Damage detection method for arch bridges based on the curvature of the strain influence line of the catenary hingeless arch

Abstract

The present invention discloses an arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line, belonging to the technical field of arch bridge damage detection. The present invention combines the analysis of hingeless single arch finite element examples for damage identification research of hingeless arch structures, studies the influence of the influence line measurement point position, local damage location and degree, and test noise on the identification results, and constructs influence line difference curvature amplitude curves under different damage conditions, fits the damage degree-amplitude relationship formula, and inverts the damage degree to achieve accurate quantification of damage. The method is verified by combining with an example of a steel truss railway arch bridge structure model, showing that the damage detection method can accurately locate the damage location of the arch structure, quantify the damage degree, and can warn of local damage to the structure and perform diagnosis, thus having engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of arch bridge damage detection, and in particular to an arch bridge damage detection method based on the curvature of the strain influence line of a catenary hingeless arch. Background Art

[0002] Hingeless arch structures are widely used in bridge engineering due to their simple construction, clear force transmission, and diverse design options. However, as the primary load-bearing component of arch bridges, hingeless arches become subject to various adverse factors over their service life, leading to cumulative structural damage, often manifesting as a reduction in localized stiffness.

[0003] As the primary load-bearing component of an arch bridge, the main arch rib is primarily subjected to compression, with complex local forces. Rapid, catastrophic changes in the bridge structure, along with the cross-scale and multi-scale evolution of damage, can lead to serious consequences. Therefore, research on arch bridge damage identification methods is of great engineering significance. Identifying early-stage local damage in arch bridges and implementing timely measures are crucial for extending bridge lifespan, ensuring the safe operation of bridge structures, and reducing public property losses. Thanks to the rapid development of bridge health monitoring, research on damage identification based on the dynamic characteristics of bridge structures has progressed significantly. Common methods for damage identification include structural time-domain signals, frequency-domain information, stiffness matrices, flexibility matrices, and modal parameters. While methods based on structural dynamic fingerprints offer high damage identification accuracy, they face challenges with the cumbersome installation and deployment of numerous sensors. Recently, damage identification methods based on influence lines have emerged, facilitating rapid bridge assessments because they can comprehensively characterize cross-sectional stiffness characteristics using a small number of sensors. However, analytical methods for damage identification based on influence lines have yet to be proposed for arch bridges with complex structural load patterns. Therefore, a damage detection method for arch bridges based on the curvature of the strain influence line of the catenary hingeless arch is proposed. Summary of the Invention

[0004] The technical problem to be solved by the present invention is: how to solve the problems faced by existing methods based on structural dynamic fingerprint indicators, such as the need to install a large number of sensors and the cumbersome layout, and provide an arch bridge damage detection method based on the curvature of the strain influence line of the catenary hingeless arch.

[0005] The present invention solves the above technical problems through the following technical solutions, which include the following steps:

[0006] S1: Establish a basic hingeless arch system in a damaged state. The damage is simulated by reducing the local elastic modulus and thus the stiffness of the structure. The bending stiffness and tensile stiffness after damage are EI′ and EA′, respectively. The redundant force influence line integral expression of the catenary hingeless arch in the damaged state is derived.

[0007] S2: Establish the internal force diagram at any measuring point G of the hingeless arch under the damaged state, and solve the integral expression of the strain influence line of any cross section G under the damaged state through the mechanical relationship between cross section strain and redundant forces x1, x2, and x3;

[0008] S3: The strain influence line ε after structural damage G ′ and the non-destructive strain influence line ε G Make a difference and calculate its second-order derivative for analysis. The curvature of the strain influence line difference is used to determine whether structural damage has occurred and then locate the damage location.

[0009] Furthermore, in step S1, the redundant force influence line integral expression of the hingeless catenary arch in the damaged state is as follows:

[0010]

[0011] Among them, δ 11 ′、δ 22 ′、δ 33 ′ is the flexibility coefficient, i.e. the hingeless arch structure is always deformed, Δ 1P ′、Δ 2P ′、Δ 3P ′ is the free term, i.e. the load displacement of the hingeless arch structure, a is the arch parameter of the suspension cable, x m is the horizontal coordinate of the moving load.

[0012] Furthermore, in step S1, the derivation process of the redundant force influence line integral expression of the catenary hingeless arch in the damaged state is as follows:

[0013] S11: Establish the basic hingeless arch system in the damaged state;

[0014] S12: Use the elastic center method to simplify the force equation:

[0015]

[0016] S13: For the hingeless catenary arch structure with uniform cross-section, the catenary line fitting is used to simplify the differential of the arch axis arc, i.e. ds = ch(x / a)dx;

[0017] S14: Discuss and analyze the relative position relationship between the moving load, measuring point and damaged section, and derive the integral expression of redundant force influence line.

[0018] Furthermore, in step S2, the integral expression of the strain influence line of any cross section G under the structural damage state is as follows:

[0019]

[0020] Among them, ε G ′ is the strain at section G in the structural damage state, xG 、y G are the horizontal and vertical coordinates of section G, are the sine and cosine angles of section G, E is the elastic modulus of the material, b is the width of the arch section, and h is the G is the height of G section, redundant force x1′=-Δ 1P ′ / δ 11 ′, x2′=-Δ 2P ′ / δ 22 ′, x3′=-Δ 3P ′ / δ 33 ′, and the corresponding constant displacement and load displacement parameters can be substituted to obtain the solution.

[0021] Furthermore, in step S3, ε G The damage elastic modulus E′ in the expression of ′ is replaced by E to obtain the lossless strain influence line ε G expression.

[0022] Furthermore, in step S3, the difference curvature (ε G -ε G ′)″, divided into the following five situations:

[0023] The first type: when -l≤x m ≤0, (ε G -ε G ')"=0;

[0024] The second type: when 0≤x m ≤d-ε, (ε G -ε G ')"=0;

[0025] The third type: when d-ε≤x m When ≤d+ε,

[0026]

[0027] The fourth type: when d+ε≤x m ≤x G When (ε G -ε G ')" = 0;

[0028] Fifth: When x G ≤x m When ≤l, (ε G -ε G ')"=0;

[0029] Where, C = f / (m-1),

[0030]

[0031] Among them, EI′ and EI are the bending stiffness of the damaged section and the intact section respectively, EA′ and EA are the tensile stiffness of the damaged section and the intact section respectively, and x m is the position of the moving load, f is the hingeless arch height, m ​​is the catenary arch axis coefficient, and a is the catenary arch parameter.

[0032] Furthermore, in step S3, when the moving load is located in the damage-free area, the curvature of the strain influence line difference (Δ G -Δ G ′)″ is 0, and when the moving load is located in the lossy area, the strain influence line difference curvature (Δ G -Δ G ′)″ is a value other than 0, which generates a mutation and further identifies the damage location.

[0033] Furthermore, in step S3, with respect to the damage degree of the hingeless arch structure, in actual engineering, the damage is first located by the strain influence line difference curvature index. After the measuring points and the damage points are determined, the strain influence line difference curvature amplitude curves under different damage conditions are simulated by finite element software, and the damage degree-amplitude relationship formula is fitted to invert the damage degree to achieve damage quantification.

[0034] Compared with the existing technology, the present invention has the following advantages: the arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line is combined with the hingeless single arch finite element example analysis to study the damage identification of hingeless arch structures. The influence of the influence line measurement point position, local damage position and degree, and test noise on the identification results are studied. By constructing the influence line difference curvature amplitude curve under different damage conditions, fitting the damage degree-amplitude relationship formula, and inverting the damage degree, accurate quantification of the damage is achieved; and combined with a steel truss railway arch bridge structure model example verification, it is shown that the damage detection method can accurately locate the damage position of the arch structure, quantify the damage degree, and can warn of local structural damage and perform diagnosis. It has engineering application value and is worthy of promotion and use. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 1 is a flow chart of an arch bridge damage detection method based on the curvature of the strain influence line of a catenary hingeless arch in the first embodiment of the present invention;

[0036] Figure 2 Schematic diagram of the basic hingeless arch system in a damaged state in Example 1 of the present invention;

[0037] Figure 3 Schematic diagram of the internal force of any measuring point of the hingeless arch in the damaged state in the first embodiment of the present invention;

[0038] Figure 4 This is the hingeless single arch structure model in the second embodiment of the present invention;

[0039] FIG5( a ) is a diagram showing damage identification results of the arch rib structure under working condition 1 in the second embodiment of the present invention (unit: με);

[0040] FIG5( b ) is a diagram showing damage identification results of the arch rib structure working condition 2 in the second embodiment of the present invention (unit: με);

[0041] FIG5( c ) is a diagram showing damage identification results of the arch rib structure working condition 3 in the second embodiment of the present invention (unit: με);

[0042] FIG5( d ) is a diagram showing damage identification results of the arch rib structure working condition 4 in the second embodiment of the present invention (unit: με);

[0043] FIG5( e ) is a diagram showing damage identification results of the arch rib structure working condition 5 in the second embodiment of the present invention (unit: με);

[0044] FIG5( f ) is a diagram showing the damage identification results of the arch rib structure working condition 6 in the second embodiment of the present invention (unit: με);

[0045] FIG6( a ) is a schematic diagram of a horizontal comparison of the damage degree of the strain influence line difference curvature index curve for working condition 1 in Example 2 of the present invention (unit: με);

[0046] FIG6( b ) is a schematic diagram of the damage degree of the strain influence line difference curvature index curve in working condition 2 of the second embodiment of the present invention (unit: με);

[0047] FIG6( c ) is a schematic diagram of the horizontal comparison of the damage degree of the strain influence line difference curvature index curve for working condition 3 in Example 2 of the present invention (unit: με);

[0048] FIG7( a ) is a curve (unit: με) showing the strain influence line difference curvature index of working condition 1 at a damage degree of 5% without using a sliding average filter for noise reduction in Example 2 of the present invention;

[0049] FIG7( b ) is a curve of the strain influence line difference curvature index (unit: με) for working condition 2 at a damage degree of 5% without using a sliding average filter for noise reduction in Example 2 of the present invention;

[0050] FIG7( c ) is a curve (unit: με) showing the strain influence line difference curvature index of working condition 3 at a damage degree of 5% without using a sliding average filter for noise reduction in Example 2 of the present invention;

[0051] Figure 8 is the relationship between the damage degree and the strain influence line difference curvature in the second embodiment of the present invention (1-24 in the figure represents the amplitude of unit 24 in working condition 1);

[0052] Figure 9 The steel truss arch bridge model in the third embodiment of the present invention;

[0053] FIG10( a ) is a schematic diagram of the overall structure of a steel truss arch bridge member in Example 3 of the present invention;

[0054] FIG10( b ) is a cross-sectional view taken along line AA in FIG10( a );

[0055] FIG10( c ) is a cross-sectional view taken along line BB in FIG10( a );

[0056] Figure 10(d) is a cross-sectional view taken along line CC in Figure 10(a);

[0057] Figure 10(e) is a cross-sectional view at DD in Figure 10(a);

[0058] Figure 11 Schematic diagram of the damage condition of the main arch span and the arrangement of measuring points in the third embodiment of the present invention;

[0059] FIG12( a ) is a diagram showing damage identification results of the arch rib structure under working condition 1 in Example 3 of the present invention (unit: με);

[0060] FIG12( b ) is a diagram showing damage identification results of the arch rib structure under working condition 2 in Example 3 of the present invention (unit: με);

[0061] FIG12( c ) is a diagram showing damage identification results of the arch rib structure under working condition 3 in Example 3 of the present invention (unit: με);

[0062] FIG12( d ) is a diagram showing damage identification results of the arch rib structure under working condition 4 in Example 3 of the present invention (unit: με);

[0063] FIG12( e ) is a diagram showing damage identification results of the arch rib structure under working condition 5 in Example 3 of the present invention (unit: με);

[0064] FIG12( f ) is a diagram showing damage identification results of the arch rib structure under working condition 6 in Example 3 of the present invention (unit: με);

[0065] Figure 13 is the damage identification result (unit: με) of the noise-containing working condition (working condition 7) in Example 3 of the present invention. DETAILED DESCRIPTION

[0066] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process. However, the protection scope of the present invention is not limited to the following embodiment.

[0067] Example 1

[0068] like Figure 1 As shown, this embodiment provides a technical solution: an arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line, comprising the following steps:

[0069] (1) Establish the basic system of hingeless arch in damaged state (see Figure 2 ), damage is simulated by reducing the local elastic modulus and thus the stiffness of the structure. The bending stiffness and tensile stiffness after damage are EI′ and EA′ respectively, and the redundant force influence line integral expression of the hingeless catenary arch in the damaged state is derived;

[0070] In this step, the integral expression of the redundant force influence line of the catenary hingeless arch in the damaged state is as follows:

[0071]

[0072]

[0073] Among them, δ 11 ′、δ 22 ′、δ 33 ′ is the flexibility coefficient, i.e. the hingeless arch structure is always deformed, Δ 1P ′、Δ 2P ′、Δ 3P ′ is the free term, i.e. the load displacement of the hingeless arch structure, a is the arch parameter of the suspension cable, x m is the horizontal coordinate of the moving load.

[0074] In this step, the derivation process of the redundant force influence line integral expression of the catenary hingeless arch in the damaged state is as follows:

[0075] S11: Establish the basic hingeless arch system in the damaged state;

[0076] S12: Use the elastic center method to simplify the force equation:

[0077]

[0078] S13: For the hingeless catenary arch structure with uniform cross-section, the catenary line fitting is used to simplify the differential of the arch axis arc, i.e. ds = ch(x / a)dx;

[0079] S14: Discuss and analyze the relative position relationship between the moving load, measuring point and damaged section, and derive the integral expression of redundant force influence line.

[0080] (2) Establish a schematic diagram of the internal forces at any measuring point of the hingeless arch under damage conditions (see Figure 3 ), taking point G as an example; through the mechanical relationship between cross-sectional strain and redundant forces x1′, x2′, x3′, the integral expression of the strain influence line of any cross-sectional area G under the structural damage state is solved:

[0081]

[0082] In this step, for the redundant force x1′=-Δ 1P ′ / δ 11 ′, x2′=-Δ 2P ′ / δ 22 ′, x3′=-Δ 3P ′ / δ 33 ′, and the corresponding constant displacement and load displacement parameters can be substituted to obtain the solution.

[0083] (3) The strain influence line ε after the arch rib structure is damaged G ′ and the non-destructive strain influence line ε G Make a difference and calculate the second-order derivative for analysis. When the moving load is located in the damage-free area of ​​the structure, the strain influence line difference curvature is zero. The strain influence line difference curvature can be used to determine whether structural damage has occurred and locate the damage location.

[0084] In step (3), the difference curvature (ε G -ε G ′)″, can be divided into the following five situations:

[0085] When -l≤x m ≤0, (ε G -ε G ')"=0, this is the first case;

[0086] When 0≤x m ≤d-ε, (ε G -ε G ')"=0, this is the second case;

[0087] When d-ε≤x m When ≤d+ε,

[0088]

[0089] This is the third case;

[0090] When d+ε≤x m ≤x G When (ε G -ε G ')"=0, this is the fourth case;

[0091] When x G ≤x m When ≤l, (ε G -ε G ')"=0, this is the fifth case;

[0092] Where, C = f / (m-1),

[0093]

[0094] From the above five cases, it can be seen that when the moving load is located in the damage-free area, the curvature of the difference of the strain influence line (Δ G -Δ G ′)″ is 0, and when the moving load is located in the lossy area, the strain influence line difference curvature (Δ G -Δ G ')" is a value other than 0, which generates a mutation and can further identify the damage location.

[0095] In step (3), for the damage degree of the hingeless arch structure, in actual engineering, the damage location can be first performed by the strain influence line difference curvature index. After the measuring point and the damage point are determined, the strain influence line difference curvature amplitude curve under different damage conditions is simulated by finite element software, and the damage degree-amplitude relationship formula is fitted to invert the damage degree to achieve accurate quantification of the damage.

[0096] It should be noted that Figure 2 、 3 Medium x m is the position of the moving load (i.e., the horizontal coordinate of the moving load), and (d-ε, d+ε) is the damaged section.

[0097] Example 2

[0098] In this embodiment, a hingeless single arch model is used to verify the method in the first embodiment. A hingeless single arch structure finite element model is established with a span of L = 50.934m, C50 concrete is used, and the cross section is a rectangle of 1.1.3m. Figure 4 shown.

[0099] During the verification process of this embodiment, local damage is simulated by reducing the unit elastic modulus. The cross-sectional size and mass of the damaged unit remain unchanged, and the degree of damage is defined by the percentage of the elastic modulus reduction.

[0100] In this embodiment, the hingeless single arch model is divided into 48 beam elements. A quasi-static moving force is applied as the influence line loading method. The loading unit length is set to 1.061 m, and a total of 49 moving loading steps are performed. Damage conditions 1-6 are shown in Table 1.

[0101] Table 1 Damage conditions of arch structure

[0102]

[0103] A moving concentrated force is applied to the arch structure. At the same time, the strain influence line difference curvature index curves of 20% and less damage in working conditions 1 and 2 and 5% damage in working condition 3 are filtered and denoised using the sliding average method. The identification curve is shown in Figure 5 below.

[0104] To better explore the impact of measurement point location and unit damage degree on the damage identification effect of strain influence line difference curvature, the strain influence line difference curvature index curves for 5% damage degree and 40% damage degree in working conditions 1, 2, and 3 are compared horizontally and vertically, as shown in Figure 6 below. At the same time, the strain influence line difference curvature index curves for 5% damage degree in working conditions 1, 2, and 3 without sliding average filtering noise reduction are shown in Figure 7.

[0105] Analyzing Figures 5-7, we can see that:

[0106] (1) The strain influence line difference curvature index identification method has a good identification effect on both single-point damage and multi-point damage in hingeless arch structures, and can accurately identify the damage location. From working conditions 1, 2, and 3, it can be seen that at the same measuring point, the height of the curve peak is proportional to the degree of damage.

[0107] (2) Comparing working conditions 1, 2, and 3, the peak value of the strain influence line difference curvature curve is the highest when the measuring point is located at the arch top, and the lowest when it is located at the arch foot. It can be seen that the peak value of the strain influence line difference curvature curve is inversely proportional to the distance between the measuring point and the damage location. In terms of damage identification effect, the arch top measuring point is the best, followed by the quarter measuring point, and the arch foot measuring point is the worst. It can be seen that the closer the measuring point is to the damage location, the better the identification effect. In addition to being affected by the position of the measuring point, the identification effect is also related to the degree of damage of the unit. The higher the degree of damage, the better the identification effect. As shown in Figure 7, in working conditions 1, 2, and 3, the strain influence line difference curvature curve with a degree of 5% damage needs to be processed by sliding average, otherwise there will be too many noise points and it will be difficult to identify the damage location.

[0108] (3) When the damage degree is 40%, the introduction of noise intensities of 1%, 3%, and 5% can still effectively identify the damage location, indicating that the strain influence line difference curvature has good noise resistance.

[0109] In order to better explore the relationship between damage degree and strain influence line difference curvature amplitude and inverse damage degree, the strain influence line difference curvature amplitude under 7 damage degrees was taken under working condition 1. The damage degree-amplitude relationship is shown in Table 2 below. Figure 8 .

[0110] Table 2 Maximum value of strain influence line difference curvature under different damage levels

[0111]

[0112] Depend on Figure 8 It can be seen that in the early stage of damage, the peak value of the strain influence line difference curvature changes relatively slowly, and the increase in the degree of unit damage has little effect on the dynamic characteristics of the structure, with a certain safety reserve. However, as the degree of damage increases, the peak value of the strain influence line difference curvature changes steeply and long, and the structural dynamic characteristics are greatly affected by the degree of damage. The more fragile the structure is, the more consistent with the actual law of structural damage change.

[0113] right Figure 8 The curvature amplitude of the difference of the medium strain influence line is fitted with the damage degree, and the fitting result is shown in the following formula:

[0114] SILDC 1-24 (x) = -6.3382x 5 +14.083x 4 -10.971x 3 +3.4664x 2 -0.3664x+0.0002

[0115] Wherein the strain influence line difference curvature amplitude SILDC a-b The subscript of represents the amplitude of unit b in working condition a;

[0116] A goodness-of-fit analysis determined the coefficient of fit, R = 0.984, indicating a good fit. The damage extent was inverted by fitting the peak value of the strain influence line difference curvature under each damage condition. In Condition 5, the mid-span weakened from a rigid connection to a hinged connection to simulate the plastic hinge present in an actual structure. Substituting the strain influence line difference curvature at the damage location into the equation, the calculated damage extent, x, was 97.575%, close to the 100.00% damage extent for complete damage.

[0117] Example 3

[0118] In this embodiment, a steel truss arch bridge model is used to verify the method in Example 1. A continuous half-through steel truss tied arch bridge model is established. The main bridge is a continuous steel truss structure of 102m+180m+102m. The steel strength grade of the model is Q235 and the elastic modulus is 205GPa. The model has a total of 1287 sections, 2561 units and 907 nodes. The finite element model and component structure of the steel truss tied arch bridge are shown in Figure 9 、10.

[0119] In order to explore the effect of strain influence line difference curvature on damage identification of steel truss tied arch bridge, four damage conditions are introduced according to the damage that is easy to occur in the arch rib of steel truss arch bridge in actual engineering, as shown in Table 3. Figure 11 To facilitate the analysis of the arch rib influence line of the tied arch bridge, only the β-β′ main arch section of the support is intercepted, see Figure 11 The damage introduction method is the same as that in Example 2.

[0120] Table 3 Damage conditions of steel truss arch bridges

[0121]

[0122] Analyze Figure 12 (a) to (f), Figure 13It can be seen that the strain influence line difference curvature index has a good identification effect on both single-point and multi-point damage of the arch rib structure of the steel truss tied arch bridge. By taking the sliding average of the strain influence line difference curvature curve under low damage conditions and when the measuring point is far away from the damage point, the damage location can be identified more accurately. (1) For the same damage location, it can be seen from working conditions 1 and 2 that the damage identification effect of the measuring point at one quarter is better than that at the arch foot, and the peak value of the strain influence line difference curvature index is also higher than that of the measuring point at the arch foot, which also verifies the conclusion in Example 2; (2) Comparing working conditions 1 and 3, the measuring point at one quarter is more sensitive to the damage at the arch crown and has a better identification effect; comparing working conditions 1 and 4, the measuring point at one quarter has a better damage identification effect on the main chord under the arch crown than on the main chord on the arch crown, and the peak value of the strain influence line difference curvature curve is also higher; (3) Comparing working conditions 1, 4, and 5, it can be seen that the damage identification effect of the strain influence line difference curvature is also related to the damage area. Under the same measuring point position, the damage identification effect of the vertical diagonal member of the arch crown is the best, and the curve peak value is also the highest.

[0123] In summary, the arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line of the above embodiment, combined with the hingeless single arch finite element example analysis, is used for the damage identification research of the hingeless arch structure. The influence of the influence line measuring point position, local damage position and degree, and test noise on the identification result are studied. The influence line difference curvature amplitude curve under different damage conditions is constructed, the damage degree-amplitude relationship formula is fitted, and the damage degree is inverted to achieve accurate quantification of the damage. The method is verified by combining with an example of a steel truss railway arch bridge structure model, which shows that the damage detection method can accurately locate the damage position of the arch structure, quantify the damage degree, and can warn of local damage to the structure and perform diagnosis. It has engineering application value and is worthy of being promoted and used.

[0124] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. Arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line, characterized by: The following steps are involved: S1: Establish a basic hingeless arch system in a damaged state. The damage is simulated by reducing the local elastic modulus and thus the stiffness of the structure. The bending stiffness and tensile stiffness after damage are EI′ and EA′, respectively. The redundant force influence line integral expression of the catenary hingeless arch in the damaged state is derived. In step S1, the integral expression of the redundant force influence line of the catenary hingeless arch in the damaged state is as follows: Among them, δ 11 ′、δ 22 ′、δ 33 ′ is the flexibility coefficient, i.e. the hingeless arch structure is always deformed, Δ 1P ′、Δ 2P ′、Δ 3P ′ is the free term, i.e. the load displacement of the hingeless arch structure, a is the arch parameter of the suspension cable, x m is the horizontal coordinate of the moving load, (d-ε, d+ε) is the damaged section, EI′ and EI are the bending stiffness of the damaged section and the intact section respectively, EA′ and EA are the tensile stiffness of the damaged section and the intact section respectively, x m is the position of the moving load, m is the catenary arch axis coefficient; S2: Establish the internal force diagram at any measuring point G of the hingeless arch under the damaged state. Based on the mechanical relationship between the cross-sectional strain and the redundant forces x1′, x2′, and x3′, solve the integral expression of the strain influence line of any cross-sectional area G under the damaged state. S3: The strain influence line ε after structural damage G ′ and the non-destructive strain influence line ε G Make a difference and calculate its second-order derivative for analysis. The curvature of the strain influence line difference is used to determine whether structural damage has occurred and then locate the damage location.

2. The arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line according to claim 1 is characterized by: In step S1, the derivation process of the redundant force influence line integral expression of the catenary hingeless arch in the damaged state is as follows: S11: Establish the basic hingeless arch system in the damaged state; S12: Use the elastic center method to simplify the force equation: S13: For the hingeless catenary arch structure with uniform cross-section, the catenary line fitting is used to simplify the differential of the arch axis arc, i.e. ds = ch(x / a)dx; S14: Discuss and analyze the relative position relationship between the moving load, measuring point and damaged section, and derive the integral expression of redundant force influence line.

3. The arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line according to claim 1 is characterized by: In step S2, the integral expression of the strain influence line of any cross section G in the structural damage state is as follows: Among them, ε G ′ is the strain at section G in the structural damage state, x G 、y G are the horizontal and vertical coordinates of section G, are the sine and cosine angles of section G, E is the elastic modulus of the material, b is the width of the arch section, h G is the height of G section, redundant force x1′=-Δ 1P ′ / δ 11 ′, x2′=-Δ 2P ′ / δ 22 ′, x3′=-Δ 3P ′ / δ 33 ′, and the corresponding constant displacement and load displacement parameters can be substituted to obtain the solution.

4. The arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line according to claim 3 is characterized by: In step S3, ε G The damage elastic modulus E′ in the expression of ′ is replaced by E to obtain the lossless strain influence line ε G expression.

5. The arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line according to claim 1, characterized in that: In step S3, the difference curvature (ε G -ε G ′)″, divided into the following five situations: The first type: when -l≤x m ≤0, (ε G -ε G ')"=0; The second type: when 0≤x m ≤d-ε, (ε G -ε G ')"=0; The third type: when d-ε≤x m When ≤d+ε, The fourth type: when d+ε≤x m ≤x G When (ε G -ε G ')"=0; Fifth: When x G ≤x m When ≤l, (ε G -ε G ')"=0; Where, C = f / (m-1), Among them, EI′ and EI are the bending stiffness of the damaged section and the intact section respectively, EA′ and EA are the tensile stiffness of the damaged section and the intact section respectively, EA′ and EA are the tensile stiffness of the damaged section and the intact section respectively, and x m is the position of the moving load, f is the hingeless arch height, m ​​is the catenary arch axis coefficient, and a is the catenary arch parameter.

6. The arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line according to claim 1, characterized in that: In step S3, when the moving load is located in the damage-free area, the curvature of the strain influence line difference (Δ G -Δ G ′)″ is 0, and when the moving load is located in the lossy area, the strain influence line difference curvature (Δ G -Δ G ′)″ is a value other than 0, which generates a mutation and further identifies the damage location.

7. The arch bridge damage detection method based on the curvature of the catenary hingeless arch strain influence line according to claim 1, characterized in that: In step S3, with respect to the damage degree of the hingeless arch structure, in actual engineering, the damage is first located by the strain influence line difference curvature index. After the measuring points and the damage points are determined, the strain influence line difference curvature amplitude curves under different damage conditions are simulated by finite element software, and the damage degree-amplitude relationship formula is fitted to invert the damage degree to achieve damage quantification.

Images