Asphalt mixture-moisture characteristic curve model and parameter calculation method

Abstract

The application discloses an asphalt mixture-moisture characteristic curve model and a parameter calculation method, and the model and the parameter calculation method comprise the following steps: 1, preparing an asphalt mixture core sample; 2, determining the initial dry mass and porosity of the asphalt mixture core sample by using a vacuum saturation method, and checking the parallelism of parallel core samples; 3, measuring the matrix suction ψ of the parallel core samples of the asphalt mixture m and a data pair corresponding to the water saturation S; 4, substituting a series of experimental data of the matrix suction ψ m and the water saturation S into an initial model of the asphalt mixture-moisture characteristic curve, and fitting to obtain the asphalt mixture-moisture characteristic curve; 5-7, bringing the determined effective parameters into the initial model; 8, deriving the effective model; 9, calculating the slope of the zero matrix suction point; and 10, calculating a residual matrix suction parameter. The asphalt mixture-moisture characteristic curve mathematical model provided by the application is continuous and monotonically decreasing in the range from zero to infinity of the matrix suction, and is convenient for calculating the unsaturated parameters.

Description

Technical Field

[0001] This invention belongs to the technical field of unsaturated hydraulic properties research of asphalt pavement materials, specifically involving an asphalt mixture-moisture characteristic curve model and parameter calculation method. Background Technology

[0002] Asphalt pavement is an artificial structure laid in the natural environment, frequently subjected to the effects of atmospheric precipitation, capillary replenishment, and evaporation. This process easily leads to the presence of liquid and gas phases and unsaturated seepage within the pore structure of asphalt mixtures. Numerous scientific studies and engineering practices have shown that long-term unsaturated moisture storage and flow weakens the asphalt-aggregate interface strength. Adding external conditions such as vehicle loads can induce crack propagation, exacerbating moisture damage and even coupled water-thermal-mechanical damage, ultimately reducing the service life and economic efficiency of asphalt pavement. The key to solving these problems lies in understanding the unsaturated hydraulic characteristics of asphalt pavement materials.

[0003] The asphalt mixture-moisture characteristic curve is a crucial constitutive relation for describing the unsaturated hydraulic properties of asphalt pavement materials, reflecting the variation of the material's matrix potential energy with humidity. As a key parameter in the unsaturated seepage control equation, the asphalt mixture-moisture characteristic curve is frequently used in the theoretical and simulation calculations of the hydrodynamic behavior of unsaturated asphalt pavements. Increasing research shows that the asphalt mixture-moisture characteristic curve can also guide the study of the unsaturated water-holding capacity, permeability, stress characteristics, strength, and deformation characteristics of asphalt pavement materials, as well as their inter-coupling problems.

[0004] Currently, many studies on asphalt mixture-moisture characteristic curve models assume that the pore characteristics of porous media are similar on a macroscopic scale, using soil-moisture characteristic curve models of unsaturated soils or matrix suction models reduced by saturation degree to replace the asphalt mixture-moisture characteristic curve model, thereby calculating the seepage response and dynamic response of unsaturated asphalt pavements. However, the analytical results obtained in this way often fail to accurately reflect the actual conditions of unsaturated asphalt pavements. This indicates that the approximate models currently available are still not very applicable to asphalt mixtures, and models for describing the asphalt mixture-moisture characteristic curve are still relatively lacking. Therefore, it is necessary to propose a model and parameter calculation method that reflects the characteristics of the asphalt mixture-moisture characteristic curve. Summary of the Invention

[0005] This invention addresses the lack of existing models describing the asphalt mixture-moisture characteristic curve. Based on the monotonically decreasing distribution characteristics of the asphalt mixture-moisture characteristic curve and specific water capacity curve as measured by field studies, this invention provides a globally continuous asphalt mixture-moisture characteristic curve model with good descriptive effect. Furthermore, it provides calculation methods for each parameter of the model, establishing important constitutive relationships for the unsaturated hydraulic properties of asphalt pavement materials and improving the accuracy of predicting the service performance of asphalt pavement in unsaturated states.

[0006] The asphalt mixture-moisture characteristic curve model and parameter calculation method of the present invention are implemented according to the following steps:

[0007] Step 1: Use the Marshall method to form multiple standard Marshall parallel specimens of asphalt mixture, and use a core sampler to obtain asphalt mixture core samples;

[0008] Step 2: Determine the initial dry mass m0 and porosity V of the asphalt mixture core sample from Step 1 using the vacuum saturation method. v Check the parallelism of the parallel core samples;

[0009] Step 3: Using an unsaturated static triaxial test system (unsaturated pressure chamber system), measure the matrix suction ψ of parallel core samples of asphalt mixture. m The specific testing process is as follows, comparing the measured data with the corresponding water saturation S:

[0010] Step 3a: Immerse the asphalt mixture core sample in a deaerated water tank at room temperature, then place the tank in a vacuum dryer with a vacuum degree set to 97.3 kPa to 98.7 kPa. After that, immerse the sample in water under normal pressure and repeat the process multiple times to obtain a saturated asphalt mixture core sample.

[0011] Step 3b: Perform a desiccation test on the saturated asphalt mixture core sample by applying matrix suction in stages until the relative drainage volume is less than 5% under 5 consecutive suction levels. Take out the core sample, weigh the mass of the residual water content, and calculate the residual water content volume according to formula (1).

[0012]

[0013] In formula (1): V r The residual water content of the asphalt mixture core sample is given in m. r ρ is the mass of the asphalt mixture core sample in the residual moisture state, m0 is the mass of the asphalt mixture core sample in the initial dry state, and ρ is the mass of the asphalt mixture core sample in the initial dry state. w The density of the degassed water;

[0014] The equilibrium water content at each stage is obtained by sequentially calculating the drainage volume. The calculation formulas for the equilibrium water content at each stage are as follows:

[0015] Vi =V r +(d r -d i (2)

[0016] In formula (2): V i Let d be the water content of the asphalt mixture core sample at the i-th equilibrium state. i Let d be the total drainage volume of the asphalt mixture core sample at the i-th equilibrium state. r This represents the total drainage volume of the asphalt mixture core sample when it is in a residual moisture state.

[0017] The saturation of each equilibrium state is calculated according to formula (3):

[0018]

[0019] In formula (3): S i Let represent the saturation of the asphalt mixture core sample at the i-th equilibrium state.

[0020] Thus, multiple sets of matrix suction-saturation (ψ) were obtained. m -S) Discrete data points are used to plot the asphalt mixture-moisture characteristic curve, with the x-axis of the curve representing the matrix suction ψ. m The vertical axis represents the water saturation S of the core sample;

[0021] Step 3c: Repeat steps 3a and 3b in sequence to test the asphalt mixture-moisture characteristic curves of multiple parallel core samples;

[0022] Step 4: Apply the matrix suction ψ obtained in Step 3. m Substituting a series of experimental data on water saturation S into the initial model of the asphalt mixture-moisture characteristic curve, the asphalt mixture-moisture characteristic curve was obtained by fitting.

[0023] The initial model of the asphalt mixture-moisture characteristic curve is in the form of:

[0024]

[0025] In formula (4): S is the water saturation of the asphalt mixture, S r ψ represents the residual water saturation of the asphalt mixture. m denoted as matrix suction of water-containing asphalt mixture, where a and b are fitting parameters of the model, and e is the base of the natural logarithm.

[0026] Step 5: Set goodness-of-fit constraints, calculate the fitting accuracy, and determine whether the fitting accuracy meets the requirements. If the fitting accuracy meets the goodness-of-fit constraints, derive the fitting parameters a and b, and the residual water saturation S of the asphalt mixture based on the initial model of the asphalt mixture-moisture characteristic curve. r;

[0027] Step 6: Combine the a and b parameter values ​​obtained from the fitting in Step 5 with the residual water saturation S of multiple parallel core samples. r The values ​​were calculated and their average values ​​were obtained to obtain the effective parameter 'a' of the asphalt mixture-moisture characteristic curve model. * b * and S r * ;

[0028] Step 7: Calculate the effective model parameters a obtained in Step 6. * b * and S r * Substitute the initial model of the asphalt mixture-moisture characteristic curve described in step four to obtain the effective model of the asphalt mixture-moisture characteristic curve.

[0029] Step 8: Differentiate the effective model of the asphalt mixture-moisture characteristic curve in Step 7, and calculate the derived parameter specific water capacity curve of the asphalt mixture-moisture characteristic curve.

[0030] The equation for the specific water capacity curve model is as follows:

[0031]

[0032] Step 9: Obtain the matrix suction ψ m The slope k0 of the asphalt mixture-moisture characteristic curve at 0 kPa is the effective parameter a of the asphalt mixture-moisture characteristic curve model obtained in step six. * b * and the residual water saturation S of the asphalt mixture r * Substitute this into the formula for the water volume with zero suction;

[0033] At the point of complete saturation (S=1), the specific water capacity is calculated, and the zero-suction specific water capacity is obtained as follows:

[0034]

[0035] Step 10: Substitute the slope k0 of the zero matrix suction point into the formula for calculating residual matrix suction. In the process, the residual matrix suction parameter ψ of the asphalt mixture is obtained. r .

[0036] Compared with existing technologies, the main advantages of the asphalt mixture-moisture characteristic curve model and parameter calculation method of the present invention are as follows:

[0037] (1) The continuous mathematical model of the asphalt mixture-moisture characteristic curve designed in this invention has a simple expression and high fitting accuracy. Based on the monotonically decreasing distribution characteristics of the asphalt mixture-moisture characteristic curve and the specific water capacity curve as measured by actual measurements, and the model compensation of the initial conditions, a two-parameter asphalt mixture-moisture characteristic curve model is constructed. The model is expressed in a display format and is simple in form, which facilitates the rapid fitting of discrete data using the global optimization (UGO) algorithm. The fitting parameter values ​​that meet the requirements of high fitting accuracy (greater than 99.0%) can be easily determined according to the goodness-of-fit constraints set by the user.

[0038] (2) The mathematical model of the asphalt mixture-moisture characteristic curve proposed in this invention overcomes the shortcomings of the existing matrix suction reduction form based on saturation and the unsaturated soil-moisture characteristic curve. On the one hand, the analysis of the pore size distribution inside the asphalt mixture reveals that its distribution range is wide and uneven. This causes the water content to be almost completely saturated when the matrix suction is close to zero, and to reach a point where the water content exceeds the residual saturation S. r Subsequently, the matrix suction becomes almost infinite; on the other hand, due to the weak hydrophilicity of asphalt materials, the specific water capacity curve derived from the moisture characteristic curve exhibits monotonicity and boundedness, especially when the matrix suction ψ m When ε = 0, the specific water capacity C (S = 1) exhibits characteristics of being neither zero nor infinite. These fundamental characteristics are constraints limiting the mathematical form of the asphalt mixture moisture characteristic curve model. Models using a reduction of matrix suction based on saturation do not satisfy the first constraint, and unsaturated soil-water characteristic curves do not meet the second constraint. Based on the aforementioned mathematical boundary constraints, this invention adopts the configuration of the McKee & Bumb model equations and introduces a compensation term ε0 to propose a mathematical model for the asphalt mixture-water characteristic curve. This model satisfies the requirement that matrix suction is globally continuous from zero to infinity, and also meets the requirement that the specific water capacity at the zero matrix suction point is neither zero nor infinite, thus avoiding the shortcomings of existing models.

[0039] (3) The parameter calculation method for the asphalt mixture-moisture characteristic curve model designed in this invention is simple to operate. Using the monotonically decreasing, globally continuous two-parameter asphalt mixture-moisture characteristic curve model established in this invention, a specific water capacity model can be derived. This model is continuous and monotonically decreasing over a range of matrix suction from zero to infinity, and can be used to reflect the water-holding characteristics of asphalt mixtures. The model can also conveniently calculate and determine unsaturated parameters of asphalt mixtures such as residual water saturation, specific water capacity, and residual matrix suction. The parameter calculation method for the asphalt mixture-moisture characteristic curve model designed in this invention provides a new means for more accurately and effectively evaluating the water-holding and unsaturated permeability characteristics of asphalt mixtures. Attached Figure Description

[0040] Figure 1 This is a flowchart of the asphalt mixture-moisture characteristic curve fitting and parameter calculation method of the present invention;

[0041] Figure 2 The figures shown are the measured results of the asphalt mixture-moisture characteristic curves for three groups of asphalt mixtures with different porosities in the example. In the figure, ● represents a sample with a porosity of 5.9%, ▲ represents a sample with a porosity of 5.6%, and ▼ represents a sample with a porosity of 5.0%.

[0042] Figure 3 The figure shows the fitting results of the three groups of asphalt mixture-moisture characteristic curve models with different porosities in the example. In the figure, ● represents a sample with a porosity of 5.9%, ▲ represents a sample with a porosity of 5.6%, and ▼ represents a sample with a porosity of 5.0%. Detailed Implementation

[0043] Specific Implementation Method 1: The asphalt mixture-moisture characteristic curve model and parameter calculation method in this implementation method are carried out according to the following steps:

[0044] Step 1: Use the Marshall method to form multiple standard Marshall parallel specimens of asphalt mixture, and use a core sampler to obtain asphalt mixture core samples;

[0045] Step 2: Determine the initial dry mass m0 and porosity V of the asphalt mixture core sample from Step 1 using the vacuum saturation method. v Check the parallelism of the parallel core samples;

[0046] Step 3: Using an unsaturated static triaxial test system, measure the matrix suction ψ of parallel core samples of asphalt mixture. m The specific testing process is as follows, comparing the measured data with the corresponding water saturation S:

[0047] Step 3a: Immerse the asphalt mixture core sample in a deaerated water tank at room temperature, then place the tank in a vacuum dryer with a vacuum degree set to 97.3 kPa to 98.7 kPa. After that, immerse the sample in water under normal pressure and repeat the process multiple times to obtain a saturated asphalt mixture core sample.

[0048] Step 3b: Perform a desiccation test on the saturated asphalt mixture core sample by applying matrix suction in stages until the relative drainage volume is less than 5% under 5 consecutive suction levels. Take out the core sample, weigh the mass of the residual water content, and calculate the residual water content volume according to formula (1).

[0049]

[0050] In formula (1): V r The residual water content of the asphalt mixture core sample is given in m. rρ is the mass of the asphalt mixture core sample in the residual moisture state, m0 is the mass of the asphalt mixture core sample in the initial dry state, and ρ is the mass of the asphalt mixture core sample in the initial dry state. w The density of the degassed water;

[0051] The equilibrium water content at each stage is obtained by sequentially calculating the drainage volume. The calculation formulas for the equilibrium water content at each stage are as follows:

[0052] V i =V r +(d r -d i (2)

[0053] In formula (2): V i Let d be the water content of the asphalt mixture core sample at the i-th equilibrium state. i Let d be the total drainage volume of the asphalt mixture core sample at the i-th equilibrium state. r This represents the total drainage volume of the asphalt mixture core sample when it is in a residual moisture state.

[0054] The saturation of each equilibrium state is calculated according to formula (3):

[0055]

[0056] In formula (3): S i Let represent the saturation of the asphalt mixture core sample at the i-th equilibrium state.

[0057] Thus, multiple sets of matrix suction-saturation (ψ) were obtained. m -S) Discrete data points are used to plot the asphalt mixture-moisture characteristic curve, with the x-axis of the curve representing the matrix suction ψ. m The vertical axis represents the water saturation S of the core sample;

[0058] Step 3c: Repeat steps 3a and 3b in sequence to test the asphalt mixture-moisture characteristic curves of multiple parallel core samples;

[0059] Step 4: Apply the matrix suction ψ obtained in Step 3. m Substituting a series of experimental data on water saturation S into the initial model of the asphalt mixture-moisture characteristic curve, the asphalt mixture-moisture characteristic curve was obtained by fitting.

[0060] The initial model of the asphalt mixture-moisture characteristic curve is in the form of:

[0061]

[0062] In formula (4): S is the water saturation of the asphalt mixture, S r ψ represents the residual water saturation of the asphalt mixture. mdenoted as matrix suction of water-containing asphalt mixture, where a and b are fitting parameters of the model, and e is the base of the natural logarithm.

[0063] Step 5: Set goodness-of-fit constraints, calculate the fitting accuracy, and determine whether the fitting accuracy meets the requirements. If the fitting accuracy meets the goodness-of-fit constraints, derive the fitting parameters a and b, and the residual water saturation S of the asphalt mixture based on the initial model of the asphalt mixture-moisture characteristic curve. r ;

[0064] Step 6: Combine the a and b parameter values ​​obtained from the fitting in Step 5 with the residual water saturation S of multiple parallel core samples. r The values ​​were calculated and their average values ​​were obtained to obtain the effective parameter 'a' of the asphalt mixture-moisture characteristic curve model. * b * and S r * ;

[0065] Step 7: Calculate the effective model parameters a obtained in Step 6. * b * and S r * Substitute the initial model of the asphalt mixture-moisture characteristic curve described in step four to obtain the effective model of the asphalt mixture-moisture characteristic curve.

[0066] Step 8: Differentiate the effective model of the asphalt mixture-moisture characteristic curve in Step 7, and calculate the derived parameter specific water capacity curve of the asphalt mixture-moisture characteristic curve.

[0067] The equation for the specific water capacity curve model is as follows:

[0068]

[0069] Step 9: Obtain the matrix suction ψ m The slope k0 of the asphalt mixture-moisture characteristic curve at 0 kPa is the effective parameter a of the asphalt mixture-moisture characteristic curve model obtained in step six. * b * and the residual water saturation S of the asphalt mixture r * Substitute this into the formula for the water volume with zero suction;

[0070] At the point of complete saturation (S=1), the specific water capacity is calculated, and the zero-suction specific water capacity is obtained as follows:

[0071]

[0072] Step 10: Substitute the slope k0 of the zero matrix suction point into the formula for calculating residual matrix suction. In the process, the residual matrix suction parameter ψ of the asphalt mixture is obtained. r .

[0073] Specific Implementation Method Two: The difference between this implementation method and Specific Implementation Method One is that the size of the cylindrical core sample in step one is φ50mm×63.5mm.

[0074] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that the difference between the measured porosity of the parallel core sample and the average value in step 2 is less than 1.3 to 1.4 times the standard deviation, thus the parallelism requirement is met.

[0075] Specific Implementation Method Four: This implementation method differs from one of the specific implementation methods one to three in that the water tank in step 3a is placed in a vacuum dryer and kept for 15 minutes.

[0076] Specific Implementation Method 5: This implementation method differs from one of the specific implementation methods one to four in that the immersion treatment time under normal pressure in step 3a is 0.5h.

[0077] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the matrix suction applied in step 3b is not less than level 10.

[0078] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the dehumidification experiment described in step 3b uses an unsaturated static triaxial test system. During the application of matrix suction, the pore water pressure is controlled at 0 kPa, and the pore gas pressure is applied step by step. The applied matrix suction ψ m The value is equal to the pore air pressure.

[0079] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that the process of establishing the asphalt mixture-moisture characteristic curve model in step four is as follows:

[0080] Step 4a: Calculate the quasi-residual water saturation of the asphalt mixture using formula (5);

[0081]

[0082] In formula (5): S represents the quasi-residual water saturation of the asphalt mixture, n represents the total number of stages of matrix suction applied, and S represents the quasi-residual water saturation of the asphalt mixture. i Let represent the saturation of the asphalt mixture core sample at the i-th equilibrium state.

[0083] Step 4b: Normalize the series of saturation data of the measured asphalt mixture to obtain the quasi-effective saturation of the asphalt mixture.

[0084]

[0085] Step 4c: Obtain the data pairs and scatter plots of the quasi-effective saturation and matrix suction of the asphalt mixture. Based on the correlation between the two, fit the configuration of the McKee & Bumb equation to obtain the McKee & Bumb model and its parameters.

[0086] The configuration of the McKee & Bumb equation is as follows:

[0087]

[0088] In formula (7): y is the explained variable of the equation, x is the explanatory variable of the equation, and α and β are the equation parameters;

[0089] Step 4d: Apply the initial matrix suction force ψ m =ψ0=0, substitute into the McKee & Bumb model described in step 4c, and calculate the initial effective saturation prediction value S. ec0 ;

[0090] Step 4e: Compensate the model according to the principle that the predicted value and the measured value are equal under the initial conditions. Calculate the initial effective saturation prediction value S according to formula (8). ec0 Measured initial effective saturation S of asphalt mixture-moisture characteristic curve e0 Compensation term ε0 between 1 and 1:

[0091]

[0092] Step 4f: Introduce the compensation term ε0 calculated in Step 4e into the denominator of the McKee & Bumb model to obtain the initial model equation:

[0093]

[0094] Step 4g: Introduce parameters a and b to simplify the McKee & Bumb model equations:

[0095]

[0096]

[0097] Step 4h: Take S e =(SS) r ) / (1-S r ), and substitute formulas (10) and (11) into the initial model equation (9), and convert it to S = f(ψ m The display format is in the form of ) to obtain the asphalt mixture-moisture characteristic curve model.

[0098] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that step four uses MATLAB or the 1stOpt (First Optimization) program to fit and give the asphalt mixture-moisture characteristic curve.

[0099] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One through Nine in that step five sets a goodness-of-fit constraint, calculates the fitting accuracy, and determines whether the fitting accuracy meets the requirements. If the fitting accuracy meets the goodness-of-fit constraint, the formula for calculating the fitting accuracy is:

[0100]

[0101] In formula (13): adjR 2 To adjust the coefficient of determination, reflecting the quality of the fit; n is the total number of data pairs; y i This represents the i-th measured value of the asphalt mixture matrix suction. Let i be the i-th predicted value of the matrix suction of the asphalt mixture. The arithmetic mean of the measured data of asphalt mixture matrix suction, where k is the number of parameters in the asphalt mixture-moisture characteristic curve model.

[0102] Example: The asphalt mixture-moisture characteristic curve model and parameter calculation method in this example are implemented according to the following steps:

[0103] Step 1: Prepare three groups of standard Marshall specimens of dense-graded asphalt mixture with different porosities, with a molding size of φ101.3mm×63.5mm, according to the Marshall design method. Each group of specimens has three parallel specimens. The specimens are sampled and trimmed using a core drilling machine to obtain core samples with a size of φ50mm×63.5mm.

[0104] Step 2: Using the vacuum saturation method, determine the initial dry mass m0 and porosity V of the three groups of asphalt mixture core samples with different porosities obtained in Step 1. v The parallelism of the parallel core samples was checked. The difference between the measured porosity of the parallel core samples and the average value was less than 1.15 times the standard deviation, and the parallelism met the requirements.

[0105] Step 3: Using an unsaturated static triaxial test system, measure the matrix suction ψ of asphalt mixture under different porosities. m The specific process is as follows: (Compare the measured data with the corresponding water saturation S.)

[0106] Step 3a: Immerse the asphalt mixture core sample with a size of φ50mm×63.5mm in a deaerated water tank at room temperature, then place the tank in a vacuum dryer for 15 minutes with the vacuum degree set to 97.3kPa~98.7kPa. After that, immerse it in water for 0.5h under normal pressure. Repeat the operation three times to saturate the core sample and obtain a saturated asphalt mixture core sample.

[0107] Step 3b: Conduct a desaturation test on the saturated asphalt mixture core samples. Apply 11 levels of matrix suction until the relative drainage volume is less than 5% under 5 consecutive levels of suction. After completing all predetermined suction levels, remove the core samples and weigh the mass of the residual water content state, recording the mass to three decimal places. Calculate the residual water content volume. Obtain the equilibrium water content volume values ​​for each level by reverse calculation using the drainage volume, thus obtaining multiple sets of matrix suction-saturation (ψ) values. m -S) Discrete data points are used to plot the asphalt mixture-moisture characteristic curve, with the x-axis of the curve representing the matrix suction ψ. m The vertical axis represents the water saturation S of the core sample;

[0108] In step 3b, the instrument used in the dehumidification experiment is an unsaturated static triaxial test system. During the application of matrix suction, the pore water pressure is controlled at 0 kPa, and the pore gas pressure is applied step by step. The loading path is set to 1 kPa, 3 kPa, 5 kPa, 10 kPa, 15 kPa, 25 kPa, 50 kPa, 100 kPa, 150 kPa, 200 kPa, and 300 kPa. Based on the basic principle of axis translation technology, the applied matrix suction values ​​are 1 kPa, 3 kPa, 5 kPa, 10 kPa, 15 kPa, 25 kPa, 50 kPa, 100 kPa, 150 kPa, 200 kPa, and 300 kPa, respectively.

[0109] Specifically, in step 3b, the residual water volume is calculated according to formula (1):

[0110]

[0111] In formula (1): V r The residual water content of the asphalt mixture core sample is given in m. r ρ is the mass of the asphalt mixture core sample in the residual moisture state, m0 is the mass of the asphalt mixture core sample in the initial dry state, and ρ is the mass of the asphalt mixture core sample in the initial dry state. w The density of the degassed water;

[0112] Specifically, in step 3b, the water volume values ​​at each equilibrium state are calculated according to formula (2):

[0113] V i =V r +(d r -d i (2)

[0114] In formula (2): V i Let d be the water content of the asphalt mixture core sample at the i-th equilibrium state. i Let d be the total drainage volume of the asphalt mixture core sample at the i-th equilibrium state. r This represents the total drainage volume of the asphalt mixture core sample when it is in a residual moisture state.

[0115] Specifically, in step 3b, the saturation of each equilibrium state is calculated according to formula (3):

[0116]

[0117] In formula (3): S i Let represent the saturation of the asphalt mixture core sample at the i-th equilibrium state.

[0118] Step 3c: Repeat steps 3a and 3c in sequence to test the asphalt mixture-moisture characteristic curves of multiple parallel core samples;

[0119] Step 4: Measure the matrix suction ψ obtained in Step 3. m Substitute the series of measured data of water saturation S into the initial model of asphalt mixture-moisture characteristic curve, and use the 1stOpt (First Optimization) program to fit the asphalt mixture-moisture characteristic curve;

[0120] Specifically, the initial model of the asphalt mixture-moisture characteristic curve is in the form of:

[0121]

[0122] In formula (4): S is the water saturation of the asphalt mixture, S r ψ represents the residual water saturation of the asphalt mixture. m denoted as matrix suction of water-containing asphalt mixture, where a and b are fitting parameters of the model, and e is the base of the natural logarithm.

[0123] Step 5: Set the goodness-of-fit constraint to an adjusted coefficient of determination greater than 99.0%, calculate the fitting accuracy, and determine whether the fitting accuracy meets the requirements. If the fitting accuracy meets the goodness-of-fit constraint, derive the fitting parameters a and b, and the residual water saturation S of the asphalt mixture based on the initial model of the asphalt mixture moisture characteristic curve. r ;

[0124] Furthermore, the fitting accuracy is:

[0125]

[0126] In formula (5), adjR 2To adjust the coefficient of determination, reflecting the quality of the fit; n is the total number of data pairs; y i This represents the i-th measured value of the asphalt mixture matrix suction. Let i be the i-th predicted value of the matrix suction of the asphalt mixture. The arithmetic mean of the measured data of asphalt mixture matrix suction, where k is the number of parameters in the initial model of the asphalt mixture-moisture characteristic curve;

[0127] Step 6: Determine the fitting parameters a, b, and residual water saturation S of the asphalt mixture in the model. r The average value of the three parallel core samples, along with the a and b parameter values ​​obtained from the fitting process in step five, and the residual water saturation S, are calculated. r The effective parameter 'a' of the asphalt mixture-moisture characteristic curve model is obtained by averaging the values ​​of each. * b * and S r * ;

[0128] Step 7: Substitute the effective parameter values ​​of the asphalt mixture-moisture characteristic curve model obtained in Step 6 into the model proposed in Step 4 to calculate the effective model of the asphalt mixture-moisture characteristic curve.

[0129] Step 8: Differentiate the effective model of the asphalt mixture-moisture characteristic curve in Step 7, and calculate the derived parameter specific water capacity curve of the asphalt mixture-moisture characteristic curve.

[0130] Specifically, the specific water capacity curve model is in the form of:

[0131]

[0132] Furthermore, at the point of complete saturation (S=1), the specific water capacity is calculated to obtain the formula for zero-suction specific water capacity;

[0133] C(S=1)=(S r -1)ae b ∈(0,∞) (7)

[0134] Step 9: Obtain the matrix suction ψ m The slope m0 of the asphalt mixture-moisture characteristic curve at 0 kPa is the effective parameter a of the asphalt mixture-moisture characteristic curve model that satisfies the goodness-of-fit constraint in step six. * b * and the residual water saturation S of the asphalt mixture r * Substitute into formula (7);

[0135] Step 10: Substitute the slope k0 at the zero matrix suction point into the formula for calculating residual matrix suction to obtain the residual matrix suction parameter ψ of the asphalt mixture. r The method for calculating residual matrix suction is as follows:

[0136]

[0137] The asphalt mixture used in this embodiment is AC-13 dense-graded asphalt concrete mixture. The porosity of the asphalt mixture is controlled by adjusting the number of compaction cycles. The measured data of the asphalt mixture-moisture characteristic curve are obtained by using an unsaturated static triaxial test system through dehumidification experiments.

[0138] The measured results of the asphalt mixture-moisture characteristic curves under three different porosity conditions are as follows: Figure 2 As shown, the matrix suction ψ m Use the horizontal axis as the logarithmic axis and the saturation S as the vertical axis.

[0139] Based on the asphalt mixture-moisture characteristic curve model in formula (4), the measured data were repeatedly fitted, calculated, and evaluated. The average value of the parameters that met the fitting accuracy (i.e., the adjusted coefficient of determination was greater than 99.0%) was calculated to obtain the effective model parameter a for three sets of asphalt mixture-moisture characteristic curves with different porosities. * b * and residual water saturation S r * As shown in Table 1 below.

[0140] Table 1 Effective parameters of the asphalt mixture-moisture characteristic curve model

[0141]

[0142] The effective parameter a of the above model * b * and residual water saturation S r * Substituting these values ​​into the asphalt mixture-moisture characteristic curve model of this embodiment, the model form is as follows:

[0143] Porosity V v =5.9%

[0144]

[0145] Porosity V v =5.6%

[0146]

[0147] Porosity V v =5.0%

[0148]

[0149] The model fitting results are plotted as follows Figure 3 As shown, the asphalt mixture-moisture characteristic curve model proposed in this embodiment has a good fitting effect. The fitting results can be helpful for further theoretical research.

[0150] Based on the effective parameter a of the model * b * and residual water saturation S r * Further calculations were performed on the specific water capacity, the slope m0 at the zero matrix suction point, and the residual matrix suction ψ. r As shown in Table 2, the task of determining the asphalt mixture-moisture characteristic curve and its parameters is now complete.

[0151] Specific water capacity is as follows:

[0152] Porosity V v =5.9%

[0153]

[0154] Porosity V v =5.6%

[0155]

[0156] Porosity V v =5.0%

[0157]

[0158] Table 2 Calculation results of characteristic parameters of asphalt mixture-moisture characteristic curve

[0159]

Claims

1. A model and parameter calculation method for asphalt mixture-moisture characteristic curve, characterized in that... The asphalt mixture moisture characteristic curve model and parameter calculation method are implemented according to the following steps: Step 1: Use the Marshall method to form multiple standard Marshall parallel specimens of asphalt mixture, and use a core sampler to obtain asphalt mixture core samples; Step 2: Determine the initial dry mass m0 and porosity V of the asphalt mixture core sample from Step 1 using the vacuum saturation method. v Check the parallelism of the parallel core samples; Step 3: Using an unsaturated static triaxial test system, measure the matrix suction ψ of parallel core samples of asphalt mixture. m The specific testing process is as follows, comparing the measured data with the corresponding water saturation S: Step 3a: Immerse the asphalt mixture core sample in a deaerated water bath at room temperature, then place the bath in a vacuum dryer with a vacuum setting of 97.3 kPa to 98.7 kPa. After that, immerse the sample in water under normal pressure and repeat the process multiple times to obtain a saturated asphalt mixture core sample. Step 3b: Perform a desiccation test on the saturated asphalt mixture core sample by applying matrix suction in stages until the relative drainage volume is less than 5% under 5 consecutive suction levels. Take out the core sample, weigh the mass of the residual water content, and calculate the residual water content volume according to formula (1). (1) In formula (1): V r The residual water content of the asphalt mixture core sample is given in m. r ρ is the mass of the asphalt mixture core sample in the residual moisture state, m0 is the mass of the asphalt mixture core sample in the initial dry state, and ρ is the mass of the asphalt mixture core sample in the initial dry state. w The density of the degassed water; The equilibrium water content at each stage is obtained by sequentially calculating the drainage volume. The calculation formulas for the equilibrium water content at each stage are as follows: (2) In formula (2): V i Let d be the water content of the asphalt mixture core sample at the i-th equilibrium state. i Let d be the total drainage volume of the asphalt mixture core sample at the i-th equilibrium state. r This represents the total drainage volume of the asphalt mixture core sample when it is in a residual moisture state. The saturation of each equilibrium state is calculated according to formula (3): (3) In formula (3): S i Let represent the saturation of the asphalt mixture core sample at the i-th equilibrium state. This yields multiple sets of discrete data points on matrix suction and saturation, allowing for the plotting of asphalt mixture-moisture characteristic curves. The abscissa of the curve represents the matrix suction ψ. m The vertical axis represents the water saturation S of the core sample; Step 3c: Repeat steps 3a and 3b in sequence to test the asphalt mixture-moisture characteristic curves of multiple parallel core samples; Step 4: Apply the matrix suction ψ obtained in Step 3. m Substituting a series of experimental data on water saturation S into the initial model of the asphalt mixture-moisture characteristic curve, the asphalt mixture-moisture characteristic curve was obtained by fitting. The initial model of the asphalt mixture-moisture characteristic curve is in the form of: (4) In formula (4): S is the water saturation of the asphalt mixture, S r ψ represents the residual water saturation of the asphalt mixture. m denoted as matrix suction of water-containing asphalt mixture, where a and b are fitting parameters of the model, and e is the base of the natural logarithm. Step 5: Set goodness-of-fit constraints, calculate the fitting accuracy, and determine whether the fitting accuracy meets the requirements. If the fitting accuracy meets the goodness-of-fit constraints, derive the fitting parameters a and b, and the residual water saturation S of the asphalt mixture based on the initial model of the asphalt mixture-moisture characteristic curve. r ; Step 6: Combine the a and b parameter values ​​obtained from the fitting in Step 5 with the residual water saturation S of multiple parallel core samples. r The values ​​were calculated and their average values ​​were obtained to obtain the effective parameter 'a' of the asphalt mixture-moisture characteristic curve model. * b * and S r * ; Step 7: Calculate the effective model parameters a obtained in Step 6. * b * and S r * Substitute the initial model of the asphalt mixture-moisture characteristic curve described in step four to obtain the effective model of the asphalt mixture-moisture characteristic curve. Step 8: Differentiate the effective model of the asphalt mixture-moisture characteristic curve in Step 7, and calculate the derived parameter specific water capacity curve of the asphalt mixture-moisture characteristic curve. The equation for the specific water capacity curve model is as follows: (14) Step 9: Obtain the matrix suction ψ m The slope k0 of the asphalt mixture-moisture characteristic curve at 0 kPa is the effective parameter a of the asphalt mixture-moisture characteristic curve model obtained in step six. * b * and the residual water saturation S of the asphalt mixture r * Substitute this into the formula for the water volume with zero suction; At the point of complete saturation, i.e., S=1, the specific water capacity is calculated, and the zero-suction specific water capacity is obtained as follows: (15) Step 10: Substitute the slope k0 of the zero matrix suction point into the formula for calculating residual matrix suction. In (16), the residual matrix suction parameter ψ of the asphalt mixture is obtained. r .

2. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... The dimensions of the cylindrical core sample in step one are ϕ50mm × 63.5mm.

3. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... If the difference between the measured porosity of the parallel core sample and the average value in step two is less than 1.3 to 1.4 times the standard deviation, then the parallelism requirement is met.

4. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... In step 3a, the water tank is placed in a vacuum dryer and kept for 15 minutes.

5. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... In step 3a, the immersion treatment time under normal pressure is 0.5h.

6. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... In step 3b, the matrix suction force should be no less than level 10.

7. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... The dehumidification experiment described in step 3b uses an unsaturated static triaxial test system. During the application of matrix suction, the pore water pressure is controlled at 0 kPa, and the pore gas pressure is applied step by step. The applied matrix suction ψ m The value is equal to the pore air pressure.

8. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... The process of establishing the asphalt mixture-moisture characteristic curve model in step four is as follows: Step 4a: Calculate the quasi-residual water saturation of the asphalt mixture using formula (5); (5) In formula (5): Ŝ r S represents the quasi-residual water saturation of the asphalt mixture, n represents the total number of stages of matrix suction applied, and S represents the quasi-residual water saturation of the asphalt mixture. i Let represent the saturation of the asphalt mixture core sample at the i-th equilibrium state. Step 4b: Normalize the series of saturation data of the measured asphalt mixture to obtain the quasi-effective saturation of the asphalt mixture. e ; (6) Step 4c: Obtain the data pairs and scatter plots of the quasi-effective saturation and matrix suction of the asphalt mixture. Based on the correlation between the two, fit the configuration of the McKee & Bumb equation to obtain the McKee & Bumb model and its parameters. The configuration of the McKee & Bumb equation is as follows: (7) In formula (7): y is the explained variable of the equation, x is the explanatory variable of the equation, and α and β are the equation parameters; Step 4d: Apply the initial matrix suction force ψ m =ψ0=0, substitute into the McKee & Bumb model described in step 4c, and calculate the initial effective saturation prediction value S. ec0 ; Step 4e: Calculate the initial effective saturation prediction value S according to formula (8). ec0 Measured initial effective saturation S of asphalt mixture-moisture characteristic curve e0 Compensation term ε0 between =1: (8) Step 4f: Introduce the compensation term ε0 calculated in Step 4e into the denominator of the McKee & Bumb model to obtain the initial model equation: (9) Step 4g: Introduce parameters a and b to simplify the McKee & Bumb model equations: (10) (11) Step 4h: Take S e = (SS r ) / (1-S r ), and substitute formulas (10) and (11) into the initial model equation (9), and transform it into S = f(ψ m The display format is in the form of ) to obtain the asphalt mixture-moisture characteristic curve model. .

9. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... Step four involves using MATLAB or 1stOpt to fit and obtain the asphalt mixture-moisture characteristic curve.

10. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, characterized in that... In step five, goodness-of-fit constraints are set, the fitting accuracy is calculated, and it is determined whether the fitting accuracy meets the requirements. If the fitting accuracy meets the goodness-of-fit constraints, the formula for calculating the fitting accuracy is: (13) In formula (13): adj R 2 To adjust the coefficient of determination, reflecting the quality of the fit; n is the total number of data pairs; y i The i-th measured value of the asphalt mixture matrix suction; i Let θ be the i-th predicted value of the asphalt mixture matrix suction, ӯ be the arithmetic mean of the measured data of the asphalt mixture matrix suction, and k be the number of parameters in the asphalt mixture-moisture characteristic curve model.

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