Numerical simulation method for predicting bearing capacity of irradiated concrete structure

Abstract

The invention discloses a numerical simulation method for predicting the bearing capacity of an irradiated concrete structure, and the method comprises the steps: building a reactor neutron flux distribution model through a Monte Carlo method, and calculating a three-dimensional neutron radiation field in a concrete shielding structure; the method comprises the following steps: generating a randomly distributed aggregate-mortar mesomechanics model based on a Fuller grading algorithm, and ensuring that an aggregate space is not overlapped by adopting an interference discrimination method; establishing a mapping relation between neutron flux data and elastic modulus degradation, and coupling neutron irradiation expansion and thermal expansion effects through an equivalent thermal expansion theory; node coordinate parameters are dynamically converted in finite element analysis, a neutron flux threshold value is matched according to a preset space condition, and a corresponding elastic modulus degradation coefficient is returned; and outputting comparison data of the stress field and the displacement field of the structure before and after irradiation. According to the method, through combined judgment of polar coordinates and a three-dimensional space, the degradation requirement of a complex geometrical shape is accurately matched.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear energy engineering structure safety assessment, and in particular relates to a numerical simulation method for predicting the bearing capacity of irradiated concrete structures. Background Art

[0002] Long-term exposure to neutron irradiation in nuclear power plant concrete shielding structures causes microcracks and volume expansion within the material, leading to stiffness degradation. In existing technologies, neutron flux distribution prediction (e.g., MCNP simulation) and mechanical property degradation analysis (e.g., Abaqus finite element simulation) are typically performed independently.

[0003] Insufficient spatial correlation between neutron flux distribution and material degradation: Traditional methods do not fully consider the impact of non-uniform neutron flux distribution on the local elastic modulus degradation of concrete, resulting in insufficient prediction accuracy.

[0004] In engineering simulation, local degradation of material properties (e.g., elastic modulus decay) is crucial for structural failure analysis. Traditional methods typically rely on uniform assumptions or manually partition regions to assign material properties. These methods suffer from the following problems: (1) Lack of flexibility: Complex geometries (e.g., curved surfaces, multi-layer structures) are difficult to partition using simple rules for degraded regions; (2) Low efficiency: A large number of boundary conditions or user intervention are required in advance, increasing computational costs; and (3) Poor dynamic adaptability: Material properties cannot be dynamically adjusted based on real-time coordinate parameters, affecting simulation accuracy. Therefore, a numerical simulation method for predicting the bearing capacity of irradiated concrete structures is urgently needed. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a numerical simulation method for predicting the bearing capacity of irradiated concrete structures, which accurately matches the degradation requirements of complex geometric shapes through the combined judgment of polar coordinates and three-dimensional space.

[0006] To achieve the above object, the present invention provides a numerical simulation method for predicting the bearing capacity of irradiated concrete structures, comprising:

[0007] The reactor neutron flux distribution model was established using the Monte Carlo method to calculate the three-dimensional neutron radiation field inside the concrete shielding structure.

[0008] A randomly distributed aggregate-mortar micromechanical model is generated based on the Fuller gradation algorithm, and the interference discrimination method is used to ensure that there is no overlap in the aggregate space.

[0009] A mapping relationship between neutron flux data and elastic modulus degradation is established, and the neutron irradiation expansion and thermal expansion effects are coupled through the equivalent thermal expansion theory;

[0010] Dynamically convert node coordinate parameters in finite element analysis, match neutron flux thresholds according to preset spatial conditions, and return the corresponding elastic modulus degradation coefficient;

[0011] Output the comparative data of stress field and displacement field of the structure before and after irradiation.

[0012] Optionally, the process of establishing the neutron flux distribution model includes: using the Fmesh card of the MCNP program to perform three-dimensional meshing on the concrete biological shielding wall in the axial, radial and angular directions, and outputting neutron injection amount distribution data at different positions.

[0013] Optionally, the generation process of the aggregate-mortar micromechanical model includes: delivering aggregates in descending order of aggregate volume, achieving random distribution of spherical aggregates within the cylindrical mortar through a Python script, and calculating the total aggregate volume fraction.

[0014] Optionally, the process of establishing the elastic modulus degradation mapping relationship includes: superimposing the volume expansion rate of α-quartz aggregate induced by neutron irradiation and the thermal expansion rate caused by irradiation heating, and inputting them into the thermal-mechanical coupling analysis model as equivalent expansion coefficients.

[0015] Optionally, the process of dynamically converting node coordinate parameters includes: converting the Cartesian coordinates of the node into polar coordinates, and ensuring that the polar coordinate angle value is in the range of [0, 2π) through angle correction.

[0016] Optionally, the process of matching the neutron flux threshold includes: judging the spatial region to which the node belongs according to polar coordinate parameters (r, θ, z), and assigning a corresponding elastic modulus degradation coefficient when the coordinates meet a preset range.

[0017] Optionally, the process of generating the stress field and displacement field comparison data includes: calling the USDFLD subroutine in Abaqus, assigning the elastic modulus degradation coefficient to the field variable FIELD, and performing thermal-mechanical coupling calculation under gravity load.

[0018] Optionally, the method is applied to the life assessment of the biological shielding wall or the cylindrical concrete structure of the containment vessel of a nuclear power plant.

[0019] Technical effects of the present invention:

[0020] (1) Combination of MCNP and Abaqus: By coupling the neutron flux distribution with the micromechanical model, the spatial resolution of stiffness degradation is significantly improved, and the error is significantly reduced compared with traditional methods;

[0021] (2) Strong engineering applicability: It can simulate the aggregate expansion and specimen stiffness degradation under real irradiation conditions and can be used for life assessment of actual structures such as biological shielding walls in nuclear power plants;

[0022] (3) High precision: Through the joint judgment of polar coordinates and three-dimensional space, the degradation requirements of complex geometric shapes can be accurately matched;

[0023] (4) Flexibility: Supports custom expansion in multiple regions and conditions to adapt to different engineering scenarios;

[0024] (5) Compatibility: Seamless integration with Abaqus software, compatible with a variety of material models and element types. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0026] Figure 1 ] is the neutron injection amount at different positions in the embodiment of the present invention.

[0027] Figure 2 Determination of aggregate position according to an embodiment of the present invention;

[0028] Figure 3 Aggregate delivery sequence code according to an embodiment of the present invention;

[0029] Figure 4 This is the test result of the Abaqus operating platform in the embodiment of the present invention;

[0030] Figure 5 Interference judgment for embodiments of the present invention;

[0031] Figure 6 Volume fraction calculation for the embodiment of the present invention;

[0032] Figure 7 An Abaqus model generated by a Python script according to an embodiment of the present invention;

[0033] Figure 8 The compressive stress-strain curve of concrete in the embodiment of the present invention;

[0034] Figure 9 This is a graph showing the relationship between stiffness degradation and neutron injection amount according to an embodiment of the present invention;

[0035] Figure 10 The relative elastic modulus at different positions of the embodiment of the present invention, where (a) is the 0-90° direction, (b) is the 90-180° direction, (c) is the 180-270° direction, and (d) is the 270-360° direction;

[0036] Figure 11 Coordinate system conversion for the embodiment of the present invention;

[0037] Figure 12The stiffness degradation at different positions of the embodiment of the present invention;

[0038] Figure 13 Comparison of stress before and after degradation in an embodiment of the present invention, where (a) is stress before degradation and (b) is stress after degradation;

[0039] Figure 14 Comparison of displacement before and after degradation of an embodiment of the present invention, where (a) is the displacement before degradation and (b) is the displacement after degradation;

[0040] Figure 15 The figure is a flow chart of a numerical simulation method for predicting the bearing capacity of irradiated concrete structures according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0042] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0043] like Figure 1 As shown, this embodiment provides a numerical simulation method for predicting the bearing capacity of irradiated concrete structures, including:

[0044] The bioshield at a nuclear power plant is a circular concrete structure with an inner diameter of approximately 8 meters, a thickness of 2 meters, and a height of 15 meters. During nuclear reactor operation, the fission of uranium-235 (U-235) within the core generates a large number of high-energy neutrons (primarily fast neutrons, with some becoming thermal neutrons after moderation). These neutrons diffuse outward through the core structural materials, coolant, and shielding, with some penetrating the bioshield concrete layer surrounding the reactor pressure vessel. As a critical barrier, the bioshield concrete structure must withstand mechanical loads while also shielding against neutrons and gamma radiation. Due to the cumulative effect of neutron interactions with concrete, long-term exposure can result in significant radiation dose accumulation. Therefore, it is necessary to provide an MCNP calculation program based on the Monte Carlo method, model the nuclear power plant reactor according to the material parameters of the core, and use the FMASH card to divide the reactor body along the axial and radial directions. Here, we take the angular direction as 4 parts and the height and radial directions as 10 cm apart as an example (for details on the division method, please refer to the MCNP user manual). The neutron radiation field in the radial, height and angular directions inside the concrete biological shielding wall is calculated to provide a data basis for the subsequent establishment of a quantitative relationship between the radiation field intensity and the degradation of the mechanical properties of the activation zone. The calculated irradiation field is as follows Figure 1 shown.

[0045] After completing the irradiation field calculation, the Abaqus program was used to build a three-dimensional microscopic finite element model of the aggregate mortar. Abaqus has a command window for executing Python, which can be used for pre- and post-processing, as well as some repetitive modeling work. Therefore, a Python script was used to generate concrete aggregate. The key steps for generating spherical aggregate and mortar using Python are as follows:

[0046] 1. Generate spherical aggregate using the axis of rotation method.

[0047] 2. Using the random statement in Python makes the aggregates randomly distributed within a certain range, such as Figure 2 As shown in the figure, this code randomly determines the position of the center of mass of the aggregate within the range of a cylindrical mortar. x1, y1, and z1 are the xyz coordinates of the center of mass of the aggregate, respectively. Agg.r represents the radius of the aggregate, R0 represents the radius of the cylindrical mortar, H0 represents the height of the cylindrical mortar, and cover represents that there should be a certain gap between the aggregates and between the mortars. The random discrimination method can indicate that the aggregates are randomly distributed inside a cylindrical mortar with a radius of R0 and a height of H0.

[0048] 3. Use the for loop to generate multiple aggregates. In order to meet the fuller level with a larger volume fraction, the large aggregates should be placed first and then the small aggregates. In order to ensure the delivery order, the tuple method is used here. The relevant code is as follows Figure 3Here is a test, for example, AGGr4 = 6, AGGr3 = 4, AGGr2 = 2, AGGr1 = 1, the number of aggregates of four different radii is 2, input into the Abaqus console and the test results are as follows: Figure 4 As shown in the figure, it can be seen that the output order of aggregates is from large to small in terms of volume, so it can be proved that the method of using tuples is reliable.

[0049] 4. Customize a def function and use the interference judgment method to make the aggregates non-intersecting. The code is as follows Figure 5 In the above code, two randomly generated points are used for distance judgment. If the distance between the centers of the two balls is less than the sum of the radius of the two aggregates, it will be "False" (deleted). The remaining points are all aggregates whose sum of the center distance is greater than the sum of the radius of the two aggregates, thus ensuring that the two aggregates do not touch each other.

[0050] 5. Calculate the volume fraction of aggregate, the relevant code is as follows Figure 6 The generated model is as follows Figure 7 shown.

[0051] During the long-term service life of concrete structures, such as nuclear reactor containment vessels, material degradation induced by fast neutron irradiation is a key scientific issue. When high-energy fast neutrons penetrate concrete, they inelastically collide with aggregate and cement hydration products, converting kinetic energy into thermal energy through ionization losses and atomic displacements. This leads to significant temperature gradients within the structure. Therefore, a thermomechanical coupling approach is employed for numerical simulations in Abaqus.

[0052] Since fast neutrons are uncharged and have stronger penetrating power, concrete will undergo inelastic scattering when irradiated by fast neutrons, generating gamma rays and electrons, which are ultimately absorbed in the form of thermal vibrations. Heat transfer analysis uses the relationship between neutron injection rate and temperature as the heat conduction equation to analyze irradiation heating, which can be described specifically by the following formula:

[0053]

[0054] Where k, ρ, and c represent thermal conductivity, density, and specific heat, respectively; Q represents the heat generated per unit volume; and x and n represent the position vector and the neutron injection amount.

[0055] Heat convection formula:

[0056]

[0057] Boundary conditions:

[0058]

[0059] in, is the surface temperature of the concrete specimen, is the heat flux transferred per unit time, h is the heat convection coefficient, T f is the ambient temperature.

[0060] The concrete damage model (CDP) used in irradiation testing of concrete is a commonly used model for simulating the true mechanical behavior of concrete. This model considers the elastic stiffness degradation caused by plastic strain and the stiffness recovery effect under cyclic loading, resulting in high reliability. In Abaqus, this model is implemented as the plastic damage modulus in the material parameters, accurately representing the entire process from specimen loading to failure. The expression is as follows:

[0061] σ=(1-d c )E c ε (4);

[0062] Where, d c is the damage evolution parameter of concrete under uniaxial compression, also known as the damage factor; σ and ε represent the stress and strain of concrete under uniaxial compression, E c is the initial elastic modulus. The stress-strain relationship diagram is as follows Figure 8 As shown in the study by Maruyama and Saklani, fast neutron irradiation of aggregates with a quartz content of more than 65% and a neutron injection dose of more than 1×10 19 n / cm 2 When the aggregate volume is significantly expanded, it is found that the expansion of the aggregate volume is the result of the combined effect of the internal temperature field of the aggregate and the neutron injection amount.

[0063] Maruyama et al. found that the nucleation growth model can better predict the volume expansion rate of α-quartz aggregate, and its expression is as follows:

[0064]

[0065] Among them, ε n，quartz，∞ represents the maximum expansion volume rate of α-quartz, generally 17.8%; n represents the fast neutron injection rate; T represents the temperature of α-quartz, in Kelvin (K); d is the dimension coefficient, generally ranging from 2 to 5, and generally 2.38; K(T) is a function of temperature and can be expressed as follows:

[0066]

[0067] Taking the maximum neutron flux in this case as an example (1.27×10 10 n / cm 2 / s, here we need to combine the actual situation of MCNP calculation). With the increase of neutron flux, the expansion coefficient of α-quartz increases exponentially, and the higher the temperature, the lower the expansion coefficient, and the larger the dimension d value, the lower the expansion coefficient.

[0068] The present invention uses the equivalent thermal expansion theory to simulate the volume expansion of aggregate induced by fast neutron irradiation. The equivalent expansion coefficient α is introduced. eq The concept of irradiation-induced aggregate volume expansion ε n，quartz The relationship between (n) is as follows:

[0069] ε n，quartz (n) = α eq ΔT=α eq (T1-T0) (7);

[0070] Where T0 is the initial ambient temperature, T1 is the aggregate temperature after irradiation, and ΔT is the temperature difference.

[0071] In Abaqus, in addition to considering the aggregate volume expansion induced by neutron irradiation, the aggregate thermal expansion caused by irradiation heating should also be considered. It should be noted that although some studies have pointed out that the aggregate thermal expansion caused by irradiation heating is 2 to 3 orders of magnitude smaller than the aggregate volume expansion induced by neutron irradiation, for the sake of rigor, this paper considers the aggregate thermal expansion caused by irradiation heating and the aggregate volume expansion induced by neutron irradiation, and uses (α eq +α th ) replaces the thermal expansion coefficient α in the classical heat transfer equation th , in order to simulate the aggregate expansion, mortar damage and degradation of concrete mechanical properties caused by the combined effects of irradiation and temperature rise.

[0072] The degradation of Young's modulus corresponding to different neutron injection amounts can be obtained through Abaqus thermal-mechanical coupling calculation. The degradation relationship between neutron flux and Young's modulus is as follows: Figure 9 shown.

[0073] Will Figure 1 The neutron injection results shown are brought into Figure 9 In the formula of n, the degradation of elastic modulus at different positions can be obtained as follows Figure 10 As shown, Figure 10 The relative elastic modulus at different positions of the embodiment of the present invention, where (a) is the 0-90° direction, (b) is the 90-180° direction, (c) is the 180-270° direction, and (d) is the 270-360° direction.

[0074] Provided is a method based on Fortran language to solve the problems of poor flexibility and low efficiency of local material performance degradation methods in the existing technology, and provide a technical solution for dynamically dividing degradation areas based on coordinate parameters. Use the COORD command to capture the Cartesian coordinates (x, y, z) of the node and convert the Cartesian coordinates into polar coordinates (r, θ, z). Among them, r = sqrt(x^2+y^2), θ = ATAN2(y, x), (if the result is a negative value, it is corrected to the range of [0, 2π) by θ = θ + 2π). Through the conversion between polar coordinates and Cartesian coordinates, the conversion code is as follows Figure 11 As shown in the figure, combined with multi-dimensional spatial condition judgment, precise control of material properties in complex structures can be achieved, improving the automation and reliability of simulation analysis.

[0075] Will Figure 10 The elastic degradation results shown are input into the subroutine as Figure 12 As shown, the number "1" in front of the line in the above code means continuous lines, because Fortran code does not allow each line to exceed 80 columns. If it exceeds 80 columns, a new line must be started. At the beginning of the new line, the number "1" is used to indicate continuity. For example: "theta.GE.1.57.AND.theta.LE.3.14" means that if the angle is between 1.57 radians and 3.14 radians (the angle is 90°-180°), the radius is between 4.0m and 4.2m, and the height is between 8.3m and 9.0m, the Young's modulus is 0.9 times the original value, where ".GE." and ".LE." respectively represent "greater than" and "less than". If neither of them meets the set range, the Young's modulus remains unchanged. Finally, the classified Young's modulus is returned to FIELD (1) in Abaqus. By linking the above code to Abaqus, the stress and deformation under gravity loads such as water tanks after irradiation can be calculated.

[0076] The stress and displacement results before and after irradiation are as follows Figure 13 、 14 As shown, Figure 13 Comparison of stress before and after degradation in an embodiment of the present invention, where (a) is stress before degradation and (b) is stress after degradation; Figure 14 1 is a comparison of the displacement before and after degradation of an embodiment of the present invention, where (a) is the displacement before degradation and (b) is the displacement after degradation.

[0077] Technical effects of the present invention:

[0078] (1) Combination of MCNP and Abaqus: By coupling the neutron flux distribution with the micromechanical model, the spatial resolution of stiffness degradation is significantly improved, and the error is significantly reduced compared with traditional methods;

[0079] (2) Strong engineering applicability: It can simulate the aggregate expansion and specimen stiffness degradation under real irradiation conditions and can be used for life assessment of actual structures such as biological shielding walls in nuclear power plants;

[0080] (3) High precision: Through the joint judgment of polar coordinates and three-dimensional space, the degradation requirements of complex geometric shapes can be accurately matched;

[0081] (4) Flexibility: Supports custom expansion in multiple regions and conditions to adapt to different engineering scenarios;

[0082] (5) Compatibility: Seamless integration with Abaqus software, compatible with a variety of material models and element types.

[0083] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A numerical simulation method for predicting the bearing capacity of irradiated concrete structures, characterized in that: include: The reactor neutron flux distribution model was established using the Monte Carlo method to calculate the three-dimensional neutron radiation field inside the concrete shielding structure. A randomly distributed aggregate-mortar micromechanical model is generated based on the Fuller gradation algorithm, and the interference discrimination method is used to ensure that there is no overlap in the aggregate space. A mapping relationship between neutron flux data and elastic modulus degradation is established, and the neutron irradiation expansion and thermal expansion effects are coupled through the equivalent thermal expansion theory; Dynamically convert node coordinate parameters in finite element analysis, match neutron flux thresholds according to preset spatial conditions, and return the corresponding elastic modulus degradation coefficient; Output the comparative data of stress field and displacement field of the structure before and after irradiation.

2. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures according to claim 1, characterized in that: The process of establishing the neutron flux distribution model includes: using the Fmesh card of the MCNP program to perform three-dimensional meshing of the concrete biological shielding wall in the axial, radial and angular directions, and outputting neutron injection amount distribution data at different positions.

3. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures according to claim 1, characterized in that: The generation process of the aggregate-mortar micromechanical model includes: delivering aggregates in descending order of aggregate volume, achieving random distribution of spherical aggregates within the cylindrical mortar using a Python script, and calculating the total aggregate volume fraction.

4. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures according to claim 1, characterized in that: The process of establishing the elastic modulus degradation mapping relationship includes: superimposing the volume expansion rate of α-quartz aggregate induced by neutron irradiation and the thermal expansion rate caused by irradiation heating, and inputting them into the thermal-mechanical coupling analysis model as the equivalent expansion coefficient.

5. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures according to claim 1, characterized in that: The process of dynamically converting node coordinate parameters includes: converting the Cartesian coordinates of the node into polar coordinates, and ensuring that the polar coordinate angle value is in the range of [0, 2π) through angle correction.

6. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures according to claim 5, characterized in that: The process of matching the neutron flux threshold includes: judging the spatial region to which the node belongs according to polar coordinate parameters (r, θ, z), and assigning a corresponding elastic modulus degradation coefficient when the coordinates meet a preset range.

7. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures according to claim 1, characterized in that: The generation process of the stress field and displacement field comparison data includes: calling the USDFLD subroutine in Abaqus, assigning the elastic modulus degradation coefficient to the field variable FIELD, and performing thermal-mechanical coupling calculation under the action of gravity load.

8. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures according to claim 1, characterized in that: The method is applied to the life assessment of the biological shielding wall or the cylindrical concrete structure of the containment vessel of a nuclear power plant.

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