Method for calculating three-dimensional tortuosity of rock-soil mass based on porosity, gradation and size

Abstract

The present application relates to the field of environmental protection and ecological restoration technology, and specifically to a method for calculating the three-dimensional tortuosity of rock-soil mass based on porosity, gradation and size. The method comprises: obtaining the particle gradation curve, fine particle part and coarse particle part of the original sample of loose broken rock-soil mass; obtaining the effective particle size, thirty-percentile particle size, sixty-percentile particle size and average particle size based on the particle gradation curve; calculating the non-uniformity coefficient and curvature coefficient according to the effective particle size, thirty-percentile particle size and sixty-percentile particle size; calculating the porosity based on the sample density, mass water content and specific gravity of the original sample of loose broken rock-soil mass obtained in advance, and using the fine particle part and coarse particle part; and calculating the three-dimensional tortuosity based on the effective particle size, average particle size, non-uniformity coefficient, curvature coefficient and porosity. The technical problem of the prior art that the calculation of the three-dimensional tortuosity of rock-soil mass cannot simultaneously consider accuracy and simplicity is solved.

Description

Technical Field

[0001] This invention relates to the field of environmental protection and ecological restoration technology, specifically a method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size. Background Technology

[0002] Tortuosity, as a process parameter characterizing fluid flow through the pore channels of porous media, reflects the degree of distribution and development of pore channels in porous media. Currently, some scholars have conducted research on the tortuosity of porous media. Yu Boming et al. derived a geometric relationship between tortuosity and porosity by assuming the soil particles are square. LI and Yuan Pei et al. derived a fractal dimension functional relationship between tortuosity and porosity based on the self-similarity of Sierpinski carpet. MATYKA studied the tortuosity-porosity relationship of porous media based on the lattice Boltzmann method. Lanfrey et al. proposed a tortuosity model regarding porosity under the assumption of constant pore channel area. Li Tao analyzed the relationship between tortuosity and pore structure in microporous media. Yan Han, Dai Shaoheng, Gan Jin et al. studied a soil tortuosity model considering the influence of porosity and particle arrangement under the assumption that the soil particles are square and of equal size. Li Zhang et al. established a geometric tortuosity model considering soil particle gradation under the assumption that the soil particles are circular. Xue Dongjie established a microscopic tortuosity expression based on the capillary model, the Hagen-Poiseuille formula, and Darcy's law. Rao Dengyu conducted simulation experiments on reconstructed three-dimensional soil columns based on the Smooth Particle Hydrodynamics (SPH) method and obtained their diffusion tortuosity values ​​by curve fitting. AHMADI et al. established a tortuosity model of equal-size spheres by considering the cubic and tetrahedral arrangement of spherical particles in three-dimensional space and using the average volume method.

[0003] For example, the Chinese invention patent with publication number "CN109993786B" and titled "Method, Apparatus, Device, and Storage Medium for Obtaining Tortuosity" obtains a pore network model of the reservoir rock, determines the straight-line distance between the first pore and the second pore based on first and second coordinate data, determines a first channel set based on distribution data, selects the first channel with the shortest distance from the first channel set as the second channel, determines the tortuosity of a first path between the first pore and the second pore based on the straight-line distance and the distance between the second channel, and determines the tortuosity of the reservoir rock based on the first path tortuosity set. This technology focuses on the research of reservoir rock, obtains its pore network model through image processing, and then uses the pore network model of the reservoir rock to obtain its tortuosity. In contrast, this invention explores the three-dimensional tortuosity of loose and fractured rock and soil, therefore, they have different methods for determining tortuosity.

[0004] For example, there is the Chinese invention patent with publication number "CN113297815A" entitled "A Method for Calculating the Diffusion Radius of Bingham-Type Cement Grout Considering the Torvature of Porous and Loose Media," and another Chinese invention patent with publication number "CN114720331B" entitled "A Method for Determining the Cylindrical Hemispherical Permeability Radius of Grout Due to the Power Law of Torvature of Soil and Rock Mass." These two invention patents only consider the influence of the tortuosity of porous media on the determination of the diffusion radius of permeable grout and assume that the tortuosity is a constant value, without proposing a specific calculation method for the tortuosity. This invention, however, explores how to calculate the three-dimensional tortuosity of loose and fractured soil and rock masses.

[0005] In summary, the current technical methods for determining the tortuosity of soil and rock masses have two main problems: (1) they assume that the soil and rock masses are square or round (spherical) particles, which cannot reflect the actual particle distribution characteristics of the soil and rock masses; (2) the current tortuosity calculation models either include only a single property index of the soil and rock masses, such as most current tortuosity calculation models that only consider the influence of the porosity of the soil and rock masses, resulting in a large difference between the theoretical tortuosity value calculated and the actual tortuosity index of the soil and rock masses; or they are complex and include many parameters, and these parameters are extremely difficult to determine, so they cannot be applied in practice to determine the tortuosity of soil and rock masses. It can be seen that the current methods for calculating the tortuosity of soil and rock masses are difficult to meet the needs of engineering practice and cannot reasonably and effectively determine the actual three-dimensional tortuosity index of loose and broken soil and rock masses.

[0006] Therefore, there is an urgent need to propose a calculation method that meets the needs of engineering practice and can reasonably and effectively determine the three-dimensional tortuosity of loose and fractured rock and soil. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size, thus solving the technical problem that existing technologies struggle to balance accuracy and simplicity in calculating the three-dimensional tortuosity of soil and rock masses.

[0008] To achieve the above objectives, this invention provides a method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size. The method includes: obtaining the particle size distribution curve, fine-grained portion, and coarse-grained portion of an original sample of loose, fractured soil and rock; obtaining the effective particle size, 30% particle size, 60% particle size, and average particle size based on the particle size distribution curve; calculating the non-uniformity coefficient and curvature coefficient based on the effective particle size, the 30% particle size, and the 60% particle size; calculating the porosity using the fine-grained portion and the coarse-grained portion based on the pre-obtained sample density, mass water content, and specific gravity of the original loose, fractured soil and rock sample; and calculating the three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity.

[0009] This invention obtains the gradation and coarse-fine particle composition of soil and rock samples sequentially to fully restore the true particle distribution, thus overcoming the bias of the assumption of equal-diameter / regular particles in traditional models. It relies on the gradation curve to read multiple characteristic particle sizes to accurately quantify the coarse-fine particle composition, and then calculates the non-uniformity and curvature coefficient to comprehensively characterize the quality of the gradation. It combines wet density, mass water content, and particle group specific gravity to calculate porosity, taking into account the porosity contribution of coarse and fine particles. Finally, it integrates multiple parameters such as particle size, gradation, and porosity to analyze the three-dimensional tortuosity. All input parameters can be obtained by conventional geotechnical tests, without the need for high-cost methods such as microscopic scanning and numerical simulation, thus balancing calculation accuracy and practicality in field engineering.

[0010] Optionally, obtaining the particle size distribution curve, fine-grained portion, and coarse-grained portion of the original loose and fractured rock and soil sample includes: sieving the original loose and fractured rock and soil sample using a sieve analysis method to obtain a coarse-grained portion and a fine-grained portion; performing particle analysis on the coarse-grained portion to obtain coarse-grained distribution data, and performing particle analysis on the fine-grained portion to obtain fine-grained distribution data; and merging the coarse-grained distribution data and the fine-grained distribution data to obtain the particle size distribution curve.

[0011] This invention separates the coarse and fine particle components of a sample using a sieve analysis method, fully capturing the particle information of the entire particle group. This avoids missing fine or coarse particle characteristics in single particle size analysis. Particle analysis is performed on coarse and fine particles separately to obtain corresponding gradation data, which are then spliced ​​and integrated to generate a complete gradation curve. This eliminates data gaps caused by segmented testing of coarse and fine particles, restores the true continuous particle distribution of soil and rock, and improves the integrity of particle gradation characterization and the reliability of experimental data.

[0012] Optionally, obtaining the effective particle size, 30% particle size, 60% particle size, and average particle size based on the particle size distribution curve includes: selecting 10, 30, 60, and 50 percentage points on the vertical axis of the particle size distribution curve; calculating the effective particle size using the particle size distribution curve based on the 10 percentage points; calculating the 30% particle size using the particle size distribution curve based on the 30 percentage points; calculating the 60% particle size using the particle size distribution curve based on the 60 percentage points; and calculating the average particle size using the particle size distribution curve based on the 50 percentage points.

[0013] This invention selects four characteristic percentage points (10%, 30%, 60%, and 50%) on the vertical axis of the particle size distribution curve, corresponding to the effective particle size, 30% particle size, 60% particle size, and average particle size, respectively. Multi-point extraction can simultaneously characterize the fine, intermediate, coarse, and overall median particle size levels of the soil. Single-point values ​​are prone to losing complete gradation characteristics. Simultaneous acquisition of multiple characteristic particle sizes can comprehensively cover the particle distribution range, improving the comprehensiveness of quantification of soil particle coarseness characteristics.

[0014] Optionally, calculating the non-uniformity coefficient and curvature coefficient based on the effective particle size, the 30% particle size, and the 60% particle size includes: calculating the non-uniformity coefficient based on the 60% particle size and the effective particle size; and calculating the curvature coefficient based on the 30% particle size, the 60% particle size, and the effective particle size.

[0015] This invention calculates the non-uniformity coefficient using the 60% particle size and the effective particle size to reflect the width of particle distribution. Then, it combines the 30% particle size, 60% particle size, and effective particle size to solve for the curvature coefficient to characterize the continuous shape of the gradation curve. The combination of the two sets of coefficients can completely evaluate the quality of soil particle gradation, making up for the deficiency that a single parameter cannot simultaneously reflect particle uniformity and distribution continuity, and improving the accuracy of soil gradation characteristic evaluation.

[0016] Optionally, the calculation of porosity based on the pre-acquired sample density, mass water content, and specific gravity of the loose and broken rock and soil original sample, using the fine-grained portion and the coarse-grained portion, includes: performing density measurement processing on the loose and broken rock and soil original sample to obtain the sample density; drying the loose and broken rock and soil original sample using a drying method, and calculating the mass water content based on the drying result; calculating the fine-grained specific gravity of the fine-grained portion using a specific gravity bottle method; calculating the coarse-grained specific gravity of the coarse-grained portion using a siphon method; calculating the specific gravity of the loose and broken rock and soil based on the fine-grained specific gravity and the coarse-grained specific gravity; and calculating the porosity using the sample density, the mass water content, the specific gravity of the loose and broken rock and soil, and the pre-acquired density of distilled water at four degrees Celsius.

[0017] This invention uses experimental sample density and drying method to measure moisture content. It uses specific gravity bottle method and siphon method to measure the specific gravity of coarse and fine particles in different particle groups and weights them to obtain the comprehensive specific gravity. Then, it combines the density of distilled water at four degrees Celsius to accurately solve the porosity. It distinguishes the difference in specific gravity of coarse and fine particles to avoid the property deviation caused by uniform value. The porosity is calculated by linking multi-dimensional geotechnical test data, which improves the accuracy of porosity measurement.

[0018] Optionally, calculating the three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity includes: obtaining the dynamic viscosity of water, the density of water, and the gravitational acceleration; and calculating the three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, the porosity, the dynamic viscosity of water, the density of water, and the gravitational acceleration.

[0019] This invention incorporates fundamental fluid parameters such as dynamic viscosity, water density, and gravitational acceleration, while simultaneously including various soil and rock indices such as effective particle size, average particle size, non-uniformity coefficient, curvature coefficient, and porosity to collaboratively calculate three-dimensional tortuosity. It takes into account the multiple influences of medium pore structure, particle size distribution, and seepage fluid properties, and abandons the simplified model that only considers porosity, thereby improving the fit between the calculated three-dimensional tortuosity of loose and fractured soil and the characteristics of real seepage channels.

[0020] Optionally, the step of calculating the three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, the porosity, the dynamic viscosity of water, the density of water, and the gravitational acceleration includes: constructing a microscale flow rate expression and a macroscale flow rate expression; constructing a basic analytical expression for the three-dimensional tortuosity based on the obtained tortuosity geometric definition, the microscale flow rate expression, and the macroscale flow rate expression; obtaining the fractal power-law distribution of pore size based on fractal theory, and obtaining an analytical expression for the average pore radius based on the fractal power-law distribution of pore size; constructing a permeability-permeability coefficient relationship expression; substituting the analytical expression for the average pore radius and the permeability-permeability coefficient relationship expression into the basic analytical expression for the three-dimensional tortuosity to obtain the final analytical expression for the three-dimensional tortuosity; and substituting the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity into the final analytical expression for the three-dimensional tortuosity to obtain the three-dimensional tortuosity.

[0021] This invention derives the basic analytical formula for tortuosity by combining microscopic and macroscopic flow formulas, derives the expression for average pore radius based on fractal theory, establishes the correlation between permeability and permeability coefficient, and then substitutes the two types of expressions into the simplified formula to obtain the final analytical formula. It transforms microscopic pore parameters into conventional geotechnical measurable indicators, eliminating the need for microscopic observation and numerical simulation. It solves tortuosity by comprehensively considering multiple influencing factors such as particles, pores, and fluids, thus improving the scientific rigor and ease of engineering practice in the theoretical calculation of three-dimensional tortuosity of loose and fractured soil and rock.

[0022] Optionally, the step of obtaining the fractal power-law distribution of pore size based on fractal theory and deriving an analytical expression for the average pore radius based on the fractal power-law distribution of pore size includes: obtaining the fractal power-law distribution of pore size based on fractal theory; obtaining a general analytical expression for the average pore radius based on the fractal power-law distribution of pore size; obtaining a basic expression for the fractal dimension and a diameter-porosity relationship; obtaining a fractal dimension expression based on the diameter-porosity relationship and the basic expression for the fractal dimension; and substituting the fractal dimension expression into the general analytical expression for the average pore radius to obtain an analytical expression for the average pore radius.

[0023] This invention establishes a power-law distribution of pore size based on fractal theory and derives a general formula for the average pore radius. By combining the basic formula of fractal dimension with the correlation formula between particle size and porosity, the fractal dimension that can be solved by geotechnical parameters is obtained. Then, the fractal dimension is substituted into the general formula to obtain an analytical solution for the average pore radius. This transforms the microscopic pore characteristics that are difficult to observe directly into a measurable index by conventional tests, avoiding microscopic testing methods such as mercury intrusion porosimetry and scanning, and improving the feasibility and calculation accuracy of the average pore radius derivation.

[0024] Optionally, constructing the permeability-permeability coefficient relationship expression includes: obtaining an initial expression for permeability-permeability coefficient and an empirical model related to the permeability coefficient; substituting the empirical model related to the permeability coefficient into the initial expression for permeability-permeability coefficient to obtain the permeability-permeability coefficient relationship expression.

[0025] This invention, by retrieving the basic conversion formulas for permeability and permeability coefficient, and integrating the empirical model of permeability coefficient including void ratio, gradation, and characteristic particle size to derive the related expressions, opens up a conversion channel between microscopic permeability and conventional geotechnical test indicators. This eliminates the complex experimental process of separately measuring permeability, realizes convenient conversion between parameters, improves the convenience of converting permeability-related parameters in the tortuosity derivation process, and simplifies the overall three-dimensional tortuosity solution process.

[0026] Optionally, the three-dimensional tortuosity satisfies the following formula: , in, For three-dimensional tortuosity, Porosity The density of water, It is the acceleration due to gravity. The average particle size is For effective particle size, The coefficient of non-uniformity, The curvature coefficient, This is the dynamic viscosity of water.

[0027] This invention integrates porosity, multiple characteristic particle sizes, gradation coefficients, and water physical parameters to construct a complete analytical formula for three-dimensional tortuosity. It incorporates fractal pore distribution laws to accurately characterize the geometric features of pore channels inside soil and rock. It eliminates the need for complex experimental methods such as microscopic scanning and numerical simulation, and can complete the calculation based solely on parameters measurable by conventional geotechnical tests. It fully considers multiple influencing factors such as particle size, gradation quality, pore size ratio, and seepage fluid properties, avoiding the distortion problems caused by traditional single-parameter simplified models. This improves the theoretical completeness and engineering calculation accuracy of the three-dimensional tortuosity calculation results for loose and fractured soil and rock. Attached Figure Description

[0028] Figure 1This is a flowchart of a method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size, according to an embodiment of the present invention. Figure 2 The particle size distribution curves of loose and fractured rock and soil in Examples 1-3 of this invention are shown. Figure 3 This is the particle size distribution curve of loose and broken rock and soil in Example 4 of the present invention; Figure 4 This is the particle size distribution curve of loose and broken rock and soil in Example 5 of the present invention; Figure 5 This is the particle size distribution curve of loose and broken rock and soil in Example 6 of the present invention; Figure 6 This is a comparison chart of the theoretical and experimental values ​​of the permeability coefficient of this invention. Detailed Implementation

[0029] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0030] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0031] Please see Figure 1 In order to solve the problems in the prior art, in an alternative embodiment, such as Figure 1 The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size, as shown, includes the following steps: Step S1: Obtain the particle size distribution curve, fine-grained portion, and coarse-grained portion of the original sample of loose and broken rock and soil.

[0032] The process of obtaining the particle size distribution curves, fine-grained fractions, and coarse-grained fractions of the original samples of loose and fractured rock and soil includes the following sub-steps: Step S101: The original sample of loose and broken rock and soil is screened using a sieve analysis method to obtain coarse and fine particles.

[0033] In this embodiment, a raw sample of loose, broken rock and soil is taken, and after removing debris such as tree roots and gravel, the sample is thoroughly mixed. A set of standard sieves is stacked from top to bottom in order of increasing mesh size, including standard sieves with different aperture sizes such as 0.075mm, 0.25mm, 0.5mm, 1mm, 2mm, 5mm, 10mm, 20mm, 40mm, and 60mm. The stacked standard sieve set is then installed on a vibrating sieve machine. The pre-dried and cooled raw sample of loose, broken rock and soil is weighed, poured into the top sieve, covered, and the vibrating sieve machine is started for sieving. The sieving time is set according to the sample type. After sieving, each sieve is removed in sequence, and the retained soil particles on each sieve are transferred to evaporating dishes, dried in an oven to constant weight, cooled in a desiccator, and weighed separately to obtain the sieve residue mass of each particle group. The soil particles collected in the chassis are considered the fine particles, and the soil particles retained on each sieve are combined as the coarse particles.

[0034] Step S102: Perform particle analysis on the coarse-grained portion to obtain coarse-grained gradation data, and perform particle analysis on the fine-grained portion to obtain fine-grained gradation data.

[0035] In this embodiment, the soil particles retained on each level of sieve are combined as the coarse particles. The percentage of the mass of each particle group relative to the total mass of the coarse particles is calculated based on the sieve residue mass of each particle group, thus obtaining the coarse particle gradation data. At the same time, the fine particles collected in the chassis are thoroughly stirred and homogenized. The hydrometer method or pipette method is used to measure the hydrometer reading or pipette suction according to the sedimentation time interval. The mass percentage of particles in each particle size range is calculated according to Stokes' law, thus obtaining the fine particle gradation data.

[0036] Step S103: The coarse particle size distribution data and the fine particle size distribution data are merged to obtain the particle size distribution curve.

[0037] In this embodiment, the coarse-grained gradation data and fine-grained gradation data obtained in step S103 are spliced ​​together according to the particle size range, and a continuous and complete particle gradation curve is plotted with particle size as the abscissa and the cumulative percentage of soil particles smaller than a certain particle size as the ordinate.

[0038] Step S2: Based on the particle size distribution curve, obtain the effective particle size, 30% particle size, 60% particle size and average particle size.

[0039] The specific steps for obtaining the effective particle size, 30% particle size, 60% particle size, and average particle size based on the particle size distribution curve include the following: Step S201: Select ten percentage points, thirty percentage points, sixty percentage points and fifty percentage points on the vertical axis of the particle size distribution curve.

[0040] In this embodiment, the horizontal axis of the particle size distribution curve represents particle size, and the vertical axis represents the cumulative percentage of soil particles smaller than a certain particle size. On the vertical axis of the particle size distribution curve, four percentage points with cumulative percentages of 10%, 30%, 60%, and 50% are selected as positioning references for subsequent reading of the corresponding particle size values.

[0041] Step S202: Calculate the effective particle size using the particle size distribution curve based on the ten percentage points.

[0042] In this embodiment, the point where the cumulative percentage reaches 10% is located on the vertical axis of the particle size distribution curve. A horizontal line is drawn from this point to intersect the particle size distribution curve, and a perpendicular line is drawn from the intersection point to intersect the horizontal axis. The particle size value corresponding to the foot of the perpendicular on the horizontal axis is read. This particle size value is the effective particle size. The effective particle size reflects the particle size of the fine particles in loose and fractured rock and soil, that is, the mass of particles with a diameter smaller than this value accounts for 10% of the total mass of the soil. It is an important basic parameter for evaluating the particle size distribution of soil and calculating the coefficient of uniformity and the coefficient of curvature.

[0043] Step S203: Calculate the 30% particle size using the particle size distribution curve based on the 30 percentage points.

[0044] In this embodiment, the point where the cumulative percentage reaches 30% is located on the vertical axis of the particle size distribution curve. A horizontal line is drawn from this point to intersect the particle size distribution curve, and then a perpendicular line is drawn from the intersection point to intersect the horizontal axis. The particle size value corresponding to the foot of the perpendicular on the horizontal axis is read. This particle size value is the 30% particle size. The 30% particle size reflects a specific quantile value of particle distribution in loose and fractured rock and soil, that is, the mass of particles with a diameter smaller than this value accounts for 30% of the total mass of the soil. It is a key parameter for calculating the curvature coefficient.

[0045] Step S204: Calculate the 60% particle size using the particle size distribution curve based on the 60 percentage points.

[0046] In this embodiment, the point where the cumulative percentage reaches 60% is located on the vertical axis of the particle size distribution curve. A horizontal line is drawn from this point to intersect the particle size distribution curve, and then a perpendicular line is drawn from the intersection point to intersect the horizontal axis. The particle size value corresponding to the foot of the perpendicular on the horizontal axis is read. This particle size value is the 60% particle size. The 60% particle size reflects the particle size of the coarse particles in loose and fractured rock and soil, that is, the mass of particles with a diameter smaller than this value accounts for 60% of the total mass of the soil. It is an important parameter for calculating the coefficient of uniformity and the coefficient of curvature.

[0047] Step S205: Calculate the average particle size using the particle size distribution curve based on the fifty percentage points.

[0048] In this embodiment, the point where the cumulative percentage reaches 50% is located on the vertical axis of the particle size distribution curve. A horizontal line is drawn from this point to intersect the particle size distribution curve, and a perpendicular line is drawn from the intersection point to intersect the horizontal axis. The particle size value corresponding to the foot of the perpendicular on the horizontal axis is read. This particle size value is the average particle size. The average particle size is the median particle size distribution in loose and fractured rock and soil, that is, the mass of particles with a diameter smaller than this value accounts for 50% of the total mass of the soil. It represents the overall level of particle fineness in the soil and is a key parameter for subsequent calculation of maximum pore size and three-dimensional tortuosity.

[0049] Step S3: Calculate the non-uniformity coefficient and curvature coefficient based on the effective particle size, the 30% particle size, and the 60% particle size.

[0050] The calculation of the non-uniformity coefficient and curvature coefficient based on the effective particle size, the 30% particle size, and the 60% particle size specifically includes the following sub-steps: Step S301: Calculate the non-uniformity coefficient based on the 60% particle size and the effective particle size.

[0051] In this embodiment, the non-uniformity coefficient The calculation formula is: , in, For 60% of the particle size, Effective particle size. Inhomogeneity coefficient. It reflects the uniformity of the soil particle size distribution. A higher value indicates a wider particle distribution range and a more uneven gradation. The closer the value is to 1, the more uniform the particle size.

[0052] Step S302: Calculate the curvature coefficient based on the 30% particle size, the 60% particle size, and the effective particle size.

[0053] In this embodiment, the curvature coefficient The calculation formula is: , in, For 30% of the particle size, For 60% of the particle size, Effective particle size. Curvature coefficient. It reflects the continuity of soil particle size distribution, that is, the shape characteristics of the particle size distribution curve, and is used to evaluate whether the soil gradation is good.

[0054] Step S4: Based on the sample density, mass water content and specific gravity of the loose and broken rock and soil original sample obtained in advance, the porosity is calculated using the fine-grained portion and the coarse-grained portion.

[0055] The calculation of porosity based on the pre-obtained sample density, mass water content, and specific gravity of the loose and fractured rock and soil original sample, using the fine-grained and coarse-grained portions, specifically includes the following sub-steps: Step S401: Perform density measurement processing on the original sample of the loose and broken rock and soil to obtain the sample density.

[0056] In this embodiment, the density of the original loose and fractured rock and soil sample is measured using the water-filling method. The test surface is leveled at a representative location, and a test pit of suitable size is excavated according to the maximum particle size of the sample and the site conditions. All the excavated wet soil sample is promptly placed into a sealed container and weighed to obtain the wet soil mass. Then, a plastic film is laid in the test pit, ensuring it adheres fully to the pit wall, and water is slowly injected into the plastic film until it reaches a predetermined reference plane. The volume of the injected water is recorded, and this volume is taken as the test pit volume. The wet density of the original loose and fractured rock and soil sample is calculated based on the ratio of the wet soil mass to the test pit volume; this wet density is the sample density. Another representative wet soil sample is placed in an aluminum box and brought back to the laboratory for step S402, where the moisture content is determined using the drying method.

[0057] Step S402: The original sample of the loose and broken rock and soil is dried using the drying method, and the mass moisture content is calculated based on the result of the drying treatment.

[0058] In this embodiment, for the original loose and fractured rock and soil sample, approximately 30g of representative wet soil sample is weighed and placed in a clean aluminum box. The box is immediately covered and weighed, and the total mass of the wet soil sample and the aluminum box is recorded. Then, the box is opened and the aluminum box and wet soil sample are placed in an oven and continuously dried at a constant temperature of 105℃ to 110℃ until the sample reaches a constant weight (usually the drying time is not less than 8 hours). The aluminum box is then removed, the box is covered, and the sample is placed in a desiccator to cool to room temperature before being weighed, and the total mass of the dry soil sample and the aluminum box is recorded. The mass water content of the loose and fractured rock and soil is calculated by dividing the mass difference before and after drying by the mass of the dry soil. The mass water content is the ratio of the mass of water in the soil to the mass of soil particles, reflecting the water content of the soil and is also one of the basic physical property indicators necessary for calculating porosity.

[0059] Step S403: Calculate the specific gravity of the fine particles using the specific gravity bottle method.

[0060] In this embodiment, the fine-grained soil sample is dried to constant weight in an oven at 105℃~110℃ and cooled to room temperature. A certain amount of the dry soil sample is weighed and placed into a clean specific gravity bottle. Half a bottle of pure water is added and the sample is heated to boiling for about 1 hour to remove air from the soil sample. After cooling, pure water is added to the scale line of the specific gravity bottle. The outer wall of the bottle is wiped dry and the total mass of the specific gravity bottle, soil sample and water is weighed. At the same time, the density of pure water at the same temperature is measured. Based on the difference between the total mass of the specific gravity bottle, soil sample and water and the total mass of the specific gravity bottle and water, the mass of water with the same volume as the soil particles is calculated, and then the specific gravity of the fine particles is obtained.

[0061] Step S404: Calculate the coarse particle specific gravity of the coarse particle portion using the siphon method.

[0062] In this embodiment, the coarse-grained soil sample is dried in an oven at 105℃~110℃ to constant weight and cooled, and its mass is measured. The dried coarse-grained soil sample is placed in a siphon tube, and water is poured into the tube until the water level exceeds the top of the siphon tube. After the water level stabilizes, the total mass of the siphon tube and the discharged water is measured. The water level in the tube is kept constant by using the siphon principle. The total volume of the coarse-grained soil sample is determined by measuring the volume of water displaced by the soil sample. The specific gravity of the coarse particles is obtained by the ratio of the dry soil mass to the total volume of the soil sample.

[0063] Step S405: Calculate the specific gravity of the loose and broken rock and soil mass based on the specific gravity of the fine particles and the specific gravity of the coarse particles.

[0064] In this embodiment, the dry masses of the fine-grained and coarse-grained portions are determined separately, and their respective mass fractions relative to the total dry mass of the original sample are calculated. Based on the principle that the solid volumes of the coarse-grained and fine-grained portions are additive, and combined with the specific gravity of the fine-grained portion, the specific gravity of the coarse-grained portion, and their corresponding dry mass fractions, the specific gravity of the loose and fractured rock and soil mass is calculated. The mass fractions of both the fine-grained and coarse-grained portions are determined based on the total dry mass of the original sample, and the sum of their mass fractions is 1.

[0065] Step S406: Calculate the porosity using the sample density, the mass water content, the specific gravity of the loose and broken rock and soil, and the pre-obtained density of distilled water at four degrees Celsius.

[0066] Porosity (Formula 2): , in, Porosity The density of the sample, The specific gravity of loose and broken rock and soil mass, The density of pure distilled water at 4℃ This refers to the water content by mass.

[0067] Step S5: Calculate the three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity.

[0068] The calculation of three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity specifically includes the following sub-steps: Step S501: Obtain the dynamic viscosity, density, and gravitational acceleration of water.

[0069] Step S502: Calculate the three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, the porosity, the dynamic viscosity of water, the density of water, and the gravitational acceleration.

[0070] The calculation of three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, the porosity, the dynamic viscosity of water, the density of water, and the gravitational acceleration specifically includes the following sub-steps: Step S50201: Construct the microscale flow expression and the macroscale flow expression.

[0071] At the microscale, we assume that the fluid flow in a single cylindrical capillary is laminar and obeys the Hagen-Poiseuille law. For a single capillary with radius r, the flow rate (Equation 4) is: , in, Let π be the flow rate of a single capillary tube, and π be the mathematical constant pi. Where is the capillary radius. The pressure difference across the capillary tube. The dynamic viscosity of the fluid. This represents the actual path length of the fluid.

[0072] If we assume that a certain representative primitive element (RVE) contains N roots with an equivalent average radius... For a capillary tube, the microscale flow rate through this cross-section can be expressed as: , in, For total micro-flow, For the number of capillaries, Average pore radius The flow rate, where π is the mathematical constant pi. Where is the capillary radius. The pressure difference across the capillary tube. The dynamic viscosity of the fluid. This represents the actual path length of the fluid.

[0073] On a macroscopic scale, the seepage of fluid in porous media follows Darcy's Law, and the macroscopic flow rate expression (Equation 6) is as follows: , in, For macroscopic flow, For penetration rate, The macroscopic cross-sectional area is perpendicular to the seepage direction. For pressure difference, The dynamic viscosity of the fluid. Let be the linear length of the fluid along the direction of the macroscopic pressure gradient.

[0074] Step S50202: Construct a three-dimensional tortuosity basic analytical expression based on the obtained tortuosity geometric definition, the microscale flow expression, and the macroscale flow expression.

[0075] According to the geometric definition of tortuosity, tortuosity Equal to the actual path length of the fluid The linear length of the fluid along the macroscopic pressure gradient direction The ratio (Formula 3): , in, The tortuosity of the pore channel. This represents the actual path length of the fluid. Let be the linear length of the fluid along the direction of the macroscopic pressure gradient.

[0076] According to porosity The definition of is the ratio of pore volume to total volume, establishing the relationship between microscopic geometric parameters and macroscopic physical property parameters (Formula 7): , in, Porosity For pore volume, For the total volume, For the number of capillaries, The average pore radius, This represents the actual path length of the fluid. The macroscopic cross-sectional area is perpendicular to the seepage direction. Let be the linear length of the fluid along the direction of the macroscopic pressure gradient.

[0077] Based on the law of conservation of mass, let the macroscopic flow rate equal the microscopic total flow rate. By simultaneously applying formulas 5, 6, and 7, we can eliminate the microscopic parameter of tube number, which cannot be directly measured. and cross-sectional area The tortuosity can be obtained through algebraic operations. With penetration rate and average pore radius The fundamental analytical relationship, namely the fundamental analytical expression of three-dimensional tortuosity (Formula 8): , in, For three-dimensional tortuosity, Porosity The average pore radius, This refers to penetration rate.

[0078] Step S50203: Obtain the fractal power-law distribution of pore size based on fractal theory, and obtain an analytical expression for the average pore radius based on the fractal power-law distribution of pore size.

[0079] The process of obtaining the fractal power-law distribution of pore size based on fractal theory and deriving the analytical expression for the average pore radius based on the fractal power-law distribution of pore size specifically includes the following sub-steps: Step S5020301: Obtain the fractal power-law distribution of pore size based on fractal theory.

[0080] According to fractal theory, porous media with pore sizes greater than or equal to a certain scale... Number of pores It follows a power-law distribution, i.e., a fractal power-law distribution (Formula 9): , in, aperture The number of pores that are greater than or equal to the pore diameter dimension λ. The maximum pore diameter, denoted as fractal dimension of pore area.

[0081] when = At that time, the total number of channels (Formula 10): , in, The total number of channels, The maximum pore diameter, Minimum pore diameter, denoted as fractal dimension of pore area.

[0082] Step S5020302: Based on the fractal power law distribution of the pore size, obtain a general analytical expression for the average pore radius.

[0083] The general analytical expression for average pore radius (Formula 11): , in, The average pore radius, The average pore diameter, The fractal dimension of the pore area is denoted as . Minimum pore diameter, This represents the maximum pore diameter.

[0084] Step S5020303: Obtain the basic expression for fractal dimension and the diameter-porosity relationship.

[0085] For three-dimensional porous media, the fundamental expression for fractal dimension is (Equation 12): , in, The fractal dimension of the pore area is denoted as . Porosity Minimum pore diameter, This represents the maximum pore diameter.

[0086] Diameter-porosity relationship (Formula 13): , in, Minimum pore diameter, The maximum pore diameter, It is the ratio of the average particle size to the minimum particle size. Porosity For microporosity, .

[0087] Minimum particle size (Formula 17): , in, Minimum particle size, This is the minimum sieve aperture size.

[0088] In the formula: Average particle size The minimum particle size obtained by sieve analysis when conducting particle size analysis tests on soil and rock masses The ratio (Formula 14): , The formula for calculating the maximum pore size (Formula 15) is as follows: , in, The maximum pore diameter, Porosity The average particle size is denoted as .

[0089] Combining formulas 13, 14, and 15, the minimum pore size can be estimated (Formula 16): , in, Minimum pore diameter, The maximum pore diameter, Porosity To determine the minimum particle size, the minimum sieve aperture size selected based on the sieve analysis method used in soil and rock particle size analysis tests is [value missing]. m can be calculated using formula 17. for m. (This constant is determined by the geometric relationship of particle packing in three-dimensional space).

[0090] Step S5020304: Obtain the fractal dimension expression based on the diameter-porosity relationship and the basic expression of the fractal dimension.

[0091] In this embodiment, the diameter-porosity relationship is substituted into the basic expression of the fractal dimension to obtain the expression of the pore area fractal dimension with respect to porosity, average particle size, and minimum particle size. This realizes the expression of the fractal dimension, a microscopic geometric parameter, as a function of a parameter measurable by conventional geotechnical tests. Thus, the microscopic pore structure characteristics that cannot be directly measured are transformed into macroscopic measurable indicators that can be calculated from the gradation curve and porosity.

[0092] Step S5020305: Substitute the fractal dimension expression into the general analytical expression for the average pore radius to obtain the analytical expression for the average pore radius.

[0093] In this embodiment, by substituting the fractal dimension expression into the general analytical expression for the average pore radius, the analytical expression for the average pore radius can be obtained. This allows the average pore radius, a microscopic pore structure parameter, to be expressed as a function of porosity, average particle size, and minimum particle size. This completes the transformation of the average pore radius from an unmeasurable microscopic parameter to a measurable macroscopic parameter, laying the foundation for subsequent substitution into the basic analytical expression for three-dimensional tortuosity.

[0094] Step S50204: Construct the permeability-permeability coefficient relationship expression.

[0095] The specific steps involved in constructing the permeability-permeability coefficient relationship expression are as follows: Step S5020401: Obtain the initial expression for permeability-permeability coefficient and the empirical model related to permeability coefficient.

[0096] Initial expression for permeability-permeability coefficient (Formula 18): , in, For penetration rate, Permeability coefficient, The dynamic viscosity of water. The density of water, This is the acceleration due to gravity.

[0097] Empirical model related to permeability coefficient (Formula 19): , in, Permeability coefficient, Porosity The coefficient of non-uniformity, The curvature coefficient, The effective particle size.

[0098] The void ratio and porosity satisfy the following conversion relationship: , Where e is the void ratio, The porosity is mentioned above.

[0099] Step S5020402: Substitute the empirical model related to the permeability coefficient into the initial expression of permeability-permeability coefficient to obtain the permeability-permeability coefficient relationship expression.

[0100] In this embodiment, the empirical model related to the permeability coefficient is substituted into the initial expression for permeability-permeability coefficient. Combined with the conversion relationship between void ratio and porosity, and after algebraic simplification, the expression for the permeability-permeability coefficient relationship can be obtained, thus expressing the microscopic parameter of permeability as porosity. Effective particle size Inhomogeneity coefficient Curvature coefficient Dynamic viscosity of water The density of water and gravitational acceleration This function transforms permeability, a microscopic parameter that cannot be directly measured, into a macroscopically measurable index that can be calculated from conventional geotechnical test parameters, laying the foundation for its subsequent substitution into the analytical expression of the three-dimensional tortuosity foundation.

[0101] Step S50205: Substitute the analytical expression for the average pore radius and the permeability-permeability coefficient relationship into the basic analytical expression for the three-dimensional tortuosity to obtain the final analytical expression for the three-dimensional tortuosity.

[0102] In this embodiment, the analytical expression for average pore radius and the permeability-permeability coefficient relationship are substituted into the basic analytical expression for three-dimensional tortuosity. After algebraic simplification, the average pore radius is eliminated. and penetration rate By obtaining intermediate parameters, the final analytical expression for the three-dimensional tortuosity can be obtained. This expression only includes porosity. Effective particle size Average particle size Inhomogeneity coefficient Curvature coefficient Dynamic viscosity of water The density of water and gravitational acceleration A total of nine macroscopically measurable parameters were established, realizing the complete transformation of three-dimensional tortuosity from microscopically unmeasurable parameters to macroscopically measurable parameters.

[0103] Step S50206: Substitute the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity into the final analytical expression of the three-dimensional tortuosity to obtain the three-dimensional tortuosity.

[0104] The three-dimensional tortuosity (Formula 1) satisfies the following formula: , in, For three-dimensional tortuosity, Porosity The density of water, It is the acceleration due to gravity. The average particle size is For effective particle size, The coefficient of non-uniformity, The curvature coefficient, This is the dynamic viscosity of water.

[0105] The core significance of this final analytical expression for three-dimensional tortuosity lies in the following: First, existing methods for determining tortuosity either rely on complex techniques such as pore network model reconstruction, numerical simulation, microscopic image analysis, or mercury intrusion porosimetry, which are costly and time-consuming, or consider only a single factor (such as porosity), leading to large deviations between calculated and actual values, making them difficult to apply in engineering practice. In contrast, in this formula, apart from the dynamic viscosity, density, and gravitational acceleration of water, which are fluid properties and physical constants, the remaining parameters (porosity, effective particle size, average particle size, non-uniformity coefficient, and curvature coefficient) can all be obtained through conventional geotechnical analysis. The parameters are obtained directly from the experiment and are simple and quick to determine, significantly reducing the difficulty and cost of obtaining tortuosity. At the same time, the formula comprehensively considers the influence of three types of factors on tortuosity: porosity, particle size, and particle size distribution. Compared with the traditional model that only considers porosity, it can more comprehensively reflect the actual distribution and development characteristics of pore channels in loose and fractured rock and soil. The tortuosity index determined in this way is more in line with the actual situation, providing a simple and reliable theoretical basis and calculation tool for the effective and reasonable determination of the three-dimensional tortuosity of loose and fractured rock and soil and for the assessment of permeability characteristics and grouting design in engineering practice.

[0106] Example Calculation: Example 1: As Figure 2 As shown, particle size distribution curves of loose and fractured rock and soil samples were obtained using particle size analysis tests, and their effective particle size was determined accordingly. , , , , , Porosity was obtained using moisture content tests, density tests, and specific gravity tests. And determine the dynamic viscosity of water. .

[0107] Porosity of loose and broken rock and soil The parameters are as follows: the density of loose, fractured rock and soil mass measured by density test, moisture content test and specific gravity test, respectively. Moisture content ,proportion The three-dimensional tortuosity of loose and fractured rock and soil mass was obtained. .

[0108] Example 2: Figure 2 As shown, particle size distribution curves of loose and fractured rock and soil samples were obtained using particle size analysis tests, and their effective particle size was determined accordingly. , , , , , Porosity was obtained using moisture content tests, density tests, and specific gravity tests. And determine the dynamic viscosity of water. .

[0109] Porosity of loose and broken rock and soil The parameters are as follows: the density of loose, fractured rock and soil mass measured by density test, moisture content test and specific gravity test, respectively. Moisture content ,proportion The three-dimensional tortuosity of loose and fractured rock and soil mass was obtained. .

[0110] Example 3: As Figure 2 As shown, particle size distribution curves of loose and fractured rock and soil samples were obtained using particle size analysis tests, and their effective particle size was determined accordingly. , , , , , Porosity was obtained using moisture content tests, density tests, and specific gravity tests. And determine the dynamic viscosity of water. .

[0111] Porosity of loose and broken rock and soil The parameters are as follows: the density of loose, fractured rock and soil mass measured by density test, moisture content test and specific gravity test, respectively. Moisture content ,proportion The three-dimensional tortuosity of loose and fractured rock and soil mass was obtained. .

[0112] Example 4: Figure 3 As shown, particle size distribution curves of loose and fractured rock and soil samples were obtained using particle size analysis tests, and their effective particle size was determined accordingly. , , , , , Porosity was obtained using moisture content tests, density tests, and specific gravity tests. And determine the dynamic viscosity of water. .

[0113] Porosity of loose and broken rock and soil The parameters are as follows: the density of loose, fractured rock and soil mass measured by density test, moisture content test and specific gravity test, respectively. Moisture content ,proportion The three-dimensional tortuosity of loose and fractured rock and soil mass was obtained. .

[0114] Example 5: Figure 4 As shown, particle size distribution curves of loose and fractured rock and soil samples were obtained using particle size analysis tests, and their effective particle size was determined accordingly. , , , , , Porosity was obtained using moisture content tests, density tests, and specific gravity tests. And determine the dynamic viscosity of water. .

[0115] Porosity of loose and broken rock and soil The parameters are as follows: the density of loose, fractured rock and soil mass measured by density test, moisture content test and specific gravity test, respectively. Moisture content ,proportion The three-dimensional tortuosity of loose and fractured rock and soil mass was obtained. .

[0116] Example 6: As Figure 5As shown, particle size distribution curves of loose and fractured rock and soil samples were obtained using particle size analysis tests, and their effective particle size was determined accordingly. , , , , , Porosity was obtained using moisture content tests, density tests, and specific gravity tests. And determine the dynamic viscosity of water. .

[0117] Porosity of loose and broken rock and soil The parameters are as follows: the density of loose, fractured rock and soil mass measured by density test, moisture content test and specific gravity test, respectively. Moisture content ,proportion The three-dimensional tortuosity of loose and fractured rock and soil mass was obtained. .

[0118] Further comparison and verification of the scaling ratio and overall accuracy were conducted, as detailed below: To further verify the effectiveness and accuracy of the three-dimensional tortuosity calculation method for soil and rock masses based on porosity, gradation, and particle size of this invention, this embodiment selects four existing soil and rock mass tortuosity calculation models—Yu model, Li model, Mauret model, and Zhang Jiajun model—as comparative examples. Under the same experimental parameters, the three-dimensional tortuosity of each group of samples was calculated using the method described in this invention and the four comparative models mentioned above, and the corresponding theoretical permeability coefficients were further obtained. The theoretical permeability coefficients obtained by each model were compared with the measured values ​​from indoor permeability tests to evaluate the calculation accuracy of different tortuosity models and their applicability to different porosity, particle gradation, and particle size conditions. The comparison results are shown in Table 1 and... Figure 6 As shown, Figure 6 Line A represents the experimental permeability coefficient, line B represents the theoretical permeability coefficient obtained from this model, line C represents the theoretical permeability coefficient obtained from the Zhang Jiajun model, line D represents the theoretical permeability coefficient obtained from the Yu model, line E represents the theoretical permeability coefficient obtained from the Li model, and line F represents the theoretical permeability coefficient obtained from the Mauret model. Table 1 compares the theoretical calculated permeability coefficients with the experimentally measured values ​​from different models. Table 1 is as follows:

[0119] Based on Table 1 and Figure 6Further analysis of the comparative results reveals that the traditional Yu, Li, and Mauret models primarily consider porosity as a single factor, resulting in generally higher theoretical permeability coefficients under various experimental conditions. They also fail to adequately reflect the differences in seepage characteristics caused by variations in particle size distribution. The Zhang Jiajun model, while considering particle size distribution in addition to porosity, shows improvement over the aforementioned models. However, some deviations still exist in certain experimental groups, indicating that considering only porosity and particle size distribution is insufficient to fully characterize the influence of different particle geometry on the tortuosity of pore channels and seepage characteristics. In contrast, the three-dimensional model of tortuosity in loose, fractured rock and soil established in this invention, which comprehensively considers the effects of porosity, particle size distribution, and particle size, generally shows higher consistency between the theoretical permeability coefficients calculated and the measured values ​​from laboratory tests. It can better reflect the variation patterns of permeability coefficients among different experimental groups and exhibits better applicability and smaller calculation deviations under different porosity and particle size distribution conditions.

[0120] The above-mentioned multiple embodiments and comparative tests show that the three-dimensional tortuosity calculation method for soil and rock masses based on porosity, gradation, and size proposed in this invention overcomes the limitation of traditional tortuosity models that consider only a single influencing factor. It can comprehensively reflect the influence of porosity, particle gradation, and particle size on the tortuosity characteristics of pore channels in loose and fractured soil and rock masses. It has good calculation accuracy and applicability to different gradation conditions. It can provide a reliable theoretical basis and technical support for the characterization of seepage characteristics of loose and fractured soil and rock masses, the prediction of seepage parameters, and the theoretical analysis and numerical simulation of related soil and rock seepage engineering.

[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size, characterized in that, The method includes: Obtain the particle size distribution curves, fine-grained fraction, and coarse-grained fraction of the original sample of loose and fractured rock and soil. Based on the particle size distribution curve, the effective particle size, 30% particle size, 60% particle size and average particle size are obtained. The non-uniformity coefficient and curvature coefficient are calculated based on the effective particle size, the 30% particle size, and the 60% particle size; Based on the sample density, mass water content and specific gravity of the loose and broken rock and soil original sample obtained in advance, the porosity is calculated using the fine-grained part and the coarse-grained part. The three-dimensional tortuosity is calculated based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity.

2. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 1, characterized in that, The process of obtaining the particle size distribution curves, fine-grained fraction, and coarse-grained fraction of the original sample of loose and fractured rock and soil includes: The original samples of loose and broken rock and soil were sieved using a sieve analysis method to obtain coarse and fine particles. The coarse-grained portion is subjected to particle analysis to obtain coarse-grained gradation data, and the fine-grained portion is subjected to particle analysis to obtain fine-grained gradation data. The coarse-grained gradation data and the fine-grained gradation data are combined to obtain the particle gradation curve.

3. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 1, characterized in that, The process of obtaining the effective particle size, 30% particle size, 60% particle size, and average particle size based on the particle size distribution curve includes: Ten percentage points, thirty percentage points, sixty percentage points, and fifty percentage points are selected on the vertical axis of the particle size distribution curve; The effective particle size is calculated using the particle size distribution curve based on the ten percentage points. The 30% particle size is calculated using the particle size distribution curve based on the 30 percentage points. The 60% particle size is calculated using the particle size distribution curve based on the 60 percentage points. The average particle size is calculated using the particle size distribution curve based on the fifty percentage points.

4. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 1, characterized in that, The calculation of the non-uniformity coefficient and curvature coefficient based on the effective particle size, the 30% particle size, and the 60% particle size includes: The non-uniformity coefficient is calculated based on the 60% particle size and the effective particle size. The curvature coefficient is calculated based on the 30% particle size, the 60% particle size, and the effective particle size.

5. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 1, characterized in that, The calculation of porosity based on the pre-obtained sample density, mass water content, and specific gravity of the loose and fractured rock and soil original sample, using the fine-grained and coarse-grained portions, includes: The density of the original loose and fractured rock and soil sample was obtained by density measurement. The original sample of the loose and broken rock and soil was dried using a drying method, and the mass moisture content was calculated based on the results of the drying treatment. The specific gravity of the fine particles in the fine fraction was calculated using the specific gravity bottle method. The coarse particle specific gravity of the coarse particle portion was calculated using the siphon method; The specific gravity of loose and fractured rock and soil mass is calculated based on the specific gravity of fine particles and the specific gravity of coarse particles. Porosity is calculated using the sample density, the mass water content, the specific gravity of the loose and broken rock and soil, and the pre-obtained density of distilled water at four degrees Celsius.

6. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 1, characterized in that, The calculation of three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity includes: To obtain the dynamic viscosity, density, and gravitational acceleration of water; The three-dimensional tortuosity is calculated based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, the porosity, the dynamic viscosity of water, the density of water, and the gravitational acceleration.

7. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 6, is characterized in that... The calculation of three-dimensional tortuosity based on the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, the porosity, the dynamic viscosity of water, the density of water, and the gravitational acceleration includes: Construct microscale flow expressions and macroscale flow expressions; Based on the obtained geometric definition of tortuosity, the microscale flow expression, and the macroscale flow expression, a three-dimensional tortuosity fundamental analytical expression is constructed. The fractal power-law distribution of pore size is obtained based on fractal theory, and the analytical expression of average pore radius is obtained based on the fractal power-law distribution of pore size. Construct an expression for the relationship between permeability and permeability coefficient; Substituting the analytical expression for the average pore radius and the permeability-permeability coefficient relationship into the basic analytical expression for the three-dimensional tortuosity, we obtain the final analytical expression for the three-dimensional tortuosity. Substituting the effective particle size, the average particle size, the non-uniformity coefficient, the curvature coefficient, and the porosity into the final analytical expression of the three-dimensional tortuosity yields the three-dimensional tortuosity.

8. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 7, is characterized in that... The process of obtaining the fractal power-law distribution of pore size based on fractal theory, and deriving the analytical expression for the average pore radius based on the fractal power-law distribution of pore size, includes: The fractal power-law distribution of pore size is obtained based on fractal theory; A general analytical expression for the average pore radius is obtained based on the fractal power law distribution of the pore size; Obtain the basic expression for fractal dimension and the diameter-porosity relationship; The fractal dimension expression is obtained based on the diameter-porosity relationship and the basic expression of the fractal dimension. Substituting the fractal dimension expression into the general analytical expression for the average pore radius yields the analytical expression for the average pore radius.

9. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 7, is characterized in that, The expression for constructing the permeability-permeability coefficient relationship includes: Obtain the initial expression for permeability-permeability coefficient and the empirical model related to permeability coefficient; Substituting the empirical model related to the permeability coefficient into the initial expression for permeability-permeability coefficient yields the expression for the permeability-permeability coefficient relationship.

10. The method for calculating the three-dimensional tortuosity of soil and rock masses based on porosity, gradation, and size according to claim 1, characterized in that, The three-dimensional tortuosity satisfies the following formula: ， in, For three-dimensional tortuosity, Porosity The density of water, It is the acceleration due to gravity. The average particle size is For effective particle size, The coefficient of non-uniformity, The curvature coefficient, This is the dynamic viscosity of water.

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