side surface displacement portion of (a). (c) is a cross-sectional view taken along line c-c of (b). [Figure 10] (a) is a plan view showing a third example of a fixing jig having a side surface displacement portion. (b) is a plan view showing an example of side surface displacement caused by the side surface displacement portion of (a). (c) is a cross-sectional view taken along line c-c of (b). [Figure 11] It is a perspective view showing a joint portion to which a method for detecting relative displacement of a concrete surface according to a modification is applied. Mode for Carrying Out the Invention
[0014] Hereinafter, embodiments of the present invention will be described with reference to the drawings. As shown in FIGS. 1(a), 1(b) and 2, a method for detecting relative displacement on a concrete surface according to an embodiment of the present invention is a method for detecting relative displacement along an optical fiber on the concrete surface based on strain generated in the optical fiber installed on the surface 2 of concrete 1. In the following embodiment, the width of a crack 3 generated in the surface 2 of concrete 1 in which a reinforcing material such as a reinforcing bar 4 or a steel material is embedded will be described as an example of the relative displacement along the optical fiber on the concrete surface. The crack 3 herein means, for example, a structural crack that can be expected to occur at regular intervals on the surface 2 of the concrete 1. In the method for detecting relative displacement on a concrete surface, the position of the crack 3 may be detected together with the width of the crack 3.
[0015] As shown in FIG. 2, in the method for detecting relative displacement on a concrete surface according to the present embodiment, as step S1, an optical fiber installation step of installing an optical fiber 10 on the surface 2 of concrete 1 is performed. In the optical fiber installation step, as shown in FIGS. 1(a) and 1(b), the optical fiber 10 is installed on the surface 2 of the concrete 1 such that the optical fiber 10 alternately has fixed portions 21 fixed to the surface 2 of the concrete 1 and non-fixed portions 22 not fixed to the surface 2 of the concrete 1.
[0016] The fixed portion 21 is the part in which the optical fiber 10 is fixed to the surface 2 of the concrete 1. The unfixed portion 22 is the part in which the optical fiber 10 is not fixed to the surface 2 of the concrete 1, and is also called the free length portion. The length L of the unfixed portion 22 is longer than the length of the spatial resolution interval S of the optical fiber 10. For example, as shown in Figure 3, when multiple measurement points 23 are set at predetermined intervals on the optical fiber 10 in order to decompose and detect each position of strain that has occurred in the optical fiber 10, the interval g1 of the measurement points 23 is determined by the measurement method for the strain that has occurred in the optical fiber 10. For example, in existing measurement systems, the interval g1 of the measurement points 23, that is, the data acquisition interval for strain that has occurred in the optical fiber 10, is typically 50 mm. Also, in this measurement system, the length of the spatial resolution interval S is typically 100 mm, which is twice the interval g1. Spatial resolution means, for example, that the average strain in the spatial resolution interval S is detected. While tensile strain is primarily assumed as the strain occurring in the optical fiber 10, compressive strain may also occur, as will be described later.
[0017] Furthermore, as shown in Figures 1(a) and 1(b), the length L of the non-fixed portion 22 is shorter than the interval g2. The interval g2 is the interval between the multiple cracks 3 that are expected to occur on the surface 2 of the concrete 1. The interval g2 is the cover c of the reinforcing bars 4 embedded in the concrete 1, and the distance c between the centers of each of the reinforcing bars 4. s The spacing can be determined by known methods, such as those found in the Standard Specifications for Concrete, based on the diameter φ of the reinforcing bar, a constant K1 relating to the surface coefficient of the steel material, and a coefficient K2 representing the effect of the number of layers of tensile steel. For example, the spacing g2 may be calculated by the following formula (1). Spacing g2=K1×K2×4×c+0.7×(c s -φ)···(1)
[0018] In the optical fiber installation process, the optical fiber 10 is installed on the surface 2 of the concrete 1 such that the direction of the expected cracks 3 intersects with the axial direction of the optical fiber 10. Preferably, the direction of the expected cracks 3 is perpendicular to the axial direction of the optical fiber 10.
[0019] As step S2, a position detection step (detection step) is performed to detect the location of cracks 3 that have formed on the surface 2 of the concrete 1 based on the strain generated in the optical fiber 10 installed on the surface 2 of the concrete 1 during the optical fiber installation step. In the position detection step, the location of cracks 3 that have formed on the surface 2 of the concrete 1 is detected based on the strain generated in the optical fiber 10 in each of the non-fixed parts 22.
[0020] For example, the frequency of Brillouin scattered light changes in proportion to the magnitude of the distortion in the optical fiber 10. Therefore, in the position detection process, an optical pulse of a predetermined frequency is incident from one end of the optical fiber 10, and the Brillouin scattered light generated by the optical pulse is measured at the other end. By measuring the change in optical frequency in the Brillouin scattered light along with the time indicating the position where the Brillouin scattered light was generated, the axial distortion of the optical fiber 10 is measured. If no distortion is detected in the unfixed part 22, it means that there are no cracks 3 in that unfixed part 22 and the fixed part 21 adjacent to that unfixed part 22.
[0021] The elongation of the optical fiber 10 in the unfixed portion 22 caused by the crack 3 is restricted between the pair of fixed portions 21 that sandwich the unfixed portion 22, making it possible to identify the location where the crack 3 occurred. In other words, the strain in the optical fiber 10 is detected using each fixed portion 21 as an independent reference point, and there is no interference between the strain detection results of different unfixed portions 22. In this embodiment, the location where the crack 3 occurred is limited to the unfixed portion 22. From the strain of the optical fiber 10 in each unfixed portion 22, the crack 3 on the surface 2 of the concrete 1 corresponding to each unfixed portion 22 is identified.
[0022] As step S3, a relative displacement detection process (detection process) is performed to detect the width of the crack 3 that has formed in the non-fixed part 22 as a relative displacement along the optical fiber 10 on the surface 2 of the concrete 1, based on the strain generated in the optical fiber 10 installed on the surface 2 of the concrete 1 during the optical fiber installation process.
[0023] If a crack 3 occurs on the surface 2 of concrete 1 at a position corresponding to the unfixed portion 22, the distance between the pair of fixed portions 21 flanking the unfixed portion 22 is relatively displaced along the optical fiber 10 by the width of the crack 3. Therefore, the elongation of the optical fiber 10 in the unfixed portion 22, using the fixed portion 21 on the surface 2 of concrete 1 as a reference point, corresponds to the width of the crack 3. The elongation of the optical fiber 10 in the unfixed portion 22 can be determined by integrating the strain of the optical fiber 10 between the fixed portions 21, which are the reference points, in the axial direction of the optical fiber 10. Thus, in the relative displacement detection process, the width of the crack 3 in the unfixed portion 22 is detected by integrating the strain generated in the optical fiber 10 in the unfixed portion 22.
[0024] Here, for example, if an optical fiber is simply fixed to the surface of concrete using a fixing method such as spot fixing with adhesive, with the optical fiber's extension direction aligned with the laying direction, the tension of the optical fiber acting on the fixing point according to the width of the crack may cause the optical fiber to shift relative to the wall surface. Specifically, in an experiment in which an RC concrete test specimen was pulled from both sides with a loading device, the crack width was measured by integrating the strain generated in the optical fiber using a pi-type displacement meter installed on the surface of the test specimen. It was found that when the measurement value from the displacement meter exceeded a predetermined value (e.g., 0.4 mm), the crack width detected by the optical fiber tended to be smaller than the measurement value from the displacement meter compared to when the measurement value from the displacement meter was below the predetermined value. In other words, as the crack width increases, the optical fiber shifts relative to the wall surface, and the crack width is calculated based on a strain smaller than the strain that should actually occur in the optical fiber. As a result, the crack width detected by the optical fiber may be smaller than the actual size of the crack width, which can lead to inaccurate calculation of the crack width. To suppress such a decrease in detection accuracy, in the method for detecting relative displacement of the concrete surface according to this embodiment, it is important to firmly fix the fixed part 21 to the surface 2 of the concrete 1 so that the elongation of the optical fiber 10 in the non-fixed part 22 accurately corresponds to the width of the crack 3.
[0025] Figure 4(a) is a perspective view showing an example of a fixing part. Figure 4(b) is a perspective view showing an enlarged view of the fixing part in Figure 4(a). As shown in Figures 4(a) and 4(b), in the optical fiber installation process, multiple fixing jigs 30 are fixed to the surface 2 of the concrete 1. The multiple fixing jigs 30 are fixed to the surface 2 of the concrete 1 so as to be aligned along the laying direction of the optical fiber 10. The multiple fixing jigs 30 are fixed to the surface 2 of the concrete 1 at regular intervals. The distance between adjacent fixing jigs 30 is the same as the interval g1 of the measurement points 23 described above. As a result, a fixed part 21 is formed where the fixing jigs 30 are fixed to the surface 2 of the concrete 1, and an unfixed part 22 is formed where the fixing jigs 30 are not fixed to the surface 2 of the concrete 1.
[0026] The fixing jig 30 includes a base 31 and an optical fiber winding portion 32 fixed to the base 31. The base 31 is the portion positioned along the surface 2 of the concrete 1. The base 31 may be, for example, a flat plate 33. The flat plate 33 is the portion positioned to abut against the surface 2 of the concrete 1. The flat plate 33 may be, for example, an iron or stainless steel flat plate, but is not limited to this example; any material that can be fixed to the surface 2 of the concrete 1 when measuring (detecting) relative displacement is acceptable. The shape of the flat plate 33 is not particularly limited, but may be, for example, a rectangle with the laying direction of the optical fiber 10 as the longitudinal direction. The short direction of the flat plate 33 may be twice or more the allowable bending radius of the optical fiber 10.
[0027] A projection 34 may be provided on the surface of the flat plate material 33 that faces the surface 2 of the concrete 1. The projection 34 is a part that firmly fixes the fixing jig 30 to the surface 2 of the concrete 1. The projection 34 restricts the relative movement of the fixing jig 30 and the surface 2 of the concrete 1 along the laying direction of the optical fiber 10. The projection 34 is fixed, for example, so as to extend in the direction normal from the center of the flat plate material 33. The projection 34 can be made of, for example, a round bar made of iron or stainless steel. The projection 34 is fixed to the flat plate material 33, for example, by welding. The surface of the projection 34 may have irregularities such as screw threads, although this is not essential.
[0028] In the optical fiber installation process, a hole 5 deeper than the length of the projection 34 is drilled into the surface 2 of the concrete 1, and the projection 34 of the fixing jig 30 is inserted into the hole 5. At this time, adhesive may be injected into the hole 5 while the projection 34 is inserted and embedded in the hole 5. The adhesive functions as an adhesive anchor, such as a chemical anchor (registered trademark). In this case, the threads formed on the projection 34 increase the adhesion of the adhesive. Alternatively, an insert nut may be embedded in the concrete 1 within the hole 5, and the threads on the projection 34 may be screwed into the insert nut.
[0029] The optical fiber winding section 32 is the part around which the optical fiber 10 is wound. The optical fiber winding section 32 is provided so as to protrude from the surface of the flat plate material 33 on the side that does not face the surface 2 of the concrete 1. The optical fiber winding section 32 protrudes from the flat plate material 33 on the opposite side from the projection 34. The optical fiber winding section 32 is fixed to the flat plate material 33, for example, so as to extend in the normal direction from the center of the flat plate material 33. The optical fiber winding section 32 can be made of, for example, iron, stainless steel, or resin, but is not limited to these examples, and any material that does not cause large deformation or displacement when measuring (detecting) relative displacement is acceptable. The optical fiber winding section 32 is fixed to the flat plate material 33 with an adhesive, for example, instant adhesive. In addition, if the optical fiber winding section 32 is made of iron or the like, it may be fixed to the flat plate material 33 by welding.
[0030] The optical fiber winding section 32 is columnar in shape and has a side surface 32a around which the optical fiber 10 is wound. The optical fiber winding section 32 is, for example, cylindrical. The side surface 32a of the optical fiber winding section 32 may be a continuous outer surface in the circumferential direction, or it may be a discontinuous outer surface forming a circle in the circumferential direction via grooves or recesses extending in the axial direction on the side surface 32a.
[0031] The radius of the optical fiber winding section 32 is set to be greater than or equal to the allowable bending radius of the optical fiber 10. For example, if the core diameter of the optical fiber 10 is φ0.9 mm, the radius of the optical fiber winding section 32 can be 15 mm or more. The core of the optical fiber 10 refers to an optical fiber (optical fiber strand) made mainly of quartz glass, covered with a coating such as an ultraviolet-curing resin, and further coated with a secondary coating such as a non-halogen resin.
[0032] Figure 5(a) is a perspective view showing an example of a fixing jig. In the example in Figure 5(a), a thick washer is used as the optical fiber winding section 32. The optical fiber winding section 32 is constructed by fixing the thick washer to the flat plate material 33 with instant adhesive. With this configuration, the optical fiber winding section 32 can be easily constructed using a thick washer.
[0033] Figure 5(b) is a perspective view showing another example of a fixing jig. In the example in Figure 5(b), a cylindrical optical fiber winding section 35 is used. The optical fiber winding section 35 has a so-called bobbin shape. The optical fiber winding section 35 has a flange 35a with a diameter larger than the diameter of the cylindrical portion. The optical fiber winding section 35 may be a resin bobbin, for example, for thread. The optical fiber winding section 35 is fixed to the flat plate material 33 with, for example, instant adhesive. In this configuration, the flange 35a restricts the movement of the optical fiber 10 along the axial direction of the optical fiber winding section 35, and the optical fiber 10 is less likely to fall out because it catches on the flange 35a, thus improving workability.
[0034] In the example shown in Figure 5(b), the projection 34 is omitted. In this case, it is not necessary to drill holes 5 in the surface 2 of the concrete 1. The flat plate material 33 may be fixed to the surface 2 of the concrete 1 with instant adhesive. Even in this case, compared to a fixing method in which the optical fiber is spot-fixed with adhesive or the like with the optical fiber extending in line with the laying direction of the optical fiber, for example, the bonding area between the end face of the flat plate material 33 and the flange 35a is larger, so the optical fiber 10 and the fixing jig 30 can be fixed more firmly to the surface 2 of the concrete 1.
[0035] Figure 6(a) is a perspective view showing the end of a separator protruding from concrete. Figure 6(b) is a cross-sectional view showing an example of a fixing part configuration using the end of the separator in Figure 6(a). As shown in Figures 6(a) and 6(b), if the male screw at the end of the separator 45 that supports the formwork used when pouring concrete 1 protrudes from the surface 2, the fixing jig 40 may be fixed using this male screw. For example, an optical fiber winding part 41 having a through hole through which the male screw at the end of the separator 45 passes may be used as the fixing jig 40. In the optical fiber installation process, the optical fiber winding part 41 is fixed to the male screw at the end of the separator 45 that supports the formwork used when pouring concrete 1, and the optical fiber 10 is wound along the side surface 41a of the optical fiber winding part 41 with one or more turns. In this case, a flat plate material 33 such as the base 31 of the fixing jig 30 may be omitted.
[0036] Figure 6(c) is a perspective view showing the end of a separator protruding from the bottom of a cone hole recessed from the concrete formwork surface. Figure 6(d) is a cross-sectional view showing an example of a fixing part configuration using the end of the separator in Figure 6(c). As shown in Figures 6(c) and 6(d), if the marks of the P-cones used to support the formwork when pouring the concrete 1 remain recessed from the surface 2, and the male threads at the end of the separator 45 protrude from the bottom 46, the fixing jig 40 may be fixed using these male threads. For example, a projection 42 similar to projection 34 may be provided to protrude from the optical fiber winding part 41 of the fixing jig 40, a long nut 47 may be screwed onto the male threads at the end of the separator 45, and the threads of projection 34 may be screwed onto this long nut 47. In other words, in the optical fiber installation process, a long nut 47 may be screwed onto the male thread at the end of the separator 45 that protrudes from the bottom 46 of the depression 2 formed when the concrete 1 is poured. The long nut 47 may be longer than the protruding length of the male thread at the end of the separator 45 and long enough so that the fixing jig 30 does not come into contact with the surface 2, and the projection 42 may be fixed to the long nut 47.
[0037] In the optical fiber installation process, the fixing part 21 is constructed by winding the optical fiber 10 along the side surface 32a of the optical fiber winding part 32 with one or more turns. This fixes the optical fiber 10 to the fixing jig 30. With this optical fiber installation process, the direction of stress due to the tension in the optical fiber 10 changes due to the winding in the fixing part 21, and the stress generated in the optical fiber 10 due to friction between the optical fiber 10 and the side surface 32a of the optical fiber winding part 32 is reduced. Therefore, even if a crack 3 occurs between a pair of adjacent fixing parts 21 and a tensile force acts on the optical fiber 10 of the unfixed part 22, the slippage of the optical fiber 10 against the side surface 32a of the optical fiber winding part 32 can be reduced. The coefficient of friction between the side surface 32a of the optical fiber winding part 32 and the optical fiber 10 is not particularly limited. The optical fiber 10 may also be fixed to the side surface 32a of the optical fiber winding part 32 with an adhesive.
[0038] In the optical fiber installation process, pretension is applied to the optical fiber in the non-fixed section adjacent to the fixed section. In the optical fiber installation process, the amount (magnitude) of pretension and the number of turns of the optical fiber 10 in the optical fiber winding section 32 are calculated using the elastic modulus of the optical fiber, the cross-sectional area of the optical fiber, the coefficient of friction between the optical fiber and the optical fiber winding section, the assumed strain expected in the optical fiber in the non-fixed section, and the capstan equation. Figure 7 is a diagram illustrating the calculation using the capstan equation. The capstan equation is the same as the belt friction equation. Pretension refers to the tensile force initially applied when winding the optical fiber 10 into the optical fiber winding section 32.
[0039] In Figure 7, we assume that the optical fiber winding section 32 corresponds to a capstan. Regarding the relationship between the tension Tload applied to the optical fiber 10 on the optical fiber winding section 32 and the tension Thold generated on the opposite side of the optical fiber winding section 32, if the coefficient of friction between the optical fiber 10 and the side surface 32a of the optical fiber winding section 32 is μ, and the total angle of the optical fiber 10 wound on the optical fiber winding section 32 is φ (radians), then the following relationship (2) holds. In the optical fiber installation process, the amount of pretension introduced in the non-fixed section 22 and the number of turns of the optical fiber 10 in the optical fiber winding section 32 are set using the following equation (2). e is the natural logarithm. Tload = Thold × e (μ×φ) ...(2)
[0040] Assuming that pretension εt is generated at the non-fixed part 22 when the optical fiber 10 is installed, and if we let E be the elastic modulus of the optical fiber 10 and A be the cross-sectional area of the optical fiber 10, then Thold on the right side of equation (2) above can be expressed as equation (3) below. Thold = εt × E × A ···(3)
[0041] If the coefficient of friction between the optical fiber 10 and the side surface 32a of the optical fiber winding portion 32 is μ, and the number of turns is n, then Tload on the left side of equation (2) above can be expressed as equation (4) below. Tload = Thold × e (μ×2πn) ...(4)
[0042] If εd is the tensile strain generated in the optical fiber 10 of the non-fixed section 22 due to the occurrence of crack 3, then the product of the tensile strain, the elastic modulus of the optical fiber 10, and the cross-sectional area of the optical fiber 10 becomes greater than the tension Tload, causing slippage between the optical fiber 10 and the side surface 32a of the optical fiber winding section 32. Therefore, the amount of pretension introduced and the number of turns are set so that the relationship shown in equation (5) below holds. εd corresponds to the assumed strain expected in the optical fiber 10 of the non-fixed section 22. Tload>εd×E×A···(5)
[0043] Substituting the above Equation (3) into Tload on the left-hand side of the above Equation (5) gives the following Equation (6). Tload=Thold×e (μ×2πn) =(εt×E×A)×e (μ×2πn) ···(6)
[0044] Accordingly, the above Equation (5) can be transformed into the following Equation (7). (εt×E×A)×e (μ×2πn) >εd×E×A···(7)
[0045] In the above Equation (7), by way of example, when the elastic modulus E of the optical fiber 10 is set to 5000 N / mm 2 , the cross-sectional area A of the optical fiber 10 is set to 0.64 mm 2 , and the friction coefficient μ between the optical fiber 10 and the side surface 32a of the optical fiber winding portion 32 is set to 0.4, Table 1 below shows the relationship between the introduction amount of pretension εt, the number of windings n (used as parameters), and the strain of the optical fiber 10 in the non-fixed portion 22 at which slippage occurs in the fixed portion 21. In Table 1 below, for example, when the length of the non-fixed portion 22 is 200 mm and to measure a crack width of 5 mm, the introduction amount of pretension εt may be set to 4000 µ or more, and the number of windings n may be set to 1 or more, or the number of windings n may be set to 2 or more, so that a strain of 25000 µ or more can be measured at the fixed portion 21 without slippage.
Table 1
[0046] Note that when compressive strain is also measured in the non-fixed portion 22, the compressive strain can also be measured within a range where the pretension is relaxed by the compressive strain. To achieve this, in the optical fiber installation step, the introduction amount of pretension is set to be equal to or larger than the magnitude of an assumed compressive strain that is assumed to occur when the concrete 1 is compressed under predetermined conditions. The predetermined conditions can be, for example, the conditions of the maximum compressive force that is assumed to act on the concrete 1 during service. The assumed compressive strain in this case means the magnitude of the compressive strain that is assumed to occur when compressed by the maximum compressive force.
[0047] Then, in the detection process, the compressive strain of concrete 1 is measured based on the amount of pretension relaxation caused by the compression of concrete 1. The amount of pretension relaxation represents the decrease in the tensile strain of the optical fiber 10, which was equal to the amount of pretension introduced, due to the compressive force acting on concrete 1 during its service, and corresponds to the compressive strain of concrete 1. The amount of pretension relaxation may also be calculated by subtracting the strain of the optical fiber 10 detected in the relative displacement detection process from the amount of pretension introduced.
[0048] According to the method for detecting relative displacement of the concrete surface described above, a fixing jig 30 including a columnar optical fiber winding section 32 is fixed to the surface 2 of the concrete 1. The optical fiber 10 is wound along the side surface 32a of the optical fiber winding section 32 with one or more turns. Therefore, compared to, for example, the case where the optical fiber is simply spot-fixed with adhesive or the like with the optical fiber's extending direction aligned with the laying direction, the fixing section 21 is configured so that the optical fiber 10 is less likely to shift relative to the surface 2 of the concrete 1. This makes it possible to suppress the occurrence of small strains in the optical fiber 10 of the unfixed section 22 compared to the strain corresponding to the width of the crack 3. In other words, with the present invention, reliable fixing of the optical fiber 10 at the fixing section 21 can be expected, so even if the width of the crack 3 increases when the optical fiber 10 is fixed at regular intervals and the width of the crack 3 is measured, the width of the crack 3 can be calculated more appropriately. Therefore, the width of the crack 3 as the relative displacement along the optical fiber 10 on the surface 2 of the concrete 1 can be detected with greater accuracy.
[0049] In the optical fiber installation process, pretension is applied to the optical fiber 10 in the non-fixed section 22 adjacent to the fixed section 21. This makes it less likely for the optical fiber 10 to slip between the optical fiber 10 and the optical fiber winding section 32.
[0050] In the optical fiber installation process, the amount and number of turns of pretension are calculated using the elastic modulus of the optical fiber 10, the cross-sectional area of the optical fiber 10, the friction coefficient between the optical fiber 10 and the optical fiber winding section 32, the assumed strain expected in the optical fiber 10 in the non-fixed section 22, and the capstan equation. This allows for the determination of the amount and number of turns of pretension so that even if assumed strain (tensile strain) occurs in the optical fiber 10 in the non-fixed section 22, slippage of the optical fiber 10 between the optical fiber 10 and the optical fiber winding section 32 is prevented.
[0051] In the optical fiber installation process, the amount of pretension introduced is set to be greater than or equal to the expected compressive strain that would occur when concrete 1 is compressed under predetermined conditions. In the detection process, the compressive strain of concrete 1 is measured based on the amount of pretension relaxation that occurs when concrete 1 is compressed. This allows for the measurement of the compressive strain of concrete 1 within the range of the amount of pretension introduced.
[0052] Although embodiments of the present invention have been described above, the present invention is not limited to the above embodiments and can be implemented in various forms.
[0053] For example, the fixing jig may have a side displacement part that displaces the side surface of the optical fiber winding portion relative to the concrete surface.
[0054] Specifically, Figure 8(a) is a plan view showing a first example of a fixing jig having a lateral displacement section. Figure 8(b) is a plan view showing an example of lateral displacement due to the lateral displacement section of Figure 8(a). Figure 8(c) is a cross-sectional view along the c-c line in Figure 8(b). Figures 8(a) to 8(c) illustrate a first modified example of the optical fiber winding section of the fixing jig.
[0055] The fixing jig 50 shown in Figures 8(a) to 8(c) has a lateral displacement section 52. The lateral displacement section 52 is a mechanism for displacing the lateral side 51a of the optical fiber winding section 51 of the fixing jig 50 to adjust the pretension of the optical fiber 10. The lateral displacement section 52 includes a rectangular plate 53, a circular projection 54, and a fastening member 55. The rectangular plate 53 is the base of the fixing jig 50. The rectangular plate 53 has a pair of tapped holes 53a with internal threads formed therein. The circular projection 54 is the optical fiber winding section of the fixing jig 50 and is, for example, cylindrical in shape. The circular projection 54 has a pair of elongated holes 54a formed therein. The longitudinal direction of the pair of elongated holes 54a is along the circumferential direction of the cross-section of the circular projection 54. A bolt of the fastening member 55 is inserted through a pair of elongated holes 54a in the circular projection 54 and screwed into the female threads of the tapped holes 53a in the rectangular plate 53. The rectangular plate 53 and the circular projection 54 are rotatable relative to each other when the fastening member 55 is loosened. After adjusting the pretension of the optical fiber 10 with the fastening member 55 loosened, the fastening member 55 is tightened to fix the rectangular plate 53 and the circular projection 54 so that they do not rotate relative to each other.
[0056] Thus, in the optical fiber installation process, a fixing jig 50 including a columnar circular projection 54 is fixed to the surface 2 of the concrete 1, and the optical fiber 10 is wrapped around the side surface 51a of the circular projection 54 in one or more turns to form the fixing part 21. Then, in the optical fiber installation process, the side surface 51a is displaced relative to the surface 2 of the concrete 1 by the side surface displacement part 52, thereby applying pretension to the optical fiber 10 of the non-fixed part 22 adjacent to the fixing part 21.
[0057] Figure 9(a) is a plan view showing a second example of a fixing jig having a lateral displacement section. Figure 9(b) is a plan view showing an example of lateral displacement due to the lateral displacement section of Figure 9(a). Figure 9(c) is a cross-sectional view along line c in Figure 9(b). Figures 9(a) to 9(c) illustrate a second modified example of the optical fiber winding section of the fixing jig.
[0058] The fixing jig 60 shown in Figures 9(a) to 9(c) has a lateral displacement section 62. The lateral displacement section 62 is a mechanism for displacing the lateral surface 61a of the optical fiber winding section 61 of the fixing jig 60 to adjust the pretension of the optical fiber 10. The lateral displacement section 62 includes a rectangular plate 63, a circular projection 64, and a fastening member 65. The rectangular plate 63 is the base of the fixing jig 60. The rectangular plate 63 has a pair of tapped holes 63a with internal threads formed therein. The circular projection 64 is the optical fiber winding section of the fixing jig 60 and is, for example, cylindrical in shape. The circular projection 64 has a pair of elongated holes 64a formed therein. The longitudinal direction of the pair of elongated holes 64a is aligned with the laying direction of the optical fiber 10. Bolts of the fastening member 65 are inserted through the pair of elongated holes 64a of the circular projection 64 and screwed into the internal threads of the tapped holes 63a of the rectangular plate 63. The rectangular plate 63 and the circular projection 64 are slidable relative to each other along the laying direction of the optical fiber 10 when the fastening member 65 is loosened. After adjusting the pretension with the fastening member 65 loosened, tightening the fastening member 65 fixes the rectangular plate 63 and the circular projection 64 so that they do not slide relative to each other along the laying direction of the optical fiber 10.
[0059] Thus, in the optical fiber installation process, a fixing jig 60 including a columnar circular projection 64 is fixed to the surface 2 of the concrete 1, and the optical fiber 10 is wrapped around the side surface 61a of the circular projection 64 with one or more turns to form the fixing part 21. Then, in the optical fiber installation process, the side surface 61a is displaced relative to the surface 2 of the concrete 1 by the side displacement part 62, thereby applying pretension to the optical fiber 10 of the non-fixed part 22 adjacent to the fixing part 21.
[0060] Figure 10(a) is a plan view showing a third example of a fixing jig having a lateral displacement section. Figure 10(b) is a plan view showing an example of lateral displacement due to the lateral displacement section of Figure 10(a). Figure 10(c) is a cross-sectional view along the c-c line of Figure 10(b). Figures 10(a) to 10(c) illustrate a third modified example of the optical fiber winding section of the fixing jig.
[0061] The fixing jig 70 shown in Figures 10(a) to 10(c) has a lateral displacement section 72. The lateral displacement section 72 is a mechanism for displacing the lateral side 75a of the optical fiber winding section 71 of the fixing jig 70 to adjust the pretension of the optical fiber 10. The lateral displacement section 72 includes a rectangular plate 73, a circular projection 75, and a fastening member 77. The rectangular plate 73 is the base of the fixing jig 70. The rectangular plate 73 has a pair of tapped holes 74 with internal threads formed therein. The pair of tapped holes 74 includes a center hole 74a located corresponding to the center of the circular projection 75, and four tapped holes 74b arranged along the circumferential direction of a virtual circle of a predetermined radius centered on the center hole 74a. The circular projection 75 is the optical fiber winding section of the fixing jig 70, and is, for example, cylindrical in shape. The circular projection 75 is divided into four sections (for example, four equal parts) in the circumferential direction of its cross-section, and has four fan-shaped projections 76. An elongated hole 76a extending radially is formed in the center of each of the four fan-shaped projections 76. When the four fan-shaped projections 76 are brought together to form a single circular projection, the elongated holes 76a of the four fan-shaped projections 76 extend radially from the center hole 74a. Bolts of the fastening member 77 are inserted through the elongated holes 76a of the four fan-shaped projections 76 and screwed into the female threads of the tapped holes 74b of the rectangular plate 73. The rectangular plate 73 and the fan-shaped projections 76 are able to slide relative to each other along the radial direction of a circle centered on the center hole 74a when the fastening member 77 is loosened.
[0062] Each of the four fan-shaped projections 76 has a tapered surface 76b formed on its center, which, when combined to form a single circular projection, creates an inner surface resembling the side of a cone. A tapered bolt 78 with a conical inclined surface is positioned in this center, coaxially with the single circular projection formed by combining the four fan-shaped projections 76. The tapered bolt 78 is screwed into the female thread of the center hole 74a of the rectangular plate 73 with its inclined surface in contact with the tapered surface 76b. When the tapered bolt 78 is tightened, the inclined surface pushes against the tapered surface 76b, causing the four fan-shaped projections 76 to slide along the radial direction of a circle centered on the center hole 74a. Four guide parts 79 are positioned around the circular projection 75, each corresponding to one of the four fan-shaped projections 76. The four guide parts 79 are plate-shaped walls that extend in an arc shape when viewed from above. The outer surfaces of the four fan-shaped projections 76 and the inner surfaces of the four guide portions 79 face each other. When the tapered bolt 78 is tightened to its maximum extent, the four fan-shaped projections 76 slide to the outermost part along the radial direction of a circle centered on the center hole 74a and come into near contact with the four guide portions 79. Recesses 75b for arranging the optical fibers 10 are formed on the outer surfaces of the four fan-shaped projections 76. After adjusting the pretension of the optical fibers 10 according to the amount the tapered bolt 78 is loosened with the fastening member 77 loosened, the fastening member 77 is tightened to fix the rectangular plate 73 and the circular projections 75 so that they do not slide relative to each other along the laying direction of the optical fibers 10.
[0063] Thus, in the optical fiber installation process, a fixing jig 70 including a columnar circular projection 75 is fixed to the surface 2 of the concrete 1, and the optical fiber 10 is wrapped around the side surface 75a of the circular projection 75 in one or more turns to form the fixing part 21. Then, in the optical fiber installation process, the side surface 75a is displaced relative to the surface 2 of the concrete 1 by the side surface displacement part 72, thereby applying pretension to the optical fiber 10 of the non-fixed part 22 adjacent to the fixing part 21.
[0064] According to the first to third modified examples shown in Figures 8 to 10, the fixing jigs 50, 60, and 70 have side displacement parts 52, 62, and 72 that displace the sides 51a, 61a, and 75a of the optical fiber winding parts 51, 61, and 71 relative to the surface 2 of the concrete 1. In the optical fiber installation process, the side displacement parts 52, 62, and 72 displace the sides 51a, 61a, and 75a relative to the surface 2 of the concrete 1, thereby applying pretension to the optical fiber 10 of the non-fixed part 22 adjacent to the fixed part 21. This makes it possible to easily adjust the pretension by adjusting the amount by which the side displacement parts 52, 62, and 72 displace the sides 51a, 61a, and 75a relative to the surface 2 of the concrete 1.
[0065] In the above embodiment, the pretension applied to the optical fiber 10 of the non-fixed portion 22 was calculated using the capstan equation, but the example is not limited to this. The pretension may be calculated by various known methods such as simulations.
[0066] Incidentally, in the example shown in Figure 4, when installing an optical fiber 10 in a straight recess made in concrete 1, the optical fiber installation process may be as follows. For example, before pouring concrete 1, a long member such as a tube is placed in the formwork. Then, concrete 1 is poured. When the long member is removed during the curing of concrete 1, a straight recess (groove) appears. The optical fiber 10 and fixing jig 30 are placed in this groove. In other words, the long member is selected so that the width of the groove is wider than the size of the fixing jig 30. The optical fiber 10 is installed inside the groove using the fixing jig 30 by various optical fiber installation processes as described above. Then, the groove is backfilled with concrete. As the backfilling material, an inorganic mortar material used for injecting into cracks in concrete 1 can be used.
[0067] In the above embodiment, the width of a crack 3 formed on the surface 2 of the concrete 1 in which reinforcing materials such as reinforcing bars 4 or steel materials are embedded was used as an example of the relative displacement along the optical fiber on the surface of the concrete, but the embodiment is not limited to this. In the modified method for detecting the relative displacement of the concrete surface, the relative displacement may be the opening dimension of a joint formed by a pair of adjacent concrete members with their respective end faces facing each other. In this case, the concrete members may be, for example, precast concrete (PCa) members, box culverts, etc.
[0068] Figure 11 is a perspective view showing a joint to which a modified example of the method for detecting relative displacement of the concrete surface is applied. Figure 11 shows a pair of concrete members (concrete) 81 and 82. The pair of concrete members 81 and 82 are adjacent to each other with their respective end faces 81a and 82a facing each other. The pair of concrete members 81 and 82 form a joint 83. The joint 83 refers to the area of the joint sandwiched between the end faces 81a and 82a of the pair of concrete members 81 and 82. In the joint 83, the distance between the end faces 81a and 82a becomes the opening dimension.
[0069] In the optical fiber installation process, the optical fiber 10 is installed on the surfaces 81c and 82c of a pair of concrete members 81 and 82 such that the extending direction of the joint 83 (the extending direction of the edges 81b and 82b of the end faces 81a and 82a) intersects with the axial direction of the optical fiber 10. In the optical fiber installation process, multiple fixing jigs 30 are fixed to the surfaces 81c and 82c of the concrete members 81 and 82. The multiple fixing jigs 30 are fixed to the surfaces 81c and 82c of the concrete members 81 and 82 so as to be aligned along the laying direction of the optical fiber 10. The multiple fixing jigs 30 are fixed to the surfaces 81c and 82c of the concrete members 81 and 82 at regular intervals. As a result, fixing portions 21 are formed at the locations where the fixing jigs 30 are fixed to the surfaces 81c and 82c of the concrete members 81 and 82. Furthermore, non-fixed portions 22 are formed in the areas where the fixing jig 30 is not fixed to the surfaces 81c and 82c of the concrete members 81 and 82, and in the joint portions 83. In other words, non-fixed portions 22 exist in the joint portions 83, and a pair of fixed portions 21 exist adjacent to the non-fixed portions 22, sandwiching the joint portions 83.
[0070] In the optical fiber installation process, a relative displacement detection process (detection process) is performed to detect the opening dimension of the joint portion 83 as a relative displacement along the optical fiber 10 on the surfaces 81c and 82c of the concrete members 81 and 82, based on the strain generated in the unfixed portion 22 present in the joint portion 83 of the optical fiber 10 installed on the surfaces 81c and 82c of the concrete members 81 and 82. When a pair of concrete members 81 and 82 are displaced so that their end faces 81a and 82a move away from each other, the joint portion 83 opens up. When the joint portion 83 opens up on the surfaces 81c and 82c of the concrete members 81 and 82, the distance between the pair of fixed portions 21 that sandwich the unfixed portion 22 present in the joint portion 83 is relatively displaced along the optical fiber 10 by the opening dimension of the joint portion 83. Therefore, the elongation of the optical fiber 10 in the non-fixed portion 22, with the fixed portion 21 on the surfaces 81c and 82c of the concrete members 81 and 82 as a reference point, corresponds to the opening dimension of the joint portion 83.
[0071] The modified method for detecting relative displacement of the concrete surface provides the same effects as the above embodiment. Specifically, it is possible to suppress the occurrence of small distortions in the optical fiber 10 of the non-fixed part 22, compared to the distortion corresponding to the opening dimension of the joint 83. In other words, because the present invention ensures reliable fixing of the optical fiber 10 at the fixing part 21, even if the opening dimension of the joint 83 becomes large when the optical fiber 10 is fixed at regular intervals and the opening dimension of the joint 83 is measured, the opening dimension of the joint 83 can be calculated more appropriately. Therefore, the opening dimension of the joint 83, as the relative displacement along the optical fiber 10 on the surfaces 81c and 82c of the concrete members 81 and 82, can be detected with greater accuracy.
[0072] The constituent elements of various aspects of this disclosure are described below. <Invention 1> A method for detecting relative displacement of a concrete surface, which detects the relative displacement of the concrete surface along the optical fiber based on the strain generated in the optical fiber installed on the surface of the concrete, An optical fiber installation step of installing the optical fiber on the surface of the concrete such that the optical fiber alternates between a fixed portion fixed to the surface of the concrete and an unfixed portion not fixed to the surface of the concrete, A detection step of detecting the relative displacement of the surface of the concrete along the optical fiber based on the strain generated in the optical fiber at each of the non-fixed parts, Equipped with, A method for detecting relative displacement of a concrete surface, wherein in the optical fiber installation process, a fixing jig including a columnar optical fiber winding section is fixed to the surface of the concrete, and the optical fiber is wound along the side surface of the optical fiber winding section with one or more turns, thereby constituting the fixing section. <Invention 2> The method for detecting relative displacement of a concrete surface according to Invention 1, wherein in the optical fiber installation step, pretension is applied to the optical fiber of the non-fixed portion adjacent to the fixed portion. <Invention 3> The method for detecting relative displacement of a concrete surface according to Invention 2, wherein in the optical fiber installation step, the magnitude of the pretension and the number of turns are calculated using the elastic modulus of the optical fiber, the cross-sectional area of the optical fiber, the coefficient of friction between the optical fiber and the optical fiber winding portion, the assumed strain assumed in the optical fiber of the non-fixed portion, and the capstan equation. <Invention 4> In the optical fiber installation process, the amount of pretension is set to be greater than or equal to the amount of assumed compressive strain that is expected to occur when the concrete is compressed under predetermined conditions. The method for detecting relative displacement of a concrete surface according to Invention 2 or 3, wherein the detection step involves measuring the compressive strain of the concrete based on the amount of relaxation of the pretension caused by the compression of the concrete. <Invention 5> The fixing jig has a side displacement part that displaces the side surface of the optical fiber winding part relative to the surface of the concrete, A method for detecting relative displacement of a concrete surface according to any one of Invention 1 to 4, wherein in the optical fiber installation step, the side surface is displaced relative to the surface of the concrete by the side displacement part, thereby applying pretension to the optical fiber of the non-fixed part adjacent to the fixed part. [Explanation of Symbols]
[0073] 1...Concrete, 2...Surface, 3...Crack, 10...Optical fiber, 21...Fixed part, 22...Unfixed part, 30, 40, 50, 60, 70...Fixing jig, 32, 35, 41, 51, 61, 71...Optical fiber winding part, 32a, 41a, 51a, 61a, 75a...Side, 52, 62, 72...Side displacement part, A...Cross-sectional area, E...Elastic modulus, n...Number of turns, εt...Pretension, μ...Coefficient of friction.
Claims
1. A method for detecting relative displacement of a concrete surface, which detects the relative displacement of the concrete surface along the optical fiber based on the strain generated in the optical fiber installed on the surface of the concrete, An optical fiber installation step of installing the optical fiber on the surface of the concrete such that the optical fiber alternates between a fixed portion fixed to the surface of the concrete and an unfixed portion not fixed to the surface of the concrete, A detection step of detecting the relative displacement of the surface of the concrete along the optical fiber based on the strain generated in the optical fiber at each of the non-fixed parts, Equipped with, In the optical fiber installation process, The fixing jig, which includes a columnar optical fiber winding section, is fixed to the surface of the concrete, and the optical fiber is wound along the side surface of the optical fiber winding section with one or more turns, thereby forming the fixing section. Pretension is applied to the optical fiber of the non-fixed portion adjacent to the fixed portion. A method for detecting relative displacement on a concrete surface, comprising calculating the magnitude of the pretension and the number of turns of the optical fiber in the fixed part using the elastic modulus of the optical fiber, the cross-sectional area of the optical fiber, the coefficient of friction between the optical fiber and the optical fiber winding portion, the assumed strain assumed in the optical fiber in the non-fixed portion, and the capstan equation.
2. A method for detecting relative displacement of a concrete surface, which detects the relative displacement of the concrete surface along the optical fiber based on the strain generated in the optical fiber installed on the surface of the concrete, An optical fiber installation step of installing the optical fiber on the surface of the concrete such that the optical fiber alternates between a fixed portion fixed to the surface of the concrete and an unfixed portion not fixed to the surface of the concrete, A detection step of detecting the relative displacement of the surface of the concrete along the optical fiber based on the strain generated in the optical fiber at each of the non-fixed parts, Equipped with, In the optical fiber installation process, The fixing jig, which includes a columnar optical fiber winding section, is fixed to the surface of the concrete, and the optical fiber is wound along the side surface of the optical fiber winding section with one or more turns, thereby forming the fixing section. Pretension is applied to the optical fiber of the non-fixed portion adjacent to the fixed portion. The magnitude of the pretension is set to be greater than or equal to the magnitude of the assumed compressive strain that is expected to occur when the concrete is compressed under predetermined conditions. A method for detecting relative displacement of a concrete surface, wherein the detection step involves measuring the compressive strain of the concrete based on the amount of relaxation of the pretension caused by the compression of the concrete.
3. The fixing jig has a side displacement part that displaces the side surface of the optical fiber winding part relative to the surface of the concrete, The method for detecting relative displacement of a concrete surface according to claim 1 or 2, wherein in the optical fiber installation step, the side surface is displaced relative to the surface of the concrete by the side displacement part, thereby applying pretension to the optical fiber of the non-fixed part adjacent to the fixed part.
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