Explosion damage assessment method for concrete frame structure

Abstract

The invention aims to provide a method for evaluating explosion damage of a concrete frame structure, which belongs to the technical field of structural damage evaluation and constructs a multi-level damage evaluation index system consisting of floor levels, component levels and specific damage states. During evaluation, a judgment matrix is established by using an interval analytic hierarchy process (IAHP), and the weight of each level of index is calculated; and then, combining an overpressure-impulse (P-I) curve and a component local damage formula as damage judgment basis, and carrying out rapid quantitative evaluation on the component damage by adopting a rapid calculation formula and a quantitative analysis method. And finally, calculating the membership degree of each level through a comprehensive evaluation method to obtain the damage level of the overall structure. According to the method, the scientificity is guaranteed, meanwhile, the damage condition of the reinforced concrete frame under explosion can be rapidly predicted and evaluated, the calculated amount is reduced, and good universality and engineering applicability are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of structural damage assessment, and particularly relates to a concrete frame structure explosion damage assessment method. BACKGROUND

[0002] Current research on damage assessment of reinforced concrete frame structures after explosion is relatively limited. The existing common assessment methods mainly include the following two types: One type of method is based on quantitative assessment at the component level. The assessment personnel usually divide the damage level of the component according to the established standard, and then calculate the response parameters of the component at each level through commercial simulation software, and then fit the P-I curve based on this. The curve reflects the overpressure and impulse values corresponding to different damage states of the component, and then a complete P-I curve graph is formed for reference. However, this method often has a large amount of calculation, needs to generate a large number of intermediate data points, has low efficiency, and is difficult to achieve clear quantitative expression of the assessment results, resulting in non-intuitive application. Another type of method relies on expert experience for qualitative judgment of the component. This method is highly subjective and is easily affected by individual judgment bias, and the assessment results have great uncertainty and contingency. In addition, the existing methods are mostly limited to damage judgment at the single component level, and lack the ability to systematically and comprehensively assess the overall damage state of the structure, so there are obvious deficiencies in actual engineering applications. SUMMARY

[0003] The purpose of the present application is to overcome the deficiencies in the prior art, and to provide a concrete frame structure explosion damage assessment method, which quickly generates a P-I curve based on component parameters, replaces complex simulation calculations, and determines the evaluation index weight using an interval analytic hierarchy process, and quantitatively models various damage modes such as bending, shearing and local rupture, and constructs a multi-level fuzzy comprehensive judgment model from components to the overall structure, and realizes systematic assessment of the overall damage state of the structure through membership degree calculation from bottom to top.

[0004] To achieve the above purpose, the present application provides a concrete frame structure explosion damage assessment method, comprising the following steps:

[0005] S1, a multi-level damage assessment index system is constructed, and the structure parameters and preset explosion load parameters of the target reinforced concrete frame structure are obtained. Based on the structure parameters, the target structure is divided into three levels from top to bottom: the first level is the overall damage state of the floor, the second level is the overall damage state of the main load-bearing component, and the third level is the specific damage state of the component, thereby constructing a multi-level damage assessment index system. At the same time, a unified damage level comment is defined, for example, divided into four levels of first level (basically intact), second level (slight damage), third level (moderate damage) and fourth level (severe damage).

[0006] S2, calculate the weight using interval analytic hierarchy process, for each level in the multi-level damage assessment index system, construct a judgment matrix using interval analytic hierarchy process, and calculate the weight vector of the next level index relative to the current level index.

[0007] S3, determine the membership degree of each component specific damage state, for each index in the component specific damage state level (such as bending failure, shear failure, local fracture failure), determine its membership degree for the preset multiple damage levels based on the structure parameters and explosion load parameters, and generate a membership degree vector. Combine the membership degree vectors of all specific damage state indexes of the same component to form a fuzzy evaluation matrix of the component.

[0008] S4, use fuzzy comprehensive evaluation method to evaluate the weight vector obtained in S2 and the fuzzy evaluation matrix obtained in S3 layer by layer, use fuzzy comprehensive evaluation method, calculate from bottom to top layer by layer. Perform fuzzy transformation operation (B=A·R) on the fuzzy evaluation matrix of the next level and the corresponding weight vector to obtain the comprehensive evaluation result of the previous level, until the final damage assessment result vector of the target reinforced concrete frame structure as a whole is calculated. Advantage: by constructing a multi-level damage assessment index system and combining interval analytic hierarchy process, fuzzy evaluation and comprehensive evaluation from bottom to top, this method overcomes the defects of traditional evaluation methods which rely on a large number of simulation calculations or subjective expert experience, and establishes a systematic, fast and quantitative evaluation process. This process can decompose the complex overall damage of the structure into clear and quantifiable hierarchical indexes, significantly reducing the computational complexity and improving the evaluation efficiency and objectivity, providing a global scientific evaluation method for the damage state of concrete frame structures under explosion.

[0009] Further, in the S1 step, the main load-bearing component level includes columns, beams, slabs and infilled wall components. The component specific damage state level is refined according to the type of component: for columns, beams and slabs, it includes three modes of overall bending failure, shear failure and local fracture failure; for infilled wall components, it includes two modes of overall bending failure and local fracture failure.

[0010] Advantage: by specifically defining the type of main load-bearing component and the corresponding damage mode, the evaluation model is more consistent with the actual physical damage characteristics of reinforced concrete frame structures under explosion. This refinement can more accurately capture the key failure behavior of different components, thereby improving the relevance of the entire evaluation model and the accuracy of the final evaluation result.

[0011] Further, in the S2 step, the step of calculating the weight vector using interval analytic hierarchy process further includes: 1. Construct an interval judgment matrix A=[a ij ] n×n , where 2. Calculate the consistency index and Perform a consistency test, and pass the test when k<=1 and beta>=1. 3. After passing the consistency test, decompose the interval judgment matrix into lower bound matrix A - and upper bound matrix A + Solve its eigenvectors respectively and perform normalization processing to obtain the weight vector.

[0012] Beneficial effect: Introduce a consistency test step when calculating the weight vector, verify the logical consistency of the judgment matrix through specific mathematical indexes k and beta. This effectively reduces the randomness and uncertainty that may be introduced by human judgment when constructing the judgment matrix, ensures the scientificity and reliability of the weight of each level of evaluation index, and further improves the objectivity and stability of the entire evaluation system.

[0013] Further, in the S3 step, for the overall bending failure or shear failure, the step of determining the membership degree comprises:

[0014] 1. Based on the structural parameters of the component, calculate the overpressure asymptote value P0 under the action of quasi-static load and the impulse asymptote value I0 under the action of impulse load;

[0015] 2. Substitute P0 and I0 into the dynamic zone empirical formula to generate the P-I curve of the component under different damage levels;

[0016] 3. Project the explosion load parameters (overpressure P and impulse I) into the plane formed by the P-I curve, and calculate the membership degree according to the relative position relationship between the projection and the P-I curve of each damage level.

[0017] Beneficial effect: A method for quickly calculating P-I curve based on component parameters is proposed, which replaces the time-consuming and laborious finite element simulation or test fitting process in traditional methods by solving the asymptotes of quasi-static and impulse zones and combining empirical formulas. This greatly improves the efficiency of component damage state evaluation, making it possible to quickly obtain reliable damage criteria in emergency evaluation or early prediction scenarios, and is one of the key technologies to realize the rapidity of the overall evaluation method.

[0018] Further, in the S3 step, the damage level of the overall bending failure is divided according to the rotation angle θ of the component support (for example, for beams and plates, light damage is 0<θ<=2°; for columns, light damage is 0<θ<=1°). The calculation of the membership degree uses a triangular membership function, and is based on the ratio of the length of the projection vector of the explosion load parameters in the P-I curve plane to the length of the boundary points of the P-I curve of each damage level in the direction of the vector.

[0019] Beneficial effects: The overall bending damage of the component is associated with the explicit physical quantity support corner θ, and the damage area divided by the P-I curve is fuzzily processed by using a triangular membership function. This way provides a clear and reliable physical basis and mathematical model for the quantification of bending damage degree, making the calculation process of membership more accurate and standardized, and improving the objectivity of evaluation.

[0020] Further, the overpressure asymptote value of the overall bending damage and the impulse asymptote The calculation formula is: Wherein, R m is the maximum resistance of the component, β is the ductility ratio, a and b are the length and width of the component, and ω is the equivalent system natural frequency.

[0021] Beneficial effects: The specific formula for calculating the P-I curve asymptote of the overall bending damage is given, which simplifies the complex dynamic response problem into algebraic operation of basic parameters such as maximum resistance of the component, ductility ratio, geometric size, etc. This makes non-professionals also can conveniently calculate the key parameters of P-I curve, further reduces the technical threshold of evaluation method, enhances the usability and operability of the method.

[0022] Further, the damage level of shear damage is divided according to the shear slip amount y s (For example, mild damage is 0<y s ≤0.1mm, moderate damage is 0.1mm<y s ≤0.3mm). The calculation formula of its overpressure asymptote value and impulse asymptote value Wherein, W s is the shear strain energy, R m is the maximum resistance of the component, M s is the equivalent shear mass, and a and b are the length and width of the component.

[0023] Beneficial effects: For the key failure mode of shear damage, the specific calculation formula of its P-I curve asymptote is provided, and the calculation is associated with parameters such as shear strain energy and equivalent mass. This provides an effective technical approach for quickly and quantitatively evaluating whether shear brittle damage occurs in the structure, enhances the recognition ability of the model for the failure mode of the structure under complex stress state, and improves the comprehensiveness and safety of the evaluation.

[0024] Further, the empirical formula for connecting the dynamic zone of P-I curve asymptote is: ​Where P is the peak overpressure, I is the impulse, q is the failure mode factor (for example, when the failure mode is bending mode and shear mode, the q value is 0.6 and 0.5 respectively), and k is the correction coefficient determined according to the shape of the explosive load (for example, for exponential, triangular and rectangular loads, the k value can be 0.9, 1.0 and 1.1 respectively).

[0025] Beneficial effects: It provides an empirical formula for the dynamic region connecting the asymptotes at both ends of the PI curve, and by introducing a correction coefficient k to consider the influence of different explosion charge patterns, the generated PI curve is not only calculated quickly, but can also adapt to different types of explosion scenarios, thus enhancing the versatility of the model.

[0026] Furthermore, in step S3, the step of determining the membership degree for localized fracture damage includes: 1. Calculating the collapse thickness T of the component based on the equivalent TNT charge Q and the distance Z from the explosion center to the component in the explosion load parameters. c 2. Utilizing the collapse thickness T c The relative collapse thickness T is obtained by comparing the collapse thickness with the total thickness T of the component. ′ c 3. Based on T ′ c The range of values ​​(e.g., T for a mild collapse) ′ c ≤1 / 3), and using the preset trapezoidal-triangular membership function, the membership degree of local fracture failure to each damage level is calculated.

[0027] Beneficial effect: Introducing relative collapse thickness T ′ c As an assessment index for localized fracture damage, a direct calculation method for it and explosion parameters is provided. This enables the model to independently and quantitatively assess localized penetrating damage caused by the near-field effect of the explosion, supplementing the shortcomings of only considering overall bending and shear responses. This allows the assessment system to cover a more comprehensive range of damage modes, and the assessment results are closer to actual working conditions.

[0028] Furthermore, following step S4, the method further includes processing the final damage assessment result vector using either the maximum membership degree method or the weighted scoring method: Maximum membership degree method: The damage level corresponding to the maximum membership degree in the final assessment result vector is selected as the final assessment conclusion. Weighted scoring method: A weighted average is calculated by combining the preset scores for each damage level (e.g., 12.5, 37.5, 62.5, and 87.5 points for levels one to four, respectively) with the corresponding membership degrees in the final assessment result vector to obtain a comprehensive score. The final damage level is determined based on the preset score range of the comprehensive score (e.g., 0-25 points corresponding to level one).

[0029] Beneficial effects: two result processing methods of maximum membership degree and weighted scoring are provided, making the output form of evaluation conclusion more flexible, and being able to meet the different engineering application requirements. The maximum membership degree method can give intuitive and clear damage grade, while the weighted scoring method can provide a continuous quantitative score, which is convenient for more detailed damage degree comparison and risk sorting, and enhances the engineering practical value of the evaluation result.

[0030] Compared with the prior art, the present application has at least the following beneficial effects:

[0031] (1) The present application overcomes the defects of traditional evaluation methods, such as relying on a large number of simulation calculations or subjective expert experience, and lacking of systematic evaluation of the structure as a whole, by constructing a multi-level evaluation index system from the structure as a whole to the floor, and then to the main load-bearing member and specific damage state, and combining interval analytic hierarchy process to determine the weight, and fuzzy comprehensive evaluation method to calculate layer by layer from bottom to top. The method divides the complex structure damage problem into clear and quantifiable hierarchical indicators, and establishes a systematic, fast and quantitative evaluation process, providing a global scientific evaluation method for the damage state of the concrete frame structure under the action of explosion.

[0032] (2) The present application can generate the required relationship curve for evaluation by directly calculating the overpressure limit value of the member under quasi-static load and the impulse limit value under impulse load, and combining the dynamic zone empirical formula. This method replaces the time-consuming and laborious finite element simulation or test fitting process in the traditional method, greatly improves the evaluation efficiency of the damage state of the member, and makes it possible to obtain reliable damage criteria quickly in the scene of emergency evaluation or early prediction, which is one of the key technologies to realize the rapidity of the overall evaluation method.

[0033] (3) In addition to evaluating the overall bending and shear failure of the member, the present application also introduces the ratio of the collapse thickness to the total thickness of the member as an evaluation index of local rupture damage, and provides a direct calculation method for the ratio and parameters such as equivalent explosive quantity and distance. This can independently and quantitatively evaluate the local penetrating damage caused by the near-field effect of explosion, supplement the deficiency of only considering the overall response of the structure, make the evaluation result closer to the actual working condition, and improve the comprehensiveness and accuracy of the evaluation.

[0034] (4) After obtaining the final evaluation result vector, the user can select the maximum membership degree method or the weighted scoring method for interpretation according to the requirements. The maximum membership degree method can give intuitive and clear qualitative damage grade, while the weighted scoring method can provide a continuous quantitative score, which is convenient for more detailed damage degree comparison and risk sorting. This flexibility makes the output form of the evaluation conclusion meet the different engineering application requirements, and enhances the engineering practical value of the evaluation result. BRIEF DESCRIPTION OF DRAWINGS

[0035] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the application and, together with the description, serve to explain the principles of the application.

[0036] The present application can be more clearly understood and appreciated from the following detailed description, taken in conjunction with the following drawings of which:

[0037] Figure 1 The working flow chart of the concrete frame structure explosion damage evaluation method described in the present application;

[0038] Figure 2 The schematic diagram of the member pressure-impulse (P-I) curve of the present application, in which the areas of different damage levels are divided;

[0039] Figure 3 The schematic diagram of the quantitative description of the pressure-impulse (P-I) curve of the present application;

[0040] Figure 4 The schematic diagram of the triangular membership function for overall bending and shear failure evaluation of the present application;

[0041] Figure 5 The schematic diagram of the trapezoidal-triangular membership function for local cracking damage evaluation of the present application. DETAILED DESCRIPTION

[0042] The technical solutions of the present application will be described in detail below with the help of the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments of the present application are detailed descriptions of the technical solutions of the present application, and not limitations of the technical solutions of the present application. In the case of no conflict, the technical features in the embodiments and the embodiments of the present application can be combined with each other. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, and cannot limit the protection scope of the present application.

[0043] The term "and / or" in this paper is only a description of the association relationship between the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " in this paper generally represents that the associated objects before and after are in an "or" relationship.

[0044] As Figure 1 shown, the present embodiment provides a concrete frame structure explosion damage evaluation method, comprising the following steps:

[0045] S1, obtaining the structure parameters of the target reinforced concrete frame structure and the preset explosion load parameters, and based on the structure parameters, dividing the target reinforced concrete frame structure from top to bottom into floor levels, main load-bearing member levels and member specific damage state levels, and constructing a multi-level damage evaluation index system;

[0046] S2, an interval analytic hierarchy process is adopted to construct a judgment matrix for each level in the multi-level damage evaluation index system, and a weight vector of an index in a next level relative to an index in a current level is calculated based on the judgment matrix;

[0047] S3, for each specific damage state index in the component specific damage state level, a membership degree of the specific damage state index to a preset plurality of damage levels is determined based on the structure parameters and the explosion load parameters, a membership degree vector is generated, and the membership degree vectors of all the specific damage state indexes of a same component are combined to form a fuzzy evaluation matrix of the component;

[0048] S4, based on the weight vector and the fuzzy evaluation matrix, a fuzzy comprehensive evaluation method is adopted to calculate from bottom to top layer by layer, a fuzzy transformation operation is performed on the fuzzy evaluation matrix of a next level and a corresponding weight vector to obtain a comprehensive evaluation result of a previous level, until a final damage evaluation result of the target reinforced concrete frame structure as a whole is calculated.

[0049] Beneficial effects: By constructing a multi-level damage evaluation index system and combining an interval analytic hierarchy process, a fuzzy evaluation and a comprehensive evaluation from bottom to top, the method overcomes the defects of traditional evaluation methods which rely on a large number of simulation calculations or subjective expert experience, and establishes a systematic, fast and quantitative evaluation process. The process can decompose the complex overall damage problem of the structure into clear and quantifiable hierarchical indexes, significantly reduces the calculation complexity, improves the evaluation efficiency and objectivity, and provides a global scientific evaluation method for the damage state of the concrete frame structure under the action of explosion.

[0050] Further, in the S1 step, the main load-bearing component level includes columns, beams, slabs and infill wall components; the component specific damage state level includes at least one of overall bending failure, shear failure and local cracking failure. By specifically defining the types of main load-bearing components and the corresponding damage modes, the evaluation model is more consistent with the actual physical damage characteristics of the reinforced concrete frame structure under explosion. This refinement can more accurately capture the key failure behavior of different components, thereby improving the relevance of the entire evaluation model and the accuracy of the final evaluation result.

[0051] Further, the step of calculating the weight vector by using the interval analytic hierarchy process further comprises: constructing an n*n interval judgment matrix [a ij ], where n represents the total number of indexes in a current level, a ij represents an importance interval of an i-th index relative to a j-th index, i,j = 1,…,n; and calculating a consistency index k and β for consistency check, where: and To determine the lower bound and upper bound of the elements in the interval judgment matrix; after passing the consistency check, the characteristic vector of the judgment matrix is solved and normalized to obtain the weight vector.

[0052] Beneficial effect: Introduce a consistency check step when calculating the weight vector, verify the logical consistency of the judgment matrix through specific mathematical indicators k and β. This effectively reduces the randomness and uncertainty that may be introduced by human judgment when constructing the judgment matrix, ensuring the scientificity and reliability of the weight of each level of evaluation index, and thus improving the objectivity and stability of the entire evaluation system.

[0053] Further, after the S4 step, the following steps are further included: using the maximum membership degree method or the weighted scoring method to process the final damage assessment result; wherein the maximum membership degree method is: selecting the damage grade corresponding to the maximum membership degree in the final damage assessment result as the final evaluation conclusion; the weighted scoring method is: weighting and averaging the preset score of each damage grade and the corresponding membership degree in the final damage assessment result to obtain a comprehensive score, and determining the final damage grade according to the preset score interval in which the comprehensive score is located.

[0054] Beneficial effect: Two result processing methods, maximum membership degree method and weighted scoring method, are provided, making the output form of the evaluation conclusion more flexible and able to meet different engineering application requirements. The maximum membership degree method can give an intuitive and clear damage grade, while the weighted scoring method can provide a continuous quantitative score, facilitating more detailed damage degree comparison and risk sorting, and enhancing the engineering practical value of the evaluation result.

[0055] Further, in the S3 step, for the overall bending failure or the shear failure, the step of determining the membership degree includes: based on the structural parameters of the member, calculating the overpressure asymptote value P0 under the action of quasi-static load and the impulse asymptote value I0 under the action of impulse load; substituting the P0 and the I0 into the dynamic zone empirical formula to generate the overpressure-impulse P-I curve of the member under different damage grades; projecting the explosion load parameter into the plane formed by the P-I curve, and calculating the membership degree according to the relative positional relationship with each P-I curve.

[0056] Beneficial effect: A method for quickly calculating the P-I curve based on the parameters of the member itself is proposed, which replaces the time-consuming and laborious finite element simulation or test fitting process in the traditional method by solving the asymptotes in the quasi-static and impulse zones and combining with the empirical formula. This greatly improves the efficiency of member damage state assessment, making it possible to quickly obtain reliable damage criteria in emergency assessment or early prediction scenarios, and is one of the key technologies to realize the rapidity of the overall assessment method.

[0057] Further, in the S3 step, the damage level of the overall bending failure is divided according to the support rotation angle θ of the component; and the calculation of the membership degree uses a triangular membership function, and is based on the ratio of the projection vector length of the explosion load parameter in the P-I curve plane to the length of the boundary point of each damage level P-I curve in the direction of the vector.

[0058] Beneficial effects: The overall bending failure of the component is associated with the clear physical quantity support rotation angle θ, and the damage area of the P-I curve is processed by the triangular membership function. This way provides a clear and reliable physical basis and mathematical model for the quantification of bending damage degree, making the calculation process of the membership degree more accurate and standardized, and improving the objectivity of the evaluation.

[0059] Further, in the S3 step, for the local rupture failure, the step of determining the membership degree includes: calculating the collapse thickness T of the component according to the TNT equivalent charge Q and the distance Z from the explosion center to the component in the explosion load parameter c ; obtaining the relative collapse thickness T c by using the ratio of the collapse thickness T ′ and the total thickness T of the component c ; and calculating the membership degree of the local rupture failure for each damage level based on the value of T ′ c and using a preset trapezoidal-triangular membership function.

[0060] Beneficial effects: The relative collapse thickness T ′ c is introduced as an evaluation index of local rupture damage, and a direct calculation method of the relative collapse thickness T m is given. This makes the model able to independently and quantitatively evaluate the local penetrating damage caused by the explosion near-field effect, and supplements the deficiency of only considering the overall bending and shear response, so that the evaluation system can cover a more comprehensive damage mode, and the evaluation result is closer to the actual working condition.

[0061] Further, the calculation formula of the overpressure asymptote value P and the impulse asymptote value I of the overall bending failure is:

[0062]

[0063] Where R m is the maximum resistance of the component, β is the ductility ratio, a and b are the length and width of the component, and ω is the equivalent system natural frequency.

[0064] Beneficial effect: The specific formula for calculating the asymptote of the overall bending failure P-I curve is given, which simplifies the complex dynamic response problem to algebraic operation of basic parameters such as maximum resistance, ductility ratio, and geometric size of the component. This enables non-professionals to conveniently calculate the key parameters of the P-I curve, further reducing the technical threshold of the evaluation method and enhancing the usability and operability of the method.

[0065] Further, the damage level of the shear failure is determined according to the shear slip y s The shear failure is divided into three stages: elastic stage, plastic stage, and shear failure stage. The calculation formula of the overpressure asymptote and the impulse asymptote

[0066]

[0067]

[0068] where W s is the shear strain energy, R m is the maximum resistance of the component, M s is the equivalent shear mass, and a and b are the length and width of the component.

[0069] Beneficial effect: For the key failure mode of shear failure, the specific calculation formula of the P-I curve asymptote is provided, and the calculation is associated with parameters such as shear strain energy and equivalent mass. This provides an effective technical approach for quickly and quantitatively evaluating whether the structure has occurred shear brittle failure, enhances the model's ability to identify the failure mode of the structure under complex loading conditions, and improves the comprehensiveness and safety of the evaluation.

[0070] Further, the empirical formula of the dynamic zone is:

[0071]

[0072] where P is the overpressure peak value, I is the impulse, q is the failure mode factor, and k is the correction coefficient determined according to the shape of the explosive load.

[0073] Beneficial effect: The empirical formula of the dynamic zone connecting the asymptotes of the P-I curve is provided, and the correction coefficient k is introduced to consider the influence of different explosive load waveforms. This makes the generated P-I curve not only fast to calculate, but also adaptable to different types of explosive scenarios.

[0074] To sum up, compared with the prior art, the present application proposes a P-I curve fast solving method, which improves the evaluation efficiency. In view of the problems of complex calculation and low efficiency in the traditional P-I curve generation process, the input parameters required by the present application are all geometric characteristics and material parameters of the component itself, or can be obtained through simple theoretical derivation, without the need for complex numerical simulation. In practical application, the calculation speed is fast, the operation is simple, and the corresponding efficiency of structural damage evaluation can be significantly improved. The P-I curve construction method of the component in the present application is based on single degree of freedom system modeling and ideal elastic-plastic response assumption, and is suitable for rapid damage evaluation of structural components under explosive load when significant deformation occurs. It has good applicability and engineering value in typical beam component failure modes (such as overall bending and shear). For other types of components, such as columns, plates, etc., due to their more complex stress mechanism or different response modes, the analysis logic proposed in the present application can also be combined to expand the scope of application of the evaluation method by introducing correction parameters, alternative indicators or response feature conversion, etc. The related expansion path can be further set according to the actual engineering situation to improve the universality and systematization level of the method. Therefore, the present application clearly defines the component damage evaluation path, has good technical openness, and is convenient for forming a reusable and expandable evaluation system in subsequent research.

[0075] The present application realizes quantitative evaluation of various component damage states, improves objectivity, and constructs corresponding P-I curve models for overall bending damage and shear damage of components under explosive action. For typical damage states such as overall bending damage, shear damage and local rupture, a quantitative calculation method is introduced for standardized processing. In the process of determining the weight of each evaluation index, interval analytic hierarchy process is used to reduce the influence of human experience factors, thereby improving the objectivity and reliability of the evaluation process.

[0076] The present application establishes a multi-level fuzzy comprehensive evaluation model to improve systematization and applicability. Based on the fuzzy set characteristics of structural damage, a fuzzy comprehensive evaluation model suitable for overall damage judgment of concrete frame structure is constructed. This model uses the comprehensive evaluation method in fuzzy mathematics to recursively propagate the membership degree from the component layer to the overall structure layer, achieving unified modeling and quantitative prediction of multi-level and multi-index damage states of the structure under explosive action. Compared with the previous local evaluation method which can only evaluate a single component, the present application has higher systematization and engineering applicability from a global perspective.

[0077] Example 1

[0078] The present embodiment is a preferred embodiment of the present application, and according to the typical damage characteristics of a reinforced concrete frame structure under explosion, the present application firstly starts from the floor level, gradually refines to the main load-bearing members (including columns, beams, slabs and infilled walls with doors and windows), and finally implements to the specific damage mode of each member, to build a multi-level damage evaluation index system. Subsequently, for different damage types of the member layer, the P-I curve of bending damage, the P-I curve of shear damage and the local rupture judgment formula are respectively used as the basis for damage evaluation, and the membership function calculation method of fuzzy mathematics is combined to obtain the quantitative evaluation results of the third level index. Then, through the weight vector calculated by the interval level analysis method, the fuzzy comprehensive judgment is carried out from bottom to top, and finally the comprehensive damage grade of the whole structure under the explosion is obtained.

[0079] Figure 1 The evaluation model process of the present application is shown, which mainly includes the following steps:

[0080] I. Building an evaluation index system

[0081] 1. Level division: considering that the explosion load mainly affects the superstructure of the building, the present application takes the superstructure as the evaluation object. Firstly, the first level is constructed by taking the floor as a unit, and the overall damage state of each floor is taken as a first level index; then the main load-bearing members (columns, beams, slabs and infilled walls) in each floor are extracted, and the damage state of each type of member is taken as a second level index; finally, according to the mechanical properties and explosion response behavior of the members, the damage state is further divided into a third level index.

[0082] 2. Component damage form refinement: the specific damage state of each type of load-bearing member is divided, and the column, beam and slab members include three damage modes of overall bending damage, shear damage and local rupture; the infilled wall member: considering the difference in member stiffness and material, the damage mode is set to overall bending damage and local rupture.

[0083] Taking a four-story reinforced concrete frame structure as an example, the damage evaluation index system established is shown in Table 1.

[0084] Table 1 Damage evaluation index system of concrete frame structure under explosion

[0085]

[0086]

[0087] 3. Define damage level: in order to quantitatively describe the damage degree of the structure under the explosion load, the present application divides the damage degree into the following four levels, and the qualitative description is as follows:

[0088] First level (basically intact): the structure is normal in use and can continue to be used without repair;

[0089] Level 2 (mild damage): The basic function of the structure is not affected, and it can be used with slight repair or without repair;

[0090] Level 3 (moderate damage): The structure function is affected, and it can continue to be used after repair;

[0091] Level 4 (severe damage): The main function of the structure is damaged, which seriously affects the use, and it is difficult to repair or loses repair value.

[0092] II. Calculate the weight value of each index

[0093] After the evaluation index system is constructed, in order to reduce the subjective influence in the evaluation process, the interval analytic hierarchy process is used to calculate the relative weight of each evaluation index in its upper index. The specific calculation steps are as follows:

[0094] 1. Construct the judgment matrix: According to the established multi-level damage evaluation index system, construct the pair-wise comparison matrix between the indexes of each level. For any two evaluation indexes in the same level, according to their relative importance in the upper level index, pairwise comparison is carried out, and 1-9 interval scale is used for quantitative assignment. The scale rule is shown in Table 2. On this basis, the interval judgment matrix A=(a ij ) n×n of this level is constructed, where each a ij is an interval number, which is in the form of , which represents the relative importance of the i-th index compared with the j-th index; n is the total number of indexes in this level.

[0095] Table 21-9 scale quantization rule

[0096]

[0097] 2. Consistency check: In order to verify the consistency of the judgment matrix, two consistency indexes and are calculated respectively. When k≤1 and β≥1, the judgment matrix passes the consistency test; when k>1 and β<1, the consistency is poor, and the judgment matrix needs to be adjusted until the conditions are met.

[0098] 3. Calculate the weight vector: After the judgment matrix passes the consistency test, it is split into upper and lower boundary matrices respectively. The maximum eigenvalue corresponding to the eigenvector - and + of A and A is calculated respectively. According to the formula (i=1, 2, …, n), the relative weight vector m of the indexes in this level is calculated. Normalize the vector m, that is (i = 1, 2, …, n), to obtain the layer weight vector W = (w1, w2, …, wn) of the layer. n

[0099] 4. Layer-by-layer recursive calculation: According to the above method, each layer in the entire hierarchical model is calculated in turn from bottom to top, and finally the comprehensive weight value of each index in the overall evaluation is obtained, providing basic parameter support for subsequent fuzzy comprehensive evaluation.

[0100] III. Determining the damage grade standards of each evaluation index of reinforced concrete frame structure under blast loading

[0101] 1. Evaluation criteria for overall bending failure of components and fast calculation method of P-I curve

[0102] The component may appear overall bending failure under blast loading, and its evaluation needs the help of P-I curve. P-I curve is a boundary curve that represents the equivalent load of the component reaching the same damage grade under blast loading. Each curve corresponds to a damage grade area.

[0103] When the overpressure and impulse value of a certain blast load combination is located to the right of a P-I curve, it means that the damage degree is higher than the grade corresponding to the curve; if it is located to the left, it means that the damage degree is lower than the grade. In the same P-I curve graph, usually several grade lines are drawn to divide several areas, as shown in Figure 2 When evaluating, the blast load can be projected into the graph, and the damage grade of the component can be directly judged according to the area it is located in.

[0104] The bending damage degree of the component is judged according to its maximum ductile plastic deformation. Since this kind of deformation mainly occurs in the mid-span area of the component, the support rotation angle θ defined by the ratio of the maximum deflection to the half-span length is taken as the basis. The larger the value is, the more serious the bending failure of the component is. According to related research, the damage grade division standards of overall bending failure of concrete beams, slabs and infilled walls are divided, as shown in Table 3.

[0105] Table 3 Damage grade division of overall bending failure of reinforced concrete beams, slabs and infilled walls

[0106]

[0107] Considering that the deformation of column components is relatively small in the failure state, the division standard is slightly tightened, and the overall bending failure grade of column components is divided.

[0108] Table 4 Damage grade division of overall bending failure of reinforced concrete columns

[0109]

[0110] ​In drawing the P-I curve corresponding to the damage level of the component, the application proposes a fast calculation method based on the single degree of freedom equivalent model (SDOF) and the parameters of the component itself. The method comprehensively uses empirical formula, dynamic load response principle and other contents, only needs to input the basic information of the material, geometric and stress characteristics of the component, and can quickly generate multi-level P-I curve through a small amount of calculation, significantly reduces the workload required by simulation analysis or test fitting, and provides efficient and reliable basic data support for subsequent damage assessment.

[0111] According to Figure 2 the P-I curve characteristics shown in the application, when the structure is subjected to quasi-static load, the response is mainly determined by the peak overpressure, and is irrelevant to the impulse size. At this time, the P-I curve tends to be an approximately horizontal overpressure asymptote P0, which represents the minimum overpressure required to cause a certain damage. On the contrary, when the structure is subjected to typical impulse load, the response is mainly determined by the impulse size of the explosion load, and is irrelevant to the peak overpressure. At this time, the P-I curve presents an approximately vertical impulse asymptote I0, which represents the minimum impulse required to produce the same damage.

[0112] In order to quickly construct the P-I curve of the component, P0 and I0 need to be calculated first. First, the motion equation of the component is established by using the SDOF model, and the ideal elastic-plastic model is selected to describe the resistance curve of the component. In the quasi-static region, since the load duration is long, the load has not been significantly attenuated before the maximum displacement is reached, so the work done by the explosion load on the structure in this stage can be approximately equal to the strain energy of the system. Based on this assumption, the overpressure asymptote equation in the quasi-static region is derived as follows:

[0113] Unit: kPa

[0114] Where, R m is the maximum resistance of the component; is the ductility ratio, where y e is the elastic limit displacement, y m is the maximum displacement; a and b are the length and width of the component.

[0115] In the impulse region, the load duration is extremely short, the displacement of the structure has not been significantly generated, and the load has disappeared, so it can be considered that the kinetic energy of the structure in this stage is finally all converted into strain energy, and the system has no strain energy at the initial time. The impulse asymptote equation derived therefrom is as follows:

[0116] Unit: kPa·ms

[0117] Where, is the equivalent system natural frequency, where K and M are the stiffness and mass of the component, K e and M e are the equivalent stiffness and mass.

[0118] For specific components, the stiffness K, maximum resistance R and natural frequency ω of the component can be calculated according to its elastic model and cross-sectional moment of inertia m . Furthermore, under the condition that the ductility ratio β corresponding to different damage states is known, the overpressure asymptote value and the impulse asymptote value

[0119] After obtaining the above two asymptote equations, the P-I curve in the dynamic region needs to be solved next. The P-I curve in this region usually exhibits bilinear characteristics. By using the SDOF model to numerically calculate the response of reinforced concrete components under different explosive loads, a series of data points corresponding to different damage levels can be obtained. Curve fitting of these data points can establish a general dynamic region empirical formula. This formula is also modified according to the shape of different explosive loads, and the form is as follows:

[0120]

[0121] When the explosive load is e exponential, triangular and rectangular explosive load respectively, the correction coefficient k is determined to be 0.9, 1 and 1.1 respectively by combining the existing test literature and simulation analysis results.

[0122] 2. Evaluation criteria and rapid calculation method of P-I curve for shear failure of components

[0123] In the shear equivalent SDOF model, the equivalent external load is composed of the actual load on the structure and the reaction force of the structure due to bending failure, and the equivalent displacement of the system is the shear slip y s . In the nonlinear motion differential equation of the shear equivalent SDOF system, the shear resistance function model is ignored, and in practical engineering applications, a trilinear model is usually used to describe it. Specifically, it is divided into: elastic stage, y s ≤0.1mm; hardening stage, 0.1mm<y s ≤0.3mm; plastic yield stage, 0.3mm<y s ≤0.6mm. Therefore, the damage degree of shear failure of the component is also divided according to the above three slip intervals. For the shear failure evaluation of typical components such as reinforced concrete columns, beams and slabs, the shear slip y s can be used as an indicator, and the corresponding damage level division criteria are shown in Table 5.

[0124] Table 5 Damage level division of reinforced concrete columns, beams, slabs and shear failure

[0125]

[0126] Based on the above shear damage classification criterion, the P-I curve is quickly generated by the following method.

[0127] In the shear equivalent SDOF analysis of reinforced concrete members, the aforementioned trilinear shear resistance model is adopted. According to the existing research results, the calculation method of the resistance function in each stage is as follows:

[0128] In the elastic response stage (y s ≤0.1mm), the shear resistance τ e is taken as:

[0129] Unit: MPa

[0130] Where f ′ c is the uniaxial compressive strength of concrete, τ m is the maximum shear resistance in the hardening stage.

[0131] In the hardening stage (0.1mm<y s ≤0.3mm), the shear resistance takes the maximum value τ m :

[0132] Unit: MPa

[0133] Where f y is the yield strength of steel, and ρ is the sectional reinforcement ratio.

[0134] In the plastic yield stage (0.3mm<y s ≤0.6mm), the shear strength remains constant τ m .

[0135] According to the above resistance model, the shear resistance R s of the member in each stage can be expressed uniformly by:

[0136]

[0137] Where b is the sectional width and h0 is the effective sectional height.

[0138] The shear strain energy W s is the area enclosed by the shear force-slip curve, which is calculated as follows:

[0139]

[0140] In the quasi-static zone, static response dominates. In this stage, the structure mainly bears static shear, and the dynamic reaction is simplified as 0.38R m +0.12P0. The work done by the dynamic reaction on the displacement is equal to the shear strain energy W sThe overpressure asymptote equation of quasi-static region is:

[0141] Unit: kPa

[0142] The impulse region is dominated by inertia. The load time in this stage is very short, and the bending deformation can be ignored. The total kinetic energy of the structure is converted into shear strain energy. According to the energy conservation relationship:

[0143] Unit: kPa·ms

[0144] Where, M s = K M ·M is the equivalent shear mass, the equivalent mass coefficient K M is 1, and M is the total mass of the component.

[0145] The shear slip y s corresponding to each damage level is brought into the above formula, and the corresponding and

[0146] The P-I curve fitting empirical formula of the dynamic region is:

[0147]

[0148] When the explosion load is e exponential, triangular and rectangular explosion load respectively, the value of k is determined to be 0.9, 1 and 1.1 respectively by combining the existing test literature and simulation analysis results.

[0149] 3. Damage grade evaluation criteria of local rupture evaluation index

[0150] Based on the local rupture characteristics of reinforced concrete components under the action of TNT explosion, this method takes the relative collapse thickness of concrete as the evaluation index of local rupture damage, and divides the local rupture behavior of the component into different grades. In this process, the influence of charge shape on the rupture range is ignored, and the following empirical formula is used to estimate the collapse thickness T c

[0151] Unit: m

[0152] Where, Q is the equivalent TNT charge quantity; R is the distance from the explosion center to the component.

[0153] In order to further unify the damage evaluation criteria, the relative collapse thickness T ′ c is introduced in this method:

[0154]

[0155] ​Where T is the total thickness of the member.

[0156] According to the value range of T ′ c The local damage level of reinforced concrete members is divided according to the value range of T, and the specific criteria are shown in Table 6.

[0157] Table 6 Local damage level division of reinforced concrete members

[0158]

[0159]

[0160] Four, determine the membership degree of the lowest level index

[0161] 1. Overall bending and shear failure index

[0162] The membership degree of the overall bending and shear failure index of the member is established based on the P-I curve corresponding to the member. The specific method is as follows: (1) According to the critical value in the damage level division criterion, three P-I curves (corresponding to the boundaries of light, moderate and severe damage respectively) are drawn. With these three curves as boundaries, the entire P-I diagram is divided into four regions, corresponding to light damage, moderate damage, severe damage and complete damage respectively; (2) Project the actual explosion load point to the P-I plane, and connect it with the origin, define the length of the vector as x; (3) Calculate the intersection points of the straight line and the three P-I curves, and record their lengths as x1, x2, x3 from short to long. Take the overall bending failure evaluation criterion of the member as an example, the schematic diagram is shown in Figure 3 ; (4) According to the position relationship between x and each intersection point, the triangular membership function of the member is constructed, as shown in Figure 4 .

[0163] The membership function corresponding to each level is:

[0164] Light damage μ1(x):

[0165]

[0166] Moderate damage μ2(x):

[0167]

[0168] Severe damage μ3(x):

[0169]

[0170] Complete damage μ4(x):

[0171]

[0172] 2. Local damage index of partial collapse

[0173] The local collapse is in the relative collapse thickness y = T c / T is the evaluation basis, according to the local damage grade division criterion of the component, the key control points of the membership function are set as follows: is the threshold value of light collapse; is the starting value of moderate collapse; is the starting value of severe collapse; y4 = 1 is the threshold value of complete collapse. In order to describe the fuzziness of the structure state under different grades, the trapezoidal and triangular membership functions are used to construct the membership function describing the local damage of the structure, as shown in Figure 5 .

[0174] The membership function corresponding to each grade is:

[0175] Light collapse η1(y):

[0176]

[0177] Moderate collapse η2(y):

[0178]

[0179] Severe collapse η3(y):

[0180]

[0181] Complete damage η4(y):

[0182]

[0183] V. Comprehensive evaluation and result processing

[0184] 1. Generation of evaluation results

[0185] According to the membership functions of the aforementioned evaluation indexes of the component, the fuzzy recognition principle is used for comprehensive evaluation. Let the ith evaluation index u i , the fuzzy evaluation result is represented as:

[0186] R i = {r i1 ,r i2 ,…,r im}

[0187] Wherein, r ij represents the membership degree of the index u i to the jth comment.

[0188] The fuzzy evaluation results of all n evaluation indexes in the same level are combined to form the fuzzy comprehensive judgment matrix of the level:

[0189]

[0190] wherein the size of matrix R is n x m, and each column represents the membership degree of all indicators to a certain evaluation.

[0191] Let the weight vector of each evaluation indicator of the layer be:

[0192] A = {a1, a2, …, a n}

[0193] Fuzzy transformation (weighted synthesis) of it with fuzzy comprehensive judgment matrix R can obtain comprehensive evaluation vector:

[0194] B = A · R = {b1, b2, …, b m}

[0195] Vector B represents the comprehensive membership degree of the evaluation object to each evaluation, and the dimension is 1 x m.

[0196] From bottom to top, such fuzzy comprehensive operation is performed on each layer, and finally the evaluation result vector B of the uppermost layer of the overall structure can be obtained. 总 .

[0197] 2. Evaluation result processing method

[0198] In order to further obtain the final damage grade of the structure, the following two processing methods can be used:

[0199] (1) Maximum membership degree method

[0200] From the final evaluation result vector: B 总 = {b1, b2, …, b m}, the element b i with the maximum membership degree is selected, and the corresponding evaluation grade is the final evaluation result. This method is simple and intuitive, and is suitable for preliminary grade calculation.

[0201] (2) Weighted average method (percentage score)

[0202] In order to obtain a more continuous and quantitative result, a percentage weighted method is introduced. Four damage grades are assigned to corresponding score intervals: the score range of the first grade (basically intact) is 0≤S<25; the score range of the second grade (slight damage) is 25≤S<50; the score range of the third grade (moderate damage) is 50≤S<75; and the score range of the fourth grade (severe damage) is 75≤S<100.

[0203] The average score of each grade is taken respectively: 12.5, 37.5, 62.5, 87.5, and a score vector is constructed:

[0204] V = [12.5 37.5 56 2.5 87.5] T

[0205] The final score of the structure is calculated as follows:

[0206] S = B 总 · V

[0207] The score S can be used to represent the comprehensive damage degree of the structure in a continuous range. According to the aforementioned interval division, the score result can be corresponded to a specific damage grade.

[0208] The above only describes the preferred embodiments of the present application, and it should be noted that for those skilled in the art, without departing from the technical principles of the present application, a number of improvements and modifications can be made, and these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. A method for assessing explosion damage to concrete frame structures, characterized in that, The method includes the following steps: S1. Obtain the structural parameters and preset explosive load parameters of the target reinforced concrete frame structure, and based on the structural parameters, divide the target reinforced concrete frame structure into floor level, main load-bearing component level and component specific damage state level from top to bottom, and construct a multi-level damage assessment index system. S2. Using the interval hierarchical analysis method, a judgment matrix is ​​constructed for each level in the multi-level damage assessment index system, and the weight vector of the next level index relative to the current level index is calculated based on the judgment matrix. S3. For each specific damage state index in the specific damage state hierarchy of the component, based on the structural parameters and the explosion load parameters, determine its membership degree to multiple preset damage levels, generate a membership degree vector, and combine the membership degree vectors of all specific damage state indices of the same component to form the fuzzy evaluation matrix of the component. S4. Based on the weight vector and the fuzzy evaluation matrix, the fuzzy comprehensive evaluation method is adopted to calculate layer by layer from bottom to top. The fuzzy evaluation matrix of the next level and the corresponding weight vector are subjected to fuzzy transformation operation to obtain the comprehensive evaluation result of the previous level, until the final damage assessment result of the target reinforced concrete frame structure as a whole is calculated.

2. The method for assessing explosion damage to concrete frame structures according to claim 1, characterized in that, In step S1, the main load-bearing component level includes columns, beams, slabs, and infill wall components; the specific damage state level of the components includes at least one of overall bending failure, shear failure, and local fracture failure.

3. The method for assessing explosion damage to concrete frame structures according to claim 1, characterized in that, In step S2, the step of calculating the weight vector using interval hierarchical analysis further includes: constructing the judgment matrix [a] for the n×n interval. ij ], where n represents the total number of indicators at the current level, a ij Let represent the importance interval of the i-th indicator relative to the j-th indicator, where i and j are positive integers, i.e., from 1 to n; calculate the consistency indices k and β for consistency testing, where: and The lower and upper bounds of the elements in the interval judgment matrix are defined; after passing the consistency check, the eigenvectors of the judgment matrix are solved and normalized to obtain the weight vector.

4. The method for assessing explosion damage to concrete frame structures according to claim 1, characterized in that, It also includes: processing the final damage assessment results using the maximum membership method or the weighted scoring method; The maximum membership method is as follows: the damage level corresponding to the maximum membership value in the final damage assessment result is selected as the final assessment conclusion. The weighted scoring method is as follows: the preset score for each damage level is weighted and averaged with the corresponding membership degree in the final damage assessment result to obtain a comprehensive score, and the final damage level is determined according to the preset score range in which the comprehensive score is located.

5. The method for assessing explosion damage to concrete frame structures according to claim 1 or 2, characterized in that, In step S3, the step of determining the membership degree for the overall bending failure or the shear failure includes: calculating the overpressure asymptote value P0 under quasi-static load and the impulse asymptote value I0 under impulse load based on the structural parameters of the component; substituting the overpressure asymptote value P0 and the impulse asymptote value I0 into the dynamic zone empirical formula to generate overpressure-impulse (PI) curves of the component under different damage levels; projecting the explosive load parameters onto the plane formed by the PI curves, and calculating the membership degree according to its relative positional relationship with each of the PI curves.

6. The method for assessing explosion damage to concrete frame structures according to claim 5, characterized in that, In step S3, the damage level of the overall bending failure is classified according to the component support rotation angle θ; the membership degree is calculated using a trigonometric membership function, based on the ratio of the length of the projection vector of the explosion load parameter in the PI curve plane to the length of the boundary point of each damage level PI curve in the direction of the vector.

7. The method for assessing explosion damage to concrete frame structures according to claim 1 or 2, characterized in that, The step S3, which involves determining the membership degree of localized fracture damage, specifically includes: Based on the explosive load parameters, including the equivalent TNT charge Q, the distance R from the explosion center to the component, and the uniaxial compressive strength f of the component's concrete. c The collapse thickness T of the component is calculated using the following empirical formula. c : The unit is m Using the calculated collapse thickness T c The relative collapse thickness T is obtained by comparing the collapse thickness to the total thickness T of the component itself. c ′: Based on the relative collapse thickness T c The value of ′ is determined, and the membership degree of the local fracture to each damage level is quantitatively calculated based on a set of preset trapezoidal-triangle membership functions. The damage levels include mild collapse, moderate collapse, severe collapse, and complete damage.

8. The method for assessing explosion damage to concrete frame structures according to claim 5, characterized in that, The overpressure asymptote value of the overall bending failure and the impulse asymptote value The calculation formula is: Among them, R m ω is the maximum resistance of the component, β is the ductility ratio, a and b are the length and width of the component, and ω is the equivalent system natural frequency.

9. The method for assessing explosion damage to concrete frame structures according to claim 5, characterized in that, The damage level of the shear failure is based on the shear slip y. s Divide into sections; the overpressure asymptote value of the shear failure. and impulse asymptotic value The calculation formula is: Among them, W s R is the shear strain energy. m M is the maximum resistance of the component. s The equivalent shear mass is given by a and b, which are the length and width of the component, respectively.

10. The method for assessing explosion damage to concrete frame structures according to claim 5, characterized in that, The empirical formula for the dynamic region is: Where P is the peak overpressure, I is the impulse, q is the failure mode factor, and k is the correction coefficient determined based on the shape of the explosion load.

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