Fatigue simulation method for nonlinear energy dissipation of asphalt mixture

Abstract

The present application discloses a fatigue simulation method for nonlinear energy dissipation of asphalt mixture, abandons the simplified assumption of traditional linear damage model, accurately describes the variation law of the residual bonding radius multiplier of asphalt mixture in the initial stage, micro-damage stage, accelerated damage stage and destruction stage through piecewise function, and can accurately capture the nonlinear mechanical behavior of the material in different damage stages. At the same time, the method combines the ant colony optimization algorithm to accurately calibrate the model parameters, and efficiently searches the model parameter space by simulating the group intelligent behavior of ant colonies foraging in nature, and finds the optimal parameter combination, so that the simulation results are highly consistent with the test results, significantly improving the accuracy of fatigue life prediction, effectively reducing the prediction error, providing a more reliable theoretical basis for the design of asphalt pavement structure, and extending the service life of the pavement.

Description

Technical Field

[0001] The present application relates to the technical field of asphalt mixture fatigue simulation, and in particular to a fatigue simulation method of asphalt mixture nonlinear energy dissipation. Background Art

[0002] Existing discrete element fatigue damage models are mainly divided into two categories: stress-based models and energy-based models. Stress-based models usually assume that the fatigue damage of the material is related to the stress level and action time, such as the parallel bond stress corrosion model (PSC). This type of model can simulate creep damage, but there are some deficiencies in the simulation of fatigue damage. Energy-based models assume that the fatigue damage of the material is related to energy dissipation, such as the cumulative dissipated energy model. This type of model usually assumes that the energy dissipation is linearly related to the number of cyclic loading.

[0003] On the other hand, fatigue damage analysis of asphalt mixtures mainly relies on indoor fatigue tests and empirical models; indoor tests can obtain fatigue performance parameters of materials, but they are costly, time-consuming, and difficult to simulate the complex load conditions of actual pavements. Empirical models are usually based on simplified assumptions and cannot accurately reflect the nonlinear damage evolution process of materials. Both stress-based and energy-based discrete element fatigue damage models have certain limitations and are difficult to accurately simulate the fatigue damage accumulation process of asphalt mixtures. Summary of the invention

[0004] In order to solve the above technical problems, an embodiment of the present application provides a fatigue simulation method of nonlinear energy dissipation of asphalt mixture to accurately simulate the fatigue damage accumulation process of asphalt mixture.

[0005] The present embodiment provides a fatigue simulation method for nonlinear energy dissipation of asphalt mixture, comprising the following steps:

[0006] Step S1: using discrete element modeling software PFC3D to create an asphalt mixture cylindrical specimen of preset size and determine the particle radius;

[0007] The contact model between particles is constructed as a linear parallel bonding model. The microscopic parameters of the linear parallel bonding model are calibrated by comparing the simulated uniaxial compression test with the actual macroscopic mechanical properties of the asphalt mixture.

[0008] Step S2: Perform a uniaxial compression test on an asphalt mixture cylindrical specimen until the specimen is destroyed to obtain its uniaxial compressive strength ;

[0009] Use the same size of asphalt mixture to carry out cyclic loading fatigue test and obtain the fatigue life data of asphalt mixture;

[0010] Step S3: Establish a nonlinear bonding degradation model based on friction energy consumption to accurately describe the fatigue damage evolution process of asphalt mixture; the nonlinear bonding degradation model captures the nonlinear damage evolution behavior of asphalt mixture at different damage stages by constructing a piecewise function model, and modifies the bonding radius between model particles after each loading through the residual bonding radius multiplier φ to change the bonding strength of the model to simulate the damage of the macroscopic mechanical properties of the material;

[0011] Step S4: Loading plates are set at the upper and lower ends of the discrete element model to apply axial cyclic loads to the model; the time step is set in the discrete element software, and a loop statement is used to control the loading process, and the residual strain-loading number data and friction energy dissipation value of the model in each time step are saved;

[0012] Step S5: construct an ant colony optimization algorithm model to calibrate the parameters of the nonlinear bonding degradation model in step S3; the calibration process uses the residual strain-loading number curve and the final failure cycle number output by the discrete element simulation as the objective function and the degree of fit between the fatigue test results in S2, and the simulation results are made close to the test results through iteration;

[0013] Step S6: Substitute the optimal parameters output in step S5 into the nonlinear bonding degradation model based on friction energy consumption established in step S3; use the calibrated model to perform discrete element simulation of uniaxial cyclic loading of asphalt mixture to obtain the residual strain-loading number curve and the number of failure cycles of the simulation results; compare the simulation results with the fatigue test results obtained in step S2, and analyze the consistency between the two to verify the accuracy and predictive ability of this model.

[0014] Furthermore, the size of the asphalt mixture cylindrical specimen in step S1 is Φ50mm×100mm.

[0015] Furthermore, in step S2, in the cyclic loading fatigue test, the cyclic loading adopts a stress control method, the loading waveform is controlled to be a sine wave, the loading frequency is 10 Hz, and the stress amplitude is 0.3 , is the uniaxial compressive strength; the stress-strain data of the cyclic loading process are collected and recorded through the dynamic measurement system, and the number of loading cycles when the final material is destroyed is recorded as .

[0016] Furthermore, in step S3, the nonlinear bond degradation model multiplies the residual bond radius multiplier φ by the accumulated friction dissipation energy Through piecewise function association, it includes the following four stages:

[0017] As the initial stage: , indicating that the asphalt mixture was not damaged during this stage and the bonding strength remained at the initial state. It represents the critical accumulated friction dissipation energy value at which material damage begins to occur;

[0018] As a micro-damage stage: , the damage begins to accumulate slowly, and the bonding strength gradually decreases; the fractional function The introduction of reflects the slow damage accumulation process, where n is the number of cyclic loading; parameters a and b control the speed of damage accumulation in the micro-damage stage; represents the critical accumulated friction dissipated energy value at which the damage accumulation rate begins to accelerate; n is the number of cyclic loading;

[0019] As an accelerated damage stage: , the damage accumulation rate increases significantly, and the bonding strength decreases rapidly; exponential function It reflects the acceleration characteristics of damage accumulation, which controls the acceleration of damage accumulation in the accelerated damage stage. Parameters e and c are the initial value and speed of damage accumulation in the accelerated damage stage, respectively. Represents the critical cumulative friction dissipation energy value for material failure;

[0020] As the destruction stage: , which means that the bonding fails completely and the material is destroyed;

[0021] In the above model, the accumulated friction dissipation energy The calculation formula is: , where is the tangential force at the contact point in the i-th loading step, is the slip increment at the contact point in the i-th loading step.

[0022] Furthermore, the nonlinear bond degradation model is based on , that is, the cumulative friction energy when the number of cyclic loading is N times is recorded as ;by The accumulated friction energy is recorded as ;by The accumulated friction energy is recorded as .

[0023] Furthermore, the specific steps of step S4 are as follows:

[0024] Step S41: parallel rigid loading plates are set at the upper and lower ends of the discrete element model, and are placed at the upper and lower ends of the model respectively; the size of the loading plate should match the cross-sectional area of ​​the specimen to ensure uniform force;

[0025] Step S42: define stress control, and define cyclic load as stress control mode;

[0026] During the loading process, the stress applied to the model by the loading plate is controlled; the stress waveform is a sine wave, and the stress applied by the loading plate The change with time t is as follows: , where is the mean stress, ; is the stress amplitude, ; f is the loading frequency;

[0027] Step S43: Cyclic loading control, controlling the stress applied by the loading plate to change with time; in each time step, calculating the stress value corresponding to the current time point t , and then apply this stress to the loading plate to simulate the loading process in the actual test;

[0028] Step S44: Collect residual strain-loading number data, and record the stress data and strain data of the model in each time step; the stress data includes the stress applied by the loading plate , strain data is obtained by calculating the compression deformation of the specimen; stress data and strain data are based on time and continuously record the entire loading process;

[0029] Step S45: Calculate the friction energy dissipation value based on the tangential force and slip increment of the particle contact point in the discrete element model in each time step: ;

[0030] Step S46: Save the residual strain-loading number data and the corresponding friction energy dissipation in each time step as a csv file for subsequent analysis and parameter calibration.

[0031] Furthermore, the specific steps of step S5 are as follows:

[0032] Step S51: Determine the parameters to be optimized. The parameters that need to be calibrated in the model include: the speeds a and b of damage accumulation in the micro-damage stage; the initial value e of damage accumulation in the accelerated damage stage; the speed c of damage accumulation in the accelerated damage stage; and the acceleration d of damage accumulation in the accelerated damage stage.

[0033] Step S52: construct an objective function, which is used to measure the difference between the discrete element simulation results and the fatigue test results. The expression formula is as follows: , , ,in: is the objective function value, representing the overall difference between the simulation results and the experimental results; is the relative error of the residual strain-loading number curve. z points are selected at equal intervals on the residual strain-loading number curve obtained by simulation and the residual strain-loading number curve obtained by experiment, and the corresponding strain values ​​are recorded. and , the simulation results are compared with the test results to obtain the relative error of strain, the relative errors of z points are superimposed, and finally the relative error of the residual strain-loading number curve is obtained; is the relative error of the number of destruction cycles, To simulate the number of loading cycles to achieve final failure, is the number of loading cycles at test failure; and is the weight coefficient, which is used to adjust the contribution of the two errors to the objective function;

[0034] Step S53: Initialize the ant colony and set the size of the ant colony, that is, the number of ants in the ant colony is m; randomly generate a value within the value range of the five parameters a, b, c, d, and e to form a set of initial solutions;

[0035] Repeat this process to generate m groups of initial solutions, which are assigned to m ants respectively;

[0036] Creating a Pheromone Matrix , used to record the attractiveness of each position in the parameter space; the pheromone matrix specifies the dimension as q×p, where q is the number of parameters to be optimized and p is the discretization degree of each parameter, that is, the number of intervals into which the value range of each parameter is divided;

[0037] Step S54: Use ant colonies to select paths; calculate parameter selection probabilities. For any ant x and any parameter to be optimized y, according to the information matrix and heuristic information , calculate the probability that the ant chooses this parameter ; Information density Reflects the effect of parameter y in the historical optimization process. The higher the concentration, the greater the possibility that the parameter will be selected. Heuristic information Reflects the distance between parameter y and the current optimal solution. Usually, it is the inverse of the objective function value. The closer the distance, the more potential the parameter has and the greater the possibility of being selected. The parameter selection probability formula is as follows: ,in, and are two weight coefficients used to adjust the influence of pheromone concentration and heuristic information on the probability of path selection; Indicates the path combination that ant x can currently choose;

[0038] According to the calculated parameter selection probability , use the roulette wheel random selection method to select a new set of parameter combinations for each ant; use the parameter combination selected by each ant to perform discrete element simulation and obtain simulation results, including residual strain-loading number curves and the number of cycles when failure occurs; calculate the objective function value corresponding to the simulation results of each ant according to the objective function defined in S52 ;

[0039] According to the objective function value of each ant , calculate the pheromone increment left on each parameter ; The pheromone increment is inversely proportional to the objective function, that is, the smaller the objective function, the larger the pheromone increment; the pheromone increment calculation formula is: , where: Q is the pheromone intensity coefficient, which is used to control the amplitude of pheromone update; is the objective function value of ant x; according to the pheromone increment of each ant, the pheromone matrix is ​​updated , the pheromone update formula is as follows: ,in is the pheromone volatility coefficient, which is used to simulate the volatilization of pheromones over time;

[0040] Step S55: Determine whether the objective function of each ant meets the preset requirements, that is, the objective function value is less than the threshold; if the termination condition is met, stop the iterative optimization process; otherwise, return to step S54 and continue to the next round of iteration; the iterated parameter combination with the highest pheromone concentration that meets the objective function is output as the optimal parameter of the model.

[0041] Beneficial effects of the present invention:

[0042] (1) Abandoning the simplified assumptions of the traditional linear damage model, the model constructed in this method accurately describes the variation law of the residual bond radius multiplier of asphalt mixture in the initial stage, micro-damage stage, accelerated damage stage and destruction stage through piecewise functions, and can accurately capture the nonlinear mechanical behavior of the material at different damage stages, such as the residual strain-loading number relationship, stiffness degradation, energy dissipation, etc. Compared with the traditional linear model, the present invention can more truly reflect the fatigue damage accumulation process of the material, providing a powerful tool for in-depth understanding of the fatigue damage mechanism of asphalt mixture;

[0043] (2) To predict the fatigue life of asphalt mixtures and to reveal the fatigue damage mechanism of materials by analyzing the discrete element simulation results. In this scheme, the initiation and propagation of cracks in the simulation process can be observed, the distribution characteristics of the damaged area can be analyzed, and the influence of different loading conditions, material components and environmental factors on fatigue damage can be studied. This is of great significance for improving the performance of asphalt mixtures, optimizing pavement structure design and formulating reasonable maintenance strategies.

[0044] (3) This method combines the ant colony optimization algorithm to accurately calibrate the model parameters. By simulating the collective intelligent behavior of ant colonies foraging in nature, it can efficiently search the model parameter space and find the optimal parameter combination, so that the simulation results are highly consistent with the test results. Based on this algorithm, this scheme significantly improves the accuracy of fatigue life prediction and effectively reduces the prediction error, providing a more reliable theoretical basis for the design of asphalt pavement structures and extending the service life of the pavement. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0046] Figure 1 is a flow chart of the simulation method of the present application;

[0047] Figure 2 It is a logic block diagram of the simulation method of the present application;

[0048] Figure 3 is a schematic diagram of the contact constitutive model;

[0049] Figure 4 is the error optimization curve;

[0050] Figure 5 This is a comparison chart between the test results and the simulation results. DETAILED DESCRIPTION

[0051] In order to make the purpose, features, and advantages of the present application more obvious and easy to understand, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the embodiments described below are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0052] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments.

[0053] In the description of the present application, it should be understood that the terms "upper", "lower", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0054] The present application is described below in conjunction with specific embodiments:

[0055] The simulation method in this application mainly includes the following steps:

[0056] Step S1: Use the discrete element modeling software PFC3D to establish an asphalt mixture cylindrical specimen of preset size and determine the particle radius; when selecting the particle radius, a larger particle radius has higher calculation efficiency, while a smaller particle radius has higher calculation accuracy. The specific selection is based on actual and empirical values.

[0057] The contact model between particles is constructed as a linear parallel bonding model. The microscopic parameters of the linear parallel bonding model are calibrated by comparing the simulated uniaxial compression test with the actual macroscopic mechanical properties of the asphalt mixture.

[0058] As a specific embodiment, the size of the asphalt mixture cylindrical specimen is Φ50mm×100mm.

[0059] Step S2: Perform a uniaxial compression test on an asphalt mixture cylindrical specimen until the specimen is destroyed to obtain its uniaxial compressive strength ;

[0060] The asphalt mixture of the same size is used to carry out cyclic loading fatigue test to obtain the fatigue life data of the asphalt mixture.

[0061] As a specific embodiment, in the cyclic loading fatigue test, the cyclic loading adopts the stress control mode, the loading waveform is controlled to be a sine wave, the loading frequency is 10 Hz, and the stress amplitude is 0.3 The stress-strain data of the cyclic loading process are collected and recorded through the dynamic measurement system, and the number of loading cycles when the material is finally damaged is recorded. .

[0062] Step S3: Establish a nonlinear bonding degradation model based on friction energy consumption to accurately describe the fatigue damage evolution process of asphalt mixture. The nonlinear bonding degradation model in this scheme captures the nonlinear damage evolution behavior of asphalt mixture at different damage stages by constructing a piecewise function model, and modifies the bonding radius between model particles after each loading through the residual bonding radius multiplier φ to change the bonding strength of the model to simulate the damage of the macroscopic mechanical properties of the material.

[0063] As a specific embodiment, the nonlinear bond degradation model combines the residual bond radius multiplier φ with the accumulated friction dissipation energy Through piecewise function association, it includes the following four stages:

[0064] As the initial stage: , indicating that the asphalt mixture was not damaged during this stage and the bonding strength remained at the initial state. It represents the critical accumulated friction dissipation energy value at which material damage begins to occur;

[0065] As a micro-damage stage: , the damage begins to accumulate slowly, and the bonding strength gradually decreases; the fractional function The introduction of reflects the slow damage accumulation process, where n is the number of cyclic loading; parameters a and b control the speed of damage accumulation in the micro-damage stage and are preset based on empirical values; It represents the critical accumulated friction dissipated energy value at which the damage accumulation rate begins to accelerate;

[0066] As an accelerated damage stage: , the damage accumulation rate increases significantly, and the bonding strength decreases rapidly; exponential function It reflects the acceleration characteristics of damage accumulation, which controls the acceleration of damage accumulation in the accelerated damage stage. Parameters e and c are the initial value and speed of damage accumulation in the accelerated damage stage, respectively. Represents the critical cumulative friction dissipation energy value for material failure;

[0067] As the destruction stage: , which means that the bonding fails completely and the material is destroyed;

[0068] In the above model, the accumulated friction dissipation energy The calculation formula is: , where is the tangential force at the contact point in the i-th loading step, is the slip increment at the contact point in the i-th loading step. In the nonlinear bond degradation model of this embodiment, , that is, the cumulative friction energy when the number of cyclic loading is n times is recorded as ;by The accumulated friction energy is recorded as ;by The accumulated friction energy is recorded as .

[0069] Step S4: Loading plates are set at the upper and lower ends of the discrete element model to apply an axial cyclic load to the model.

[0070] As a specific embodiment, the cyclic load is controlled by stress control, the loading wave waveform is controlled to be a sine wave, and the stress applied by the loading plate is The change with time t is as follows: , where is the mean stress; is the stress amplitude; f is the loading frequency; the time step is set in the discrete element software, and the loop statement is used to control the loading process. In each time step, according to the sine function Calculate the current stress value and apply it to the loading plate; use the recording function to save the residual strain-load number data and friction energy dissipation value of the model in each time step.

[0071] S5: The nonlinear bonding degradation model parameters in step S3 are calibrated by constructing an ant colony optimization algorithm model through Python. The calibration process takes the residual strain-loading number curve and the final failure cycle number output by the discrete element simulation as the fitting degree with the fatigue test results in step S2 as the objective function, and the simulation results are made close to the test results through iteration. The specific steps are as follows:

[0072] Step S51: Determine the parameters to be optimized. The parameters that need to be calibrated in the model include: the speeds a and b of damage accumulation in the micro-damage stage; the initial value e of damage accumulation in the accelerated damage stage; the speed c of damage accumulation in the accelerated damage stage; and the acceleration d of damage accumulation in the accelerated damage stage.

[0073] Step S52: construct an objective function, which is used to measure the difference between the discrete element simulation results and the fatigue test results. The expression formula is as follows: , , ,in: is the objective function value, representing the overall difference between the simulation results and the experimental results; is the relative error of the residual strain-loading number curve. z points are selected at equal intervals on the residual strain-loading number curve obtained by simulation and the residual strain-loading number curve obtained by experiment, and the corresponding strain values ​​are recorded. and , the simulation results are compared with the test results to obtain the relative error of strain, the relative errors of z points are superimposed, and finally the relative error of the residual strain-loading number curve is obtained; is the relative error of the number of destruction cycles, To simulate the number of loading cycles to achieve final failure, is the number of loading cycles at test failure; and is the weight coefficient, which is used to adjust the contribution of the two errors to the objective function;

[0074] Step S53: Initialize the ant colony and set the size of the ant colony, that is, the number of ants in the ant colony is m; randomly generate a value within the value range of the five parameters a, b, c, d, and e to form a set of initial solutions;

[0075] Repeat this process to generate m groups of initial solutions, which are assigned to m ants respectively;

[0076] Creating a Pheromone Matrix , used to record the attractiveness of each position in the parameter space; the pheromone matrix specifies the dimension as q×p, where q is the number of parameters to be optimized and p is the discretization degree of each parameter, that is, the number of intervals into which the value range of each parameter is divided;

[0077] Step S54: Use ant colonies to select paths; calculate parameter selection probabilities. For any ant x and any parameter to be optimized y, according to the information matrix and heuristic information , calculate the probability that the ant chooses this parameter ; Information density Reflects the effect of parameter y in the historical optimization process. The higher the concentration, the greater the possibility that the parameter will be selected. Heuristic information Reflects the distance between parameter y and the current optimal solution. Usually, it is the inverse of the objective function value. The closer the distance, the more potential the parameter has and the greater the possibility of being selected. The parameter selection probability formula is as follows: ,in, and are two weight coefficients used to adjust the influence of pheromone concentration and heuristic information on the probability of path selection; Indicates the path combination that ant x can currently choose;

[0078] According to the calculated parameter selection probability , use the roulette wheel random selection method to select a new set of parameter combinations for each ant; use the parameter combination selected by each ant to perform discrete element simulation and obtain simulation results, including residual strain-loading number curves and the number of cycles when failure occurs; calculate the objective function value corresponding to the simulation results of each ant according to the objective function defined in S52 ;

[0079] According to the objective function value of each ant , calculate the pheromone increment left on each parameter ; The pheromone increment is inversely proportional to the objective function, that is, the smaller the objective function, the larger the pheromone increment; the pheromone increment calculation formula is: , where: Q is the pheromone intensity coefficient, which is used to control the amplitude of pheromone update; is the objective function value of ant x; according to the pheromone increment of each ant, the pheromone matrix is ​​updated , the pheromone update formula is as follows: ,in is the pheromone volatility coefficient, which is used to simulate the volatilization of pheromones over time;

[0080] Step S55: Determine whether the objective function of each ant meets the preset requirements, that is, the objective function value is less than the threshold; if the termination condition is met, stop the iterative optimization process; otherwise, return to step S54 and continue to the next round of iteration; the iterated parameter combination with the highest pheromone concentration that meets the objective function is output as the optimal parameter of the model.

[0081] Step S6: Substitute the optimal parameters output in step S5 into the nonlinear bond degradation model established in step S3; use the calibrated model to perform discrete element simulation of uniaxial cyclic loading of asphalt mixture to obtain the residual strain-loading number curve and the number of failure cycles of the simulation results; compare the simulation results with the fatigue test results obtained in step S2, and analyze the consistency between the two to verify the accuracy and predictive ability of this model.

[0082] This example demonstrates the accuracy of this simulation method. The specific steps are as follows:

[0083] Step S1: Use the discrete element modeling software PFC3D to create a Φ50mm×100mm SMA asphalt mixture cylindrical specimen, and the particle radius is set to 0.75mm.

[0084] The contact model between particles is defined as a linear parallel bond model in the model (refer to the schematic diagram of the parallel bond model (PBM) and PFC5.0 contact model - built-in contact model - linear parallel bond model (translated from the help file) - Zhihu). Then, a simulated uniaxial compression test is carried out to obtain the simulated mechanical properties data, which are compared with the macroscopic mechanical properties of the actual asphalt mixture, and the accuracy of the model is calibrated by adjusting the microscopic parameters in the model.

[0085] Step S2: Use a Φ50mm×100mm SMA asphalt mixture cylindrical specimen to carry out an actual uniaxial compression test until the specimen is destroyed, and obtain a uniaxial compressive strength of 6.8MPa. Use a cylindrical specimen of the same size to carry out a cyclic loading fatigue test to obtain the fatigue life data of the asphalt mixture. The fatigue test adopts a stress control method, the loading waveform is a sine wave, the loading frequency is 10Hz, and the stress amplitude is 2.04MPa. The number of loading times-residual strain data during the test is collected and recorded by the dynamic measurement system. The number of loading cycles when the final material is destroyed is recorded as 7943 times.

[0086] Step S3: Establish a nonlinear bonding degradation model based on friction energy consumption to accurately describe the fatigue damage evolution process of asphalt mixture. The bonding radius degradation equation is as follows:

[0087] Initial stage, ,

[0088] Micro-damage stage, ,

[0089] Accelerate the damage stage, ,

[0090] Destruction phase, ,

[0091] Step S4: Loading plates are set at the upper and lower ends of the discrete element model to simulate the axial cyclic load applied in the test. The specific steps are as follows:

[0092] Step S41: Loading plate setting: In the discrete element software PFC3D, two parallel rigid loading plates are created and placed at the upper and lower ends of the model. The size of the loading plate should match the cross-sectional area of ​​the specimen to ensure uniform force.

[0093] Step S42: define stress control, define the cyclic load as a stress control mode, that is, during the loading process, control the stress applied to the model by the loading plate.

[0094] The waveform of stress is a sine wave, and the expression is: .

[0095] Step S43: Cyclic loading control, by writing a loop statement, control the stress applied by the loading plate to change with time. In each time step, first calculate the stress value corresponding to the current time point t , and then apply the stress to the loading plate to simulate the loading process in the actual test.

[0096] Step S44: Residual strain-loading times data collection, using the recording function in the discrete element software, record the stress and strain data of the model in each time step. The stress data includes the stress applied by the loading plate. , and the strain data is obtained by calculating the compression deformation of the specimen. The data is based on time and continuously records the entire loading process.

[0097] Step S45: Friction energy dissipation calculation: In each time step, the friction energy dissipation value is calculated based on the tangential force and slip increment of the particle contact point in the discrete element model: .

[0098] Step S46: Save the residual strain-loading number data and the corresponding friction energy dissipation in each time step as a csv file for subsequent analysis and parameter calibration.

[0099] Step S5: Use Python to build an ant colony optimization algorithm model to calibrate the parameters of the nonlinear bonding degradation model based on friction energy consumption in S3. The specific steps are as follows:

[0100] Step S51: Determine the parameters to be optimized: a and b damage accumulation speeds in the micro-damage stage; e the initial value of damage accumulation in the accelerated damage stage; c the damage accumulation speed in the accelerated damage stage; d the acceleration of damage accumulation in the accelerated damage stage.

[0101] Step S52: construct an objective function to measure the difference between the discrete element simulation results and the actual fatigue test results. The objective function consists of two parts: the relative error of the residual strain-loading number curve and the relative error of the failure cycle number. The expression of the objective function is: , , , , All are automatically calculated by Python.

[0102] Step S53: Initialize the ant colony: set the size of the ant colony, that is, the number of ants m=150; randomly generate m groups of initial solutions within the value range of the parameters to be optimized, and these initial solutions correspond to the initial parameter combination of each ant; construct the pheromone matrix , used to record the objective function value of each parameter combination, the dimension of the pheromone matrix is ​​5×5.

[0103] Step S54: Ant colony path selection and simulation: Calculate the selection probability. For each ant x and each parameter to be optimized y, calculate the probability of selecting the parameter based on the pheromone concentration τ and the heuristic information η: , according to the selection probability ,A roulette wheel random selection method is used to select a new set of parameter combinations for each ant.

[0104] Objective function calculation, discrete element simulation is performed using the parameter combination selected by each ant to obtain simulation results (residual strain-loading number curve and number of failure cycles).

[0105] According to the previously defined objective function F, calculate the objective function value corresponding to each ant .

[0106] According to the objective function value of each ant , calculate the pheromone increment at each parameter: .

[0107] Update the pheromone matrix according to the pheromone increment: .

[0108] Step S55: Determine whether the objective function value of each ant meets the preset requirements ( ).

[0109] If the termination condition is met, the iteration stops and the optimal parameter combination is output. If the termination condition is not met, the process returns to step S54 and continues to the next round of iteration. Through multiple rounds of iteration, the ant colony gradually optimizes the parameter combination and finally finds the optimal solution. The error change of the optimization process is as follows: Figure 4 The optimal parameter combination obtained through iterative optimization is shown in Table 1 and is used as the final calibrated model parameters for subsequent simulation and analysis.

[0110] Table 1 Optimization parameter combinations

[0111]

[0112] Step S6: Substitute the optimal parameters obtained in step S5 into the nonlinear bond degradation model of S3, and perform uniaxial cyclic loading discrete element simulation of asphalt mixture. Obtain the residual strain-loading number curve and failure cycle number of the simulation results, and compare and analyze them with the fatigue test results in step S2. The comparison diagram is as follows: Figure 5 shown.

[0113] Figure 5It is shown that the test results are highly consistent with the simulation results, and the calculation error between the two is less than 5%, indicating that the established nonlinear dissipative model considering friction energy can well simulate the fatigue failure process of asphalt mixture. It also shows that the present invention is helpful to further study the generation and development process of fatigue failure of asphalt mixture at the microscopic scale.

[0114] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0115] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations (such as quantity, shape, position, etc.) can be made to the technical scheme of the present invention, and these equivalent transformations are all protected by the present invention.

Claims

1. A fatigue simulation method for nonlinear energy dissipation of asphalt mixture, characterized by: The steps include: Step S1: using discrete element modeling software PFC3D to create an asphalt mixture cylindrical specimen of preset size and determine the particle radius; The contact model between particles is constructed as a linear parallel bonding model; the microscopic parameters of the linear parallel bonding model are calibrated by comparing the simulated uniaxial compression test with the actual macroscopic mechanical properties of the asphalt mixture; Step S2: Perform a uniaxial compression test on the asphalt mixture cylindrical specimen until the specimen is destroyed to obtain its uniaxial compressive strength σ c ; Cyclic loading fatigue tests were performed using asphalt mixture cylindrical specimens of the same size to obtain fatigue life data of the asphalt mixture; Step S3: Establish a nonlinear bond degradation model based on friction energy dissipation to accurately describe the fatigue damage evolution process of asphalt mixture; the nonlinear bond degradation model captures the nonlinear damage evolution behavior of asphalt mixture at different damage stages by constructing a piecewise function model, and The bonding radius between model particles after each loading is modified to change the bonding strength of the model to simulate the damage of the macroscopic mechanical properties of the material; The nonlinear bond degradation model multiplies the residual bond radius by and the accumulated friction dissipation energy E fr Through piecewise function association, it includes the following four stages: As the initial stage: This means that the asphalt mixture has not been damaged during this stage and the bonding strength remains at the initial state. It represents the critical accumulated friction dissipation energy value at which material damage begins to occur; As a micro-damage stage: The damage begins to accumulate slowly, and the bonding strength gradually decreases; parameters a and b control the speed of damage accumulation in the micro-damage stage; represents the critical accumulated friction dissipated energy value at which the damage accumulation rate begins to accelerate; n is the number of cyclic loading; As an accelerated damage stage: The damage accumulation rate increases significantly, and the bonding strength decreases rapidly. The exponential function exp(d*n) reflects the acceleration characteristics of damage accumulation, which controls the acceleration of damage accumulation in the accelerated damage stage. The parameter e is the initial value of damage accumulation in the accelerated damage stage, and the parameter c is the speed of damage accumulation in the accelerated damage stage. Represents the critical cumulative friction dissipation energy value for material failure; As the destruction stage: This means that the bonding has completely failed and the material has been destroyed; In the above model, the cumulative friction dissipation energy E fr The calculation formula is: In the formula, F i s is the tangential force at the contact point in the i-th loading step, is the slip increment at the contact point in the i-th loading step; In the nonlinear bond degradation model, n = N f The accumulated friction energy is recorded as With n = 0.8N f The accumulated friction energy is recorded as With n = 0.1N f The accumulated friction energy is recorded as N f is the number of loading cycles until the final material failure; Step S4: Loading plates are set at the upper and lower ends of the discrete element model to apply an axial cyclic load to the model; The time step is set in the discrete element software, and the loading process is controlled by a loop statement, and the residual strain-loading number data and friction energy dissipation value of the model in each time step are saved; Step S5: construct an ant colony optimization algorithm model to calibrate the parameters of the nonlinear bonding degradation model in step S3; the calibration process uses the residual strain-loading number curve and the final failure cycle number output by the discrete element simulation as the objective function and the degree of fit between the fatigue test results in S2, and the simulation results are made close to the test results through iteration; Step S6: Substitute the optimal parameters output in step S5 into the nonlinear bonding degradation model based on friction energy consumption established in step S3; use the calibrated model to perform discrete element simulation of uniaxial cyclic loading of asphalt mixture to obtain the residual strain-loading number curve and the number of failure cycles of the simulation results; compare the simulation results with the fatigue test results obtained in step S2, and analyze the consistency between the two to verify the accuracy and predictive ability of this model.

2. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 1 is characterized in that: The size of the asphalt mixture cylindrical specimen in step S1 is Φ50mm×100mm.

3. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 1 is characterized in that: In the step S2, in the cyclic loading fatigue test, the cyclic loading adopts a stress control method, the loading waveform is controlled to be a sine wave, the loading frequency is 10 Hz, and the stress amplitude is 0.3σ c , σ c is the uniaxial compressive strength; the stress-strain data of the cyclic loading process is collected and recorded through the dynamic measurement system, and the number of loading cycles when the final material is destroyed is recorded as N f .

4. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 1 is characterized in that: The specific steps of step S4 are as follows: Step S41: parallel rigid loading plates are arranged at the upper and lower ends of the discrete element model, and are placed at the upper and lower ends of the model respectively; the size of the loading plates should match the cross-sectional area of ​​the specimen to ensure uniform force; Step S42: define stress control, and define cyclic load as stress control mode; During the loading process, the stress applied to the model by the loading plate is controlled; the waveform of the stress is a sine wave, and the stress σ(t) applied by the loading plate changes with time t as follows: In the formula is the mean stress, taking 0.15σ c ; σ amp is the stress amplitude, taking 0.3σ c ; f is the loading frequency; Step S43: cyclic loading control, controlling the stress applied by the loading plate to change with time; in each time step, calculating the stress value σ(t) corresponding to the current time point t, and then applying the stress to the loading plate to simulate the loading process in the actual test; Step S44: collecting residual strain-loading number data, and recording the stress data and strain data of the model in each time step; the stress data includes the stress σ(t) applied by the loading plate, and the strain data is obtained by calculating the compression deformation of the specimen; the stress data and strain data are based on time and continuously record the entire loading process; Step S45: Calculate the friction energy dissipation value E based on the tangential force and slip increment of the particle contact point in the discrete element model in each time step. fr ; Step S46: Save the residual strain-loading number data and the corresponding friction energy dissipation in each time step as a csv file for subsequent analysis and parameter calibration.

5. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 4 is characterized in that: The specific steps of step S5 are as follows: Step S51: Determine the parameters to be optimized. The parameters that need to be calibrated in the model include: the speeds a and b of damage accumulation in the micro-damage stage; the initial value e of damage accumulation in the accelerated damage stage; the speed c of damage accumulation in the accelerated damage stage; and the acceleration d of damage accumulation in the accelerated damage stage. Step S52: construct an objective function, which is used to measure the difference between the discrete element simulation results and the fatigue test results. The expression formula is as follows: bj =ω1*ε1+ω2*ε2, Among them: bj is the objective function value, representing the overall difference between the simulation results and the test results; ε1 is the relative error of the residual strain-loading number curve, and z points are selected at equal intervals on the residual strain-loading number curve obtained by simulation and the residual strain-loading number curve obtained by test, and the corresponding strain values ​​are recorded and The simulation results are compared with the test results to obtain the relative error of strain. The relative errors of z points are superimposed to finally obtain the relative error of residual strain-loading number curve; ε2 is the relative error of the number of failure cycles, N pred is the number of loading cycles to simulate the final failure, N f is the number of loading cycles during the test failure; ω1 and ω2 are weight coefficients, which are used to adjust the contribution of the two errors to the objective function; Step S53: Initialize the ant colony and set the size of the ant colony, that is, the number of ants in the ant colony is m; randomly generate a value within the value range of the five parameters a, b, c, d, and e to form a set of initial solutions; Repeat this process to generate m groups of initial solutions, which are assigned to m ants respectively; Create a pheromone matrix τ to record the attractiveness of each position in the parameter space; The dimension of the pheromone matrix is ​​specified to be q×p, where q is the number of parameters to be optimized and p is the degree of discretization of each parameter, that is, the number of intervals into which the value range of each parameter is divided; Step S54: Use the ant colony to select the path; calculate the parameter selection probability. For any ant x and any parameter to be optimized y, calculate the probability P of the ant selecting the parameter in the tth cycle according to the information matrix τ and the heuristic information η. xy (t); information concentration τ xy (t) reflects the effect of parameter y in the historical optimization process. The higher the concentration, the greater the possibility of the parameter being selected. Heuristic information η xy Reflects the distance between parameter y and the current optimal solution. It is usually the inverse of the objective function value. The closer the distance, the more potential the parameter has and the greater the possibility of being selected. The parameter selection probability formula is as follows: Among them, α and β are two weight coefficients used to adjust the influence of pheromone concentration and heuristic information on path selection probability; allowed k Indicates the path combination that ant x can currently choose; According to the calculated parameter selection probability P xy (t), using the roulette wheel random selection method, select a new set of parameter combinations for each ant; use the parameter combination selected by each ant to perform discrete element simulation to obtain simulation results, including residual strain-loading number curves and the number of cycles when failure occurs; according to the objective function defined in S52, calculate the objective function value corresponding to the simulation result of each ant bj ; According to the objective function value O of each ant bj , calculate the pheromone increment Δτ left on each parameter xy ; The pheromone increment is inversely proportional to the objective function, that is, the smaller the objective function, the larger the pheromone increment; the pheromone increment calculation formula is: Where: Q is the pheromone intensity coefficient, which is used to control the amplitude of pheromone renewal; bj x is the objective function value of ant x; according to the pheromone increment of each ant, the pheromone matrix τ is updated, and the pheromone update formula is as follows: τ xy (t+1)=(1-ρ)*τ xy (t)+Δτ xy , where ρ is the pheromone volatility coefficient, which is used to simulate the volatilization of pheromones over time; Step S55: Determine whether the objective function of each ant meets the preset requirements, that is, the objective function value is less than the threshold; if the termination condition is met, stop the iterative optimization process; otherwise, return to step S54 and continue to the next round of iteration; the iterated parameter combination with the highest pheromone concentration that meets the objective function is output as the optimal parameter of the model.

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