CN116332563A - Method for designing proportion of asphalt mixture of anti-ice and snow-melting agent based on response surface method - Google Patents
Method for designing proportion of asphalt mixture of anti-ice and snow-melting agent based on response surface method Download PDFInfo
- Publication number
- CN116332563A CN116332563A CN202211536749.9A CN202211536749A CN116332563A CN 116332563 A CN116332563 A CN 116332563A CN 202211536749 A CN202211536749 A CN 202211536749A CN 116332563 A CN116332563 A CN 116332563A
- Authority
- CN
- China
- Prior art keywords
- temperature
- road performance
- asphalt mixture
- test
- snow
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 239000010426 asphalt Substances 0.000 title claims abstract description 90
- 239000000203 mixture Substances 0.000 title claims abstract description 78
- 238000000034 method Methods 0.000 title claims abstract description 72
- 230000004044 response Effects 0.000 title claims abstract description 69
- 239000003795 chemical substances by application Substances 0.000 title claims abstract description 40
- 238000002844 melting Methods 0.000 title claims abstract description 40
- 238000013461 design Methods 0.000 claims abstract description 19
- 238000011156 evaluation Methods 0.000 claims abstract description 18
- 230000008569 process Effects 0.000 claims abstract description 18
- 238000009826 distribution Methods 0.000 claims abstract description 6
- 238000012360 testing method Methods 0.000 claims description 76
- 238000002156 mixing Methods 0.000 claims description 34
- 239000004575 stone Substances 0.000 claims description 24
- 239000011159 matrix material Substances 0.000 claims description 22
- 238000010257 thawing Methods 0.000 claims description 15
- 230000008018 melting Effects 0.000 claims description 14
- 238000005056 compaction Methods 0.000 claims description 13
- 238000011056 performance test Methods 0.000 claims description 13
- 230000003993 interaction Effects 0.000 claims description 10
- 230000008859 change Effects 0.000 claims description 8
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 8
- 230000009021 linear effect Effects 0.000 claims description 6
- 238000010606 normalization Methods 0.000 claims description 5
- 238000002474 experimental method Methods 0.000 claims description 4
- 102100029469 WD repeat and HMG-box DNA-binding protein 1 Human genes 0.000 claims description 3
- 101710097421 WD repeat and HMG-box DNA-binding protein 1 Proteins 0.000 claims description 3
- 238000010276 construction Methods 0.000 claims description 3
- 238000005336 cracking Methods 0.000 claims description 3
- 208000024780 Urticaria Diseases 0.000 claims description 2
- 239000005413 snowmelt Substances 0.000 claims description 2
- 239000004567 concrete Substances 0.000 abstract description 2
- 230000007613 environmental effect Effects 0.000 abstract description 2
- 238000010561 standard procedure Methods 0.000 description 7
- 229910052500 inorganic mineral Inorganic materials 0.000 description 5
- 239000011707 mineral Substances 0.000 description 5
- 238000000465 moulding Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 230000000694 effects Effects 0.000 description 4
- 238000003776 cleavage reaction Methods 0.000 description 3
- 238000003801 milling Methods 0.000 description 3
- 238000005457 optimization Methods 0.000 description 3
- 239000000843 powder Substances 0.000 description 3
- 230000007017 scission Effects 0.000 description 3
- 238000010998 test method Methods 0.000 description 3
- 239000004568 cement Substances 0.000 description 2
- 230000009467 reduction Effects 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 238000010008 shearing Methods 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 239000011800 void material Substances 0.000 description 2
- JXLYSJRDGCGARV-WWYNWVTFSA-N Vinblastine Natural products O=C(O[C@H]1[C@](O)(C(=O)OC)[C@@H]2N(C)c3c(cc(c(OC)c3)[C@]3(C(=O)OC)c4[nH]c5c(c4CCN4C[C@](O)(CC)C[C@H](C3)C4)cccc5)[C@@]32[C@H]2[C@@]1(CC)C=CCN2CC3)C JXLYSJRDGCGARV-WWYNWVTFSA-N 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 230000032683 aging Effects 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 239000011384 asphalt concrete Substances 0.000 description 1
- 239000011230 binding agent Substances 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 238000012938 design process Methods 0.000 description 1
- 239000000945 filler Substances 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000005461 lubrication Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 239000002344 surface layer Substances 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
- 229960003048 vinblastine Drugs 0.000 description 1
- JXLYSJRDGCGARV-XQKSVPLYSA-N vincaleukoblastine Chemical group C([C@@H](C[C@]1(C(=O)OC)C=2C(=CC3=C([C@]45[C@H]([C@@]([C@H](OC(C)=O)[C@]6(CC)C=CCN([C@H]56)CC4)(O)C(=O)OC)N3C)C=2)OC)C[C@@](C2)(O)CC)N2CCC2=C1NC1=CC=CC=C21 JXLYSJRDGCGARV-XQKSVPLYSA-N 0.000 description 1
Images
Classifications
-
- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01C—CONSTRUCTION OF, OR SURFACES FOR, ROADS, SPORTS GROUNDS, OR THE LIKE; MACHINES OR AUXILIARY TOOLS FOR CONSTRUCTION OR REPAIR
- E01C7/00—Coherent pavings made in situ
- E01C7/08—Coherent pavings made in situ made of road-metal and binders
- E01C7/18—Coherent pavings made in situ made of road-metal and binders of road-metal and bituminous binders
- E01C7/26—Coherent pavings made in situ made of road-metal and binders of road-metal and bituminous binders mixed with other materials, e.g. cement, rubber, leather, fibre
-
- C—CHEMISTRY; METALLURGY
- C04—CEMENTS; CONCRETE; ARTIFICIAL STONE; CERAMICS; REFRACTORIES
- C04B—LIME, MAGNESIA; SLAG; CEMENTS; COMPOSITIONS THEREOF, e.g. MORTARS, CONCRETE OR LIKE BUILDING MATERIALS; ARTIFICIAL STONE; CERAMICS; REFRACTORIES; TREATMENT OF NATURAL STONE
- C04B26/00—Compositions of mortars, concrete or artificial stone, containing only organic binders, e.g. polymer or resin concrete
- C04B26/02—Macromolecular compounds
- C04B26/26—Bituminous materials, e.g. tar, pitch
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
- G01N33/42—Road-making materials
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- C—CHEMISTRY; METALLURGY
- C04—CEMENTS; CONCRETE; ARTIFICIAL STONE; CERAMICS; REFRACTORIES
- C04B—LIME, MAGNESIA; SLAG; CEMENTS; COMPOSITIONS THEREOF, e.g. MORTARS, CONCRETE OR LIKE BUILDING MATERIALS; ARTIFICIAL STONE; CERAMICS; REFRACTORIES; TREATMENT OF NATURAL STONE
- C04B2111/00—Mortars, concrete or artificial stone or mixtures to prepare them, characterised by specific function, property or use
- C04B2111/00474—Uses not provided for elsewhere in C04B2111/00
- C04B2111/0075—Uses not provided for elsewhere in C04B2111/00 for road construction
-
- C—CHEMISTRY; METALLURGY
- C04—CEMENTS; CONCRETE; ARTIFICIAL STONE; CERAMICS; REFRACTORIES
- C04B—LIME, MAGNESIA; SLAG; CEMENTS; COMPOSITIONS THEREOF, e.g. MORTARS, CONCRETE OR LIKE BUILDING MATERIALS; ARTIFICIAL STONE; CERAMICS; REFRACTORIES; TREATMENT OF NATURAL STONE
- C04B2111/00—Mortars, concrete or artificial stone or mixtures to prepare them, characterised by specific function, property or use
- C04B2111/76—Use at unusual temperatures, e.g. sub-zero
-
- C—CHEMISTRY; METALLURGY
- C04—CEMENTS; CONCRETE; ARTIFICIAL STONE; CERAMICS; REFRACTORIES
- C04B—LIME, MAGNESIA; SLAG; CEMENTS; COMPOSITIONS THEREOF, e.g. MORTARS, CONCRETE OR LIKE BUILDING MATERIALS; ARTIFICIAL STONE; CERAMICS; REFRACTORIES; TREATMENT OF NATURAL STONE
- C04B2201/00—Mortars, concrete or artificial stone characterised by specific physical values
- C04B2201/20—Mortars, concrete or artificial stone characterised by specific physical values for the density
-
- C—CHEMISTRY; METALLURGY
- C04—CEMENTS; CONCRETE; ARTIFICIAL STONE; CERAMICS; REFRACTORIES
- C04B—LIME, MAGNESIA; SLAG; CEMENTS; COMPOSITIONS THEREOF, e.g. MORTARS, CONCRETE OR LIKE BUILDING MATERIALS; ARTIFICIAL STONE; CERAMICS; REFRACTORIES; TREATMENT OF NATURAL STONE
- C04B2201/00—Mortars, concrete or artificial stone characterised by specific physical values
- C04B2201/50—Mortars, concrete or artificial stone characterised by specific physical values for the mechanical strength
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
Landscapes
- Engineering & Computer Science (AREA)
- Chemical & Material Sciences (AREA)
- Physics & Mathematics (AREA)
- Life Sciences & Earth Sciences (AREA)
- Health & Medical Sciences (AREA)
- Structural Engineering (AREA)
- Ceramic Engineering (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Architecture (AREA)
- Geometry (AREA)
- Computer Hardware Design (AREA)
- Organic Chemistry (AREA)
- Materials Engineering (AREA)
- Civil Engineering (AREA)
- Evolutionary Computation (AREA)
- Food Science & Technology (AREA)
- Medicinal Chemistry (AREA)
- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- General Health & Medical Sciences (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Road Paving Structures (AREA)
Abstract
The invention belongs to the field of concrete, and particularly relates to a method for designing a proportion of an anti-ice and snow-melting agent asphalt mixture based on a response surface method. The method comprises the following steps: determining key factors and road performance evaluation indexes which influence the road performance of the asphalt mixture; carrying out single-factor experimental study on key factors influencing the road performance of the asphalt mixture; establishing a response surface model of the key factors and the road performance evaluation indexes by adopting a Box-Behnken design method in a response surface method; and according to different using conditions, performing weight distribution on each evaluation index of the road performance by using an analytic hierarchy process, and obtaining the optimal value of each key factor and the road performance. The invention adopts a response surface method to realize the functional relation between a plurality of influencing factors and a plurality of road performance evaluation indexes; the analytic hierarchy process is utilized to distribute weights for the road performances of the asphalt mixture, so that the method provided by the invention can be suitable for different environmental conditions, and the accuracy and the universality of the method are improved.
Description
Technical Field
The invention belongs to the field of concrete, and particularly relates to a method for designing a proportion of an anti-ice and snow-melting agent asphalt mixture based on a response surface method.
Background
The Marshall compaction method and the wheel milling method are most commonly used in the forming method of the ice and snow resistant asphalt mixture, and are widely adopted in all countries of the world. However, the forming process of asphalt mixture by compaction and wheel milling has various control factors, such as determination of oil-stone ratio, mixing temperature, compaction temperature and snow-melting agent amount, and many tests are required for asphalt and mixture. For the determination of the oil-stone ratio, 5 parameters of the density, the void fraction, the asphalt saturation, the Marshall stability and the flow value of the asphalt mixture test piece are tested. However, extensive studies have shown that there is not a wide correlation between the volume parameter and the road performance of the asphalt mix. Determination of the mixing temperature and compaction temperature requires testing the viscosity of the asphalt at a plurality of temperature conditions and drawing a viscosity-temperature curve fit. The determination of the amount of the snow-melting anti-icing agent is more complicated, and multiple indexes of asphalt and asphalt mixtures need to be repeatedly tested and adjusted according to different properties of the snow-melting anti-icing agent. The road performance of the asphalt mixture is the result of the interaction of factors such as the oil-stone ratio, the mixing and compacting temperature, the amount of the snow-melting anti-icing agent and the like. Therefore, it is necessary to systematically optimize the asphalt mixture molding method by comprehensively considering various control factors.
The final objective of optimizing the anti-ice and snow-melting asphalt mixture forming method is to ensure that the road performance is optimal, and the road performance and the control factors have nonlinear implicit relation, which belongs to the problem of multiple responses. In the current method, a specific set of input variables (control factors) are difficult to find so that the road performance of the asphalt mixture is optimal.
Disclosure of Invention
The invention aims to provide a method for designing the proportion of an anti-ice and snow-melting agent asphalt mixture based on a response surface method, so that the whole forming process of the anti-ice and snow-melting asphalt mixture is more flexible, logical and predictive.
The technical solution for realizing the purpose of the invention is as follows: a method for designing the proportion of an anti-ice and snow-melting agent asphalt mixture based on a response surface method comprises the following steps:
step (1): determining key factors and road performance evaluation indexes which influence the road performance of the asphalt mixture;
step (2): carrying out single-factor experimental study on key factors influencing the road performance of the asphalt mixture;
step (3): establishing a response surface model of the key factors and the road performance evaluation indexes by adopting a Box-Behnken design method in a response surface method;
step (4): and according to different using conditions, performing weight distribution on each evaluation index of the road performance by using an analytic hierarchy process, and obtaining the optimal value of each key factor and the road performance.
Further, the key factors which influence the road performance of the asphalt mixture and are determined in the step (1) are the oil-stone ratio, the mixing/compacting temperature and the amount of the snow-melting anti-icing agent;
the road performance evaluation indexes comprise low-temperature splitting strength, dynamic stability and freeze thawing splitting strength, and the three road performance evaluation indexes are used for evaluating the low-temperature cracking resistance, high-temperature stability and water stability of the asphalt mixture respectively.
Further, in the step (2), the specific steps of carrying out single-factor test and research on key factors influencing the road performance of the asphalt mixture are as follows:
step (21): determining the range of each influencing factor: wheal ratio x 1 3.5-5.5%, mixing/compacting temperature x 2 The dosage x of the snow-melting anti-icing agent is 120-200 ℃/110-190 DEG C 3 4-6%;
step (22): oil-stone ratio test: in the process of forming an asphalt mixture test piece, preparing a test piece by adopting 0.5% interval change of the oil-stone ratio, and taking the mixing temperature, the compacting temperature and the snow melting anti-icing agent dosage as fixed values, and obtaining a road performance test result by a test;
step (23): mixing/compaction temperature test: the mixing temperature and the compacting temperature are treated as a factor, the mixing temperature and the compacting temperature are set to be different by 10 ℃, and the mixing temperature and the compacting temperature are changed at intervals of 10 ℃; the oil-stone ratio, the amount of the snow melting anti-icing agent adopts a fixed value, and a test piece road performance test result is obtained;
step (24): and (3) testing the dosage of the snow melting anti-icing agent: the snow-melting anti-icing agent content adopts 4%, 4.5%, 5%, 5.5% and 6% of interval change, mixing temperature, compaction temperature and oil stone ratio to obtain road performance test results.
Further, the step (3) specifically includes the following steps:
step (31): taking low-temperature splitting strength, freeze thawing splitting strength ratio and dynamic stability as output variables, taking three factors of oil-stone ratio, mixing/compacting temperature and snow melting anti-icing agent dosage in a single factor experiment as input variables, and respectively representing high, medium and low levels of independent variables by 1, 0 and-1 to carry out 3-factor 3-level test design on the SMA-13 graded asphalt mixture; encoding an argument as follows
X i ＝(x i -x 0 )/Δx
Wherein: x is X i A coded value that is an argument; x is x i Is the true value of the argument; x is x 0 The true value of the independent variable at the test center point; Δx is the step size of the change of the argument;
step (32): the response curved surface model is a second-order model, and is specifically as follows:
wherein: beta i Represents x i Linear effects of (2); beta ij Represents x i And x j Linear interactions between; beta ii Representation ofx i Epsilon is a random variable;
in matrix form can be expressed as:
Y＝β 0 +X′b+X′BX+ε
wherein: x= (X 1 ，x 2 ，…，x k ) T ；b＝(β 1 ，β 2 ，…，β k ) T Is a regression coefficient matrix; b is a k-order symmetric matrix:
taking low-temperature splitting strength, freeze thawing splitting strength ratio and dynamic stability as output values, X 1 、X 2 、X 3 The corresponding 3 factor 3 level is taken as an input value to obtain a response surface model parameter beta 0 And epsilon.
Further, the step (4) specifically includes the following steps:
step (41): determining a judgment matrix A:
according to
Giving a judgment construction judgment matrix A;
wherein: a, a ij Representing the relative importance of the ith target and the jth target; omega i Is attribute x i Weights of (2);
step (42): normalization:
according to
Normalizing each column vector of the judgment matrix,
according to the formula
Summing by row and according to the formula->
Normalization is carried out to obtain a weight coefficient w i ；
Step (43): for calculating knotAnd (5) carrying out consistency test: first, the maximum characteristic root lambda of the judgment matrix A is calculated max ：
Calculating a consistency index CI:
CI >0, and the smaller the CI value, the better the consistency, the consistency index CI <0.0001, indicating that the weight calculation result has high consistency, the method is feasible.
Compared with the prior art, the invention has the remarkable advantages that:
(1) The design method of the invention adopts a response surface method, realizes the functional relation between a plurality of influencing factors and a plurality of road performance evaluation indexes, can quantitatively analyze the influence of each factor and interaction thereof on a response value, and ensures that the whole forming process of the ice and snow resistant asphalt mixture is more flexible, logical and predictive.
(2) The design method of the invention utilizes the analytic hierarchy process to carry out weight distribution on the road performance of the asphalt mixture, so that the method of the invention can be suitable for different environmental conditions, and the accuracy and the universality of the method are improved.
Drawings
FIG. 1 is a graph of dynamic stability and response curves and contour plots of various influencing factors according to the present invention; wherein (a) mixing temperature-amount of snow-melting anti-icing agent, (b) oil-stone ratio-amount of snow-melting anti-icing agent, (c) oil-stone ratio-mixing temperature.
FIG. 2 is a graph of calculation errors of a response surface model according to the present invention; wherein (a) is a low-temperature splitting strength calculation error map, (b) a freezing-thawing splitting strength ratio calculation error map, and (c) a dynamic stability calculation error map.
FIG. 3 is a road performance test result; wherein (a) a low temperature cleavage test, (b) a freeze-thaw cleavage test, (c) a rutting test.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
Example 1
Based on a response surface method, taking the optimal value of road performance as a target, and carrying out systematic optimization design on the forming method of the SMA-13 graded asphalt mixture. First, the key factors affecting the road performance of asphalt mixtures are: carrying out single factor experimental study on the oil-stone ratio, the mixing (compacting) temperature and the amount of the snow-melting anti-icing agent; then, according to a Box-Behnken design theory in a response surface method, a response surface model of each factor and the road performance index is established; finally, according to different using conditions, weighting distribution is carried out on each evaluation index of the road performance by using an analytic hierarchy process, and the optimal values of each factor and the road performance are obtained, so that the whole forming process of the ice and snow resistant asphalt mixture is more flexible, logical and predictive.
The method for adding the snow-melting anti-icing agent adopts a method for replacing part of fine aggregate or mineral powder by adding a low-freezing-point filler into the surface layer of the 4cm fine-grained SBS modified asphalt concrete.
TABLE 1 target mix design mineral Material proportions
Asphalt mixture molding optimization design process
The road performance is taken as a comprehensive evaluation index, and the comprehensive evaluation index specifically comprises low-temperature splitting strength, dynamic stability and 3 performance indexes of freeze thawing splitting strength ratio, so that the low-temperature cracking resistance, high-temperature stability and water stability of the asphalt mixture are respectively evaluated. Carrying out a low-temperature splitting test and a freeze thawing splitting test on a standard Marshall test piece by means of an MTS multifunctional testing machine, wherein the temperature of the low-temperature splitting test is-10 ℃, and the loading rate is 1mm/min; the freeze thawing cleavage test temperature is 25 ℃ and the loading rate is 50mm/min. And (3) carrying out a rutting test on the test piece at 60 ℃, wherein the wheel pressure of a rutting instrument is 0.7MPa.
Single factor test design
In the asphalt mixture forming process, 3 parameters of oil-stone ratio, mixing (compacting) temperature and the dosage of the snow melting anti-icing agent are used as influencing factors. First, the range of each influencing factor is determined through specification or experience, as shown in table 2.
TABLE 2 influence factors and application ranges
1. Effect of whetstone on road performance of asphalt mixtures
In the forming process of the asphalt mixture test piece, the oil-stone ratio adopts 0.5% interval change, and other influencing factors adopt fixed values: the mixing temperature is 150 ℃, the compacting temperature is 140 ℃, and the dosage of the snow melting anti-icing agent is 5 percent. The test results of the test piece set of road performance tests are shown in Table 3.
TABLE 3 Effect of whetstone ratio on asphalt mixture pavement performance
As can be seen from table 3: the low-temperature splitting strength, the freeze-thawing splitting strength ratio and the dynamic stability of the asphalt mixture are increased and then reduced along with the increase of the oil-stone ratio. This is because, when the oilstone is small, the thickness of the asphalt film on the surface of the aggregate is small or the asphalt cannot cover the surface of the aggregate completely, resulting in insufficient adhesion between the asphalt and the aggregate and being susceptible to attack by moisture; when the oilstone ratio is too large, free asphalt in the test piece is increased to play a role in lubrication, and weak parts can appear in the test piece, so that the strength of the asphalt mixture is reduced, and shearing deformation is easy to occur.
2. Effect of blending/compaction temperature on road performance of asphalt mixtures
In the process of forming the asphalt mixture test piece, in order to simplify the problem, the mixing temperature and the compacting temperature are treated as a factor, and according to practical experience, the mixing temperature and the compacting temperature are generally different by about 10 ℃, and both are changed at intervals of 10 ℃. Other influencing factors adopt fixed values: the oil-stone ratio is 4.5%, and the dosage of the snow-melting anti-icing agent is 5%. The test piece road performance test results are shown in table 4.
TABLE 4 influence of mixing/compaction temperatures on road performance of asphalt mixtures
As can be seen from table 4: the various indexes of the asphalt mixture respectively reach the maximum value at a certain temperature, and the too high or too low mixing/compacting temperature can lead to the reduction of road performance. As the mixing temperature increases, the fluidity of the asphalt binder increases, the better the compactness of the test piece is, and the asphalt and the aggregate are fully bonded. And too high a temperature can cause aging of the asphalt, so that the adhesion between the asphalt and the aggregate is reduced, and the performance of the test piece is reduced.
3. The dosage of the snow melting anti-icing agent is the influence on the road performance of the asphalt mixture
The group of tests are used for carrying out single-factor test analysis on the dosage of the snow-melting anti-icing agent, and the content of the snow-melting anti-icing agent is changed at intervals of 4%, 4.5%, 5%, 5.5% and 6%. Other influencing factors adopt fixed values: the mixing temperature was 150℃and the compaction temperature was 140℃and the oil-to-stone ratio was 4.5%. The test results of the test piece set of road performance tests are shown in Table 5.
As can be seen from table 5: various indexes of the asphalt mixture have a tendency of gradually decreasing along with the increase of the dosage of the snow-melting anti-icing agent. The snow melting anti-icing agent is added into the asphalt mixture to replace mineral powder, so that the temperature sensing performance of asphalt cement is reduced along with the reduction of the powder-cement ratio when the consumption is increased, and the rut resistance is further affected; the interaction of asphalt and mineral powder is weakened, the cohesive force is insufficient, the shearing resistance of the asphalt mixture is reduced, and the high-temperature stability of the self-fluxing asphalt mixture is weakened.
TABLE 5 Effect of snow melt anti-icing agent usage on asphalt mixture road Performance
Multi-factor test design
1. Creation of quadric model
The test takes low-temperature splitting strength, freeze thawing splitting strength ratio and dynamic stability as output variables, takes 3 factors of oil-stone ratio, mixing/compacting temperature and snow melting anti-icing agent dosage in a single factor test as input variables, and takes 1, 0 and-1 as high, medium and low levels of independent variables respectively to carry out 3-factor 3-level test design on the SMA-13 graded asphalt mixture. The independent variables were encoded according to the following formula, and the experimental factor codes and levels are shown in table 6.
X i ＝(x i -x 0 )/Δx
Wherein: x is X i A coded value that is an argument; x is x i Is the true value of the argument; x is x 0 The true value of the independent variable at the test center point; Δx is the step size of the change in the argument.
Table 6 trial factor codes and levels
The process of constructing a response surface model is described by taking an SMA-13 graded asphalt mixture as an example. Firstly, a Box-Behnken Design (BBD) method in a response surface method is adopted to carry out 3-factor 3-level 3 response test Design, 3 center points are set for calculating a pure error, and the response surface test Design and test results are shown in table 7.
TABLE 7 response surface design and results
The response variable and the influence factor are in nonlinear relation, and the response curved surface model is a second-order model:
wherein: beta i Represents x i Linear effects of (2); beta ij Represents x i And x j Linear interactions between; beta ii Represents x i Epsilon is a random variable.
In matrix form can be expressed as:
Y＝β 0 +X′b+X′BX+ε
wherein: x= (X 1 ，x 2 ，…，x k ) T ；b＝(β 1 ，β 2 ，…，β k ) T Is a regression coefficient matrix; b is a k-order symmetric matrix:
taking low-temperature splitting strength, freeze thawing splitting strength ratio and dynamic stability as output values, X 1 、X 2 、X 3 The corresponding 3 factor 3 level is taken as an input value to obtain a response surface model parameter beta 0 And epsilon, drawing a response curve surface diagram and a contour diagram between each road performance and influence factors of the SMA-13 graded asphalt mixture according to the fitting model, and the response curve surface diagram and the contour diagram are shown in figures 1-3.
The interaction of the test factors with each response output can be evaluated by the response curves and contours of FIGS. 1-3, thereby determining the optimal horizontal range of each factor, i.e., the area near the peak of the response curve. If the gradient of the response curved surface is relatively gentle, the response output can inhibit the variation of the relative influence factors without influencing the magnitude of the response value; conversely, if the slope of the response surface is very steep, it is indicated that the response value is very sensitive to changes in the process conditions. Meanwhile, the shape of the contour line can reflect the strength of interaction of two factors, and in general, the shape of the contour line is elliptical, which indicates that the interaction of the two factors is remarkable, and the shape of the contour line is circular, which indicates that the interaction of the two factors is weaker.
The single response output optimal value of the SMA-13 graded asphalt mixture can be obtained through the response surface model and is shown in table 8.
Table 8 form response output optimum value
As can be seen from table 8, the optimum values of the corresponding influence factors are different when the respective response output values are maximum. Therefore, the above results must be weighted according to different usage conditions, and then the optimal values of the response output and the influence factor must be obtained.
2. Determination of weight coefficients
Under different use conditions, the requirements on the road performance of the asphalt mixture are different. For example, in the vinblastine region of China, the winter time is longer, and the number of days when the lowest air temperature is lower than 0 ℃ per year is about 150 days; the rainwater is sufficient, and the annual rainfall in the last 5 years is over 700 mm. In addition, the freeze-thaw cycle action places higher demands on the water stability of the pavement. Therefore, the requirements on low-temperature performance and water stability of the asphalt pavement in such areas are high, and the requirements on high-temperature performance are relatively low. The analytic hierarchy process is used for weight distribution of asphalt mixture road performance.
According to
A judgment construction judgment matrix a is given.
Wherein: a, a ij Representing the relative importance of the ith target and the jth target; omega i Is attribute x i Is a weight of (2).
The low-temperature performance and the water stability of the asphalt mixture are set as important factors, the importance of the low-temperature performance and the water stability is equal to each other, and the importance of the low-temperature performance and the water stability is 3 relative to the importance of the high-temperature performance.
According to
Normalizing each column vector of the judgment matrix can obtain:
according to the formula
Summing by row and according to the formula->
Normalization is carried out to obtain a weight coefficient w i ：
TABLE 9 weight coefficient and consistency results
Finally, the consistency test is needed to be carried out on the calculation result, and the maximum characteristic root lambda of the judgment matrix A is calculated first max ：
Calculating a consistency index CI:
typically, CI >0, and the smaller the CI value, the better the consistency. The consistency index CI <0.0001, which indicates that the weight calculation results are highly consistent, is a viable approach.
Calculate the consistency ratio CR:
wherein: RI is a random consistency index. When CR <0.1, the judgment matrix is considered to have satisfactory consistency. Otherwise, the element value of the judgment matrix A needs to be adjusted to meet the requirement of consistency.
Finally, the final optimized value of each influencing factor is determined by the following formula.
X＝[γ CR ，T，N，ω]＝0.43X 1 +0.43X 2 +0.14X 3
3. Calculation result of response surface model
And 3-level 3-element test design is carried out on the SMA-13 graded asphalt mixture by using the response surface calculation model, and the optimal conditions of each grade are shown in table 10 by carrying out optimal solution on the model.
TABLE 10 optimal test conditions and response output
As can be seen from the calculation result of the optimal test condition, the response surface model of the SMA-13 graded asphalt mixture has stable points. The optimal molding conditions of the SMA-13 graded asphalt mixture are as follows: the proportion of the oilstone is 4.8 percent, the mixing temperature is 165.5 ℃, and the dosage of the snow melting anti-icing agent is 5 percent.
As can be seen from the response output result, the model predicted value has good consistency with the test value, and the relative error is small, so that the response curved surface model is suitable and effective, and the road performance of the mixture can be effectively predicted.
Response surface model error analysis and result verification
Response surface model error analysis
In order to examine the accuracy of the response surface model, the fitting residual error and the significance of the model are analyzed. The residual consists of two parts: one part is a pure error, namely, the error obtained by repeating the experiment under the same condition, the pure error is random, and if the pure error is large, the experiment repeated condition is proved to be not uniform enough, and the investigated factors are not comprehensive enough; the other part is the mismatch error, the mismatch error is related to the selected model, the model is proper, the value of the mismatch error is small, and conversely, the value of the mismatch error is large. The results of the model error analysis are shown in table 11, and the test point calculation error analysis is shown in fig. 2.
TABLE 11 response surface model error analysis results
As can be seen from the analysis results in Table 11, the model residual error is relatively small, the error of the mismatch is far greater than the pure error, but the significance levels are all>0.1, the model is acceptable, indicating that the model is not significantly misshapen. Calculation results of significance level of model<0.01 shows that the model selected by the test is highly significant, and can accurately reflect the relation between the input variable and the response output. Correlation coefficient R of model 2 The response value changes are all above 0.9, which indicates that the model can explain the response value changes by more than 90 percent, and the fitting degree of the model is higher.
As can be seen from fig. 2, the error amount of the model is smaller, the calculation error of the ratio of the low-temperature splitting strength to the freeze-thawing splitting strength is distributed within a range of +/-1.2%, and the calculation error of the dynamic stability is within a range of +/-0.4%, so that the fitting precision and stability of the model are further proved.
The research results show that the response curved surface model has higher fitting precision and prediction stability in the optimization design of the asphalt mixture molding parameters, and can accurately reflect the functional relation between the road performance of the asphalt mixture and the influencing factors.
Response surface model result verification
In order to further verify the rationality of the test conditions and response output determined by the model, the test method is compared with the current standard method, and the control factor values of the test method and the current standard method are shown in table 12.
Table 12 response surface method and standard method test conditions
The volume parameters of the asphalt mixture test pieces prepared by the test method and the current standard method are tested respectively, and the density, the void fraction, the mineral aggregate gap rate and the asphalt saturation of the two groups of test pieces are tested according to the standard method, and the test results are shown in table 13.
TABLE 13 results of volume parameter testing
The volume parameter test results show that the volume parameter values determined by the response surface method and the standard method have certain differences due to different control factors such as the oil-stone ratio, the temperature and the like, but the differences are not obvious, the relative error is controlled within 10%, and all indexes meet the standard requirements.
The road performance test is carried out on the asphalt mixture test pieces prepared by the two molding methods, the low-temperature splitting strength, the freeze thawing splitting strength ratio and the dynamic stability of the two groups of test pieces are respectively tested, the test results are shown in figure 3, and the test result pairs are shown in a table 14.
Table 14 comparison of the results of the road Performance test (%)
As can be seen from the road performance test results, the road performance of the parametric molded asphalt mixture test piece determined by the response surface model method is obviously better than that of the test piece molded by the standard method, and the average improvement amplitude of the road performance is 2.7%. The asphalt mixture forming method based on the response surface method mainly aims at road performance as a final target, meanwhile, the volume parameter is considered, and the Marshall compaction and wheel milling method aims at the volume parameter, so that the asphalt mixture forming method has certain unilaterality.
Claims (5)
1. The method for designing the proportion of the asphalt mixture of the anti-ice and snow-melting agent based on the response surface method is characterized by comprising the following steps:
step (1): determining key factors and road performance evaluation indexes which influence the road performance of the asphalt mixture;
step (2): carrying out single-factor experimental study on key factors influencing the road performance of the asphalt mixture;
step (3): establishing a response surface model of the key factors and the road performance evaluation indexes by adopting a Box-Behnken design method in a response surface method;
step (4): and according to different using conditions, performing weight distribution on each evaluation index of the road performance by using an analytic hierarchy process, and obtaining the optimal value of each key factor and the road performance.
2. The method of claim 1, wherein the key factors determined in step (1) that affect the road performance of the asphalt mixture are the whetstone ratio, the mix/compaction temperature, and the amount of snow melt anti-icing agent;
the road performance evaluation indexes comprise low-temperature splitting strength, dynamic stability and freeze thawing splitting strength, and the three road performance evaluation indexes are used for evaluating the low-temperature cracking resistance, high-temperature stability and water stability of the asphalt mixture respectively.
3. The method according to claim 2, wherein the step (2) of performing a single-factor test on the key factors affecting the road performance of the asphalt mixture comprises the following specific steps:
step (21): determining the range of each influencing factor: wheal ratio x 1 3.5-5.5%, mixing/compacting temperature x 2 The dosage x of the snow-melting anti-icing agent is 120-200 ℃/110-190 DEG C 3 4-6%;
step (22): oil-stone ratio test: in the process of forming an asphalt mixture test piece, preparing a test piece by adopting 0.5% interval change of the oil-stone ratio, and taking the mixing temperature, the compacting temperature and the snow melting anti-icing agent dosage as fixed values, and obtaining a road performance test result by a test;
step (23): mixing/compaction temperature test: the mixing temperature and the compacting temperature are treated as a factor, the mixing temperature and the compacting temperature are set to be different by 10 ℃, and the mixing temperature and the compacting temperature are changed at intervals of 10 ℃; the oil-stone ratio, the amount of the snow melting anti-icing agent adopts a fixed value, and a test piece road performance test result is obtained;
step (24): and (3) testing the dosage of the snow melting anti-icing agent: the snow-melting anti-icing agent content adopts 4%, 4.5%, 5%, 5.5% and 6% of interval change, mixing temperature, compaction temperature and oil stone ratio to obtain road performance test results.
4. A method according to claim 3, wherein step (3) comprises the steps of:
step (31): taking low-temperature splitting strength, freeze thawing splitting strength ratio and dynamic stability as output variables, taking three factors of oil-stone ratio, mixing/compacting temperature and snow melting anti-icing agent dosage in a single factor experiment as input variables, and respectively representing high, medium and low levels of independent variables by 1, 0 and-1 to carry out 3-factor 3-level test design on the SMA-13 graded asphalt mixture; encoding an argument as follows
X i ＝(x i -x 0 )/Δx
Wherein: x is X i A coded value that is an argument; x is x i Is the true value of the argument; x is x 0 The true value of the independent variable at the test center point; Δx is the step size of the change of the argument;
step (32): the response curved surface model is a second-order model, and is specifically as follows:
wherein: beta i Represents x i Linear effects of (2); beta ij Represents x i And x j Linear interactions between; beta ii Represents x i Epsilon is a random variable;
in matrix form can be expressed as:
Y＝β 0 +X′b+X′BX+ε
wherein: x= (X 1 ，x 2 ，…，x k ) T ；b＝(β 1 ，β 2 ，…，β k ) T Is a regression coefficient matrix; b is a k-order symmetric matrix:
taking low-temperature splitting strength, freeze thawing splitting strength ratio and dynamic stability as output values, X 1 、X 2 、X 3 The corresponding 3 factor 3 level is taken as an input value to obtain a response surface model parameter beta 0 And epsilon.
5. The method of claim 4, wherein step (4) comprises the steps of:
step (41): determining a judgment matrix A:
according to
Giving a judgment construction judgment matrix A;
wherein: a, a ij Representing the relative importance of the ith target and the jth target; omega i Is attribute x i Weights of (2);
step (42): normalization:
according to
Normalizing each column vector of the judgment matrix,
according to the formula
Summing by row and according to the formula->
Normalization is carried out to obtain a weight coefficient w i ；
Step (43): and (3) carrying out consistency test on the calculation result: first, the maximum characteristic root lambda of the judgment matrix A is calculated max ：
Calculating a consistency index CI:
CI >0, and the smaller the CI value, the better the consistency, the consistency index CI <0.0001, indicating that the weight calculation result has high consistency, the method is feasible.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211536749.9A CN116332563A (en) | 2022-12-02 | 2022-12-02 | Method for designing proportion of asphalt mixture of anti-ice and snow-melting agent based on response surface method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211536749.9A CN116332563A (en) | 2022-12-02 | 2022-12-02 | Method for designing proportion of asphalt mixture of anti-ice and snow-melting agent based on response surface method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116332563A true CN116332563A (en) | 2023-06-27 |
Family
ID=86882780
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211536749.9A Pending CN116332563A (en) | 2022-12-02 | 2022-12-02 | Method for designing proportion of asphalt mixture of anti-ice and snow-melting agent based on response surface method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116332563A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117805351A (en) * | 2024-03-01 | 2024-04-02 | 吉林建筑大学 | Comprehensive evaluation method for fatigue resistance of asphalt mixture |
-
2022
- 2022-12-02 CN CN202211536749.9A patent/CN116332563A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117805351A (en) * | 2024-03-01 | 2024-04-02 | 吉林建筑大学 | Comprehensive evaluation method for fatigue resistance of asphalt mixture |
| CN117805351B (en) * | 2024-03-01 | 2024-05-03 | 吉林建筑大学 | Comprehensive evaluation method for fatigue resistance of asphalt mixture |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Guo et al. | Analysis of factors that influence anti-rutting performance of asphalt pavement | |
| Ajayi et al. | Epoxy–resin–based chemical stabilization of a fine, poorly graded soil system | |
| CN102503244A (en) | Composition of skeleton interlocking coarse grain-type high-modulus asphalt concrete and determination method thereof | |
| CN116332563A (en) | Method for designing proportion of asphalt mixture of anti-ice and snow-melting agent based on response surface method | |
| CN110078417A (en) | A kind of anti-rutting asphalt mixture mixing proportion design method | |
| Liu et al. | Permanent Deformation Monitoring and Remaining Life Prediction of Asphalt Pavement Combining Full‐Scale Accelerated Pavement Testing and FEM | |
| Zborowski et al. | A fracture energy approach to model the thermal cracking performance of asphalt rubber mixtures | |
| Ullidtz et al. | Calibration of incremental-recursive flexible damage models in CalME using HVS experiments | |
| CN103184717A (en) | Method for designing AC-20 asphalt mixture | |
| Gu et al. | Experimental and theoretical framework for illustrating the dependency of fracture toughness with tensile, bending, and compression loading in asphaltic samples | |
| CN103122603A (en) | Design method of ATB-30 asphalt mixture | |
| Golsefidi et al. | Effect of reclaimed asphalt pavement (RAP) on fracture properties of stone matrix asphalt (SMA) at low temperature | |
| CN109020338B (en) | Design method of cement-stabilized iron-like tailing sand base material | |
| Zborowski et al. | Predictive equations to evaluate thermal fracture of asphalt rubber mixtures | |
| CN106289682A (en) | A kind of evaluate Colophonium and the method and application thereof wrapping up in attached property of gathering materials | |
| Chen | Use of semi-circular bend test to characterize fracture properties of asphalt concrete with virgin and recycled materials | |
| Gusty | The effect of using asbuton with used waste diesel oil on the stability of the porus asphalt mix with hot mix cold laid method | |
| Rodezno et al. | Implementation of asphalt-rubber mixes into the mechanistic empirical pavement design guide | |
| CN103147374A (en) | Design method of AC-13 asphalt mixture | |
| Esfandiarpour | Calibrating MEPDG inputs prediction models for asphalt mixes containing reclaimed asphalt pavement | |
| Munir et al. | Activated Crumb Rubber Modified Binder as a Sustainable Paving Material: Pavement Performance Consideration | |
| Rath et al. | Advances in Pavement Performance Enhancement with Dry Process Engineered Ground Tire Rubber | |
| Šimun et al. | Rutting resistance of waterproofing–asphalt pavement systems on bridges | |
| CN111046477A (en) | Mix proportion design method of normal-temperature construction asphalt mixture for road pit and groove restoration | |
| Liu et al. | Influence of the skid resistance of ultrathin wearing course with various types of asphalt binders |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |