A deviation coefficient method for designing intermittent gradation skeleton of flowable asphalt mixture

Abstract

This invention relates to a deviation coefficient method for the design of discontinuous gradation skeletons in flowable aggregate asphalt mixtures (FMA). This method uses a deviation coefficient λ to reduce the passing rate of key aggregate sizes, thereby controlling the degree of gradation discontinuity, fine aggregate content, and skeleton gap ratio. In a gradation curve coordinate system with the sieve aperture size raised to the power of 0.45 as the abscissa, the maximum density line is a straight line, and λ represents the degree of deviation of the key sieve aperture passing rate from the maximum density line. The smaller the deviation coefficient λ, the closer the aggregate gradation is to the maximum density line; the larger λ is, the higher the degree of gradation deviation, the lower the fine aggregate content, and the correspondingly larger the skeleton gap ratio. This method achieves wide-range adjustable asphalt-aggregate ratio while ensuring that the road performance of FMA meets the specifications, and provides a scientifically feasible technical path for the discontinuous gradation design of FMA aggregates.

Description

Technical Field

[0001] This invention belongs to the field of road traffic technology and relates to a deviation coefficient method for the design of discontinuous gradation skeleton of flowable asphalt mixture. Background Technology

[0002] Under the current pavement theory system, to ensure that the asphalt mixture does not leak during construction, it is difficult to increase the asphalt-aggregate ratio, necessitating the design of a high porosity. This highlights the contradictions between the performance characteristics of asphalt mixtures, making it difficult to solve early-stage problems such as cracking, rutting, potholes, and water damage in asphalt pavements, directly shortening their service life. If highway pavements have a short service life and require frequent maintenance, the total life-cycle cost of roads will increase significantly, affecting traffic efficiency and the stability of the road network. Therefore, the technical bottleneck caused by insufficient durability of asphalt pavement materials is a problem that urgently needs to be solved in the field of asphalt pavement.

[0003] Professor Wu Kuanghuai's team proposed the theory of Fluid Mastic Asphalt (FMA), and their main findings, "Theory and Design Method of Fluid Mastic Asphalt (FMA)," were published in the *China Journal of Highway and Transport* in June 2024. Fluid mastic asphalt refers to a skeleton-ultra-dense asphalt mixture with a near-zero internal porosity, formed by filling the gaps in the aggregate structure with highly fluid mastic through its own flow or vibration-assisted compaction techniques. The term "mass flow" is in contrast to the "no segregation" characteristic of current hot-mix asphalt (HMA) construction processes. Compared to current HMA mixtures, FMA mixtures form a skeleton-ultra-dense structure with near-zero internal porosity, an increased asphalt-aggregate ratio that is flexible and adjustable over a wide range, enhanced tensile deformation capacity, increased flexibility, and enhanced toughness, exhibiting comprehensive performance advantages. FMA (Fluorescent Aggregate Mixture) is expected to solve current early-stage pavement problems such as water damage, fatigue and reflective cracking, aging, and skid resistance and durability, significantly improving the durability of asphalt pavements. In particular, the wide-range adjustable asphalt-aggregate ratio of FMA allows for performance-based design, addressing various working conditions and diverse needs in pavement construction and maintenance. FMA can not only be used for road maintenance to extend the life of existing pavements, but also for various layers in new and upgraded long-life pavement structures. It can also be used as a functional layer in pavement structures or as a surface layer to achieve skid resistance and durability.

[0004] However, since FMA is still in the initial research stage, the coarse and fine aggregates in the skeleton design are currently determined only by the volume relationship of the skeleton gap filling. They are often designed as discontinuous gradation based on experience, and a unified design method has not yet been formed.

[0005] Currently, the gradation design of dense HMA is mostly based on the maximum density line theory, and is mainly divided into two categories: one is the empirical gradation design method, which relies on empirical parameters accumulated through long-term engineering practice to determine the gradation range; the other is the theoretical calculation design method, which uses the Talbol formula P i =100(d i / D) n The passing rate of each aggregate is calculated, where the parameter n is a key indicator characterizing the shape of the gradation curve, and its value is strictly limited to the range of 0.3-0.7 to ensure the compactness of the mixture gradation.

[0006] The SUPERPAVE design method is based on the maximum density line at n=0.45, and designs the aggregate gradation curve by setting control points and restriction zones. Based on this, five asphalt-aggregate ratios are selected, specimens are prepared using corresponding molding methods, and mechanical and volumetric property tests are conducted to determine the optimal asphalt-aggregate ratio. From a design perspective, this method prioritizes determining the aggregate gradation before determining the optimal asphalt-aggregate ratio, belonging to a gradation-priority design process. Clearly, this gradation design method cannot be applied to FMA theory, cannot design FMA skeletons suitable for different binder dosages, and cannot achieve the wide-range adjustable asphalt-aggregate ratio characteristic of FMA. Summary of the Invention

[0007] To address the shortcomings and deficiencies of existing technologies, this invention aims to provide a deviation coefficient method for discontinuous gradation skeleton design of flowable asphalt mixtures (FMA). This method uses the maximum density curve at the 0.45 power of the sieve aperture as a reference, and adjusts the degree of discontinuity and coarseness characteristics of the skeleton gradation by reducing the passing rate of key sieve apertures. This achieves directional changes in the skeleton gap ratio, simplifies the gradation design process, clarifies the physical meaning of the control parameters, and ensures a continuous and smooth gradation curve. It effectively solves the technical problems of complex operation and difficulty in accurately controlling the gradation state in existing gradation design methods during engineering applications. This method achieves wide-range adjustable asphalt-aggregate ratio while ensuring that the road performance of FMA meets the specifications, and provides a scientifically feasible technical path for discontinuous gradation design of FMA aggregates. The deviation coefficient method, as a method for discontinuous gradation design of FMA skeletons, can complement the n-value extension method (the continuous gradation design method for FMA). In practical applications, a suitable method can be selected according to specific design requirements, or the two methods can be used in combination.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] A deviation coefficient method for discontinuous gradation skeleton design of flowable asphalt mixtures (FMA) includes the following steps:

[0010] Step 1: Determine the maximum particle size D of the gradation max According to the Talbol formula Pi =100(d i / D) n The maximum throughput of each sieve aperture is calculated by raising the sieve aperture to the power of 0.45, which forms the maximum density line. At this point, the deviation coefficient λ is 0.

[0011] Maximum particle size D max The passing rate of the minimum particle size of 0.075 mm is taken as the corresponding value on the maximum density line. With 4.75 mm or 2.36 mm as the key particle size, the maximum density line is deviated, and the deviation coefficient λ is 0~1. The deviation of the maximum density line is achieved by setting the value range of the deviation coefficient λ with a gradient of 0.1 to quantify and classify it, resulting in 10 discontinuous gradation curves with different deviation coefficients.

[0012] The 10 discontinuous gradation curves with different deviation coefficients obtained from the deviation processing are plotted as a gradation curve diagram.

[0013] The skeleton gap ratio V of each discontinuous gradation aggregate was determined using the wet mix test method. ag V was measured for each gradation under different deviation coefficients. ag λ-V can be obtained through post-regression analysis. ag The relational model is shown in equation (1):

[0014] V ag =a+bλ (1)

[0015] In the formula:

[0016] a is V when the deviation coefficient λ is 0. ag Value, that is, the value on the maximum density line;

[0017] b represents the deviation coefficient affecting V. ag The dominant factor is the slope of the model;

[0018] λ is the deviation coefficient, which ranges from 0 to 1;

[0019] Step 2: Determine the maximum particle size D of the gradation according to the actual needs. max And the amount of adhesive P used in FMA ma ;

[0020] Step 3: Calculate the V corresponding to the required amount of adhesive using the MAFF method. ag ;

[0021] Step 4: Calculate V in Step 3. ag Substituting into equation (1) shows λ-V ag In the relational model, determine the corresponding deviation coefficient λ value;

[0022] Step 5: First, calculate the throughput P of the critical particle size under any deviation coefficient λ using equation (4):

[0023] P = P2 - λ(P2 - P3) (4)

[0024] In the formula, P2 and P3 are the critical particle size and the sieve aperture passing rate of 0.075 mm corresponding to the maximum density line, respectively;

[0025] Then, the sieve passing rate of the remaining aggregates is determined by linear interpolation, thus obtaining the FMA skeleton discontinuous gradation design.

[0026] Furthermore, the maximum particle size D of the gradation described in steps 1 and 2 max same.

[0027] Furthermore, the wet-mix test method described in step 1 is a wet-mix test method for determining the skeleton void ratio of a flowable asphalt mixture, disclosed in Chinese patent application No. 202510470312.7.

[0028] Furthermore, the V calculated in step 3 ag Multiply by the reduction factor α and then substitute into equation (1) λ-V ag In the relational model, α is 0.7-0.9.

[0029] Furthermore, in the MAFF method described in step 3, the aggregate dosage, adhesive dosage, and V of the FMA mixture are... ag The relationship between the parameters is shown in formulas (2) and (3):

[0030] P ag +P ma =100 (2)

[0031] P ag This refers to the aggregate usage (by weight) of the FMA mixture.

[0032] P ma The amount of adhesive used in the FMA mixture (by weight percentage).

[0033] (3)

[0034] V ag The skeleton gap ratio of the FMA mixture;

[0035] VV represents the design internal porosity; the measured internal porosity of FMA is typically less than 1%.

[0036] F d The filling degree represents the extent to which the adhesive fills the voids in the skeleton, and its value ranges from 0 to 1.0.

[0037] γ c γ is the bulk density of aggregates in a compacted or compacted state, also known as the compacted density of aggregates. It is measured in practice and can be obtained by referring to the method disclosed in Chinese patent application No. 202510470312.7. First, FMA specimens are formed according to the mix proportion, and then their height, bottom area, and weight are measured to calculate their density, which is γ. c ;

[0038] P ma0 The amount of adhesive paste used (by weight) can be determined through a mixing test.

[0039] γ ma The relative density of the adhesive paste is the synthetic density.

[0040] The actual measurement of the parameters mentioned in the MAFF method refers to first molding FMA specimens according to the calculated mix proportion (preferably the gradation with a deviation coefficient of 0), and then conducting the test.

[0041] Furthermore, in step 5, the key particle size is 4.75 mm or 2.36 mm;

[0042] The linear interpolation method involves drawing lines between 0.075mm and the critical particle size, and between the critical particle size and 13.2mm, respectively. Based on the location of the sieve aperture pass rate of the critical particle size, the sieve aperture pass rate of the remaining aggregates is determined by linear interpolation.

[0043] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0044] (1) The control parameter is simplified: the overall gradation can be accurately controlled by a single deviation coefficient, which is simple and easy to implement.

[0045] (2) The physical connotation is clear and explicit: The deviation coefficient λ directly affects the difference between the passing rate of the key sieve aperture (4.75mm or 2.36mm) and the 0.075mm sieve aperture. The value of λ directly reflects the degree to which the gradation deviates from the maximum density line. The smaller the value of λ, the higher the passing rate of the 4.75mm or 2.36mm sieve aperture, the greater the proportion of fine aggregate, the finer the gradation tends to be, and the closer the gradation is to the maximum density line; the larger the value of λ, the lower the passing rate of the 4.75mm or 2.36mm sieve aperture, the smaller the proportion of fine aggregate, the coarser the gradation tends to be, and the further away from the maximum density line it is. The deviation coefficient λ can intuitively and quantitatively characterize the discontinuity and coarseness of the gradation.

[0046] (3) Continuous and smooth gradation: The passing rate of each particle size is determined by linear interpolation, which can effectively ensure that the gradation curve is continuous and smooth, and avoid gradation abrupt changes and discontinuities.

[0047] (4) Compatibility with the 0.45 power maximum density line of the Superpave system: In the case of d 0.45 In the gradation coordinate system with the horizontal axis as the abscissa, the reference gradation curve exhibits an ideal linear distribution, and the interpolation calculation process is simple and intuitive, facilitating gradation design and verification. Attached Figure Description

[0048] Figure 1 V is the gap ratio of the skeleton. ag Relationship diagram with deviation coefficient value λ;

[0049] Figure 2 FMA aggregate gradation curves corresponding to different deviation coefficient values;

[0050] Figure 3 A schematic diagram of constructing discontinuous gradation curves based on the deviation coefficient λ;

[0051] Figure 4 This is a flowchart of the deviation coefficient method for the discontinuous gradation skeleton design of the flowable asphalt mixture (FMA) of the present invention. Detailed Implementation

[0052] The present invention will be further described in detail below with reference to embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto. All raw materials involved in the present invention can be purchased directly from the market. For process parameters not specifically specified, conventional techniques can be referred to.

[0053] This invention provides a deviation coefficient method for discontinuous gradation skeleton design of flowable asphalt mixtures (FMA), comprising the following steps:

[0054] Step 1: Determine the maximum particle size D of the gradation max According to the Talbol formula P i =100(d i / D) n The maximum throughput of each sieve aperture is calculated by raising the sieve aperture to the power of 0.45, which forms the maximum density line. At this point, the deviation coefficient λ is 0.

[0055] Maximum particle size D maxThe throughput of the minimum particle size of 0.075 mm is still taken as the corresponding value on the maximum density line. With 4.75 mm or 2.36 mm as the key particle size, the maximum density line is deviated, and the deviation coefficient λ is 0~1. The deviation of the maximum density line is carried out by setting the value range of the deviation coefficient λ in a quantitative gradation with a gradient of 0.1 (λ=0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1), resulting in 10 discontinuous gradation curves with different deviation coefficients (corresponding to any deviation coefficient λ, connecting three points can construct a broken line gradation curve that deviates from the maximum density line, which can be used as the discontinuous gradation curve of FMA).

[0056] The 10 discontinuous gradation curves with different deviation coefficients obtained from the deviation processing are plotted as a gradation curve diagram.

[0057] The skeleton gap ratio V of each discontinuous gradation aggregate was determined using the wet mix test method. ag V was measured for each gradation under different deviation coefficients. ag λ-V can be obtained through post-regression analysis. ag The relational model is shown in equation (1):

[0058] V ag =a+bλ (1)

[0059] In the formula:

[0060] a is V when the deviation coefficient λ is 0. ag Value, that is, the value on the maximum density line;

[0061] b represents the deviation coefficient affecting V. ag The dominant factor is the slope of the model;

[0062] λ is the deviation coefficient, which ranges from 0 to 1;

[0063] Step 2: Determine the maximum particle size D of the gradation according to the actual needs. max And the amount of adhesive P used in FMA ma ;

[0064] Step 3: Calculate the V corresponding to the required amount of adhesive using the MAFF method. ag ;

[0065] Step 4: Calculate V in Step 3. ag Substituting into equation (1) shows λ-V ag In the relational model, determine the corresponding deviation coefficient λ value;

[0066] Step 5: First, calculate the throughput P of the critical particle size under any deviation coefficient λ using equation (4):

[0067] P = P2 - λ(P2 - P3) (4)

[0068] In the formula, P2 and P3 are the critical particle size and the sieve aperture passing rate of 0.075 mm corresponding to the maximum density line, respectively;

[0069] Then, the sieve passing rate of the remaining aggregates is determined by linear interpolation, thus obtaining the FMA skeleton discontinuous gradation design.

[0070] Furthermore, the maximum particle size D of the gradation described in steps 1 and 2 max same.

[0071] Further, the wet-mix test method mentioned in step 1 is a wet-mix test method for determining the skeleton void ratio of a flowable asphalt mixture, disclosed in Chinese patent application No. 202510470312.7. The wet-mix test method includes the following steps:

[0072] (1) Select the gradation and weigh each grade of aggregate, and weigh 2% of the aggregate weight of asphalt; according to the asphalt viscosity-temperature curve obtained by the asphalt rotation viscosity test, determine the temperature T0℃ when the asphalt viscosity is 0.28 Pa•s.

[0073] The asphalt, aggregates, and test tools are heated in stages. The heating temperature for the first period is T0-20 ℃, and the heating temperature for the last hour is T0 ℃.

[0074] (2) Pour the heated aggregate into the mixer and mix. After the aggregate is evenly mixed, add asphalt and continue to mix thoroughly. The mixing temperature is T0+10℃.

[0075] (3) According to the weight of one specimen, the aggregate mixed with asphalt is added to the mold and tamped;

[0076] (4) After tamping, place the mold in a Marshall compactor or rotary compactor and compact it according to the set number of tamping times; after compaction, take out the aggregate, let it cool naturally, and then demold to obtain the specimen.

[0077] (5) Measure the height of the specimen;

[0078] (6) Based on the measured height of the specimen, calculate the volume of the specimen using the cylinder volume formula, and then divide the weight of the specimen by the volume to obtain the compaction density of the specimen; finally, the porosity V of the specimen skeleton can be calculated using the following formula. ag ;

[0079]

[0080] In the formula:

[0081] Vag —This represents the aggregate skeleton porosity, %;

[0082] ρ1 — Represents the compacted density of the aggregate, g / cm³ 3 ;

[0083] ρ2 — represents the composite bulk density of the aggregate, g / cm³ 3 .

[0084] Furthermore, the V calculated in step 3 ag Multiply by the reduction factor α and then substitute into equation (1) λ-V ag In the relational model, α ranges from 0.7 to 0.9. The construction methods and compaction work in actual field construction differ from those in laboratory tests. Furthermore, the smaller specimen volume in the tests can lead to boundary effects. In contrast, during on-site compaction of FMA pavement, the aggregate is more evenly and densely distributed, and the lubricating effect of asphalt results in a more compact aggregate structure. Therefore, the obtained V... ag It needs to be multiplied by a reduction factor α before it can be used in the design, so as to match the construction site V. ag Consistent. The reduction factor is derived from experience in construction examples and is taken as 0.7-0.9.

[0085] Further, the MAFF method described in step 3 is the Mastic Flow for Filling (MaFF) method disclosed in the literature (Wu Kuanghuai, Wu Chuanhai, Nie Guihai, et al. Theory and design method of Flowable Asphalt Mixture (FMA) [J]. China Journal of Highway and Transport, 2025, 38(2):102-113.DOI:10.19721 / j.cnki.1001-7372.2025.02.008.). According to the MAFF method, the aggregate content, mortar content and V of the FMA mixture are... ag The relationship between the parameters is shown in formulas (2) and (3):

[0086] P ag +P ma =100 (2)

[0087] P ag This refers to the aggregate usage (by weight) of the FMA mixture.

[0088] P ma The amount of adhesive used in the FMA mixture (by weight percentage).

[0089] (3)

[0090] V ag The skeleton gap ratio of the FMA mixture;

[0091] VV represents the design internal porosity; the measured internal porosity of FMA is typically less than 1%.

[0092] F d The filling degree represents the extent to which the adhesive fills the voids in the skeleton, and its value ranges from 0 to 1.0.

[0093] γ c The bulk density of aggregates in compacted or compacted state, also known as the compacted density of aggregates, can be measured using the method disclosed in Chinese patent application No. 202510470312.7. First, FMA specimens are molded according to the mix proportions, then their height, base area, and weight are measured, and the density is calculated as γ. c ;

[0094] P ma0 The amount of adhesive paste used (by weight) can be determined through a mixing test.

[0095] γ ma The relative density of the adhesive paste is the synthetic density.

[0096] γ ma According to the formula γ ma =100 / (P b / ρ b +P f / ρ f P is obtained. b P f The percentages of asphalt and mineral powder by mass (in %) are ρ. b ρ f These are the relative density of asphalt and the apparent relative density of mineral powder, respectively (dimensionless, which can be calculated using the "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025)).

[0097] The actual measurement of the parameters mentioned in the MAFF method refers to first molding FMA specimens according to the calculated mix proportion (preferably the gradation with a deviation coefficient of 0), and then conducting the test.

[0098] Furthermore, in step 5, the key particle size is 4.75 mm or 2.36 mm;

[0099] The linear interpolation method involves drawing lines between 0.075mm and the critical particle size, and between the critical particle size and 13.2mm, respectively. Based on the location of the sieve aperture pass rate of the critical particle size, the sieve aperture pass rate of the remaining aggregates is determined by linear interpolation. Figure 3To illustrate the calculation using P=P2-λ(P2-P3), the dashed line represents the maximum density line; the red line uses 4.75mm as the critical particle size and λ as the deviation coefficient. P1, P2, and P3 represent the sieve passing rates at the maximum density line corresponding to 13.2mm, the critical particle size (4.75mm or 2.36mm), and the sieve opening at 0.075mm, respectively. Maximum particle size D max After connecting the critical particle size, the relationship becomes a linear function. Given the x and y coordinates of the two points, the throughput of any point on the line segment between them (e.g., 9.5 mm) can be calculated by solving the equation. Similarly, the throughput of the minimum particle size (0.0%) can be obtained. Linear interpolation: Given the difference in x-coordinates... y-axis difference For any interval y-axis interpolation: .

[0100] The gradation of FMA (Feed-Mesh Aggregate) can be determined by varying the FMA aggregate gradation curves under different deviation coefficients λ. In engineering, it is only necessary to determine the type of FMA required and calculate the V of that skeleton. ag Value, from λ-V ag Find the value of λ in the relational model, and then directly substitute it into the FMA aggregate gradation curve under different deviation coefficients to obtain the corresponding discontinuous gradation design.

[0101] This invention uses a deviation coefficient λ to reduce the passing rate of key particle sizes, thereby controlling the degree of discontinuity in gradation, the amount of fine aggregate, and the skeleton gap ratio. In a gradation curve coordinate system with the sieve aperture size raised to the power of 0.45 as the abscissa, the maximum density line is a straight line, and λ represents the degree of deviation of the key sieve aperture passing rate from the maximum density line, defined as the deviation coefficient, with a value ranging from 0 to 1. In the gradation curve, the smaller the deviation coefficient λ, the closer the aggregate gradation is to the maximum density line; the larger λ is, the higher the degree of gradation deviation, the lower the content of fine aggregate, and the correspondingly larger the skeleton gap ratio. By continuously changing the deviation coefficient λ, a discontinuously graded mixture with continuously adjustable skeleton gap ratio can be constructed to match different binder amounts and flexibly optimize the mix proportion according to the road performance requirements of FMA. This invention's method of controlling the passing rate of key sieve apertures through the deviation coefficient, and thus constructing a discontinuous gradation curve for the FMA skeleton, is defined as the deviation coefficient method.

[0102] The method provided by this invention is based on the core design goal of "zero" porosity and ultra-dense structure. Its gradation design is based on the maximum density curve. The fineness of the gradation is adjusted by reducing the throughput of key sieve holes, thereby achieving the control of the skeleton gap ratio.

[0103] When plotting the gradation curve using a coordinate system with the sieve aperture to the power of 0.45, the maximum density line is a straight line. However, the skeleton gap ratio of the maximum density line is too small to be directly used as the FMA skeleton. Therefore, when constructing the FMA skeleton gradation curve, it should deviate from the maximum density line to increase the skeleton gap ratio (V). ag The deviation coefficient λ is used to quantify the degree of deviation between the passing rate of the key sieve aperture and the maximum density line, and its value ranges from 0 to 1. The smaller the deviation coefficient λ, the closer the actual aggregate gradation is to the maximum density line; conversely, the larger the value of λ, the more significant the deviation of the gradation curve, the lower the proportion of fine aggregate, and the further the gap ratio of the mixture skeleton increases.

[0104] By continuously adjusting the deviation coefficient λ, discontinuous gradation mixtures with varying skeleton void ratios can be prepared to meet the design requirements of different asphalt mastic content. This, combined with the actual performance indicators of the FMA (Frequency Modified Asphalt Machining) material, allows for precise adjustment of the mix proportions. In summary, the design method for controlling the passing rate of key sieve openings and constructing FMA skeleton-type discontinuous gradation curves using the deviation coefficient is defined as the deviation coefficient method.

[0105] The aggregate used in the following examples is diabase with a particle size range of 0.075 mm to 13.2 mm. The specific parameters are shown in Table 1.

[0106] Table 1 Technical Specifications of Coarse and Fine Aggregates

[0107]

[0108] The λ-V described in the following embodiments ag Relational model ( Figure 1 ) and gradation curve ( Figure 2 The determination process is as follows:

[0109] (1) The maximum particle size of the gradation was determined to be 13.2 mm, according to the Talbol formula P i =100(d i / D) n Calculate the maximum throughput (d) of each sieve aperture to the power of 0.45. i These are the various particle sizes, for example: d i It is 0.15. 13.33, in %

[0110] =9.76, and so on), and the maximum density line can be formed, at which point the deviation coefficient λ is 0;

[0111] Maximum particle size D maxThe throughput for the minimum particle size of 0.075mm is still taken as the corresponding value on the maximum density line. With 4.75mm as the critical particle size, the maximum density line of the aggregate is deviated from, with a deviation coefficient λ ranging from 0 to 1. The deviation coefficient range (0-1) is quantified and graded with a gradient of 0.1, resulting in λ = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1. A broken-line gradation curve deviating from the maximum density line is constructed by connecting three points (e.g., maximum particle size, critical particle size, and particle size 0.075mm), resulting in 10 discontinuous gradation curves with different deviation coefficients. These gradation curves are plotted as shown in the figure. Figure 2 As shown;

[0112] The V of each discontinuous graded aggregate was determined using a wet-mix test method (referring to the Marshall method disclosed in patent application 202510470312.7). ag V was measured for each gradation under different deviation coefficients. ag (Table 2) The obtained data can be used for regression analysis to obtain λ-V. ag Relational models such as Figure 1 (V) ag =a + bλ, where a = 23.84 ± 0.19, b = 14.80 ± 0.32, and λ is the deviation coefficient, ranging from 0 to 1. The fitted R-squared value is > 0.99, indicating that the fitting result is ideal.

[0113] Table 2 V of gradation under each deviation coefficient ag value

[0114]

[0115] Figure 1 The λ-V shown ag V in the relational model ag The value is the original value of the skeleton gap ratio measured by the wet method on indoor Marshall specimens.

[0116] Example 1:

[0117] In this embodiment, the maximum particle size of the gradation was determined to be 13.2 mm, and the required oil-aggregate ratio (P) was determined for the experiment. a The content of the filler is 7.0, the powder-to-binder ratio (F / A) is 1, and the filler content is F. d For FMA with an internal porosity VV of 1 and 0, the equivalent adhesive usage is 13.08%.

[0118] 1. The conversion process for adhesive usage is as follows:

[0119] (1) Conversion of asphalt content (based on 100g of mixture)

[0120]

[0121] Asphalt quality: M 沥青 =100 × 6.5421% = 6.5421 g

[0122] Mineral powder mass: From F / A=1.0, we get M 矿粉 =M 沥青 =6.5421 g

[0123] (2) Calculation of adhesive dosage

[0124]

[0125] Substitute parameters: .

[0126] 2. Constructing discontinuous gradation design of FMA using the deviation coefficient method

[0127] Step 1: Based on actual needs, determine the maximum particle size of the gradation to be 13.2 mm, and the amount of FMA adhesive P to be used. ma It was 13.08%;

[0128] Step 2: Calculate the V corresponding to the required adhesive content of 13.08% using the MAFF method. ag It was 21.26%. Aggregate dosage, mortar dosage, and V... ag The relationship between the parameters is shown in formulas (2) and (3):

[0129] P ag +P ma =100 (2)

[0130] In the formula:

[0131] P ag This refers to the aggregate usage (by weight) of the FMA mixture.

[0132] P ma The amount of adhesive used in the FMA mixture (by weight percentage).

[0133] (3)

[0134] In the formula:

[0135] V ag The skeleton gap ratio of the FMA mixture;

[0136] VV represents the designed internal porosity, which is 0 in this embodiment;

[0137] F d For fill factor, the value in this embodiment is 1.0;

[0138] γ c Bulk density of aggregate in compacted or compacted state;

[0139] P ma0 The amount of adhesive paste used (by weight) can be determined through a mixing test.

[0140] γ ma The relative density of the adhesive paste during synthesis;

[0141] Step 3: Calculate the V corresponding to a glue content of 13.08% under the conditions of this embodiment using the MAFF method in Step 2. ag It is 21.26%; V ag Multiply the value by the reduction factor of 0.84, then substitute it into the equation. Figure 1 The λ-V shown ag The value of λ calculated in the relational model is 0.1.

[0142] Step 4: Substitute λ=0.1 into the equation. Figure 2 The FMA gradation design required for this actual situation can be obtained by using the deviation coefficient method in the gradation curve diagram shown (see Table 3).

[0143] The specific steps are as follows: Calculate the passing rate P of the critical particle size of 4.75mm under λ=0.1: P=P2-λ(P2-P3), where P2 and P3 are the sieve passing rates of the critical particle size of 4.75mm and 0.075mm respectively on the maximum density line; then, use linear interpolation to determine the sieve passing rates of the other aggregate grades.

[0144] Table 3. Passing rate of each aggregate grade when λ is 0.1

[0145]

[0146] In step 2 above, the bulk density γ of the aggregate in the compacted or compacted state is... c Also known as the compacted density of aggregates, the experiment is conducted according to the Marshall method disclosed in patent application 202510470312.7. First, FMA specimens are molded according to the mix proportions, and then their height, base area, and weight are measured to calculate their density, which is γ. c γ can be obtained c =2.25g / cm 3 (in λ-V) ag (Measured during the determination of the relational model).

[0147] The relative density γ of the gel synthesis ma According to the formula γ ma =100 / ( P b / ρ b +P f / ρ f P is obtained. b Pf The percentages of asphalt and mineral powder by mass (in %) are ρ. b ρ f These are the relative densities of asphalt and mineral powder, respectively (dimensionless, calculated according to the "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025)). In reality, VV cannot be 100% zero; it is recommended to use 0.5% for calculation. In this embodiment, since the powder-to-binder ratio is 1, P... b P f Both are 50; ρ b ρ f Given 1.03 and 2.817 respectively, we can obtain γ ma =1.508;

[0148] P ma0 The actual measured value in the mixing test was 5.4% (JTG E20-2011 T 0762 Asphalt Mixture Mixing Test).

[0149] Substituting the above parameters into equation (3) yields the V corresponding to the required amount of adhesive. ag It is 21.26%.

[0150] Track performance verification

[0151] This test case verifies the rutting performance of FMA from Example 1 (maximum particle size 13.2 mm, oil-aggregate ratio 7.0, powder-to-binder ratio 1.0, filling degree 1, internal porosity 0). The specific test procedure is as follows:

[0152] (1) According to the gradation design method described above, the value of λ under this condition can be taken as 0.1. Substituting this into the equation... Figure 2 Calculate the content of aggregates, asphalt and mineral powder, and form rutted slab specimens according to the T 0703-2025 standard in the "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025);

[0153] (2) Rutting tests shall be conducted in accordance with T 0719-2025 of the "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025);

[0154] (3) The data recorded by the rutting tester is shown in Table 4. It can be seen that the rutting performance of FMA with an asphalt-aggregate ratio of 7.0 under this design method meets the requirement of rutting dynamic stability greater than 3000 times / mm in the "Technical Specification for Construction of Highway Asphalt Pavement" (JTG F40-2004).

[0155] Table 4. Dynamic stability of FMA-13 ​​at an oil-stone ratio of 7.0

[0156]

[0157] Example 2:

[0158] The maximum particle size in this embodiment is 13.2 mm. The test requires FMA with an oil-stone ratio of 8.0, a powder-to-binder ratio of 1, a filling degree of 1, and an internal porosity of 0, which translates to a glue content of 14.81%.

[0159] The process of obtaining the gradation design of FMA using the deviation coefficient method is as follows:

[0160] Step 1: Based on actual needs, determine the maximum particle size of the gradation to be 13.2 mm and the amount of FMA adhesive to be 14.81%;

[0161] Step 2: Calculate the V value corresponding to a required adhesive content of 14.81% using the MAFF method. ag It was 23.49%. Aggregate dosage, mortar dosage, and V... ag The relationship between the parameters is shown in formulas (2) and (3):

[0162] P ag +P ma =100 (2)

[0163] In the formula:

[0164] P ag This refers to the aggregate usage (by weight) of the FMA mixture.

[0165] P ma The amount of adhesive used in the FMA mixture (by weight percentage).

[0166] (3)

[0167] In the formula:

[0168] V ag The skeleton gap ratio of the FMA mixture;

[0169] VV represents the designed internal porosity, which is 0 in this embodiment;

[0170] F d For fill factor, the value in this embodiment is 1.0;

[0171] γ c The bulk density of aggregate in compacted or compacted state; in λ-V ag The determination of the relational model has been measured;

[0172] P ma0 The amount of adhesive mortar used (by weight percentage) was 5.4% as measured by the mixing test (JTG E20-2011 T0762 Asphalt Mixture Mixing Test).

[0173] γ ma γ represents the relative density of the adhesive paste during synthesis. ma =1.508, the test method is described in Example 1;

[0174] Step 3: Calculate the V corresponding to a glue content of 14.81% under these conditions using the MAFF method described in Step 2. ag It is 23.49%, V ag Multiply the value by the reduction factor of 0.84, then substitute it into the equation. Figure 1 The λ-V shown ag The value of λ calculated in the relational model is 0.28.

[0175] Step 4: Substitute the value of λ into Figure 2 The FMA gradation design required for this actual situation can be obtained by using the deviation coefficient method (see Table 5). For the specific calculation method, please refer to Example 1.

[0176] Table 5. Passing rate of aggregates at a λ value of 0.28

[0177]

[0178] Track performance verification

[0179] This test case verifies the rutting performance of FMA from Example 2 (maximum particle size 13.2 mm, oil-aggregate ratio 8.0, powder-to-binder ratio 1.0, filling degree 1, internal porosity 0). The specific test procedure is as follows:

[0180] (1) According to the gradation design method mentioned above, the λ value under this condition can be taken as 0.28. Substitute it into the formula to calculate the content of aggregate, asphalt and mineral powder, and form rutted slab specimens according to the T 0703-2025 standard in the "Test Procedure for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025).

[0181] (2) Rutting tests shall be conducted in accordance with T 0719-2025 of the "Test Procedures for Asphalt and Asphalt Mixtures in Highway Engineering" (JTG 3410-2025);

[0182] (3) The data recorded by the rutting tester is shown in Table 6. It can be seen that the rutting performance of FMA with an asphalt-aggregate ratio of 8.0 under this design method meets the requirement of rutting dynamic stability greater than 3000 times / mm in the "Technical Specification for Construction of Highway Asphalt Pavement" (JTG F40-2004).

[0183] Table 6. Dynamic stability of FMA-13 ​​at an oil-stone ratio of 8.0

[0184]

[0185] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A deviation coefficient method for designing discontinuous gradation skeletons of flowable asphalt mixtures, characterized in that, Includes the following steps: Step 1: Determine the maximum particle size D of the gradation max According to the Talbol formula P i =100(d i / D) n The maximum throughput of each sieve aperture is calculated by raising the sieve aperture to the power of 0.45, which forms the maximum density line. At this point, the deviation coefficient λ is 0. Maximum particle size D max The passing rate of the minimum particle size of 0.075 mm is taken as the corresponding value on the maximum density line. With 4.75 mm or 2.36 mm as the key particle size, the maximum density line is deviated, and the deviation coefficient λ is 0~1. The deviation of the maximum density line is achieved by setting the value range of the deviation coefficient λ with a gradient of 0.1 to quantify and classify it, resulting in 10 discontinuous gradation curves with different deviation coefficients. The 10 discontinuous gradation curves with different deviation coefficients obtained from the deviation processing are plotted as a gradation curve diagram. The skeleton gap ratio V of each discontinuous gradation aggregate was determined using the wet mix test method. ag V was measured for each gradation under different deviation coefficients. ag λ-V can be obtained through post-regression analysis. ag The relational model is shown in equation (1): V ag =a+bλ (1) In the formula: a is V when the deviation coefficient λ is 0. ag Value, that is, the value on the maximum density line; b represents the deviation coefficient affecting V. ag The dominant factor is the slope of the model; λ is the deviation coefficient, which ranges from 0 to 1; Step 2: Determine the maximum particle size D of the gradation according to the actual needs. max And the amount of adhesive P used in FMA ma ; Step 3: Calculate the V corresponding to the required amount of adhesive using the MAFF method. ag ; Step 4: Calculate V in Step 3. ag Substituting into equation (1) shows λ-V ag In the relational model, determine the corresponding deviation coefficient λ value; Step 5: First, calculate the throughput P of the critical particle size under any deviation coefficient λ using equation (4): P = P2 - λ(P2 - P3) (4) In the formula, P2 and P3 are the critical particle size and the sieve aperture passing rate of 0.075 mm corresponding to the maximum density line, respectively; Then, the sieve passing rate of the remaining aggregates is determined by linear interpolation, thus obtaining the FMA skeleton discontinuous gradation design.

2. The deviation coefficient method for discontinuous gradation skeleton design of flowable asphalt mixture according to claim 1, characterized in that, The maximum particle size D mentioned in steps 1 and 2 max same.

3. The deviation coefficient method for discontinuous gradation skeleton design of fluidized asphalt mixtures according to claim 1, characterized in that, Step 3 calculates V ag Multiply by the reduction factor α and then substitute into equation (1) λ-V ag In the relational model, α is 0.7-0.

9.

4. The deviation coefficient method for discontinuous gradation skeleton design of fluidized asphalt mixtures according to claim 1, characterized in that, In step 3 of the MAFF method, the aggregate dosage, binder dosage, and V of the FMA mixture are... ag The relationship is shown in formulas (2) and (3): P ag +P ma =100 (2) P ag This refers to the aggregate content of the FMA mixture, expressed as a weight percentage. P ma This refers to the amount of adhesive used in the FMA mixture, expressed as a weight percentage. （3） V ag The skeleton gap ratio of the FMA mixture; VV represents the design internal porosity; the measured internal porosity of FMA is typically less than 1%. F d The filling degree represents the extent to which the adhesive fills the voids in the skeleton, and its value ranges from 0 to 1.

0. γ c The bulk density of aggregates in compacted or compacted state, also known as the compacted density of aggregates, is measured in practice. P ma0 The amount of adhesive paste used, by weight percentage, was measured through a mixing test. γ ma The relative density of the adhesive paste is the synthetic density.

5. The deviation coefficient method for discontinuous gradation skeleton design of fluidized asphalt mixtures according to claim 1, characterized in that, In step 5, the key particle size is 4.75 mm or 2.36 mm; The linear interpolation method involves drawing lines between 0.075mm and the critical particle size, and between the critical particle size and 13.2mm, respectively. Based on the location of the sieve aperture pass rate of the critical particle size, the sieve aperture pass rate of the remaining aggregates is determined by linear interpolation.

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