A method for measuring concrete surface porosity based on nuclear magnetic resonance

Abstract

This invention discloses a method for measuring the surface porosity of concrete using small samples based on nuclear magnetic resonance (NMR). It belongs to the field of non-destructive testing technology for building materials, specifically for determining the maximum aggregate size in concrete and establishing a standard representative cylinder diameter. The method involves calibrating the equipment to accommodate small core sample diameters and calculating the equivalent area fractions. The number of virtual representative units and the number of samples per unit are set according to the target measurement accuracy. A dual-counting algorithm is used to solve for the theoretical minimum number of basic samples, and the existence of an integer allocation scheme that satisfies the group-sharing constraint is verified. If grouping is not feasible, the algorithm automatically increments until a valid grouping is obtained. Basic samples are collected to construct virtual units according to the allocation scheme. The porosity of each unit is calculated, averaged, and the overall surface porosity is output. This method avoids the need for direct measurement of large-size standard samples, reduces core sampling costs and measurement time, and improves the reliability of the results.

Description

Technical Field

[0001] This invention belongs to the field of non-destructive testing technology for building materials, specifically relating to a method for measuring the surface porosity of concrete based on low-field nuclear magnetic resonance (LF-NMR). It is particularly suitable for non-destructive and highly representative determination of the overall porosity of aggregate-containing concrete by scientifically combining and stacking multiple small-sized samples to simulate standard-sized concrete under limited physical space conditions. Background Technology

[0002] In concrete quality testing, porosity is a key indicator, directly affecting the strength, durability, and impermeability of concrete. Currently, low-field nuclear magnetic resonance (NMR) technology is widely used for measuring concrete porosity due to its non-destructive, rapid, and easy-to-operate advantages. When using low-field NMR, the porosity and internal pore structure of the concrete sample are obtained by analyzing the transverse relaxation time distribution spectrum of the sample. This method allows for data acquisition without damaging the sample.

[0003] However, concrete is a typical heterogeneous material, especially when it contains coarse aggregate. To ensure the uniformity and representativeness of the surface porosity measurement results, the sample size should be no less than 10 times the maximum aggregate particle size (for example, when the maximum aggregate particle size is 20 mm, the minimum side length of the sample should be ≥200 mm). Current mainstream LF-NMR equipment, limited by its magnet structure, typically only supports columnar samples with a diameter ≤60 mm and a height ≤150 mm. This creates a technical bottleneck: the physical contradiction between the need for large samples and the limited capacity of the equipment results in large fluctuations and poor representativeness of single-point data when using small samples for measurement due to the randomness of aggregate distribution.

[0004] Currently, there are two main approaches to solving this problem: one is to customize special large-size NMR equipment, but this is costly and impractical; the other is to simply take multiple small samples, measure them, and then take the average, but there is no scientific basis to determine how many samples are sufficient. With the development of statistical sampling theory and spatial weighted analysis methods in materials science, it has become possible to construct a dataset that meets size requirements through scientific combination and data fusion, thereby overcoming size limitations and obtaining the most representative and accurate porosity data without changing the hardware. Summary of the Invention

[0005] This invention provides a data combination calculation method based on small-sized samples to achieve non-destructive determination of the surface porosity of large aggregate concrete.

[0006] This invention includes the setting of the maximum aggregate particle size in concrete. The diameter of the standard representative cylinder was determined based on the measurement. ; Compatible with equipment for small core sample diameters The calibration and calculation of the equivalent number of areas ,in Reflecting the total amount of information required to meet the statistical representativeness of aggregates; setting the number of virtual representative units based on the target measurement accuracy. and the number of samples per unit ,satisfy The theoretical minimum number of fundamental samples is determined using a dual-counting algorithm. And verify whether there exists a pair sharing constraint that satisfies the number of samples shared by any two units. The integer allocation scheme is used; if grouping is not feasible, the increment is automatically increased to the nearest integer. ( ), until a valid group is obtained; collect A base sample is constructed according to the allocation scheme. The porosity of each virtual unit is calculated and then averaged to output the overall surface porosity.

[0007] Specifically: Calculate the diameter of the standard representative cylinder The maximum aggregate particle size in concrete is obtained through sieve analysis, mix proportion data, or image analysis. To ensure the uniformity and representativeness of the results, the minimum size of the representative sample should be no less than 10 times the maximum aggregate particle size. Its representative equation is as follows:

[0008] ;

[0009] Calibrate the diameter of the small test block and calculate the number of equivalent area portions. The diameter of the small cylindrical specimen supported by the low-field nuclear magnetic resonance equipment is... To ensure statistical representativeness, the number of equivalent area portions is defined. Its representative equation is

[0010] ;

[0011] Set the number of virtual representative datasets With the number of samples in the group The number of virtual representative units is set according to the target measurement accuracy. and the number of basic samples contained in each unit satisfy

[0012] ;

[0013] The maximum sharing ratio between groups is It meets the requirement of a data duplication rate of less than 40%.

[0014] ;

[0015] The maximum number of shared samples between any two virtual units. for:

[0016] ;

[0017] To derive the theoretical minimum basic sample size, we first need to group the total number of pairs. (P is the number of combinations of any two units) is:

[0018] ;

[0019] According to equations (5) and (6), the maximum allowed shared logarithm upper limit of the system is... for:

[0020] ;

[0021] Let the minimum total number of basic samples be , No. One sample was assigned to For each different data set (i.e., the number of times it is used), the required number of equivalent area portions must be met. :

[0022] ;

[0023] Satisfying the equivalent number of areas At the same time, it is also necessary to meet the upper limit of the maximum number of shared logs in the data group. :

[0024] ;

[0025] Expanding equation (9) yields:

[0026] ;

[0027] Substituting into equation (8), we get:

[0028] ;

[0029] According to the Cauchy-Schwarz inequality:

[0030] ;

[0031] Substituting equations (8) and (11) into equation (12) yields:

[0032] ;

[0033] After simplification, the theoretical minimum number of basic samples can be determined. for:

[0034] ;

[0035] Note: Equation (14) gives The lower bound, but because It must be a positive integer; a feasible solution may need to satisfy... If in No integer assignments satisfying equations (8)–(9) can be found. If so, adaptive incrementing is required.

[0036] Use auto-increment to ensure grouping feasibility: if in There is no integer allocation scheme that satisfies equations (8)–(9). This can increase the number of samples. :

[0037] ;

[0038] For each Virtual Data Group (VDG) Its porosity is the percentage of its constituent elements. The arithmetic mean of the samples:

[0039] ;

[0040] Will Averaging the porosity of each data set:

[0041] ;

[0042] Substituting equation (16) into equation (17), we get:

[0043] ;

[0044] The meaning of double summation is: "Iterate through each data set, then iterate through each sample within it, and sum all..." "Add it all up."

[0045] This is equivalent to: "Iterating through each original sample i and seeing how many datasets it appears in (i.e., ...)" (times), then add Second-rate"

[0046] Therefore, we can obtain:

[0047] ;

[0048] Substituting equation (19) into equation (18), we get:

[0049] ;

[0050] And from constraint (8), we know that:

[0051] ;

[0052] Therefore, the equivalent weighted formula (20) used to derive the overall surface porosity can be written as:

[0053] ;

[0054] Compared with existing technologies, this invention can construct virtual representative samples that meet the specifications by collecting only a small number of small core samples, thus avoiding the need for direct measurement of large-sized standard samples.

[0055] This invention scientifically determines the minimum number of samples using a dual counting algorithm, eliminating the need for empirical blind sampling, significantly reducing core sampling costs and measurement time, while ensuring the statistical representativeness of the results.

[0056] This invention introduces an inter-group shared proportion constraint mechanism to ensure that data groups maintain sufficient independence, overcomes the measurement bias problem caused by excessive correlation of data in the traditional simple averaging method, and improves the reliability of the results.

[0057] The adaptive incremental mechanism of this invention can automatically adjust the number of samples to meet the feasibility of grouping, and can obtain effective results even under limited sample conditions, thus expanding the engineering applicability of the method. Attached Figure Description

[0058] Figure 1 A flowchart for the overall calculation of surface porosity. Detailed Implementation

[0059] like Figure 1 As shown, the entire computational process is used to implement this invention, which will be further described in detail below:

[0060] The first step is to determine the maximum aggregate size of the concrete and set representative dimensions;

[0061] First, the maximum aggregate particle size parameter in concrete was obtained through sieve analysis. A standard sieve set (apertures of 5mm, 10mm, 16mm, 20mm, 25mm, and 31.5mm) was used to sieve the aggregate in the concrete to be tested, determining the maximum aggregate particle size to be 25mm, which necessitates a standard representative cylinder diameter of 250mm. Combined with the maximum core sample size (Φ50mm) supported by the low-field nuclear magnetic resonance equipment used, the area equivalent fraction was calculated to be 25, which was then used as the baseline parameter for subsequent virtual sample construction.

[0062] The second step is to design a virtual data grouping scheme;

[0063] Five virtual data groups were set to be constructed, each containing five samples, with a sample sharing limit of 1 (20% overlap) between groups. The total information content of all groups was equivalent to a standard cylinder. Theoretically, the minimum basic sample size was calculated using a double-counting algorithm to be 14, but this proved insufficient to construct effective groups that satisfied the sharing constraint. Therefore, an adaptive incremental mechanism was used to adjust the sample size to 15 to meet the requirements of a feasible grouping scheme. The specific allocation is as follows: Group 1 consists of samples 1 to 5; Group 2 consists of samples 1, 6 to 9; Group 3 consists of samples 2, 6, 10 to 12; Group 4 consists of samples 3, 7, 10, 13, and 14; and Group 5 consists of samples 4, 8, 11, 13, and 15.

[0064] The third step is core sample acquisition and LF-NMR measurement;

[0065] Fifteen cylindrical core samples (Φ50mm × 100mm) were drilled from concrete using an electric coring machine, numbered 1 to 15. Each sample was sequentially placed into a low-field nuclear magnetic resonance (NMR) instrument for measurement. Measurement parameters were set as follows: CPMG pulse sequence, echo interval TE = 0.2ms, echo number NECH = 8000, and waiting time TW = 3000ms. Only the side surface signal (depth ≤ 1mm) was analyzed; the end-face cutting disturbance area was removed, and the surface porosity of each sample was obtained through T2 spectrum inversion.

[0066] The fourth step is to construct a virtual dataset and calculate the unit porosity;

[0067] Following the grouping scheme in step two, the 15 basic samples were assigned to 5 virtual data groups. The porosity of the samples within each virtual data group was calculated by taking the arithmetic mean, and the porosity of each group was obtained to obtain the porosity value of each virtual data group.

[0068] Step 5: Output the overall surface porosity and verify the results;

[0069] The porosity of the five virtual data groups was calculated using a weighted average method: the porosity of each basic sample was multiplied by the number of times it was used in the group, the sum was divided by the total number of uses, and the weighted average porosity was obtained. This value was then used as the determination result of the overall surface porosity of the concrete.

Claims

1. A method for measuring the surface porosity of concrete using small samples based on nuclear magnetic resonance (NMR), characterized in that, Including the maximum aggregate size of concrete The diameter of the standard representative cylinder was determined based on the measurement. ; Compatible with small core sample diameters The calibration and calculation of the equivalent number of areas ,in Reflecting the total amount of information required to meet the statistical representativeness of aggregates; setting the number of virtual representative units based on the target measurement accuracy. and the number of samples per unit ,satisfy The theoretical minimum number of fundamental samples is determined using a dual-counting algorithm. It also verifies whether there exists an integer allocation scheme that satisfies the group-pair sharing constraint; if grouping is not feasible, it automatically increments to... Continue until a valid group is obtained; collect data. A base sample is constructed according to the allocation scheme. The porosity of each virtual unit is calculated and then averaged to output the overall surface porosity.

2. The method for measuring the surface porosity of concrete using small samples based on nuclear magnetic resonance according to claim 1, characterized in that, Calculate the diameter of a standard representative cylinder The maximum aggregate particle size in concrete is obtained through sieve analysis, mix proportion data, or image analysis. The minimum size of the representative sample should be no less than 10 times the maximum aggregate particle size to ensure the uniformity and representativeness of the results. Its representative equation is: ； Calibrate the diameter of the small test block and calculate the number of equivalent area portions. The diameter of the small cylindrical specimen supported by the low-field nuclear magnetic resonance equipment is... To ensure statistical representativeness, the number of equivalent area portions is defined. Its representative equation is: ； Set the number of virtual representative datasets With the number of samples in the group The number of virtual representative units is set according to the target measurement accuracy. and the number of basic samples contained in each unit satisfy: ； The maximum sharing ratio between groups is It meets the requirement of a data duplication rate of less than 40%. ； The maximum number of shared samples between any two virtual units. for: 。 3. The method for measuring the surface porosity of concrete using small samples based on nuclear magnetic resonance according to claim 2, characterized in that, To derive the theoretical minimum basic sample size, we first need to group the total number of pairs. for: ； Based on equations (5) and (6), the maximum allowed shared logarithm upper limit is... for: ； Let the minimum total number of basic samples be , No. One sample was assigned to For each different data set, the required number of equivalent area portions must be met. : ； Satisfying the equivalent number of areas At the same time, it is also necessary to meet the upper limit of the maximum number of shared logs in the data group. : ； Expanding equation (9) as follows: ； Substituting into equation (8), we get: ； According to the Cauchy-Schwarz inequality: ； Then substitute equations (8) and (11) into equation (12): ； After simplification, the theoretical minimum number of basic samples can be determined. for: ； Equation (14) gives The lower bound, because It must be a positive integer; a feasible solution may need to satisfy... If in No integer assignments satisfying equations (8)–(9) can be found. Then adaptive incrementing is required; Use auto-increment to ensure grouping feasibility: if in There is no integer allocation scheme that satisfies equations (8)–(9). This can increase the number of samples. : ； For each virtual data group Its porosity is the percentage of its constituent elements. The arithmetic mean of the samples: ； Will Averaging the porosity of each data set: ； Substituting equation (16) into equation (17), we get: 。 4. The method for measuring the surface porosity of concrete using small samples based on nuclear magnetic resonance according to claim 3, characterized in that, Iterate through each data set, then iterate through each sample within it, and then... Add it up; This is equivalent to: iterating through each original sample i and counting how many datasets it appears in. Next time, just put add Next; obtained: ； Substituting equation (19) into equation (18), we get: ； And from constraint (8), we know that: ； Therefore, the equivalent weighted formula (20) used to derive the overall surface porosity is written as: 。 5. The method for measuring the surface porosity of concrete using small samples based on nuclear magnetic resonance according to claim 1, characterized in that, The first step is to determine the maximum aggregate size of the concrete and set representative dimensions; First, the maximum aggregate particle size parameter in concrete is obtained through sieve analysis. Then, the aggregate of the concrete to be tested is sieved using a standard sieve set to determine that the maximum aggregate particle size is 25 mm, which means that the diameter of the standard representative cylinder needs to be 250 mm. Combined with the maximum core sample size supported by the low-field nuclear magnetic resonance equipment used, the area equivalent number is calculated to be 25, and this is used as the benchmark parameter for the subsequent construction of virtual samples. The second step is to design a virtual data grouping scheme; The number of virtual data groups to be constructed is set to 5, each containing 5 samples, and the number of samples shared between each group is 1. The total information content of all groups is superimposed and is equivalent to a standard cylinder. The minimum theoretical basic sample size is calculated using the double counting algorithm, which is 14. The specific allocation is as follows: the first group consists of samples 1 to 5, the second group consists of samples 1, 6 to 9, the third group consists of samples 2, 6, 10 to 12, the fourth group consists of samples 3, 7, 10, 13, and 14, and the fifth group consists of samples 4, 8, 11, 13, and 15. The third step is core sample acquisition and LF-NMR measurement; Fifteen cylindrical core samples, numbered 1 to 15, were drilled from concrete using an electric coring machine. Each sample was then placed into a low-field nuclear magnetic resonance (NMR) instrument for measurement. Only the side surface signal was analyzed, and the end face cutting disturbance area was removed. The surface porosity of each sample was obtained by T2 spectrum inversion. The fourth step is to construct a virtual dataset and calculate the unit porosity; According to the grouping scheme in step two, the 15 basic samples were assigned to 5 virtual data groups; The porosity of the samples within each virtual data group is taken as an arithmetic mean, and the porosity of each group is calculated to obtain the porosity value of each virtual data group. Step 5: Output the overall surface porosity and verify the results; The arithmetic mean of the porosity of the five virtual data groups was obtained by using a weighted average method: the porosity of each basic sample was multiplied by the number of times it was used in the group, the sum was divided by the total number of times it was used, and this value was used as the result of the determination of the overall surface porosity of concrete.

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