Containment prestress failure safety margin analysis method, device, equipment and medium

Abstract

This invention discloses a method, apparatus, equipment, and medium for analyzing the safety margin of prestressed containment failure. The method includes: determining the re-anchoring length after steel strand fracture and constructing a prestress distribution model after steel strand fracture based on the re-anchoring length; constructing multiple steel strand fracture cases based on the prestress distribution model and obtaining the stress-strain field of the containment structure under each fracture case through finite element simulation; evaluating the strength safety margin of structural components based on the stress-strain field and determining the maximum allowable number of fractures; calculating the strain difference on the concrete surface before and after steel strand fracture based on the stress-strain field, and evaluating the detectability of steel strand fracture based on the strain difference and the detection accuracy of the monitoring system to obtain the target evaluation result. This invention can accurately quantify the re-anchoring length and stress distribution after steel strand fracture, systematically evaluate the structural strength safety margin, and effectively correlate the strain change on the concrete surface with the detection accuracy of the monitoring system.

Description

Technical Field

[0001] This application relates to the field of nuclear power plant containment structure safety analysis technology, and in particular to a method, apparatus, equipment and medium for analyzing the safety margin of containment prestress failure. Background Technology

[0002] Prestressed concrete structures, with their superior load-bearing capacity and durability, are widely used in critical infrastructure projects such as nuclear power plant containment vessels, liquid storage tanks, large-span industrial buildings, bridges, and water conservancy projects. In post-tensioned bonded prestressed systems, prestress is achieved by tensioning bundles of high-strength, low-relaxation steel strands. However, the quality of grouting in the ducts during construction is difficult to guarantee completely, often resulting in defects such as incomplete compaction or voids. This exposes the steel strands to air, moisture, and chloride ions, accelerating the corrosion process. Because the prestressed steel strands are deeply embedded within the concrete, their corrosion process is difficult to observe directly. Once fracture occurs, it will trigger a sudden loss of prestress and a sharp drop in load-bearing capacity, even causing sudden structural collapse. Studies have shown that defects in grouting and chloride corrosion significantly weaken the strength of the steel strands and their bond performance with concrete. Furthermore, after fracture, the steel strands may re-anchor within the grout through friction and mechanical interlocking, leading to complex changes in stress distribution and consequently affecting the residual load-bearing capacity of the structure. Although various non-destructive testing techniques have been explored for steel strand corrosion and fracture, including electromagnetic methods such as residual magnetism and leakage magnetic flux, as well as acoustic emission, ultrasonic guided waves and electromagnetic resonance, these methods mainly rely on indirect judgment based on changes in characteristic signals, and still face serious challenges in practical engineering applications.

[0003] Existing technologies struggle to accurately quantify the re-anchoring length after steel strand fracture and its impact on stress distribution. They lack systematic assessment methods for structural strength safety margins under fracture conditions and fail to effectively correlate concrete surface strain changes with monitoring system accuracy, resulting in blind spots in the assessment of fracture event detectability. For in-service structures with bonded steel strands and complex internal environments with variable conditions, existing analytical methods cannot fully simulate the stress-strain field after fracture, making it difficult to determine the maximum allowable number of fractures and providing reliable assurance for the integrity of containment structures. Related research results are largely limited to laboratory verification and have not yet formed a mature, widely applicable field safety margin analysis system. Summary of the Invention

[0004] The purpose of this application is to propose a method, apparatus, equipment, and medium for analyzing the safety margin of prestressed containment failure. This method can accurately quantify the re-anchoring length and stress distribution after steel strand fracture, systematically evaluate the structural strength safety margin, and effectively correlate the strain changes on the concrete surface with the detection accuracy of the monitoring system, thereby improving the integrity of the containment structure and the detectability of fracture events.

[0005] To address the aforementioned technical problems, embodiments of this application provide a method for analyzing the safety margin of containment prestress failure, including: Determine the re-anchoring length after the steel strand breaks, and construct a prestress distribution model after the steel strand breaks based on the re-anchoring length; Based on the prestress distribution model, multiple steel strand fracture conditions were constructed, and the stress-strain field of the containment structure under each fracture condition was obtained through finite element simulation. The strength safety margin of the structural members is assessed based on the stress-strain field, and the maximum allowable number of fracture roots is determined. The strain difference on the concrete surface before and after the steel strand fracture is calculated based on the stress-strain field, and the detectability of the steel strand fracture is assessed based on the strain difference and the detection accuracy of the monitoring system, thus obtaining the target assessment result.

[0006] To address the aforementioned technical problems, this application provides a containment prestress failure safety margin analysis device, comprising: The re-anchoring length determination module is used to determine the re-anchoring length after the steel strand breaks, and to construct a prestress distribution model after the steel strand breaks based on the re-anchoring length. The stress-strain field simulation module is used to construct multiple steel strand fracture conditions based on the prestress distribution model, and to obtain the stress-strain field of the containment structure under each fracture condition through finite element simulation. The safety margin assessment module is used to assess the strength safety margin of structural components based on the stress-strain field and determine the maximum allowable number of fracture roots. The detectability assessment module is used to calculate the strain difference on the concrete surface before and after the steel strand fracture based on the stress-strain field, and to assess the detectability of the steel strand fracture based on the strain difference and the detection accuracy of the monitoring system, so as to obtain the target assessment result.

[0007] To solve the above-mentioned technical problems, one technical solution adopted by the present invention is to provide a computer device, including one or more processors; and a memory for storing one or more programs, so that the one or more processors implement the containment prestress failure safety margin analysis method described in any one of the above-mentioned methods.

[0008] To solve the above-mentioned technical problems, one technical solution adopted by the present invention is: a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program, when executed by a processor, implements the containment prestress failure safety margin analysis method described in any one of the above-mentioned methods.

[0009] This invention provides a method, apparatus, equipment, and medium for analyzing the safety margin of prestressed containment failure. By determining the re-anchoring length, constructing a prestress distribution model, simulating fracture conditions, and evaluating the strength safety margin and detectability, it solves the blind spots in the prior art regarding quantifying the re-anchoring length, evaluating the safety margin, and correlating strain changes with detection accuracy. It can accurately quantify the re-anchoring length and stress distribution after steel strand fracture, systematically evaluate the structural strength safety margin, and effectively correlate concrete surface strain changes with the detection accuracy of the monitoring system, thereby improving the integrity assurance of the containment structure and the detectability of fracture events. Attached Figure Description

[0010] To more clearly illustrate the solutions in this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a flowchart of an implementation of the containment prestress failure safety margin analysis method provided in the embodiments of this application; Figure 2 This is a flowchart illustrating the implementation of the first sub-process in the containment prestress failure safety margin analysis method provided in this application embodiment; Figure 3 This is a flowchart illustrating the implementation of the second sub-process in the containment prestress failure safety margin analysis method provided in this application embodiment; Figure 4 This is a flowchart illustrating the implementation of the third sub-process in the containment prestress failure safety margin analysis method provided in this application embodiment; Figure 5 This is a schematic diagram of circumferential concrete pressure under prestressing provided in an embodiment of this application; Figure 6 This is a flowchart illustrating the implementation of the fourth sub-process in the containment prestress failure safety margin analysis method provided in this application embodiment; Figure 7 This is a flowchart illustrating the implementation of the fifth sub-process in the containment prestress failure safety margin analysis method provided in this application embodiment; Figure 8 This is a flowchart illustrating the implementation of the sixth sub-process in the containment prestress failure safety margin analysis method provided in this application embodiment; Figure 9 This is a strain diagram provided in an embodiment of this application; Figure 10 This is a cross-sectional schematic diagram of the safety margin analysis provided in the embodiments of this application; Figure 11This is a schematic diagram of the positive direction of the cross-sectional force provided in the embodiments of this application; Figure 12 This is a flowchart illustrating the implementation of the seventh sub-process in the containment prestress failure safety margin analysis method provided in this application embodiment; Figure 13 This is a schematic diagram of a standard section of vertical steel strand fracture provided in an embodiment of this application; Figure 14 This is a schematic diagram of a standard section of horizontal steel strand fracture provided in an embodiment of this application; Figure 15 This is a schematic diagram of the fracture of the steel strands in the dome provided in an embodiment of this application; Figure 16 This is a schematic diagram of the fracture of the horizontal steel strand of the equipment gate provided in the embodiment of this application; Figure 17 This is another implementation flowchart of the containment prestress failure safety margin analysis method provided in the embodiments of this application; Figure 18 This is a schematic diagram of the containment prestress failure safety margin analysis device provided in the embodiments of this application; Figure 19 This is a schematic diagram of the computer device provided in the embodiments of this application. Detailed Implementation

[0012] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings of this application, are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings of this application are used to distinguish different objects, not to describe a particular order.

[0013] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0014] Traditional prestressed concrete structures, especially in critical infrastructure such as nuclear power plant containment vessels, are prone to corrosion and fracture of steel strands due to construction defects and environmental erosion. Steel strand fracture leads to sudden loss of prestress and a sharp drop in load-bearing capacity, potentially causing structural failure. Existing non-destructive testing technologies have limitations in practical engineering applications, making it difficult to accurately and stably identify and assess damage to in-service steel strands in complex internal environments. This results in unresolved issues regarding safety margin assessment and detectability after steel strand fracture.

[0015] To address this, this application proposes a method for analyzing the safety margin of prestressed containment failure, comprising: determining the re-anchoring length after the steel strand fracture, and constructing a prestress distribution model after the steel strand fracture based on the re-anchoring length; constructing multiple steel strand fracture conditions based on the prestress distribution model, and obtaining the stress-strain field of the containment structure under each fracture condition through finite element simulation; evaluating the strength safety margin of structural components based on the stress-strain field, and determining the maximum allowable number of fractures; calculating the strain difference on the concrete surface before and after the steel strand fracture based on the stress-strain field, and evaluating the detectability of the steel strand fracture based on the strain difference and the detection accuracy of the monitoring system, thereby obtaining the target evaluation result.

[0016] For ease of understanding, the following explains some key terms in this embodiment: The safety margin analysis method for prestressed containment failure refers to a systematic analysis process used to assess the remaining structural load-bearing capacity of a nuclear power plant containment structure after the fracture failure of prestressed steel strands, as well as the degree to which the fracture event can be detected by the monitoring system.

[0017] The re-anchoring length after a prestressed steel strand fracture refers to the minimum length required for the fractured end to re-establish effective anchorage through friction and mechanical interlocking with the grout or concrete in the duct after fracture. This length determines the actual impact range of prestress loss after fracture.

[0018] A prestress distribution model is a mathematical or physical model used to describe the magnitude and distribution of prestress along the length of a prestressed steel strand after fracture. This model reflects prestress loss and the re-anchoring effect.

[0019] The steel strand fracture scenario refers to the hypothetical scenario in the analysis process where different numbers, locations, and types of prestressed steel strands in the containment structure fracture.

[0020] Finite element simulation refers to the process of using numerical calculation methods to discretize a complex structure into a finite number of elements, and then obtaining the stress, strain, displacement, and other responses of the entire structure under a specific load by solving the mechanical equilibrium equations of each element.

[0021] The stress-strain field refers to the collection of stress and strain states at various points within or on the surface of a structure. It comprehensively describes the deformation and stress state of a structure under load.

[0022] Strength safety margin assessment refers to the process of quantifying the remaining safety reserve of a structure by comparing the actual stress on structural members under steel strand fracture conditions with their ultimate bearing capacity.

[0023] The maximum allowable number of fracture strands refers to the maximum number of prestressed steel strands that are allowed to fracture at the same location or within the same area, provided that the strength safety margin of the structural members meets the design requirements.

[0024] The detectability assessment of steel strand fracture refers to the process of analyzing the strain changes on the structural surface caused by steel strand fracture and comparing them with the detection accuracy of existing monitoring systems to determine whether steel strand fracture events can be effectively identified and monitored. In this application, the detectability assessment is based on the containment strain changes caused by steel strand fracture events, combined with the detection accuracy of the EAU (Equipment Access Opening Monitoring System) system, to evaluate the detectability of steel strand fracture.

[0025] The target assessment result refers to the final judgment conclusion of the assessment of the detectability of steel strand fracture, such as determining whether the steel strand fracture is detectable.

[0026] This application accurately reflects the stress redistribution after steel strand fracture by precisely determining the re-anchoring length and constructing a prestress distribution model. By constructing various fracture scenarios and performing finite element simulations, the stress-strain response of the containment structure can be comprehensively obtained. Based on this, a strength safety margin assessment and determination of the maximum allowable number of fracture elements are performed, quantifying the remaining load-bearing capacity of the structure. Simultaneously, by combining the detection accuracy of the monitoring system, a detectability assessment is conducted, enabling early warning of steel strand fracture events. This method effectively solves the problems of safety margin assessment and detectability of prestress failure in nuclear power plant containment structures, improving the safety of structural operation.

[0027] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0028] Please see Figure 1 , Figure 1 This paper illustrates a specific implementation of a method for analyzing the safety margin of containment prestress failure.

[0029] It should be noted that if substantially the same result is obtained, the method of this invention is not based on... Figure 1 Limited to the order of the processes shown, this method includes the following steps: S1: Determine the re-anchoring length after the steel strand breaks, and construct a prestress distribution model after the steel strand breaks based on the re-anchoring length.

[0030] Specifically, the re-anchoring length after the steel strand fractures is determined, and a prestress distribution model after the steel strand fractures is constructed based on this re-anchoring length. The re-anchoring length can be determined based on empirical data or simplified theoretical calculations. For example, a predetermined re-anchoring length value can be set for steel strands with different diameters and effective stresses based on previous experimental results. Alternatively, a simplified linear function can be used to correlate the re-anchoring length with the diameter or prestress level of the steel strand. When constructing the prestress distribution model, it can be assumed that the prestress is completely lost at the fracture point and recovers in a uniform or linearly decreasing manner within the re-anchoring length. For example, the prestress can be set to zero at the fracture point, and then along the steel strand direction, within the re-anchoring length, the prestress value gradually recovers from zero to its effective prestress level.

[0031] Please see Figure 2 , Figure 2 A specific implementation of step S1 is shown below: S11: Obtain the effective stress and equivalent diameter of the steel strand. S12: Calculate the re-anchoring length after the steel strand fracture using a preset formula based on the effective stress and equivalent diameter. S13: Determine the influence range of the steel strand fracture, and construct the prestress distribution model after the steel strand fracture based on the re-anchoring length and the influence range.

[0032] The preset formula is: in, The length of the re-anchoring is [length]. The effective stress, The equivalent diameter is given.

[0033] Specifically, in obtaining the effective stress and equivalent diameter of the steel strands, the effective stress refers to the actual stress borne by the steel strands under normal operating conditions. It can be obtained from the initial tension stress in the design documents, after deducting various prestress losses (such as elastic compression, concrete creep, steel relaxation, friction losses, etc.); or, by performing non-destructive testing on the in-service structure, such as using magnetic flux density or acoustic emission methods, combined with structural response inversion technology, to obtain the current effective stress of the steel strands in real time. The equivalent diameter refers to the diameter of a single circular cross-section steel bar with the same bonding characteristics, equivalent to a steel strand composed of multiple steel strands, when considering the bonding performance between the steel strands and the surrounding grouting material. It can be obtained directly from the steel strand product specifications or design drawings, or calculated based on the equivalence principle after experimentally determining the bonding performance between the steel strands and the grouting material.

[0034] In the step of calculating the re-anchoring length after the steel strand fracture based on the effective stress and the equivalent diameter using a preset formula, the preset formula is a mathematical expression used to quantify the minimum length required for the steel strand to re-establish effective bonding with the surrounding grouting material after fracture. By substituting the aforementioned effective stress and equivalent diameter into this preset formula, the re-anchoring length after the steel strand fracture can be accurately calculated.

[0035] In determining the influence range of strand fracture, the influence range refers to the area where the prestress loss and stress redistribution significantly affect the structure after strand fracture. For example, strands outside the re-anchoring range of 2lc are unaffected and maintain their original stress; within the re-anchoring range of 2lc, the stress of the strand linearly transitions from both sides to the zero-stress point of fracture. Alternatively, preliminary numerical simulations, such as finite element analysis, can be used to simulate the fracture of a single strand and observe the attenuation law of prestress loss along the strand length, thereby accurately defining its influence range.

[0036] In the step of constructing the prestress distribution model after the steel strand fracture based on the re-anchoring length and the influence range, the prestress distribution model is a mathematical or numerical representation describing the change in prestress magnitude along the length direction after the steel strand fractures. This model can be a piecewise linear model, where the prestress is zero at the fracture point, linearly recovers from zero to the effective stress within the re-anchoring length, and remains effective stress outside the influence range; alternatively, a numerical interpolation model can be used, combining the re-anchoring length and the influence range, and constructing a continuous prestress distribution curve within the steel strand fracture region through spline interpolation or polynomial interpolation methods.

[0037] In one specific embodiment, the re-anchoring length is determined according to clause 1.12.9 of ACI 318-08 standard. When fracture occurs, the prestressed steel strand does not fail entirely; due to the adhesion and friction between the strand and the grout within the casing, the strand is re-anchored at the fracture site. The prestress reduction occurs within a finite length segment, referred to as the re-anchoring length. The influence range of the strand fracture is then determined. Strands outside this 2lc range are left unaffected, maintaining their original stress. Within the 2lc re-anchoring range, the stress in the strand linearly transitions from both sides to the zero-stress point at fracture.

[0038] This application can accurately obtain the effective stress and equivalent diameter of the steel strand as key input parameters for calculating the re-anchoring length, and uses scientifically pre-defined formulas for quantitative calculation, thereby avoiding the uncertainty caused by subjective estimation and significantly improving the objectivity and accuracy of the re-anchoring length calculation. Simultaneously, by reasonably determining the influence range of steel strand fracture, this application can construct a more accurate and realistic prestress distribution model after steel strand fracture. This provides reliable and accurate initial conditions for subsequent stress-strain field analysis of containment structures based on finite element simulation, effectively solving the problem of distortion in the prestress distribution model caused by inaccurate re-anchoring length calculation in traditional methods. This greatly improves the accuracy and reliability of the safety margin analysis for containment prestress failure, ensuring that the safety assessment results of critical infrastructure such as nuclear power plant containment structures are more consistent with reality.

[0039] S2: Based on the prestress distribution model, multiple steel strand fracture conditions are constructed, and the stress-strain field of the containment structure under each fracture condition is obtained through finite element simulation.

[0040] Specifically, the construction of prestressing strand fracture scenarios can involve selecting a single type of prestressing strand for analysis, such as considering only the fracture of horizontal strands. The fracture location can be concentrated in a region of the containment, for example, setting fracture locations only in standard sections. Each fracture scenario can be set to involve the fracture of a number of strands, for example, setting only one strand to fracture at a time. Finite element simulation can simulate prestress loss by directly removing strand elements or by directly applying a reverse load at the fracture point. For example, in the finite element model, the element stiffness of the fractured strand can be set to a minimum, or a concentrated force equal in magnitude and opposite in direction to the prestress can be applied at the fracture location to simulate the sudden loss of prestress.

[0041] Please see Figure 3 , Figure 3 A specific implementation of step S2 is shown below: S21: Select at least one type of steel strand from the following: Γ-shaped steel strands, purely vertical steel strands, and horizontal steel strands. S22: Set fracture locations in at least one target critical area among the standard section of the containment, the weak prestressed area of ​​the dome, and the equipment gate opening. S23: For each fracture location, ensure that at least one steel strand fractures to form the steel strand fracture condition. S24: Obtain the stress-strain field of the containment structure under each fracture condition through finite element simulation.

[0042] Specifically, when selecting at least one type of prestressed steel strand from among Γ-shaped, purely vertical, and horizontal strands, the diverse arrangement of prestressed steel strands in containment structures, their varying mechanical behaviors, and their contributions to structural load-bearing capacity are taken into account. Γ-shaped strands are typically used in complex curved surfaces or corner areas, providing multi-directional prestressing; their fracture can lead to complex local stress redistribution. Purely vertical strands primarily bear vertical loads, significantly impacting the structure's shear and bending resistance. Horizontal strands mainly resist circumferential tensile stress and are crucial for the overall stability of the containment. Simulating these typical strand types comprehensively covers strand failure scenarios with different stress characteristics and arrangements. Furthermore, other types of strands, such as oblique strands or reinforced strands in specific areas, can be selected based on actual engineering conditions to ensure comprehensive analysis.

[0043] Setting fracture locations in at least one of the target critical areas—the standard section of the containment structure, the prestressed weak zone of the dome, and the equipment gate opening—is based on the understanding that the containment structure is not uniformly stressed and has some inherent weak areas or stress concentration areas. The standard section represents the main body of the structure, and its failure mode is universal; the prestressed weak zone of the dome, due to its geometry and prestressing arrangement, may contain areas of stress concentration or significant prestress loss, making it a potential high-risk point for failure; the equipment gate opening, as an opening in the structure, can cause stress disturbances and local weakening, and is also a sensitive area for steel strand fracture. By setting fracture locations in these target critical areas, the structure's response under the most unfavorable conditions can be assessed in a targeted manner. In addition to the above areas, other potential weak areas, such as structural connections and material defect areas, can be identified based on structural design drawings, construction quality reports, or historical monitoring data, and these can be included in the range of fracture location settings.

[0044] For each fracture location, at least one steel strand is designed to fracture to form the steel strand fracture condition. By setting different numbers of steel strands to fracture at the selected fracture locations, various scenarios ranging from single-strand failure to multi-strand failure can be simulated. Setting "at least one" steel strand fracture means that the number of fractured steel strands can be gradually increased from the most basic single-strand fracture, such as two, three, or even more, to systematically study the impact of the number of fractured strands on the structural safety margin. Each specific combination of fractured steel strands and its location constitutes an independent steel strand fracture condition, providing explicit input conditions for subsequent finite element simulations.

[0045] The stress-strain fields of the containment structure under various fracture conditions were obtained through finite element simulation. Finite element simulation is a mature and widely used numerical analysis method capable of accurately calculating the stress, strain, and deformation distribution of complex structures under various loads. For the steel strand fracture condition, finite element simulation can capture the redistribution of internal forces, crack propagation, and nonlinear behavior of components caused by prestress loss. By performing finite element analysis on each set fracture condition, detailed stress-strain field data of the containment structure under different failure scenarios can be obtained. These data form the basis for subsequent strength safety margin assessment and detectability assessment.

[0046] This application effectively addresses the problem of incomplete simulation in containment prestress failure analysis. Specifically, by systematically selecting various typical steel strand types, such as Γ-shaped steel strands, purely vertical steel strands, and horizontal steel strands, it ensures comprehensive coverage of steel strand failure scenarios with different mechanical properties and arrangements, avoiding biases caused by analysis of a single type. Simultaneously, fracture locations are set in key target areas such as the standard section of the containment, the weak prestressed area of ​​the dome, and equipment gate openings, allowing the analysis to precisely focus on the parts of the structure most likely to fail or most sensitive to failure, thereby improving the relevance and effectiveness of the simulation. By setting at least one steel strand to fracture at each fracture location and gradually increasing the number of fractures, the diversity and complexity of actual fracture scenarios can be simulated, making the constructed steel strand fracture conditions more representative. Finally, the stress-strain field of the containment structure under each fracture condition is obtained through finite element simulation, providing comprehensive, accurate, and reliable data support for subsequent strength safety margin assessment and steel strand fracture detectability assessment. This meticulous and comprehensive approach to constructing operating conditions significantly improves the accuracy and reliability of safety margin analysis for containment prestress failure, enabling the assessment results to more realistically reflect the safety status of the structure under prestress failure conditions, thereby providing a more solid technical guarantee for the long-term operation and maintenance of nuclear power containment.

[0047] Please see Figure 4 , Figure 4 A specific implementation of step S24 is shown below: S241: The cooling method is used to simulate prestress while maintaining the geometric continuity of the steel strand elements in the finite element model. S242: The steel strand stress is set to zero at the fracture point, and linear interpolation is performed on the stress within the influence range of the re-anchoring length to generate a triangular stress distribution. S243: The cooling load on the corresponding steel strand elements is adjusted according to the triangular stress distribution to perform finite element calculations and generate the stress-strain field.

[0048] The method of simulating prestress while maintaining the geometric continuity of the steel strand elements in the finite element model involves applying an equivalent temperature drop to the steel strand elements, causing them to shrink and deform in accordance with the prestress. This simulates the effect of prestress on the structure without altering the geometry of the steel strand elements. This method effectively avoids stress calculation errors caused by element discontinuities and ensures the integrity of the prestress state in the model. Specifically, the required equivalent temperature drop can be calculated based on the elastic modulus, linear expansion coefficient, and prestress value of the steel strands and applied to the steel strand elements in the finite element model; alternatively, the initial strain of the steel strand elements can be directly set to the strain caused by the prestress in the finite element software to achieve the same prestress simulation effect.

[0049] At the fracture point of the steel strand, the stress is set to zero, and linear interpolation is performed on the stress within the influence range of the re-anchoring length to generate a triangular stress distribution. This aims to accurately simulate the stress loss after the steel strand fracture and its redistribution in the re-anchoring region. Setting the stress at the fracture point to zero directly reflects the complete loss of prestress at that location at the instant of fracture. Subsequently, within the influence range of the re-anchoring length, the stress is gradually restored from its zero value at the fracture point to its effective prestress value through linear interpolation, thus forming a triangular stress distribution pattern. This linear interpolation can be achieved using a piecewise linear function, that is, dividing the steel strand unit into several sub-units within the re-anchoring length and linearly assigning stress to each sub-unit; or, defining a distance-based stress recovery function so that the stress value changes linearly with the distance from the fracture point.

[0050] Adjusting the cooling load on the corresponding steel strand unit based on the triangular stress distribution for finite element analysis (FEM) to generate a stress-strain field involves transforming the simulated stress distribution after steel strand fracture into a load form recognizable by the finite element model. Since prestressing is initially simulated using cooling loads, the stress changes caused by steel strand fracture also need to be reflected by adjusting these cooling loads. Specifically, one can first calculate the initial cooling load before steel strand fracture, then calculate a new equivalent cooling load based on the triangular stress distribution formed after fracture, and apply the difference between the old and new loads as an incremental load to the model for calculation; alternatively, one can directly replace the old load with the new equivalent cooling load and re-perform the finite element analysis. In this way, the finite element calculation can accurately reflect the structural stress state after steel strand fracture, thereby generating a precise stress-strain field.

[0051] like Figure 5 As shown, Figure 5This is a schematic diagram of circumferential concrete pressure under prestressing provided in an embodiment of this application. In one specific embodiment, the Γ-shaped steel strands pass through both the cylinder and the dome regions. In the cylinder region, they generate vertical prestress together with the purely vertical steel strands. In the dome region, they are arranged bidirectionally orthogonally to generate dome prestress. This orthogonal distribution results in relatively weak areas in the prestressing system. The prestressing system of the standard section consists of horizontal steel strands and vertical steel strands (pure vertical + Γ-shaped steel strands). According to the results of the containment ultimate bearing capacity analysis, the standard section on the left side of the equipment gate experiences large steel strain under compressive load, making it a key area for structural strength design. According to the results of the containment ultimate bearing capacity analysis, there are structurally weak areas around the containment equipment gate under internal pressure. In a specific example, the selected steel strand area is as follows: Figure 5 As shown.

[0052] The change in effective stress in the prestressed steel strand after fracture is limited to the range of 2lc; therefore, the effect of the steel strand fracture is a local effect. When simulating the fracture of the prestressed steel strand, adjacent steel strands at the same location will be selected to study the most unfavorable impact after the superposition of local effects.

[0053] This application's embodiments can accurately simulate the changes in prestress distribution after steel strand fracture, particularly considering the stress abrupt loss at the fracture point and the stress redistribution within the influence range of the re-anchoring length, thus solving the problem of simulation result distortion that may be caused by traditional simulation methods. A cooling method is used to maintain the geometric continuity of the steel strand elements, avoiding calculation errors caused by element discontinuities and ensuring the integrity of the prestress state. Setting the steel strand stress to zero at the fracture point and performing linear interpolation to generate a triangular stress distribution realistically reflects the physical process of stress gradually recovering from zero after steel strand fracture, making the simulation results more consistent with reality. Furthermore, by adjusting the cooling load for finite element calculations, the stress-strain field of the containment structure can be accurately generated, providing reliable and accurate data support for subsequent strength safety margin assessment and fracture detectability analysis, significantly improving the accuracy and reliability of the assessment results.

[0054] S3: Based on the stress-strain field, assess the strength safety margin of the structural components and determine the maximum allowable number of fracture roots.

[0055] Specifically, strength safety margin assessment can employ simplified verification methods from design specifications. For example, the maximum stress of a component section can be extracted from finite element simulation results and directly compared with the allowable stress of the material to determine whether the component meets strength requirements. The maximum allowable number of fracture roots can be determined based on a pre-defined safety factor. For instance, the maximum allowable number of fracture roots can be determined by setting a safety limit when the number of fractured steel strands reaches a certain percentage of the total number of steel strands.

[0056] Please see Figure 6 , Figure 6 A specific implementation of step S3 is shown below: S31: Construct the bearing capacity envelope curve of the component section based on the plane section strain assumption. S32: Extract the normal force and bending moment acting on the component section under various fracture conditions and accident condition combinations from the finite element simulation results. S33: Compare the stress points formed by the normal force and bending moment with the bearing capacity envelope curve in the same coordinate system to obtain the comparison results. S34: Determine the strength safety margin of the structural component under the current fracture condition based on the relative positions of the stress points and the bearing capacity envelope curve in the comparison results. S35: Determine the maximum allowable number of fracture roots.

[0057] Specifically, the plane section strain assumption is a fundamental principle in structural mechanics. Its core is that the cross-section of a structural member remains planar after deformation under stress, and perpendicular to the deformed axis, thus resulting in a linear strain distribution across the cross-section. Constructing the load-bearing capacity envelope curve of a structural member's cross-section aims to accurately depict the ultimate load-bearing capacity boundary of the cross-section under different combinations of normal force and bending moment. This can be achieved in several ways. For example, a series of different cross-sectional strain states can be set, and based on the constitutive relations of concrete and steel reinforcement, the ultimate combination of normal force and bending moment that the cross-section can withstand under each strain state can be calculated, thereby generating the envelope curve. Alternatively, specialized structural analysis software can be used. By inputting parameters such as the member's geometric dimensions and material strength, the software will automatically generate the load-bearing capacity envelope curve of that cross-section based on the plane section strain assumption. This step provides a solid theoretical foundation and quantitative standard for subsequent strength safety margin assessments.

[0058] Extracting the normal force and bending moment of the structural member cross-section under various fracture conditions from the finite element simulation results is crucial for obtaining the actual internal force state of the structural member cross-section under steel strand fracture conditions and accident combination conditions. This data serves as key input for assessing its safety margin. Specifically, after completing finite element simulations of multiple steel strand fracture conditions, the post-processing function of the finite element software can be used to directly extract or integrate the element stresses on the predefined key member cross-sections to obtain the resultant force (normal force) and resultant moment (bending moment) acting on that cross-section. Alternatively, the required normal force and bending moment data can be automatically extracted in batches from the finite element analysis result files via a programming interface or script. These data directly reflect the actual impact of steel strand fracture on the internal force distribution of the structural member.

[0059] The stress point formed by the normal force and bending moment is compared with the bearing capacity envelope curve in the same coordinate system to obtain the comparison results. This step aims to visually compare the actual stress state of the component section under specific fracture conditions with its ultimate bearing capacity through graphical or numerical methods. Typically, the bearing capacity envelope curve can be plotted in a two-dimensional coordinate system with the normal force as the horizontal axis and the bending moment as the vertical axis. Subsequently, the combination of normal force and bending moment under various fracture conditions and accident condition combinations extracted from the finite element simulation results is plotted as a point (i.e., the stress point) in this coordinate system. Since the prestressed portion bears the cross-sectional bearing capacity, the bearing capacity envelope curve shrinks as the fracture range of the prestressed steel strands decreases. Therefore, by observing the position of the stress point relative to the envelope curve, the safety status of the component can be preliminarily determined. Another approach is to perform numerical comparison, calculating the distance or relative position parameters from the stress point to the envelope curve to obtain quantitative comparison results.

[0060] Based on the relative positions of the stress point and the bearing capacity envelope curve in the comparison results, the strength safety margin of the structural member under the current fracture condition is determined. This step is a quantitative assessment of the strength safety margin of the member based on the comparison results of the previous step. If the stress point is located inside the bearing capacity envelope curve, it indicates that the member still has sufficient bearing capacity under the current fracture condition, and a strength safety margin exists. The magnitude of the safety margin can be quantified by the distance from the stress point to the envelope curve, or by the ratio between the intersection of the line connecting the stress point and the origin and the envelope curve. For example, the safety margin can be defined as the ratio of the bearing capacity at the intersection of the line connecting the envelope curve and the origin to the bearing capacity at the stress point. Conversely, if the stress point is located on or outside the envelope curve, it indicates that the member has reached or exceeded its ultimate bearing capacity, and the safety margin is zero or negative, meaning that the structure may be at risk of failure.

[0061] Determining the maximum permissible number of fracture roots aims to identify the maximum number of steel strand fractures that the containment structure can withstand while ensuring structural safety. This is typically achieved through iterative evaluation. For example, it can start by assuming the fracture of one steel strand and gradually increase the assumed number of fracture roots, repeating finite element simulations and strength safety margin assessments for each fracture root count. When the stress point of the component section first reaches or exceeds the load-bearing capacity envelope curve, the fracture root count of the previous load case (i.e., the last load case where the stress point is still within the envelope curve) is determined as the maximum permissible number of fracture roots. Alternatively, optimization algorithms can be used to search for steel strand combinations that can lead to the maximum number of fracture roots, while meeting safety margin requirements. This result provides important quantitative evidence for the safety assessment and maintenance decisions of critical structures such as nuclear power plant containment structures.

[0062] This application provides a systematic and quantitative method for assessing strength safety margin, effectively addressing the problem of existing assessment methods lacking a precise quantitative framework and resulting in insufficient reliability of the maximum allowable fracture number. Specifically, by constructing the bearing capacity envelope curve of the component section based on the plane section strain assumption, a solid theoretical foundation and quantitative boundary of ultimate bearing capacity are provided for the assessment. Subsequently, the normal force and bending moment on the component section under various fracture conditions and accident condition combinations are accurately extracted from the finite element simulation results, ensuring the accuracy and objectivity of the assessment data. Comparing these actual stress points with the bearing capacity envelope curve in the same coordinate system makes the relationship between the actual stress state of the component and the ultimate bearing capacity clear at a glance, facilitating intuitive judgment and quantification of the safety margin. Based on the relative position of the stress points and the envelope curve, the strength safety margin of the structural component under the current fracture condition can be objectively and accurately determined, avoiding the bias of subjective judgment. Ultimately, the maximum permissible number of fracture elements was determined through an iterative or optimization process, providing a clear quantitative indicator for the safety margin of critical structures such as nuclear power plant containment structures under prestressed steel strand failure conditions. This significantly improves the reliability and guidance of the assessment results, providing a scientific basis for the safe operation, maintenance, and risk management of the structure. This method, combined with the aforementioned steel strand fracture scenario construction and finite element simulation, forms a complete closed-loop analysis system from failure modes to safety assessment, ensuring the comprehensiveness and accuracy of the assessment results.

[0063] Please see Figure 7 , Figure 7 A specific implementation of step S31 is shown below: S311: Set multiple different cross-sectional strain states, wherein each cross-sectional strain state is determined by the ratio of the strain of the bottom reinforcement to the strain of the top concrete. S312: Determine the maximum allowable strain of the concrete according to preset specification information. S313: For each cross-sectional strain state, calculate the normal force and bending moment when the cross-section reaches its ultimate limit state, obtaining the calculation results. S314: Connect the multiple ultimate limit state coordinate points in the calculation results to generate the bearing capacity envelope curve.

[0064] Please see Figure 8 , Figure 8 A specific implementation of step S35 is shown below: S351: At the same location of the structural member, gradually increase the assumed number of steel strand fractures. S352: For each increase in the number of fractures, repeat the finite element simulation and the load-bearing capacity envelope curve evaluation until the stress point of the structural member section reaches or exceeds the load-bearing capacity envelope curve, and determine the number of fractures in the previous condition as the maximum allowable number of fractures.

[0065] Specifically, progressively increasing the assumed number of fractured steel strands at the same location on structural members refers to systematically and incrementally setting the number of fractured steel strands at specific, pre-selected weak or critical sections of structural members (such as containment walls, beams, or columns). This step aims to simulate a variety of fracture scenarios, from minor to severe, to comprehensively examine the structure's response under different levels of damage. For example, one could start by assuming the fracture of one steel strand, then gradually increase to two, three, until a preset maximum number of fractures or structural failure is reached. Another approach is to increase the number of fractured steel strands in preset increments (e.g., every two or three additional strands) based on the importance of the structure or potential failure modes, thereby covering a wider range of fracture conditions.

[0066] For each additional fracture element condition, the finite element simulation and the aforementioned bearing capacity envelope curve evaluation are repeated. This means that for each assumed steel strand fracture condition, a complete structural analysis and strength assessment process must be performed. Finite element simulation is used to accurately calculate the stress, strain, and internal force distribution of structural members under specific fracture conditions, such as normal force and bending moment. The bearing capacity envelope curve evaluation is based on the internal force results obtained from the finite element simulation, combined with the material properties and geometric dimensions of the member section, to determine whether the section meets the strength requirements. For example, specialized finite element analysis software (such as ABAQUS, ANSYS, etc.) can be used to model and calculate the containment structure to obtain internal force data for key sections. Subsequently, this internal force data is input into a pre-programmed bearing capacity envelope curve evaluation program, which calculates the bearing capacity of the section based on the constitutive relationship of concrete and steel reinforcement and the geometric properties of the section, and compares it with the actual internal forces.

[0067] The process of gradually increasing the number of steel strand fractures and conducting assessments until the stress point of the structural member section reaches or exceeds the bearing capacity envelope curve means that this process will continue until, under a certain fracture condition, the combination of normal force and bending moment (i.e., the stress point) borne by the structural member section, as determined by finite element simulation and the bearing capacity envelope curve assessment, touches or exceeds the bearing capacity envelope curve of that section in the coordinate system of the bearing capacity envelope curve. The bearing capacity envelope curve represents the ultimate bearing capacity of that section under different combinations of normal force and bending moment. For example, on the coordinate graph of the bearing capacity envelope curve, when the stress point under a certain fracture condition falls outside the bearing capacity envelope curve, it indicates that the section has reached or exceeded its ultimate bearing capacity, and the structure may fail.

[0068] Determining the number of fracture strands in the previous failure condition as the maximum permissible number of fracture strands means that once a failure condition causes the stress points of a structural member's cross-section to reach or exceed the bearing capacity envelope curve, the number of fracture strands corresponding to the previous failure condition that was still in a safe state is considered the maximum permissible number of fracture strands for that structural member. This is to ensure that the determined maximum permissible number of fracture strands is conservative and safe, meaning that at this number, the structural member can still maintain its integrity and bearing capacity. For example, if it is assumed that when 5 steel strands fracture, the stress points of the structural member's cross-section exceed the bearing capacity envelope curve, while when 4 steel strands fracture, the stress points are still within the envelope curve, then the maximum permissible number of fracture strands is determined to be 4.

[0069] Please see Figures 9 to 11 , Figure 9 This is a strain diagram provided in an embodiment of this application; Figure 10 This is a cross-sectional schematic diagram of the safety margin analysis provided in the embodiments of this application; Figure 11 This is a schematic diagram of the positive direction of the cross-sectional force provided in the embodiments of this application.

[0070] When calculating the strength margin of a component, the number of fractures is accumulated until the section fails. For fracture detectability, it is assumed that several steel strands fracture at the same location. If this value is too large, it may exceed the ultimate bearing capacity of the section; if it is too small, strain detection will be difficult. Considering the strength margin of the component and the accuracy of commonly used concrete strain gauges in power plants, three strands are selected as targets for fracture detection. The fracture conditions are set as shown in Table 1 below.

[0071] Table 1 Summary of Strand Fracture Scenarios The strength safety margin assessment of structural members utilizes the aforementioned bearing capacity envelope curve. The normal force N and bending moment M acting on the cross-section are plotted on the same coordinate system as the strength envelope curve, making the safety margin visible. Based on the ASME code, it is assumed that the concrete satisfies the plane section strain assumption, such as... Figure 9 As shown, 30 different ratios of bottom reinforcement strain to top concrete strain at each cross-section (Z=εsb / [εc], where εc is the maximum allowable value [εc] in the ASME standard) are taken to represent different cross-sectional strain states. For each strain state, the corresponding cross-sectional normal force N and bending moment M are calculated. Connecting the MN coordinate points of these limit states yields the bearing capacity envelope curve.

[0072] In the post-processing process output, the reaction force and displacement that vary with time (or increment step) are selected. The reaction force curve and data curve are compared for each steel strand fracture analysis to study the stress conditions of the two sections perpendicular to and parallel to the steel strand (e.g., Figure 11 As shown in the figure, by comparing MN with the bearing capacity envelope curve, the safety margin of the section strength can be determined.

[0073] This application provides a systematic and progressive evaluation method that effectively addresses potential accuracy and reliability issues in determining the maximum permissible number of fracture roots. By progressively increasing the assumed number of steel strand fractures at the same location on the structural member, and repeatedly performing finite element simulations and load-bearing capacity envelope curve evaluations for each load condition, the response of the structure under different damage levels can be comprehensively and meticulously captured. This iterative evaluation mechanism, combined with a failure criterion based on the load-bearing capacity envelope curve, can accurately identify the safety limits of structural members. When the stress point reaches or exceeds the load-bearing capacity envelope curve, the number of fracture roots in the previous load condition is immediately determined as the maximum permissible number of fracture roots, ensuring that the determined safety margin is based on a safe state before the actual failure critical point, thereby avoiding underestimation or overestimation of fracture risk. This method not only improves the accuracy and reliability of the evaluation results but also provides stronger technical support for the failure prevention of critical infrastructure such as nuclear power plant containment structures.

[0074] S4: Calculate the strain difference on the concrete surface before and after the steel strand fracture based on the stress-strain field, and evaluate the detectability of the steel strand fracture based on the strain difference and the detection accuracy of the monitoring system to obtain the target evaluation result.

[0075] Specifically, the strain difference on the concrete surface before and after the steel strand fracture can be calculated based on a simplified model. For example, only the strain change in the region near the fracture point can be considered, and the strain difference can be estimated using empirical formulas or simplified mechanical models. The detectability of steel strand fracture can be assessed qualitatively. For example, the detectability of the fracture can be determined by observing whether the strain difference reaches an observable level or exceeds an empirically determined threshold.

[0076] Please see Figure 12 , Figure 12 A specific implementation of step S4 is shown below: S41: Select normal operating conditions as the evaluation load conditions. S42: Extract the stress-strain field of the concrete surface before and after the steel strand fracture from the finite element simulation results. S43: Calculate the strain difference of the concrete surface before and after the steel strand fracture based on the evaluation load conditions and the stress-strain field. S44: Compare the strain difference with the detection accuracy threshold of the embedded strain gauge. S45: If the absolute value of the strain difference is greater than the detection accuracy threshold, generate the target evaluation result, wherein the target evaluation result determines that the steel strand fracture at the steel strand location is detectable.

[0077] Specifically, the normal operating condition of the containment is selected as the evaluation load condition. Under this condition, the load combination borne by the containment structure includes: structural self-weight, prestressed load, design reference internal pressure (normal operating pressure), and normal operating temperature. This condition represents the most typical stress state of the containment during normal service. Performing a detectability assessment of tendon fracture under this condition can reflect the monitoring system's ability to warn of potential prestressing failure before an accident occurs. Then, the stress-strain field of the concrete surface before and after tendon fracture is extracted from the finite element simulation results. Based on the evaluation load condition under normal operating conditions, the strain field of the concrete surface before fracture extracted in S42 is subtracted point by point from the strain field of the concrete surface after fracture to obtain the strain difference value. This strain difference value reflects the amount of strain change on the concrete surface caused by tendon fracture. If the absolute value of the strain difference value is greater than the detection accuracy threshold, the target evaluation result is generated, wherein the target evaluation result determines that the tendon fracture at the tendon location is detectable. If the absolute value of the strain difference value is less than or equal to the detection accuracy threshold, the tendon fracture at the tendon location is determined to be undetectable.

[0078] The normal operating condition refers to the load combination that the containment structure experiences during normal service, including the structure's self-weight, prestressed loads, design reference internal pressure (normal operating pressure), and normal operating temperature. This condition is used for detectability analysis to assess the monitoring system's ability to provide early warning of prestressed failure before an accident occurs.

[0079] Please see Figures 13 to 16 , Figure 13 This is a schematic diagram of a standard section of vertical steel strand fracture provided in an embodiment of this application; Figure 14 This is a schematic diagram of a standard section of horizontal steel strand fracture provided in an embodiment of this application; Figure 15 This is a schematic diagram of the fracture of the steel strands in the dome provided in an embodiment of this application; Figure 16 This is a schematic diagram of the fracture of the horizontal steel strand of the equipment gate provided in the embodiment of this application; In a specific example, under a load combination, the stress state (N, M) of the cross-section changes from the fracture of 0 to 5 steel strands. On the cross-section perpendicular to the steel strands, the envelope curves of the same color represent the changes in the ultimate bearing capacity of the cross-section during the fracture of 0 to 5 steel strands. By comparing the positions of the stress MN of the cross-section with the bearing capacity envelope curves, it can be seen that the safety margin for the fracture of horizontal steel strands is 4 strands; the safety margin for the fracture of vertical steel strands is 3 strands; the safety margin for the fracture of dome steel strands is 5 strands; and the safety margin for the fracture of horizontal steel strands in the equipment gate area is 5 strands.

[0080] The containment monitoring system (EAU) is based on strain gauges embedded in concrete. The main parameter for assessing the detectability of steel strand fracture is the strain change before and after fracture. The containment EAU system typically deploys strain gauges in three orientations (thickness direction, horizontal direction, and vertical direction) at the same location. By studying concrete strain, the feasibility of detecting steel strand fracture through the monitoring system is roughly assessed. The strain difference caused by steel strand fracture is displayed as a contour plot in the range [-10⁻⁵, 10⁻⁵]. Gray areas outside this range indicate sufficiently significant changes in concrete strain that can be detected by the monitoring system.

[0081] Please see Figure 17 , Figure 17 A specific implementation method following step S4 is shown below: S51: Obtain test data through scaled-down testing or digital imaging technology. S52: Compare and verify the results of the finite element simulation with the test data to calibrate the parameters of the prestress distribution model and the finite element simulation.

[0082] The purpose of acquiring experimental data through scaled-down testing or digital imaging technology is to obtain actual physical response data as a benchmark for verifying the finite element simulation results. Specifically, one approach is to conduct scaled-down testing, which involves building a reduced-scale model of the containment structure and simulating the steel strand fracture condition on this model, directly measuring the strain response of the concrete surface using pre-positioned sensors. Another approach is to employ digital imaging technology, such as using a high-speed camera combined with a digital image correlation (DIC) algorithm, to capture the surface deformation field of the containment structure under simulated fracture conditions, and then calculate the strain data of the concrete surface. Furthermore, when conditions permit, full-scale tests on actual or decommissioned structures can also be conducted to directly obtain experimental data that most closely approximates the actual conditions.

[0083] Subsequently, the results of the finite element simulation are compared and verified with the experimental data. The purpose is to evaluate the accuracy of the finite element model and identify deviations between the simulation results and actual physical behavior. Specifically, the comparison and verification can take several forms: for example, a quantitative comparison can be made between the strain values ​​of the concrete surface obtained from the finite element simulation and the strain values ​​measured from the experimental data, calculating statistical indicators such as the error rate, correlation coefficient, or root mean square error. Simultaneously, a qualitative comparison can also be performed, such as comparing the strain distribution patterns, the location of strain peaks, and the strain variation trends over time or space between the simulation and the experiment to determine their consistency. Furthermore, visualization techniques can be used to present the simulation results and experimental data in the same coordinate system or a three-dimensional view, allowing for a direct observation of the differences between the two.

[0084] Based on this, the parameters of the prestress distribution model and finite element simulation are calibrated. This step aims to adjust and optimize the input parameters in the finite element model based on the results of comparative verification, so that it can more accurately reflect the actual physical behavior of the containment structure. Specifically, the calibration process can include: one approach is to use parameter optimization algorithms, such as least squares, genetic algorithms, or particle swarm optimization algorithms, to automatically adjust key parameters in the prestress distribution model (such as re-anchoring length, prestress loss coefficient) or material parameters in the finite element model (such as the elastic modulus, Poisson's ratio, tensile strength, etc. of concrete) based on the error between the simulation results and experimental data. Another approach is for engineers to manually adjust key parameters in the finite element model, such as the constitutive model parameters of concrete and the interface characteristics between steel strands and concrete, based on the comparative results and their professional knowledge and experience, until the consistency between the simulation results and experimental data reaches the preset accuracy requirements. In addition, parameter sensitivity analysis can be performed before calibration to identify the parameters that have the greatest impact on the simulation results, thereby prioritizing the calibration of these sensitive parameters and improving calibration efficiency.

[0085] This application introduces experimental data acquisition and model calibration steps, effectively addressing the potential accuracy limitations of finite element simulation. Specifically, experimental data acquired through scaled-down experiments or digital imaging technology provides a reliable physical benchmark for the finite element simulation results, enabling direct comparison between the simulation results and actual structural behavior. This comparative verification mechanism identifies deviations between the finite element model and actual working conditions, thereby guiding the calibration of the prestress distribution model and finite element simulation parameters. The calibrated model has more realistic parameter settings, enabling more accurate prediction of the structural response after tendon fracture, thus improving the accuracy and reliability of subsequent strength safety margin assessments and tendon fracture detectability assessments. This ensures that the entire analysis method is built on a solid empirical foundation, avoiding assessment risks caused by model inaccuracies, and making the final target assessment results more instructive.

[0086] Please refer to Figure 18 As a response to the above Figure 1 The implementation of the method shown in this application provides an embodiment of a containment prestress failure safety margin analysis device, which is similar to... Figure 1 Corresponding to the method embodiments shown, this device can be specifically applied to various electronic devices.

[0087] like Figure 18 As shown, the containment prestress failure safety margin analysis device of this embodiment includes: a re-anchoring length determination module 61, a stress-strain field simulation module 62, a safety margin assessment module 63, and a detectability assessment module 64, wherein: The re-anchoring length determination module 61 is used to determine the re-anchoring length after the steel strand breaks, and to construct a prestress distribution model after the steel strand breaks based on the re-anchoring length. The stress-strain field simulation module 62 is used to construct multiple steel strand fracture conditions based on the prestress distribution model, and to obtain the stress-strain field of the containment structure under each fracture condition through finite element simulation. Safety margin assessment module 63 is used to assess the strength safety margin of structural components based on the stress-strain field and determine the maximum allowable number of fracture roots. The detectability assessment module 64 is used to calculate the strain difference on the concrete surface before and after the steel strand fracture based on the stress-strain field, and to assess the detectability of the steel strand fracture based on the strain difference and the detection accuracy of the monitoring system, so as to obtain the target assessment result.

[0088] Furthermore, the re-anchoring length determination module 11 includes: The steel strand parameter acquisition unit is used to obtain the effective stress and equivalent diameter of the steel strand; The re-anchoring length calculation unit is used to calculate the re-anchoring length after the steel strand breaks using a preset formula based on the effective stress and the equivalent diameter. A prestress distribution model construction unit is used to determine the influence range of steel strand fracture and to construct the prestress distribution model after steel strand fracture based on the re-anchoring length and the influence range.

[0089] Furthermore, the preset formula is: in, The length of the re-anchoring is [length]. The effective stress, The equivalent diameter is given.

[0090] Furthermore, the stress-strain field simulation module 12 includes: The steel strand type selection unit is used to select at least one steel strand type among Γ-shaped steel strands, pure vertical steel strands, and horizontal steel strands; The fracture location setting unit is used to set fracture locations in at least one target critical area among the standard section of the containment, the weak prestressed area of ​​the dome, and the equipment gate opening. A steel strand fracture condition generation unit is used to set at least one steel strand to fracture for each fracture location, so as to form the steel strand fracture condition. The stress-strain field generation unit is used to obtain the stress-strain field of the containment structure under various fracture conditions through the finite element simulation.

[0091] Furthermore, the stress-strain field generating unit includes: Simulation sub-elements are used to simulate prestressing in a finite element model while maintaining the geometric continuity of the steel strand elements; A linear interpolation subunit is used to set the steel strand stress to zero at the steel strand fracture point and to perform linear interpolation on the steel strand stress within the influence range of the re-anchoring length to generate a triangular stress distribution. The reduced-dimensional load sub-unit is used to adjust the cooling load of the corresponding steel strand unit according to the triangular stress distribution in order to perform finite element calculations and generate the stress-strain field.

[0092] Furthermore, the safety margin assessment module 63 includes: Curve construction unit, used to construct the bearing capacity envelope curve of a component section based on the plane section strain assumption; The normal force extraction unit is used to extract the normal force and bending moment of the component section under various fracture conditions and accident condition combinations from the results of finite element simulation. The comparison unit is used to compare the stress point formed by the normal force and bending moment with the bearing capacity envelope curve in the same coordinate system to obtain the comparison result. The safety margin determination unit is used to determine the strength safety margin of the structural member under the current fracture condition based on the relative position of the stress point and the bearing capacity envelope curve in the comparison results. The permissible number of fracture roots determination unit is used to determine the maximum permissible number of fracture roots.

[0093] Furthermore, the curve building unit includes: The state setting subunit is used to set multiple different cross-sectional strain states, wherein each cross-sectional strain state is determined by the ratio of the strain of the bottom steel reinforcement to the strain of the top concrete of the cross-section; The maximum allowable strain determination sub-unit is used to determine the maximum allowable strain of concrete based on preset specification information; The calculation results generate sub-units, which are used to calculate the normal force and bending moment when the cross-section reaches the limit state for each cross-section strain state, and obtain the calculation results; The coordinate point connection sub-unit is used to connect multiple limit state coordinate points in the calculation results to generate the bearing capacity envelope curve.

[0094] Furthermore, the safety margin determination unit includes: The number of strands increasing sub-unit is used to progressively increase the assumed number of strand fractures at the same location in the structural member; The maximum allowable number of fracture roots determination sub-unit is used to repeatedly perform finite element simulation and the load-bearing capacity envelope curve evaluation for each increase in the number of fracture roots, until the stress point of the structural member section reaches or exceeds the load-bearing capacity envelope curve, and the number of fracture roots in the previous condition is determined as the maximum allowable number of fracture roots.

[0095] Furthermore, the detectability assessment module 64 includes: The load condition selection unit is used to select normal operating conditions as the load conditions for evaluation. The stress-strain field extraction unit is used to extract the stress-strain field of the concrete surface before and after the steel strand fracture from the results of finite element simulation. The strain difference calculation unit is used to calculate the strain difference of the concrete surface before and after the steel strand fracture based on the evaluation load conditions and the stress-strain field. The comparison unit is used to compare the strain difference value with the detection accuracy threshold of the pre-embedded strain gauge; The target evaluation result generation unit is used to generate the target evaluation result if the absolute value of the strain difference is greater than the detection accuracy threshold, wherein the target evaluation result determines that the steel strand fracture occurring at the steel strand location is detectable.

[0096] Furthermore, the detectability assessment module 64 also includes: The test data acquisition module is used to acquire test data through scaled-down testing or digital imaging technology; The calibration module is used to compare and verify the results of the finite element simulation with the experimental data in order to calibrate the parameters of the prestress distribution model and the finite element simulation.

[0097] To address the aforementioned technical problems, embodiments of this application also provide a computer device. Please refer to [link / reference needed]. Figure 19 , Figure 19 This is a basic structural block diagram of the computer device in this embodiment.

[0098] Computer device 7 includes a memory 71, a processor 72, and a network interface 73 that are interconnected via a system bus. It should be noted that... Figure 19Only a computer device 7 with three components—memory 71, processor 72, and network interface 73—is shown. It should be understood that implementing all shown components is not required; more or fewer components may be implemented alternatively. Those skilled in the art will understand that this computer device is a device capable of automatically performing numerical calculations and / or information processing according to pre-set or stored instructions. Its hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), and embedded devices.

[0099] Computer devices can include desktop computers, laptops, handheld computers, and cloud servers. These devices allow for human-computer interaction with users through keyboards, mice, remote controls, touchpads, or voice-activated devices.

[0100] The memory 71 includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 71 may be an internal storage unit of the computer device 7, such as the hard disk or memory of the computer device 7. In other embodiments, the memory 71 may also be an external storage device of the computer device 7, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the computer device 7. Of course, the memory 71 may also include both internal storage units and external storage devices of the computer device 7. In this embodiment, the memory 71 is typically used to store the operating system and various application software installed on the computer device 7, such as the program code of the containment prestress failure safety margin analysis method. In addition, the memory 71 can also be used to temporarily store various types of data that have been output or will be output.

[0101] In some embodiments, processor 72 may be a central processing unit (CPU), controller, microcontroller, microprocessor, or other data processing chip. This processor 72 is typically used to control the overall operation of computer device 7. In this embodiment, processor 72 is used to run program code stored in memory 71 or process data, for example, to run the program code of the above-described containment prestress failure safety margin analysis method to implement various embodiments of the containment prestress failure safety margin analysis method.

[0102] The network interface 73 may include a wireless network interface or a wired network interface, which is typically used to establish a communication connection between the computer device 7 and other electronic devices.

[0103] This application also provides another embodiment, namely, a computer-readable storage medium storing a computer program that can be executed by at least one processor to cause the at least one processor to perform the steps of the above-described containment prestress failure safety margin analysis method.

[0104] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods of the various embodiments of this application.

[0105] Obviously, the embodiments described above are merely some embodiments of this application, not all embodiments. The accompanying drawings show preferred embodiments of this application, but do not limit the scope of this application. This application can be implemented in many different forms; rather, these embodiments are provided to provide a more thorough and comprehensive understanding of the disclosure of this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing specific embodiments, or make equivalent substitutions for some of the technical features. Any equivalent structures made using the content of this application's specification and drawings, directly or indirectly applied to other related technical fields, are similarly within the scope of protection of this application.

Claims

1. A containment prestress failure safety margin analysis method, characterized by, include: Determine the re-anchoring length after the steel strand breaks, and construct a prestress distribution model after the steel strand breaks based on the re-anchoring length; Based on the prestress distribution model, multiple steel strand fracture conditions were constructed, and the stress-strain field of the containment structure under each fracture condition was obtained through finite element simulation. The strength safety margin of the structural members is assessed based on the stress-strain field, and the maximum allowable number of fracture roots is determined. The strain difference on the concrete surface before and after the steel strand fracture is calculated based on the stress-strain field, and the detectability of the steel strand fracture is assessed based on the strain difference and the detection accuracy of the monitoring system, thus obtaining the target assessment result.

2. The containment pre-stress failure safety margin analysis method of claim 1, wherein, The process of determining the re-anchoring length after the steel strand fracture, and constructing a prestress distribution model after the steel strand fracture based on the re-anchoring length, includes: Obtain the effective stress and equivalent diameter of the steel strand; The re-anchoring length after the steel strand fracture is calculated using a preset formula based on the effective stress and the equivalent diameter. Determine the influence range of the steel strand fracture, and construct the prestress distribution model after the steel strand fracture based on the re-anchoring length and the influence range.

3. The containment pre-stress failure margin analysis method of claim 2, wherein, The preset formula is: in, The length of the re-anchoring is [length]. The effective stress, The equivalent diameter is given.

4. The method for analyzing the safety margin of containment prestress failure according to claim 1, characterized in that, The process involves constructing multiple steel strand fracture scenarios based on the prestress distribution model, and obtaining the stress-strain field of the containment structure under each fracture scenario through finite element simulation, including: Select at least one type of steel strand from the following: Γ-shaped steel strand, pure vertical steel strand, and horizontal steel strand; Fault locations are set in at least one of the target critical areas in the standard section of the containment, the weak prestressed area of ​​the dome, and the equipment gate opening; For each fracture location, at least one steel strand is set to fracture to form the steel strand fracture condition; The stress-strain field of the containment structure under various fracture conditions was obtained through the finite element simulation.

5. The method for analyzing the safety margin of containment prestress failure according to claim 4, characterized in that, The process of obtaining the stress-strain field of the containment structure under various fracture conditions through the finite element simulation includes: The cooling method was used to simulate prestress while maintaining the geometric continuity of the steel strand elements in the finite element model; The stress in the steel strand is set to zero at the break point, and the stress in the steel strand is linearly interpolated within the influence range of the re-anchoring length to generate a triangular stress distribution. Adjust the cooling load of the corresponding steel strand unit according to the triangular stress distribution to perform finite element calculations and generate the stress-strain field.

6. The method for analyzing the safety margin of containment prestress failure according to claim 1, characterized in that, The assessment of the strength safety margin of structural members based on the stress-strain field, and the determination of the maximum allowable number of fracture roots, includes: The bearing capacity envelope curve of the component section is constructed based on the plane section strain assumption; The normal force and bending moment of the component section under various fracture conditions and accident condition combinations are extracted from the results of finite element simulation. The stress point formed by the normal force and bending moment is compared with the bearing capacity envelope curve in the same coordinate system to obtain the comparison results; Based on the relative position of the stress point and the bearing capacity envelope curve in the comparison results, the strength safety margin of the structural component under the current fracture condition is determined. Determine the maximum permissible number of fracture roots.

7. The method for analyzing the safety margin of containment prestress failure according to claim 6, characterized in that, The envelope curve of the bearing capacity of the component section constructed based on the plane section strain assumption includes: Multiple different cross-sectional strain states are defined, wherein each cross-sectional strain state is determined by the ratio of the strain of the bottom steel reinforcement to the strain of the top concrete. Determine the maximum allowable strain of concrete based on the pre-set specification information; For each of the strain states of the cross section, the normal force and the bending moment when the cross section reaches the limit state are calculated to obtain the calculation results; Connect the coordinates of multiple extreme states in the calculation results to generate the bearing capacity envelope curve.

8. The method for analyzing the safety margin of containment prestress failure according to claim 6, characterized in that, Determining the maximum permissible number of fracture roots includes: At the same location of the structural member, the assumed number of steel strand fractures is gradually increased; For each additional fracture element condition, the finite element simulation and the load-bearing capacity envelope curve evaluation are repeated until the stress point of the structural member section reaches or exceeds the load-bearing capacity envelope curve. The fracture element number of the previous condition is then determined as the maximum allowable fracture element number.

9. The method for analyzing the safety margin of containment prestress failure according to any one of claims 1 to 8, characterized in that, The process involves calculating the strain difference on the concrete surface before and after the steel strand fracture based on the stress-strain field, and then assessing the detectability of the steel strand fracture based on the strain difference and the detection accuracy of the monitoring system, to obtain the target assessment result, including: Normal operating conditions were selected as the evaluation load conditions; The stress-strain field of the concrete surface before and after the steel strand fracture was extracted from the results of the finite element simulation. The strain difference on the concrete surface before and after the steel strand fracture is calculated based on the evaluation load conditions and the stress-strain field. The strain difference value is compared with the detection accuracy threshold of the pre-embedded strain gauge; If the absolute value of the strain difference is greater than the detection accuracy threshold, the target evaluation result is generated, wherein the target evaluation result determines that the steel strand fracture occurring at the steel strand location is detectable.

10. The method for analyzing the safety margin of containment prestress failure according to any one of claims 1 to 8, characterized in that, The method further includes: calculating the strain difference on the concrete surface before and after the steel strand fracture based on the stress-strain field, and assessing the detectability of the steel strand fracture based on the strain difference and the detection accuracy of the monitoring system to obtain the target assessment result. Obtain test data through scaled-down testing or digital imaging technology; The results of the finite element simulation are compared and verified with the experimental data to calibrate the parameters of the prestress distribution model and the finite element simulation.

11. A device for analyzing the safety margin of containment prestress failure, characterized in that, include: The re-anchoring length determination module is used to determine the re-anchoring length after the steel strand breaks, and to construct a prestress distribution model after the steel strand breaks based on the re-anchoring length. The stress-strain field simulation module is used to construct multiple steel strand fracture conditions based on the prestress distribution model, and to obtain the stress-strain field of the containment structure under each fracture condition through finite element simulation. The safety margin assessment module is used to assess the strength safety margin of structural components based on the stress-strain field and determine the maximum allowable number of fracture roots. The detectability assessment module is used to calculate the strain difference on the concrete surface before and after the steel strand fracture based on the stress-strain field, and to assess the detectability of the steel strand fracture based on the strain difference and the detection accuracy of the monitoring system, so as to obtain the target assessment result.

12. The containment prestress failure safety margin analysis device according to claim 11, characterized in that, The re-anchoring length determination module includes: The steel strand parameter acquisition unit is used to obtain the effective stress and equivalent diameter of the steel strand; The re-anchoring length calculation unit is used to calculate the re-anchoring length after the steel strand breaks using a preset formula based on the effective stress and the equivalent diameter. A prestress distribution model construction unit is used to determine the influence range of steel strand fracture and to construct the prestress distribution model after steel strand fracture based on the re-anchoring length and the influence range.

13. The containment prestress failure safety margin analysis device according to claim 11, characterized in that, The stress-strain field simulation module includes: The steel strand type selection unit is used to select at least one steel strand type among Γ-shaped steel strands, pure vertical steel strands, and horizontal steel strands; The fracture location setting unit is used to set fracture locations in at least one target critical area among the standard section of the containment, the weak prestressed area of ​​the dome, and the equipment gate opening. A steel strand fracture condition generation unit is used to set at least one steel strand to fracture for each fracture location, so as to form the steel strand fracture condition. The stress-strain field generation unit is used to obtain the stress-strain field of the containment structure under various fracture conditions through the finite element simulation.

14. A computer device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the containment prestress failure safety margin analysis method as described in any one of claims 1 to 10.

15. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the containment prestress failure safety margin analysis method as described in any one of claims 1 to 10.

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