CN119314603A - Fatigue simulation method for nonlinear energy dissipation of asphalt mixture - Google Patents
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Abstract
本申请公开了一种沥青混合料非线性能量耗散的疲劳仿真方法，摒弃传统线性损伤模型的简化假设，通过分段函数精确刻画沥青混合料在初始阶段、微损伤阶段、加速损伤阶段和破坏阶段的剩余粘结半径乘子变化规律，能够准确捕捉材料在不同损伤阶段的非线性力学行为，同时本方法中结合蚁群优化算法对模型参数进行精确校准，通过模拟自然界中蚁群觅食的群体智能行为，高效搜索模型参数空间，并找到最优参数组合，使得模拟结果与试验结果高度吻合，显著提高疲劳寿命预测的准确性，有效降低预测误差，为沥青路面结构设计提供更为可靠的理论依据，延长路面的使用寿命。
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
The application relates to the technical field of asphalt mixture fatigue simulation, in particular to a fatigue simulation method for nonlinear energy dissipation of an asphalt mixture.
Background
Existing discrete element fatigue damage models are mainly divided into two types, namely stress-based models and energy-based models. Stress-based models generally assume that fatigue damage of a material is related to stress level and time of action, such as parallel bond stress corrosion models (PSCs). Such models are capable of modeling creep damage, but have some drawbacks for modeling fatigue damage. The energy-based model then assumes that fatigue damage of the material is related to energy dissipation, such as a cumulative dissipation energy model. Such models generally assume that energy dissipation is linear with cyclic loading times.
On the other hand, fatigue damage analysis of the asphalt mixture mainly depends on an indoor fatigue test and an empirical model, and the indoor test can obtain fatigue performance parameters of the material, but has high cost and long period, and is difficult to simulate the complex load working condition of an actual pavement. Whereas empirical models are typically based on simplifying assumptions, they do not accurately reflect the nonlinear damage evolution process of the material. The fatigue damage model based on the discrete elements of stress and energy has certain limitations, and the fatigue damage accumulation process of the asphalt mixture is difficult to accurately simulate.
Disclosure of Invention
In order to solve the technical problems, the embodiment of the application provides a fatigue simulation method for nonlinear energy dissipation of an asphalt mixture, so as to accurately simulate the fatigue damage accumulation process of the asphalt mixture.
The fatigue simulation method for nonlinear energy dissipation of asphalt mixture provided by the embodiment comprises the following steps:
S1, building an asphalt mixture cylinder test piece with a preset size by utilizing discrete element modeling software PFC3D, and determining the radius of particles;
the contact model among the particles is constructed as a linear parallel bonding model, and the microscopic parameters of the linear parallel bonding model are calibrated by comparing the simulated uniaxial compression test with the macroscopic mechanical properties of the actual asphalt mixture;
step S2, adopting an asphalt mixture cylinder test piece to carry out uniaxial compression test until the test piece is destroyed, and obtaining uniaxial compressive strength ;
Carrying out a cyclic loading fatigue test by using the asphalt mixture time with the same size to obtain fatigue life data of the asphalt mixture;
Step S3, a nonlinear bonding degradation model based on friction energy consumption is established to accurately describe the fatigue damage evolution process of the asphalt mixture, the nonlinear bonding degradation model captures nonlinear damage evolution behaviors of the asphalt mixture in different damage stages by constructing a piecewise function model, and modifies bonding radii among model particles loaded each time by a residual bonding radius multiplier phi to change bonding strength of the model so as to simulate macroscopic mechanical property damage of the material;
Setting loading plates at the upper end and the lower end of the discrete meta-model, applying axial cyclic load to the model, setting time steps in the discrete meta-software, adopting a cyclic statement to control the loading process, and storing the residual strain-loading times data and friction energy dissipation value of the model in each time step;
step 5, constructing an ant colony optimization algorithm model to calibrate the nonlinear bonding degradation model parameters in the step 3, wherein the calibration process takes a residual strain-loading frequency curve and the final failure cycle frequency which are simulated and output by discrete elements as an objective function, and the simulation result approximates to the test result through iteration;
And S6, substituting the optimal parameters output in the step S5 into the nonlinear bonding degradation model based on friction energy consumption established in the step S3, performing single-axis cyclic loading discrete element simulation on the asphalt mixture by using the calibrated model to obtain a residual strain-loading frequency curve and a failure cycle frequency of a simulation result, comparing the simulation result with the fatigue test result obtained in the step S2, and analyzing the consistency between the simulation result and the fatigue test result to verify the accuracy and the prediction capability of the model.
Further, the dimensions of the asphalt mixture cylinder test piece in step S1 were Φ50mm×100deg.M.
Further, in step S2, in the cyclic loading fatigue test, the cyclic loading is controlled to be a sine wave by adopting a stress control method, the loading frequency is 10Hz, and the stress amplitude is 0.3,The stress strain data in the cyclic loading process is acquired and recorded through a dynamic measurement system, and the loading cycle number when the final material is damaged is recorded as。
Further, in step S3, the nonlinear bond degradation model multiplies the residual bond radius by φ and the cumulative friction dissipation energyBy piecewise function correlation, the following four phases are included:
As an initial stage at this time Indicating that the asphalt mixture is not damaged in the stage, the bonding strength is kept in an initial state,A critical cumulative frictional dissipation energy value representing the onset of damage to the material;
As a micro-injury stage at this time The damage begins to accumulate slowly and the adhesive strength gradually decreases, and the function of the divisionThe introduction of the method reflects the characteristic of slower damage accumulation process, wherein n is the cyclic loading times; a critical accumulated friction dissipation energy value representing that the damage accumulation speed starts to be accelerated, wherein n is the number of cyclic loading times;
As an accelerated injury stage at this time The damage accumulation speed is obviously increased, the bonding strength is rapidly reduced, and the exponential function is realizedEmbodying the acceleration characteristic of damage accumulation, wherein the acceleration of the damage accumulation in the acceleration damage stage is controlled, and parameters e and c are respectively the initial value and the speed of the damage accumulation in the acceleration damage stage; a critical cumulative frictional dissipation energy value representing the occurrence of material failure;
as a breaking stage at this time Meaning that the bond is completely disabled and the material is broken;
In the above model, cumulative friction dissipation energy The calculation formula of (2) is as follows: In which, in the process, For tangential forces at the contact point in the ith loading step,Is the slip delta at the contact point in the ith loading step.
Further, in a nonlinear bonding degradation modelThe accumulated friction energy consumption when the cyclic loading times are N times is recorded asTo take the following stepsThe accumulated friction energy consumption is recorded asTo take the following stepsThe accumulated friction energy consumption is recorded as。
Further, the specific steps of step S4 are as follows:
s41, arranging parallel rigid loading plates at the upper end and the lower end of a discrete element model, and respectively placing the parallel rigid loading plates at the upper end and the lower end of the model, wherein the size of the loading plates is matched with the cross section area of a test piece so as to ensure uniform stress;
step S42, defining stress control, and defining cyclic load as a stress control mode;
During loading, the stress applied by the loading plate to the model is controlled The variation with time t is as follows: In the following For average stress, take;For the stress amplitude, takeF is the loading frequency;
Step S43, cyclic loading control, controlling the stress applied by the loading plate to change along with time, and calculating the stress value corresponding to the current time point t in each time step Then applying the stress to the loading plate to simulate the loading process in the actual test;
Step S44, collecting data of residual strain-loading times, and recording stress data and strain data of the model in each time step, wherein the stress data comprises stress applied by a loading plate The stress data and the strain data are used as references, and the whole loading process is continuously recorded;
step S45, calculating a friction energy dissipation value based on tangential force and slip increment of a particle contact point in the discrete meta-model in each time step: ;
And step S46, saving the data of the residual strain-loading times in each time step and the corresponding friction energy consumption as a csv file for subsequent analysis and parameter calibration.
Further, the specific steps of step S5 are as follows:
Step S51, determining parameters to be optimized, wherein the parameters to be calibrated in the model comprise the speed a and b of damage accumulation in a micro-damage stage, an initial value e of damage accumulation in an acceleration damage stage, the speed c of damage accumulation in the acceleration damage stage, and the acceleration d of damage accumulation in the acceleration damage stage;
And S52, constructing an objective function, wherein the objective function is used for measuring the difference between the discrete element simulation result and the fatigue test result, and the expression formula is as follows: ,, Wherein: as objective function values, representing the overall difference between the simulation result and the test result; for the relative error of the residual strain-loading frequency curve, z points are respectively and equally selected on the simulated residual strain-loading frequency curve and the tested residual strain-loading frequency curve, and the corresponding strain value is recorded AndComparing the simulation result with the test result to obtain the relative error of the strain, and superposing the relative errors of the z points to finally obtain the relative error of the residual strain-loading frequency curve; In order to destroy the relative error of the number of cycles, To simulate the number of load cycles at the time of final corruption,The number of loading cycles at test failure; And The method is used for adjusting the contribution degree of two errors to the objective function;
step S53, initializing an ant colony, setting the ant colony scale, namely the number of the ant colony ants as m, randomly generating a value in the value range of five parameters a, b, c, d, e, and forming a group of initial solutions;
repeating the process to generate m groups of initial solutions which are respectively distributed to m ants;
Creating a pheromone matrix The pheromone matrix is provided with dimensions of q multiplied by p, wherein q is the number of parameters to be optimized, and p is the discretization degree of each parameter, namely the number of intervals in which the value range of each parameter is divided;
Step S54, selecting paths by ant colony, calculating parameter selection probability, and selecting any ant x and any parameter y to be optimized according to the information matrix And heuristic informationCalculating the probability of the ant selecting the parameterInformation concentrationReflecting the effect of the parameter y in the history optimization process, the higher the concentration, the greater the probability of the parameter being selected, heuristic informationThe distance between the parameter y and the current optimal solution is reflected, the inverse of the objective function value is generally taken, the closer the distance is, the more potential the parameter is represented, the greater the possibility of being selected is, and the parameter selection probability formula is as follows: Wherein, the method comprises the steps of, wherein, AndThe method is characterized by comprising two weight coefficients, wherein the two weight coefficients are used for adjusting the influence degree of pheromone concentration and heuristic information on the path selection probability; Representing the path combinations that ant x can currently select;
According to the calculated parameter selection probability Selecting a new set of parameter combinations for each ant by using a wheel disk random selection method, performing discrete element simulation by using the selected parameter combinations of each ant to obtain simulation results including a residual strain-loading frequency curve and the cycle frequency when damage occurs, and calculating objective function values corresponding to the simulation results of each ant according to the objective function defined in S52;
According to the objective function value of each antCalculate the pheromone increment it leaves on each parameterThe pheromone increment is inversely proportional to the objective function, namely the smaller the objective function is, the larger the pheromone increment is, and the pheromone increment calculation formula is as follows: Wherein Q is a pheromone intensity coefficient used for controlling the update amplitude of the pheromone; Updating the pheromone matrix according to the increment of the pheromone of each ant The pheromone update formula is as follows: Wherein The pheromone volatilization coefficient is used for simulating the volatilization of the pheromone along with time;
Step S55, judging whether the objective function of each ant reaches the preset requirement, namely, the objective function value is smaller than the threshold value, stopping the iterative optimization process if the termination condition is met, otherwise, returning to step S54, continuing the next iteration, and combining the iterated parameters with the highest pheromone concentration meeting the objective function as the optimal parameters of the model.
The invention has the beneficial effects that:
(1) The model constructed in the method accurately describes the residual bonding radius multiplier change rules of the asphalt mixture in an initial stage, a micro-damage stage, an acceleration damage stage and a damage stage through a piecewise function, can accurately capture nonlinear mechanical behaviors of the material in different damage stages, such as residual strain-loading frequency relation, rigidity degradation, energy dissipation and the like;
(2) The method can observe the crack initiation and expansion process in the simulation process, analyze the distribution characteristics of a damaged area, and research the influence rules of different loading conditions, material components and environmental factors on fatigue damage, and has important significance for improving the performance of the asphalt mixture, optimizing the pavement structural design and formulating a reasonable maintenance strategy;
(3) According to the method, the model parameters are accurately calibrated by combining with the ant colony optimization algorithm, the model parameter space can be efficiently searched by simulating the intelligent group behaviors of ant colony foraging in the nature, and the optimal parameter combination is found, so that the simulation result is highly consistent with the test result.
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In order to more clearly illustrate the embodiments of the application or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a simulation method of the present application;
FIG. 2 is a logical block diagram of a simulation method of the present application;
FIG. 3 is a schematic view of a contact constitutive model;
FIG. 4 is an error optimization graph;
Fig. 5 is a graph comparing test results with simulation results.
Detailed Description
In order to make the application object, feature and advantage of the present application more obvious and understandable, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the embodiments described below are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The invention is further elucidated below in connection with the drawings and the specific embodiments.
In the description of the present application, it should be understood that the directions or positional relationships indicated by the terms "upper", "lower", "top", "bottom", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present application.
The application is illustrated below with reference to specific examples:
the simulation method in the application mainly comprises the following steps:
Step S1, building an asphalt mixture cylinder test piece with a preset size by utilizing discrete element modeling software PFC3D, determining the particle radius, and selecting larger particle radius to have higher calculation efficiency and smaller particle radius to have higher calculation precision when selecting the particle radius, and particularly selecting how to combine actual and experience values.
And comparing the simulated uniaxial compression test with the macroscopic mechanical property of the actual asphalt mixture, and calibrating the microscopic parameters of the linear parallel bonding model.
As a specific example, the dimensions of the asphalt mixture cylinder test piece were Φ50mm×100deg.M.
Step S2, adopting an asphalt mixture cylinder test piece to carry out uniaxial compression test until the test piece is destroyed, and obtaining uniaxial compressive strength;
And (3) performing a cyclic loading fatigue test by using the asphalt mixture time with the same size to obtain fatigue life data of the asphalt mixture.
As a specific embodiment, in the cyclic loading fatigue test, the cyclic loading adopts a stress control mode, the loading waveform is controlled to be sine wave, the loading frequency is 10Hz, and the stress amplitude is 0.3. The dynamic measurement system is used for collecting and recording stress-strain data in the cyclic loading process, and the loading cycle number when the final material is damaged is recorded as follows。
And S3, establishing a nonlinear bonding degradation model based on friction energy consumption for accurately describing the fatigue damage evolution process of the asphalt mixture, capturing nonlinear damage evolution behaviors of the asphalt mixture in different damage stages by constructing a piecewise function model, modifying bonding radii among model particles loaded each time by a residual bonding radius multiplier phi, and changing the bonding strength of the model to realize simulation of macroscopic mechanical property damage of the material.
As a specific example, the nonlinear bond degradation model multiplies the residual bond radius by phi and the cumulative friction dissipation energyBy piecewise function correlation, the following four phases are included:
As an initial stage at this time Indicating that the asphalt mixture is not damaged in the stage, the bonding strength is kept in an initial state,A critical cumulative frictional dissipation energy value representing the onset of damage to the material;
As a micro-injury stage at this time The damage begins to accumulate slowly and the adhesive strength gradually decreases, and the function of the divisionThe introduction of the method reflects the characteristic of slower damage accumulation process, wherein n is the cyclic loading times, and parameters a and b control the damage accumulation speed in the micro-damage stage and are preset according to an empirical value; A critical accumulated frictional dissipation energy value representing an onset of increased damage accumulation rate;
As an accelerated injury stage at this time The damage accumulation speed is obviously increased, the bonding strength is rapidly reduced, and the exponential function is realizedEmbodying the acceleration characteristic of damage accumulation, wherein the acceleration of the damage accumulation in the acceleration damage stage is controlled, and parameters e and c are respectively the initial value and the speed of the damage accumulation in the acceleration damage stage; a critical cumulative frictional dissipation energy value representing the occurrence of material failure;
as a breaking stage at this time Meaning that the bond is completely disabled and the material is broken;
In the above model, cumulative friction dissipation energy The calculation formula of (2) is as follows: In which, in the process, For tangential forces at the contact point in the ith loading step,For the slip increment at the contact point in the ith loading step, the nonlinear bond degradation model of the embodiment usesThe accumulated friction energy consumption when the cyclic loading times are n times is recorded asTo take the following stepsThe accumulated friction energy consumption is recorded asTo take the following stepsThe accumulated friction energy consumption is recorded as。
And S4, arranging loading plates at the upper end and the lower end of the discrete element model, and applying axial cyclic load to the model.
As a specific embodiment, the cyclic load is controlled to be sine wave by adopting a stress control mode, and the stress applied by the loading plate is controlled by the loading wave waveformThe variation with time t is as follows: In the following Is the average stress; Setting time steps in discrete meta-software, and using cyclic statement to control loading process, in every time step according to sine function The current stress value is calculated and applied to the load plate, and the residual strain-load times data and friction energy dissipation values of the model for each time step are saved using a recording function.
And S5, constructing an ant colony optimization algorithm model through Python, and calibrating the nonlinear bonding degradation model parameters in the step S3, wherein in the calibration process, a residual strain-loading frequency curve and the final destruction cycle frequency which are output by discrete element simulation are used as objective functions, and the simulation results approach the test results through iteration, and the specific steps are as follows:
Step S51, determining parameters to be optimized, wherein the parameters to be calibrated in the model comprise the speed a and b of damage accumulation in a micro-damage stage, an initial value e of damage accumulation in an acceleration damage stage, the speed c of damage accumulation in the acceleration damage stage, and the acceleration d of damage accumulation in the acceleration damage stage;
And S52, constructing an objective function, wherein the objective function is used for measuring the difference between the discrete element simulation result and the fatigue test result, and the expression formula is as follows: ,, Wherein: as objective function values, representing the overall difference between the simulation result and the test result; for the relative error of the residual strain-loading frequency curve, z points are respectively and equally selected on the simulated residual strain-loading frequency curve and the tested residual strain-loading frequency curve, and the corresponding strain value is recorded AndComparing the simulation result with the test result to obtain the relative error of the strain, and superposing the relative errors of the z points to finally obtain the relative error of the residual strain-loading frequency curve; In order to destroy the relative error of the number of cycles, To simulate the number of load cycles at the time of final corruption,The number of loading cycles at test failure; And The method is used for adjusting the contribution degree of two errors to the objective function;
step S53, initializing an ant colony, setting the ant colony scale, namely the number of the ant colony ants as m, randomly generating a value in the value range of five parameters a, b, c, d, e, and forming a group of initial solutions;
repeating the process to generate m groups of initial solutions which are respectively distributed to m ants;
Creating a pheromone matrix The pheromone matrix is provided with dimensions of q multiplied by p, wherein q is the number of parameters to be optimized, and p is the discretization degree of each parameter, namely the number of intervals in which the value range of each parameter is divided;
Step S54, selecting paths by ant colony, calculating parameter selection probability, and selecting any ant x and any parameter y to be optimized according to the information matrix And heuristic informationCalculating the probability of ant selecting the parameterInformation concentrationReflecting the effect of the parameter y in the history optimization process, the higher the concentration, the greater the probability of the parameter being selected, heuristic informationThe distance between the parameter y and the current optimal solution is reflected, the inverse of the objective function value is generally taken, the closer the distance is, the more potential the parameter is represented, the greater the possibility of being selected is, and the parameter selection probability formula is as follows: Wherein, the method comprises the steps of, wherein, AndThe method is characterized by comprising two weight coefficients, wherein the two weight coefficients are used for adjusting the influence degree of pheromone concentration and heuristic information on the path selection probability; Representing the path combinations that ant x can currently select;
According to the calculated parameter selection probability Selecting a new set of parameter combinations for each ant by using a wheel disk random selection method, performing discrete element simulation by using the selected parameter combinations of each ant to obtain simulation results including a residual strain-loading frequency curve and the cycle frequency when damage occurs, and calculating objective function values corresponding to the simulation results of each ant according to the objective function defined in S52;
According to the objective function value of each antCalculate the pheromone increment it leaves on each parameterThe pheromone increment is inversely proportional to the objective function, namely the smaller the objective function is, the larger the pheromone increment is, and the pheromone increment calculation formula is as follows: Wherein Q is a pheromone intensity coefficient used for controlling the update amplitude of the pheromone; Updating the pheromone matrix according to the increment of the pheromone of each ant The pheromone update formula is as follows: Wherein The pheromone volatilization coefficient is used for simulating the volatilization of the pheromone along with time;
Step S55, judging whether the objective function of each ant reaches the preset requirement, namely, the objective function value is smaller than the threshold value, stopping the iterative optimization process if the termination condition is met, otherwise, returning to step S54, continuing the next iteration, and combining the iterated parameters with the highest pheromone concentration meeting the objective function as the optimal parameters of the model.
And S6, substituting the optimal parameters output in the step S5 into the nonlinear bonding degradation model established in the step S3, performing single-axis cyclic loading discrete element simulation on the asphalt mixture by using the calibrated model to obtain a residual strain-loading frequency curve and a damage cycle frequency of a simulation result, comparing the simulation result with the fatigue test result obtained in the step S2, and analyzing the consistency between the simulation result and the fatigue test result to verify the accuracy and the prediction capability of the model.
The example demonstrates the accuracy of the simulation method, which comprises the following specific steps:
and S1, building an SMA asphalt mixture cylinder test piece with phi of 50mm multiplied by 100mm by using discrete element modeling software PFC3D, wherein the particle radius is set to be 0.75mm.
The inter-particle contact model is defined in the model as a linear parallel bond model (see Parallel Bond Model (PBM) schematic and PFC5.0 contact model-built-in contact model-linear parallel bond model (translated from hellp document) -note). Then, a simulated uniaxial compression test is carried out, simulated mechanical property data are obtained, the simulated mechanical property data are compared with the macroscopic mechanical property of the actual asphalt mixture, and the accuracy of the model is calibrated by adjusting the mesoscopic parameters in the model.
And S2, carrying out an actual uniaxial compression test by adopting an SMA asphalt mixture cylindrical test piece with the diameter of phi 50mm multiplied by 100mm until the test piece is destroyed, and obtaining the uniaxial compression strength of 6.8MPa. And (3) performing a cyclic loading fatigue test by using a cylindrical test piece with the same size to obtain fatigue life data of the asphalt mixture. The fatigue test adopts a stress control mode, the loading waveform is sine wave, the loading frequency is 10Hz, and the stress amplitude is 2.04MPa. The loading times-residual strain data in the test process are collected and recorded through a dynamic measurement system. The number of loading cycles at which the final material was destroyed was recorded to be 7943.
And step S3, establishing a nonlinear bonding degradation model based on friction energy consumption to accurately describe the fatigue damage evolution process of the asphalt mixture. The bond radius degradation equation is as follows:
In the initial stage of the process, ,
In the stage of micro-damage,,
The stage of the injury is accelerated,,
In the stage of the destruction of the material,,
And S4, arranging loading plates at the upper end and the lower end of the discrete element model, and simulating the axial cyclic load applied in the test. The method comprises the following specific steps:
In step S41, loading plates are arranged, and in the discrete meta-software PFC3D, two parallel rigid loading plates are created and respectively placed at the upper end and the lower end of the model. The size of the loading plate is matched with the cross-sectional area of the test piece so as to ensure uniform stress.
Step S42, defining stress control, and defining cyclic load as a stress control mode, namely controlling stress applied to the model by the loading plate in the loading process.
The waveform of the stress is sine wave, and the expression is:。
and S43, circularly loading control, namely controlling the stress applied by the loading plate to change along with time by writing a circular statement. In each time step, firstly calculating the stress value corresponding to the current time point t The stress was then applied to the load plate, simulating the loading process in an actual test.
And S44, collecting residual strain-loading times data, and recording stress and strain data of the model in each time step by utilizing a recording function in discrete meta-software. The stress data includes stress applied by the loadboardThe strain data is obtained by calculating the compression deformation of the test piece. The data is used as a reference of time, and the whole loading process is continuously recorded.
Step S45, friction energy consumption calculation, wherein in each time step, a friction energy dissipation value is calculated based on tangential force and slip increment of a particle contact point in a discrete element model:。
And step S46, saving the residual strain-loading frequency data and the corresponding friction energy consumption in each time step as a csv file for subsequent analysis and parameter calibration.
And S5, constructing an ant colony optimization algorithm model through Python, and calibrating parameters of the nonlinear bonding degradation model based on friction energy consumption in the step S3. The method comprises the following specific steps:
And S51, determining parameters to be optimized, namely, the speed of damage accumulation in a micro-damage stage a and b, the initial value of damage accumulation in an acceleration damage stage e, the speed of damage accumulation in an acceleration damage stage c, and the acceleration of damage accumulation in an acceleration damage stage d.
And S52, constructing an objective function for measuring the difference between the discrete element simulation result and the actual fatigue test result. The objective function consists of two parts, namely the relative error of the residual strain-loading times curve and the relative error of the damage cycle times. The expression of the objective function is:,,,、 Are all automatically calculated by Python.
Step S53, initializing ant colony, namely setting the scale of ant colony, namely, the number of ants m=150, randomly generating m groups of initial solutions in the range of the values of the parameters to be optimized, wherein the initial solutions correspond to the initial parameter combination of each ant, and constructing a pheromone matrixThe objective function value of each group of parameter combination is recorded, and the dimension of the pheromone matrix is 5 multiplied by 5.
Step S54, ant colony path selection and simulation, namely calculating selection probability, and for each ant x and each parameter y to be optimized, calculating the probability of selecting the parameter according to the pheromone concentration tau and heuristic information eta: according to the probability of selection A new set of parameter combinations is selected for each ant using a roulette random selection method.
And calculating an objective function, performing discrete element simulation by using parameter combinations selected by each ant, and obtaining simulation results (a residual strain-loading frequency curve and a damage cycle frequency).
Calculating the objective function value corresponding to each ant according to the objective function F defined before。
According to the objective function value of each antCalculating the pheromone increment of the pheromone on each parameter:。
updating the pheromone matrix according to the pheromone increment: 。
step S55, judging whether the objective function value of each ant reaches the preset requirement )。
And stopping iteration if the termination condition is met, and outputting the optimal parameter combination. If the termination condition is not satisfied, the process returns to step S54, and the next iteration is continued. Through multiple iterations, the ant colony gradually optimizes the parameter combination, and finally an optimal solution is found, and the error change in the optimization process is shown in fig. 4. The iteratively optimized optimal parameter combinations are shown in table 1 as final calibrated model parameters for subsequent simulation and analysis.
Table 1 optimization parameter combinations
And S6, substituting the optimal parameters obtained by optimization in the step S5 into the nonlinear bonding degradation model of the step S3, and performing uniaxial cyclic loading discrete element simulation on the asphalt mixture. The residual strain-loading frequency curve and the breaking cycle frequency of the simulation result are obtained, and are compared and analyzed with the fatigue test result in the step S2, and a comparison chart is shown in FIG. 5.
In fig. 5, the test result and the simulation result have higher matching degree, and the calculation error between the test result and the simulation result is smaller than 5%, which indicates that the established nonlinear dissipation model considering friction energy can well simulate the fatigue failure process of the asphalt mixture. Meanwhile, the invention is also helpful for further researching fatigue damage generation and development process research of the asphalt mixture under a microscopic scale.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other.
The preferred embodiments of the present invention have been described in detail above, but the present invention is not limited to the specific details of the above embodiments, and various equivalent changes (such as number, shape, position, etc.) may be made to the technical solution of the present invention within the scope of the technical concept of the present invention, and these equivalent changes all belong to the protection of the present invention.
Claims (7)
1. A fatigue simulation method for nonlinear energy dissipation of asphalt mixture is characterized by comprising the following steps:
S1, building an asphalt mixture cylinder test piece with a preset size by utilizing discrete element modeling software PFC3D, and determining the radius of particles;
The contact model among the particles is constructed as a linear parallel bonding model, and the microscopic parameters of the linear parallel bonding model are calibrated by comparing the simulated uniaxial compression test with the macroscopic mechanical properties of the actual asphalt mixture;
S2, adopting the asphalt mixture cylinder test piece to carry out a uniaxial compression test until the test piece is destroyed, and obtaining the uniaxial compressive strength of the asphalt mixture cylinder test piece ;
Carrying out a cyclic loading fatigue test by using the asphalt mixture time with the same size to obtain fatigue life data of the asphalt mixture;
Step S3, a nonlinear bonding degradation model based on friction energy consumption is established to accurately describe the fatigue damage evolution process of the asphalt mixture, the nonlinear bonding degradation model captures nonlinear damage evolution behaviors of the asphalt mixture at different damage stages by constructing a piecewise function model, and the bonding radius between model particles loaded each time is modified by a residual bonding radius multiplier phi to change the bonding strength of the model so as to realize the simulation of macroscopic mechanical property damage of the material;
Setting loading plates at the upper end and the lower end of the discrete meta-model, applying axial cyclic load to the model, setting time steps in the discrete meta-software, adopting a cyclic statement to control the loading process, and storing the residual strain-loading times data and friction energy dissipation value of the model in each time step;
step 5, constructing an ant colony optimization algorithm model to calibrate the nonlinear bonding degradation model parameters in the step 3, wherein the calibration process takes a residual strain-loading frequency curve and the final failure cycle frequency which are simulated and output by discrete elements as an objective function, and the simulation result approximates to the test result through iteration;
And S6, substituting the optimal parameters output in the step S5 into the nonlinear bonding degradation model based on friction energy consumption established in the step S3, performing single-axis cyclic loading discrete element simulation on the asphalt mixture by using the calibrated model to obtain a residual strain-loading frequency curve and a failure cycle frequency of a simulation result, comparing the simulation result with the fatigue test result obtained in the step S2, and analyzing the consistency between the simulation result and the fatigue test result to verify the accuracy and the prediction capability of the model.
2. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 1, wherein the dimensions of the asphalt mixture cylinder test piece in step S1 are Φ50mm×100deg.mm.
3. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 1, wherein in the step S2, in the cyclic loading fatigue test, the cyclic loading is controlled by adopting a stress control mode, the loading waveform is controlled to be a sine wave, the loading frequency is 10Hz, and the stress amplitude is 0.3,The stress strain data in the cyclic loading process is acquired and recorded through a dynamic measurement system, and the loading cycle number when the final material is damaged is recorded as。
4. The method for fatigue simulation of non-linear energy dissipation of asphalt mixture according to claim 1, wherein in step S3,
The nonlinear bond degradation model multiplies phi the residual bond radius by the cumulative friction dissipation energyBy piecewise function correlation, the following four phases are included:
As an initial stage at this time Indicating that the asphalt mixture is not damaged in the stage, the bonding strength is kept in an initial state,A critical cumulative frictional dissipation energy value representing the onset of damage to the material;
As a micro-injury stage at this time The damage begins to slowly accumulate, and the bonding strength gradually decreases; a critical accumulated friction dissipation energy value representing that the damage accumulation speed starts to be accelerated, wherein n is the number of cyclic loading times;
As an accelerated injury stage at this time The damage accumulation speed is obviously increased, the bonding strength is rapidly reduced, and the exponential function is realizedEmbodying the acceleration characteristic of damage accumulation, wherein controlling the acceleration of damage accumulation in the acceleration damage stage, wherein the parameter e is the initial value of damage accumulation in the acceleration damage stage, and the parameter c is the speed of damage accumulation in the acceleration damage stage; a critical cumulative frictional dissipation energy value representing the occurrence of material failure;
as a breaking stage at this time Meaning that the bond is completely disabled and the material is broken;
In the above model, cumulative friction dissipation energy The calculation formula of (2) is as follows: In which, in the process, For tangential forces at the contact point in the ith loading step,Is the slip delta at the contact point in the ith loading step.
5. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 4, wherein the nonlinear bonding degradation model is characterized byThe accumulated friction energy consumption is recorded asTo take the following stepsThe accumulated friction energy consumption is recorded asTo take the following stepsThe accumulated friction energy consumption is recorded as。
6. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 4, wherein the step S4 specifically comprises the following steps:
s41, arranging parallel rigid loading plates at the upper end and the lower end of a discrete element model, and respectively placing the parallel rigid loading plates at the upper end and the lower end of the model, wherein the size of the loading plates is matched with the cross section area of a test piece so as to ensure uniform stress;
step S42, defining stress control, and defining cyclic load as a stress control mode;
During loading, the stress applied by the loading plate to the model is controlled The variation with time t is as follows: In the following For average stress, take;For the stress amplitude, takeF is the loading frequency;
Step S43, cyclic loading control, controlling the stress applied by the loading plate to change along with time, and calculating the stress value corresponding to the current time point t in each time step Then applying the stress to the loading plate to simulate the loading process in the actual test;
Step S44, collecting data of residual strain-loading times, and recording stress data and strain data of the model in each time step, wherein the stress data comprises stress applied by a loading plate The stress data and the strain data are used as references, and the whole loading process is continuously recorded;
Step S45, calculating a friction energy dissipation value based on tangential force and slip increment of particle contact points in the discrete meta-model in each time step ;
And step S46, saving the data of the residual strain-loading times in each time step and the corresponding friction energy consumption as a csv file for subsequent analysis and parameter calibration.
7. The fatigue simulation method for nonlinear energy dissipation of asphalt mixture according to claim 4, wherein the step S5 specifically comprises the following steps:
Step S51, determining parameters to be optimized, wherein the parameters to be calibrated in the model comprise the speed a and b of damage accumulation in a micro-damage stage, an initial value e of damage accumulation in an acceleration damage stage, the speed c of damage accumulation in the acceleration damage stage, and the acceleration d of damage accumulation in the acceleration damage stage;
And S52, constructing an objective function, wherein the objective function is used for measuring the difference between the discrete element simulation result and the fatigue test result, and the expression formula is as follows: ,, Wherein: as objective function values, representing the overall difference between the simulation result and the test result; for the relative error of the residual strain-loading frequency curve, z points are respectively and equally selected on the simulated residual strain-loading frequency curve and the tested residual strain-loading frequency curve, and the corresponding strain value is recorded AndComparing the simulation result with the test result to obtain the relative error of the strain, and superposing the relative errors of the z points to finally obtain the relative error of the residual strain-loading frequency curve; In order to destroy the relative error of the number of cycles, To simulate the number of load cycles at the time of final corruption,The number of loading cycles at test failure; And The method is used for adjusting the contribution degree of two errors to the objective function;
step S53, initializing an ant colony, setting the ant colony scale, namely the number of the ant colony ants as m, randomly generating a value in the value range of five parameters a, b, c, d, e, and forming a group of initial solutions;
repeating the process to generate m groups of initial solutions which are respectively distributed to m ants;
Creating a pheromone matrix Recording the attractive force for each location in the parameter space;
The pheromone matrix is provided with dimensions of q multiplied by p, wherein q is the number of parameters to be optimized, and p is the discretization degree of each parameter, namely the number of intervals in which the value range of each parameter is divided;
Step S54, selecting paths by ant colony, calculating parameter selection probability, and selecting any ant x and any parameter y to be optimized according to the information matrix And heuristic informationCalculating the probability of selecting the parameter in the t-th cycleInformation concentrationReflecting the effect of the parameter y in the history optimization process, the higher the concentration, the greater the probability of the parameter being selected, heuristic informationReflecting the distance between the parameter y and the current optimal solution, generally taking the reciprocal of the objective function value, the closer the distance is, the more potential the parameter is, the greater the likelihood of being selected;
The parameter selection probability formula is as follows: Wherein, the method comprises the steps of, wherein, AndThe method is characterized by comprising two weight coefficients, wherein the two weight coefficients are used for adjusting the influence degree of pheromone concentration and heuristic information on the path selection probability; Representing the path combinations that ant x can currently select;
According to the calculated parameter selection probability Selecting a new set of parameter combinations for each ant by using a wheel disk random selection method, performing discrete element simulation by using the selected parameter combinations of each ant to obtain simulation results including a residual strain-loading frequency curve and the cycle frequency when damage occurs, and calculating objective function values corresponding to the simulation results of each ant according to the objective function defined in S52;
According to the objective function value of each antCalculate the pheromone increment it leaves on each parameterThe pheromone increment is inversely proportional to the objective function, namely the smaller the objective function is, the larger the pheromone increment is, and the pheromone increment calculation formula is as follows: Wherein Q is a pheromone intensity coefficient used for controlling the update amplitude of the pheromone; Updating the pheromone matrix according to the increment of the pheromone of each ant The pheromone update formula is as follows: Wherein The pheromone volatilization coefficient is used for simulating the volatilization of the pheromone along with time;
Step S55, judging whether the objective function of each ant reaches the preset requirement, namely, the objective function value is smaller than the threshold value, stopping the iterative optimization process if the termination condition is met, otherwise, returning to step S54, continuing the next iteration, and combining the iterated parameters with the highest pheromone concentration meeting the objective function as the optimal parameters of the model.
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