Quantitative analysis method for uncertainty of three-phase mesoscopic finite element of fully-graded concrete

Abstract

The invention discloses a full-graded concrete three-phase mesoscopic finite element uncertainty quantitative analysis method, and relates to the technical field of building engineering material computer simulation, and the method comprises the following steps: generating a reference finite element grid based on an obtained three-dimensional mesoscopic structure sample, carrying out three-phase material unit division by identifying aggregate area nodes, and carrying out three-phase material unit division; after corresponding material constitutive models are given to the divided three-phase units, a three-phase finite element model corresponding to the three-dimensional microstructure sample is formed, and mechanical property numerical simulation is executed; and macroscopic mechanical property indexes are extracted from the simulation result in batches, and uncertainty quantification and correlation analysis are carried out. According to the method, a complete and efficient solution from an aggregate structure to a three-phase model and then to uncertainty analysis is formed, and a technical support is provided for probability design and performance evaluation of the fully-graded concrete.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer simulation of construction engineering materials, in particular to an uncertainty quantification analysis method for three-phase mesoscopic finite element of fully graded concrete. BACKGROUND

[0002] Fully Graded Concrete (FGC) is widely used in large-scale hydraulic structures such as high dams and nuclear power plants due to its excellent mechanical properties and economic construction. Unlike ordinary concrete, FGC uses continuous grading, with the largest aggregate size reaching 150mm and high coarse aggregate content, forming a complex spatial skeleton structure. To test its macroscopic mechanical properties, the specification requires large specimen sizes (cubic edge length up to 450mm), resulting in high costs and long periods for indoor physical tests, and making it difficult to observe the internal damage evolution process.

[0003] Mesoscopic numerical simulation provides an effective way to study the mechanical behavior and failure mechanism of concrete by explicitly constructing a three-phase geometric model of aggregates, mortar, and interfacial transition zones (ITZ) in the computer.

[0004] However, for complex and large FGC models, three-phase meshing is a major technical bottleneck. Traditional methods rely on Boolean operations on complex geometries such as aggregates and mortar matrices, which not only require large amounts of computation and long processing times (often several hours to days), but also are highly susceptible to geometric topology errors (such as face intersections and gaps), leading to meshing failures and poor robustness. This problem severely restricts the efficiency and application of FGC mesoscopic simulation.

[0005] In addition, the mesostructure of concrete (such as aggregate distribution) has inherent randomness, which leads to inherent dispersion in its macroscopic mechanical properties. Traditional deterministic simulation methods can only provide a single result and cannot assess this uncertainty. Due to the aforementioned meshing difficulties, constructing a sufficient number of statistically meaningful mesoscopic model samples is too costly and time-consuming, making it difficult to conduct systematic quantitative analysis of how the uncertainty of the mesostructure affects the macroscopic properties, and restricting the development of probability-based concrete design and safety evaluation theories.

[0006] Therefore, there is an urgent need in the art for a solution that can efficiently and robustly construct three-phase mesoscopic finite element models and perform uncertainty quantification analysis based on them. SUMMARY

[0007] To solve the above problems, the present application provides an uncertainty quantification analysis method for three-phase mesoscopic finite element of fully graded concrete, comprising the following steps: Based on the obtained three-dimensional microstructure sample, a reference finite element mesh is generated. By identifying the nodes in the aggregate region, three-phase material elements are divided. After assigning the corresponding material constitutive model to the divided three-phase elements, a three-phase finite element model corresponding to the three-dimensional microstructure sample is formed, and numerical simulation of mechanical properties is performed. Macroscopic mechanical performance indicators are extracted in batches from the simulation results and uncertainty quantification and correlation analysis are performed.

[0008] Preferably, when obtaining the reference finite element mesh, a simulation region representing the fully graded concrete specimen is created and meshed, generating a reference finite element mesh containing only node and element information.

[0009] Preferably, when identifying aggregate region nodes, the method of ray projection is used to identify all aggregate region nodes located within the closed volume of the aggregate by judging the parity of the number of intersection points between the rays emitted from the node and the aggregate boundary.

[0010] Preferably, when dividing the three-phase material elements, all elements containing nodes within the "aggregate node base" are deleted from the reference finite element mesh, and the remaining elements are defined as mortar elements. From all elements of the reference finite element mesh, remove all mortar elements and extract the outer layer of the remaining elements, which are defined as ITZ elements. The thickness of the ITZ is naturally defined by the mesh size. In the baseline finite element mesh, the remaining elements after removing mortar elements and ITZ elements are defined as aggregate elements.

[0011] Preferably, when performing numerical simulation of mechanical properties, a finite element solver is invoked to perform the numerical simulation of mechanical properties.

[0012] Preferably, when performing numerical simulation of mechanical properties, uniaxial compressive and tensile simulations are performed based on a three-phase finite element model.

[0013] Preferably, when performing uncertainty quantification and correlation analysis, macroscopic mechanical performance indicators are extracted, including: elastic modulus, compressive strength, axial tensile strength and ultimate tensile strain; For all samples, the sample mean, sample standard deviation, and coefficient of variation of each macroscopic mechanical performance index are calculated. Correlation analysis, regression analysis, or visualization charts are used to quantitatively analyze the correlation between the dispersion of macroscopic mechanical performance index and the microstructural characteristic parameters, thus completing the uncertainty quantification analysis.

[0014] Based on the same inventive concept, this invention also discloses an uncertainty quantification analysis system for three-phase mesoscopic finite element method of fully graded concrete, comprising: The three-phase finite element model construction module is used to generate a reference finite element mesh based on the acquired three-dimensional microstructure sample. By identifying the nodes in the aggregate region, it divides the three-phase material elements and assigns the corresponding material constitutive models to the divided three-phase elements to form the three-phase finite element model corresponding to the three-dimensional microstructure sample, and performs numerical simulation of mechanical properties. The quantitative analysis module is used to extract macroscopic mechanical performance indicators in batches from simulation results and perform uncertainty quantification and correlation analysis.

[0015] The present invention discloses the following technical effects: The mesh generation method proposed in this invention, based on ray casting and set operations, completely eliminates the dependence on Boolean operations for the original complex geometric model, solving the industry problem of cumbersome and failure-prone mesh generation processes. For a model containing hundreds of thousands of elements, three-phase mesh generation can be completed within ten minutes, improving efficiency by more than ten times, with a success rate approaching 100%.

[0016] Based on the efficient and automated modeling process provided by this invention, a large number of statistical samples can be generated quickly. Thus, for the first time at an economically feasible cost, a systematic and accurate quantitative analysis of the dispersion of macroscopic mechanical properties caused by the randomness of the microstructure of fully graded concrete is carried out. This reveals important laws such as the tensile properties being more sensitive to microstructure inhomogeneity and the trade-off between aggregate gradation and compressive and tensile properties. This invention integrates the advantages of multiple professional software such as Rhino and Abaqus, forming a complete and efficient solution from "aggregate structure" to "three-phase model" to "uncertainty analysis", providing a powerful theoretical tool for the probabilistic design and performance evaluation of fully graded concrete. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the overall process of the method described in this invention.

[0019] Figure 2 This is a schematic diagram illustrating the principle of dividing the three-phase material units as described in this invention.

[0020] Figure 3 This is a sequence cloud diagram of the damage evolution process of the calibration section (z75) described in this invention under uniaxial compression (a) and tension (b).

[0021] Figure 4 This is a box plot of the stress-strain curves of the 30 sections described in this invention and the statistical results of uncertainty quantification analysis. The meanings of each subplot are as follows: (a) elastic modulus, (b) ultimate tensile strain, (c) compressive strength, (d) axial tensile strength, (e) group of compressive stress-strain curves, and (f) group of tensile stress-strain curves. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0023] like Figures 1-4 As shown, this invention provides an uncertainty quantification analysis method for three-phase micro-finite element method of fully graded concrete, specifically including the following: On the one hand, this invention proposes a rapid construction method for a three-phase micro-finite element model of fully graded concrete. This method utilizes information representing the spatial distribution of aggregates generated in any way, and includes the following processes: Step S1: Generate the reference finite element mesh: In finite element analysis software (such as Abaqus), create a simulation region (two-dimensional section or three-dimensional solid) representing a fully graded concrete specimen, and mesh it to generate a baseline finite element mesh (such as an INP file) containing only node and element information. For two-dimensional analysis, a 450mm × 450mm plane can be meshed with CPS4R elements with a mesh size of 0.5-2mm.

[0024] Step S2: Rapid identification of aggregate region nodes based on ray casting method: The coordinates of all nodes in the reference finite element mesh, as well as the aggregate 3D model exported from the engine, are imported into the 3D modeling software Rhinoceros. Using its built-in "select objects by closed volume" function (the core algorithm is ray casting), the system quickly and accurately identifies all mesh nodes located within the closed volume of the aggregate by judging the parity of the number of intersection points between rays emitted from the nodes and the aggregate boundary, thus forming an "aggregate node set".

[0025] Step S3: Three-phase material element partitioning based on set operations: In finite element analysis software, based on the "aggregate node set," a series of set operations are used to divide the three-phase material elements. The entire process does not require Boolean operations on complex geometries. S3.1: Define mortar elements: In the reference finite element mesh, delete all elements that contain nodes within the "aggregate node base", and define the remaining elements as mortar elements.

[0026] S3.2: Interface Definition Surface Transition Zone (ITZ) Element: From all elements of the reference finite element mesh, remove all mortar elements and extract the outer layer of the remaining elements, which is defined as the ITZ element. The thickness of the ITZ is naturally defined by the mesh size.

[0027] S3.3: Define aggregate elements: In the reference finite element mesh, the remaining elements after removing mortar elements and ITZ elements are defined as aggregate elements.

[0028] Step S4: Assigning values ​​to the material constitutive model: The three-phase units were assigned corresponding material constitutive models: the aggregate units were assigned linear elastic constitutive models; the mortar units and ITZ units were assigned concrete damage plasticity models, where the strength parameters of the ITZ material were reduced to 80% of the strength parameters of the mortar material; the concrete damage plasticity model parameters of the mortar were calibrated mainly by comparing with macroscopic experimental data.

[0029] Secondly, based on the three-phase mesoscopic finite element model of fully graded concrete constructed in this invention, this invention provides a method for quantitatively analyzing the uncertainty of the mechanical properties of fully graded concrete, used to quantitatively evaluate the influence of the randomness of the mesoscopic structure on the macroscopic mechanical properties. Building upon S4, it further includes the following steps: Step S5: Generate a statistically independent set of microstructure samples: For two-dimensional analysis, based on the three-dimensional aggregate packing model constructed by the modeling software, multiple statistically independent two-dimensional mesostructure samples in terms of aggregate spatial distribution are generated by taking sections along the coordinates; for three-dimensional analysis, based on the modeling software, multiple three-dimensional aggregate packing models are constructed, and each model itself constitutes an independent three-dimensional mesostructure sample.

[0030] Step S6: Perform batch mechanical performance simulation on the sample set: For each sample generated in step S5, the rapid construction of the three-phase mesoscopic finite element model as mentioned in the first aspect is performed to generate its corresponding three-phase finite element model. Subsequently, the finite element solver is called to perform numerical simulation of mechanical properties, including uniaxial compressive and tensile simulations.

[0031] Step S7: Extract macroscopic mechanical performance indicators in batches from the simulation results and perform uncertainty quantification and correlation analysis; From the numerical simulation results file of the mechanical properties of each sample completed in step S7, manually extract the key macroscopic mechanical property indicators, including: elastic modulus, compressive strength, axial tensile strength, and ultimate tensile strain. Perform statistical analysis on the macroscopic mechanical property indicators of all samples, calculate the sample mean, sample standard deviation, and coefficient of variation for each indicator; quantitatively analyze the correlation between the dispersion of macroscopic mechanical property indicators and microstructural characteristic parameters through correlation analysis, regression analysis, or visualization methods, and output an uncertainty quantification analysis report.

[0032] The core idea of ​​this invention is to propose a non-Boolean operation meshing strategy based on ray casting and set operations, which completely avoids direct interaction with complex geometries, thereby achieving efficient and robust construction of three-phase models; and based on this, a large number of samples can be generated economically to achieve systematic quantification of macroscopic mechanical performance uncertainties.

[0033] Example: The process of constructing a two-dimensional microstructure model of fully graded concrete and quantifying its uncertainty mentioned in this invention includes the following specific implementation details: The entire process of performing refined two-dimensional microscopic simulation and uncertainty quantification analysis on concrete mix design.

[0034] 1. Acquisition of aggregate model: This embodiment is based on a 450mm×450mm×450mm three-dimensional aggregate packing model (FBX format) constructed by other methods.

[0035] 2. Rapid Construction of Three-Phase Micro-Finite Element Model (corresponding to steps S1-S4): Baseline Finite Element Mesh Generation (S1): In Abaqus / CAE 2024, create a 450mm × 450mm two-dimensional planar component. Mesh it with CPS4R (four-node planar stress quadrilateral) elements with a global seed size of 0.5mm, generating approximately 810,000 elements and 820,000 nodes. Export the mesh model as a "0-point.inp" file.

[0036] Aggregate region node rapid identification (S2): To perform 2D analysis, a cross section is cut every 50mm along the X, Y, and Z axes of the Cartesian coordinate system, resulting in a total of 30 cross sections. For each cross section (e.g., Z=75mm), in Rhino, the "SelVolumeObject" command (whose core algorithm is ray casting) is executed to select all mesh nodes and the imported aggregate model, quickly calculating all nodes located inside the aggregate polygons and defining these nodes as the "aggregate node set".

[0037] 3. Three-phase material unit division (S3): Define mortar elements (S3.1): Since Abaqus deletes all elements containing a node when deleting a node, when deleting all nodes in the "aggregate node set" in the model, all elements directly related to the aggregate (including aggregate body elements and interface elements adjacent to the aggregate) will be deleted together. Define the remaining elements as mortar elements.

[0038] Define ITZ element (S3.2): Temporarily remove the mortar element from the overall model, extract the outermost element of the remaining elements, and define it as an ITZ element. The thickness of the ITZ element is naturally defined as the element size of 0.5mm.

[0039] Define aggregate elements (S3.3): Define elements other than mortar and ITZ as aggregate elements.

[0040] Material constitutive model assignment (S4): Create three materials in Abaqus and mainly calibrate the constitutive model parameters of the mortar.

[0041] Aggregate material: named Guliao, with a linear elastic constitutive structure, elastic modulus of 50 GPa, and Poisson's ratio of 0.16.

[0042] Mortar material: named Shajiang, it is used to model the plasticity of concrete damage. The initial calibration data of its constitutive model comes from the existing simulation data. By repeatedly conducting uniaxial compressive and tensile simulation tests on the calibration section (z75), the stress-strain curve and damage evolution curve are adjusted until they are basically consistent with the actual engineering data provided.

[0043] ITZ material: named Jiemian, it is also given a concrete damage plasticity model, with its parameters reduced to 80% of the mortar strength.

[0044] Finally, the material Guliao is assigned to the aggregate unit, the material Jiemian is assigned to the interface unit, and the material Shajiang is assigned to the mortar unit.

[0045] 4. Uncertainty Quantification Analysis (corresponding to steps S5-S7): Steps S2 to S3 were repeated for 30 cross-sections to construct 30 different two-dimensional mesoscopic models. A batch script was written using the Abaqus command-line interface to sequentially submit uniaxial compression and uniaxial tension simulations for each of the 30 models. After the calculations were completed, the macroscopic responses—elastic modulus E and peak compressive strength f—were extracted from the ODB result file of each model. c Peak axial tensile strength ft, ultimate tensile strain ε tFinally, Excel was used for statistical analysis to calculate the mean, standard deviation, and coefficient of variation (CV) of the four indicators. The results are shown in Table 1. Table 1

[0046] To further demonstrate the significance of this invention, the following verification work was also performed: 1. A group of stress-strain curves for 30 models was plotted. Figure 4 (a) and box plot of mechanical properties ( Figure 4 (be) visually demonstrates the performance discreteness; 2. It was found that the coefficient of variation of axial tensile strength (7.23%) was much greater than that of compressive strength (3.14%), indicating that tensile properties are more sensitive to microstructural inhomogeneity; 3. By comparing cross-sections with good and poor aggregate distribution uniformity, it was found that uneven aggregate distribution leads to stress concentration and weakens the effective force transmission path, resulting in a 20%-30% performance degradation. 4. Analysis of aggregate particle size distribution revealed that sections with a high proportion of small and medium-sized aggregates tend to have higher compressive strength but lower tensile strength. The presumed reason is that while small and medium-sized aggregates increase bulk density, which is beneficial for compressive strength, they also increase the total in-tensile zone (ITZ) length, providing more pathways for tensile cracks. 5. This embodiment successfully verifies the effectiveness of the method proposed in this invention. It not only achieves efficient and robust construction of a three-phase microstructure model for fully graded concrete, but also reveals the influence of microstructure randomness on macroscopic mechanical properties through systematic quantitative analysis, providing important theoretical basis and technical tools for engineering mix design and probabilistic design.

[0047] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0048] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0049] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for quantifying uncertainty of three-phase meso-finite element of full-graded concrete, characterized in that, The method comprises the following steps: Based on the obtained three-dimensional microstructure sample, a reference finite element mesh is generated, three-phase material unit division is performed by identifying aggregate region nodes, and after the divided three-phase units are assigned with corresponding material constitutive models, a three-phase finite element model corresponding to the three-dimensional microstructure sample is constructed, and numerical simulation of mechanical properties is performed; Macroscopic mechanical property indexes are extracted from the simulation results in batches, and uncertainty quantification and correlation analysis are performed.

2. The uncertainty quantification analysis method of the three-phase mesoscopic finite element of the full-grade concrete according to claim 1, characterized in that: When the reference finite element mesh is obtained, a simulation area representing the full-grade concrete specimen is created and meshed to generate the reference finite element mesh containing only node and element information.

3. The uncertainty quantification analysis method of the three-phase mesoscopic finite element of the full-grade concrete according to claim 2, characterized in that: When the aggregate region nodes are identified, based on the ray projection method, the number of intersections of the rays emitted from the nodes with the aggregate boundary is judged for oddness or evenness to identify all aggregate region nodes located in the closed volume inside the aggregate.

4. The uncertainty quantification analysis method of the three-phase mesoscopic finite element of the full-grade concrete according to claim 1, characterized in that: When the three-phase material unit division is performed, in the reference finite element mesh, all elements containing "aggregate node base" nodes are deleted, and the remaining elements are defined as mortar elements; All mortar elements are removed from the reference finite element mesh, and the outer elements of the remaining elements are defined as ITZ elements, and the thickness of the ITZ is naturally defined by the mesh size; In the reference finite element mesh, the elements remaining after the mortar elements and the ITZ elements are removed are defined as aggregate elements.

5. The uncertainty quantification analysis method of the three-phase mesoscopic finite element of the full-grade concrete according to claim 3, characterized in that: When the numerical simulation of mechanical properties is performed, a finite element solver is called to perform the numerical simulation of mechanical properties.

6. The uncertainty quantification analysis method of the three-phase mesoscopic finite element of the full-grade concrete according to claim 5, characterized in that: When the numerical simulation of mechanical properties is performed, based on the three-phase finite element model, uniaxial compression and tensile simulation are performed.

7. The uncertainty quantification analysis method of the three-phase mesoscopic finite element of the full-grade concrete according to claim 6, characterized in that: When the uncertainty quantification and correlation analysis are performed, macroscopic mechanical property indexes are extracted, including elastic modulus, compressive strength, axial tensile strength, and ultimate tensile strain; For the macroscopic mechanical property indexes of all samples, the sample mean, sample standard deviation, and coefficient of variation of each index are calculated, the correlation between the dispersion of the macroscopic mechanical property indexes and the mesoscopic structure characteristic parameters is quantitatively analyzed through correlation analysis, regression analysis, or visualization chart methods, and the uncertainty quantification analysis is completed.

8. A system for performing the uncertainty quantification analysis of full-graded concrete three-phase meso-finite elements according to claim 1, characterized by, It comprises: A three-phase finite element model construction module is configured to generate a reference finite element grid based on the obtained three-dimensional mesostructure sample, divide three-phase material units by identifying aggregate area nodes, and assign corresponding material constitutive models to the divided three-phase units to form a three-phase finite element model corresponding to the three-dimensional mesostructure sample, and perform numerical simulation of mechanical properties; A quantitative analysis module is configured to batch extract macroscopic mechanical performance indicators from the simulation results and perform uncertainty quantification and correlation analysis.

Images