A method for detecting cable force of a tunnel prestressed ring anchor steel strand based on string vibration method

Abstract

The application discloses a tunnel prestressed ring anchor steel strand cable force detection method based on a string vibration method, which calculates the internal force of the steel strand based on a cable force calculation formula of a horizontal straight beam model with both ends fixed in tension in the string vibration method and established by a numerical method, wherein the rigidity of the steel strand can be calculated by collecting multi-order vibration frequencies of the steel strand, and the linear density can be obtained by an additional mass method, and the anchor plate of the steel strand is fixed by using an anchor plate fixer before vibration collection, so that the both ends of the steel strand are ensured to be in a fixed state.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering technology, specifically relating to a method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method. Background Technology

[0002] A ring anchor is a special type of engineering anchorage. In its mechanism, the anchoring end and tensioning end of the prestressed tendon are located on the same anchor plate. The tensioning function of the prestressed tendon is achieved by the movement of the anchor plate and the change of angle within the pre-reserved tensioning groove. Ring anchors have technical advantages such as saving anchor pads, reducing friction, enhancing effective prestress, and being suitable for ring stress engineering applications. Their application is increasingly common in hydraulic prestressed engineering projects such as tunnels and culverts. However, for projects involving the tensioning of large-tonnage, high-curvature anchor cables, ring anchor technology suffers from problems such as insufficient elongation and easy wire breakage. Therefore, measuring the internal force of the prestressed ring anchor steel strands in tunnels is a crucial guarantee against insufficient tension of the steel strands and a key issue that needs to be addressed in tunnel inspection and construction monitoring. Currently, however, there is a lack of methods that can meet engineering needs and quickly measure the tension of prestressed ring anchor steel strands. Summary of the Invention

[0003] The purpose of this invention is to provide a method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method, so as to solve the above-mentioned problems.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method, the specific steps of which are as follows:

[0005] Step 1: Secure the anchor plate using an anchor plate fixer and clean the surface of the steel strand;

[0006] Step 2: Measure the effective calculated length between the two ends of the anchor steel strand using a measuring tape. ;

[0007] Step 3: Install steel strand mass extenders of appropriate length on the steel strands;

[0008] Step 4: Obtain the vibration frequency of the steel strand after the steel strand mass enhancer is installed by tapping the steel strand. ;

[0009] Step 5: After removing the steel strand mass extender, tap the steel strand again to obtain the vibration frequency. ;

[0010] Step 6: Calculate the linear density m of the steel strand using the mass addition method;

[0011] Step 7: Calculate the stiffness EI of the steel strand fixed at both ends using the frequency decomposition method;

[0012] Step 8: Calculate T using the cable force formula The cable force of the prestressed ring anchor steel strand was calculated.

[0013] Preferably, the anchor plate retainer in step S1 is provided with rubber for increasing friction at both the claw part and the root, and the anchor plate retainer is also provided on both sides of the anchor plate.

[0014] Preferably, a steel strand mass adder is provided on the steel strand in step S3.

[0015] Preferably, step S7 further includes the following: Since the tension of the steel strand is equal during the two strikes, the cable force calculation formula for a horizontal straight beam model with fixed supports at both ends under tension is:

[0016]

[0017]

[0018] In the formula:

[0019] T – Steel strand tension;

[0020] —The nth order vibration frequency was measured by striking the steel strand;

[0021] —The nth order vibration frequency was measured by striking the steel strand after installing a mass adder;

[0022] n—the order of the vibration frequency of the steel strand;

[0023] EI – Bending stiffness of steel strand;

[0024] —Effective calculated length of steel strand;

[0025] , —Steel strand linear density, steel strand mass additive linear density;

[0026] From (1) and (2), the linear density m of the steel strand can be obtained:

[0027] m (3)

[0028] Preferably, step S8 further includes: because the influence of stiffness on vibration frequency in short cables cannot be ignored, the stiffness of the tensioned steel strands fixed at both ends is solved by frequency decomposition method.

[0029] 7. Preferably, the method of solving the stiffness of a tensioned steel strand fixed at both ends using the frequency decomposition method is as follows: First, assume that the stiffness of the steel strand is negligible, and then use the cable force calculation formula T. We can obtain:

[0030] At this point, T in the formula is the cable force value that ignores the bending stiffness of the steel strand; The actual vibration frequency of the steel strand includes the influence of the bending stiffness EI of the steel strand. In the cable force calculation formula, the first term on the right side of the equation is the value T, and the second term is the increment of the cable force caused by the bending stiffness, denoted as T. ,but

[0031] (5)

[0032] (6)

[0033] In the formula:

[0034] —Remove the increase in cable force caused by the bending stiffness of the steel strand;

[0035] —Increase in cable force due to bending stiffness;

[0036] From equation (6), we can see that The physical meaning is the increase in cable force caused by removing the bending stiffness of the steel strand. The final cable force value, that is, the cable force value when the bending stiffness of the steel strand EI = 0, is assumed to be the cable force value when EI = 0.

[0037] The linear vibration frequency is but:

[0038]

[0039] In the formula:

[0040] — The vibration frequency of the steel strand when EI = 0 is ;

[0041] because The increase in cable force is entirely due to the bending stiffness, so it can also be considered as the increase in cable force caused by the vibration frequency generated by the bending stiffness when the tension of the steel strand is zero. At this time, the cable tension model of the steel strand becomes a simply supported beam model, and the relationship between the vibration frequency and the bending stiffness can be calculated from the simply supported beam model:

[0042]

[0043] In the formula:

[0044] —The vibration frequency generated by bending stiffness when the tension is zero;

[0045] (9)

[0046] Substituting equation (9) into equation (5), we get:

[0047] (10)

[0048] Substituting equations (4), (7), and (10) into equation (6), we get:

[0049]

[0050] And because , Therefore:

[0051]

[0052] At this point, the least squares method is used to plot the quadratic curves of the squares of several measured steel strand vibration frequencies.

[0053] The polynomial coefficients can be obtained by fitting. and The value of the tensile steel strand bending resistance can be calculated from equation (9).

[0054] Stiffness.

[0055] The technical effects and advantages of this invention are as follows: This invention solves the problem of determining the effective length when measuring the tension of prestressed ring anchor steel strands by using an anchor plate fixer, ensuring that the measured prestressed ring anchor steel strands after tension conform to the horizontal straight beam model with both ends fixed in tension. Furthermore, it solves the problem of determining the linear density and stiffness of the prestressed ring anchor steel strands through the mass addition method and frequency addition method. This method solves the problem of difficulty in measuring the cable force of prestressed ring anchor steel strands by using a cable force calculation formula obtained through numerical methods from the horizontal straight beam model with both ends fixed in tension.

[0056] Specifically, this method is based on the cable force calculation formula established numerically using a horizontal straight beam model with both ends fixed in tension in the string vibration method. The internal forces of the steel strand are calculated. The stiffness of the steel strand can be obtained by collecting multiple vibration frequencies of the steel strand, and the linear density can be obtained by the added mass method. Anchor plates are used to fix the steel strands before vibration data collection.

[0057] Ensure that both ends of the steel strand are fixed. Attached Figure Description

[0058] Figure 1 This is a diagram illustrating the operation steps of the present invention;

[0059] Figure 2 This is a schematic diagram of the prestressed ring anchor steel strand in this invention;

[0060] Figure 3 This is a schematic diagram of the anchor plate fixer in this invention;

[0061] Figure 4 This is a schematic diagram of the steel strand quality enhancer in this invention;

[0062] Figure 5 This is a schematic diagram of the effective computational length l used in this invention. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0064] The present invention provides as shown in Figure 1- Figure 4 The method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method, as shown, includes the following steps:

[0065] Step S1: First, adjust the width of the gripper parts of the two anchor plates, from both sides of the anchor plate as follows: Figure 2 Grasp the anchor plate as shown, and then simultaneously adjust the length of the crossbars of the two anchor plate fixing devices to fix the anchor plate in place. Then clean the surface of the annular anchor strand. The anchor plate fixing device is shown in Figure 3. It has rubber on the claw part and the root to increase friction. When using it, adjust the width of the claw part of the anchor plate fixing device to be the same as the thickness of the anchor plate, and then install the anchor plate fixing devices on both sides of the anchor plate at the same time. Adjust the length of the crossbar of the anchor plate fixing device to fix the anchor plate in a fixed state.

[0066] Step S2: Measure the effective calculated length l between the two ends of the anchor steel strand using a measuring tape;

[0067] Step S3: Install a steel strand mass attacher of length l on the annular anchor steel strand. The specific design of the steel strand mass attacher is shown in the attached figure. Figure 2 As shown, based on the effective calculated length of the steel strand, a steel strand mass attacher of the corresponding length is installed on the steel strand, and the linear density of the steel strand mass attacher is m1.

[0068] Step S4: At the midpoint of the effective calculated length of the annular anchor steel strand, attach the vibration transmission sensor equipped with a magnetic base. After confirming that the vibration sensor will not shake, tap the steel strand to obtain the vibration frequency of the steel strand after the steel strand mass extender is installed. ;

[0069] Step S5: After removing the steel strand mass extender, tap the steel strand again to obtain the vibration frequency. ;

[0070] Step S6: Using formula m The linear density m of the steel strand was calculated.

[0071] Step S7: Calculate the stiffness EI of the steel strand fixed at both ends using the frequency decomposition method.

[0072] First, the least squares method was used to perform a 2x2 operation on the square values ​​of several measured vibration frequencies of steel strands.

[0073] The coefficients are obtained by curve fitting. and The value is then obtained through the formula EI. Calculate the prestressed ring

[0074] The stiffness of the anchor steel strand,

[0075] Because the cable tension is equal during the two strikes, the formula for calculating the cable force in a horizontal straight beam model with fixed supports at both ends is as follows:

[0076]

[0077]

[0078] In the formula:

[0079] T – Steel strand tension;

[0080] —The nth order vibration frequency was measured by striking the steel strand;

[0081] —The nth order vibration frequency was measured by striking the steel strand after installing a mass adder;

[0082] n—the order of the vibration frequency of the steel strand;

[0083] EI – Bending stiffness of steel strand;

[0084] —Effective calculated length of steel strand;

[0085] , —Steel strand linear density, steel strand mass additive linear density;

[0086] From (1) and (2), the linear density m of the steel strand can be obtained:

[0087] m (3)

[0088] Step S8: Calculate T using the cable force formula The tension of the prestressed ring anchor steel strand was calculated;

[0089] Because the effect of stiffness on vibration frequency in short cables cannot be ignored, the stiffness of the tensioned steel strands fixed at both ends is solved using the frequency decomposition method. We first assume that the stiffness of the steel strands is negligible and calculate it from the cable force.

[0090] Formula T We can obtain:

[0091]

[0092] At this point, T in the formula is the cable force value that ignores the bending stiffness of the steel strand; This represents the actual vibration frequency of the steel strand, incorporating the influence of the steel strand's bending stiffness EI. In the cable force calculation formula, the first term on the right-hand side is the value T, while the second term is the increment of the cable force caused by the bending stiffness, denoted as T. ,but

[0093] (5)

[0094] (6)

[0095] In the formula:

[0096] —Remove the increase in cable force caused by the bending stiffness of the steel strand;

[0097] —Increase in cable force due to bending stiffness;

[0098] From equation (6), we can see that The physical meaning is the increase in cable force caused by removing the bending stiffness of the steel strand. The final cable force value, that is, the cable force value when the bending stiffness of the steel strand EI = 0. Let the vibration frequency of the steel strand when EI = 0 be... but:

[0099]

[0100] In the formula:

[0101] — The vibration frequency of the steel strand when EI = 0 is ;

[0102] because The increase in cable force is entirely due to the bending stiffness, so it can also be considered as the increase in cable force caused by the vibration frequency generated by the bending stiffness when the tension of the steel strand is zero. At this point, the cable tension model becomes a simply supported beam model, and the relationship between the vibration frequency and the bending stiffness can be calculated using the simply supported beam model:

[0103]

[0104] In the formula:

[0105] —The vibration frequency generated by bending stiffness when the tension is zero;

[0106] EI (9)

[0107] Substituting equation (9) into equation (5), we get:

[0108] (10)

[0109] Substituting equations (4), (7), and (10) into equation (6), we get:

[0110]

[0111] And because , Therefore:

[0112]

[0113] At this point, the least squares method is used to plot the quadratic curves of the squares of several measured steel strand vibration frequencies.

[0114] The polynomial coefficients can be obtained by fitting. and The value of the tensile steel strand bending resistance can be calculated from equation (9).

[0115] Stiffness;

[0116] In summary, the present invention employs the above-mentioned method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method. This method can effectively measure the cable tension of prestressed ring anchor steel strands. In projects involving the tensioning of anchor cables with large tonnage and high curvature, it can effectively detect problems such as insufficient elongation and easy wire breakage of the ring anchor steel strands, resulting in significant social and economic benefits.

[0117] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the scope of the invention.

[0118] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method, characterized in that: The specific steps are as follows: Step 1: Secure the anchor plate using an anchor plate fixer and clean the surface of the steel strand; Step 2: Measure the effective calculated length between the two ends of the anchor steel strand using a measuring tape. ; Step 3: Install steel strand mass extenders of appropriate length on the steel strands; Step 4: Obtain the vibration frequency of the steel strand after the steel strand mass enhancer is installed by tapping the steel strand. ; Step 5: After removing the steel strand mass extender, tap the steel strand again to obtain the vibration frequency. ; Step 6: Calculate the linear density m of the steel strand using the mass addition method; Step 7: Calculate the stiffness EI of the steel strand fixed at both ends using the frequency decomposition method; Step 8: Calculate T using the cable force formula The cable force of the prestressed ring anchor steel strand is calculated, where n is the order of the steel strand vibration frequency.

2. The method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method according to claim 1, characterized in that: In step S1, the anchor plate retainer is provided with rubber for increasing friction at both the claw part and the root, and the anchor plate retainer is also provided on both sides of the anchor plate.

3. The method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method according to claim 1, characterized in that: In step S3, a steel strand mass enhancer is installed on the steel strand.

4. The method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method according to claim 1, characterized in that: Step S6 also includes the following: Since the tension in the steel strand is equal during the two strikes, the cable force calculation formula for a horizontal straight beam model with fixed supports at both ends under tension is as follows: ； ； In the formula: T – Steel strand tension; —The nth order vibration frequency was measured by striking the steel strand; —The nth order vibration frequency was measured by striking the steel strand after installing a mass adder; n—the order of the vibration frequency of the steel strand; EI – Bending stiffness of steel strand; l — Effective calculated length of steel strand; , —Steel strand linear density, steel strand mass additive linear density; From (1) and (2), the linear density m of the steel strand can be obtained: （3） 。 5. The method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method according to claim 1, characterized in that: Step S7 also includes: because the influence of stiffness on vibration frequency in short cables cannot be ignored, the stiffness of the tensioned steel strands fixed at both ends is solved by frequency decomposition method.

6. The method for detecting the tension of prestressed ring anchor steel strands in tunnels based on the string vibration method according to claim 5, characterized in that: Specifically, the stiffness of a tensioned steel strand fixed at both ends is determined using the frequency decomposition method. First, it is assumed that the stiffness of the steel strand is negligible, and then the cable force is calculated using the formula... We can obtain: (4) ； At this point, T represents the cable force value neglecting the bending stiffness of the steel strand; fn is the actual vibration frequency of the steel strand, which includes the influence of the bending stiffness EI of the steel strand. The first term on the right side of the cable force calculation formula is the value T, while the second term is the increment of the cable force value caused by the bending stiffness, denoted as T. ,but (5) ； (6) ； In the formula: —Remove the increase in cable force caused by the bending stiffness of the steel strand; —Increase in cable force due to bending stiffness; From equation (6), we can see that The physical meaning is the increase in cable force caused by removing the bending stiffness of the steel strand. The final cable force value, that is, the cable force value when the bending stiffness of the steel strand EI = 0, is given by the following: Let the vibration frequency of the steel strand when EI = 0 be... but: ； In the formula: — The vibration frequency of the steel strand when EI = 0 is ; because The increase in cable force is entirely due to the bending stiffness, so it can also be considered as the increase in cable force caused by the vibration frequency generated by the bending stiffness when the tension of the steel strand is zero. At this time, the cable tension model of the steel strand becomes The relationship between vibration frequency and bending stiffness in a simply supported beam model can be calculated using this model: ； In the formula: —The vibration frequency generated by bending stiffness when the tension is zero; NO (9); Substituting equation (9) into equation (5), we get: （10） ； Substituting equations (4), (7), and (10) into equation (6), we get: ； And because , Therefore: ； At this point, the least squares method is used to plot the quadratic curves of the squares of several measured steel strand vibration frequencies. The polynomial coefficients can be obtained by fitting. and The value of can be used to calculate the bending stiffness of the tensioned steel strand by equation (9).

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