CN115758718A - Asphalt mixture-water characteristic curve model and parameter calculation method - Google Patents
Asphalt mixture-water characteristic curve model and parameter calculation method Download PDFInfo
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Abstract
The invention discloses an asphalt mixture-water characteristic curve model and a parameter calculation method, wherein the model and the parameter calculation method comprise the following steps: 1. preparing an asphalt mixture core sample; 2. determining the initial drying quality and porosity of the asphalt mixture core sample by adopting a vacuum water saturation method, and checking the parallelism of the parallel core sample; 3. measuring the substrate suction of the asphalt mixture parallel core sampleψ m And a data pair corresponding to water saturation S; 4. suction of substrate psi m Substituting a series of experimental data of water saturation S into the initial model of the asphalt mixture-water characteristic curve, and fitting to obtain an asphalt mixture-water characteristic curve; fifthly, substituting the determined effective parameters into the initial model; 8. derivation of an effective model; 9. calculating the slope of a zero substrate suction point; 10. the residual matrix suction parameter is calculated. The mathematical model of the asphalt mixture-water characteristic curve provided by the invention is continuously and monotonically decreased in a range from zero to infinity in the substrate suction, and is convenient for calculating unsaturated parameters.
Description
Technical Field
The invention belongs to the technical field of research on unsaturated hydraulic characteristics of asphalt pavement materials, and particularly relates to an asphalt mixture-water characteristic curve model and a parameter calculation method.
Background
Asphalt pavements are artificial structures laid in natural environments and are subject to frequent water circulation effects such as atmospheric precipitation, capillary water replenishing and evaporation effects. This effect also leads to the common occurrence of liquid-gas two-phase and unsaturated seepage in the pore structure of asphalt mixtures. Many scientific researches and engineering practices show that the long-term unsaturated occurrence and flow of moisture can weaken the strength of an asphalt-aggregate interface, and can induce crack propagation after external conditions such as vehicle load and the like are added, so that the moisture damage and even the water-heat-force coupling damage of the asphalt pavement are aggravated, and the service life and the economical efficiency of the asphalt pavement are finally reduced. The key to solving the above problems is to define the unsaturated hydraulic characteristics of the asphalt pavement material.
The asphalt mixture-water characteristic curve is a vital constitutive relation for describing unsaturated hydraulic characteristics of the asphalt pavement material and reflects the change rule of material matrix potential energy along with the humidity state. As a key parameter of the unsaturated seepage control equation, an asphalt mixture-water characteristic curve is often used for theoretical and simulation calculation of the hydrodynamic behavior of unsaturated asphalt pavement. More and more research conclusions show that the research on the unsaturated water holding property, the permeability property, the stress property, the strength and the deformation property of the asphalt pavement material and the mutual coupling problem can also be guided by the aid of an asphalt mixture-water characteristic curve.
At present, in terms of an asphalt mixture-moisture characteristic curve model, a large amount of research assumes that pore characteristics of porous media are similar on a macroscopic scale, and an unsaturated soil-moisture characteristic curve model or a matrix suction degree-dependent saturation reduction model is adopted to replace the asphalt mixture-moisture characteristic curve model, so that seepage response and dynamic response of unsaturated asphalt pavements are calculated. However, the analysis results thus obtained often do not accurately reflect the true condition of unsaturated asphalt pavements. This indicates that the existing approximate model is still not strong in applicability to asphalt mixture, and the model for describing the asphalt mixture-water characteristic curve is relatively lacking. Therefore, it is necessary to provide a model and a parameter calculation method that reflect the characteristics of the asphalt mixture-water characteristic curve.
Disclosure of Invention
Aiming at the problem that a model for describing an asphalt mixture-water characteristic curve is relatively lacked in the prior art, the invention provides an asphalt mixture-water characteristic curve model which is globally continuous and has a good description effect according to the monotonous decreasing distribution characteristics of the actual measurement results of the asphalt mixture-water characteristic curve and a specific water capacity curve, and provides a calculation method of each parameter of the model on the basis, so that an important constitutive relation is established for the unsaturated hydraulic characteristics of an asphalt pavement material, and the estimation precision of the service performance of the asphalt pavement in an unsaturated state is improved.
The asphalt mixture-water characteristic curve model and the parameter calculation method are realized according to the following steps:
step one, forming a plurality of standard Marshall parallel samples of the asphalt mixture by adopting a Marshall method, and obtaining an asphalt mixture core sample by adopting a core taking machine;
step two, determining the initial drying quality m of the asphalt mixture core sample in the step one by adopting a vacuum saturation method 0 And a porosity V v Checking the parallelism of the parallel core samples;
step three, measuring the matrix suction psi of the asphalt mixture parallel core sample by using an unsaturated static triaxial test system (unsaturated pressure chamber system) m And a series of measured data pairs corresponding to the water saturation S, wherein the specific process of the test is as follows:
step 3a, immersing the asphalt mixture core sample in a normal-temperature deaerated water tank, then placing the water tank in a vacuum drier, setting the vacuum degree to 97.3-98.7 kPa, then performing immersion treatment under the normal pressure state, and repeating for multiple times to obtain a saturated asphalt mixture core sample;
step 3b, carrying out a dehumidification experiment for gradually applying a matrix suction force on the saturated asphalt mixture core sample until the relative water discharge under continuous 5-stage suction force is less than 5%, taking out the core sample, weighing the mass of the residual water-containing state, and calculating the residual water-containing volume according to the formula (1);
in equation (1): v r Is the residual water volume, m, of the core sample of the bituminous mixture r Mass of the core sample of the bituminous mixture in the residual hydrated state, m 0 Mass of the core sample of the bituminous mixture in the initial dry state, p w Is the density of the degassed water;
and sequentially carrying out inverse calculation on the drainage volume to obtain the water-containing volume value of each stage of balance state, wherein the calculation formula of the water-containing volume value of each stage of balance state is as follows:
V i ＝V r +(d r -d i ) (2)
in equation (2): v i Is the water volume of the asphalt mixture core sample in the i-th level equilibrium state, d i Is the total displacement volume of the asphalt core sample in the i-th stage equilibrium state, d r The total displacement volume of the asphalt mixture core sample in a residual water-containing state;
the saturation of each level of equilibrium state is calculated according to the formula (3):
in equation (3): s. the i The saturation of the asphalt mixture core sample in the i-level equilibrium state is obtained;
thereby obtaining multiple groups of substrate suction-saturation (psi) m -S) discrete data points,drawing a characteristic curve of the asphalt mixture and the water, wherein the abscissa of the curve is the substrate suction psi m The ordinate is the water saturation S of the core sample;
step 3c, repeating the step 3a and the step 3b in sequence, and testing the asphalt mixture-water characteristic curves of a plurality of parallel core samples;
step four, the substrate suction force psi obtained in the step three is used m Substituting a series of experimental data of water saturation S into the initial model of the asphalt mixture-water characteristic curve, and fitting to obtain an asphalt mixture-water characteristic curve;
wherein the initial model of the asphalt mixture-water characteristic curve is in the form of:
in equation (4): s is the water saturation of the bituminous mixture, S r Is the residual water saturation of the bituminous mixture,. Psi m The matrix suction of the water-containing asphalt mixture is shown, a and b are fitting parameters of a model, and e is the base number of a natural logarithm;
step five, setting a goodness-of-fit constraint condition, calculating fitting precision, judging whether the fitting precision meets the requirement or not, if the fitting precision meets the goodness-of-fit constraint condition, obtaining fitting parameters a and b and residual water saturation S of the bituminous mixture based on the bituminous mixture-water characteristic curve initial model r ；
Step six, obtaining a parameter value and a parameter value b of a plurality of parallel core samples through the step five fitting, and obtaining the residual water saturation S r The values are respectively averaged to obtain an effective parameter a of the asphalt mixture-water characteristic curve model * 、b * And S r * ；
Step seven, obtaining the effective parameter a of the model in the step six * 、b * And S r * Bringing the model into the initial model of the asphalt mixture-water characteristic curve in the step four to obtain an effective model of the asphalt mixture-water characteristic curve;
step eight, derivation is conducted on the effective model of the asphalt mixture-water characteristic curve in the step seven, and a derivative parameter specific water capacity curve of the asphalt mixture-water characteristic curve is obtained through calculation;
the specific water capacity curve model equation form is as follows:
step nine, acquiring matrix suction force psi m Slope k of asphalt mixture-water characteristic curve at position of =0kPa 0 The effective parameter a of the asphalt mixture-water characteristic curve model obtained in the step six * 、b * And residual water saturation S of asphalt mixture r * Substituting into a zero suction ratio water capacity formula;
at the point of complete saturation (S = 1), the specific water capacity value is calculated, resulting in a zero suction specific water capacity as follows:
step ten, the slope k of the suction point of the zero substrate 0 Substitution into residual matrix suction calculation formula
In the method, the residual matrix suction parameter psi of the asphalt mixture is obtained r 。
Compared with the prior art, the asphalt mixture-water characteristic curve model and the parameter calculation method have the main beneficial effects that:
(1) The continuous mathematical model of the asphalt mixture-water characteristic curve designed by the invention has the advantages of simple expression form and high fitting accuracy. The model adopts a display format to express and has a simple form, is convenient for performing discrete data fast fitting by using a global optimization (UGO) algorithm, and can conveniently determine fitting parameter values meeting the requirement of high fitting accuracy (more than 99.0%) according to the fitting goodness constraint condition set by a user.
(2) The mathematical model of the asphalt mixture-water characteristic curve provided by the invention makes up the defects of two alternative models of the prior matrix suction according to a saturation reduction form and an unsaturated soil-water characteristic curve. On the one hand, analysis of the pore size distribution inside the bituminous mixture revealed that it was broad and not uniform, thus causing near complete saturation of the water content when the matrix suction was close to zero, and exceeding the residual saturation S when the water content exceeded r Then, the substrate suction is nearly infinite; on the other hand, the specific water capacity curve obtained by derivation of the moisture characteristic curve shows monotonicity and delimitation due to the weak hydrophilicity of the asphalt material, particularly when the substrate suction force ψ m And (3) when =0, the specific water volume value C (S = 1) is non-zero and non-infinite. The basic characteristics are constraint conditions for limiting the mathematical form of the asphalt mixture moisture characteristic curve model. The model of the substrate suction in the form of a reduction in saturation does not meet the limitations of the first aspect, and the unsaturated soil-moisture characteristic curve does not meet the limitations of the second aspect. The invention employs McKee according to the mathematical boundary constraints&The construction of a Bumb model equation and introducing a compensation term epsilon 0 The mathematical model of the asphalt mixture-water characteristic curve is provided, which not only meets the requirement of global continuity from zero to infinity of the matrix suction force, but also meets the requirement of non-zero and non-infinite specific water capacity of a zero matrix suction force point, and avoids the defects of the existing model.
(3) The method for calculating the parameters of the asphalt mixture-water characteristic curve model is simple to operate. The two-parameter asphalt mixture-water characteristic curve monotonously decreases and the overall continuous model established by the invention can be used for obtaining the specific water capacity model by derivation, the model is continuous and monotonously decreases in a range from zero to infinity in the substrate suction force and can be used for reflecting the water retention characteristic of the asphalt mixture, and the model can also be used for conveniently calculating and determining the unsaturated parameters of the asphalt mixture, such as residual water saturation, specific water capacity value, residual substrate suction force and the like. The method for calculating the parameters of the asphalt mixture-water characteristic curve model provides a new means for more accurately and effectively evaluating the water retention characteristic and the unsaturated permeability characteristic of the asphalt mixture.
Drawings
FIG. 1 is a flow chart of a method for asphalt mixture-moisture characteristic curve fitting and parameter calculation according to the present invention;
FIG. 2 is a plot of actual results for 3 sets of asphalt-moisture profiles for different porosities in the examples, wherein # 9679A represents a 5.9% sample porosity, a represents a 5.6% sample porosity, and a t represents a 5.0% sample porosity;
FIG. 3 is a plot of the results of model fits of 3 sets of asphalt-moisture characteristics curves for different porosities in the examples, wherein a value of 9679; represents a porosity of 5.9% samples, a value of a porosity of 5.6% samples, and a t represents a porosity of 5.0% samples.
Detailed Description
The first specific implementation way is as follows: the asphalt mixture-water characteristic curve model and the parameter calculation method are implemented according to the following steps:
step one, forming a plurality of standard Marshall parallel samples of the asphalt mixture by adopting a Marshall method, and obtaining an asphalt mixture core sample by adopting a core-taking machine;
step two, determining the initial drying quality m of the asphalt mixture core sample in the step one by adopting a vacuum saturation method 0 And a porosity V v Checking the parallelism of the parallel core samples;
step three, measuring the matrix suction psi of the parallel core sample of the asphalt mixture by using a non-saturated static triaxial test system m And a series of measured data pairs corresponding to the water saturation S, wherein the specific process of the test is as follows:
step 3a, immersing the asphalt mixture core sample in a normal-temperature deaerated water tank, then placing the water tank in a vacuum drier, setting the vacuum degree to 97.3-98.7 kPa, then performing immersion treatment under the normal pressure state, and repeating for multiple times to obtain a saturated asphalt mixture core sample;
step 3b, carrying out a dehumidification experiment for gradually applying a matrix suction force on the saturated asphalt mixture core sample until the relative water discharge under continuous 5-stage suction force is less than 5%, taking out the core sample, weighing the mass of the residual water-containing state, and calculating the residual water-containing volume according to the formula (1);
in formula (1): v r Is the residual water volume, m, of the core sample of the bituminous mixture r Mass of the core sample of the bituminous mixture in the residual hydrated state, m 0 Mass of the core sample of the bituminous mixture in the initial dry state, p w Is the density of the degassed water;
and sequentially carrying out inverse calculation on the drainage volume to obtain the water-containing volume value of each stage of balance state, wherein the calculation formula of the water-containing volume value of each stage of balance state is as follows:
V i ＝V r +(d r -d i ) (2)
in equation (2): v i Is the water volume of the asphalt mixture core sample in the i-th level equilibrium state, d i Is the total displacement volume of the asphalt core sample at the i-th stage equilibrium state, d r The total displacement volume of the asphalt mixture core sample in a residual water-containing state;
the saturation of each level of equilibrium state is calculated according to the formula (3):
in equation (3): s. the i The saturation of the asphalt mixture core sample in the i-level equilibrium state is obtained;
thereby obtaining a plurality of groups of substrate suction-saturation (psi) m -S) discrete data points, drawing a bituminous mixture-moisture characteristic curve, the abscissa of the curve being the substrate suction psi m The ordinate is the water saturation S of the core sample;
step 3c, repeating the step 3a and the step 3b in sequence, and testing the asphalt mixture-water characteristic curves of a plurality of parallel core samples;
step four, mixingThe substrate suction psi obtained in step three m Substituting a series of experimental data of the water saturation S into the initial model of the asphalt mixture-water characteristic curve, and fitting to obtain an asphalt mixture-water characteristic curve;
wherein the initial model of the asphalt mixture-water characteristic curve is in the form of:
in equation (4): s is the water saturation of the bituminous mixture, S r Is the residual water saturation, psi, of the bituminous mixture m The matrix suction of the water-containing asphalt mixture is shown, a and b are fitting parameters of a model, and e is the base number of a natural logarithm;
step five, setting a goodness-of-fit constraint condition, calculating fitting precision, judging whether the fitting precision meets the requirement or not, if the fitting precision meets the goodness-of-fit constraint condition, obtaining fitting parameters a and b and residual water saturation S of the bituminous mixture based on the bituminous mixture-water characteristic curve initial model r ；
Step six, obtaining a parameter value and a parameter value b of a plurality of parallel core samples through the step five fitting, and obtaining the residual water saturation S r The values are respectively averaged to obtain an effective parameter a of the asphalt mixture-water characteristic curve model * 、b * And S r * ；
Step seven, obtaining the effective parameter a of the model obtained in the step six * 、b * And S r * Bringing the model into the initial model of the asphalt mixture-water characteristic curve in the step four to obtain an effective model of the asphalt mixture-water characteristic curve;
step eight, derivation is conducted on the effective model of the asphalt mixture-water characteristic curve in the step seven, and a derived parameter-water capacity curve of the asphalt mixture-water characteristic curve is obtained through calculation;
the specific water capacity curve model equation form is as follows:
step nine, acquiring matrix suction force psi m Slope k of asphalt mixture-water characteristic curve at position of =0kPa 0 The effective parameter a of the asphalt mixture-water characteristic curve model obtained in the step six * 、b * And the residual water saturation S of the bituminous mixture r * Substituting into a zero suction ratio water capacity formula;
at the full saturation point (S = 1), specific water capacity values were calculated, resulting in zero suction specific water capacity as follows:
step ten, the slope k of the zero substrate suction point 0 Substitution into residual matrix suction calculation formula
In the method, the residual matrix suction parameter psi of the asphalt mixture is obtained r 。
The second embodiment is as follows: the difference between this embodiment and the embodiment is that the cylindrical core sample of step one has dimensions phi 50mm x 63.5mm.
The third concrete implementation mode: this embodiment is different from the first or second embodiment in that the difference between the measured value of the parallel core porosity and the average value in the second step is less than 1.3 to 1.4 times the standard deviation, and the parallelism satisfies the requirement.
The fourth concrete implementation mode: this embodiment differs from one of the first to third embodiments in that the water bath in step 3a is kept in a vacuum drier for 15min.
The fifth concrete implementation mode: the present embodiment is different from one of the first to fourth embodiments in that the immersion treatment time in the atmospheric pressure state in step 3a is 0.5h.
The sixth specific implementation mode is as follows: this embodiment differs from one of the first to fifth embodiments in that the substrate suction force is applied in step 3b at not less than 10 stages.
The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is that the dehumidification experiment in step 3b adopts an unsaturated static triaxial test system, and in the process of applying the substrate suction, the pore water pressure is controlled to be 0kPa, the pore air pressure is respectively applied step by step, and the applied substrate suction psi m The value is equal to the pore gas pressure.
The specific implementation mode eight: the difference between the embodiment and one of the first to seventh embodiments is that the process for establishing the asphalt mixture-water characteristic curve model in the fourth step is as follows:
step 4a: calculating the quasi-residual water saturation of the asphalt mixture through a formula (5);
in equation (5):
is the quasi-residual water saturation of the bituminous mixture, n is the total number of stages of the application of the suction force of the substrate, S i The saturation of the asphalt mixture core sample in the i-level equilibrium state is obtained;
and 4b: carrying out normalization processing on a series of saturation data of the actually measured asphalt mixture, and converting to obtain the quasi-effective saturation of the asphalt mixture
And 4c: obtaining a data pair and a scatter diagram of the quasi-effective saturation and the matrix suction of the asphalt mixture, and fitting by adopting a configuration of a McKee & Bumb equation according to the correlation relationship of the data pair and the scatter diagram to obtain a McKee & Bumb model and parameters thereof;
the configuration of the McKee & Bumb equation is as follows:
in equation (7): y is an explained variable of the equation, x is an explained variable of the equation, and alpha and beta are equation parameters;
and 4d: the initial substrate suction psi m ＝ψ 0 =0, carry-in step 4c said McKee&A Bumb model, calculating an initial effective saturation prediction value S ec0 ；
And 4e: compensating the model according to the principle that the predicted value and the measured value are equal under the initial condition, and calculating the predicted value S of the initial effective saturation according to a formula (8) ec0 And the measured value S of the initial effective saturation of the asphalt mixture-water characteristic curve e0 Compensation term epsilon between =1 0 ：
And 4f: the compensation term epsilon calculated in the step 4e 0 Introduction of McKee&Obtaining an initial model equation by the denominator item of the Bumb model:
step 4g: parameters a and b are introduced, and the McKee & Bumb model equation is simplified:
step 4h: get S e ＝(S-S r )/(1-S r ) And substituting equations (10) and (11) into the initial model equation (9), and converting into S = f (ψ) m ) Display of the formShowing the format, thereby obtaining an asphalt mixture-water characteristic curve model
The specific implementation method nine: the difference between the embodiment and the embodiment I to the embodiment II is that the fourth step adopts matlab or 1st Optic (First Optimization) program to fit to give the asphalt mixture-water characteristic curve.
The specific implementation mode is ten: the difference between this embodiment and one of the first to ninth embodiments is that in the fifth step, a goodness-of-fit constraint condition is set, fitting accuracy is calculated, whether the fitting accuracy meets the requirement is judged, and if the fitting accuracy meets the goodness-of-fit constraint condition, a fitting accuracy calculation formula is as follows:
in equation (13): adjR 2 Reflecting the quality of the fitting result for adjusting the coefficient; n is the total amount of data to samples; y is i The measured data value is the ith measured data value of the suction force of the asphalt mixture matrix;
the ith predicted value of the suction force of the asphalt mixture matrix,
and k is the parameter number of the asphalt mixture-water characteristic curve model.
The embodiment is as follows: the asphalt mixture-water characteristic curve model and the parameter calculation method are implemented according to the following steps:
step one, preparing and molding 3 groups of dense-graded asphalt mixture standard Marshall test pieces with the size of phi 101.3mm multiplied by 63.5mm and different porosities according to a Marshall design method, wherein each group of samples comprises 3 parallel samples, and sampling and trimming are carried out by adopting a drilling core-pulling machine to obtain core samples with the size of phi 50mm multiplied by 63.5 mm;
step two, measuring the initial drying mass m of the asphalt mixture core samples with different porosities obtained in the step one by adopting a vacuum water saturation method 0 And a porosity V v Checking the parallelism of the parallel core sample, wherein the difference between the porosity measurement value of the parallel core sample and the average value is less than 1.15 times of the standard deviation, and the parallelism meets the requirement;
step three, measuring the suction psi of the asphalt mixture matrix under the condition of different porosities by using a non-saturated static triaxial test system m And a series of measured data pairs corresponding to the water saturation S, the specific process is as follows:
step 3a: immersing an asphalt mixture core sample with the size of phi 50mm multiplied by 63.5mm in a normal-temperature deaerated water tank, then placing the water tank in a vacuum drier for 15min, setting the vacuum degree to be 97.3 kPa-98.7 kPa, then immersing for 0.5h under the normal pressure state, and repeatedly operating for three times to complete saturation of the core sample to obtain a saturated asphalt mixture core sample;
and step 3b: carrying out dehumidification experiment on a saturated asphalt mixture core sample, applying 11 levels of matrix suction until the relative water discharge under continuous 5 levels of suction is less than 5%, finishing all preset suction, taking out the core sample, weighing the mass of the residual water-containing state, recording the mass until the relative water discharge is accurate to three decimal places, calculating the residual water-containing volume, obtaining the water-containing volume values of all levels of equilibrium states through sequential inverse calculation of the water discharge volume, and obtaining a plurality of groups of matrix suction-saturation (psi) m -S) discrete data points, drawing a bituminous mixture-moisture characteristic curve, the abscissa of the curve being the substrate suction psi m The ordinate is the water saturation S of the core sample;
in step 3b, the instrument used for the dehumidification experiment is an unsaturated static triaxial test system, the pore water pressure is controlled to be 0kPa during the application of the substrate suction force, the pore water pressure is respectively applied step by step, the loading paths are set to be 1kPa, 3kPa, 5kPa, 10kPa, 15kPa, 25kPa, 50kPa, 100kPa, 150kPa, 200kPa, 300kPa, and the applied substrate suction values are respectively 1kPa, 3kPa, 5kPa, 10kPa, 15kPa, 25kPa, 50kPa, 100kPa, 150kPa, 200kPa, 300kPa according to the basic principle of the shaft translation technology;
in particular, in step 3b, the residual aqueous volume is calculated according to equation (1):
in equation (1): v r Is the residual water volume, m, of the core sample of the bituminous mixture r Mass of the core sample of the bituminous mixture in residual water content, m 0 Mass of the core sample of the bituminous mixture in the initial dry state, p w Is the density of the degassed water;
specifically, in step 3b, the water-containing volume value of each stage in the equilibrium state is calculated according to the formula (2):
V i ＝V r +(d r -d i ) (2)
in equation (2): v i Is the water volume of the asphalt mixture core sample in the i-th level equilibrium state, d i Is the total displacement volume of the asphalt core sample in the i-th stage equilibrium state, d r The total displacement volume of the asphalt mixture core sample in a residual water-containing state;
specifically, in step 3b, the saturation of each stage of equilibrium state is calculated according to equation (3):
in equation (3): s. the i The saturation of the asphalt mixture core sample in the i-level equilibrium state is obtained;
and step 3c: sequentially repeating the step 3a and the step 3c, and testing the asphalt mixture-water characteristic curves of the plurality of parallel core samples;
step four, measuring the substrate suction force psi measured in the step three m Substituting the serial measured data of the water saturation S into an initial model of the asphalt mixture-water characteristic curve, and fitting the asphalt mixture-water characteristic curve by adopting a 1stOpt (First Optimization) program;
in particular, the initial model of the bituminous mixture-moisture characteristic curve is in the form of:
in equation (4): s is the water saturation of the bituminous mixture, S r Is the residual water saturation of the bituminous mixture,. Psi m The matrix suction of the water-containing asphalt mixture is shown, a and b are fitting parameters of a model, and e is the base number of a natural logarithm;
step five, setting the constraint condition of the goodness-of-fit to adjust the coefficient of certainty to be more than 99.0%, calculating the fitting precision, judging whether the fitting precision meets the requirement, if the fitting precision meets the constraint condition of the goodness-of-fit, obtaining fitting parameters a and b and the residual water saturation S of the asphalt mixture based on the initial model of the water characteristic curve of the asphalt mixture r ；
Further, the fitting accuracy is as follows:
in the formula (5), adjR 2 Reflecting the quality of the fitting result for adjusting the coefficient; n is the total amount of data to samples; y is i The measured data value is the ith measured data value of the suction force of the asphalt mixture matrix;
is the ith predicted value of the suction force of the asphalt mixture matrix,
the arithmetic mean value of the actually measured data of the suction force of the asphalt mixture matrix, wherein k is the parameter number of an initial model of an asphalt mixture-water characteristic curve;
step six, determining fitting parameters a and b in the model and residual water saturation S of the asphalt mixture r The values of a and b parameters and the residual water saturation S obtained by fitting the 3 parallel core samples in the fifth step r Respectively calculating the values to obtain an effective parameter a of the asphalt mixture-water characteristic curve model * 、b * And S r * ；
Step seven, substituting the effective parameter values of the asphalt mixture-water characteristic curve model obtained in the step six into the model provided in the step four, and calculating to obtain an asphalt mixture-water characteristic curve effective model;
step eight, derivation is conducted on the effective model of the asphalt mixture-water characteristic curve in the step seven, and a derived parameter-water capacity curve of the asphalt mixture-water characteristic curve is obtained through calculation;
in particular, the specific water capacity curve model is of the form:
further, at a complete saturation point (S = 1), calculating a specific water capacity value to obtain a formula zero suction specific water capacity;
C(S＝1)＝(S r -1)ae b ∈(0，∞) (7)
step nine, acquiring the suction force psi of the substrate m Slope m of asphalt mixture-water characteristic curve at position of =0kPa 0 That is, the effective parameter a of the asphalt mixture-water characteristic curve model satisfying the goodness of fit constraint condition in the sixth step * 、b * And the residual water saturation S of the bituminous mixture r * Substituting into formula (7);
step ten, the slope k of the zero substrate suction point 0 Substituting into the calculation formula of the residual matrix suction force to obtain the residual matrix suction force parameter psi of the asphalt mixture r The method for calculating the residual matrix suction force comprises the following steps:
the asphalt mixture used in this example is a dense-graded asphalt concrete mixture AC-13, the porosity of the asphalt mixture is controlled by adjusting the compaction frequency, and an unsaturated static triaxial test system is used to obtain an actual measurement data pair of an asphalt mixture-moisture characteristic curve through a dehumidification experiment.
The actual measurement results of the asphalt mixture-water characteristic curves under 3 groups of different porosity conditions are shown in figure 2, wherein the substrate suction psi is adopted m The abscissa is a logarithmic axis, and the ordinate is the saturation S.
Repeatedly fitting, calculating and evaluating the measured data according to the asphalt mixture-water characteristic curve model in the formula (4), and calculating the average value of the parameters which accord with the fitting precision (namely the adjustment coefficient is more than 99.0 percent), so as to obtain the effective parameter a of the model of 3 groups of asphalt mixture-water characteristic curves with different porosities * 、b * And residual water saturation S r * As shown in table 1 below.
TABLE 1 effective parameters of asphalt mixture-water characteristic curve model
The effective parameter a of the model is calculated * 、b * And residual water saturation S r * The model is substituted into the asphalt mixture-water characteristic curve model of the embodiment, and the obtained model form is as follows:
porosity V v ＝5.9％：
Porosity V v ＝5.6％：
Porosity V v ＝5.0％：
The result of model fitting is shown in fig. 3, and it can be seen that the asphalt mixture-water characteristic curve model provided by the embodiment has a good fitting effect. Fitting can help further theoretical research.
According to the effective parameter a of the model * 、b * And residual water saturation S r * Further calculating the slope m of the specific water capacity and the zero substrate suction point 0 Residual matrix suction psi r The task to determine the asphalt-moisture characteristic curve and its parameters thus far was completed as shown in table 2.
Specific water capacities were as follows:
porosity V v ＝5.9％：
Porosity V v ＝5.6％：
Porosity V v ＝5.0％：
TABLE 2 calculation results of characteristic parameters of asphalt mixture-water characteristic curve
Claims (10)
1. The asphalt mixture-water characteristic curve model and the parameter calculation method are characterized by being realized according to the following steps:
step one, forming a plurality of standard Marshall parallel samples of the asphalt mixture by adopting a Marshall method, and obtaining an asphalt mixture core sample by adopting a core-taking machine;
step two, measuring the initial drying quality m of the asphalt mixture core sample in the step one by adopting a vacuum water saturation method 0 And a porosity V v Checking the parallelism of the parallel core samples;
step three, measuring the matrix suction psi of the parallel core sample of the asphalt mixture by using a non-saturated static triaxial test system m And a series of measured data pairs corresponding to the water saturation S, wherein the specific process of the test is as follows:
step 3a, immersing the asphalt mixture core sample in a normal-temperature deaerated water tank, then placing the water tank in a vacuum drier, setting the vacuum degree to 97.3-98.7 kPa, then performing immersion treatment under the normal pressure state, and repeating for multiple times to obtain a saturated asphalt mixture core sample;
step 3b, carrying out a dehumidification experiment for gradually applying a matrix suction force on the saturated asphalt mixture core sample until the relative water discharge under continuous 5-stage suction force is less than 5%, taking out the core sample, weighing the mass of the residual water-containing state, and calculating the residual water-containing volume according to the formula (1);
in equation (1): v r Is the residual water volume, m, of the core sample of the bituminous mixture r Mass of the core sample of the bituminous mixture in residual water content, m 0 Mass of the core sample of the bituminous mixture in the initial dry state, p w Density of the deaerated water;
and sequentially carrying out inverse calculation on the drainage volume to obtain the water-containing volume value of each stage of balance state, wherein the calculation formula of the water-containing volume value of each stage of balance state is as follows:
V i ＝V r +(d r -d i )(2)
in equation (2): v i Is the water volume of the asphalt mixture core sample in the i-th level equilibrium state, d i Is the total displacement volume of the asphalt core sample in the i-th stage equilibrium state, d r The total displacement volume of the asphalt mixture core sample in a residual water-containing state;
the saturation of each level of equilibrium state is calculated according to the formula (3):
in equation (3): s. the i The saturation of the asphalt mixture core sample in the i-level equilibrium state is obtained;
thereby obtaining a plurality of groups of matrix suction-saturation discrete data points, drawing an asphalt mixture-water characteristic curve, wherein the abscissa of the curve is the matrix suction psi m The ordinate is the water saturation S of the core sample;
step 3c, repeating the step 3a and the step 3b in sequence, and testing the asphalt mixture-water characteristic curves of a plurality of parallel core samples;
step four, the substrate suction force psi obtained in the step three is processed m Substituting a series of experimental data of water saturation S into the initial model of the asphalt mixture-water characteristic curve, and fitting to obtain an asphalt mixture-water characteristic curve;
wherein the initial model of the asphalt mixture-water characteristic curve is in the form of:
in equation (4): s is the water saturation of the asphalt mixture, S r Is the residual water saturation of the bituminous mixture,. Psi m The matrix suction of the water-containing asphalt mixture is shown, a and b are fitting parameters of a model, and e is the base number of a natural logarithm;
step five, setting a constraint condition of goodness-of-fit, calculating fitting precision, judging whether the fitting precision meets the requirement, if the fitting precision meets the constraint condition of goodness-of-fit, obtaining fitting parameters a and b and residual water saturation S of the bituminous mixture based on the bituminous mixture-water characteristic curve initial model r ；
Step six, obtaining a parameter value and a parameter value b of a plurality of parallel core samples through the step five fitting, and obtaining the residual water saturation S r Value andrespectively calculating the average value to obtain the effective parameter a of the asphalt mixture-water characteristic curve model * 、b * And S r * ；
Step seven, obtaining the effective parameter a of the model in the step six * 、b * And S r * Bringing the model into the initial model of the asphalt mixture-water characteristic curve in the step four to obtain an effective model of the asphalt mixture-water characteristic curve;
step eight, derivation is conducted on the effective model of the asphalt mixture-water characteristic curve in the step seven, and a derived parameter-water capacity curve of the asphalt mixture-water characteristic curve is obtained through calculation;
the specific water capacity curve model equation form is as follows:
step nine, acquiring matrix suction force psi m Slope k of asphalt mixture-water characteristic curve at position of =0kPa 0 Namely, the effective parameter a of the asphalt mixture-water characteristic curve model obtained in the sixth step * 、b * And residual water saturation S of asphalt mixture r * Substituting into a zero suction ratio water capacity formula;
at the point of complete saturation (S = 1), the specific water capacity value is calculated, resulting in a zero suction specific water capacity as follows:
step ten, the slope m of the suction point of the zero substrate 0 Substitution into residual matrix suction calculation formula
In the method, a residual matrix suction parameter psi of the asphalt mixture is obtained r 。
2. The asphalt mixture-moisture characteristic curve model and the parameter calculation method according to claim 1, wherein the size of the cylindrical core sample in the first step is phi 50mm x 63.5mm.
3. The asphalt mixture-water characteristic curve model and the parameter calculation method according to claim 1, wherein in the second step, the difference between the measured value of the porosity of the parallel core sample and the average value is less than 1.3 to 1.4 times of the standard deviation, and the parallelism meets the requirement.
4. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, wherein the water tank in step 3a is placed in a vacuum dryer and kept for 15min.
5. The asphalt mixture-water characteristic curve model and the parameter calculation method according to claim 1, wherein the soaking treatment time in the step 3a under the normal pressure state is 0.5h.
6. The asphalt mixture-moisture characteristic curve model and parameter calculation method according to claim 1, wherein the substrate suction force in step 3b is applied at not less than 10 steps.
7. The asphalt mixture-water characteristic curve model and the parameter calculation method according to claim 1, wherein the dehumidification experiment in the step 3b adopts an unsaturated static triaxial test system, the pore water pressure is controlled to be 0kPa during the matrix suction force application process, the pore air pressure is respectively applied step by step, and the applied matrix suction force psi m The value is equal to the pore gas pressure.
8. The asphalt mixture-water characteristic curve model and the parameter calculation method according to claim 1, wherein the asphalt mixture-water characteristic curve model in the fourth step is established in the following steps:
step 4a: calculating the quasi-residual water saturation of the asphalt mixture through a formula (5);
in equation (5):
is the quasi-residual water saturation of the bituminous mixture, n is the total number of stages of matrix suction application, S i The saturation of the asphalt mixture core sample in the i-level equilibrium state is obtained;
and 4b: carrying out normalization processing on a series of actually measured saturation data of the asphalt mixture, and converting to obtain the quasi-effective saturation of the asphalt mixture
And 4c: obtaining a data pair and a scatter diagram of the quasi-effective saturation and the substrate suction of the asphalt mixture, and fitting by adopting a configuration of McKee & Bumb equation according to the correlation between the data pair and the scatter diagram to obtain an McKee & Bumb model and parameters thereof;
the configuration of the McKee & Bumb equation is as follows:
in equation (7): y is an explained variable of the equation, x is an explained variable of the equation, and alpha and beta are equation parameters;
and 4d: sucking original matrix by psi m ＝ψ 0 =0, carry-in step 4c said McKee&The Bumb model calculates an initial effective saturation prediction value S ec0 ；
And 4e: calculating an initial effective saturation prediction value S according to a formula (8) ec0 And asphalt mixtureInitial effective saturation measured value S of moisture characteristic curve e0 Compensation term epsilon between =1 0 ：
And 4f: the compensation term epsilon calculated in the step 4e 0 Introduction of McKee&Obtaining an initial model equation by a denominator item of the Bumb model:
step 4g: parameters a and b are introduced, and the McKee & Bumb model equation is simplified:
step 4h: get S e ＝(S-S r )/(1-S r ) And substituting equations (10) and (11) into the initial model equation (9), and converting into S = f (ψ) m ) Form display format to obtain asphalt mixture-water characteristic curve model
9. The asphalt mixture-water characteristic curve model and the parameter calculation method according to claim 1, wherein the asphalt mixture-water characteristic curve is obtained by fitting matlab or 1st Opt program in the fourth step.
10. The asphalt mixture-water characteristic curve model and the parameter calculation method according to claim 1, wherein in the fifth step, a goodness-of-fit constraint condition is set, fitting accuracy is calculated, whether the fitting accuracy meets the requirement is judged, and if the fitting accuracy meets the goodness-of-fit constraint condition, the fitting accuracy calculation formula is as follows:
in equation (13): adjR 2 Reflecting the quality of the fitting result for adjusting the coefficient; n is the total amount of data to samples; y is i The measured data value is the ith measured data value of the suction force of the asphalt mixture matrix;
the ith predicted value of the suction force of the asphalt mixture matrix,
and k is the parameter number of the asphalt mixture-water characteristic curve model.
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