A numerical simulation method for predicting the bearing capacity of irradiated concrete structures

Abstract

The application discloses a numerical simulation method for predicting the bearing capacity of an irradiated concrete structure, and comprises the following steps: a neutron flux distribution model in a reactor is established by using a Monte Carlo method, and a three-dimensional neutron radiation field inside a concrete shielding structure is calculated; a random distribution aggregate-mortar micromechanics model is generated based on a Fuller grading algorithm, and an interference discrimination method is used to ensure that the aggregate space is not overlapped; a mapping relationship between neutron flux data and elastic modulus degradation is established, and neutron irradiation expansion and thermal expansion effects are coupled through an equivalent thermal expansion theory; node coordinate parameters are dynamically converted in finite element analysis, a neutron flux threshold is matched according to a preset space condition, and a corresponding elastic modulus degradation coefficient is returned; and comparison data of stress fields and displacement fields of the structure before and after irradiation are output. The application can accurately match the degradation requirements of complex geometric shapes through joint judgment of polar coordinates and three-dimensional space.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of nuclear power engineering structure safety evaluation, and particularly relates to a numerical simulation method for predicting the bearing capacity of irradiated concrete structures. BACKGROUND

[0002] The concrete shielding structure of a nuclear power plant is exposed to a neutron irradiation environment for a long time, which causes micro-cracks and volume expansion in the material, and further causes stiffness degradation. In the prior art, neutron flux distribution prediction (such as MCNP simulation) and mechanical property degradation analysis (such as Abaqus finite element simulation) are usually carried out independently.

[0003] The spatial correlation between neutron flux distribution and material degradation is insufficient: the traditional method does not fully consider the influence of non-uniform distribution of neutron flux on the local elastic modulus degradation of concrete, resulting in insufficient prediction accuracy.

[0004] In engineering simulation, local degradation of material properties (such as elastic modulus attenuation) is crucial for structural failure analysis. The traditional method usually relies on uniform assumption or manual division of regions to assign material properties, which has the following problems: (1) insufficient flexibility: complex geometry (such as curved surfaces, multi-layer structures) is difficult to divide degradation regions by simple rules; (2) low efficiency: a large number of boundary conditions need to be defined in advance or user intervention is required, increasing the calculation cost; (3) poor dynamic adaptability: unable to dynamically adjust material properties according to real-time coordinate parameters, affecting simulation accuracy. Therefore, it is urgent to propose a numerical simulation method for predicting the bearing capacity of irradiated concrete structures. SUMMARY

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

[0006] To achieve the above purpose, the application provides a numerical simulation method for predicting the bearing capacity of irradiated concrete structures, which comprises:

[0007] A Monte Carlo method is used to establish a neutron flux distribution model in the reactor to calculate the three-dimensional neutron radiation field inside the concrete shielding structure;

[0008] A random distribution of aggregate-mortar mesoscopic mechanical model is generated based on the Fuller grading algorithm, and an interference discrimination method is used to ensure that the aggregate space is not overlapped;

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

[0010] The node coordinate parameters are dynamically converted in the finite element analysis, a neutron flux threshold is matched according to preset space conditions, and a corresponding elastic modulus degradation coefficient is returned;

[0011] The stress field and displacement field comparison data of the structure before and after irradiation are output.

[0012] Optionally, the process of establishing the neutron flux distribution model comprises: adopting the Fmesh card of the MCNP program to perform three-dimensional grid division on the concrete biological shielding wall in the axial direction, the radial direction and the angle direction, and outputting the neutron injection amount distribution data at different positions.

[0013] Optionally, the process of generating the aggregate-mortar mesoscopic mechanics model comprises: delivering the aggregate in the order of aggregate volume from large to small, realizing the random distribution of spherical aggregate in the cylindrical mortar range through a Python script, and calculating the total volume fraction of the aggregate.

[0014] Optionally, the process of establishing the elastic modulus degradation mapping relationship comprises: superimposing the volume expansion rate of the alpha-quartz aggregate induced by neutron irradiation and the thermal expansion rate caused by irradiation heating to serve as an equivalent expansion coefficient input into a thermal-mechanical coupling analysis model.

[0015] Optionally, the process of dynamically converting the node coordinate parameters comprises: converting the Cartesian coordinates of the node into polar coordinates, and correcting the polar coordinate angle value to be in the range of [0, 2π) through angle correction.

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

[0017] Optionally, the process of generating the stress field and displacement field comparison data comprises: 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 the gravity load.

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

[0019] Technical effects of the present application:

[0020] (1) MCNP and Abaqus are combined: through the coupling of the neutron flux distribution and the mesoscopic mechanics model, the spatial resolution capability of stiffness degradation is significantly improved, and the error is obviously reduced compared with the traditional method;

[0021] (2) Strong engineering applicability: the aggregate expansion and the stiffness degradation of the specimen under real irradiation conditions can be simulated, and the method can be used for the service life evaluation of a nuclear power plant biological shielding wall and other actual structures;

[0022] (3) High precision: By polar coordinates and three-dimensional space joint judgment, accurate matching of complex geometric shape degradation needs;

[0023] (4) Flexibility: Support multi-region, multi-condition custom extension, adapt to different engineering scenarios;

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

[0025] The drawings constituting a part of this application are used to provide further understanding of the application, the illustrative embodiments of the application and the description thereof are used to explain the application, and do not constitute undue limitation on the application. In the drawings:

[0026] Figure 1 The neutron injection amount at different positions of the embodiment of the application.

[0027] Figure 2 The aggregate position determination of the embodiment of the application;

[0028] Figure 3 The aggregate delivery sequence code of the embodiment of the application;

[0029] Figure 4 The Abaqus operation table running test result of the embodiment of the application;

[0030] Figure 5 The interference judgment of the embodiment of the application;

[0031] Figure 6 The volume fraction calculation of the embodiment of the application;

[0032] Figure 7 The Abaqus model generated by the Python script of the embodiment of the application;

[0033] Figure 8 The concrete compression stress-strain curve of the embodiment of the application;

[0034] Figure 9 The relationship between the stiffness degradation and the neutron injection amount of the embodiment of the application;

[0035] Figure 10 The relative elastic modulus at different positions of the embodiment of the application, wherein (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 The coordinate system conversion of the embodiment of the application;

[0037] Figure 12Stiffness degradation for different locations of the embodiments of the present application;

[0038] Figure 13 Stress comparison before and after degradation for the embodiments of the present application, wherein (a) is the stress before degradation, and (b) is the stress after degradation;

[0039] Figure 14 Displacement comparison before and after degradation for the embodiments of the present application, wherein (a) is the displacement before degradation, and (b) is the displacement after degradation;

[0040] Figure 15 A flowchart of a numerical simulation method for predicting the bearing capacity of an irradiated concrete structure according to an embodiment of the present application. DETAILED DESCRIPTION

[0041] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. 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 flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0043] As shown in Figure 1 The present embodiment provides a numerical simulation method for predicting the bearing capacity of an irradiated concrete structure, comprising:

[0044] The biological shield of nuclear power plant is a concrete ring structure, with an inner diameter of about 8 m, a thickness of 2 m and a height of 15 m. During the operation of the nuclear reactor, a large number of high-energy neutrons (mainly in the range of fast neutrons, and some of them become thermal neutrons after moderation) are produced by the nuclear fission of uranium-235 (U-235) in the reactor core. When these neutrons diffuse outward through the reactor core structure material, coolant and shielding layer, some of them will penetrate the biological shielding concrete layer on the periphery of the reactor pressure vessel. The biological shielding concrete structure, as a key barrier, not only bears mechanical load, but also shields neutrons and gamma radiation. Due to the cumulative effect of the interaction between neutrons and concrete materials, long-term irradiation will cause significant accumulation of radioactive dose. Therefore, it is necessary to provide a Monte Carlo method-based MCNP calculation program to model the nuclear power plant reactor according to the material parameters of the reactor core, use the FMASH card to divide the reactor body along the axial and radial directions, and here take the example of dividing it into 4 parts in the angular direction, and dividing it into 10 cm parts in height and radial direction (see the MCNP user manual for the division method), to calculate the neutron radiation field in the radial, height and angular directions of the concrete biological shielding wall, and to provide data basis for the subsequent establishment of the quantitative relationship between the radiation field intensity and the mechanical performance degradation of the activated area. The calculated irradiation field is shown in the following table. Figure 1

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

[0046] 1. Use the rotation axis method to generate spherical aggregates.

[0047] 2. Use the random statement in Python to randomly distribute the aggregates within a certain range as shown in the following code: Figure 2 This code randomly determines the position of the aggregate centroid within a cylindrical mortar range. x1, y1 and z1 are the xyz coordinates of the aggregate centroid, 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 the existence of a certain gap between the aggregate and the aggregate, and between the mortar and the mortar. The random judgment method can represent the random distribution of aggregates within 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 grading with a large volume fraction, the aggregates with large volume should be placed first, followed by the aggregates with small volume. In order to ensure the delivery order, the tuple method is used here. The related code is as follows: Figure 3 ​As shown. Here's a test: for example, if we input AGGr4=6, AGGr3=4, AGGr2=2, and AGGr1=1, with each of the four different aggregate radii having a quantity of 2, the test results output in the Abaqus console are as follows. Figure 4 As shown in the figure, the aggregate output order is from largest to smallest volume, thus proving that the tuple method is reliable.

[0049] 4. Define a custom `def` function and use the interference discrimination method to prevent aggregates from intersecting. The code is as follows: Figure 5 As shown in the code above, the distance between two randomly generated points is compared. If the distance between the centers of the two small balls is less than the sum of the radii of the two aggregates, then the point is marked "False" (deleted). The remaining points are aggregates whose sum of center distance is greater than the sum of the radii of the two aggregates, thus ensuring that the two aggregates do not come into contact.

[0050] 5. Calculate the volume fraction of aggregates; the relevant code is as follows: Figure 6 As shown. The generated model is as follows. Figure 7 As shown.

[0051] During the long-term service of concrete structures such as nuclear reactor containment vessels, the degradation of material properties caused by fast neutron irradiation is a key scientific issue. When high-energy fast neutron streams penetrate concrete, they undergo inelastic collisions with aggregates and cement hydration products, converting kinetic energy into heat energy through ionization losses and atomic displacement effects, resulting in a significant temperature gradient field within the structure. Therefore, a thermo-mechanical coupling method is used for numerical simulation in Abaqus.

[0052] Because fast neutrons are uncharged and have stronger penetrating power, concrete exposed to fast neutron irradiation will undergo inelastic scattering to generate gamma rays and form electrons, which are ultimately absorbed in the form of thermal vibrations. The heat transfer analysis uses the relationship between the neutron injection amount and temperature as the heat conduction equation to analyze the irradiation-induced temperature rise, which can be specifically described 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 amount of neutron injection.

[0055] Heat convection formula:

[0056]

[0057] Boundary conditions:

[0058]

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

[0060] The concrete plastic damage model (CDP) is one of the commonly used models for simulating the real mechanical behavior of concrete, which takes into account the elastic stiffness degradation caused by plastic strain and the stiffness recovery effect under cyclic loading. It is highly reliable. In Abaqus, it is implemented in the plastic damage modulus of the material parameters, which can accurately express the whole process of the specimen from loading to failure. The expression is as follows:

[0061] σ=(1-d c )E c ε (4);

[0062] In the formula, d c is the uniaxial compression damage evolution parameter of concrete, that is, the damage factor; σ and ε represent the stress and strain of uniaxial compression of concrete; E c is the initial elastic modulus. The stress-strain relationship is shown in the following figure Figure 8 In the studies of Maruyama and Saklani, the aggregate containing more than 65% of quartz expands significantly when the neutron injection amount exceeds 1×10 19 n / cm 2 . The reason for this is that the volume expansion of the aggregate is the result of the combined action of the temperature field inside the aggregate and the neutron injection amount.

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

[0064]

[0065] Where ε n，quartz，∞ represents the maximum expansion volume rate of α-quartz, generally taking a value of 17.8%; n represents the fast neutron injection amount; T represents the temperature of α-quartz, in Kelvin (K); d is the dimension coefficient, generally ranging from 2 to 5, generally taking 2.38; K(T) is a function of temperature, which can be expressed in the following form:

[0066]

[0067] Taking the maximum neutron flux of this example as an example (1.27×10 10 n / cm 2 / s, which needs to be combined with the actual situation of MCNP calculation), with the increase of neutron flux, the expansion coefficient of α-quartz presents exponential increase, and the higher the temperature, the lower the expansion coefficient, the larger the dimension d value, the lower the expansion coefficient.

[0068] This invention utilizes the theory of equivalent thermal expansion to simulate the volume expansion of aggregates induced by fast neutron irradiation. An equivalent expansion coefficient α is introduced. eq The concept of irradiation-induced aggregate volume expansion rate ε n，quartz The relationship between (n) is shown below:

[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 thermal expansion of aggregate caused by irradiation heating should also be considered. It should be noted that although some studies indicate that the thermal expansion of aggregate caused by irradiation heating is 2-3 orders of magnitude smaller than the aggregate volume expansion induced by neutron irradiation, for the sake of rigor, this invention considers both the thermal expansion of aggregate caused by irradiation heating and the aggregate volume expansion induced by neutron irradiation, using (α... eq +α th Replace the coefficient of thermal expansion α in the classical heat transfer equation th This simulates the aggregate expansion, mortar damage, and decline in concrete mechanical properties caused by the combined effects of irradiation and heating.

[0072] The degradation of Young's modulus for different neutron injection rates can be obtained through Abaqus thermo-coupling calculations. The degradation relationship between neutron flux and Young's modulus is as follows: Figure 9 As shown.

[0073] Will Figure 1 The neutron injection amount results shown are substituted into Figure 9 From the formula n, we can obtain the degradation of the elastic modulus at different locations, such as... Figure 10 As shown, Figure 10 The values ​​represent the relative elastic modulus at different locations in the embodiments of the present invention, where (a) is in the 0-90° direction, (b) is in the 90-180° direction, (c) is in the 180-270° direction, and (d) is in the 270-360° direction.

[0074] This paper proposes a Fortran-based solution to address the inflexibility and low efficiency of existing methods for local material property degradation. The solution provides a technique for dynamically partitioning degradation regions based on coordinate parameters. The COORD command is used to capture the Cartesian coordinates (x, y, z) of nodes and convert them to polar coordinates (r, θ, z). Here, r = sqrt(x^2 + y^2), θ = ATAN2(y, x), (if the result is negative, it is corrected to the range [0, 2π) using θ = θ + 2π). The conversion code between polar and Cartesian coordinates is shown below. Figure 11 As shown, by combining multi-dimensional spatial condition judgment, precise control of material properties within complex structures can be achieved, thereby improving the automation and reliability of simulation analysis.

[0075] Will Figure 10 The elastic degradation result shown is input into the subroutine as follows: Figure 12 As shown, in the above code, the number "1" before the line indicates a consecutive line, because Fortran code does not allow each line to exceed 80 columns. If it exceeds 80 columns, a new line is required, and the number "1" is used at the beginning of the new line 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 (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." represent "greater than" and "less than" respectively. If none of the set ranges are met, the Young's modulus remains unchanged. Finally, the classified Young's modulus is returned to FIELD(1) in Abaqus. By associating the above code with 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 This is a comparison of stress before and after degradation in an embodiment of the present invention, where (a) is the stress before degradation and (b) is the stress after degradation; Figure 14 This is a comparison of displacement before and after degradation in 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) Combining MCNP with Abaqus: By coupling neutron flux distribution with micromechanical models, the spatial resolution of stiffness degradation is significantly improved, and the error is significantly reduced compared with traditional methods.

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

[0080] (3) High precision: precise matching of complex geometric shape degradation requirements through polar coordinate and three-dimensional space joint judgment;

[0081] (4) Flexibility: supports multi-region, multi-condition customization and extension, and adapts to different engineering scenarios;

[0082] (5) Compatibility: seamlessly integrated with Abaqus software, compatible with multiple material models and element types.

[0083] The above is only the preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A numerical simulation method for predicting the bearing capacity of irradiated concrete structures, characterized in that, include: A reactor neutron flux distribution model was established using the Monte Carlo method, and the three-dimensional neutron radiation field inside the concrete shielding structure was calculated. A randomized 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. Establish a mapping relationship between neutron flux data and elastic modulus degradation, and couple neutron irradiation expansion and thermal expansion effects through the equivalent thermal expansion theory; The process of establishing the mapping relationship between neutron flux data and elastic modulus degradation includes: superimposing the volume expansion rate of α-quartz aggregate induced by neutron irradiation with the thermal expansion rate caused by irradiation heating, and inputting it as the equivalent expansion coefficient into the thermo-mechanical coupling analysis model; In finite element analysis, the nodal coordinate parameters are dynamically transformed, the neutron flux threshold is matched according to the preset spatial conditions, and the corresponding elastic modulus degradation coefficient is returned. Output comparative data on the stress and displacement fields of the structure before and after irradiation.

2. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures as described in claim 1, characterized in that, The process of establishing the neutron flux distribution model includes: using the Fmesh card of the MCNP program to divide the concrete biological shield wall into three-dimensional meshes in the axial, radial and angular directions, and outputting neutron injection distribution data at different locations.

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

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

5. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures as described in claim 4, characterized in that, The process of matching the neutron flux threshold includes: determining the spatial region to which the node belongs based on the polar coordinate parameters (r, θ, z), and assigning the corresponding elastic modulus degradation coefficient when the coordinates meet the preset range.

6. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures as described in claim 1, characterized in that, 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 thermo-mechanical coupling calculations under gravity load.

7. The numerical simulation method for predicting the bearing capacity of irradiated concrete structures as described in claim 1, characterized in that, The method is applied to the life assessment of biological shielding walls or containment cylindrical concrete structures in nuclear power plants.

Images