Water-stable aggregate multi-physical field coupling damage deterioration simulation method based on near-field dynamics

Abstract

The application belongs to the technical field of material science and technology, and particularly relates to a water-stable macadam multi-physical field coupling damage deterioration simulation method based on near-field dynamics, which comprises geometric configuration modeling: the water-stable macadam is discretized into aggregate phase, interface transition zone phase, mortar phase, pore phase and crack phase, and multi-phase geometric modeling is realized through the following modes, aggregate phase: three-dimensionally reconstructing randomly distributed aggregate particles based on CT scanning data, and the volume ratio is 60-70%, interface transition zone phase: generating an equal-thickness transition zone according to the interface transition zone thickness measured by a microscope image. The application can accurately simulate the damage deterioration process of the water-stable macadam under the multi-physical field coupling effect, and provides a new technical means for the research and engineering application in the related field.

Description

Technical Field

[0001] This invention belongs to the field of materials science and technology, specifically relating to a multi-physics field coupled damage and degradation simulation method for water-stabilized crushed stone based on near-field dynamics. Background Technology

[0002] Cement-stabilized crushed stone (CMS) is a key building material for road base and subbase layers, and is widely used in infrastructure construction such as highways and airport runways due to its excellent mechanical properties and durability. However, in actual engineering scenarios, CMS faces the combined effects of many complex environmental factors, among which traffic loads, freeze-thaw cycles, moisture, and ion erosion have particularly significant impacts.

[0003] Long-term, repeated traffic loads can cause fatigue damage to water-stabilized crushed stone materials, leading to the initiation and propagation of cracks. In cold regions, moisture seeps into the material and causes freeze-thaw damage due to expansion. Simultaneously, the penetration of moisture and corrosive ions (such as chloride ions) further accelerates the material's deterioration process. These multi-physics coupling effects cause the mechanical properties of water-stabilized crushed stone to gradually decline, ultimately leading to pavement structural failure.

[0004] Currently, simulations of damage and deterioration of water-stabilized crushed stone are mainly based on the theory of continuum mechanics, among which the finite element method (FEM) and discrete element method (DEM) are more commonly used. For example, in the study "Research on Mechanical Properties of Cement Stabilized Crushed Stone Without Vibration Compression", Yuan Jiaquan and Han Zhonggui used the finite element method to simulate the mechanical behavior of water-stabilized crushed stone under a single load. To a certain extent, it can present the macroscopic mechanical response of the material and provide a reference for analyzing the mechanical performance of cement stabilized crushed stone under conventional loads.

[0005] However, these traditional methods reveal significant limitations when faced with multiphysics coupling effects. Traditional continuum mechanics methods struggle to accurately describe the discontinuous characteristics within materials, such as crack initiation, propagation, and the evolution of multi-scale damage. They typically rely on pre-defined cracks or simplified damage models, failing to realistically represent the dynamic development of material damage. Furthermore, in simulating multiphysics coupling, simplified models are frequently employed, hindering the in-depth understanding of damage mechanisms at the microscopic level. For instance, in simulating freeze-thaw damage, most methods focus solely on the deterioration of macroscopic mechanical properties, neglecting microscopic processes such as ice crystal nucleation and frost heave stress.

[0006] Furthermore, traditional methods have low computational efficiency when dealing with multi-scale, multi-physics coupled problems, making it difficult to meet the needs of large-scale engineering applications. Moreover, their computational accuracy and stability are poor when dealing with complex geometries and non-uniform material distributions.

[0007] Given the shortcomings of existing technologies, there is an urgent need for a more advanced and accurate simulation method to effectively solve the problem of simulating the damage and deterioration of water-stabilized crushed stone under the coupling effect of multiple physical fields, thereby improving the design level of pavement structures and the accuracy of durability assessment. Summary of the Invention

[0008] The purpose of this invention is to provide a multi-physics field coupling damage and degradation simulation method for water-stabilized crushed stone based on near-field dynamics. This method can accurately simulate the damage and degradation process of water-stabilized crushed stone under the action of multi-physics field coupling, providing a new technical means for research and engineering applications in related fields.

[0009] The specific technical solution adopted by this invention is as follows:

[0010] A multi-physics coupled damage degradation simulation method for water-stabilized crushed stone based on near-field dynamics includes the following steps:

[0011] A: Geometric configuration modeling: The water-stabilized crushed stone is discretized into aggregate phase, interface transition zone phase, mortar phase, porous phase, and crack phase, and multiphase geometric modeling is achieved through the following methods:

[0012] Aggregate phase: Randomly distributed aggregate particles based on 3D reconstruction of CT scan data, accounting for 60-70% of the volume;

[0013] Interface transition zone phase: The thickness of the interface transition zone is measured based on the microscopic image to generate a transition zone of equal thickness;

[0014] Porous and crack phases: Pores and microcracks were randomly generated based on mercury intrusion porosimetry and CT data;

[0015] After the aggregate, interface transition zone, pores and cracks are formed, the remaining space is filled by the mortar phase;

[0016] B: Multiphysics coupling model;

[0017] Fatigue damage module under load: The Drucker-Prager constitutive model is used to describe plastic deformation, the energy density fracture criterion is used to determine crack initiation, and the relationship between crack propagation rate and stress intensity factor is simulated based on Paris law.

[0018] Moisture transport module: A moisture migration model is constructed based on the modified Darcy's law, which is transformed into a peri-field dynamic equation and combined with the peri-field dynamic equation to describe moisture diffusion;

[0019] Ion transport model: Introducing a seepage effect term into Fick's second law to simulate the diffusion behavior of ion concentration as it migrates with water;

[0020] Freeze-thaw damage module: Trigger freeze-thaw stress by ice crystal nucleation conditions, simulate crack propagation by combining random pre-damage method, and introduce salt solution concentration-dependent aggravation factor to quantify salt-freeze damage and form salt-freeze damage aggravation factor.

[0021] C: Numerical discretization and asymptotic temporal coupling;

[0022] An adaptive meshless point-discretion spatial discretization method based on the quadtree principle is adopted, and the discretization accuracy is dynamically adjusted according to the material composition to eliminate the zero-energy mode.

[0023] By solving the mechanical field and the diffusion field step by step using an asymptotic temporal coupling method, the computational accuracy and efficiency of multi-field coupling are optimized.

[0024] The material properties of the interface transition zone in A include the elastic modulus and Poisson's ratio, which are lower than those of the aggregate phase and the mortar phase.

[0025] The method for randomly generating pores and cracks in A includes:

[0026] The Poisson distribution function is used to generate pore location, size, crack length, and orientation.

[0027] Collision detection algorithms ensure that pores, cracks, aggregates, and interface transition zones do not overlap.

[0028] The threshold of the energy density fracture criterion in B is a function of the material fracture energy, determined by fatigue testing.

[0029] The salt-freezing damage aggravating factor α in B s The calculation formula is:

[0030] α s =1+kC s

[0031] Where k is an empirical constant, determined experimentally, C s This refers to the salt solution concentration, with units of mol / m³. 3 k and C s Determined through experiments.

[0032] In the adaptive meshless point spatial discretization method in C, the discretization accuracy is controlled by the material point spacing h, and the value ranges from 1 / 10 to 1 / 100 of the material characteristic size.

[0033] In the asymptotic timing coupling method in C:

[0034] The number of coupling steps during the melting period is set according to the number of daily axle load applications;

[0035] The number of coupling steps during the freezing period is set based on the number of nighttime freeze-thaw cycles calculated from the simulated road section.

[0036] The calculation of frost heave stress in B is based on the ice crystallization pressure theory, and the formula is:

[0037]

[0038] Where, ρ ce The density of ice is expressed in kg / m³. 3 ΔV is the rate of volume change when water freezes. The rate of temperature change is expressed in K / s, ρ. ice The ice crystal pressure, and both ΔV and ΔV are determined experimentally.

[0039] The technical effects achieved by this invention are as follows:

[0040] This invention employs near-field dynamics theory, which can naturally describe the discontinuous characteristics within materials, such as crack initiation, propagation, and multi-scale damage evolution. By introducing damage variables and energy density fracture criteria, it can accurately simulate fatigue damage and crack propagation behavior.

[0041] Secondly, this invention combines near-field dynamic thermal diffusion theory and a modified Darcy's law to construct a water and ion transport model, which can accurately describe the transport behavior of water and ions within materials. Simultaneously, based on ice crystal pressure theory and a random distribution pre-damage method, a freeze-thaw damage model is constructed, which can reveal the freeze-thaw damage mechanism at the microscopic level.

[0042] Furthermore, this invention employs an adaptive meshless point-discretion method based on the four-fold tree principle, improving computational efficiency and accuracy. It also achieves efficient coupled simulation of multiple physical fields, including load, freeze-thaw cycles, moisture, and ion transport, through a progressive temporal coupling method. Finally, by comparing computational and experimental data, this invention verifies the model's accuracy in simulating ion transport behavior and crack propagation evolution, providing reliable theoretical support for the design and durability assessment of water-stabilized crushed stone materials.

[0043] This invention has broad application prospects and can be applied to multiple fields such as road engineering, materials science, and engineering education. In road engineering, this invention can provide theoretical support for pavement structure design and durability assessment; in materials science, it can provide technical means for the research and development and performance optimization of novel water-stabilized crushed stone materials; and in engineering education, it can provide advanced teaching and research tools for universities and research institutions. By introducing near-field dynamics theory, this invention can accurately simulate the damage and degradation process of water-stabilized crushed stone under multi-physics coupling, providing new technical means for research and engineering applications in related fields. Attached Figure Description

[0044] Figure 1 This is a flowchart of the overall model of the present invention;

[0045] Figure 2 This is a flowchart of the construction of the geometric model of water-stabilized crushed stone in this invention;

[0046] Figure 3 This is a flowchart of the near-field dynamics model for fatigue crack propagation in this invention;

[0047] Figure 4 This is a flowchart of the near-field dynamics model of water and ion transport in this invention;

[0048] Figure 5 This is a flowchart of the freeze-thaw damage and salt-freeze damage model in this invention;

[0049] Figure 6 This is a flowchart of the numerical discretization and coupling model in this invention. Detailed Implementation

[0050] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0051] like Figures 1-6 As shown, the multi-physics field coupled damage degradation simulation method for water-stabilized crushed stone based on near-field dynamics includes the following steps:

[0052] A: Geometric Configuration Modeling: The water-stabilized crushed stone is discretized into aggregate phase, interface transition zone phase, mortar phase, porous phase, and crack phase. Multiphase geometric modeling is achieved through the following methods (see appendix). Figure 2 As shown:

[0053] A1: Aggregate phase modeling:

[0054] Aggregate phase is the main component of water-stabilized crushed stone, and its geometry and distribution have a significant impact on the mechanical properties of the material. The method involves three-dimensional reconstruction of randomly distributed aggregate particles based on CT scan data, and the specific steps are as follows:

[0055] Data collection:

[0056] Use a high-resolution CT scanner or laser scanner to scan the actual aggregate particles and obtain three-dimensional point cloud data.

[0057] Point cloud data processing:

[0058] Import the scanned point cloud data into image processing software (such as MATLAB) for denoising and preprocessing; use filtering algorithms (such as Gaussian filtering or median filtering) to remove noise points.

[0059] 3D Reconstruction:

[0060] A multi-view geometric reconstruction algorithm is used to reconstruct a three-dimensional geometric model from a two-dimensional image sequence; a scale-invariant feature transform algorithm is used to extract feature points, which are then matched with images from different viewpoints to generate a three-dimensional point cloud; the point cloud data is then converted into a triangular mesh model for subsequent processing.

[0061] Geometric optimization:

[0062] Meshlab was used to smooth and optimize the reconstructed 3D model to ensure the accuracy of the geometric model and computational efficiency; the model's closure and topology were checked to ensure it was suitable for numerical simulation.

[0063] Random distribution:

[0064] Write a Python script to randomly generate the position and orientation of aggregate particles within the computational domain of the near-field dynamics model; use a collision detection algorithm to ensure that aggregate particles do not overlap; the volume fraction of aggregate particles accounts for 60-70% of the water-stabilized crushed stone.

[0065] A2: Modeling the interface transition area:

[0066] The interface transition zone is a weak area between aggregate and mortar. Its geometry and material properties have a significant impact on the mechanical properties of water-stabilized crushed stone. The specific steps for modeling the interface transition zone are as follows: The thickness of the interface transition zone is measured using microscopic images to generate a transition zone of uniform thickness.

[0067] Determine the thickness of the interface transition area:

[0068] Microscopic images of multiple locations in the interface transition zone of water-stabilized crushed stone were acquired using a high-resolution optical microscope or scanning electron microscope, ensuring coverage of the interface transition zone for different aggregate particles. After image acquisition, image processing software was used to denoise and enhance the microscopic images, adjusting contrast and brightness to make the boundaries of the interface transition zone clearly visible. The boundaries of the interface transition zone were marked on the images. The interface transition zone typically appears as a grayscale gradient area between the aggregate and mortar. Using the measurement tools in the image processing software, the thickness of the interface transition zone was measured along a direction perpendicular to the interface, with multiple measurement points randomly selected in each image to ensure the representativeness of the measurement results. Finally, statistical analysis was performed on the thickness data from all measurement points, calculating statistical quantities such as the mean and standard deviation, and the characteristic thickness value of the interface transition zone was experimentally measured.

[0069] Generate a transition region:

[0070] To generate an interface transition zone of uniform thickness on the surface of aggregate particles, a geometric offset algorithm can be used to offset the aggregate surface outward by a certain distance, treating the generated transition zone as an independent geometric phase.

[0071] Material property assignment:

[0072] The interface transition zone is assigned corresponding material properties such as elastic modulus and Poisson's ratio.

[0073] A3: Modeling of porous and crack phases:

[0074] Porous and crack phases are important internal features of water-stabilized crushed stone, and their distribution and topological properties significantly influence the material's mechanical properties and transport behavior. Based on mercury intrusion porosimetry and CT data, porosity and microcracks are randomly generated. The specific steps for modeling the porous and crack phases are as follows:

[0075] Hole structure data:

[0076] Data on porosity, pore size distribution, and pore connectivity of water-stabilized crushed stone were obtained through mercury intrusion porosimetry and CT scanning. The data from these tests were then imported into image processing software for denoising and binarization, and pore structure characterization indicators such as porosity, average pore size, and pore size distribution were extracted.

[0077] Crack network data:

[0078] The cross-section of the water-stabilized crushed stone specimen was observed using an optical microscope or scanning electron microscope to obtain the distribution and topological characteristics of microcracks. Three-dimensional crack network data of the water-stabilized crushed stone was acquired using a high-resolution CT scanner. The images obtained from the microscope or CT scan were imported into image processing software for denoising and binarization, and crack characterization indicators such as crack density, crack length, crack width, and crack orientation were extracted.

[0079] Randomly generated porous and crack phases:

[0080] Write a Python script to randomly generate pores based on experimentally measured porosity and pore size distribution. Use the Poisson distribution function to randomly generate the pore locations and sizes. The pore shapes can be simplified to spheres or ellipsoids to reduce computational complexity. Also use the Poisson distribution function to randomly generate the crack locations, lengths, and orientations. The crack shapes can be simplified to straight lines or curves to reduce computational complexity.

[0081] Parameter indicators:

[0082] Porosity: The ratio of pore volume to total volume, typically 5-15%.

[0083] Average pore size: The average diameter of the pores, typically 10-100 micrometers.

[0084] Pore ​​size distribution: The range of pore diameter distribution, which usually follows a log-normal distribution.

[0085] Crack density: The number of cracks per unit volume, typically 1-10 cracks / mm. 3 .

[0086] Crack length: The average length of a crack, typically 100-500 micrometers.

[0087] Crack width: The average width of the crack, typically 10-50 micrometers.

[0088] Crack orientation: The direction of crack distribution, which usually follows a uniform distribution or a specific orientation distribution.

[0089] Deployed to the model:

[0090] Collision detection algorithms are used to ensure that pores and cracks do not overlap with aggregates or interface transition zones. A Python script is written to implement random placement and collision detection of pores and cracks. The generated pores and cracks are imported into geometric modeling software for geometry optimization and mesh generation. The geometry and distribution of pores and cracks are ensured to meet the experimentally measured characterization parameters.

[0091] A4: Mortar Phase Modeling:

[0092] The mortar phase is the matrix material of water-stabilized crushed stone. Its geometry and material properties have a significant impact on the overall performance of the material. After the aggregate, interface transition zone, pores, and cracks are generated, the remaining space is filled by the mortar phase. The specific steps for modeling the mortar phase are as follows:

[0093] Fill the remaining space:

[0094] After the aggregate, interface transition zone, pores, and cracks are generated, the remaining space is filled by the mortar phase. The mortar phase is obtained by subtracting the aggregate, transition zone, pores, and cracks from the computational domain using Boolean operations.

[0095] Material property assignment:

[0096] The mortar phase is endowed with material properties such as elastic modulus and Poisson's ratio, the values ​​of which are determined experimentally.

[0097] B: Multiphysics coupling model;

[0098] B1: Fatigue damage module under load: The Drucker-Prager constitutive model is used to describe plastic deformation, the energy density fracture criterion is used to determine crack initiation, and the relationship between crack propagation rate and stress intensity factor is simulated based on Paris law.

[0099] Fatigue damage under load is the main failure mode of water-stabilized crushed stone under cyclic loading. First, a damage mechanics model is used to introduce damage variables to describe the stiffness softening and damage accumulation process of the material under fatigue loading. The energy density fracture criterion is used to determine crack initiation, while the Drucker-Prager constitutive model is used to simulate the plastic deformation and yielding behavior of the material. Based on this, a near-field dynamics model of fatigue damage is constructed to simulate the damage evolution of water-stabilized crushed stone under fatigue loading. To reflect the crack propagation process, a fracture mechanics model is further introduced to analyze the relationship between crack propagation rate and stress intensity factor amplitude, constructing a near-field dynamics model of fatigue crack propagation under load based on fracture mechanics to simulate the crack propagation evolution process during the fatigue failure of water-stabilized crushed stone under fatigue loading. (Refer to Appendix) Figure 3 As shown.

[0100] The following are the detailed implementation measures and methods for this module:

[0101] Fatigue damage model: The fatigue damage model is used to describe the stiffness softening process and crack initiation behavior of water-stabilized crushed stone under cyclic loading. It includes the following steps:

[0102] Damage variable definition:

[0103] Damage variable D is used to characterize the degree of damage to the material, and its value ranges from 0 (no damage) to 1 (complete failure). The evolution equation of the damage variable is:

[0104]

[0105] Where C and m are material constants, determined through fatigue testing, σ kocal For local stress, calculated using a near-field dynamic model; σ f The fatigue strength of the material is determined through testing;

[0106] Material constant determination:

[0107] The fatigue strength σ of the material was determined by fatigue testing. f Record the stress-strain response and fatigue life of the specimen, and obtain c and m by fitting.

[0108] Energy density fracture criterion:

[0109] Energy density W:

[0110] Energy density W is used to characterize the local energy state of a material, and its calculation formula is:

[0111]

[0112] Where σ is the local stress and ε is the local strain.

[0113] Fracture threshold W c :

[0114] When the local energy density W exceeds the threshold W c At this time, the bonds between material points break, simulating crack initiation. Threshold W c It is determined experimentally and is usually a function of the material's fracture energy;

[0115] Druker-Prager constitutive model;

[0116] Yield function:

[0117] The Drucker-Prager model is used to describe the plastic behavior of the material, and the yield function is:

[0118]

[0119] Where: J2 is the second invariant of the deviatoric stress; I1 is the first invariant of the stress tensor; α DP and k are material constants, determined experimentally;

[0120] Material constant determination;

[0121] α was determined by triaxial compression test. DP and k.

[0122] Near-field dynamics model;

[0123] State function T:

[0124] The interaction forces between matter points are described by the state function T, which has the following form:

[0125] T = (1-D)T0

[0126] Where T0 is the state function in the lossless state.

[0127] Near-field dynamics governing equations;

[0128] The fundamental governing equations of peridynamics are:

[0129]

[0130] Where ρ is the material density, u is the displacement field, H is the neighborhood of matter x, and b is the volume force;

[0131] Crack propagation model;

[0132] The crack propagation model is used to describe the propagation behavior of water-stabilized crushed stone after cracks appear. The specific implementation steps are as follows:

[0133] Stress intensity factor calculation;

[0134] Stress intensity factor K:

[0135]

[0136] Where: σ is the far-field stress, and a is the crack length;

[0137] Calculation method;

[0138] The stress intensity factor at the crack tip was calculated using a near-field dynamics method.

[0139] Crack propagation rate model;

[0140] Paris's law is used to describe crack propagation rate:

[0141]

[0142] Where N is the number of cycles, and ΔK is the stress intensity factor amplitude;

[0143] Near-field dynamics model;

[0144] A crack propagation model is embedded into a near-field dynamics framework to simulate the crack propagation process. The breakage of the "bonds" between material points is controlled by the crack propagation rate, and the fracture condition is as follows:

[0145]

[0146] B2: Moisture transport module, which constructs a moisture migration model based on the modified Darcy's law, transforms the modified Darcy's law into a peri-field dynamic equation, and combines the peri-field dynamic equation to describe moisture diffusion;

[0147] Moisture and ion transport are significant factors contributing to the deterioration of water-stabilized crushed stone. This study begins by describing the fundamental principles of a moisture transport model, employing a modified Darcy's law as the governing equation for moisture transport within the crushed stone. This equation establishes the relationship between moisture flux, permeability coefficient, and hydraulic head. The permeability coefficient, a key parameter describing moisture flow within the crushed stone, is closely related to the material's moisture content and changes accordingly. Next, the model transforms the modified Darcy's law into a peri-field dynamic equation, considering the microscopic effects of moisture diffusion. The micro-diffusion coefficient is correlated with the permeability coefficient and is influenced by factors such as water density and gravity. For boundary conditions, the moisture transport model uses dry / wet boundary conditions, while the ion transport model uses high / low concentration boundary conditions.

[0148] The following are the detailed implementation measures and methods for this module, including specific formulas, parameter definitions, implementation steps, and tools;

[0149] A moisture transport model is used to describe the transport process of moisture within water-stabilized crushed stone. A modified Darcy's law is adopted as the governing equation for moisture transport within the crushed stone. The specific implementation steps are as follows:

[0150] Governing equations;

[0151] Modified Darcy's Law;

[0152] The modified Darcy's law is adopted as the governing equation for water transport within water-stabilized crushed stone:

[0153]

[0154] Where q is the water flux (unit: m / s); K(θ) is the permeability coefficient, which is related to the water content θ (unit: m / s); and h is the hydraulic head (unit: m).

[0155] Permeability coefficient K(θ);

[0156] The permeability coefficient K(θ) is usually expressed as a function of water content:

[0157]

[0158] Where: K s θ is the saturated permeability coefficient (unit: m / s); s is the saturated water content; n is an empirical constant, usually taking a value of 3-5.

[0159] Near-field dynamic equations;

[0160] Near-field dynamics;

[0161] Transforming the modified Darcy's law into a near-field dynamics form:

[0162]

[0163] Where: κ is the micro-diffusion coefficient (unit: m) 2 / s); Let X be the neighborhood of the matter point X.

[0164] Near-field dynamics;

[0165] The micro-diffusion coefficient k is related to the permeability coefficient K(θ):

[0166]

[0167] Where: ρ is the density of water (unit: kg / m³) 3 g is the acceleration due to gravity (unit: m / s²). 2 );

[0168] Set boundary conditions;

[0169] Dry / wet boundary conditions;

[0170] A dry boundary condition indicates that the moisture content at the model boundary is low, typically close to the dry state of the material. The mathematical expression for the dry boundary condition is:

[0171] θ=θ dry

[0172] Where θ dry This refers to the moisture content in a dry state.

[0173] In the numerical simulation software, select the model boundary and set the water content to θ. dry .

[0174] A wetting boundary condition indicates that the moisture content at the model boundary is high, typically close to the material's saturation state. The mathematical expression for a wetting boundary condition is:

[0175] θ=θ wet

[0176] Where θ wet This represents the moisture content in a dry state.

[0177] Initial conditions;

[0178] The initial moisture content θ0 represents the moisture distribution within the water-stabilized crushed stone at the start of the simulation. The mathematical expression for the initial moisture content is:

[0179] θ(X, t=0)=θ0(X)

[0180] Where θ0(X) is a function of the spatial coordinate X.

[0181] In numerical simulation software, the initial water content θ0 is set to a uniform distribution or a non-uniform distribution based on experimental data. If a uniform distribution is used, θ0 is a constant; if a non-uniform distribution is used, θ0(X) needs to be determined experimentally.

[0182] If the moisture distribution inside the water-stabilized crushed stone is uniform, the initial moisture content θ0 is a constant:

[0183] θ0(X)=θ0

[0184] θ0 is determined experimentally and is usually the average moisture content of the specimen.

[0185] If the moisture distribution inside the water-stabilized crushed stone is uneven, the initial moisture content θ0(X) is a function of the spatial coordinate X. The distribution function of θ0(X) is obtained by experimentally determining the moisture content of the specimen at different locations and fitting the data.

[0186] B3: Ion Transport Model: Introducing a seepage effect term into Fick's second law to simulate the diffusion behavior of ion concentration as it migrates with water. See Appendix. Figure 4 As shown;

[0187] The ion transport model is used to describe the ion transport process within water-stabilized crushed stone. The specific implementation steps are as follows:

[0188] Governing equations;

[0189] Fick's Second Law;

[0190] Based on Fick's second law, a term incorporating the effect of water infiltration on ion transport is added:

[0191]

[0192] Among them, C t C represents the total ion concentration. f Let denoted as ρ be the free ion concentration, D be the diffusion coefficient, and t be the diffusion time. For ion-binding ability, x i Let be the i-th material point in the near-field dynamics theoretical model, ω be the moisture content in the water-stabilized crushed stone, and μ be the influence factor of moisture seepage on chloride ion transport.

[0193] Near-field dynamic equations;

[0194] Near-field dynamics form:

[0195]

[0196] Among them, κ C Micro-diffusion coefficient (unit: m) 2 / s).

[0197] Micro-ion diffusion coefficient:

[0198] Micro-ion diffusion coefficient κ C With diffusion coefficient D d Related:

[0199]

[0200] Set boundary conditions and initial conditions;

[0201] Ion concentration boundary conditions;

[0202] A high-concentration boundary condition indicates a high ion concentration at the model boundary, typically equivalent to the ion concentration in the external environment (such as de-icing salt solution). The mathematical expression for a high-concentration boundary condition is:

[0203] C = C hight

[0204] Where C hight This represents the ion concentration at the high-concentration boundary.

[0205] In the numerical simulation software, select the model boundary and set the ion concentration to C. hight The ion concentration in the external environment is measured using an ion concentration meter, and the measurement results are input into numerical simulation software as high-concentration boundary conditions.

[0206] Low-concentration boundary conditions indicate that the ion concentration at the model boundary is low, typically close to the initial ion concentration inside the material. The mathematical expression for low-concentration boundary conditions is:

[0207] C = C 1ow

[0208] Where C low This represents the ion concentration at the low-concentration boundary.

[0209] In the numerical simulation software, select the model boundary and set the ion concentration to C. low The initial ion concentration inside the material was measured using an ion concentration meter, and the measurement results were input into numerical simulation software as low-concentration boundary conditions.

[0210] Initial conditions

[0211] The initial ion concentration C0(X) represents the ion distribution state inside the water-stabilized crushed stone at the start of the simulation. The mathematical expression for the initial ion concentration is:

[0212] C(X, t=0) = C0(X)

[0213] Where C0(X) is a function of the spatial coordinate X.

[0214] In the numerical simulation software, the initial ion concentration C0 is set to either a uniform distribution or a non-uniform distribution based on experimental data. If a uniform distribution is used, C0 is a constant; if a non-uniform distribution is used, C0(X) needs to be determined experimentally. The ion concentration at different locations on the water-stabilized crushed stone specimen is determined through sampling experiments.

[0215] If the ion distribution inside the water-stabilized crushed stone is uniform, the initial ion concentration C0 is a constant:

[0216] C0(X)=C0

[0217] C0 is determined experimentally and is usually the average ion concentration of the specimen.

[0218] If the ion distribution inside the water-stabilized crushed stone is uneven, the initial ion concentration C0(X) is a function of the spatial coordinate X. The distribution function of C0(X) is obtained by experimentally determining the ion concentration at different locations of the specimen and fitting the data.

[0219] B4: Freeze-thaw damage module: Trigger freeze-thaw stress by ice crystal nucleation conditions (pore size, temperature), simulate crack propagation by combining random pre-damage method, and introduce a salt solution concentration-dependent aggravation factor to quantify salt-freeze damage and form a salt-freeze damage aggravation factor.

[0220] Freeze-thaw damage is the main failure mode of water-stabilized crushed stone in cold regions. First, based on ambient temperature, water film thickness, ice / water interfacial energy, and the freezing entropy of the snow-melting salt solution, the minimum pore size that can form ice within the water-stabilized crushed stone under different ambient temperatures is calculated. Then, considering the pore structure of the mortar matrix, the interfacial transition zone, and the characteristics of microcracks within the water-stabilized crushed stone, a method of introducing randomly distributed pre-damage is proposed to simulate the influence of the mortar matrix pore structure, the interfacial transition zone, and initial microcracks on the freeze-thaw damage of the water-stabilized crushed stone, thereby constructing a near-field dynamic model of freeze-thaw damage in water-stabilized crushed stone. Finally, based on the ice crystallization pressure theory, the frost heave stress (i.e., ice crystallization pressure) on the pore walls of the ice crystals is calculated. Tracing the crack propagation path, the calculated ice crystallization pressure is applied along the fractured bonds on the crack surface by applying equal and opposite displacement increments to the material points at both ends of the crack, thus simulating the coupling effect of frost heave failure and crack propagation during pure water freeze-thaw cycles in water-stabilized crushed stone. The following are the detailed implementation measures and methods for this module, including specific formulas, parameter definitions, implementation steps, and tools. Please refer to the appendix. Figure 5 As shown;

[0221] Freeze-thaw damage model;

[0222] The freeze-thaw damage model is used to describe the damage evolution process of water-stabilized crushed stone under freeze-thaw cycles. The specific implementation steps are as follows:

[0223] Ice crystal nucleation conditions;

[0224] Ice crystal nucleation is the initial stage of freeze-thaw damage, and its conditions are determined by ambient temperature, water film thickness, and pore size. The minimum pore size r for ice crystal nucleation... min Calculated using the following formula:

[0225]

[0226] Wherein: γ iw Ice / water interface energy (unit: J / m) 2 );ΔG v Free energy difference between ice and water phase transition (unit: J / m) 3 ). γ iw and ΔG v It is determined experimentally and is usually a function of temperature and pressure.

[0227] Pre-damage introduction;

[0228] Randomly distributed pre-damage;

[0229] Write a Python script to randomly generate microcracks based on experimentally measured crack density λ and crack length distribution. The crack shape can be simplified to a straight line or curve to reduce computational complexity. Also write a Python script to randomly generate pores based on experimentally measured porosity φ and pore size distribution. The pore shape can be simplified to a sphere or ellipsoid to reduce computational complexity.

[0230] Pre-damage generation;

[0231] Crack location: The start and end points of the crack are randomly generated within the computational domain.

[0232] Crack length: The crack length is randomly generated based on the crack length distribution measured in the experiment.

[0233] Crack direction: The direction of the crack is randomly generated based on the crack orientation distribution measured in the experiment.

[0234] Pore ​​location: The center point of the pore is randomly generated within the computational domain.

[0235] Pore ​​size: The radius of the pores is randomly generated based on the pore size distribution measured in the experiment.

[0236] Use a collision detection algorithm to ensure that cracks and pores do not overlap. Write a Python script to implement the random generation of cracks and pores and collision detection.

[0237] Ice crystal pressure calculation

[0238] When ice crystals form in pores, they exert frost heave stress (ice crystallization pressure) on the pore walls. Ice crystallization pressure P ice The calculation formula is:

[0239]

[0240] Where: ρ ice Density of ice (unit: kg / m³) 3 ); ΔV is the rate of volume change when water freezes; ρ is the rate of temperature change (unit: K / s). ice ΔV is determined experimentally and is usually a function of temperature and pressure.

[0241] Crack propagation simulation;

[0242] Crack propagation model;

[0243] Ice crystallization pressure was applied to the crack surface to simulate the crack propagation process. The driving force for crack propagation was the ice crystallization pressure P. ice .

[0244] Crack propagation model;

[0245] When ice crystal pressure P ice Exceeding the tensile strength σ of the material t At that time, the crack began to propagate:

[0246] P ice ≥σ t

[0247] Salt-freezing damage model;

[0248] Salt damage is an aggravated form of freeze-thaw damage, caused by de-icing salt solutions. The following are the specific implementation steps:

[0249] Salt-freezing damage aggravating factors

[0250] Salt-freezing damage aggravation factor α s Used to describe the aggravating effect of snow-melting salt solutions on freeze-thaw damage. α s The calculation formula is:

[0251] α s =1+kC s

[0252] Where: k is an empirical constant, determined experimentally; C s Salt solution concentration (unit: mol / m³) 3 k and C s It is determined experimentally and is usually a function of temperature and pressure.

[0253] Salt freezing pressure calculation;

[0254] Salt freeze-pressed P s ;

[0255] Salt freeze-pressed P s The calculation formula is:

[0256] P s =α s P ice

[0257] Where P ice This is the pressure of ice crystals.

[0258] Crack propagation simulation;

[0259] Salt freeze-press P s The load was applied to the crack surface to simulate the salt-freezing damage process.

[0260] C: Numerical discretization and asymptotic temporal coupling;

[0261] An adaptive meshless point-discretion spatial discretization method based on the quadtree principle is adopted, and the discretization accuracy is dynamically adjusted according to the material composition to eliminate the zero-energy mode.

[0262] By using an asymptotic temporal coupling method to solve the mechanical field (implicit solution) and the diffusion field (explicit solution) step by step, the computational accuracy and efficiency of multi-field coupling are optimized.

[0263] Numerical discretization and asymptotic temporal coupling are key steps in simulating the damage and degradation process of water-stabilized crushed stone under multi-physics coupling. First, an asymptotic temporal coupling method is employed to simulate the fatigue mechanics model during freeze-thaw damage. This method progressively improves computational accuracy and adapts to different calculation steps to accommodate the damage and freeze-thaw effects on water-stabilized crushed stone. Second, the asymptotic temporal coupling method further addresses how to describe the evolution of damage under freeze-thaw cycles when considering the mechanical changes of water-stabilized crushed stone during freeze-thaw processes. This method, based on experimental data, progressively calculates stress and temperature changes during freeze-thaw damage, providing a relatively efficient simulation approach. Finally, the computational accuracy in the model is improved by optimizing the calculation steps. The accuracy of the calculation process is adjusted by setting an appropriate number of steps, and the numerical model is optimized based on experimental results to ensure the accuracy and stability of the calculations. The following are detailed implementation measures and methods for this module, including specific formulas, parameter definitions, implementation steps, and tools; please refer to the appendix. Figure 6 As shown;

[0264] C1: Numerical Discreteness;

[0265] Numerical discretization involves dividing a continuous computational domain into discrete material points or units to facilitate numerical computation. The specific implementation steps are as follows:

[0266] Adaptive meshless collocation space discretization method;

[0267] Quadtree principle:

[0268] An adaptive meshless collocation spatial discretization method based on the quadtree principle is employed to divide the computational domain into multiple subdomains. A quadtree is a spatially partitioned data structure that can adaptively adjust the discretization accuracy according to the material composition characteristics.

[0269] Discrete steps:

[0270] The computational domain is divided into a uniform initial grid. The grid is then adaptively refined based on the material composition characteristics (e.g., aggregates, mortar, porosity, etc.). Material points are generated within each subdomain; the location and number of these points are determined by the discretization precision.

[0271] Discrete precision:

[0272] Discretization accuracy is determined by the spacing h between material points, which is typically 1 / 10 to 1 / 100 of the material's characteristic size.

[0273] Eliminate zero-energy mode;

[0274] An unconventional peri-field dynamics model based on continuous motion units is employed to eliminate zero-energy modes. Kinematic constraints are introduced to limit the non-physical deformation of material points.

[0275] C2: Asymptotic timing coupling;

[0276] Asymptotic temporal coupling is used to achieve efficient coupled simulations of multiple physics fields such as load, freeze-thaw cycles, moisture, and ion transport. The specific implementation steps are as follows:

[0277] Implicit solution;

[0278] Fatigue damage module:

[0279] The fatigue damage module employs an implicit solution method to solve the evolution equations of the damage variables. The advantage of implicit solutions is their good stability, making them suitable for solving problems with large stiffness matrices.

[0280] Fatigue damage module:

[0281] Assemble the stiffness matrix based on the near-field dynamics model. Solve the nonlinear equations using the Newton-Raphson iterative method.

[0282] Explicit solution;

[0283] Moisture and ion diffusion module:

[0284] The moisture and ion diffusion module employs an explicit solution method to solve the transport equations for moisture and ions. The advantage of explicit solutions is their high computational efficiency, making them suitable for problems with small time steps.

[0285] Solution steps:

[0286] Use explicit time integration methods (such as Euler's method) to advance the time step. Update the variable values ​​for the next time step based on the variable values ​​at the current time step.

[0287] Progressive temporal coupling method;

[0288] Solution steps:

[0289] The asymptotic temporal coupling method controls the coupling accuracy by adjusting the number of coupling steps. The larger the number of coupling steps, the higher the coupling accuracy, but the greater the computational cost.

[0290] Coupling steps:

[0291] Set initial and boundary conditions. Within each time step, solve the fatigue damage module and the moisture and ion diffusion module sequentially. Pass the output variables (such as damage variables) of the fatigue damage module to the moisture and ion diffusion module, and vice versa.

[0292] Coupling accuracy optimization:

[0293] A reasonable number of coupling steps is determined through trial and error to balance computational efficiency and accuracy.

[0294] Assume that in the i-th freeze-thaw cycle, the number of coupling steps during the daytime thawing period is N. day i Coupling steps N during the nighttime freezing period night i ,but:

[0295] The diffusion times of water and ions in each coupled step during the melting period are as follows:

[0296] T w / sal i =T day i / N day i

[0297] The number of fatigue load applications in each coupling step during the melting period is as follows:

[0298] Q Mday i =Q day i / N day i

[0299] The number of fatigue load applications in each coupling step during the freezing period is as follows:

[0300] Q Fnight i =c / N night i

[0301] In the formula: T day i Q represents the duration during the day when snow on the road surface remains in a melted state after de-icing salt is applied; dry i Q represents the number of fatigue loads applied during the daytime thawing period in the i-th freeze-thaw cycle; night i Let Q be the number of fatigue loads applied during the nighttime freezing period in the i-th freeze-thaw cycle. night i +Q day i It equals the number of daily axle load applications after conversion from the simulated road section.

[0302] The core of this invention lies in constructing a numerical model based on peri-field dynamics theory that can accurately simulate the damage and deterioration process of water-stabilized crushed stone under the coupling of multiple physical fields such as freeze-thaw, fatigue, and ion transport. Peri-field dynamics theory is a mechanical theory based on the idea of ​​nonlocal interaction. Its core idea is to describe the mechanical behavior of materials through the interaction between material points, rather than the traditional local differential equations based on continuum mechanics. This method can naturally describe the discontinuous characteristics inside the material (such as crack initiation and propagation), and is particularly suitable for simulating multi-scale, multi-physical field coupled problems.

[0303] Peri-field dynamics theory discretizes materials into a series of points, each interacting with other points in its neighborhood through "bonds." The interactions between these points are described by "state functions," which can be functions of physical quantities such as displacement, strain, and stress. The fundamental governing equations of peri-field dynamics describe the motion state of each point and its interaction with other points in its neighborhood. This concept of nonlocal interaction gives peri-field dynamics a natural advantage in handling discontinuous problems such as crack initiation and propagation, without requiring pre-defined crack paths or the introduction of additional fracture criteria.

[0304] In this invention, near-field dynamics theory is extended to simulate multi-physics coupling problems. By introducing different state functions, this invention can simultaneously describe the interactions between mechanical fields, moisture transport fields, ion transport fields, and freeze-thaw damage fields. For example, in the mechanical field, by introducing damage variables and energy density fracture criteria, fatigue damage and crack propagation behavior can be accurately simulated. In the moisture transport field, by combining modified Darcy's law, the transport process of moisture within the material can be described. In the ion transport field, based on Fick's second law, the diffusion behavior of ions in the material can be simulated. In the freeze-thaw damage field, by using ice crystal pressure theory and random distribution pre-damage methods, the microscopic mechanism of freeze-thaw damage can be revealed.

[0305] Furthermore, this invention employs an adaptive meshless point-discretion method based on the four-fold tree principle, dividing the computational domain into multiple subdomains and adaptively adjusting the discretization precision according to the material composition characteristics, thereby improving computational efficiency while ensuring computational accuracy. Through a progressive temporal coupling method, this invention achieves efficient coupled simulation of multiple physical fields such as load, freeze-thaw cycles, moisture, and ion transport, enabling accurate prediction of the damage and degradation behavior of water-stabilized crushed stone under actual working conditions.

[0306] This invention proposes a multi-physics coupled damage degradation simulation method for water-stabilized crushed stone based on peri-field dynamics theory, which has significant innovations. First, this invention employs peri-field dynamics theory, which can naturally describe the discontinuous characteristics within the material, such as crack initiation, propagation, and multi-scale damage evolution. By introducing damage variables and energy density fracture criteria, it can accurately simulate fatigue damage and crack propagation behavior. Second, this invention combines peri-field dynamics thermal diffusion theory and a modified Darcy's law to construct a moisture and ion transport model, which can accurately describe the transport behavior of moisture and ions within the material. Simultaneously, based on ice crystallization pressure theory and a random distribution pre-damage method, a freeze-thaw damage model is constructed, which can reveal the freeze-thaw damage mechanism at the microscopic level. Furthermore, this invention uses a four-tree principle-based adaptive meshless point-discretion method, improving computational efficiency and accuracy, and achieves efficient coupled simulation of multiple physical fields such as load, freeze-thaw, moisture, and ion transport through an asymptotic temporal coupling method. Finally, by comparing calculation and experimental data, this invention verifies the accuracy of the model in simulating ion transport behavior and crack propagation evolution, providing reliable theoretical support for the design and durability assessment of water-stabilized crushed stone materials.

[0307] This invention has broad application prospects and can be applied to multiple fields such as road engineering, materials science, and engineering education. In road engineering, this invention can provide theoretical support for pavement structure design and durability assessment; in materials science, it can provide technical means for the research and development and performance optimization of novel water-stabilized crushed stone materials; and in engineering education, it can provide advanced teaching and research tools for universities and research institutions. By introducing near-field dynamics theory, this invention can accurately simulate the damage and degradation process of water-stabilized crushed stone under multi-physics coupling, providing new technical means for research and engineering applications in related fields.

[0308] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A multi-physics field coupled damage degradation simulation method for water-stabilized crushed stone based on near-field dynamics, characterized in that, Includes the following steps: A: Geometric configuration modeling: The water-stabilized crushed stone is discretized into aggregate phase, interface transition zone phase, mortar phase, porous phase, and crack phase, and multiphase geometric modeling is achieved through the following methods: Aggregate phase: Randomly distributed aggregate particles based on 3D reconstruction of CT scan data, accounting for 60-70% of the volume; Interface transition zone phase: The thickness of the interface transition zone is measured based on the microscopic image to generate a transition zone of equal thickness; Porous and crack phases: Pores and microcracks were randomly generated based on mercury intrusion porosimetry and CT data; After the aggregate, interface transition zone, pores and cracks are formed, the remaining space is filled by the mortar phase; B: Multiphysics coupling model; Fatigue damage module under load: The Drucker-Prager constitutive model is used to describe plastic deformation, the energy density fracture criterion is used to determine crack initiation, and the relationship between crack propagation rate and stress intensity factor is simulated based on Paris law. Moisture transport module: A moisture migration model is constructed based on the modified Darcy's law, which is transformed into a peri-field dynamic equation and combined with the peri-field dynamic equation to describe moisture diffusion; Ion transport model: Introducing a seepage effect term into Fick's second law to simulate the diffusion behavior of ion concentration as it migrates with water; Freeze-thaw damage module: Trigger freeze-thaw stress by ice crystal nucleation conditions, simulate crack propagation by combining random pre-damage method, and introduce salt solution concentration-dependent aggravation factor to quantify salt-freeze damage and form salt-freeze damage aggravation factor. C: Numerical discretization and asymptotic temporal coupling; An adaptive meshless point-discretion spatial discretization method based on the quadtree principle is adopted, and the discretization accuracy is dynamically adjusted according to the material composition to eliminate the zero-energy mode. By solving the mechanical field and the diffusion field step by step using an asymptotic temporal coupling method, the computational accuracy and efficiency of multi-field coupling are optimized.

2. The method for simulating damage degradation of water-stabilized crushed stone based on near-field dynamics using multi-physics field coupling, as described in claim 1, is characterized in that: The material properties of the interface transition zone in A include the elastic modulus and Poisson's ratio, which are lower than those of the aggregate phase and the mortar phase.

3. The method for simulating damage degradation of water-stabilized crushed stone based on near-field dynamics using multi-physics field coupling, as described in claim 1, is characterized in that: The method for randomly generating pores and cracks in A includes: The Poisson distribution function is used to generate pore location, size, crack length, and orientation. Collision detection algorithms ensure that pores, cracks, aggregates, and interface transition zones do not overlap.

4. The method for simulating damage degradation of water-stabilized crushed stone based on near-field dynamics using multi-physics field coupling, as described in claim 1, is characterized in that: The threshold of the energy density fracture criterion in B is a function of the material fracture energy, determined by fatigue testing.

5. The method for simulating damage degradation of water-stabilized crushed stone based on near-field dynamics using multi-physics field coupling, as described in claim 1, is characterized in that: The salt-freezing damage aggravating factor α in B s The calculation formula is: a s =1+kC s Where k is an empirical constant, determined experimentally, C s This refers to the salt solution concentration, with units of mol / m³. 3 k and C s Determined through experiments.

6. The method for simulating damage degradation of water-stabilized crushed stone based on near-field dynamics using multi-physics coupling, as described in claim 1, is characterized in that: In the adaptive meshless point spatial discretization method in C, the discretization accuracy is controlled by the material point spacing h, and the value ranges from 1 / 10 to 1 / 100 of the material characteristic size.

7. The method for simulating damage degradation of water-stabilized crushed stone based on near-field dynamics using multi-physics field coupling, as described in claim 1, is characterized in that: In the asymptotic timing coupling method in C: The number of coupling steps during the melting period is set according to the number of daily axle load applications; The number of coupling steps during the freezing period is set based on the number of nighttime freeze-thaw cycles calculated from the simulated road section.

8. The method for simulating damage degradation of water-stabilized crushed stone based on near-field dynamics using multi-physics field coupling, as described in claim 1, is characterized in that: The calculation of frost heave stress in B is based on the ice crystallization pressure theory, and the formula is: Where, ρ ice The density of ice is expressed in kg / m³. 3 ΔV is the rate of volume change when water freezes. The rate of temperature change is expressed in K / s, ρ. ice The ice crystal pressure, and both ΔV and ΔV are determined experimentally.

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