Discrete element modeling method of composite material

Abstract

The invention discloses a discrete element modeling method for a composite material, belongs to the technical field of engineering material modeling, and aims to solve the problems of insufficient systematicness, indefinite parameter physical significance, limited applicable working conditions and long calibration time consumption existing in discrete element (DEM) simulation depending on macroscopic experiment inversion calibration interface and internal contact parameters. The method comprises three core contents of system calibration, discrete element modeling and parameter verification on a target material, basic components and composite components are calibrated step by step, multiple test means such as an unconfined compressive strength test, an indirect tensile strength test and a direct tensile test are combined, mechanical properties and contact behaviors of different components are considered, and the performance of the target material is greatly improved. The obtained contact parameters are clear in physical meaning and wide in application range, and the problems that a traditional parameter calibration method is insufficient in systematicness and poor in parameter generalization ability are effectively solved.

Description

Technical Field

[0001] This invention relates to the field of engineering material modeling technology, specifically to a discrete element modeling method for composite materials. Background Technology

[0002] Cement-stabilized crushed stone is widely used in road base construction; however, cracking of the material affects the performance of the road structure. Fiber-reinforced cement-stabilized materials exhibit excellent performance in controlling shrinkage deformation and crack growth. However, traditional macroscopic experiments are difficult to reveal the internal cracking mechanism of the material and suffer from drawbacks such as being time-consuming and having high discreteness. Currently, the Discrete Element Method (DEM) shows significant advantages in mesoscopic analysis and has become a commonly used method for studying the cracking behavior of many engineering materials.

[0003] DEMs can be used to intuitively monitor the evolution of cracks and fracture processes inside materials. However, the parameter calibration in current discrete element simulations often adopts a method based on the inversion of multiple interface parameters and internal contact parameters of the DEM model from macroscopic material experiments. This method lacks systematicity, cannot obtain material parameters with clear physical meaning, and its results are difficult to apply to various loading conditions. Moreover, the calibration process consumes a lot of time. Therefore, it is urgent to develop a systematic calibration method that combines sophisticated modeling techniques and effective parameter verification methods to construct a discrete element model that can accurately reflect the mechanical behavior of composite materials.

[0004] To address the above problems, a discrete element modeling method for composite materials is proposed. Summary of the Invention

[0005] The purpose of this invention is to provide a discrete element modeling method for composite materials. By using this invention, the problems of systematic deficiencies, unclear physical meaning of parameters, limited applicability, and long calibration time in discrete element (DEM) simulations that rely on macroscopic experimental inversion to calibrate interface and internal contact parameters are solved.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a discrete element modeling method for composite materials, comprising system calibration of the target material, discrete element modeling, and parameter verification, as detailed below: S1: Define the basic components and internal contact types of the target material: The target material is fiber-cement stabilized crushed stone, which includes three basic components: coarse aggregate, fiber, and cement stabilized sand; there are eight types of internal contact, including coarse aggregate-coarse aggregate contact, cement stabilized sand-cement stabilized sand contact, cement stabilized sand-coarse aggregate contact, cement stabilized sand-fiber contact, single fiber internal contact, fiber-fiber contact, fiber-coarse aggregate contact, and contact within the rigid cluster of coarse aggregate; S2: Simplification and determination of internal contact types of fiber cement stabilized crushed stone: Since the discrete element modeling of fiber cement stabilized crushed stone involves multiple contact types, its mechanical mechanism is complex and has many parameters. Under the premise of ensuring experimental accuracy, the modeling process is simplified by assuming that there is no contact between fibers, contact between fibers and coarse aggregates, and contact within the rigid clusters of coarse aggregates. Based on the actual physical structure and contact characteristics of the internal particles of fiber cement stabilized crushed stone, the internal contact types can be divided into eight types. After introducing the above assumptions and simplifications, five main contact types are finally retained, including coarse aggregate-coarse aggregate contact, cement stabilized sand-cement stabilized sand contact, cement stabilized sand-coarse aggregate contact, cement stabilized sand-fiber contact, and single fiber internal contact. S3: System calibration of contact parameters: The system is calibrated step by step based on the basic components and composite components. The basic components include coarse aggregate, fiber and cement stabilized sand, and the composite components include fiber cement stabilized sand and cement stabilized crushed stone. The fine parameters of each contact type are obtained through corresponding indoor and virtual tests. S4: Discrete Element Modeling: Based on the contact parameters calibrated in S3, a three-phase particle system is generated collaboratively within the geometric domain of the specimen according to the gradation ratio of coarse aggregate, fiber and cement-stabilized sand. The discrete element model of fiber cement-stabilized crushed stone is then integrated and constructed through rigid cluster reconstruction, flexible cluster transformation and contact parameter assignment. S5: Parameter Verification: The contact parameters of the constructed discrete element global model were verified using a three-point bending beam test. The validity of the parameters was verified and confirmed by comparing the load-displacement curves and crack distribution of the indoor three-point bending beam test and the virtual three-point bending beam test.

[0007] Furthermore, the specific basis for the contact type assumptions and simplifications in S2 is as follows: The fiber selected is a short chopped fiber with a length of 15mm. Since the content of short chopped fiber in fiber cement stabilized crushed stone is low, and there is a distance between the short chopped fibers, and the few short chopped fibers that are in contact with each other do not have adhesive force, it is assumed that there is no fiber-to-fiber contact. The fiber surface is coated with cement mortar, which minimizes its contact with the coarse aggregate and the two have no adhesion. Therefore, it is assumed that there is no contact between the fiber and the coarse aggregate. Meanwhile, a single coarse aggregate is characterized by a rigid cluster, in which the internal particles are consolidated into a rigid body with no relative displacement and no internal contact is generated. Therefore, it is assumed that internal contact does not exist.

[0008] Furthermore, in S3, the contact parameter calibration of the basic components includes the following: Calibration of internal contact parameters of a single fiber: A uniaxial tensile test was conducted on the virtual fiber to obtain the stress-strain curve, which reflects the tensile properties of the fiber, and the contact behavior inside the single fiber was expressed by a linear parallel bonding model. Calibrated parameters of cement-stabilized sand contact: The unconfined compressive strength test and the indirect tensile strength test were used for joint calibration to reflect the mechanical behavior of cement-stabilized sand under tension and compression, and the contact behavior between cement-stabilized sand was expressed by the flat joint model. Calibration of coarse aggregate-coarse aggregate contact parameters: Since coarse aggregates have stable properties and small differences, the micro-parameters of coarse aggregates can be directly determined from the data in the literature, and the contact behavior between coarse aggregates can be expressed by a linear model.

[0009] Furthermore, in S3, the contact parameter calibration of the composite components includes the following: Calibrating parameters of cement stabilized sand-fiber contact: The cement stabilized sand-fiber contact model is a linear parallel bonding model. Based on the contact parameters between cement stabilized sand and the internal contact of a single fiber, macroscopic mechanical parameters are obtained by using unconfined compressive strength test and indirect tensile strength test of fiber-stabilized cement sand in the laboratory. Then, the corresponding discrete element model of fiber-stabilized cement sand is established to jointly calibrate the interface parameters between cement stabilized sand and fiber, that is, the mesoscopic parameters of the linear parallel bonding model corresponding to cement stabilized sand-fiber contact. Calibrating parameters of cement-stabilized sand-coarse aggregate contact: The cement-stabilized sand-coarse aggregate contact model is a planar joint model. Based on the cement-stabilized sand-cement-stabilized sand and coarse aggregate-coarse aggregate contact parameters, macroscopic mechanical parameters are obtained by indoor unconfined compressive strength test and indirect tensile strength test of cement-stabilized crushed stone. Then, corresponding discrete element models of cement-stabilized crushed stone are established to jointly calibrate the interface parameters between cement-stabilized sand and coarse aggregate, that is, the mesoscopic parameters of the planar joint model corresponding to the cement-stabilized sand-coarse aggregate contact.

[0010] Furthermore, the specific steps for discrete element modeling in S4 are as follows: Discrete Element Overall Model Construction: First, a wall is generated based on the shape and size of the specimen. Then, within the wall area, circular particles with corresponding gradations are randomly and uniformly generated according to the gradation and proportion of coarse aggregate, fiber, and cement-stabilized sand. Rigid cluster templates are made based on the particle outline shape of each component. Then, the original circular particles are replaced according to the principle of area equivalence, and the rigid clusters are transformed into breakable flexible clusters to simulate fibers. Finally, refined modeling is achieved according to the corresponding contact type, calibration parameters, and servo loading. The irregular geometric shape of coarse aggregate is reconstructed using rigid cluster particles, and a discrete element coarse aggregate model with real geometric features is constructed. Specifically, non-uniform diameter pebbles are used to fill the space inside the rigid cluster particles according to the central axis approximation method, and the ratio of the minimum diameter to the maximum diameter is 0.15, and the particle intersection angle is 150°. Single fiber model construction: In the discrete element method, the shape of the fiber is first generated by using rigid clusters. The pebble inside the rigid cluster is rigidly connected and cannot simulate the situation where the fiber is pulled apart. Therefore, when simulating the fractured flexible fiber, the rigid cluster is transformed into a breakable flexible cluster, and a linear parallel bonding model is added for servoing, so that the fiber is bonded to the surrounding cement-stabilized sand particles. Cement stabilized sand model construction: The particle size of the sand ranges from 1.18 mm to 4.75 mm and follows a normal distribution. The cracking behavior of cement stabilized sand is captured using a flat joint model, and then cement stabilized sand particles are generated by command.

[0011] Furthermore, in S5, the specific steps for parameter verification are as follows: Indoor three-point bending beam test: Three parallel specimens were prepared as needed. After the specimens were cured, a pre-cut crack was made in the middle of the bottom. Then, a monotonic load was applied using a multi-functional hydraulic servo road material dynamic testing system, and the load-displacement curve was recorded and the cracked beam was photographed. Virtual three-point bending beam test: Based on the discrete element modeling method in S4, a three-point bending beam discrete element model of corresponding size is established, and pre-cut cracks are set at the positions corresponding to the above specimens. The same load conditions as the indoor test are applied to obtain the simulated load-displacement curves and crack distribution. Verification and comparison: By comparing the development trends and deviations of the load-displacement curves of the indoor test and the virtual test, it was found that the development trends of the two were consistent and the deviation was controlled within the preset threshold range; at the same time, the crack morphology and distribution characteristics were highly consistent, which indicates that the calibrated contact parameters are accurate and reliable.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention calibrates from basic components to composite components step by step, combining various testing methods such as unconfined compressive strength test, indirect tensile strength test and direct tensile test, taking into account the mechanical properties and contact behavior of different components. The obtained contact parameters have clear physical meanings and a wide range of applications.

[0013] 2. This invention uses rigid cluster particles to construct an irregularly shaped coarse aggregate model, accurately restoring the angular features and interlocking effect of the coarse aggregate; it transforms rigid clusters into flexible clusters to simulate fibers, taking into account the flexible bending characteristics of fibers, making it consistent with the actual fiber morphology and more realistic.

[0014] 3. The cement-stabilized sand model in this invention is based on the particle size distribution assumption, while taking into account both computational efficiency and simulation accuracy.

[0015] 4. This invention uses a three-point bending beam test, which is different from the calibration test, for verification. This test is a composite stress form, which can more comprehensively verify the applicability of the parameters under different stress states. After verification, the simulation results have small deviations from the indoor test results, and the crack distribution and propagation trend are consistent, proving the accuracy and reliability of the parameters.

[0016] 5. This invention solves the problems of lack of systematicity and narrow applicability of traditional discrete element parameter calibration methods, and provides a standardized and accurate method for discrete element modeling of composite materials. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the system calibration and verification method of the present invention; Figure 2 This is a schematic diagram of a virtual uniaxial tensile test of a single fiber according to the present invention; Figure 3 This is a schematic diagram comparing the stress-strain curves of the cement-stabilized sand indirect tensile test with the simulation results of the present invention. Figure 4 This is a schematic diagram of the uniaxial compression test failure simulation of cement-stabilized sand according to the present invention; Figure 5 This is a schematic diagram of the indirect tensile test failure simulation of cement-stabilized sand according to the present invention; Figure 6 This is a photograph of the failure mode of the cement-stabilized sand in the indirect tensile test according to the present invention. Figure 7 This is a schematic diagram comparing the stress-strain curves of the uniaxial compression test of cement-stabilized sand according to the present invention with those of the simulation. Figure 8 This is a photograph of the failure mode of the cement-stabilized sand in the uniaxial compression test of the present invention. Figure 9 This is a schematic diagram of the indirect tensile test failure simulation of fiber cement stabilized sand according to the present invention; Figure 10 This is a photograph of the failure mode of the fiber cement stabilized sand in the indirect tensile test according to the present invention. Figure 11 This is a schematic diagram comparing the stress-strain curves of the fiber cement stabilized sand in the indirect tensile test with the simulation results of the present invention. Figure 12 This is a schematic diagram of the uniaxial compression test failure simulation of fiber cement stabilized sand according to the present invention; Figure 13 This is a photograph of the failure mode of the fiber cement stabilized sand under uniaxial compression test according to the present invention. Figure 14This is a schematic diagram comparing the stress-strain curves of the uniaxial compression test of the fiber cement stabilized sand of the present invention with those of the simulation. Figure 15 This is a schematic diagram comparing the level of detail in rigid cluster modeling according to the present invention; Figure 16 This is a schematic diagram of the flexible polypropylene fiber model of the present invention; Figure 17 This is a schematic diagram of the cement-stabilized sand model of the present invention; Figure 18 This is a photograph of the three-point bending beam specimen of the present invention; Figure 19 This is a schematic diagram of the discrete element model of the three-point bending beam of the present invention; Figure 20 This is a schematic diagram of the load-displacement curves in the three-point bending test and simulation of the present invention; Figure 21 This is a comparison diagram of the failure modes in the three-point bending test of the present invention and the failure modes in the three-point bending test simulation; Figure 22 This is a schematic diagram of the method steps of the present invention. Detailed Implementation

[0018] 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 only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] To address the current technical problems in discrete element method (DEM) simulations that rely on macroscopic experimental inversion to calibrate interface and internal contact parameters, such as systematic deficiencies, unclear physical meaning of parameters, limited applicability to various operating conditions, and long calibration time.

[0020] like Figures 1-7 As shown, the following preferred technical solution is provided: a discrete element modeling method for composite materials, including systematic calibration of the target material, discrete element modeling, and parameter verification, specifically: S1: The target material is fiber cement stabilized crushed stone, which is a composite material composed of three basic components: coarse aggregate, cement stabilized sand and fiber.

[0021] The strength and stiffness of the three basic components directly affect the mechanical properties of the material.

[0022] Meanwhile, the interfacial transition zones between cement-stabilized sand and fibers, as well as between cement-stabilized sand and coarse aggregate, also affect the mechanical behavior of materials.

[0023] To systematically analyze and determine the parameters of the discrete element model, the particle contact in fiber-reinforced cement-stabilized crushed stone is classified into eight types, as follows: Based on the particle contact within fiber-cement stabilized crushed stone, it is classified into eight types: coarse aggregate-coarse aggregate contact, cement stabilized sand-cement stabilized sand contact, cement stabilized sand-coarse aggregate contact, cement stabilized sand-fiber contact, single fiber internal contact, fiber-fiber contact, fiber-coarse aggregate contact, and contact within rigid clusters of coarse aggregate.

[0024] S2: Simplification and determination of the internal contact type of fiber-cement stabilized crushed stone, as detailed below: Since the discrete element modeling of fiber cement stabilized crushed stone involves multiple contact types, its mechanical mechanism is complex and has numerous parameters; To ensure experimental accuracy, the modeling process is simplified by assuming that there are no contacts between fibers, between fibers and coarse aggregate, or within the rigid clusters of coarse aggregate. The specific steps are as follows: The fiber content in fiber cement stabilized crushed stone is relatively low, with an admixture of only 0.9 kg / m³. Furthermore, the short chopped fibers with a length of 15 mm are spaced apart from each other. The few fibers that come into contact with each other do not have adhesive force and have minimal impact on the overall mechanical properties of the material. Therefore, it is assumed that there is no fiber-to-fiber contact.

[0025] During the mixing and molding process of fiber cement stabilized crushed stone, the surface of the fiber is coated with cement stabilized sand, resulting in very little contact between the fiber and the coarse aggregate. Furthermore, the two do not have the ability to bond together and will not have a significant impact on the mechanical response of the material.

[0026] Therefore, it is assumed that there is no contact between the fiber and the coarse aggregate.

[0027] For a single coarse aggregate, a rigid cluster (Clump) is used to characterize the irregular outline of the coarse aggregate. There is no contact between the constituent particles inside the rigid cluster (Clump). Therefore, a rigid cluster (Clump) is defined as a rigid body with no relative motion inside, so it does not generate contact and does not participate in mechanical calculations.

[0028] Based on the actual physical structure and contact characteristics of the internal particles of fiber-cement stabilized crushed stone, eight types of internal contact can be classified. After introducing the above assumptions and simplifications, five main contact types are ultimately retained, as follows: As can be seen from the above description, the five contact types include coarse aggregate-coarse aggregate contact, cement stabilized sand-cement stabilized sand contact, cement stabilized sand-coarse aggregate contact, cement stabilized sand-fiber contact, and single fiber internal contact.

[0029] like Figure 1As shown in Table 1, by making the above assumptions and simplifications about contact types, while ensuring the accuracy of the model, we not only reduced the number of contact types, but also reduced the complexity of modeling and calibration, thereby improving computational efficiency.

[0030] The five contact types are as follows: Table 1. Particle Contact Types Inside Fiber Cement Stabilized Crushed Stone

[0031] S3: System calibration contact parameters: such as Figure 1 As shown, the system was calibrated step by step based on the basic components and composite components. Building upon the basic components, the interface parameters of the composite components were then calibrated. The basic components included coarse aggregate, fiber, and cement-stabilized sand, while the composite components included fiber-reinforced cement-stabilized sand and cement-stabilized crushed stone. Detailed parameters for each contact type were obtained through corresponding indoor and virtual experiments, as detailed below: During the calibration process, there is a corresponding relationship between macroscopic and microscopic parameters, such as: macroscopic Young's modulus. Subject to effective modulus and effective modulus of bonding Control; Poisson's ratio and the ratio of normal to tangential stiffness in the early stage of linear deformation They have a specific correspondence; the failure mode depends on the tensile-shear bond strength ratio.

[0032] Basic component contact parameter calibration: The basic components include coarse aggregate, fiber, and cement-stabilized sand. The calibration of their contact parameters is the basis for the calibration of composite component parameters. The specific calibration steps are as follows: Single-fiber internal contact parameter calibration: The internal contact of a single fiber is simulated using a linear parallel bonding model. The failure mechanism of this model is consistent with the fiber fracture behavior, specifically: Figure 2 As shown, a virtual single fiber was subjected to a uniaxial tensile test (UTT) at a loading rate of 1 mm / min. At the end of the loading, the bond between the spheres fractured, and the cohesion decreased. When contact disappears, a stress-strain curve can be obtained; then, based on the test results in "Synthetic Fibers for Cement Concrete and Mortar" (GB / T21120—2018), the fiber Young's modulus is determined. It reaches 5100MPa, with a uniaxial tensile strength of 574MPa and a Poisson's ratio of 0.2.

[0033] To simplify the calibration process, the following assumptions are made: tensile strength and bond strength are the same, and normal stiffness and tangential stiffness are equal (stiffness ratio...). (1) First, analyze the material parameters based on empirical values, and then adjust the effective modulus. and effective modulus of bonding The range was increased from 500 MPa to 3000 MPa, making the simulated modulus closer to the experimental results; calibration results show that the effective modulus... and effective modulus of bonding When set to 2600MPa, the Young's modulus obtained by the model The tensile strength is 5400 MPa, which is close to the experimental result of 5100 MPa; and cohesion The pressure was set to 560 MPa to ensure that the simulation results were consistent with the measured tensile strength; the friction angle... and coefficient of friction Analysis showed that the effect on tensile strength was not significant, so the friction angle was set. The angle is 45°, and the coefficient of friction is... The value was set to 0.5 to make the peak stress closer to the experimental results. The calibration results of the internal contact model of a single fiber are shown in Table 2. Table 2. Calibration results of the internal contact model of a single fiber.

[0034] Cement stabilized sand - Cement stabilized sand contact parameter calibration: The internal contact of cement stabilized sand adopts the flat joint model, which is widely used to simulate the mechanical behavior of bond cracking. The contact interface of the flat joint model is divided into independent bond units with independent bond properties, which allows the interface to crack locally and still resist friction and particle rotation after cracking, making the simulated tensile and compressive strength ratio more reasonable.

[0035] The bond model parameters of cement-stabilized sand were calibrated using a combination of indirect tensile strength testing (IDT) and unconfined compressive strength testing (UCT); such as Figures 6-7 As shown, in the indirect tensile test, a 100mm diameter arc-shaped loading bar was used, and the curvature of the loading bar surface was the same as that of the specimen, consistent with the actual test. Microcracks initiated near the edge of the loading bar, then expanded and merged, distributing along the vertical direction to form radial macrocracks, consistent with the cracking mode of the indoor indirect tensile test; as shown... Figure 3 As shown, the indoor test results indicate that Young's modulus and indirect tensile strength The effective modulus is 223.46 MPa and 1.7 MPa, respectively. and tensile strength When the values ​​are 1280MPa and 6.2MPa respectively, the stress-strain curves obtained by the discrete element model are consistent with the experimental results, indicating that the parameter is relatively accurate. This invention proves that the sensitivity of a single component to tension and compression is not consistent through tensile and compressive experiments. Then, the parameters of the single component are calibrated through multiple experiments. Compared with calibrating the parameters of a single component through a single experiment, the experimental results are more accurate.

[0036] Specifically, such as Figure 4 and Figure 8 As shown, in the unconfined compressive strength test, the failure mode of the specimen in both the indoor test and the discrete element simulation is "X" shaped. Microcracks are mainly distributed along the diagonal of the specimen and form macrocracks. The cement stabilized sand specimen bulges in the middle and some cement stabilized sand falls off the specimen along the macrocracks, which is consistent with the indoor test. like Figure 7 As shown, the cohesion was determined based on the results of indoor tests. Strength is 5.9 MPa, effective modulus When the value is 1580 MPa, the stress-strain ratio obtained from the indoor test is consistent with that obtained from the discrete element model, but the peak strength deviation is 4.0%. When effective modulus When the pressure is reduced to 1280 MPa, the errors of the simulated indirect tensile strength and unconfined compressive strength are 5.5% and 6.7%, respectively, with the smallest overall error. The ratio of normal to tangential adhesion strength It is a key parameter for controlling the cracking mode of the model. The value was set to 2.0 to ensure that the cracking mode was consistent with the indoor test. Friction angle and coefficient of friction It only takes effect after parallel adhesion failure and has a small impact on the result; setting the friction angle... The angle is 45°, and the coefficient of friction is... A value of 0.4 makes the post-peak behavior of the model more stable; the calibration results of the cement-stabilized sand-cement-stabilized sand contact model are shown in Table 3: Table 3. Calibration results of cement-stabilized sand-cement-stabilized sand contact model

[0037] Coarse aggregate-coarse aggregate contact parameter calibration: The coarse aggregate uses rigid clusters (Clump) to represent irregular contours. A rigid cluster is a collection of rigid spheres (pebble). Rigid spheres of different diameters overlap each other to approximate the boundary of the coarse aggregate model. The rigid spheres inside the rigid cluster are rigidly connected and will not deform. The rigid cluster will not break during the movement of the solid, so the contact inside the rigid cluster is ignored.

[0038] The coarse aggregate-coarse aggregate contact was simulated using a linear model (LM) because the linear spring in the linear model controls the linear elastic behavior (compression) through linear force, while the damping force controls the slippage behavior between coarse aggregates according to the Coulomb criterion. Furthermore, the point contact area of ​​the linear model is very small, which can only transmit force and not torque, consistent with the skeleton support behavior between coarse aggregates.

[0039] Since uniaxial compression cannot be used to measure aggregate-to-aggregate contact independently, and triaxial compression tests are inconsistent with indoor unconfined compressive strength tests, the microscopic parameters of coarse aggregate-to-coarse aggregate contact cannot be directly obtained through experiments. Literature review revealed that coarse aggregate properties are relatively stable with minimal variation. Therefore, the microscopic parameters of coarse aggregate-to-coarse aggregate contact are directly derived from data in the literature; that is, the linear model parameters are: effective modulus... It has a strength of 1200 MPa, a stiffness ratio of 2.0, and a coefficient of friction. It is 0.5.

[0040] Contact parameter calibration of composite components: The composite components include fiber-reinforced cement stabilized sand and cement stabilized crushed stone. The contact parameters are calibrated based on the calibration results of the basic components, and are jointly calibrated through corresponding indoor and virtual tests, as follows: Cement stabilized sand-fiber contact parameter calibration: Fiber cement stabilized sand can be regarded as a composite material, in which cement stabilized sand is the matrix and fiber is the reinforcing filler. The interface contact between cement stabilized sand and fiber is simulated by a linear parallel bonding model. There are chemical bonding and frictional bonding between fiber and cement stabilized sand, which is the essence of fiber's bridging ability and crack resistance.

[0041] Based on the contact parameters of cement-stabilized sand, a discrete element model of fiber cement-stabilized sand was established, and indirect tensile strength test and unconfined compressive strength test were carried out. like Figures 9-10 As shown, in the indirect tensile test, the macroscopic cracks propagate vertically from the center, and the indoor test results are consistent with the simulation results. Under the action of the fiber, the microcrack network becomes more dispersed in the horizontal direction, and the fiber bridging effect slows down the stress decrease trend. If loading continues, the diffuse crack quickly evolves into a macroscopic master crack, which then extends from the inside to the surface and penetrates the specimen vertically. like Figure 11 As shown, the comparison error between the experimental and simulated stress-strain curves is 9.3%; at peak stress, a rapid decrease occurs within a relatively small deformation range, which is caused by local contact failure; then stress release and the bridging effect of surrounding fibers slow down the decreasing trend; Due to the toughening effect of fibers, the indirect tensile strength of fiber-stabilized sand is higher than that of cement-stabilized sand.

[0042] The average compressive strength in the indoor tests reached 20.2 MPa, which is 34% higher than that of cement-stabilized sand. The strength deviation from the results obtained by the discrete element model was only 4.5%, and the crack network distribution was similar to... Figure 4 The phenomena observed are similar; like Figures 12-13As shown, due to the limitation of the fibers, the crack density is reduced and the distribution is more uniform, and no large-area peeling phenomenon occurs. like Figure 14 As shown, the stress reduction rate is smaller than that of cement-stabilized sand due to the fiber bridging effect, which improves the axial compressive deformation capacity.

[0043] To ensure consistency between the cracking mode in the discrete element model and the indoor test results, the ratio of normal to tangential adhesion force is... The value is 1.5; Finally, the model was fine-tuned to minimize the overall error and the friction angle. and coefficient of friction The calibration results of the cement-stabilized sand-fiber contact model at 45° and 0.5° are shown in Table 4. Table 4. Calibration results of the cement-stabilized sand-fiber contact model

[0044] Calibrating parameters of cement stabilized sand-coarse aggregate contact: Cement stabilized crushed stone uses cement stabilized sand as the matrix and coarse aggregate as the filler. The cement stabilized sand-coarse aggregate contact is simulated using a flat joint model. The interfacial mechanical behavior between the two depends on the bonding strength generated by cement hydration products. In the transition zone (ITZ), the presence of water film or pores leads to uneven porosity distribution. The gradient distribution and directional arrangement of hydration crystals make the transition zone a weak area. Essentially, it is similar to the internal bonding of cement stabilized sand, only the bonding strength is different.

[0045] Based on the contact parameters between cement-stabilized sand and coarse aggregate, a discrete element model of cement-stabilized crushed stone was established, and indirect tensile strength and unconfined compressive strength tests were conducted. In the indirect tensile test, through-cracks appeared on the surface of both the simulated and laboratory test specimens, with consistent cracking modes. The cracks first appeared at the interface between the cement-stabilized sand and coarse aggregate. As the load increased, the cracks propagated along the edge of the coarse aggregate and formed macroscopic cracks. The difference between the indirect tensile strength obtained from the discrete element simulation and the laboratory test was small (8.8%), indicating that the model can reproduce the tensile mechanical response of cement-stabilized crushed stone well. According to the test results, the elastic modulus was 208 MPa, therefore the effective modulus was... and effective modulus of bonding The tensile strength between cement-stabilized sand and coarse aggregate is set at 780 MPa and 1.22 MPa after 28 days. It is 2.8 MPa.

[0046] In the unconfined compressive strength test, cracks tend to propagate along the interface between the aggregate and cement-stabilized sand. The bulging and spalling in the middle of the specimen are similar to those observed in the laboratory test. The simulation and experimental results are close, with significant fluctuations and some deviations after the stress peak. This is due to the uneven fracture of the bond bonds during loading. The compressive strength in the laboratory test was 14.39 MPa, therefore the cohesion... It is 3.2 MPa. The ratio of normal to tangential adhesion strength. The value was set to 2.0 to ensure the cracking mode in the discrete element model was consistent with the results of laboratory experiments; finally, the model was fine-tuned to minimize the overall error and the friction angle. and coefficient of friction The values ​​are 50° and 0.4, respectively; the calibration results of the cement-stabilized sand-coarse aggregate contact model are shown in Table 5: Table 5. Calibration results of the cement-stabilized sand-coarse aggregate contact model.

[0047] Based on indoor tests, the internal contact model parameters of fiber-cement stabilized crushed stone were obtained through a systematic calibration method for the above five contact types. The results are summarized in Table 6. Table 6. Parameters of the internal contact model for fiber cement stabilized crushed stone

[0048] S4: Discrete Element Modeling: Based on the contact parameters calibrated in S3, a three-phase particle system is collaboratively generated within the specimen's geometric domain according to the gradation ratio of coarse aggregate, fiber, and cement-stabilized sand. Through rigid cluster reconstruction, flexible cluster transformation, and contact parameter assignment, a discrete element model of fiber-cement stabilized crushed stone is integrated and constructed, as detailed below: Model construction of irregularly shaped coarse aggregate: Spherical particles are more reasonable for simulating homogeneous soil or fine sand in discrete element method. However, in cement-stabilized crushed stone, coarse aggregate has a greater impact on performance. The sharp edges of the outer contour of crushed pebbles can better play the interlocking effect. If spherical particles are used directly, only the size of the particles can be expressed and the particle contour features are missing. Therefore, rigid cluster particles are used to reconstruct the irregular shape of the aggregate. That is, non-uniform diameter pebbles are used to fill the space inside the rigid cluster particles according to the central axis approximation method.

[0049] The specific modeling steps are as follows: (1) Select representative particles based on the spherical characteristics of the normal distribution; (2) Combining scanning imaging technology, the geometric shape of the particle outline is obtained through AutoCAD processing and converted into a dxf format file in PFC2D; (3) Import the geometry file into PFC to generate a template; (4) Generate coarse aggregate model using Taghavi's (2011) Bubble Pack algorithm.

[0050] like Figure 15 As shown, the statistical values ​​of coarse aggregate filling degree under different particle cross angles and diameter ratios are as follows: Particle cross angle (0 < Distance < 180°) and the ratio of minimum diameter to maximum diameter (0 < Ratio < 1) control the level of detail of the generated model; Distance (D) determines the amount of overlap between adjacent spheres, which can be used to control the smoothness of the outer contour. The closer the angle is to 180°, the closer the geometry is to the real particles; Ratio (R) determines the diameter of the smallest sphere. The smaller the ratio, the more refined the angularity.

[0051] To evaluate the quality of coarse-grained modeling, the fill degree was selected. (fill area) Compared with the actual area The ratio is used as a metric, and the specific formula is as follows: ; Table 7 shows the statistical values ​​of coarse aggregate filling degree under different particle cross angles and diameter ratios: Table 7. Statistics on Coarse Aggregate Filling Degree

[0052] To balance modeling accuracy and computational efficiency, the ratio of minimum to maximum diameter and the particle cross angle were set to 0.15 and 150°, respectively. For each grade of coarse aggregate, representative particle shapes were selected, and rigid clusters were used for geometric reconstruction. This effectively approximated the irregular shape of the real aggregate while significantly improving modeling efficiency (avoiding scanning and modeling each particle individually). The generated rigid cluster particles were then randomly placed within the specimen's geometric domain to construct a discrete element model of coarse aggregate with a phase angle of 0, balancing realism and computational feasibility. Based on these parameters, coarse particle templates for different gradations were obtained, as shown in Table 8. Table 8 Coarse Particle Templates with Different Gradation

[0053] Single fiber model construction: The fiber model consists of circular particles of equal diameter. To reduce the influence of internal stress, the circular particles do not overlap. The diameter of the circular particles is equal to the diameter of the fiber. The same, both are 0.1mm, fiber length The fiber is 15mm in diameter, therefore there are 150 particles in a single fiber.

[0054] In Discrete Element Method (DEM), the shape of the fiber is first generated using rigid clusters. However, the rigid spheres inside the rigid cluster are rigidly connected together, which cannot simulate the situation where the fiber is broken. Therefore, when simulating a breakable flexible polypropylene fiber, the rigid cluster is transformed into a breakable flexible cluster to simulate the fiber.

[0055] Traditional fiber modeling methods generate straight fibers, which are suitable for steel fibers with high elastic modulus. However, polypropylene fibers are short-cut flexible fibers. After undergoing tests such as stirring and compaction, they undergo flexible bending and adhere tightly to the surrounding cement-stabilized sand particles. If straight fibers are still used in the model, gaps will inevitably be created between them and the cement-stabilized sand particles, resulting in loss of bonding force and reducing the overall strength of the material.

[0056] The specific steps for fiber modeling are as follows: The number and location of fibers are determined by single-particle rigid clusters (Clumps); Based on the principle of volume equivalence, the original rigid cluster (Clump) is replaced with a Clump template. The rigid fibers (rigid clusters) are replaced in situ with flexible clusters (Clusters); Add linear parallel bond model parameters and apply servo control to ensure the fiber adheres to the surrounding cement-stabilized sand particles, such as... Figure 16 As shown.

[0057] Cement stabilized sand model construction: When the particle size of cement stabilized sand is small, the generated model contains a large number of tiny spherical particles, resulting in low discrete element calculation efficiency. Since particles with a particle size of less than 1.18 mm can be regarded as homogeneous viscous bodies and these particles have little impact on the simulation results, 1.18 mm is used as the minimum particle size of the discrete element model, and the particle size range is 1.18 to 4.75 mm, which follows a normal distribution. Then, the flat joint model is used to capture the cracking behavior of cement stabilized sand.

[0058] The specific steps for modeling cement-stabilized sand are as follows: Determine the single-particle Clump template and the shape of the cement-stabilized sand particles; The particle size is determined based on the gradation of cement-stabilized sand. Use the "distribute" command to generate cement-stabilized sand particles, such as... Figure 17 As shown.

[0059] Overall model assembly: Based on the material ratio and structural characteristics of fiber-cement stabilized crushed stone, the coarse aggregate model, fiber model, and cement-stabilized sand model constructed above are assembled according to the following principles: Coarse aggregate is evenly distributed in the model according to the gradation requirements to form a skeleton structure; Cement-stabilized sand particles fill the voids between coarse aggregates and coat the surface of the coarse aggregates; The fibers are randomly distributed in the cement-stabilized sand according to the required dosage and are closely bonded to the cement-stabilized sand particles. Based on the contact parameters in Table 6, the model parameters for each contact type are set to complete the construction of the discrete element model of fiber cement stabilized crushed stone, as follows: First, a boundary wall is generated based on the geometry and dimensions of the specimen. Then, within this area, circular basic particles of corresponding sizes are randomly and uniformly generated according to the target volume fractions and gradations of coarse aggregate, cement-stabilized sand, and fibers. A rigid cluster template is constructed based on the actual particle profile characteristics of each component, and the original circular particles are replaced with non-spherical rigid clusters according to the principle of area equivalence to more realistically reflect the particle morphology. Considering the flexibility and fracture characteristics of fibers, the rigid clusters characterizing the fibers are further transformed into breakable flexible clusters. Finally, by defining a corresponding contact model and applying servo-controlled loading, precise control of key microscopic characteristics such as porosity, compaction, and particle shape is achieved, allowing the fibers to deform appropriately under pressure and naturally conform to the surrounding particles.

[0060] S5: Parameter Verification: The contact parameters of the constructed discrete element global model were verified using a three-point bending beam test. The validity of the parameters was confirmed by comparing the load-displacement curves and crack distribution of the indoor three-point bending beam test and the virtual three-point bending beam test, as detailed below: Indoor three-point bending beam test: Specimen preparation: Cement content was 5% (by mass of aggregate), fiber content was 0.9 kg / m³, fiber length was 15 mm, and three parallel specimens of the three-point bending beam were prepared as a group. Specimen dimensions were: length 550 mm, width 100 mm, height 100 mm. Figure 18 As shown.

[0061] Test conditions: After curing the specimen for 28 days, a crack with a height of 20 mm and a width of 2 mm was pre-cut in the middle of the bottom. Then, a monotonic load was applied using a multi-functional hydraulic servo road material dynamic testing system. The loading point was located in the middle of the top of the beam, and the bottom support points were 0.1 times the length of the bottom edge and symmetrically distributed.

[0062] Data acquisition: Record load-displacement curves and take photos of the cracked beam to observe the failure mode and crack distribution of the specimen.

[0063] Virtual three-point bending beam test: Model Construction: Based on the discrete element modeling method in S4, and according to the size of the indoor specimens and the pre-cut joint settings, a discrete element model of a three-point bending beam of fiber cement stabilized crushed stone was established, as follows: Figure 19 As shown.

[0064] Pre-cut cracks: Pre-cut cracks are set at positions corresponding to the above-mentioned specimens.

[0065] Loading settings: Apply the same load conditions as in the indoor test to simulate the monotonic load process.

[0066] Results output: Obtain the simulated load-displacement curve and crack distribution, and statistically analyze the growth trend of the number of internal microcracks with mid-span displacement.

[0067] Verification and comparative analysis: Comparison of load-displacement curves: such as Figure 20 As shown in the figure, the load-displacement curves of the three-point bending beam are displayed, with the black and red dotted lines representing the experimental and simulation results, respectively. Due to the influence of experimental conditions (such as the hinge gap of the MTS), the initial modulus of the experiment is slightly lower than that of the numerical simulation. This deviation gradually disappears as the gap closes. In addition, the distribution of coarse aggregate has a significant impact on crack path and flexural strength. The discrete element model assumes that the coarse aggregate is randomly and uniformly distributed, but the aggregate distribution cannot be completely uniform when preparing specimens in the laboratory test. This is also one of the reasons for the error between the two curves. The simulation and experimental results show the same trend and have a small deviation (10.9%), indicating that the discrete element model can reproduce the mechanical response of the three-point bending beam well.

[0068] Crack distribution comparison: By comparison Figure 21 The failure modes observed in the laboratory tests and simulations show that the crack morphology and distribution observed in the discrete element model are consistent with the laboratory test results. That is, as the load continues, the cracks extend from the bottom pre-cut joint to the top of the beam until they completely penetrate. The internal cracking process cannot be observed in the laboratory tests, but the simulation results provide the distribution of microcracks inside the three-point bending beam specimen. The microcracks are distributed along the interface between the coarse aggregate and the cement-stabilized sand and extend upwards, indicating that the bond between the coarse aggregate and the cement-stabilized sand is weak, which is consistent with the weak points of the actual material.

[0069] Crack propagation stage analysis: In the discrete element model, the growth trend of the number of microcracks inside a three-point bending beam with mid-span displacement was statistically analyzed, and it was found that the internal crack growth curve can be divided into three stages: Slow development stage: A small number of microcracks initiate at the interface between cement-stabilized sand and coarse aggregate, but macrocracks have not yet formed; Crack propagation stage: As the load continues, the number of microcracks increases rapidly and merges into a main crack that propagates along the pre-cut. The failure stage: a large number of microcracks accumulate and penetrate the three-point bending beam, and the specimen completely fails.

[0070] The crack propagation characteristics of the above three stages are consistent with the actual failure process of the material, further verifying the accuracy of the calibration parameters and the rationality of the model.

[0071] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0072] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A discrete element modeling method for composite materials, characterized in that, This includes systematic calibration of the target material, discrete element modeling, and parameter verification, as detailed below: S1: Define the basic components and internal contact types of the target material: The target material is fiber-cement stabilized crushed stone, which includes three basic components: coarse aggregate, fiber, and cement stabilized sand; there are eight types of internal contact, including coarse aggregate-coarse aggregate contact, cement stabilized sand-cement stabilized sand contact, cement stabilized sand-coarse aggregate contact, cement stabilized sand-fiber contact, single fiber internal contact, fiber-fiber contact, fiber-coarse aggregate contact, and contact within the rigid cluster of coarse aggregate; S2: Simplification and determination of internal contact types of fiber cement stabilized crushed stone: Since the discrete element modeling of fiber cement stabilized crushed stone involves multiple contact types, its mechanical mechanism is complex and has many parameters. Under the premise of ensuring experimental accuracy, the modeling process is simplified by assuming that there is no contact between fibers, contact between fibers and coarse aggregates, and contact within the rigid clusters of coarse aggregates. Based on the actual physical structure and contact characteristics of the internal particles of fiber cement stabilized crushed stone, the internal contact types can be divided into eight types. After introducing the above assumptions and simplifications, five main contact types are finally retained, including coarse aggregate-coarse aggregate contact, cement stabilized sand-cement stabilized sand contact, cement stabilized sand-coarse aggregate contact, cement stabilized sand-fiber contact, and single fiber internal contact. S3: System calibration of contact parameters: The system is calibrated step by step based on the basic components and composite components. The basic components include coarse aggregate, fiber and cement stabilized sand, and the composite components include fiber cement stabilized sand and cement stabilized crushed stone. The fine parameters of each contact type are obtained through corresponding indoor and virtual tests. S4: Discrete Element Modeling: Based on the contact parameters calibrated in S3, a three-phase particle system is generated collaboratively within the geometric domain of the specimen according to the gradation ratio of coarse aggregate, fiber and cement-stabilized sand. The discrete element model of fiber cement-stabilized crushed stone is then integrated and constructed through rigid cluster reconstruction, flexible cluster transformation and contact parameter assignment. S5: Parameter Verification: The contact parameters of the constructed discrete element global model were verified using a three-point bending beam test. The validity of the parameters was verified and confirmed by comparing the load-displacement curves and crack distribution of the indoor three-point bending beam test and the virtual three-point bending beam test.

2. The discrete element modeling method for composite materials according to claim 1, characterized in that: The specific basis for the contact type assumptions and simplifications in S2 is as follows: The fiber selected is a short chopped fiber with a length of 15mm. Since the content of short chopped fiber in fiber cement stabilized crushed stone is low, and there is a distance between the short chopped fibers, and the few short chopped fibers that are in contact with each other do not have adhesive force, it is assumed that there is no fiber-to-fiber contact. The fiber surface is coated with cement mortar, which minimizes its contact with the coarse aggregate and the two have no adhesion. Therefore, it is assumed that there is no contact between the fiber and the coarse aggregate. Meanwhile, a single coarse aggregate is characterized by a rigid cluster, in which the internal particles are consolidated into a rigid body with no relative displacement and no internal contact is generated. Therefore, it is assumed that internal contact does not exist.

3. The discrete element modeling method for composite materials according to claim 2, characterized in that: In S3, the contact parameter calibration of the basic components includes the following: Calibration of internal contact parameters of a single fiber: A uniaxial tensile test was conducted on the virtual fiber to obtain the stress-strain curve, which reflects the tensile properties of the fiber, and the contact behavior inside the single fiber was expressed by a linear parallel bonding model. Calibrated parameters of cement-stabilized sand contact: The unconfined compressive strength test and the indirect tensile strength test were used for joint calibration to reflect the mechanical behavior of cement-stabilized sand under tension and compression, and the contact behavior between cement-stabilized sand was expressed by the flat joint model. Calibration of coarse aggregate-coarse aggregate contact parameters: Since coarse aggregates have stable properties and small differences, the micro-parameters of coarse aggregates can be directly determined from the data in the literature, and the contact behavior between coarse aggregates can be expressed by a linear model.

4. The discrete element modeling method for composite materials according to claim 3, characterized in that: In S3, the contact parameter calibration of the composite components includes the following: Calibrating parameters of cement stabilized sand-fiber contact: The cement stabilized sand-fiber contact model is a linear parallel bonding model. Based on the contact parameters between cement stabilized sand and the internal contact of a single fiber, macroscopic mechanical parameters are obtained by using unconfined compressive strength test and indirect tensile strength test of fiber-stabilized cement sand in the laboratory. Then, the corresponding discrete element model of fiber-stabilized cement sand is established to jointly calibrate the interface parameters between cement stabilized sand and fiber, that is, the mesoscopic parameters of the linear parallel bonding model corresponding to cement stabilized sand-fiber contact. Calibrating parameters of cement-stabilized sand-coarse aggregate contact: The cement-stabilized sand-coarse aggregate contact model is a planar joint model. Based on the cement-stabilized sand-cement-stabilized sand and coarse aggregate-coarse aggregate contact parameters, macroscopic mechanical parameters are obtained by indoor unconfined compressive strength test and indirect tensile strength test of cement-stabilized crushed stone. Then, corresponding discrete element models of cement-stabilized crushed stone are established to jointly calibrate the interface parameters between cement-stabilized sand and coarse aggregate, that is, the mesoscopic parameters of the planar joint model corresponding to the cement-stabilized sand-coarse aggregate contact.

5. The discrete element modeling method for composite materials according to claim 4, characterized in that: In S4, the specific steps for discrete element modeling are as follows: Discrete Element Overall Model Construction: First, a wall is generated based on the shape and size of the specimen. Then, within the wall area, circular particles with corresponding gradations are randomly and uniformly generated according to the gradation and proportion of coarse aggregate, fiber, and cement-stabilized sand. Rigid cluster templates are made based on the particle outline shape of each component. Then, the original circular particles are replaced according to the principle of area equivalence, and the rigid clusters are transformed into breakable flexible clusters to simulate fibers. Finally, refined modeling is achieved according to the corresponding contact type, calibration parameters, and servo loading. The irregular geometric shape of coarse aggregate is reconstructed using rigid cluster particles, and a discrete element coarse aggregate model with real geometric features is constructed. Specifically, non-uniform diameter pebbles are used to fill the space inside the rigid cluster particles according to the central axis approximation method, and the ratio of the minimum diameter to the maximum diameter is 0.15, and the particle intersection angle is 150°. Single fiber model construction: In the discrete element method, the shape of the fiber is first generated by using rigid clusters. The pebble inside the rigid cluster is rigidly connected and cannot simulate the situation where the fiber is pulled apart. Therefore, when simulating the fractured flexible fiber, the rigid cluster is transformed into a breakable flexible cluster, and a linear parallel bonding model is added for servoing, so that the fiber is bonded to the surrounding cement-stabilized sand particles. Cement stabilized sand model construction: The particle size of the sand ranges from 1.18 mm to 4.75 mm and follows a normal distribution. The cracking behavior of cement stabilized sand is captured using a flat joint model, and then cement stabilized sand particles are generated by command.

6. The discrete element modeling method for composite materials according to claim 5, characterized in that: In S5, the specific steps for parameter verification are as follows: Indoor three-point bending beam test: Three parallel specimens were prepared as needed. After the specimens were cured, a pre-cut crack was made in the middle of the bottom. Then, a monotonic load was applied using a multi-functional hydraulic servo road material dynamic testing system, and the load-displacement curve was recorded and the cracked beam was photographed. Virtual three-point bending beam test: Based on the discrete element modeling method in S4, a three-point bending beam discrete element model of corresponding size is established, and pre-cut cracks are set at the positions corresponding to the above specimens. The same load conditions as the indoor test are applied to obtain the simulated load-displacement curves and crack distribution. Verification and comparison: By comparing the development trends and deviations of the load-displacement curves of the indoor test and the virtual test, it was found that the development trends of the two were consistent and the deviation was controlled within the preset threshold range; at the same time, the crack morphology and distribution characteristics were highly consistent, which indicates that the calibrated contact parameters are accurate and reliable.

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