Method for analyzing mechanical properties of cement stabilized macadam based on maximum nominal aggregate size

Abstract

The application discloses a cement stabilized macadam mechanical property analysis method based on maximum aggregate nominal particle size, relates to the technical field of cement stabilized macadam mechanical property analysis, and comprises the following steps: preparing skeleton dense type cement stabilized macadam test pieces with different nominal maximum particle sizes; performing macroscopic mechanical test to obtain stress-strain curves and crushing values; establishing a three-dimensional discrete element numerical model corresponding to the test pieces and performing uniaxial compression simulation, and verifying the model to ensure the reliability of the model; and based on the verified model, quantitatively analyzing contact force distribution, contact quantity characteristics and microcrack evolution law from a microcosmic aspect. According to the analysis method, the macroscopic performance of the material is improved by regulating the internal force chain network and inhibiting damage accumulation through the nominal maximum particle size, and the analysis method discloses the mechanism that the nominal maximum particle size improves the macroscopic performance of the material by regulating the internal force chain network and inhibiting damage accumulation, and provides a scientific microcosmic mechanical basis and a quantitative analysis tool for gradation optimization and high-performance design of the cement stabilized macadam base.

Description

Technical Field

[0001] This invention relates to the field of mechanical property analysis technology for cement-stabilized crushed stone, and in particular to a method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal particle size of the aggregate. Background Technology

[0002] Cement-stabilized crushed stone (CSM) is widely used in high-grade highways and heavy-duty pavement structures due to its excellent mechanical properties and cost-effectiveness. However, under the coupled effects of long-term cyclic loading and environmental factors, problems such as mechanical property degradation, reflective cracking, and fatigue failure still limit the service life of pavements. With the rapid development of transportation infrastructure and the increasing traffic load, the demand for improving the performance of pavement materials is becoming increasingly urgent, making it particularly important to conduct in-depth research on the mechanical behavior of CSM and its influencing factors.

[0003] Among numerous influencing factors, aggregate gradation is a key determinant of the mechanical properties of CSM (compound mixed aggregate). Existing research has extensively explored gradation types, design methods, evaluation indicators, and gradation development for different materials. Regarding gradation types, studies have shown that a dense skeleton structure can effectively form a stable skeleton, significantly improving the mechanical properties and crack resistance of the material. For example, Tian found that a strongly interlocked skeleton gradation composed of three types of coarse aggregates (19-31.5 mm, 9.5-19 mm, and 4.75-9.5 mm) in a mass ratio of 5:3:2 significantly improved the material's resistance to shrinkage deformation. Ji's research shows that by controlling the passing rate of key sieve apertures to achieve an interlocked skeleton dense gradation, both mechanical properties and crack resistance can be improved simultaneously. Kong designed an interlocked skeleton dense gradation using the discrete element method, proving that recycled brick mixed aggregates can also form an effective force chain transmission system. In terms of gradation design methods, Liu systematically analyzed the performance variation laws of five gradation types from coarse to fine using the uniform interpolation method, finding that the maximum dry density has a quadratic curve relationship with the gradation. Kong, based on the discrete element method, gradually designed the optimal interlocking skeleton dense gradation. Regarding the evaluation system, Li innovatively proposed microscopic evaluation indicators such as skeleton density and skeleton stability, and verified their strong correlation with macroscopic mechanical strength. Liang used CT scanning technology to reveal the distribution characteristics of voids within different gradations. In the development of gradations for different materials, the research covered a variety of special materials. For example, Zeng's research on coral aggregate found that it could only form a strongly suspended dense structure but could not establish an effective skeleton, and determined that a maximum particle size of 53 mm and a fine aggregate content of 45% were the optimal gradations. Khamseh explored the stabilization treatment of iron tailings, finding that a cement content of 5%–10% could significantly improve its mechanical properties. Li also compared the performance differences of different drainage base course gradations, such as dense and skeleton-void types. Furthermore, the research found that 4.75 mm is often used as the dividing point between coarse and fine aggregates, and that vibration compaction is better than static compaction in ensuring the realization of gradation design. Despite significant progress in CSM gradation design research, current work primarily focuses on gradation type and mix proportion design methods. Research on isolating the nominal maximum particle size (NMAS) as a separate key variable to elucidate its specific impact on CSM performance remains lacking, hindering a fundamental understanding of the formation and mechanism of the skeletal structure. Summary of the Invention

[0004] This invention provides a method for analyzing the mechanical properties of cement-stabilized crushed stone based on the nominal particle size of the maximum aggregate. By combining macroscopic and microscopic methods, it reveals the mechanism by which the nominal maximum particle size improves the macroscopic properties of the material by regulating the internal force chain network and inhibiting damage accumulation. This provides a scientific microscopic mechanical basis and quantitative analysis tool for the gradation optimization and high-performance design of cement-stabilized crushed stone base courses.

[0005] To solve the above-mentioned technical problems, the technical solution proposed by this invention is as follows:

[0006] A method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size includes the following steps:

[0007] Step S1, specimen preparation and macroscopic mechanical testing: Prepare at least two kinds of skeleton-dense cement-stabilized crushed stone specimens with different nominal maximum particle sizes, conduct uniaxial compression tests on the specimens, obtain macroscopic stress-strain curves, and conduct crushing value tests;

[0008] Step S2, Discrete Element Numerical Model Construction and Verification: Based on the gradation information of each specimen in Step S1, construct the corresponding three-dimensional discrete element uniaxial compression numerical model; run the numerical model to perform simulation, and compare the stress-strain curve obtained from the simulation with the test curve of the corresponding specimen in Step S1 to verify the reliability of the model.

[0009] Step S3, Macroscopic Mechanical Performance Analysis: Based on the validated model, extract and quantify the macroscopic features that reflect the essence of mechanics;

[0010] Step S4, Micromechanical Feature Extraction and Analysis: Extract and analyze the micromechanical features of the model during the loading process. The micromechanical features include contact force distribution features, contact quantity features, and microcrack evolution features.

[0011] A further improvement to the above technical solution is as follows:

[0012] Preferably, in step S1, the different nominal maximum particle sizes include at least a first particle size, a second particle size, and a third particle size, wherein the third particle size is larger than the second particle size, and the second particle size is larger than the first particle size.

[0013] Preferably, in step S2, constructing the three-dimensional discrete element uniaxial compression numerical model specifically includes:

[0014] S2-1, Particle Generation and Initial Equilibrium: Based on the number of particles calculated from the actual gradation, a discrete particle assembly is generated within the cylindrical modeling domain. The particle density and damping parameters are defined, the loading plate and lateral constraint boundaries are set, and initial equilibrium calculations are performed.

[0015] S2-2, Coarse aggregate clustering modeling: replace coarse aggregate particles with a particle size greater than a predetermined threshold with a cluster structure composed of multiple basic particles bonded together to simulate the real shape of irregular aggregates.

[0016] S2-3, Contact Model Assignment: Assigning a mechanical model to the contact between different components.

[0017] Preferably, the coarse aggregate clustering modeling is achieved by importing STL format geometric files to define the shape of the cluster structure and controlling the volume error before and after cluster replacement to be within ±1%.

[0018] Preferably, a mechanical model is provided for the contact between different components. The contact between coarse aggregate and loading plate, and between coarse aggregates, adopts a rolling resistance linear contact model. The contact between cement mortar particles in the aggregate matrix is ​​simulated by a parallel bonding model.

[0019] Preferably, in step S4, analyzing the contact force distribution characteristics includes: statistically analyzing the average and maximum contact forces borne by aggregate particles in different particle size ranges, and analyzing the load transmission levels and dominant skeleton within the material.

[0020] Preferably, in step S4, analyzing the contact quantity characteristics includes: defining strong contact as above the average contact force and weak contact as below the average contact force; and statistically analyzing the number and proportion of strong and weak contacts undertaken by aggregate particles in each particle size range to quantify the mechanical role of particles of different sizes in the skeleton structure.

[0021] Preferably, in step S4, analyzing the microcrack evolution characteristics includes: monitoring and recording the development curve of the number of microcracks with axial strain during loading, extracting the crack initiation strain threshold, crack propagation rate, and the total number of cracks at macroscopic failure; and extracting the spatial and angular distribution characteristics of cracks at the peak stress moment.

[0022] Preferably, extracting the crack angle distribution characteristics specifically involves: statistically analyzing the projection angles of the normal vectors of all microcracks onto the horizontal plane, and drawing a crack statistical rose diagram to analyze the directional initiation and propagation patterns of cracks.

[0023] Preferably, in step S4, a three-stage crack evolution prediction model is constructed to predict crack resistance performance, and the following prediction parameters are set to correlate microstructural parameters with macroscopic damage behavior:

[0024] (1) Damage initiation threshold strain That is, the strain point at which the crack begins to grow significantly:

[0025]

[0026] in, The larger the interface, the stronger its crack resistance. The entropy of the skeleton structure is represented by A, where A is a coefficient and ε0 is the reference strain.

[0027] (2) Damage steady growth rate for:

[0028] G d = B / λ + G0

[0029] Where λ is the tortuosity of the force chain, therefore G d It is inversely proportional to λ; B is the coefficient, and G0 is the background growth rate.

[0030] (3) Total number of microcracks at final failure :

[0031] N total = N max × C L (-k)

[0032] in, For load transfer concentration, N max denoted as the theoretical maximum value of the microcrack, and k is the attenuation exponent.

[0033] The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size provided by this invention has the following advantages compared with the prior art:

[0034] (1) The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size of this invention establishes a complete and repeatable macro-micro correlation analysis process by combining standardized macroscopic mechanical tests with high-fidelity discrete element microscopic simulation. This method can intuitively and quantitatively reveal how changes in NMAS cause the reconstruction of the internal force chain network, changes in load transfer paths, and differences in damage evolution modes, thereby fundamentally explaining the microscopic mechanisms of changes in macroscopic strength, stiffness, and deformation capacity. This method provides strong micromechanical theoretical support and advanced numerical analysis tools for optimizing the gradation design of cement-stabilized crushed stone and improving the performance of pavement base materials.

[0035] (2) The mechanical property analysis method of cement-stabilized crushed stone based on the maximum nominal aggregate size of the present invention increases the NMAS to improve the macroscopic strength and deformation resistance of CSM by optimizing the microstructure. This optimization is manifested in a more efficient chain network dominated by coarse aggregate and the resulting suppression of damage accumulation. The analysis method provides a solid micromechanical basis for gradation optimization and supports the design of strong skeleton structures in cement-stabilized layers to improve pavement performance. Attached Figure Description

[0036] Figure 1 This is a CSM gradation curve diagram in this invention.

[0037] Figure 2 This is a flowchart of the numerical model construction in this invention.

[0038] Figure 3 (a) is a diagram of the linear contact model of rolling resistance in this invention.

[0039] Figure 3 (b) is a diagram of the parallel bonding model in this invention.

[0040] Figure 4 This is a flowchart of the parameter calibration process for the numerical experimental model in this invention.

[0041] Figure 5 (a) shows the stress-strain curves of the measured and simulated values ​​of CSM-30.

[0042] Figure 5 (b) shows the stress-strain curves of the measured and simulated values ​​of CSM-40.

[0043] Figure 5 (c) shows the stress-strain curves of the measured and simulated values ​​of CSM-50.

[0044] Figure 6 This is a diagram showing the development law of compressive strength in the mechanical properties of CSM in this invention.

[0045] Figure 7 This is the stress-strain curve of the CSM mechanical properties in this invention.

[0046] Figure 8 This is a comparison of mechanical strength in the CSM mechanical properties of this invention.

[0047] Figure 9 (a) is a diagram of the coarse-grained skeleton structure in the mechanical properties of the CSM of the present invention.

[0048] Figure 9 (b) is a diagram of the fine-grained skeleton structure in the CSM mechanical properties of the present invention.

[0049] Figure 10 (a) shows the changes in aggregate particle size before and after the crushing test at CSM-30.

[0050] Figure 10 (b) shows the changes in aggregate particle size before and after the crushing test at CSM-40.

[0051] Figure 10 (c) shows the changes in aggregate particle size before and after the crushing test at CSM-50.

[0052] Figure 11 (a) shows the contact force distribution of aggregate particles of different sizes under CSM-30 conditions.

[0053] Figure 11 (b) shows the contact force distribution of aggregate particles of different sizes under CSM-40 conditions.

[0054] Figure 11 (c) shows the contact force distribution of aggregate particles of different sizes under CSM-50 conditions.

[0055] Figure 12 (a) shows the statistical results of the maximum and average contact forces under CSM-30 conditions.

[0056] Figure 12 (b) shows the statistical results of the maximum and average contact forces at CSM-40.

[0057] Figure 12 (c) shows the statistical results of the maximum and average contact forces under CSM-50 conditions.

[0058] Figure 13 (a) is the number distribution of contact forces under CSM-30 conditions.

[0059] Figure 13 (b) shows the number distribution of contact forces under CSM-40 conditions.

[0060] Figure 13 (c) shows the number distribution of contact forces under CSM-50 conditions.

[0061] Figure 14 (a) Statistics on the proportion of strong contact forces under CSM-30 conditions.

[0062] Figure 14 (b) Statistics on the proportion of strong contact forces under CSM-40 conditions.

[0063] Figure 14 (c) is a statistical representation of the proportion of strong contact forces under CSM-50 conditions.

[0064] Figure 15 (a) shows the development process of the number of microcracks under CSM-30 conditions.

[0065] Figure 15 (b) shows the development process of the number of microcracks at CSM-40.

[0066] Figure 15 (c) shows the development process of the number of microcracks at CSM-50.

[0067] Figure 16 (a) is a uniaxial compression test specimen under CSM-30 conditions.

[0068] Figure 16 (b) shows the crack morphology in the uniaxial compression numerical test under CSM-30 conditions.

[0069] Figure 17 (a) shows the crack angle distribution characteristics of the uniaxial compression numerical specimen under CSM-30 conditions.

[0070] Figure 17 (b) shows the crack angle distribution characteristics of the uniaxial compression numerical specimen under CSM-40 conditions.

[0071] Figure 17(c) shows the crack angle distribution characteristics of the uniaxial compression numerical specimen under CSM-50 conditions. Detailed Implementation

[0072] The following provides a detailed description of specific embodiments of the present invention. It should be understood that the specific embodiments described herein are for illustrative and explanatory purposes only and are not intended to limit the scope of the invention.

[0073] The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size of this invention specifically includes the following steps:

[0074] Step S1: Specimen preparation and macroscopic mechanical testing.

[0075] Macroscopic mechanical response data of different NMAS cement-stabilized crushed stone were obtained as a reference and verification basis for subsequent microscopic analysis.

[0076] S1-1, Material Preparation and Gradation Design: The aggregate used is limestone crushed stone, and the cement is ordinary Portland cement, whose technical indicators meet the specifications. Three different nominal maximum particle size (NMAS) skeleton-dense gradations are designed, and the gradation curves are as follows: Figure 1 As shown. The nominal maximum particle size (NMAS) is 30mm (CSM-30), 40mm (CSM-40), and 50mm (CSM-50). Weigh each grade of aggregate and cement according to the design gradation, and fix the cement dosage at a certain value (e.g., 5%). Add water and mix evenly to ensure that the moisture content of the mixture is the optimum moisture content.

[0077] S1-2, Specimen Molding and Curing: Specimens were prepared using vibration molding, with dimensions of 150 mm in diameter and 150 mm in height. The molded specimens were immersed in water at 20°C ± 2°C for 24 hours, then removed and dried.

[0078] S1-3, Uniaxial Compression Test: The specimen is placed on a pressure testing machine for an unconfined uniaxial compression test. The loading rate is set to 1 mm / min, and pressure and displacement data are continuously recorded until the specimen fails. Based on the recorded data, stress and strain are calculated, stress-strain curves are plotted, and macroscopic mechanical parameters such as unconfined compressive strength and peak strain are determined. The unconfined compressive strength is calculated according to formula (1):

[0079] (1)

[0080] In the formula, denoted as unconfined compressive strength, P as the maximum pressure at which the specimen fails, and A as the cross-sectional area of ​​the specimen.

[0081] S1-4, Crushing Value Test: A standard crushing value test is performed on the coarse aggregate portion (e.g., aggregates with a particle size greater than 4.75 mm) in each group of mixtures. After the test, the crushed material is sieved to analyze the change in the mass percentage of each grade before and after crushing, in order to evaluate the load transfer stability of the coarse aggregate skeleton in different NMAS mixtures.

[0082] Step S2: Construction and verification of the discrete element numerical model.

[0083] Establish a discrete element numerical model that corresponds to physical experiments and can truly reflect the microstructure of materials, and verify its reliability by comparing macroscopic responses.

[0084] S2-1, Overall Model Construction Process: PFC3D software is used to establish uniaxial compression numerical models of CSM three-dimensional cylinders with different nominal maximum particle sizes, such as... Figure 2 As shown, first, a basic particle system is generated, then the coarse aggregate is refined into clusters, and finally, a contact model is assigned and boundary conditions are set.

[0085] S2-2, Particle Generation and Initial Equilibrium: Based on the three gradations designed in S1-1, the number of particles in each particle size range was calculated. CSM specimens were generated within a cylindrical domain using the "spherical distribution method." To analyze the mechanical behavior of aggregate and cement mortar, different particles were assigned corresponding densities and damping coefficients. Particles with a diameter less than 2.36 mm were defined as the cement mortar matrix. Upper and lower loading plates and cylindrical lateral constraint boundaries were created to generate a rigid wall representing the upper and lower pressure plates of the press. The system underwent 2000 calculation steps of equilibrium operations to achieve initial stress equilibrium and a stable state.

[0086] S2-3, Coarse Aggregate Clustering Modeling: To accurately simulate the geometric morphology and mechanical interlocking effect of irregular coarse aggregates, coarse aggregate particles with a diameter greater than 9.5 mm are clustered. The specific steps are as follows: First, an STL format surface model file with an irregular shape is generated through 3D scanning or a geometric algorithm. Then, a series of tightly bonded pebbles are used to fill the volume space defined by the STL model, forming a rigid cluster. This cluster is then used to replace the single spherical particles of the corresponding diameter generated in S2-2 one by one. The error in the aggregate volume change represented by each cluster before and after replacement is ensured to be within ±1%, guaranteeing the geometric accuracy of the model.

[0087] S2-4, Contact Model Assignment: By controlling the wall displacement, a uniaxial compressive load is applied until the specimen undergoes macroscopic failure, thus fully simulating the entire process of a physical uniaxial compression test.

[0088] In the numerical model, the macroscopic properties of the mixture are characterized by defining the contact relationships between particles. To improve computational efficiency, the contact types in the model are simplified to three categories: contact between coarse aggregate particles and the loading plate, contact between coarse aggregate particles, and contact between cement mortar particles. By assigning different mechanical models to these three types of contact, the uniaxial compression behavior of CSM is simulated. The rolling resistance linear contact model and the parallel bond model in PFC3D software are used to simulate the above contact relationships. The rolling resistance linear contact model is suitable for the contact between coarse aggregate and the loading plate, and for contact between coarse aggregate particles, while the parallel bond model is used to simulate the contact between cement mortar particles. Schematic diagrams of these two models are shown below. Figure 3 As shown. The linear contact model of rolling resistance can simulate sliding friction, rolling friction, and elastic deformation between aggregates. For the contact between small particles labeled as cement mortar matrix, a parallel bond model is used. This model establishes finite-sized bond bonds at the particle contact points, which can withstand forces and moments, and can simulate the tensile and shear failure of the bond, thus reproducing the cementing effect and cracking process of cement mortar.

[0089] S2-5, Model Parameter Calibration and Verification: Model parameters are calibrated and validated according to... Figure 4 The numerical experimental model parameters are calibrated using the method shown below. The specific steps are as follows:

[0090] Step 1: Laboratory preparation of specimens and determination of material parameters.

[0091] ① Preparation of specimens for indoor testing

[0092] Cylindrical specimens were prepared according to the target proportions (CSM-30, CSM-40, CSM-50).

[0093] ② Obtain measured data

[0094] Uniaxial compression mechanical tests were conducted in the laboratory, and stress-strain curves and other mechanical response data were recorded.

[0095] Step 2: Construct PFC numerical specimens.

[0096] ① Establish a numerical model

[0097] Based on the aggregate gradation and actual structure of the specimen, the corresponding numerical specimen is generated in PFC.

[0098] ② Initial setting of model parameters

[0099] Based on experience or literature, preliminary model parameters are given, including micromechanical parameters such as particle stiffness, friction coefficient, and bond strength.

[0100] Step 3: Numerical mechanics simulation and parameter iterative adjustment.

[0101] ① Perform numerical experiments

[0102] Simulate the same mechanical loading conditions as in the laboratory in PFC to obtain simulated stress-strain curves.

[0103] ②Results Comparison

[0104] The simulation results were compared with the measured stress-strain curves to assess the differences.

[0105] ③ Parameter adjustment

[0106] If the error is large, adjust the micro parameters in the PFC model (such as elastic modulus, bond strength, friction angle, etc.) and re-simulate.

[0107] Step 4: Error judgment and parameter determination.

[0108] ① Set error threshold

[0109] Based on the required research accuracy, an acceptable error range (stress error <5%) is set.

[0110] ② Determine convergence

[0111] If the error between the simulated curve and the measured curve is less than the specified value, the parameter calibration is considered complete, and the process proceeds to the next step; otherwise, return to step three to continue adjusting.

[0112] ③ Determine the final parameters

[0113] When the simulation results meet the error requirements, the current parameter combination is determined as the final model parameters, which can be used for subsequent PFC numerical analysis.

[0114] The calibrated parameters are summarized in Table 1.

[0115] Table 1. Calibration results of microscopic contact parameters

[0116]

[0117] To verify the reliability of the established discrete element model, the numerical simulation stress-strain curves of three sets of CSM specimens with different gradations were compared and analyzed with the results of laboratory tests. The results are as follows: Figure 5 As shown in the figure. Analysis shows that the numerical simulation curves closely match the experimental curves during the loading process up to the peak stress point, and the peak strength and its corresponding strain are highly consistent with the experimental values. Although there are some differences in the later stages, the high consistency of the main mechanical behavior stages confirms that the numerical model can accurately reproduce the macroscopic mechanical response of the material. Therefore, a micromechanical mechanism analysis is conducted based on this verification model.

[0118] Step S3, macroscopic mechanical property analysis.

[0119] Based on the validated model, macroscopic features that reflect the essence of mechanics are extracted and quantified.

[0120] S3-1, Mechanical Strength Analysis:

[0121] To quantitatively describe the intensity development pattern, a corresponding growth model is fitted, the expression of which is:

[0122] (1)

[0123] in, For maintenance time, For compressive strength, These are the regression coefficients of the model. Ultimate strength represents the theoretical progressive peak strength that CSM can reach over an infinitely long curing period. It is a key indicator for evaluating the ultimate mechanical properties and long-term durability of materials.

[0124] To overcome the empirical dependence on specific NMAS, this invention constructs a macroscopic strength prediction model based on micromechanical mechanisms. This model shows that the ultimate strength... The load-bearing capacity is determined by two core factors: "framework load-bearing efficiency" and "interfacial bonding strength," and their functional relationship is as follows:

[0125] (2)

[0126] in: The effective load-bearing capacity of the force chain network is used to quantify the skeleton efficiency. It is the proportion of the sum of strong contact forces bearing the main load to the total contact force. Strong contact forces are identified through discrete element simulation or three-dimensional microstructure analysis based on CT images (such as force chains that are more than one standard deviation above the average contact force). A value close to 1 indicates that the load transfer path is highly optimized. This is the equivalent interface reinforcement coefficient, used to quantify interface performance; These are model parameters. Logarithmic terms. This reflects the law of diminishing marginal returns in improving skeletal efficiency; power function term This reflects the nonlinear gain of interface enhancement.

[0127] The formula for calculation is:

[0128] (3)

[0129] Where C represents the amount of cement used per unit volume; The total specific surface area of ​​the aggregate is estimated based on the gradation. and The values ​​are the average nanoindentation hardness of the interface transition zone and the distant mortar matrix, respectively, obtained through microscopic experiments.

[0130] Through macroscopic intensity prediction models, it is possible to predict the strength of raw materials (gradation, cement) and microscopic parameters (…). , Predicting the ultimate strength at that time .

[0131] Further design a quantifiable, detailed indicator system to provide input for the macro-intensity prediction model. Specifically:

[0132] Orderliness of the skeleton network: Degree of tortuosity of the force chain λ and entropy of the skeleton structure S s Measurement. λ is defined as the ratio of the actual transmission path of the force chain to the straight-line distance; S s Calculation based on the probability distribution of strong contact between aggregates of different particle sizes: .in, This represents the proportion of strong contacts undertaken by particle size group i out of the total number of strong contacts. The lower λ is, the higher the S... s The smaller the size, the more direct and orderly the skeleton, and the higher its effective load-bearing capacity η.

[0133] Interface crack resistance: measured by the interface brittleness index Auxiliary evaluation, and its relationship with Closely related. The parameters η and δ in the macro-intensity prediction model. eff It is precisely by carefully observing the indicators This is a comprehensive macro-level reflection.

[0134] Figure 6 The evolution of compressive strength of three gradations of CSM at different curing ages is shown. The strength of all mixtures initially increases rapidly with increasing curing time, then gradually stabilizes. Throughout the curing period, the larger the maximum nominal particle size (NMAS), the better the strength performance of the CSM. This trend is illustrated in the stress-strain curves obtained at 7 days (e.g., ...). Figure 7 Further verification was obtained as shown in the figure: the larger the NMAS, the higher the peak stress and peak strain of the mixture curve, and the steeper the slope before the peak stress. This indicates that the larger the NMAS, the higher the strength of the mixture, and the greater its stiffness and deformation capacity at failure.

[0135] Figure 8 The 7-day compressive strength and fitted ultimate strength of the three gradations were compared. (Value). The results confirmed that the larger the NMAS, the higher the short-term and long-term strength index of the CSM mixture.

[0136] To analyze the mechanical mechanism behind the improved performance of mixtures with larger NMAS (maximum nominal size), a comparative schematic diagram of stress transfer in the coarse and fine aggregate skeleton structures was constructed (e.g., Figure 9(As shown in (a) and (b)). The strength advantage of coarse NMAS mixtures stems from their optimized force chain network and enhanced interfacial properties. The skeleton formed by coarse aggregates establishes a more direct force chain network, such as... Figure 9 As indicated by the thick red arrows, stress is transmitted through stronger and more efficient paths. In contrast, although fine NMAS mixtures also exhibit dense gradation characteristics, their force chains are more numerous, relatively weaker, and more tortuous, resulting in lower stress distribution efficiency under high loads. Furthermore, with the same cement content, larger NMAS mixtures have a significantly lower total aggregate surface area, resulting in a thicker and denser cement paste film in the interfacial transition zone. This enhances the bond strength at the aggregate-mortar interface and effectively inhibits the initiation and propagation of microcracks, thereby synergistically improving the macroscopic mechanical strength and deformation resistance of the material.

[0137] S3-2, Load Contribution Analysis:

[0138] This invention proposes a particle size-stress sharing function F(d) based on a particle size-load sharing prediction method. Under standard load, the probability of aggregate with particle size d breaking is related to its theoretical average contact stress in the aggregate skeleton. The relationship is expressed as:

[0139] (4)

[0140] Where, σ avg(d) Theoretical predictions are made based on the contact force distribution; and m are material crushing parameters related to the strength of the aggregate parent rock. By... Figure 10 The test crushing data is fitted with formula (4), and the actual stress sharing weight of each aggregate grade in any gradation can be derived. This realizes the leap from "phenomenon observation" to "law prediction", which can be used to evaluate and optimize the load distribution rationality of new gradations in the design stage and avoid premature crushing of key particle size groups.

[0141] The crushing value test was used to evaluate the crushing resistance of coarse aggregate in CSM to reflect the particle stability of the material under load.

[0142] The experiment simulates the process of external load transfer through the aggregate skeleton, and the degree of particle crushing can indirectly reflect the load transfer efficiency between aggregates. The changes in gradation before and after the crushing test were analyzed by sieve analysis, and the results are as follows: Figure 10As shown in the figure, after the crushing test, the mass proportion of coarse aggregates larger than 19 mm decreased in all three mixtures, indicating that particles within this size range underwent significant crushing. This phenomenon reveals that large-diameter particles play a dominant role in load transfer and are therefore more prone to crushing under load. Furthermore, the mass proportion of aggregates in the 9.5–19 mm size range in CSM-50 remained almost unchanged. This can be attributed to two reasons: firstly, some particles in this size range originated from the crushing products of larger-diameter aggregates during the test; secondly, the contact force borne by this size aggregate in the skeleton structure is relatively small, allowing it to remain stable under crushing load. In contrast, the proportion of 9.5–19 mm size aggregates in CSM-40 and CSM-30 decreased significantly, indicating that this size aggregate plays a more critical load-bearing role in these two fine-gradation mixtures.

[0143] Step S4: Micromechanical characteristic analysis.

[0144] To standardize the characterization of skeletal stability by contact force and contact quantity, and to establish a direct quantitative link between them and macroscopic performance, this invention defines load transfer concentration. Ultimate strength is the proportion of the total load transmitted by the aggregate particles that bear the strongest 20% of the contact force to the total load. and and skeletal structure entropy The following empirical relationships must be satisfied:

[0145] (5)

[0146] Formula (5) shows that a high-strength, high-efficiency skeleton is characterized by a high concentration of load on a few key particles (high strength, high efficiency, high efficiency). At the same time, the skeletal structure is simple and orderly (low). This provides a clear micromechanical objective for optimizing gradation design.

[0147] The analysis and verification process is as follows:

[0148] S4-1, Contact Force Distribution Characteristics Analysis: Figure 11 The distribution of contact forces for different aggregate sizes under different gradations is shown. As the aggregate size increases, the range of contact force distribution gradually widens, with the largest aggregate size exhibiting the widest distribution. This indicates that coarse aggregate particles constitute the main load-bearing skeleton, transferring most of the external load. With increasing maximum nominal size (NMAS), the 37.5–53 mm aggregate in CSM-50 shows the widest distribution, further confirming the dominant skeleton role of the largest coarse aggregate. In contrast, the contact force distribution between fine aggregate and mortar is narrower, but numerous outliers exist, indicating localized stress concentration within the mortar matrix.

[0149] To further quantify the role of aggregates in load transfer, Figure 12 The maximum and average contact forces of aggregate particles with a diameter greater than 2.36 mm were analyzed. Although numerous microscale force chains exist in the mortar matrix, their contribution to macroscopic strength is limited; therefore, only the contact forces between aggregates were considered. The results show that larger-diameter aggregates exhibit higher average and maximum contact forces. This trend clearly reveals a hierarchical load transfer structure within the material: larger aggregates form the skeletal framework of the force chain network and dominate the transfer of external loads. The larger the aggregate particle size, the greater its contribution to resisting external loads.

[0150] S4-2, Contact Quantity Characteristics Analysis: Figure 13 The distribution of strong and weak contact forces in aggregate particles of different sizes is shown. Strong and weak contact are defined relative to the average contact force: contact above the average is strong contact, and contact below the average is weak contact. Analysis shows that in all gradations, strong contact is primarily provided by aggregates larger than 9.5 mm. This finding provides micromechanical evidence for the finding that "coarse aggregates above this size constitute the load-bearing skeleton and are the primary source of strength." In contrast, relatively finer aggregates in the 2.36–4.75 mm and 4.75–9.5 mm ranges primarily provide weak contact. Their structural role tends to be filling voids and stabilizing the skeleton, rather than dominating load transfer. This mechanically explains why excessive amounts of these aggregate sizes should be avoided in mix design—as they may interfere with the formation of an effective main skeleton. Furthermore, in gradations with smaller NMAS, the proportion of strong contact contributed by aggregates smaller than 9.5 mm is relatively increased. This suggests that when the coarse aggregate skeleton is insufficient, finer aggregates may shift from a filling role to partially undertaking a secondary load-bearing function.

[0151] Figure 14 The statistical analysis results of the strong contact ratio for each aggregate size range are presented. The analysis shows that the load transfer path within the material is mainly dominated by coarse aggregate, and this dominance increases with increasing particle size. In the CSM-50 gradation, the strong contact ratio of aggregates in the 37.5–53 mm range exceeds 90%, which, at the microscale, proves that these largest particle sizes constitute the main load-bearing skeleton and become the key force transfer path for maintaining the vast majority of external loads.

[0152] S4-3, Analysis of Crack Evolution Characteristics:

[0153] To achieve predictive design for crack resistance, this invention constructs a three-stage crack evolution prediction model, which correlates microstructural parameters with macroscopic damage behavior:

[0154] (1) Damage initiation threshold strain This refers to the strain point where the crack begins to grow significantly.

[0155] (6)

[0156] in, The larger the interface, the stronger its crack resistance. A reduction means that stress concentration is more controllable, and the ratio of the two factors together determines the difficulty of crack initiation. A is a coefficient, and ε0 is the reference strain.

[0157] (2) Damage steady growth rate During the stable propagation stage, the number of microcracks increases with the slope of strain growth.

[0158] G d = B / λ + G0(7)

[0159] Among them, the higher the tortuosity λ of the force chain, the more circuitous the crack propagation path, and the lower the propagation efficiency per unit strain. Therefore, G d It is inversely proportional to λ; B is the coefficient, and G0 is the background growth rate.

[0160] (3) Total number of microcracks at final failure :

[0161] N total = N max × C L (-k) (8)

[0162] Among them, the more concentrated the load transfer (C) L The higher the value (N), the fewer potential parallel crack initiations there are, and therefore the fewer the total number of cracks. max denoted as the theoretical maximum value of the microcrack, and k is the attenuation exponent.

[0163] Formulas (6), (7), and (8) are derived from the parameter δ. eff S s , λ, C L The parameter calculation process enables positive prediction from material design to its final failure mode and toughness.

[0164] In the parallel bond model, when the tensile or shear stress of the bond exceeds its strength, the bond will fracture, recorded as a "microcrack". From the start of loading, the total number of microcracks accumulated in the model at each step (or each strain increment) is recorded. A curve of the number of microcracks as a function of axial strain is plotted, from which three key features can be extracted: the strain threshold at which cracks begin to increase significantly (initiation threshold), the slope of the rising segment of the curve (propagation rate), and the total number of cracks at final failure.

[0165] Figure 15The study demonstrates the development of microcrack number with strain in three CSM (Continuous Mass Scale) mixtures. Compared to smaller NMAS (Non-Mass Scale) specimens, larger NMAS specimens exhibit significantly delayed microcrack initiation, indicating a higher strain threshold for crack formation. In the subsequent stable crack growth stage, the crack growth curve of larger NMAS specimens shows a gentler slope, indicating a slower crack propagation rate. More importantly, these specimens show a significantly lower total number of cracks at macroscopic failure. Analysis reveals that the robust force chain skeleton formed by larger aggregates constitutes a more efficient and stable load transfer system. This skeleton significantly optimizes the internal stress distribution, reduces local stress concentration, and thus delays damage initiation. Simultaneously, the large aggregates act as an effective "barrier," forcing microcracks to deflect and bypass, hindering their propagation and penetration, thereby significantly increasing the energy required to generate each crack. Therefore, the combination of fewer cracks, later initiation, and slower propagation demonstrates that increasing the NMAS inherently improves the structural efficiency of the material and inhibits damage accumulation. This mechanistic understanding explains the superior mechanical strength observed at the macroscopic scale.

[0166] To further analyze the influence of maximum nominal particle size (NMAS) on the crack distribution characteristics of CSM, the crack morphology at the peak stress time of the uniaxial compression numerical test was extracted, such as... Figure 16 As shown. The statistical rose diagrams of cracks in the three mixtures are further illustrated in... Figure 17 The results show that the crack distribution differs significantly with increasing NMAS. In the CSM-30 specimen, microcracks randomly initiate under shear stress, resulting in dispersed crack directions and a nearly circular rose diagram. As NMAS increases, the crack directions tend to concentrate, forming a distinct bimodal petal-like distribution in the rose diagram. In the CSM-50, the rigid skeleton formed by coarse aggregate dominates the internal stress field, prompting microcracks to initiate directionally along the principal stress directions of 30°–80°. During propagation, these cracks are forced to deflect, bypass, or terminate due to the obstruction of surrounding large aggregates, and their propagation path and direction are strongly restricted within the skeleton pores. This mechanism not only delays crack penetration but also ultimately forms single, localized macroscopic cracks. In contrast, the fine aggregate in the CSM-30 disperses stress through numerous contact points, allowing microcracks to randomly initiate and propagate freely in multiple directions, ultimately forming a diffusely distributed microcrack network, exhibiting a more ductile failure mode.

[0167] This invention analyzes the influence of maximum nominal particle size (NMAS) on the macroscopic and mesoscopic mechanical properties of CSM using a combination of indoor experiments and discrete element simulation. The main conclusions are as follows:

[0168] (1) On a macroscopic scale, the mechanical properties of CSMs significantly improve with increasing NMAS. Larger NMAS specimens exhibit higher unconfined compressive strength, greater stiffness, and stronger deformation capacity at failure. Crushing value tests further confirm that the coarse aggregate skeleton in larger NMAS mixtures has better stability and load-bearing capacity under compressive loads.

[0169] (2) Discrete element analysis shows that a larger NMAS promotes the formation of a stronger and more heterogeneous force chain network. Coarse aggregates, especially particles with a diameter greater than 9.5 mm, act as the dominant skeletal framework and bear significantly higher average and maximum contact forces. The statistical distribution of strong contact clearly confirms that these particles are the main load transfer paths.

[0170] (3) The microcrack evolution characteristics show that larger NMAS mixtures have a higher crack initiation strain threshold, a lower crack propagation rate, and a smaller total number of cracks at failure. This superior damage tolerance is attributed to the optimized stress distribution within the coarse aggregate skeleton and the effective inhibition of propagating cracks by the large aggregate.

[0171] The above embodiments are merely preferred examples of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size, characterized in that, Includes the following steps: Step S1, specimen preparation and macroscopic mechanical testing: Prepare at least two kinds of skeleton-dense cement-stabilized crushed stone specimens with different nominal maximum particle sizes, conduct uniaxial compression tests on the specimens, obtain macroscopic stress-strain curves, and conduct crushing value tests; Step S2, Discrete Element Numerical Model Construction and Verification: Based on the gradation information of each specimen in Step S1, construct the corresponding three-dimensional discrete element uniaxial compression numerical model; run the numerical model to perform simulation, and compare the stress-strain curve obtained from the simulation with the test curve of the corresponding specimen in Step S1 to verify the reliability of the model. Step S3, Macroscopic Mechanical Performance Analysis: Based on the validated model, extract and quantify the macroscopic features that reflect the essence of mechanics; Step S4, Micromechanical Feature Extraction and Analysis: Extract and analyze the micromechanical features of the model during the loading process. The micromechanical features include contact force distribution features, contact quantity features, and microcrack evolution features. In step S4, the analysis of microcrack evolution characteristics includes: monitoring and recording the development curve of the number of microcracks with axial strain during loading, extracting the crack initiation strain threshold, crack propagation rate and the total number of cracks at macroscopic failure; and extracting the spatial and angular distribution characteristics of cracks at the peak stress moment. The extraction of crack angle distribution characteristics specifically involves: statistically analyzing the projection angle of the normal vector of all microcracks onto the horizontal plane, and drawing a crack statistical rose diagram to analyze the directional initiation and propagation patterns of cracks. In step S4, a three-stage crack evolution prediction model is constructed to predict crack resistance performance. The following prediction parameters are set to correlate microstructural parameters with macroscopic damage behavior: (1) Damage initiation threshold strain That is, the strain point at which the crack begins to grow significantly: ； in, This is the equivalent interface reinforcement coefficient. The larger the interface, the stronger its crack resistance. The entropy of the skeleton structure is represented by A, where A is a coefficient and ε0 is the reference strain. (2) Damage steady growth rate for: G d = B / λ + G 0 ； Where λ is the tortuosity of the force chain, therefore G d It is inversely proportional to λ; B is the coefficient, and G0 is the background growth rate; (3) Total number of microcracks at final failure : N total = N max × C L (-k) ; in, For load transfer concentration, N max denoted as the theoretical maximum value of the microcrack, and k is the attenuation exponent.

2. The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size according to claim 1, characterized in that, In step S1, the different nominal maximum particle sizes include at least a first particle size, a second particle size, and a third particle size, wherein the third particle size is larger than the second particle size, and the second particle size is larger than the first particle size.

3. The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size according to claim 1, characterized in that, In step S2, constructing the three-dimensional discrete element uniaxial compression numerical model specifically includes: S2-1, Particle Generation and Initial Equilibrium: Based on the number of particles calculated from the actual gradation, a discrete particle assembly is generated within the cylindrical modeling domain. The particle density and damping parameters are defined, the loading plate and lateral constraint boundaries are set, and initial equilibrium calculations are performed. S2-2, Coarse aggregate clustering modeling: replace coarse aggregate particles with a particle size greater than a predetermined threshold with a cluster structure composed of multiple basic particles bonded together to simulate the real shape of irregular aggregates. S2-3, Contact Model Assignment: Assigning a mechanical model to the contact between different components.

4. The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size according to claim 3, characterized in that, The coarse aggregate clustering modeling is achieved by importing STL format geometric files to define the shape of the cluster structure and controlling the volume error before and after cluster replacement to within ±1%.

5. The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size according to claim 3, characterized in that, The mechanical model is used to simulate the contact between different components. The contact between coarse aggregate and loading plate, and between coarse aggregates, adopts the rolling resistance linear contact model. The contact between cement mortar particles in the aggregate matrix adopts the parallel bonding model.

6. The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size according to claim 1, characterized in that, In step S4, the analysis of contact force distribution characteristics includes: statistically analyzing the average and maximum contact forces borne by aggregate particles in different particle size ranges, and analyzing the load transmission hierarchy and dominant skeleton within the material.

7. The method for analyzing the mechanical properties of cement-stabilized crushed stone based on the maximum nominal aggregate size according to claim 1, characterized in that, In step S4, the analysis of contact quantity characteristics includes: defining strong contact as above the average contact force and weak contact as below the average contact force; and statistically analyzing the number and proportion of strong and weak contacts undertaken by aggregate particles in each particle size range to quantify the mechanical role of particles of different sizes in the skeleton structure.

Images