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

Abstract

The present invention discloses a method for detecting arch bridge damage based on the curvature of the deflection influence line of a catenary hingeless arch, belonging to the technical field of arch bridge damage detection. The present invention takes the arch ribs, the main load-bearing components of hingeless arch bridges, as the research object. By constructing a curve of the curvature amplitude of the deflection influence line under different damage conditions, fitting a damage degree-amplitude relationship formula, and inverting the damage degree, the present invention achieves accurate quantification of the damage degree. The method is verified by combining it with a case study of a top-supported box-type arch bridge structure model, demonstrating that the proposed damage identification method is effective for arch bridge structure damage identification, has engineering application value, and is worthy of promotion and use.

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 a catenary hingeless arch deflection influence line. Background Art

[0002] Hingeless arch bridges, as statically indeterminate cubic-curved structures, are widely used due to their high overall stiffness, simple construction, easy construction, and low maintenance. However, due to their high degree of static indeterminacy, temperature fluctuations, material shrinkage, structural deformation, and especially pier displacement can generate significant additional stresses, leading to settlement and cracking of the main arch ring, often accompanied by a reduction in localized structural stiffness.

[0003] The main arch ribs or arch rings are the primary load-bearing components of arch bridges. Damage to them can significantly reduce the bridge's bearing capacity or even lead to its collapse. Therefore, rapid damage location and assessment of hingeless arch structures are of great practical significance. Holistic detection techniques based on dynamic indicators offer advantages such as speed, accuracy, and comprehensiveness. Common dynamic indicators include structural natural frequencies, mode shapes, time-domain signals, frequency-domain information, stiffness matrices, and flexibility matrices. However, current methods based on structural dynamic fingerprints require the deployment of a large number of sensors and face challenges such as optimizing their placement and incomplete measurement information. Bridge damage identification methods based on influence lines can rapidly assess the structure by reflecting comprehensive structural information using a small number of measurement points. This reduces the number of sensors and more comprehensively captures bridge data, minimizing errors in data analysis and processing, offering a new approach to bridge damage identification. Deck arch bridges are mostly masonry structures. Due to the complex internal force distribution and discrete mechanical properties of masonry materials, research on damage identification based on influence lines is rare. Therefore, a damage detection method for arch bridges based on the curvature of the influence line of the hingeless arch deflection is proposed. Summary of the Invention

[0004] The technical problem to be solved by the present invention is: how to solve the problem that the current methods based on structural dynamic indicators require the deployment of a large number of sensors, and face problems such as how to optimize the layout of sensors and incomplete measurement information. A method for arch bridge damage detection based on the curvature of the deflection influence line of the catenary hingeless arch is provided.

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

[0006] S1: Establish a 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 a deflection calculation diagram for any measuring point G of a hingeless arch under damage. Based on the mechanical relationship between the section deflection and the redundant forces x1, x2, and x3, solve the integral expression of the deflection influence line of any section G under damage.

[0008] S3: The deflection influence line Δ after structural damage G ′ and the lossless deflection influence line Δ G Make a difference and calculate its second-order derivative for analysis. The curvature of the deflection 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 catenary hingeless 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, and (d-ε, d+ε) is the damaged section.

[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: Using the elastic center method to simplify the force equation, we get:

[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: 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 deflection influence line of any section G in the structural damage state is as follows:

[0019]

[0020] Among them, Δ′G is the deflection at point G, Δ GP is the deflection caused by the moving load at point G, Δ G1 , Δ G2 , Δ G3 are the deflections generated by the redundant forces x1′, x2′, and x3′ at point G, respectively. 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, Δ G The elastic modulus of damage E′ in the expression ′ is replaced by E to obtain the influence line of lossless deflection Δ G expression.

[0022] Furthermore, in step S3, the difference curvature (Δ G -Δ G ')" is divided into the following five situations:

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

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

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

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

[0030]

[0031] Where 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, f is the rise of the hingeless arch, m is the catenary arch axis coefficient, a is the cable arch parameter.

[0032] Furthermore, in step S3, when the moving load is located in the damage-free area, the curvature difference (Δ G -Δ G ′)″ is 0, and when the moving load is located in the lossy area, the curvature of the deflection influence line difference (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, for the damage degree of the hingeless arch structure, in actual engineering, the damage is first located by the deflection influence line difference curvature index. After the measuring point and the damage point are determined, the deflection 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 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 deflection influence line takes the arch rib of the main load-bearing component of the hingeless arch bridge as the research object, constructs the deflection influence line difference curvature amplitude curve under different damage conditions, fits the damage degree-amplitude relationship formula, and inverts the damage degree to achieve accurate quantification of the damage degree. It is verified by combining with an example of a top-supported box-type arch bridge structure model, which shows that the proposed damage identification method is effective for arch bridge structure damage identification, 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 catenary hingeless arch deflection influence line 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 calculation of deflection of an arbitrary measuring point G of a hingeless arch in a damaged state in Example 1 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 working condition 1 in the second embodiment of the present invention (unit: mm);

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

[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: mm);

[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: mm);

[0043] Figure 6 This is a damage identification result diagram (unit: mm) for the noise-containing working condition (working condition 5) in Example 2 of the present invention;

[0044] FIG7( a ) is a schematic diagram showing a transverse comparison of the damage degree of the deflection influence line difference curvature index curve for working condition 1 in Example 2 of the present invention (unit: mm);

[0045] FIG7( b ) is a schematic diagram of the horizontal comparison of the damage degree of the deflection influence line difference curvature index curve under working condition 2 in the second embodiment of the present invention (unit: mm);

[0046] Figure 8 is the deflection influence line difference curvature index curve (unit: mm) for working condition 2 in Example 2 of the present invention without using the sliding average filter noise reduction process;

[0047] Figure 9 Schematic diagram of the relationship between the damage degree and the curvature amplitude of the deflection influence line difference in Example 2 of the present invention; (1-24 in the figure represents the amplitude of unit 24 in working condition 1)

[0048] Figure 10 This is the box-type arch bridge model in the third embodiment of the present invention;

[0049] FIG11( a ) is a schematic diagram of the overall structure of a box-type arch bridge member in Example 3 of the present invention;

[0050] FIG11( b ) is a cross-sectional view taken along line AA in FIG11( a );

[0051] FIG11( c ) is a cross-sectional view taken along line BB in FIG11( a );

[0052] Figure 11(d) is a cross-sectional view taken along line CC in Figure 11(a);

[0053] Figure 12 This is a schematic diagram of the main arch ring damage condition and measurement point arrangement in Example 3 of the present invention;

[0054] FIG13( a ) is a diagram showing damage identification results of the arch ring structure working condition 1 in Example 3 of the present invention (unit: mm);

[0055] FIG13( b ) is a diagram showing damage identification results of the arch ring structure under working condition 2 in Example 3 of the present invention (unit: mm);

[0056] FIG13( c ) is a diagram showing damage identification results of the arch ring structure working condition 3 in Example 3 of the present invention (unit: mm);

[0057] FIG13( d ) is a diagram showing damage identification results of the arch ring structure under working condition 4 in Example 3 of the present invention (unit: mm);

[0058] Figure 14 This is the damage identification result (unit: mm) of the noise-containing working condition (working condition 5) in Example 3 of the present invention. DETAILED DESCRIPTION

[0059] 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.

[0060] Example 1

[0061] 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 deflection influence line, comprising the following steps:

[0062] (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;

[0063] In this step, the integral expression of the redundant force influence line of the catenary hingeless arch in the damaged state is as follows:

[0064]

[0065]

[0066] 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 mis the horizontal coordinate of the moving load, and (d-ε, d+ε) is the damaged section.

[0067] 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:

[0068] S11: Establish the basic hingeless arch system in the damaged state;

[0069] S12: Using the elastic center method to simplify the force equation, we get:

[0070]

[0071] 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;

[0072] S14: Analyze the relative position relationship between the moving load, measuring point and damaged section, and derive the integral expression of redundant force influence line.

[0073] (2) Using the principle of virtual work, a diagram for calculating the deflection of a hingeless arch at any measuring point G under a damaged state is established (see Figure 3 ), through the mechanical relationship between the section deflection and the redundant forces x1′, x2′, x3′, the integral expression of the deflection influence line of any section G under the structural damage state is solved:

[0074]

[0075] 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.

[0076] (3) The deflection influence line Δ after the arch rib structure is damaged G ′ and the lossless deflection influence line Δ 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 curvature of the deflection influence line difference is zero. The curvature of the deflection influence line difference can be used to determine whether structural damage has occurred and locate the damage location.

[0077] In this step, the difference curvature of the deflection influence line of any section G of the arch rib before and after damage (Δ G -Δ G ′)″ can be divided into the following five situations:

[0078] When -l≤x m ≤0, (ΔG -Δ G ')"=0, this is the first case;

[0079] When 0≤x m ≤d-ε, (Δ G -Δ G ')"=0, this is the second case;

[0080] This is the third case;

[0081] When d+ε≤x m ≤x G When (Δ G -Δ G ')"=0, this is the fourth case;

[0082] When x G ≤x m When ≤l, (Δ G -Δ G ')"=0, this is the fifth case;

[0083] Where, C = f / (m-1);

[0084]

[0085] From the above five cases, it can be seen that when the moving load is located in the damage-free area, the curvature difference of the deflection influence line of the arch rib section G (Δ G -Δ G ′)″ is 0, and when the moving load is located in the lossy area, the curvature of the deflection influence line difference (Δ G -Δ G ')" is a value other than 0, which generates a mutation and can then identify the damage location.

[0086] In the step (3), with respect to the damage degree of the hingeless arch structure, in actual engineering, the damage location can be first performed by the deflection influence line difference curvature index. After the measuring point and the damage point are determined, the deflection 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.

[0087] 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.

[0088] Example 2

[0089] 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, and a rectangular cross section of 1m × 1.3m. Figure 4 shown.

[0090] During the verification process of this embodiment, local damage is simulated by reducing the elastic modulus of the unit. 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.

[0091] In this embodiment, the hingeless single arch model is divided into 48 beam units. A quasi-static moving force is applied as the influence line loading method. The loading unit length is set to 1.061 m. There are 49 moving loading steps in total. Damage conditions 1-5 are shown in Table 1.

[0092] Table 1 Damage conditions of arch structure

[0093]

[0094] Apply moving load to the hingeless single arch structure, extract the deflection influence line difference curvature curve of the corresponding measuring point in Table 1, and use the sliding average method to filter and reduce noise on the deflection influence line difference curvature index curve in working condition 2. Draw the identification curve as shown below Figure 5(a) to Figure 5(d) 、 Figure 6 .

[0095] In order to better explore the influence of the measuring point location and unit damage degree on the damage identification effect of the deflection influence line difference curvature. The deflection influence line difference curvature index curves of 40% damage and 5% damage in working condition 1 and working condition 2 are compared horizontally and vertically, respectively, as shown in Figure 7 (a) and Figure 7 (b) below; at the same time, the deflection influence line difference curvature index curve of working condition 2 without sliding average filter noise reduction is shown in Figure 7 (a). Figure 8 .

[0096] Analysis Chart Figure 5(a) to Figure 5(d) 、 Figure 6 , Figure 7(a), Figure 7(b), Figure 8 It can be seen that:

[0097] (1) The deflection influence line difference curvature index identification method has a good identification effect on both single-point damage and multi-point damage of hingeless arch structures and can accurately identify the damage location.

[0098] (2) In working condition 1 or working condition 2, at the same measuring point location, the peak value of the curve is proportional to the degree of damage. Comparing working condition 1 and working condition 2, the peak value of the deflection influence line difference curvature index curve when the measuring point is located at one-quarter span is greater than that at the arch foot, and the damage identification effect of the measuring point at one-quarter span is better than that at the arch foot. It can be seen that the closer the measuring point is to the damage location, the better the identification effect. It is worth noting that under the working condition of one-quarter span, the deflection influence line difference curvature has a better damage identification effect for the unit damage of 40% than for the unit damage of 5%, while the opposite is true when the measuring point is located at the arch foot.

[0099] (3) By Figure 6 It can be seen that when the damage degree is 40%, the damage location can still be effectively identified by introducing noise intensities of 1%, 3%, and 5%, indicating that the deflection influence line difference curvature has good noise resistance.

[0100] In order to better explore the relationship between the damage degree and the deflection influence line difference curvature amplitude and inverse damage degree, the deflection 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 9 .

[0101] Table 2 Maximum value of curvature of deflection influence line difference under different damage levels

[0102] Damage level: x 0％ 20％ 40％ 60％ 80％ 90％ 99.9％ Amplitude S(x)max 0 2.10E-5 5.40E-5 1.21E-4 2.93E-4 5.67E-4 2.05E-2

[0103] Depend on Figure 9 It can be seen that in the early stage of damage, the peak value of the difference curvature of the deflection influence line 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 difference curvature of the deflection influence line 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.

[0104] right Figure 9 The curvature amplitude of the difference of the medium deflection influence line is fitted with the damage degree, and the fitting result is shown in the following formula:

[0105] DILDC 1-24 (x) = 1.2372x 5 -2.7658x 4 +2.1637x 3 -0.687x 2 +0.0725x-0.00004

[0106] Where the deflection influence line difference curvature amplitude DILDC a-b The subscript of represents the amplitude of unit b in working condition a;

[0107] A goodness of fit analysis was performed, and the coefficient R was determined to be 0.981, indicating that the fitting effect was good. Taking the arch rib structure as an example, for the determined working conditions, the deflection influence line difference curvature amplitude was substituted into the above formula to directly obtain the damage degree.

[0108] In working condition 4, the mid-span joint is weakened from a rigid connection to a hinge to simulate the plastic hinge that appears in the actual structure. The curvature value of the deflection influence line difference at the damage location is substituted into the formula. The calculated damage degree x is 90.95%, which is close to the damage degree of 100.00% under complete damage.

[0109] Example 3

[0110] In this embodiment, a deck arch bridge model is used to verify the method in Example 1. A single-span deck concrete box arch bridge model is established. The span of the arch bridge model is 116m. The main arch ring is made of C40 strength concrete with an elastic modulus of 32.5GPa. The model has 82 units and 96 nodes. The finite element model and component structure of the deck box arch bridge are shown in Figure 2. Figure 10 、 Figure 11(a) to Figure 11(d) .

[0111] In order to explore the damage identification effect of the deflection influence line difference curvature on the top-decker box arch bridge, five damage conditions are introduced according to the damage that is easy to occur in the main arch ring of the main load-bearing components in actual engineering, as shown in Table 3. Figure 12 The damage introduction method is the same as that of the second embodiment.

[0112] Table 3 Damage conditions of box arch bridges

[0113]

[0114]

[0115] analyze Figures 13(a) to 13(d) ,For top-supported box-type arch bridges, due to the limited number of actual force-transmitting structural columns and the redistribution of stress stiffness, the identification effect is poor, so the obtained deflection influence line difference curvature index is subjected to sliding average filtering. The example shows that the filtered deflection influence line difference curvature index has a good effect on the damage identification of the main arch ring structure, and the peak value of the deflection influence line difference curvature index curve changes with the degree of damage. The higher the degree of damage, the higher the peak value. It can be seen from working conditions 1, 2, and 3 that the peak value of the curve decreases from the mid-span, one-quarter, and arch foot in sequence with the position of the deflection measurement point; it can be seen from working condition 4 that there is still a good identification effect for multi-point damage of the structure. Figure 14 It can be seen that the deflection influence line difference curvature index after filtering and noise reduction processing has good noise resistance even for a low damage level of 5% of the structure.

[0116] In summary, the arch bridge damage detection method based on the curvature of the catenary hingeless arch deflection influence line in the above embodiment takes the arch rib of the main load-bearing component of the hingeless arch bridge as the research object, constructs the deflection influence line difference curvature amplitude curve under different damage conditions, fits the damage degree-amplitude relationship formula, and inverts the damage degree to achieve accurate quantification of the damage degree. It is verified by combining with an example of a top-supported box-type arch bridge structure model, which shows that the proposed damage identification method is effective for arch bridge structure damage identification, has engineering application value, and is worthy of promotion and use.

[0117] 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. An arch bridge damage detection method based on the curvature of the catenary hingeless arch deflection influence line is characterized by: The following steps are involved: S1: Establish a 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 a deflection calculation diagram for any measuring point G of a hingeless arch in a damaged state. Based on the mechanical relationship between the section deflection and the redundant forces x1′, x2′, and x3′, solve the integral expression of the deflection influence line of any section G in the damaged state. S3: The deflection influence line Δ after structural damage G ′ and the lossless deflection influence line Δ G Make a difference and calculate its second-order derivative for analysis. The curvature of the deflection 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 deflection 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: Using the elastic center method to simplify the force equation, we get: 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: 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 deflection influence line according to claim 1 is characterized by: In step S2, the integral expression of the deflection influence line of any section G in the structural damage state is as follows: Among them, Δ′ G is the deflection at point G, Δ GP is the deflection caused by the moving load at point G, Δ G1 , Δ G2 , Δ G3 are the deflections generated by the redundant forces x1′, x2′, and x3′ at point G, respectively. 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 deflection influence line according to claim 3 is characterized by: In step S3, Δ G The elastic modulus of damage E′ in the expression ′ is replaced by E to obtain the influence line of lossless deflection Δ G expression.

5. The arch bridge damage detection method based on the curvature of the catenary hingeless arch deflection influence line according to claim 4 is characterized in that: In step S3, the difference curvature (Δ G -Δ G ')" is divided into the following five situations: The first type: when -l≤x m ≤0, (Δ G -Δ G ')"=0; The second type: when 0≤x m ≤d-ε, (Δ G -Δ G ')"=0; The third type: when d-ε≤x m When ≤d+ε, The fourth type: when d+ε≤x m ≤x G When (Δ G -Δ G ')"=0; Fifth: When x G ≤x m When ≤l, (Δ G -Δ 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, 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 deflection 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 difference (Δ G -Δ G ′)″ is 0, and when the moving load is located in the lossy area, the curvature of the deflection influence line difference (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 deflection influence line according to claim 1, characterized in that: In step S3, for the damage degree of the hingeless arch structure, in actual engineering, the damage is first located by the deflection influence line difference curvature index. After the measuring point and the damage point are determined, the deflection 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 damage quantification.

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