A method for evaluating three-dimensional spatial heterogeneity of a core region of a granular random packing system

Abstract

The application discloses a method for evaluating three-dimensional spatial heterogeneity of a core region of a granular random packing system, and belongs to the technical field of performance evaluation of road asphalt mixture.The application solves the problem that the spatial heterogeneity of the granular random packing system cannot be evaluated in the prior art.The application detects the edge of the edge wall effect influence region by using the mutation characteristics of the distribution of foreground pixels (aggregate or void) in three-dimensional space, locks the core distribution analysis region, and further develops multiple fractal analysis to obtain a spatial probability distribution wide degree index Wid and a dominant component dominant degree evaluation index Dom, so as to evaluate the non-homogeneous characteristics of the three-dimensional microstructure of the asphalt mixture.The method can be applied to performance evaluation of road asphalt mixture.

Description

Technical Field

[0001] This invention belongs to the technical field of performance evaluation of road asphalt mixtures, specifically relating to a three-dimensional spatial heterogeneity evaluation method for the core region of a randomly packed particle system. Background Technology

[0002] Traditional microscopic mechanical calculations typically treat asphalt mixtures as homogeneous materials. However, with in-depth research, this equivalence has severely impacted the accuracy of calculations and subsequent analysis. In fact, hot-mix asphalt mixtures (HMAs) exhibit typical heterogeneous properties in their composition, meaning they possess three-dimensional spatial heterogeneity. From a microscopic perspective, HMAs consist of coarse aggregates, asphalt mortar, and voids. The asphalt mortar, composed of asphalt binder, mineral fillers, and some fine aggregates, exhibits strong viscoelastic properties, making its mechanical properties relatively easy to obtain using rheological experiments. However, the irregular shapes and random spatial distribution of the coarse aggregates and voids are difficult to characterize, which is also the main source of the three-dimensional spatial heterogeneity of asphalt mixtures—a system of randomly packed particles. This three-dimensional spatial heterogeneity not only makes evaluation difficult but also poses significant challenges to the analysis and calculation of the mechanical properties of HMAs. Therefore, it is essential to effectively evaluate and analyze the non-uniform characteristics of the internal structure of asphalt mixtures.

[0003] In recent years, the analysis of microstructural features using digital image processing (DIP) and non-destructive testing techniques (such as industrial CT) has been considered capable of providing reliable structural characterization parameters for randomly packed particle systems. For coarse aggregate skeletons with very fine structures, the microstructural features are mainly related to the distribution, orientation, and contact relationships of the internal aggregates; similarly, the internal structural system composed of voids is also related to the statistical characteristics of the distribution of voids of different sizes. Although a large amount of research has been conducted in this field, many challenges remain to be overcome. On the one hand, the irregular geometry of voids and aggregate particles means that the evaluation and analysis of the internal structure cannot rely on a single mathematical index; theoretically, describing heterogeneity in nature requires nearly infinite mathematical parameters. On the other hand, the tortuousness of void formation paths further complicates the process; in particular, the complex and varied design and construction conditions of asphalt pavements lead to structural variations, thus making single microstructural evaluation techniques unsustainable, requiring a powerful mathematical tool to compensate for these shortcomings. In summary, existing technologies still cannot evaluate the strong spatial heterogeneity of randomly packed particle systems, making it essential to propose a three-dimensional spatial heterogeneity evaluation method for asphalt mixtures. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing technologies cannot evaluate the spatial heterogeneity of randomly packed particle systems, and to propose a three-dimensional spatial heterogeneity evaluation method for the core region of randomly packed particle systems.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] A method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system, the method specifically includes the following steps:

[0007] Step 1: Prepare cylindrical specimens of asphalt mixture and place them on an industrial CT stage. Perform X-ray scanning on the cylindrical specimens of asphalt mixture on the industrial CT stage to obtain raw industrial CT data.

[0008] The raw industrial CT data is reconstructed in three dimensions to obtain the aggregate skeleton and void structure. The aggregate particles in the aggregate skeleton structure are screened and the aggregate particles with a screen size less than or equal to the threshold are removed. The remaining aggregate particle system is used as the processed aggregate skeleton structure.

[0009] Step 2: Determine the boundaries of the regions in the void structure and the treated aggregate skeleton structure that are not affected by the sidewall effect;

[0010] Step 3: Cut the three-dimensional spatial matrix of the void structure and the processed aggregate skeleton structure according to the boundary determined in Step 2 to obtain the cut three-dimensional void structure and aggregate skeleton structure.

[0011] Multiple fractal analysis was conducted on the three-dimensional void structure and aggregate skeleton structure after cutting.

[0012] Step 4: Based on the results of multifractal analysis, evaluate the three-dimensional spatial heterogeneity of the cylindrical specimens of the mixture, and analyze the mechanical properties of the asphalt mixture based on the evaluation results.

[0013] The beneficial effects of this invention are:

[0014] This invention first combines DIP technology and high-precision industrial CT scanning technology to propose an effective scheme for evaluating the spatial heterogeneity of random particle packing systems within asphalt mixtures. By utilizing the abrupt changes in the distribution of foreground pixels (aggregates or voids) in three-dimensional space, the edges of the boundary effect-affected regions are detected, thereby locking down the core distribution analysis area. Further multifractal analysis is conducted to obtain the spatial probability distribution breadth index Wid and the dominant component dominance index Dom, which are used to evaluate the heterogeneous characteristics of the three-dimensional microstructure of asphalt mixtures, i.e., to evaluate the three-dimensional spatial heterogeneity of asphalt mixtures. The heterogeneity evaluation index proposed in this invention has high sensitivity and strong applicability to the spatial randomness and variation characteristics of asphalt mixtures. It not only enriches the microstructure evaluation system but also serves as a methodological basis for revealing the relationship between the microstructure characteristics and mechanical properties of asphalt mixtures. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method of the present invention;

[0016] Figure 2 This is a schematic diagram of multifractal spectrum and parameter calculation;

[0017] Figure 3 This is a schematic diagram of the horizontal sidewall effect analysis in Example 1;

[0018] Figure 4 This is a schematic diagram of the vertical sidewall effect analysis in Example 1;

[0019] Figure 5 This is a schematic diagram of the horizontal sidewall effect analysis in Example 2;

[0020] Figure 6 This is a schematic diagram of the vertical sidewall effect analysis in Example 2. Detailed Implementation

[0021] The present application will now be described in further detail with reference to specific embodiments and accompanying drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention, and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are all within the scope of protection of the present invention.

[0022] Specific Implementation Method 1: Combination Figure 1 This embodiment describes a method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system. The method specifically includes the following steps:

[0023] Step 1: Prepare cylindrical specimens of asphalt mixture and place them on an industrial CT stage. Perform X-ray scanning on the cylindrical specimens of asphalt mixture on the industrial CT stage to obtain raw industrial CT data.

[0024] The raw industrial CT data is reconstructed in three dimensions to obtain the aggregate skeleton and void structure. The aggregate particles in the aggregate skeleton structure are screened using a real three-dimensional virtual screening method for asphalt mixture. Aggregate particles with a screen size (screen size refers to the aperture of the square hole sieve through which aggregate particles can pass) less than or equal to the threshold are removed. The remaining aggregate particle system is used as the processed aggregate skeleton structure.

[0025] Step 2: Determine the boundaries of the regions in the void structure and the treated aggregate skeleton structure that are not affected by the sidewall effect; the regions not affected by the sidewall effect are the core regions of the random particle packing system.

[0026] Step 3: Cut the three-dimensional spatial matrix of the void structure and the processed aggregate skeleton structure according to the boundary determined in Step 2 to obtain the cut three-dimensional void structure and aggregate skeleton structure (i.e., obtain the void structure and aggregate skeleton structure in the region unaffected by the sidewall effect).

[0027] Multiple fractal analysis was conducted on the three-dimensional void structure and aggregate skeleton structure after cutting.

[0028] Step 4: Evaluate the three-dimensional spatial heterogeneity of the cylindrical specimens of the asphalt mixture based on the multifractal analysis results, and analyze the mechanical properties of the asphalt mixture based on the evaluation results. The performance analysis results can guide the optimization of asphalt mixture performance.

[0029] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the cylindrical asphalt mixture specimens are prepared by rotary compaction molding or Marshall molding.

[0030] The other steps and parameters are the same as in Specific Implementation Method 1.

[0031] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that it removes aggregate particles with a screening size less than or equal to a threshold value of 1.18 mm.

[0032] Other steps and parameters are the same as in specific implementation method one or two.

[0033] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the specific process of step two is as follows:

[0034] Step 21: For void structures, use void particles as foreground pixels;

[0035] Step 2: Along the height direction of the cylindrical specimen of asphalt mixture, take a cylindrical slice at every Δh, calculate the pixel ratio of the foreground pixel in each cylindrical slice, and draw the curve l1 of the pixel ratio of the foreground pixel as a function of the slice height.

[0036] Steps 2 and 3: Along the radial direction of the cylindrical specimen of asphalt mixture, starting from the axis of the cylindrical specimen, take a circumferential slice at every Δr interval, calculate the pixel ratio of the foreground pixel in each circumferential slice, and draw the curve l2 of the pixel ratio of the foreground pixel as a function of the slice radius.

[0037] Step 24: From the various maxima of the curve showing the change in the pixel ratio of the foreground pixels as a function of the slice height, select the two largest maxima; denote the heights corresponding to the two selected maxima as h. 11 and h 12 , and h 12 >h 11 From the maximum values ​​of the curve showing the change of the pixel ratio of the foreground pixels with the slice radius, select the radius corresponding to the largest maximum value and denote the radius corresponding to the largest maximum value as r1.

[0038] Step 25: For the processed aggregate skeleton structure, use the methods in Step 21 to Step 23 to draw the curve l3 showing the change of the pixel ratio of the foreground pixel with the slice height and the curve l4 showing the change of the pixel ratio of the foreground pixel with the slice radius (the aggregate skeleton particles are used as the foreground pixels when drawing).

[0039] Then, from the various maxima of curve l3, select the two largest maxima, and denote the heights corresponding to the two selected maxima as h. 21 and h 22 , and h 22 >h 21 From the maxima of curve l4, select the radius r2 corresponding to the largest maximum value;

[0040] Step 26: For the cylindrical asphalt mixture specimens, the height range is max(h) 11 ,h 21 )≤h≤min(h 12 ,h 22 ), and all voxel points within the radius range of r ≤ min(r1,r2) are considered as regions unaffected by the wall effect, max(h 11 ,h 21 )≤h≤min(h 12 ,h 22 The height boundary of the region is r, and the radius boundary of the region is r≤min(r1,r2).

[0041] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0042] Specific Implementation Method 5: This implementation method differs from Specific Implementation Methods 1 to 4 in that the value of Δh is 0.01mm.

[0043] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0044] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the value of Δr is 0.01mm.

[0045] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0046] Specific implementation method seven: Combination Figure 2 This embodiment is described below. The difference between this embodiment and one of the specific embodiments one through six is ​​that, in step three, multifractal analysis is performed on the cut three-dimensional void structure and the aggregate skeleton structure, respectively; specifically:

[0047] Multifractal analysis was performed on the three-dimensional void structure, and multifractal spectra f1(α)~α were plotted based on the analysis results. Here, α is the abscissa of the multifractal spectrum, and f1(α) is the ordinate of the multifractal spectrum of the void structure. Then, the difference Δα1 between the two endpoints of the multifractal spectrum f1(α)~α in the horizontal direction and the absolute value Δf1(α) between the two endpoints in the vertical direction were calculated.

[0048] Multifractal analysis was performed on the three-dimensional aggregate skeleton structure, and the multifractal spectrum f2(α)~α was plotted based on the analysis results. Here, f2(α) is the ordinate of the multifractal spectrum of the aggregate skeleton structure. Then, the difference Δα2 between the two endpoints of the multifractal spectrum f2(α)~α in the horizontal direction and the absolute value Δf2(α) between the two endpoints in the vertical direction were calculated.

[0049] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0050] Specific Implementation Method Eight: This implementation method differs from one of the specific implementation methods one to seven in that, in step four, the evaluation of the three-dimensional spatial heterogeneity of the cylindrical specimen of the mixture requires the calculation of the spatial probability distribution breadth index and the dominant component dominance evaluation index.

[0051] The improvement in both classifications indicates stronger three-dimensional spatial heterogeneity in the randomly packed particle system.

[0052] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0053] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the calculation method of the spatial probability distribution breadth index is: Wid = Ceil((Δα1-0.3) / 0.05) + Ceil(Δα2 / 0.04), where Wid is the spatial probability distribution breadth index and Ceil(·) is the rounding up of the number.

[0054] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0055] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the calculation method of the dominant component dominance evaluation index is: Dom=Ceil((Δf1(α)-0.3) / 0.05)+Ceil(Δf2(α) / 0.04), where Dom is the dominant component dominance evaluation index.

[0056] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0057] Example 1

[0058] The present invention provides a method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system, the method specifically comprising the following steps:

[0059] Step 1: Prepare cylindrical specimens of asphalt concrete (AC) by rotary compaction.

[0060] The prepared cylindrical asphalt mixture specimen was placed on an industrial CT stage, and X-ray scanning was performed on the cylindrical asphalt mixture specimen on the industrial CT stage to obtain the raw industrial CT data.

[0061] The raw industrial CT data is reconstructed in three dimensions to obtain the aggregate skeleton and void structure. The aggregate particles in the aggregate skeleton structure are screened using a real three-dimensional virtual screening method for asphalt mixture. Aggregate particles with a screen size (screen size refers to the aperture of the square hole sieve through which aggregate particles can pass) less than or equal to the threshold are removed. The remaining aggregate particle system is used as the processed aggregate skeleton structure.

[0062] The aggregate skeleton particles are grouped into 16mm, 13.2mm, 9.5mm, 4.75mm, and 2.36mm.

[0063] Step Two, as follows Figure 3 and Figure 4 As shown, the boundaries of the regions in the void structure and the treated aggregate skeleton structure that are not affected by the sidewall effect are determined; the regions that are not affected by the sidewall effect are the core regions of the random particle packing system.

[0064] Step 21: For void structures, use void particles as foreground pixels;

[0065] Step 2: Along the height direction of the cylindrical asphalt mixture specimen, take a cylindrical slice every 0.01 mm, calculate the pixel ratio of the foreground pixel in each cylindrical slice, and plot the curve l1 of the pixel ratio of the foreground pixel as a function of the slice height.

[0066] Steps 2 and 3: Along the radial direction of the cylindrical asphalt mixture specimen, starting from the axis of the cylindrical specimen, take a circumferential slice every 0.01 mm, calculate the pixel ratio of the foreground pixel in each circumferential slice, and draw the curve l2 of the pixel ratio of the foreground pixel as a function of the slice radius.

[0067] Step 24: From the various maxima of the curve showing the change in the pixel ratio of the foreground pixels as a function of the slice height, select the two largest maxima; denote the heights corresponding to the two selected maxima as h. 11 and h 12 , and h 12 >h 11 From the maximum values ​​of the curve showing the change of the pixel ratio of the foreground pixels with the slice radius, select the radius corresponding to the largest maximum value and denote the radius corresponding to the largest maximum value as r1.

[0068] Step 25: For the processed aggregate skeleton structure, use the methods in Step 21 to Step 23 to draw the curve l3 showing the change of the pixel ratio of the foreground pixel with the slice height and the curve l4 showing the change of the pixel ratio of the foreground pixel with the slice radius (the aggregate skeleton particles are used as the foreground pixels when drawing).

[0069] Then, from the various maxima of curve l3, select the two largest maxima, and denote the heights corresponding to the two selected maxima as h. 21 and h 22 , and h 22 >h 21 From the maxima of curve l4, select the radius r2 corresponding to the largest maximum value;

[0070] Step 26: For the cylindrical asphalt mixture specimens, the height range is max(h) 11 ,h 21 )≤h≤min(h 12 ,h 22 ), and all voxel points within the radius range of r ≤ min(r1,r2) are considered as regions unaffected by the wall effect, max(h 11 ,h 21 )≤h≤min(h12 ,h 22 The height boundary of the region is r, and the radius boundary of the region is r≤min(r1,r2).

[0071] Step 3: Cut the three-dimensional spatial matrix of the void structure and the processed aggregate skeleton structure according to the boundary determined in Step 2 to obtain the cut three-dimensional void structure and aggregate skeleton structure.

[0072] Multiple fractal analysis was conducted on the three-dimensional void structure and aggregate skeleton structure after cutting.

[0073] In step three, multifractal analysis is performed on the cut three-dimensional void structure and aggregate skeleton structure, respectively; specifically:

[0074] Multifractal analysis was performed on the three-dimensional void structure, and multifractal spectra f1(α)~α were plotted based on the analysis results, where α is the abscissa of the multifractal spectrum and f1(α) is the ordinate of the multifractal spectrum of the void structure. The difference between the two endpoints of the multifractal spectrum f1(α)~α in the horizontal direction was calculated to be Δα1=0.315, and the absolute value of the difference between the two endpoints in the vertical direction was Δf1(α)=0.325.

[0075] Multifractal analysis was performed on the three-dimensional aggregate skeleton structure, and the multifractal spectrum f2(α)~α was plotted based on the analysis results. Here, f2(α) is the ordinate of the multifractal spectrum of the aggregate skeleton structure. The difference between the two endpoints of the multifractal spectrum f2(α)~α in the horizontal direction was calculated as Δα2=0.012, and the absolute value of the difference between the two endpoints in the vertical direction was calculated as Δf2(α)=0.035.

[0076] Step 4: Evaluate the three-dimensional spatial heterogeneity of the cylindrical specimens of the mixture based on the results of multifractal analysis;

[0077] The method for calculating the breadth index of the spatial probability distribution is as follows:

[0078] Wid=Ceil((Δα1-0.3) / 0.05)+Ceil(Δα2 / 0.04)

[0079] Where Wid is an index of the breadth of the spatial probability distribution, and Ceil(·) is the rounding up of the number;

[0080] The calculation method for the dominance index of the dominant component is as follows:

[0081] Dom=Ceil((Δf1(α)-0.3) / 0.05)+Ceil(Δf2(α) / 0.04)

[0082] Among them, Dom is the evaluation index of the degree of dominance of the dominant component;

[0083] In this embodiment, Wid = 2 and Dom = 2 were calculated. The increase in both grades indicates that the three-dimensional spatial heterogeneity of the randomly packed particle system is stronger.

[0084] Example 2

[0085] The present invention provides a method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system, the method specifically comprising the following steps:

[0086] Step 1: Prepare cylindrical specimens of asphalt mixture (stone matrix asphalt, abbreviated as SMA) using the Marshall molding method;

[0087] The prepared cylindrical asphalt mixture specimen was placed on an industrial CT stage, and X-ray scanning was performed on the cylindrical asphalt mixture specimen on the industrial CT stage to obtain the raw industrial CT data.

[0088] The raw industrial CT data is reconstructed in three dimensions to obtain the aggregate skeleton and void structure. The aggregate particles in the aggregate skeleton structure are screened using a real three-dimensional virtual screening method for asphalt mixture. Aggregate particles with a screen size (screen size refers to the aperture of the square hole sieve through which aggregate particles can pass) less than or equal to the threshold are removed. The remaining aggregate particle system is used as the processed aggregate skeleton structure.

[0089] The aggregate skeleton particles are grouped into 13.2mm, 9.5mm, 4.75mm, and 2.36mm.

[0090] Step 2, as follows Figure 5 and Figure 6 As shown, the boundaries of the regions in the void structure and the treated aggregate skeleton structure that are not affected by the sidewall effect are determined; the regions that are not affected by the sidewall effect are the core regions of the random particle packing system.

[0091] Step 21: For void structures, use void particles as foreground pixels;

[0092] Step 2: Along the height direction of the cylindrical asphalt mixture specimen, take a cylindrical slice every 0.01 mm, calculate the pixel ratio of the foreground pixel in each cylindrical slice, and plot the curve l1 of the pixel ratio of the foreground pixel as a function of the slice height.

[0093] Steps 2 and 3: Along the radial direction of the cylindrical asphalt mixture specimen, starting from the axis of the cylindrical specimen, take a circumferential slice every 0.01 mm, calculate the pixel ratio of the foreground pixel in each circumferential slice, and draw the curve l2 of the pixel ratio of the foreground pixel as a function of the slice radius.

[0094] Step 24: From the various maxima of the curve showing the change in the pixel ratio of the foreground pixels as a function of the slice height, select the two largest maxima; denote the heights corresponding to the two selected maxima as h. 11 and h 12 , and h 12 >h 11 From the maximum values ​​of the curve showing the change of the pixel ratio of the foreground pixels with the slice radius, select the radius corresponding to the largest maximum value and denote the radius corresponding to the largest maximum value as r1.

[0095] Step 25: For the processed aggregate skeleton structure, use the methods in Step 21 to Step 23 to draw the curve l3 showing the change of the pixel ratio of the foreground pixel with the slice height and the curve l4 showing the change of the pixel ratio of the foreground pixel with the slice radius (the aggregate skeleton particles are used as the foreground pixels when drawing).

[0096] Then, from the various maxima of curve l3, select the two largest maxima, and denote the heights corresponding to the two selected maxima as h. 21 and h 22 , and h 22 >h 21 From the maxima of curve l4, select the radius r2 corresponding to the largest maximum value;

[0097] Step 26: For the cylindrical asphalt mixture specimens, the height range is max(h) 11 ,h 21 )≤h≤min(h 12 ,h 22 ), and all voxel points within the radius range of r ≤ min(r1,r2) are considered as regions unaffected by the wall effect, max(h 11 ,h 21 )≤h≤min(h 12 ,h 22 The height boundary of the region is r, and the radius boundary of the region is r≤min(r1,r2).

[0098] Step 3: Cut the three-dimensional spatial matrix of the void structure and the processed aggregate skeleton structure according to the boundary determined in Step 2 to obtain the cut three-dimensional void structure and aggregate skeleton structure.

[0099] Multiple fractal analysis was conducted on the three-dimensional void structure and aggregate skeleton structure after cutting.

[0100] In step three, multifractal analysis is performed on the cut three-dimensional void structure and aggregate skeleton structure, respectively; specifically:

[0101] Multifractal analysis was performed on the three-dimensional void structure, and multifractal spectra f1(α)~α were plotted based on the analysis results, where α is the abscissa of the multifractal spectrum and f1(α) is the ordinate of the multifractal spectrum of the void structure. The difference between the two endpoints of the multifractal spectrum f1(α)~α in the horizontal direction was calculated to be Δα1=0.448, and the absolute value of the difference between the two endpoints in the vertical direction was Δf1(α)=0.435.

[0102] Multifractal analysis was performed on the three-dimensional aggregate skeleton structure, and the multifractal spectrum f2(α)~α was plotted based on the analysis results. Here, f2(α) is the ordinate of the multifractal spectrum of the aggregate skeleton structure. The difference between the two endpoints of the multifractal spectrum f2(α)~α in the horizontal direction was calculated as Δα2=0.031, and the absolute value of the difference between the two endpoints in the vertical direction was calculated as Δf2(α)=0.078.

[0103] Step 4: Evaluate the three-dimensional spatial heterogeneity of the cylindrical specimens of the mixture based on the results of multifractal analysis;

[0104] The method for calculating the breadth index of the spatial probability distribution is as follows:

[0105] Wid=Ceil((Δα1-0.3) / 0.05)+Ceil(Δα2 / 0.04)

[0106] Where Wid is an index of the breadth of the spatial probability distribution, and Ceil(·) is the rounding up of the number;

[0107] The calculation method for the dominance index of the dominant component is as follows:

[0108] Dom=Ceil((Δf1(α)-0.3) / 0.05)+Ceil(Δf2(α) / 0.04)

[0109] Among them, Dom is the evaluation index of the degree of dominance of the dominant component;

[0110] In this embodiment, Wid = 4 and Dom = 5 were calculated. The increase in both grades indicates that the three-dimensional spatial heterogeneity of the randomly packed particle system is stronger.

[0111] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system, characterized in that, The method specifically includes the following steps: Step 1: Prepare cylindrical specimens of asphalt mixture and place them on an industrial CT stage. Perform X-ray scanning on the cylindrical specimens of asphalt mixture on the industrial CT stage to obtain raw industrial CT data. The raw industrial CT data is reconstructed in three dimensions to obtain the aggregate skeleton and void structure. The aggregate particles in the aggregate skeleton structure are screened and the aggregate particles with a screen size less than or equal to the threshold are removed. The remaining aggregate particle system is used as the processed aggregate skeleton structure. Step 2: Determine the boundaries of the regions in the void structure and the treated aggregate skeleton structure that are not affected by the sidewall effect; The specific process of step two is as follows: Step 21: For void structures, use void particles as foreground pixels; Step 22: Along the height direction of the cylindrical asphalt mixture specimen, at intervals... Take a cylindrical slice image, calculate the pixel ratio of the foreground pixels in each cylindrical slice image, and plot the curve l1 of the pixel ratio of the foreground pixels as a function of the slice height. Steps 2 and 3: Along the radial direction of the cylindrical asphalt mixture specimen, starting from the center of the cylindrical specimen, at intervals... Take a ring-cut slice image, calculate the pixel ratio of the foreground pixels in each ring-cut slice image, and plot the curve l2 of the pixel ratio of the foreground pixels as a function of the slice radius. Step 24: From the various maxima of the curve showing the change in the pixel ratio of the foreground pixels as a function of the slice height, select the two largest maxima; denote the heights corresponding to the two selected maxima as h. 11 and h 12 , and h 12 >h 11 From the maximum values ​​of the curve showing the change of the pixel ratio of the foreground pixels with the slice radius, select the radius corresponding to the largest maximum value and denote the radius corresponding to the largest maximum value as r1. Step 25: For the processed aggregate skeleton structure, use the methods in Steps 21 to 23 to draw the curve l3 showing the change of the pixel ratio of the foreground pixels with the slice height and the curve l4 showing the change of the pixel ratio of the foreground pixels with the slice radius. Then, from the various maxima of curve l3, select the two largest maxima, and denote the heights corresponding to the two selected maxima as h. 21 and h 22 , and h 22 >h 21 From the maxima of curve l4, select the radius r2 corresponding to the largest maximum value; Step 26: For the cylindrical asphalt mixture specimens, the height range is max(h) 11 ,h 21 )≤h≤min(h 12 ,h 22 ), and all voxel points within the radius range of r ≤ min(r1,r2) are considered as regions unaffected by the wall effect, max(h 11 ,h 21 )≤h≤min(h 12 ,h 22 The height boundary of the region is r, and the radius boundary of the region is r≤min(r1,r2). Step 3: Cut the three-dimensional spatial matrix of the void structure and the processed aggregate skeleton structure according to the boundary determined in Step 2 to obtain the cut three-dimensional void structure and aggregate skeleton structure. Multiple fractal analysis was conducted on the three-dimensional void structure and aggregate skeleton structure after cutting. Step 4: Based on the results of multifractal analysis, evaluate the three-dimensional spatial heterogeneity of the cylindrical specimens of the mixture, and analyze the mechanical properties of the asphalt mixture based on the evaluation results.

2. The method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system according to claim 1, characterized in that, The cylindrical specimens of the asphalt mixture were prepared by rotary compaction or Marshall molding.

3. The method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system according to claim 2, characterized in that, The removal of aggregate particles with a screening size less than or equal to a threshold value of 1.18 mm.

4. The method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system according to claim 3, characterized in that, The The value is 0.01mm.

5. The method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system according to claim 4, characterized in that, The The value is 0.01mm.

6. The method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system according to claim 5, characterized in that, In step three, multifractal analysis is performed on the cut three-dimensional void structure and aggregate skeleton structure, respectively; specifically: Multifractal analysis was performed on the three-dimensional void structure, and the multifractal spectrum f1(α)~α was plotted based on the analysis results. Here, α is the abscissa of the multifractal spectrum, and f1(α) is the ordinate of the multifractal spectrum of the void structure. Then, the difference Δα1 between the two endpoints of the multifractal spectrum f1(α)~α in the horizontal direction and the absolute value Δf1(α) between the two endpoints in the vertical direction were calculated. Multifractal analysis was performed on the three-dimensional aggregate skeleton structure, and the multifractal spectrum f2(α)~α was plotted based on the analysis results. Here, f2(α) is the ordinate of the multifractal spectrum of the aggregate skeleton structure. Then, the difference Δα2 between the two endpoints of the multifractal spectrum f2(α)~α in the horizontal direction and the absolute value Δf2(α) between the two endpoints in the vertical direction were calculated.

7. The method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system according to claim 6, characterized in that, In step four, evaluating the three-dimensional spatial heterogeneity of the cylindrical specimens of the mixture requires calculating the breadth index of the spatial probability distribution and the dominance index of the dominant component.

8. The method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system according to claim 7, characterized in that, The calculation method for the spatial probability distribution breadth index is as follows: Wid=Ceil((Δα1-0.3) / 0.05)+Ceil(Δα2 / 0.04), where Wid is the spatial probability distribution breadth index and Ceil(·) is the rounding up of the number.

9. The method for evaluating the three-dimensional spatial heterogeneity of the core region of a randomly packed particle system according to claim 8, characterized in that, The calculation method for the dominant component dominance evaluation index is as follows: Dom=Ceil((Δf1(α)-0.3) / 0.05)+Ceil(Δf2(α) / 0.04), where Dom is the dominant component dominance evaluation index.

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