A random discrete element-based concrete spatial variability simulation method and system

Abstract

This invention relates to a method and system for simulating the spatial variability of concrete based on stochastic discrete element method (DEM). The method includes: modeling the concrete material using the DEM based on the Monte Carlo approach, assigning a corresponding particle contact model according to the material's mechanical characteristics; using a random seed number to characterize the random distribution of aggregates; simulating the spatial distribution characteristics of strength parameters between particles using Monte Carlo simulation based on the random aggregates; and introducing a random field into the spatial variation of strength parameters, changing the internal strength spatial distribution of the material through different random parameters. Compared with existing technologies, the numerical simulation method of this invention, based on the DEM and employing a coupling of direct and indirect methods, fully considers the random distribution of aggregates and the spatial variation of strength parameters in concrete materials, and can better reproduce the mechanical variability characteristics of concrete materials.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology, and in particular to a method and system for simulating the spatial variability of concrete based on stochastic discrete elements. Background Technology

[0002] Concrete is a typical anisotropic composite material. Due to the random distribution of internal aggregates, microcracks, and nanopores, the macroscopic mechanical parameters of concrete, such as uniaxial compressive strength, elastic modulus, tensile strength, fracture toughness, and fracture energy, exhibit significant dispersion. In practical engineering, due to the non-homogeneity of large-volume concrete and the inhomogeneity of the pouring process, the strength parameters of concrete gravity dams exhibit obvious randomness and variability. For example, during strong earthquakes, gravity dams typically develop cracks at weak points such as the neck, upstream face, and heel. These factors determine the actual load-bearing capacity and reliability of concrete, the performance assessment of the structure during earthquakes, and the seismic performance and mechanical response of gravity dams.

[0003] Current simulations of the uncertainty and variability of concrete properties are mostly based on the Monte Carlo method, employing either direct or indirect approaches. Direct methods directly simulate the random shape, distribution, fiber distribution, and distribution of cracks, voids, and defects in concrete to reflect the dispersion of macroscopic mechanical parameters. Indirect methods introduce random fields to simulate the random distribution of parameters such as strength in the numerical model, reflecting the dispersion of macroscopic mechanical parameters. However, the heterogeneous nature of concrete is the result of the combined effects of multiple factors, including aggregate, microcracks, nanopores, cement matrix strength variability, interfacial transition zone strength variability, and size. Simply using either direct or indirect methods only considers the influence of one type of factor on the mechanical properties of concrete and cannot accurately reflect its heterogeneity and spatial variability. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method and system for simulating the spatial variability of concrete based on random discrete elements.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for simulating the spatial variability of concrete based on stochastic discrete element method includes the following steps:

[0007] S1. Based on the Monte Carlo method, random discrete element method is used to model concrete material. According to the mechanical characteristics of concrete material, the corresponding particle contact model is selected to simulate the mechanical properties of concrete and the propagation and initiation of cracks.

[0008] S2. Based on the heterogeneous characteristics of concrete materials, characterize the random distribution of aggregates inside the concrete material;

[0009] S3. Generate and calculate multiple samples, select a specific proportion of samples for micro-parameter calibration, and use the calibrated micro-parameters to simulate the stress-strain curves of the remaining samples.

[0010] S4. Based on the random distribution of the aggregate, a random field is used to perform a random analysis on the spatial variability of the bond strength between concrete material particles.

[0011] S5. Determine the minimum number of simulations based on the number of simulations corresponding to the convergence of the random distribution of aggregates and the Monte Carlo simulation number curve;

[0012] S6. Select the random aggregate distribution corresponding to the upper and lower limits of the stress-strain curve obtained in step S3, consider the combined influence of different spatial variation parameters on the spatial variability of the material, and determine reasonable variation parameter values ​​based on the principle of matching the numerical simulation results with the experimental results, and simulate the concrete stress-strain curve considering the influence of spatial variation parameters.

[0013] Furthermore, in step S2, the random seed number is used to characterize the random distribution of aggregates inside the concrete material.

[0014] Furthermore, in step S3, selecting a specific proportion of samples for micro-parameter calibration specifically involves: comparing the peak load calculated by numerical simulation with the experimental results to calibrate the input micro-parameters;

[0015] The stress-strain curves of the remaining samples were obtained by simulating the calibrated micro parameters. Specifically, uniaxial compression tests were simulated on the remaining samples using the calibrated micro parameters, and the stress-strain curves of concrete with different random aggregates were analyzed to obtain the range and limit of the uniaxial compressive strength of concrete with random aggregates.

[0016] Furthermore, in step S4, a random field analysis is performed on the spatial variability of the material's internal strength parameters, including the following steps:

[0017] The autocorrelation function is chosen as follows:

[0018]

[0019] In the formula, δ x δ represents the horizontal fluctuation scale. y The vertical fluctuation scale value; Δx rs Let Δy be the distance between any two points of interest in the horizontal direction. rs The distance between any two points of interest in the vertical direction;

[0020] A series of random fields are generated by expanding the KL transform.

[0021] Furthermore, in step S6, the different spatial variation parameters include the coefficient of variation (COV) and the fluctuation scale (SOF).

[0022] A simulation system for spatial variability of concrete based on stochastic discrete element method includes a model building module, an aggregate distribution characterization module, a parameter calibration module, a spatial variability analysis module, and a mechanical property analysis module.

[0023] The model building module is used to model concrete materials based on the Monte Carlo method and using random discrete elements. According to the mechanical characteristics of concrete materials, a corresponding particle contact model is selected to simulate the mechanical properties of concrete and the propagation and initiation of cracks.

[0024] The aggregate distribution characterization module is used to characterize the random distribution of aggregates inside concrete materials based on the heterogeneous characteristics of concrete materials.

[0025] The parameter calibration module is used to generate and calculate multiple samples, select a specific proportion of samples for micro-parameter calibration, and use the calibrated micro-parameters to simulate the stress-strain curves of the remaining samples.

[0026] The spatial variability analysis module is used to perform random analysis on the spatial variability of the bond strength between concrete material particles based on the random distribution of aggregates and using a random field; and to determine the minimum number of simulations based on the number of simulations corresponding to the convergence of the random distribution of aggregates and the Monte Carlo simulation number curve.

[0027] The mechanical property analysis module is used to select the random aggregate distribution corresponding to the upper and lower limits of the simulated stress-strain curve, consider the combined influence of different spatial variation parameters on the spatial variability of the material, determine reasonable variation parameter values ​​based on the principle of matching numerical simulation results and experimental results, and simulate the concrete stress-strain curve considering the influence of spatial variation parameters.

[0028] Furthermore, in the aggregate distribution characterization module, the random seed number is used to characterize the random distribution of aggregates inside the concrete material.

[0029] Furthermore, in the parameter calibration module, selecting a specific proportion of samples for micro-parameter calibration specifically involves comparing the peak load calculated by numerical simulation with the experimental results to calibrate the input micro-parameters.

[0030] The stress-strain curves of the remaining samples were obtained by simulating the calibrated micro parameters. Specifically, uniaxial compression tests were simulated on the remaining samples using the calibrated micro parameters, and the stress-strain curves of concrete with different random aggregates were analyzed to obtain the range and limit of the uniaxial compressive strength of concrete with random aggregates.

[0031] Furthermore, in the spatial variability analysis module, a random field is used to perform a random analysis on the spatial variability of the material's internal strength parameters, including the following steps:

[0032] The autocorrelation function is chosen as follows:

[0033]

[0034] In the formula, δ x δ represents the horizontal fluctuation scale. y The vertical fluctuation scale value; Δx rs Let Δy be the distance between any two points of interest in the horizontal direction. rs The distance between any two points of interest in the vertical direction;

[0035] A series of random fields are generated by expanding the KL transform.

[0036] Furthermore, in the mechanical property analysis module, the different spatial variation parameters include the coefficient of variation (COV) and the wave scale (SOF).

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] This invention employs a combination of direct and indirect methods. Based on the random distribution of aggregates, it utilizes the Monte Carlo method to introduce a random field to simulate the spatial variability of concrete. This achieves accurate simulation of the heterogeneity and spatial variability of strength parameters in concrete, effectively reproducing the mechanical variation characteristics of concrete materials and providing a more accurate reference. It overcomes the shortcomings of existing technologies that simply use direct or indirect methods, which cannot accurately reflect the heterogeneity and spatial variability of concrete. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0040] Figure 2 This refers to the force-displacement relationship in the linear softening bonding model of this invention.

[0041] Figure 3 This is a schematic diagram of the random distribution of aggregates in an embodiment of the present invention;

[0042] Figure 4 This is the convergence curve of the uniaxial compressive strength of concrete as a function of the number of samples in an embodiment of the present invention;

[0043] Figure 5 The concrete stress-strain curve obtained by random analysis in an embodiment of the present invention;

[0044] Figure 6 The effect of the coefficient of variation COV;

[0045] Figure 7 This refers to the effect of the volatility coefficient SOF. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0047] To address the shortcomings of existing technologies that fail to accurately reflect the heterogeneity and spatial variability of concrete when simply employing direct or indirect methods to simulate the uncertainty and variability of concrete properties, this invention proposes a method and system for simulating the spatial variability of concrete based on stochastic discrete element method.

[0048] The system includes a model building module, an aggregate distribution characterization module, a parameter calibration module, a spatial variability analysis module, and a mechanical property analysis module.

[0049] The model building module is used to model concrete materials based on the Monte Carlo method and using random discrete elements. According to the mechanical characteristics of concrete materials, the corresponding particle contact model is selected to simulate the mechanical properties of concrete and the propagation and initiation of cracks.

[0050] The aggregate distribution characterization module is used to characterize the random distribution of aggregates within concrete materials based on the heterogeneous characteristics of concrete materials.

[0051] The parameter calibration module is used to generate and calculate multiple samples, select a specific proportion of samples for micro-parameter calibration, and use the calibrated micro-parameters to simulate the stress-strain curves of the remaining samples.

[0052] The spatial variability analysis module is used to perform stochastic analysis on the spatial variability of the bond strength between concrete particles based on the random distribution of aggregates and using a random field; the minimum number of simulations is determined based on the number of simulations corresponding to the convergence of the random distribution of aggregates and the Monte Carlo simulation number curve.

[0053] The mechanical property analysis module is used to select the random aggregate distribution corresponding to the upper and lower limits of the stress-strain curve obtained by simulation, consider the combined influence of different spatial variation parameters on the spatial variability of materials, determine reasonable variation parameter values ​​based on the principle of matching numerical simulation results with experimental results, and simulate the stress-strain curve of concrete considering the influence of spatial variation parameters.

[0054] Based on this system, a method for simulating the spatial variability of concrete based on stochastic discrete elements can be implemented, such as... Figure 1 As shown, the specific implementation steps of this method include:

[0055] (1) Based on the Monte Carlo method, a model is established for concrete material using the stochastic discrete element method. According to the mechanical characteristics of concrete material, a corresponding particle contact model is selected to simulate the mechanical properties of concrete and the propagation and initiation of cracks. In this embodiment, the linear softening contact model is selected.

[0056] (2) Based on the heterogeneous characteristics of concrete, considering the random distribution of aggregates within the material, the random seed number is used to characterize the random distribution of aggregates.

[0057] (3) Generate and calculate a small number of samples, and calibrate the input micro parameters by comparing the numerical simulation results and laboratory test results; use the calibrated micro parameters to simulate uniaxial compression tests for the remaining samples, analyze the stress-strain curves of concrete with different random aggregates, and obtain the range and limit of uniaxial compressive strength of concrete with random aggregates.

[0058] (4) Based on the random aggregate distribution, random fields are used to conduct random analysis on the spatial variation of the bonding strength between material particles;

[0059] (5) Determine the minimum number of simulations based on the number of simulations corresponding to the convergence of the random aggregate distribution and the Monte Carlo simulation number curve;

[0060] (6) Select the random aggregate distribution corresponding to the upper and lower limits of the stress-strain curve obtained in step (3), consider the combined influence of different spatial variation parameters on the spatial variability of concrete, determine the reasonable variation parameter value according to the principle of matching the numerical simulation calculation results and the test results, and simulate the stress-strain curve of concrete considering the influence of spatial variation parameters.

[0061] In step (4) above, a random field is used to perform a random analysis on the spatial variability of the internal strength parameters of the material. The selected autocorrelation function is:

[0062]

[0063] In the formula, δ x δ represents the horizontal fluctuation scale. y The vertical fluctuation scale value; Δx rs Let Δy be the distance between any two points of interest in the horizontal direction. rs Let be the distance between any two points of interest in the vertical direction; use the KL (Karhunen-Loève) transform to generate a series of random fields.

[0064] In step (6) above, different spatial variation parameters are considered, including the coefficient of variation (COV) and the fluctuation scale (SOF).

[0065] The following is a preferred embodiment of the present invention:

[0066] The spatial variability of uniaxial compressive strength and failure mechanism of self-compacting concrete were simulated using the discrete element method (PFC2D). The steps included are as follows:

[0067] (1) Based on the uniaxial compression characteristics of self-compacting concrete, concrete typically exhibits tensile softening during the failure process under load. To simulate the failure process of test specimens, a linear softening-bond model based on a softening-bond model is used to simulate the mechanical properties of concrete. For example... Figure 2 As shown, this is the force-displacement relationship in the linear softening bond model. In the linear softening bond model, when the bond strength between the contact points exceeds the normal bond strength Cn, the contact enters the softening bond contact state.

[0068] (2) Based on the heterogeneous characteristics of concrete, considering the random distribution of aggregates within the material, the random seed number is used to characterize the random distribution of aggregates, such as... Figure 3 The diagram shows the random distribution of aggregates. One hundred samples were generated and calculated. The calculated uniaxial compressive strength (UCS) was used to calibrate the input microscopic parameters, and these values ​​are shown in Table 1. Based on the calibrated micromechanical parameters, the stress-strain relationship for the analysis was simulated.

[0069] Table 1. Microscopic parameters after calibration.

[0070]

[0071]

[0072] (3) Further research was conducted on the influence of random aggregate distribution on self-compacting concrete. 200 samples were generated using 200 different random seed numbers. The simulated samples were 10 cm wide and 30 cm high. Further simulations were performed on the 200 random aggregate specimens. The results of laboratory testing and random aggregate analysis are shown in Table 2. The uniaxial compressive strength of the concrete obtained from the simulated random aggregate samples was 31.37-39.15 MPa, which does not cover the actual test results.

[0073] Table 2 Results of laboratory tests and random aggregate analysis

[0074]

[0075] (4) The convergence of Monte Carlo simulations with different aggregate distributions is similar. As the number of simulations increases, the average UCS tends to converge. When the number of simulations approaches 200, the change in UCS is limited, such as... Figure 4 As shown. Therefore, in the following analysis, each scheme needs to consider 200 MCS operations.

[0076] (5) Selecting the random aggregate distribution corresponding to the maximum UCS value on the stress-strain curve, and considering the combined influence of different COV and SOF values ​​on the spatial variability of bond strength, the COV and SOF of the self-compacting concrete were determined to be 4.5 and 800 mm, respectively, and δ x Level and δ y With the same SOF value in the vertical direction, the stress-strain curve of the self-compacting concrete was obtained through simulation, as shown below. Figure 5 As shown.

[0077] (6) Based on this, select the random aggregate corresponding to the minimum UCS value. Consider the combined influence of different COV and SOF values ​​on the spatial variability of bond strength based on the distribution of these two random aggregates. The UCS (COV) value obtained by the numerical simulation is then calculated. UCS The coefficient of variation of the δ value is similar to that of the laboratory test results, and the COV and SOF of the self-compacting concrete are determined to be 4.5 and 800 mm, respectively. x Level and δ y The stress-strain curves of self-compacting concrete under two aggregate conditions were obtained with the same SOF value in the vertical direction.

[0078] (7) Since the micro-stiffness remains unchanged, the Young's modulus of the simulated sample remains unchanged. During the 200MCS operation, the UCS range of the self-compacting concrete is 42.77MPa to 27.17MPa, as shown in Table 3, which is consistent with the UCS range of the laboratory test.

[0079] Table 3. Results of random aggregate analysis considering the combined effects of COV and SOF values.

[0080]

[0081] (8) The causes of spatial variability in concrete are studied using stochastic simulation methods. First, the influence of COV value on concrete failure modes is investigated, such as... Figure 6 As shown, the larger the COV, the greater the variation in bond strength, the smaller the minimum bond strength of concrete, the larger the maximum bond strength, the wider the range of bond strength variation, and the greater the spatial variability of concrete. This leads to a decrease in the uniaxial compressive strength of concrete, with greater differences, and more obvious crack propagation. For the same random aggregate distribution, the failure mode of concrete remains consistent across hundreds of MCS processes.

[0082] (9) such as Figure 7As shown, the spatial variation region of the internal bond strength of concrete is affected by the correlation distance. By changing the correlation distance coefficient SOF value and considering the influence of the specimen size, the UCS of concrete is the smallest when the correlation distance is about half the width of the specimen. As SOF increases, the size of the spatial distribution of the same bond strength increases, the influence of the specimen size gradually decreases, the properties of the concrete itself become more homogeneous and the UCS increases. When the SOF value exceeds 800 mm, the increase of SOF has little effect on the uniaxial compressive strength and failure mechanism.

[0083] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for simulating the spatial variability of concrete based on stochastic discrete element method, characterized in that, Includes the following steps: S1. Based on the Monte Carlo method, random discrete element method is used to model concrete material. According to the mechanical characteristics of concrete material, the corresponding particle contact model is selected to simulate the mechanical properties of concrete and the propagation and initiation of cracks. S2. Based on the heterogeneous characteristics of concrete materials, characterize the random distribution of aggregates inside the concrete material; S3. Generate and calculate multiple samples, select a specific proportion of samples for micro-parameter calibration, and use the calibrated micro-parameters to simulate the stress-strain curves of the remaining samples. S4. Based on the random distribution of the aggregate, a random field is used to perform a random analysis on the spatial variability of the bond strength between concrete material particles. S5. Determine the minimum number of simulations based on the number of simulations corresponding to the convergence of the random distribution of aggregates and the Monte Carlo simulation number curve; S6. Select the random aggregate distribution corresponding to the upper and lower limits of the stress-strain curve obtained in step S3, consider the combined influence of different spatial variation parameters on the spatial variability of materials, determine reasonable variation parameter values ​​based on the principle of matching numerical simulation results and experimental results, and simulate the concrete stress-strain curve considering the influence of spatial variation parameters. In step S3, selecting a specific proportion of samples for micro-parameter calibration specifically involves comparing the peak load calculated by numerical simulation with the experimental results to calibrate the input micro-parameters. The stress-strain curves of the remaining samples were obtained by simulating the calibrated micro parameters. Specifically, uniaxial compression tests were simulated on the remaining samples using the calibrated micro parameters, and the stress-strain curves of concrete with different random aggregates were analyzed to obtain the range and limit of the uniaxial compressive strength of concrete with random aggregates.

2. The method for simulating the spatial variability of concrete based on stochastic discrete element method according to claim 1, characterized in that, In step S2, the random seed number is used to characterize the random distribution of aggregates inside the concrete material.

3. The method for simulating the spatial variability of concrete based on stochastic discrete element method according to claim 1, characterized in that, In step S4, a random field analysis is performed on the spatial variability of the material's internal strength parameters, including the following steps: The autocorrelation function is chosen as follows: In the formula, This represents the horizontal fluctuation scale value. This represents the vertical fluctuation scale value; The distance between any two points of interest in the horizontal direction. The distance between any two points of interest in the vertical direction; A series of random fields are generated by expanding the KL transform.

4. The method for simulating the spatial variability of concrete based on stochastic discrete element method according to claim 1, characterized in that, In step S6, the different spatial variation parameters include the coefficient of variation (COV) and the fluctuation scale (SOF).

5. A simulation system for the spatial variability of concrete based on stochastic discrete element method, characterized in that, It includes a model building module, an aggregate distribution characterization module, a parameter calibration module, a spatial variability analysis module, and a mechanical property analysis module; The model building module is used to model concrete materials based on the Monte Carlo method and using random discrete elements. According to the mechanical characteristics of concrete materials, a corresponding particle contact model is selected to simulate the mechanical properties of concrete and the propagation and initiation of cracks. The aggregate distribution characterization module is used to characterize the random distribution of aggregates inside concrete materials based on the heterogeneous characteristics of concrete materials. The parameter calibration module is used to generate and calculate multiple samples, select a specific proportion of samples for micro-parameter calibration, and use the calibrated micro-parameters to simulate the stress-strain curves of the remaining samples. The spatial variability analysis module is used to perform random analysis on the spatial variability of the bond strength between concrete material particles based on the random distribution of aggregates and using a random field; and to determine the minimum number of simulations based on the number of simulations corresponding to the convergence of the random distribution of aggregates and the Monte Carlo simulation number curve. The mechanical property analysis module is used to select the random aggregate distribution corresponding to the upper and lower limits of the simulated stress-strain curve, consider the combined influence of different spatial variation parameters on the spatial variability of the material, determine reasonable variation parameter values ​​based on the principle of matching numerical simulation results and experimental results, and simulate the stress-strain curve of concrete considering the influence of spatial variation parameters. In the parameter calibration module, the specific process of selecting a certain proportion of samples for micro-parameter calibration is as follows: the input micro-parameters are calibrated by comparing the peak load calculated by numerical simulation with the experimental results. The stress-strain curves of the remaining samples were obtained by simulating the calibrated micro parameters. Specifically, uniaxial compression tests were simulated on the remaining samples using the calibrated micro parameters, and the stress-strain curves of concrete with different random aggregates were analyzed to obtain the range and limit of the uniaxial compressive strength of concrete with random aggregates.

6. The concrete spatial variability simulation system based on stochastic discrete element method according to claim 5, characterized in that, In the aggregate distribution characterization module, the random seed number is used to characterize the random distribution of aggregates inside the concrete material.

7. The concrete spatial variability simulation system based on stochastic discrete element method according to claim 5, characterized in that, The spatial variability analysis module utilizes random fields to perform stochastic analysis on the spatial variability of the material's internal strength parameters, including the following steps: The autocorrelation function is chosen as follows: In the formula, This represents the horizontal fluctuation scale value. This represents the vertical fluctuation scale value; The distance between any two points of interest in the horizontal direction. The distance between any two points of interest in the vertical direction; A series of random fields are generated by expanding the KL transform.

8. A concrete spatial variability simulation system based on stochastic discrete element method according to claim 5, characterized in that, In the mechanical property analysis module, the different spatial variation parameters include the coefficient of variation (COV) and the wave scale (SOF).

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