A concrete mesoscopic mechanics discrete element simulation method containing coal gangue instead of aggregate

Abstract

This invention discloses a discrete element method for simulating the micromechanics of concrete using coal gangue as an alternative aggregate, belonging to the field of geotechnical engineering and discrete element numerical simulation technology. The method includes: generating an initial set of spherical particles and constructing a homogeneous equilibrium sample; applying prestress through servo feedback to achieve equilibrium; importing a real crushed stone STL model to generate an irregular Clump template, proportionally replacing the spheres in situ with coal gangue and natural aggregate Clumps; employing a parallel bonding model and assigning differentiated mechanical parameters, then randomly reducing the strength of some contact bonds proportionally to simulate micro-defects; performing uniaxial compression loading, simultaneously monitoring the stress-strain curve, and tracking microcrack evolution based on DFN. This invention significantly improves the accuracy of the simulation through irregular aggregate reconstruction, differentiated parameter assignment of multi-material components, and a random weak contact algorithm, realistically reproducing the mechanical response and failure mode of permeable concrete made from coal gangue, providing a reliable numerical tool for the resource utilization of solid waste.

Description

Technical Field

[0001] This invention relates to the fields of geotechnical engineering and discrete element numerical simulation, and in particular to a discrete element simulation method for the micromechanics of concrete with coal gangue as an alternative aggregate. Background Technology

[0002] With the advancement of sponge city construction and ecological environmental protection concepts, permeable concrete has been widely used due to its excellent water permeability, air permeability, and sound absorption properties. Traditional permeable concrete, having removed fine aggregate (with little or no sand), relies primarily on the cement paste on the surface of coarse aggregates to interlock and bond, forming a continuous pore-structured skeleton-pore structure. Meanwhile, in response to the national call for "resource utilization of bulk industrial solid waste," incorporating solid waste such as coal gangue as coarse aggregate to partially or completely replace natural crushed stone in permeable concrete has become a current research hotspot in the building materials field.

[0003] However, the macroscopic mechanical properties of permeable concrete are greatly affected by its internal microstructure, and traditional physical tests are time-consuming and difficult to observe the internal damage evolution process. Therefore, researchers often use discrete element method (DEM) software (such as PFC3D) to perform micromechanical simulations.

[0004] While existing discrete element simulation techniques have made some progress, some shortcomings still exist: 1) The morphological representation of aggregates is too idealized: most of them directly use standard three-dimensional spheres or simple combinations to represent real aggregates, ignoring the edges and irregular shapes of real aggregates, which leads to distortion of mechanical interlocking effect and internal friction angle, and the simulation results deviate significantly from reality.

[0005] 2) Single material property setting: Treating all aggregates as a homogeneous and uniform material system, and assigning a uniform particle stiffness and density globally, makes it impossible to distinguish the significant differences between natural aggregates and coal gangue in terms of density, elastic modulus, strength, etc. This results in the inability to accurately simulate the non-uniform transmission of stress in complex multi-element aggregate systems, and also makes it impossible to accurately capture the damage phenomenon caused by the crushing of coal gangue aggregates themselves.

[0006] 3) Over-homogenization of the cementation model: All contacts between aggregates are assigned uniform and homogeneous parallel bonding model parameters, ignoring the "weak bonding" defects caused by uneven cement paste coating in actual molding. This results in an artificially high simulated strength and fails to reproduce the real failure mode in permeable concrete, where "cracks originate from local weak bonding defects, gradually extend along the weak interface, and bypass high-strength aggregates".

[0007] Therefore, there is an urgent need for a discrete element method that can accurately represent aggregate morphology, distinguish the properties of multi-source aggregates, and simulate micro-cementation defects. Summary of the Invention

[0008] The purpose of this invention is to provide a discrete element method for simulating the micromechanics of concrete with coal gangue as an alternative aggregate, in order to solve the problems of idealized aggregate shape, single material properties, and overly homogenized cementation model in existing discrete element simulations, and to achieve high-precision simulation of the mechanical properties and fracture mechanism of permeable concrete with coal gangue.

[0009] To achieve the above objectives, this invention provides a discrete element method for simulating the micromechanics of concrete using coal gangue as an alternative aggregate, comprising the following steps: Step 1: Generate an initial set of spherical particles in three-dimensional space. After boundary trimming and iterative calculation, construct a homogeneous equilibrium sample with a set porosity as the initial spherical model. Step 2: Apply multi-directional target pre-stress to the initial model through a servo feedback mechanism to bring the model to a state of force equilibrium. Step 3: Import the pre-acquired three-dimensional geometric model of real aggregates, generate an irregular Clump template, and use a random algorithm to replace the spheres in the model obtained in Step 2 with coal gangue Clumps and natural aggregate Clumps in situ according to a preset ratio. Step 4: Using a parallel bonding model, differentiated mechanical parameters are assigned to coal gangue Clump and natural aggregate Clump respectively, and contact bonds are randomly selected according to a preset ratio for strength reduction to simulate microscopic heterogeneity. Step 5: Then, apply displacement-controlled uniaxial compression loading to the model processed in Step 4, simultaneously monitor the macroscopic stress-strain curve, and track the initiation and evolution of microcracks based on discrete crack network technology to obtain simulated mechanical response data.

[0010] Preferably, in step 1, the porosity is set to 0.25, and the sphere radius distribution range is 5.5mm~6.5mm; The three-dimensional space is a 150mm×150mm×150mm cube area enclosed by six rigid walls.

[0011] Preferably, in step 2, the multi-directional target preload stress is a stress of 2.0 MPa applied in the X, Y, and Z directions respectively.

[0012] Preferably, in step 3, the preset ratio is: coal gangue clumps account for 70%, and natural aggregate clumps account for 30%; the density of coal gangue clumps is 2400 kg / m³. 3 Natural aggregate Clump density 2700 kg / m³ 3 .

[0013] Preferably, in step 3, the three-dimensional geometric model of the real aggregate is an STL format model obtained by scanning real crushed stone, with four different forms; the irregular Clump template is generated by the surfcalcbubblepack algorithm, and each Clump is randomly assigned three-dimensional rotation Euler angles and spatial coordinate axes during replacement.

[0014] Preferably, in step 4, the differentiated mechanical parameters include: For natural aggregate Clump: the effective modulus of parallel bond is 30.0 GPa, the friction angle of parallel bond is 30°, and the coefficient of friction of parallel bond is 1.0; For coal gangue Clump: the effective modulus of parallel bonding is 15.0 GPa, the friction angle of parallel bonding is 25°, and the coefficient of friction of parallel bonding is 0.4.

[0015] Preferably, in step 4, randomly selecting contact bonds for strength reduction according to a preset ratio specifically involves using the Monte Carlo random sampling method to multiply the tensile strength and cohesion of 20% of the randomly distributed contact bonds in the model by a reduction factor of 0.55.

[0016] Preferably, in step 5, the displacement-controlled uniaxial compression loading specifically involves: releasing the servo confining pressure in the horizontal X and Y directions, and applying a 1×10⁻⁶ pressure to the top loading plate. -2 Compression is achieved at a constant normal velocity of mm / s.

[0017] Preferably, in step 5, tracking the initiation and evolution of microcracks based on discrete crack network technology includes: capturing the three-dimensional spatial coordinates and normal vector of the failure contact point in real time, calculating the inclination angle and tendency of the microcrack, determining whether it is tensile failure or shear failure according to the failure mode, and generating a microcrack disk using discrete crack network.

[0018] Preferably, the method further includes a verification step: comparing the simulation results obtained in step 5 with the measured data from physical experiments to verify the consistency between the simulation results and real concrete; the comparison includes numerical error analysis of compressive strength, comparison of the fit of stress-strain curve morphology, and similarity assessment of crack failure modes.

[0019] Therefore, the discrete element method for micromechanical simulation of concrete containing coal gangue as an alternative aggregate, as described in this invention, has the following beneficial effects: (1) Realistic reproduction of irregular geometric features of aggregates: By using an irregular Clump template to replace the spheres in situ according to coordinates and volume ratio, the real irregular geometric shape of aggregates in permeable concrete is reproduced, effectively restoring the mechanical interlocking effect and internal friction angle between aggregates, making the simulated contact force chain distribution, shear resistance and macroscopic strength closer to the physical test results.

[0020] (2) Realize differentiated and refined modeling of multi-source aggregates: A material property grouping algorithm based on random probability is proposed, which can accurately control the proportion of coal gangue in the discrete element model and assign different density and mechanical parameters to coal gangue and natural aggregates respectively, thus realizing refined modeling of heterogeneous material systems and accurately simulating the non-uniform transmission of stress between strong and weak aggregates.

[0021] (3) Reconstructing microscopic defects caused by uneven cement paste coating: A stochastic weak contact algorithm is proposed to introduce a "strength reduction factor" with a certain probability inside the model. This algorithm successfully simulates the initial weak bonding defects caused by uneven cement paste coating inside real permeable concrete. The cracks in the numerical simulation start from the weak bonding surface and gradually expand. The failure mode is highly consistent with the real physical test, which significantly improves the accuracy of the simulated compressive strength.

[0022] (4) Promote the utilization of solid waste resources: This invention supports the mechanical evaluation and proportion optimization of coal gangue as an alternative aggregate concrete through simulation, providing a technical path to reduce the surface stockpiling of coal gangue and alleviate the ecological pressure caused by solid waste accumulation, and has significant environmental protection and engineering application value.

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 This is a technical roadmap for the discrete element simulation method of concrete micromechanics with coal gangue as aggregate in an embodiment of the present invention. Figure 2 This is a schematic diagram of the STL model corresponding to real crushed stone in an embodiment of the present invention; Figure 3 This is a schematic diagram of the model after replacing the spheres with irregular Clumps in an embodiment of the present invention; Figure 4 This is a schematic diagram of the Contact key according to an embodiment of the present invention; Figure 5 The stress-strain curves simulated under uniaxial compressive loading according to an embodiment of the present invention are shown below. Figure 6 This is a schematic diagram of the evolution of internal microcracks during the simulation process of an embodiment of the present invention; Figure 7 This is a comparison diagram of stress-strain curves from simulation and physical experiments in an embodiment of the present invention. Detailed Implementation

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0027] Example This embodiment uses PFC3D discrete element software as a platform and employs the built-in FISH language to write control code, but the present invention is not limited to this software.

[0028] Please see Figure 1 This includes the following steps: Step 1: Initial homogeneous particle assembly: Based on the discrete element method, an initial homogeneous spherical particle sample is first constructed in three-dimensional physical space.

[0029] The basic model dimensions are set to 150mm × 150mm × 150mm. A six-sided rigid wall is generated using the `wall generate box` command as the boundary condition. A set of spherical particles with a porosity of 0.25 and a radius distribution of 5.5mm to 6.5mm is generated using the radius enlargement method. After 1000 mechanical cycles, cubic particles exceeding the wall boundaries are automatically searched and deleted using a spatial coordinate range reference to obtain the initial homogeneous spherical model.

[0030] Step 2: Isotropic servo pre-compression and system consolidation: To eliminate the initial excessive overlap between particles and simulate the initial compaction of real samples, a servo feedback mechanism is introduced.

[0031] Servo control was applied to the walls in the X, Y, and Z directions, with a target preload stress of 2.0 MPa. During startup, the contact forces on the walls were calculated by extracting the walls and calculating their contact area in real time. The current wall force was calculated, and the servo speed of each wall was dynamically adjusted based on stiffness feedback until the model reached force equilibrium. To prevent divergence, a lower limit protection for contact stiffness was set (a maximum value of 1e10 was assigned when the total stiffness was 0). Initial excessive overlap was eliminated to obtain a compacted spherical model.

[0032] Step 3: Replacement of complex irregular aggregates based on real three-dimensional morphology.

[0033] like Figure 2To accurately recreate the morphology of coarse aggregate within high-density concrete, surface non-data of real crushed stone was extracted. Four different morphologies of crushed stone were imported into STL 3D geometric models, and corresponding Clump (regular cluster) templates were generated using surfcalc bubblepack. A random number mechanism (math.random.uniform) was introduced, and a random replacement algorithm was written: iterating through all spheres in the compacted model, 70% of them were replaced with coal gangue Clumps (density 2400 kg / m³). 3 With a 30% probability, it will be replaced with natural aggregate Clump (density 2700 kg / m³). 3 Then, the STL template is copied as a Clump at a specified position, diameter, and rotation angle using the clumpreplicate command, and then grouped into the template name group and the material type group respectively. The model after replacement is shown below. Figure 3 .

[0034] Step 4: Heterogeneity of binary cement constitutive properties and microstructure strength.

[0035] The internal contact of the model adopts a linear parallel bond model (linearpbond). The differentiated mechanical parameters shown in Table 1 are assigned to natural aggregate Clump and coal gangue Clump, respectively.

[0036] Table 1: Differentiated Mechanical Parameters

[0037] Natural aggregates, acting as the primary load-bearing support, contribute higher strength, while coal gangue contributes lower elastic modulus and tensile strength. To accurately represent the heterogeneous distribution characteristics of the model, a function called `Two_Strength_fenbu` is implemented. Using Monte Carlo random sampling, a random number `rand_val` is generated for each contact. If `rand_val` < 0.20, a reduction factor `factor = 0.55` is set. Then, the tensile strength `pb_ten` and cohesion `pb_coh` of the current contact are read, multiplied by `factor`, and reassigned, reducing the strength of approximately 20% of the contact bonds in the model by 45%. A schematic diagram of the contact bonds is shown below. Figure 4 As shown (black indicates weak contact bonds, gray indicates strong contact bonds).

[0038] Step 5: Uniaxial compression loading and microscopic fracture mechanism tracking.

[0039] Release the servo confinement pressure in the X and Y directions (set the X and Y direction confinement pressure to 0.0), and apply a 1×10 to the top loading plate (the wall with ID=2). -2 Uniaxial compression is performed at a constant normal velocity of mm / s. The wall reaction force is monitored in real time, and the stress-strain curve is calculated (e.g., ...). Figure 5(As shown). In this process, a fracture capture mechanism is constructed. When the parallel bond model reaches its ultimate strength and fractures, the fracture location (three-dimensional spatial coordinates) and normal vector of the failure contact point are captured in real time, and the inclination and tendency of the microcracks are calculated. Based on the failure mode determination (tensile failure mode=1 or shear failure mode=2), a discrete crack network (DFN) is used to generate and record microcrack disks with real spatial properties in real time. The final compressive strength is approximately 30 MPa.

[0040] Throughout the process, crack detection was implemented. First, the save interval was set to baocunpinlv=0.01, and the initial time was recorded as time_record=mech.age. In the savefile function, whenever the difference between the current calculation time mech.age and the last save time exceeds 0.01, incrementally incrementing filenames such as jieguo0, jieguo1, etc., were generated, and the save command was executed to save the model, while simultaneously updating the time record. Finally, setfishcallback-1.0@savefile was used to automatically call this function after each time step, thus achieving periodic automatic archiving. Cracks were detected at each time interval, and the cracking process of the model at each time interval was as follows... Figure 6 As shown.

[0041] The simulated stress-strain curves, compressive strength values, and final crack morphology were compared with the results of physical tests in the same batch. For example, the stress-strain curves were compared... Figure 7 As shown.

[0042] The results show that the compressive strength error is less than 5%, and the failure mode of crack initiation from the weakly cemented area and propagation around the aggregate is highly consistent with the physical test, verifying the effectiveness of the method.

[0043] Therefore, this invention employs the aforementioned discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate. Specifically for permeable concrete with coal gangue as an alternative aggregate, it proposes a complete discrete element modeling method encompassing aggregate geometry reconstruction, material property differentiation, and microscopic defect simulation. This method effectively overcomes the three major defects of traditional simulations: idealized aggregate shape, homogenized materials, and homogenized cementation. It significantly improves simulation accuracy and the ability to reproduce failure modes, providing a highly reliable numerical platform for the mechanical evaluation and mix design optimization of solid waste concrete. Furthermore, it is not limited to a specific single particle size; researchers only need to change the particle size distribution parameters of the Clump template to quickly construct numerical specimens under different gradation schemes. This provides an efficient platform for exploring the coupling relationship between "aggregate particle size" and "coal gangue substitution rate," greatly saving the labor costs of sieving and gradation combination in physical experiments, and providing scientific microscopic guidance for the mix design optimization of coal gangue concrete.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A discrete element method for micromechanical simulation of concrete using coal gangue as aggregate substitute, characterized in that, Includes the following steps: Step 1: Generate an initial set of spherical particles in three-dimensional space. After boundary trimming and iterative calculation, construct a homogeneous equilibrium sample with a set porosity as the initial spherical model. Step 2: Apply multi-directional target pre-stress to the initial model through a servo feedback mechanism to bring the model to a state of force equilibrium. Step 3: Import the pre-acquired three-dimensional geometric model of real aggregates, generate an irregular Clump template, and use a random algorithm to replace the spheres in the model obtained in Step 2 with coal gangue Clumps and natural aggregate Clumps in situ according to a preset ratio. Step 4: Using a parallel bonding model, differentiated mechanical parameters are assigned to coal gangue Clump and natural aggregate Clump respectively, and contact bonds are randomly selected according to a preset ratio for strength reduction to simulate microscopic heterogeneity. Step 5: Then, apply displacement-controlled uniaxial compression loading to the model processed in Step 4, simultaneously monitor the macroscopic stress-strain curve, and track the initiation and evolution of microcracks based on discrete crack network technology.

2. The discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate, as described in claim 1, is characterized in that: In step 1, the porosity is set to 0.25, and the sphere radius distribution range is 5.5mm~6.5mm.

3. The discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate according to claim 2, characterized in that: In step 2, the multi-directional target preload stress is a stress of 2.0 MPa applied in the X, Y, and Z directions respectively.

4. The discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate according to claim 3, characterized in that: In step 3, the preset ratio is: 70% coal gangue and 30% natural aggregate.

5. The discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate according to claim 4, characterized in that: In step 3, the three-dimensional geometric model of the real aggregate is an STL format model obtained by scanning real crushed stone, with four different shapes; the irregular Clump template is generated by the surfcalcbubblepack algorithm, and each Clump is randomly assigned three-dimensional rotation Euler angles and spatial coordinate axes during replacement.

6. The discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate according to claim 5, characterized in that: In step 4, the differentiated mechanical parameters include: For natural aggregate Clump: the effective modulus of parallel bond is 30.0 GPa, the friction angle of parallel bond is 30°, and the coefficient of friction of parallel bond is 1.0; For coal gangue Clump: the effective modulus of parallel bonding is 15.0 GPa, the friction angle of parallel bonding is 25°, and the coefficient of friction of parallel bonding is 0.

4.

7. The discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate, as described in claim 6, is characterized in that: In step 4, the contact bonds are randomly selected according to a preset ratio for strength reduction. Specifically, the Monte Carlo random sampling method is used to multiply the tensile strength and cohesion of 20% of the contact bonds randomly distributed in the model by a reduction factor of 0.

55.

8. The discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate according to claim 7, characterized in that: In step 5, the displacement-controlled uniaxial compression loading specifically involves: releasing the servo confining pressure in the horizontal X and Y directions, and applying a 1×10⁻⁶ pressure to the top loading plate. -2 Compression is achieved at a constant normal velocity of mm / s.

9. The discrete element method for micromechanical simulation of concrete with coal gangue as an alternative aggregate, as described in claim 8, is characterized in that: In step 5, tracking the initiation and evolution of microcracks based on discrete crack network technology includes: capturing the three-dimensional spatial coordinates and normal vector of the failure contact point in real time, calculating the inclination angle and tendency of the microcrack, determining whether it is tensile failure or shear failure according to the failure mode, and generating microcrack disks using discrete crack network.

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