Method for calculating sand fineness modulus and grading

Abstract

The present application belongs to the field of civil engineering material research and application technology, and particularly relates to a method for measuring and calculating sand fineness modulus and grading, which is based on the relationship between two-dimensional mortar section particle size and three-dimensional real particle size, establishes the relationship between the number of particles in each group of two-dimensional section and the number of particles in each group of sieving method, and combines with image analysis method to calculate sand fineness modulus and particle grading, which can not only avoid the defects such as large labor intensity and low efficiency of conventional sieving method, but also avoid the error caused by repeated weighing, effectively solve the problems of small particle radius invisible and large error caused by difficult dispersion of sand in image analysis process, and has important reference value for the research on sand in hardened concrete; the principle is scientific and reliable, the labor intensity is low, the efficiency is high, and good consistency is obtained compared with conventional sieving method.

Description

Technical fields:

[0001] This invention belongs to the field of civil engineering materials research and application technology, specifically involving a method for calculating the fineness modulus and gradation of sand. It analyzes the relationship between the particle size of the mortar cross section and the three-dimensional true particle size through a two-dimensional cross section of hardened concrete. Background technology:

[0002] Concrete is an essential material in civil engineering, and the fineness of sand plays a crucial role in concrete mix design. If the fineness of the sand changes, the sand ratio and water content must be adjusted accordingly to maintain the workability of the concrete. The fineness modulus of sand is an indicator characterizing the coarseness and type of natural and manufactured sand particles. Although it cannot fully reflect the particle gradation, as a simple indicator, it can still reflect the differences in fine aggregates to a certain extent. Therefore, in engineering applications and concrete testing, most engineering technicians and related researchers use the fineness modulus of sand to evaluate the coarseness and particle gradation of sand.

[0003] The calculation method for fineness modulus is specified in "Construction Sand" (GB / T 14684-2022): (1) After taking sand samples according to regulations, use a square sieve with a sieve aperture of 9.5 mm to remove sand particles with a particle size greater than 10 mm, reduce the sample to 1100 g, dry it in a drying oven until constant weight, and after cooling, divide it into two equal portions as samples for later use; (2) Place the sieve set on a shaking sieve machine and shake it for ten minutes, then remove the sieve set and sieve it by hand one by one according to the size of the sieve set until the amount of sample passing through per minute is less than 0.1% of the total sample. The samples that pass through are then incorporated into the next sieve set. In the middle, and together with the sample in the next set of sieves, they are sieved in sequence until all sets of sieves are sieved. Then weigh the residue of each set of sieves to an accuracy of 1g; (3) Record the individual sieve residue percentages of the sieves with sieve hole sizes of 4.75mm, 2.36mm, 1.18mm, 0.6mm, 0.3mm and 0.15mm as P1, P2, P3, P4, P5 and P6, and the cumulative sieve residue percentages as A1, A2, A3, A4, A5 and A6; The fineness modulus calculation formula of sand is shown in the following table:

[0004]

[0005]

[0006] Substituting equations ①-⑥ into equation ⑦, the fineness modulus of sand is expressed as:

[0007]

[0008] It not only requires specific related equipment, but also involves high labor intensity and low efficiency. Because it requires repeated weighing and manual judgment to ensure that the sample throughput per minute is less than 0.1% of the total sample volume, it is prone to errors.

[0009] Fine aggregate is a major component of concrete, accounting for more than 30% of its total volume. With the increasing use of concrete, natural sand resources are gradually becoming scarce and facing depletion. The development of modern construction demands natural sand year by year, leading to a prominent supply-demand imbalance. To address this imbalance, manufactured sand is gradually replacing natural sand to promote the development of eco-friendly building materials. However, manufactured sand produced by crushers exhibits inconsistent gradation and fineness modulus, directly affecting the amount of raw material used in concrete and its performance strength. Traditional methods for measuring the gradation of manufactured sand include vibrating sieving, but the high labor and time costs of this process make it unsuitable for practical engineering needs. With the rapid development of image processing technology, more and more researchers are using digital image processing technology for particle detection.

[0010] Bagheri et al. used scanning electron microscopy, micro-CT, and image analysis to study the volume and surface area of ​​particles, estimating the surface area, equivalent diameter, and sphericity of particles through their projected area. Watano et al. developed a particle image detector that uses a CCD to capture images of dispersed particles, inputs them into an image processing system, and processes them through linear filtering, binarization, denoising, and morphological separation of adhered particles. They used the Feret diameter to characterize particle size and roundness to characterize particle shape. Masad, E et al. performed erosion followed by dilation processing on fine aggregate images, calculated the angular features and area loss at the boundaries, evaluated angularity, and found that fractal length increases with increasing angularity. They proposed radius-based and contour gradient-based angularity indices as particle shape evaluation parameters. Bagheri, GH et al. found that particle volume and surface area are related to their sphericity, obtaining the equivalent ellipsoid of the particle through its projected area, and using this to estimate the particle's surface area, equivalent diameter, and sphericity. Okpeafoh, SA et al. obtained reliable particle size and aspect ratio distributions through image processing and measured chord length data. Huang et al. used microscopes to collect images of manufactured sand and natural sand, and combined with image processing techniques, found that natural sand is closer to spherical and smoother, while manufactured sand is finer, flatter, and rougher. Yang et al. developed a method for measuring the particle size of machine-made sand using vibration dispersion and high-speed video imaging technology, proving that the particle size and shape measurement system based on imaging methods meets the detection requirements of manufactured sand. Maitre et al. used optical microscopes to acquire images of mineral particles, and based on image technology and machine vision, for the first time used superpixel segmentation instead of traditional segmentation methods to segment mineral particles. Dai Zhenchao et al. proposed a formula for calculating the fineness modulus and compared it with the sieve separation formula. Tian Wenyu et al. modified the sieve separation formula, deducting the portion below 0.16mm from the bottom of the pan. Sun Zhigang et al. improved the sieve separation formula, replacing the cumulative percentage of sieve residue with a fractional sieve residue, avoiding rounding errors that might occur during calculation by directly processing the raw data, and reducing tedious steps in the calculation process. Qin Xue et al. proposed a new calculation method, employing image analysis for the first time to calculate the fineness modulus of sand. They applied the criterion of equal volume ratio and weight ratio, avoiding the weighing process of sand, and used the minimum Freret diameter as the equivalent particle size for sieveable sand, thus better ensuring the accuracy of the measurement data. Liu Shuming et al. disclosed a new method for measuring fineness modulus. They used image processing technology to extract the contour image information of the fully exposed sand particles in the upper layer for data classification, statistics, and analysis. The images of the fully and partially covered sand particles in the lower layer were blurred and used as background images, improving the accuracy of sand particle analysis. They innovatively introduced a rotating cylindrical scanning device into the measurement of the fineness modulus of sand particles. Cai Yuanyuan et al. disclosed a manufactured sand detection system based on digital image processing. The system extracts the contour features of particles, has a fast detection speed, and uses non-contact measurement to avoid damaging the original shape of the particles.Huang Xiaoyu et al. proposed a dynamic image-based measurement of manufactured sand gradation, studied preprocessing methods such as grayscale conversion, filtering, and binarization of dynamically falling manufactured sand particle images, as well as methods for extracting particle size and shape features, and disclosed an image processing algorithm for extracting features and morphological parameters of manufactured sand images.

[0011] However, the aforementioned methods or existing technologies, whether modifying the sieving formula, exploring various parameters through image analysis, or improving equipment, still suffer from significant errors. Therefore, it is essential to develop and design a method for calculating the fineness modulus and gradation of sand, and to solve the problem of sand's difficulty in dispersion during image analysis. Summary of the Invention:

[0012] The purpose of this invention is to overcome the shortcomings of existing technologies and to develop a method for calculating the fineness modulus and gradation of sand, effectively avoiding the problem of large error in results caused by the difficulty in dispersing sand during image analysis.

[0013] To achieve the above objectives, the specific process of the preparation method for calculating the fineness modulus and gradation of sand, as disclosed in this invention, includes the following steps:

[0014] (1) Making mortar test blocks

[0015] According to the set mix ratio, sand with a nominal particle size of 0.16-10mm is mixed with cement and water to make mortar test blocks, which are then cured for 3 days according to standard.

[0016] (2) Obtaining and photographing the cross-section

[0017] First, the mortar test blocks are cut;

[0018] Then, the cut surface is polished to obtain a smooth cut surface;

[0019] Finally, the cross-section is photographed, and the images are imported into image analysis software.

[0020] (3) Image analysis and processing

[0021] ①Preprocessed images

[0022] Background correction after enhancing contrast;

[0023] ② Calibration scale

[0024] First, drag the calibration bar to the two scales of the ruler in the image to obtain the pixel values ​​in the length direction of the two scales. Then, determine the length of the ruler by converting the pixel values ​​and the length of the two scales. Use the actual length value to represent the measurement data.

[0025] Then, save the relationship between pixel values ​​and ruler length as a file for later use;

[0026] Finally, fill the ruler area image with the background color of the picture or crop it out directly;

[0027] ③ Separate sand particles from the background

[0028] First, the sand grains are separated from the mortar by determining thresholds for the same or similar colors, and numbered sequentially. The color value is repeatedly sampled from the sand grains using a dropper tool to separate all sand grains or individual areas on the sand grains from the background.

[0029] Then, using the RGB color value histogram tool, the range of RGB values ​​is determined based on the RGB color values ​​of the sand grain pixels;

[0030] Finally, select pixels with RGB values ​​within this range to separate the sand particles from the mortar;

[0031] ④ Low-pass processing

[0032] Use a low-pass filter to preserve large-scale graphics in the image while blurring details;

[0033] ⑤ Separate the adhering sand particles

[0034] Separate the adhering sand particles;

[0035] ⑥ Treating sand particles with holes

[0036] Fill the pores in the sand particles that form closed curves;

[0037] ⑦ Treat sand particles at the boundary

[0038] Remove sand particles that have been clipped off around the edges of the image;

[0039] (4) Extract the number of sand particles per grade

[0040] ① Determine the radius of the two-dimensional tangent

[0041] After removing sand particles with a cross-section smaller than 0.05mm, substitute the actual three-dimensional particle sizes r = R and m = 0.05mm for the corresponding sieve aperture sizes r1 = 9.5mm, r2 = 4.75mm, r3 = 2.36mm, r4 = 1.18mm, r5 = 0.6mm, r6 = 0.3mm, and r7 = 0.15mm into the formula: The corresponding two-dimensional radii are: r′1=7.50mm, r′2=3.77mm, r′3=1.89mm, r′4=0.96mm, r′5=0.50mm, r′6=0.26mm and r′7=0.14mm;

[0042] ② Determine the sand grading particle size

[0043] Using the minimum Ferete diameter as a reference for image analysis, the number of particles corresponding to each layer r'2~r'1, r'3~r'2, r'4~r'3, r'5~r'4, r'6~r'5, and r'7~r'6 were selected as a1, a2, a3, a4, a5, and a6, respectively.

[0044] (5) Calculate the amount of sieve residue

[0045] First, the quantity for each group is determined from Table 1:

[0046]

[0047]

[0048] Table 1 (Theoretically, a7 can be calculated; however, for the sieve method, only a1-a6 need to be calculated)

[0049] Then, substitute it into the formula: Calculate the weights g1, g2, g3, g4, g5, and g6;

[0050] Finally, according to the formula: Calculate the sieve residue P for each stage. Similarly, calculate P2, P3, P4, P5 and P6.

[0051] Where γ is the specific gravity of sand, g is the weight of sand in each group, and d is the average value of the upper and lower sieves;

[0052] (6) Calculate the fineness modulus

[0053] Using Dai Zhenchao's fineness modulus formula: Calculate the fineness modulus, where F · M · d is the fineness modulus of sand. m Let the geometric mean particle size of the sand be (in millimeters), given by the formula: Calculated;

[0054] (7) Determine the type of sand

[0055] According to the sieve residue, follow Table 1 and Figure 1 The standard for determining the gradation curve and type of sand.

[0056] The step ③ of this invention, which involves separating sand particles from the background, can also be achieved by adjusting the HIS value to separate the sand particles from the mortar.

[0057] Compared with existing technologies, this invention establishes the relationship between the particle size of the two-dimensional mortar cross-section and the actual particle size in three dimensions, and establishes the relationship between the number of particles in each group of the two-dimensional cross-section and the number of particles in each group of the sieving method. Combined with image analysis methods, it calculates the fineness modulus and particle size distribution of sand. This not only avoids the defects of conventional sieving methods such as high labor intensity and low efficiency, but also avoids the errors caused by repeated weighing. It effectively solves the problems of small particle radius not being visible and large errors caused by the difficulty in dispersing sand during image analysis. It has important reference value for the study of sand in hardened concrete. Its principle is scientific and reliable, with low labor intensity and high efficiency. Compared with conventional sieving methods, it has achieved good consistency. Attached image description:

[0058] Figure 1 This is a schematic diagram of the range corresponding to the radius involved in the present invention.

[0059] Figure 2 This is a schematic diagram of the sand particles and mortar after separation, as per the present invention.

[0060] Figure 3 This is a diagram showing the number of particles in each layer according to the screening method involved in this invention.

[0061] Figure 4 This is a schematic diagram of the gradation curve involved in the present invention. Detailed implementation method:

[0062] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0063] Example 1:

[0064] The specific process of the method for calculating the fineness modulus and gradation of sand involved in this embodiment includes the following steps:

[0065] (1) Making mortar test blocks

[0066] Following the sampling method specified in "Construction Sand" (GB / T 14684-2022), sand with a nominal particle size of 9.5 mm or less was obtained and divided into 6 groups: 4.75 mm, 2.36 mm, 1.18 mm, 0.6 mm, 0.3 mm, and 0.15 mm. Different fineness moduli A1, A2, and A3 were prepared. A set of mortar test blocks (3 blocks) was prepared according to the mix ratio of sand:cement:water = 0.5:1:0.32 = 900 g:1800 g:572 g. After standard curing for 3 days, the fineness moduli were calculated using the comparative sieve analysis method and image analysis method. The results are as follows:

[0067]

[0068] (2) Obtaining and photographing the cross-section

[0069] First, the mortar test blocks are cut using a cutting machine;

[0070] Then, the cut surface is polished with a grinding mill, using grinding wheels of different fineness according to the desired smoothness, until a smooth cut surface is obtained;

[0071] Finally, the cross-section was photographed with a camera, and the images were imported into image analysis software.

[0072] (3) Image analysis and processing

[0073] ①Preprocessed images

[0074] Image analysis software is used to enhance the contrast of the imported image, and a background correction tool is used to correct the background so that the pixel values ​​of areas similar to the background in the image are replaced by pixel values ​​similar to the main background, resulting in an image with contrast between the image and the background, so that the sand grains can be separated from the background.

[0075] ② Calibration scale

[0076] First, drag the calibration bar in the image analysis software to the two scales of the ruler in the image to obtain the pixel values ​​in the length direction of the two scales of the ruler: select millimeters or micrometers as the unit of length measurement, determine the length of the ruler by converting the pixel values ​​and the length of the two scales of the ruler, and use the actual length value to represent the measurement data;

[0077] Then, save the relationship between pixel values ​​and ruler length as a file for later use;

[0078] Finally, fill the scale area image with the background color of the picture or crop it out to prevent it from participating in the subsequent analysis.

[0079] ③ Separate sand particles from the background

[0080] First, the sand grains are separated from the mortar by determining a threshold for the same or similar colors, and numbered sequentially. The eyedropper tool in the image analysis software is used to repeatedly sample the color values ​​on the sand grains until all sand grains or individual areas on the sand grains are separated from the background.

[0081] Then, using the RGB color value histogram tool in the image analysis software, the range of RGB values ​​is determined based on the RGB color values ​​of the sand grain pixels in the image: R (54-151), G (30-205), B (45-105).

[0082] Finally, select pixels in the image whose RGB values ​​fall within this range, and separate the sand particles from the mortar. The result is as follows. Figure 2 As shown;

[0083] Alternatively, the sand particles can be separated from the mortar by adjusting the HIS value;

[0084] ④ Low-pass processing

[0085] A low-pass filter is used to retain large-scale graphics in the image while blurring details to filter out minor traces that may appear during the polishing process.

[0086] ⑤ Separate the adhering sand particles

[0087] Sand grains are segmented by manual or automatic segmentation: In manual segmentation, the image is magnified and a line is drawn between two adhered sand grains to separate them into two target sand grains; in automatic segmentation, opening and closing operations in morphological operations are used to separate targets connected by bridges.

[0088] ⑥ Treating sand particles with holes

[0089] The pores of the sand grains that form closed curves are filled. The filled sand grains are counted as independent particles, and the original area where the pores were formed is no longer counted.

[0090] ⑦ Treat sand particles at the boundary

[0091] The sand grains that are cut off by the boundary in the area around the image are identified and removed. They are not colored, not numbered, and are not used as the objects of analysis.

[0092] (4) Extract the number of sand particles per grade

[0093] ① Determine the radius of the two-dimensional tangent

[0094] The sand was divided into 7 radii within 6 ranges according to the sieving method. Sand with a cross-section smaller than 0.05mm was removed, resulting in sand with corresponding sieve aperture sizes r1 = 9.5mm, r2 = 4.75mm, ...

[0095] Substituting the actual three-dimensional particle sizes r = R and m = 0.05 mm for r3 = 2.36 mm, r4 = 1.18 mm, r5 = 0.6 mm, r6 = 0.3 mm, and r7 = 0.15 mm into the formula: The corresponding two-dimensional radii are obtained as follows: r′1 = 7.50 mm, r′2 = 3.77 mm, r′3 = 1.89 mm, r′4 = 0.96 mm.

[0096] r'5 = 0.50 mm, r'6 = 0.26 mm and r'7 = 0.14 mm;

[0097] ② Determine the sand grading particle size

[0098] Using the minimum Ferete diameter as a reference for image analysis, the corresponding particle numbers r'2~r'1, r'3~r'2, r'4~r'3, r'5~r'4, r'6~r'5, and r'7~r'6 for each layer were selected as a1, a2, and a3, respectively.

[0099] a3, a4, a5, a6, such as Figure 3 As shown;

[0100] (5) Calculate the fineness modulus

[0101] According to the formula: Calculate the fineness modulus, where F · M · d is the fineness modulus of sand. m Let the geometric mean particle size of the sand be (in millimeters), given by the formula:

[0102] The calculations yielded the following results:

[0103]

[0104] Based on the sieve residue, the gradation curve is as follows: Figure 4 As shown, the gradation curve of this sand is in zone 2.

[0105] (6) Determine the type of sand

[0106] According to the criteria for judging the coarseness of sand in "Construction Sand" (GB / T 14684-2022):

[0107]

[0108]

[0109] It can be concluded that the sand is coarse sand.

Claims

1. A method for calculating the fineness modulus and gradation of sand, characterized in that, The process includes the following steps: (1) Making mortar test blocks According to the set mix ratio, sand, cement and water are mixed to make mortar test blocks, which are then cured for 3 days according to standard. (2) Obtaining and photographing the cross-section First, the mortar test blocks are cut; Then, the cut surface is polished to obtain a smooth cut surface; Finally, the cross-section is photographed, and the images are imported into image analysis software. (3) Analyzing and processing images ①Preprocessed images Background correction after enhancing contrast; ② Calibration scale First, drag the calibration bar to the two scales of the ruler in the image to obtain the pixel values ​​in the length direction of the two scales. Then, determine the length of the ruler by converting the pixel values ​​and the length of the two scales. Use the actual length value to represent the measurement data. Then, save the relationship between pixel values ​​and ruler length as a file for later use; Finally, fill the ruler area image with the background color of the picture or crop it out directly; ③ Separate sand particles from the background First, the sand grains are separated from the mortar by determining thresholds for the same or similar colors, and numbered sequentially. The color value is repeatedly sampled from the sand grains using a dropper tool to separate all sand grains or individual areas on the sand grains from the background. Then, using the RGB color value histogram tool, the range of RGB values ​​is determined based on the RGB color values ​​of the sand grain pixels; Finally, select pixels with RGB values ​​within this range to separate the sand particles from the mortar; Alternatively, the sand particles can be separated from the mortar by adjusting the HIS value; ④ Low-pass processing Use a low-pass filter to preserve large-scale graphics in the image while blurring details; ⑤ Separate the adhering sand particles Separate the adhering sand particles; ⑥ Treating sand particles with holes Fill the pores in the sand particles that form closed curves; ⑦ Treat sand particles at the boundary Remove sand particles that have been clipped off around the edges of the image; (4) Extract the number of sand particles per grade. ① Determine the radius of the two-dimensional tangent After removing sand from the cut surface below 0.05mm, substitute the true three-dimensional particle size r=R and m=0.05mm corresponding to the sieve aperture size into the formula: This yields the corresponding two-dimensional tangent radius; ② Determine the sand grading particle size Using the minimum Ferete diameter as a reference for image analysis, the number of particles corresponding to each layer was selected. (5) Calculate the amount of residue on the sieve. First, the quantity for each group is determined from Table 1: Then, calculate the weights g1, g2, g3, g4, g5, and g6; Finally, according to the formula: Calculate the sieve residue P for each stage. Similarly, calculate P2, P3, P4, P5 and P6. Where γ is the specific gravity of sand, g is the weight of sand in each group, and d is the average value of the upper and lower sieves; (6) Calculate the fineness modulus Using Dai Zhenchao's fineness modulus formula: Calculate the fineness modulus, where, The fineness modulus of sand. Let be the geometric mean particle size of the sand, in millimeters, given by the formula: Calculated; (7) Determine the type of sand Determine the gradation curve and type of sand based on the amount of residue on the sieve.

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