Method and system for determining the cylindrical permeable radius of a bingham cement slurry diffusion path

Abstract

The present application relates to the field of environmental protection and ecological restoration, in particular to a method and system for determining the cylindrical penetration radius of a Bingham cement slurry diffusion path, comprising the following steps: obtaining the density, mass water content, specific gravity, permeability coefficient and average particle size of the rock-soil body through a rock-soil body mechanics experiment, and obtaining the porosity of the rock-soil body; obtaining the length ratio of the pore channels in the rock-soil body based on the porosity of the rock-soil body and the above-mentioned parameter information; obtaining the water viscosity, Bingham fluid plastic viscosity and Bingham fluid yield stress based on a rheological test scheme, and obtaining the water-cement ratio of the Bingham cement slurry, the grouting time, the grouting pressure, the grouting pipe radius and the groundwater pressure at the grouting point according to the grouting requirements; and obtaining the cylindrical penetration radius result under the Bingham cement slurry diffusion path based on the comprehensive action information of the particle size distribution, the diffusion path influence and the parameter information. The present application can calculate and predict the cylindrical penetration radius, reduce the risk of grouting engineering and ensure the safety and stability of the engineering.

Description

Technical Field

[0001] This invention relates to the field of environmental protection and ecological restoration technology, specifically to a method and system for determining the cylindrical penetration radius of Bingham cement slurry diffusion path. Background Technology

[0002] In grouting engineering practice, Bingham cement grout is an important grouting material, and its diffusion morphology and penetration mechanism have a decisive influence on the grouting effect. However, different types of cement grout have different diffusion patterns in soil and rock masses and are affected by multiple factors, resulting in significant differences in the methods for determining the penetration radius. Currently, a complete method for determining the cylindrical penetration radius of Bingham cement grout considering its diffusion path has not yet been developed for grouting technology, which to some extent limits the design and construction effectiveness of grouting projects.

[0003] Existing permeation grouting technologies are mostly based on empirical formulas or simplified models, which cannot fully consider the specific columnar diffusion pattern of Bingham cement grout in soil and rock. This leads to discrepancies between the predicted permeation radius and the actual engineering situation, and ignores the influence of the diffusion path, making it difficult to achieve the optimal effect in grouting design.

[0004] With the continuous development of grouting engineering technology and the increasing requirements for grouting effect, the existing permeation grouting technology is difficult to meet the complex geological conditions and engineering needs. Therefore, it is necessary to propose a method for determining the columnar permeation radius that is more in line with the practice of grouting engineering. Summary of the Invention

[0005] To address the shortcomings of existing methods and their limitations in practical application, and to meet the needs of complex geological conditions and diverse engineering projects, this invention aims to further achieve accurate prediction of the columnar penetration radius of Bingham cement grout, optimize grouting parameters, improve grouting effectiveness, and ensure the mechanical properties of soil and rock. Firstly, this invention provides a method for determining the columnar penetration radius of the diffusion path of Bingham cement grout. This method includes the following steps: obtaining the density, water content, specific gravity, permeability coefficient, and average particle size of the soil and rock through soil and rock mechanical experiments; obtaining the porosity of the soil and rock based on the density, water content, and specific gravity; analyzing the length ratio of pore channels based on the porosity, density, water content, specific gravity, permeability coefficient, and average particle size, and obtaining the length ratio of pore channels within the soil and rock; and obtaining the water viscosity and Bingham cement grout viscosity based on a rheological testing scheme. Based on the fluid plastic viscosity and Bingham fluid yield stress, the water-cement ratio of Bingham cement grout, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure at the grouting point are obtained according to the grouting requirements. Combining the comprehensive effect information of particle size distribution, diffusion path influence, the porosity of the soil and rock mass, the length ratio, the water viscosity, the plastic viscosity of Bingham fluid, the yield stress of Bingham fluid, the water-cement ratio of Bingham cement grout, the grouting time, the grouting pressure, the grouting pipe radius, and the groundwater pressure, the columnar permeability radius under the diffusion path of Bingham cement grout is predicted, and the columnar permeability radius analysis results are obtained.

[0006] When predicting the permeability radius of a column, this invention comprehensively considers multiple factors, including the combined effect of particle size distribution, the influence of diffusion path, the porosity of the soil and rock, the length ratio, water viscosity, Bingham fluid plastic viscosity, Bingham fluid yield stress, Bingham cement grout water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure, making the prediction results more consistent with actual engineering conditions.

[0007] Optionally, obtaining the density, water content, specific gravity, permeability coefficient, and average particle size of the soil and rock mass through soil and rock mechanics experiments, and obtaining the porosity result of the soil and rock mass based on the density, water content, and specific gravity, includes: obtaining soil and rock mechanics experimental data based on the soil and rock mechanics experiments, wherein the soil and rock mechanics experimental data includes soil and rock mass density, water content, specific gravity, permeability coefficient, and average particle size; and obtaining the porosity result of the soil and rock mass based on the density, water content, and specific gravity.

[0008] The porosity results of the soil and rock mass satisfy the following relationship;

[0009]

[0010] in, Indicates the porosity of soil and rock mass. Indicates the density of rock and soil mass. Indicates the specific gravity of the rock and soil mass. express The density of pure distilled water, Indicates the water content by mass.

[0011] The parameters such as density, mass water content, and specific gravity of the rock and soil are important indicators for describing the physical properties of rock and soil. Obtaining these parameters through experiments is beneficial for accurately assessing the basic properties of rock and soil, and provides reference information for subsequent engineering design and construction schemes.

[0012] Optionally, the step of analyzing the ratio of pore channel length to the porosity of the soil and rock mass, the density of the soil and rock mass, the mass water content, the specific gravity, the permeability coefficient, and the average particle size, and obtaining the pore channel length ratio within the soil and rock mass includes: deriving an expression for the pore channel length ratio based on the Hagen-Poiseuille formula, Darcy's law, the porosity-fractal dimension relationship, and the porosity of the soil and rock mass; deriving and transforming the ratio of pore channel length to the porosity of the soil and rock mass, the density of the soil and rock mass, the mass water content, the specific gravity, the permeability coefficient, and the average particle size, based on the relationship between the bidispersion model and porosity, the length ratio expression, and obtaining a target expression for the pore channel length ratio within the soil and rock mass; and using the target expression for the pore channel length ratio within the soil and rock mass to obtain the pore channel length ratio within the soil and rock mass.

[0013] The pore channel length ratio expression derived in this invention can provide a deeper understanding of the microstructure and pore distribution characteristics of soil and rock masses, and is beneficial for effectively evaluating the permeability, mechanical properties and stability of soil and rock masses.

[0014] Optionally, the expression for the ratio of pore channel length derived from the Hagen-Poiseuille formula, Darcy's law, porosity-fractal dimension relationship, and the porosity result of the soil and rock mass includes:

[0015] The porosity-fractal dimension relationship satisfies the following relationship:

[0016]

[0017] in, Indicates the porosity of soil and rock mass. Indicates the minimum radius of the pore channel. Indicates the maximum radius of the pore channel. Represents the fractal dimension of the pores;

[0018] The expression for the ratio of pore channel lengths satisfies the following relationship:

[0019]

[0020] in, This represents the ratio of the lengths of pore channels within the soil or rock mass. Indicates the equivalent length of the pore channel. Indicates the radius of the pore channel.

[0021] The expression of this invention can link porosity with the minimum radius, maximum radius and fractal dimension of pore channels, providing technical support for the derivation of pore channel length ratios.

[0022] Optionally, the derivation and transformation of the length ratio of pore channels based on the relationship between the bidispersion model and porosity, the length ratio expression, the porosity result of the soil and rock mass, the density of the soil and rock mass, the mass water content, the specific gravity, the permeability coefficient, and the average particle size to obtain the target expression for the length ratio of pore channels in the soil and rock mass includes:

[0023] The target expression for the ratio of pore channel lengths within the soil and rock mass satisfies the following relationship;

[0024]

[0025] in, This represents the ratio of the lengths of pore channels within the soil or rock mass. Indicates the average particle size. Indicates the porosity of soil and rock mass. It represents pi (π).

[0026] The target expression of this invention comprehensively considers multiple factors such as porosity, average particle size, density, mass water content, specific gravity and permeability coefficient of rock and soil, which can more accurately predict the length ratio of pore channels in rock and soil and improve the accuracy of prediction results.

[0027] Optionally, the prediction of the columnar permeability radius under the diffusion path of Bingham cement grout, based on the combined information of particle size distribution, diffusion path influence, soil porosity, length ratio, water viscosity, Bingham fluid plastic viscosity, Bingham fluid yield stress, Bingham cement grout water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure, and the obtaining of the columnar permeability radius analysis results, includes: introducing the basic rheological equation of Bingham grout and the flow of grout in the pore channels; and analyzing the velocity distribution in the piston zone and shear zone based on the basic rheological equation of Bingham grout, the flow of grout in the pore channels, the plastic viscosity of Bingham fluid, the yield stress of Bingham fluid, and the grouting pipe radius. The expression is used to calculate the average flow velocity of laminar flow in a single pore channel of Bingham cement grout based on the velocity distribution expression of the piston zone and shear zone. The starting gradient pressure, grout volume relationship, and diffusion total surface area calculation formula are introduced. Combining the starting gradient pressure, grout volume relationship, diffusion total surface area calculation formula, soil porosity result, length ratio, water viscosity, Bingham fluid plastic viscosity, Bingham fluid yield stress, Bingham cement grout water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure, the columnar permeability radius determination function under the influence of the diffusion path is obtained using the separation variable integration method. The columnar permeability radius determination function is used to predict the columnar permeability radius, and the columnar permeability radius analysis results are obtained.

[0028] This invention introduces Bingham's basic rheological equation for grout, and by combining the flow conditions with multiple influencing factors, it can more accurately describe the flow behavior of Bingham cement grout in soil and rock, thereby improving the prediction accuracy of columnar permeability radius.

[0029] Optionally, the introduction of Bingham's basic rheological equation for slurry and the flow of slurry in pore channels includes:

[0030] The Bingham slurry basic rheological equation satisfies the following relationship;

[0031]

[0032] in, The basic rheological equation of Bibbingham slurry This represents the yield stress of the Bingham fluid. This indicates the plastic viscosity of Bingham fluid. Indicates shear rate;

[0033] The flow condition satisfies the following relationship;

[0034]

[0035] in, Represents pi (π). This represents the distance from the center of the circular tube to any point of arbitrary radius. This represents the pressure difference between the left and right ends of the microfluidic unit column. Represents shear stress. This represents a small length segment of a microfluidic unit column in the flow direction.

[0036] This invention can more accurately predict the flow behavior of slurry in pore channels, including flow velocity, pressure distribution, and shear stress distribution, which helps to improve the accuracy of the prediction results of columnar permeability radius and provides a more reliable reference for engineering design.

[0037] Optionally, the method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path further includes:

[0038] The velocity distribution expressions of the piston region and the shear region are obtained based on the pressure gradient, and the velocity distribution expressions of the piston region and the shear region satisfy the following relationship;

[0039]

[0040] in, This indicates the flow velocity of Bingham grout in the pores of the rock and soil mass. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. Indicates the maximum radius of the pore channel. Indicates the radius of the pore channel. This represents the yield stress of the Bingham fluid. Indicates radial distance;

[0041] The average flow velocity satisfies the following relationship:

[0042]

[0043] in, This indicates the average flow rate of Bingham cement grout. Indicates the maximum radius of the pore channel. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. This represents the yield stress of the Bingham fluid.

[0044] This invention provides prediction of slurry flow and calculation of average flow velocity, which helps to better understand the diffusion of slurry in soil and rock masses, thereby enabling the development of more reasonable engineering implementation plans and ensuring the safety and stability of the project.

[0045] Optionally, the introduction of the initiation gradient pressure, grout volume relationship, and diffusion total surface area calculation formula, combined with the initiation gradient pressure, the grout volume relationship, the diffusion total surface area calculation formula, the soil porosity result, the length ratio, the water viscosity, the Bingham fluid plastic viscosity, the Bingham fluid yield stress, the Bingham cement grout water-cement ratio, the grouting time, the grouting pressure, the grouting pipe radius, and the groundwater pressure, combined with the separation variable integration method to derive the columnar permeability radius determination function under the influence of the diffusion path includes:

[0046] The initiation gradient pressure satisfies the following relationship:

[0047]

[0048] in, Indicates the initiation of gradient pressure. This represents the yield stress of the Bingham fluid. Indicates the maximum radius of the pore channel;

[0049] The formula for slurry volume relationship satisfies the following relationship:

[0050]

[0051] in, Indicates the amount of grout injected. Represents pi (π). This indicates the diffusion radius of Bingham cement grout in soil and rock mass. Indicates the diffusion height. Indicates the porosity of soil and rock mass;

[0052] The formula for calculating the total diffusion surface area satisfies the following relationship:

[0053]

[0054] in, This represents the total surface area of ​​the Bingham cement grout diffusion. Represents pi (π). Indicates the diffusion radius. Indicates the diffusion height;

[0055] The function for determining the cylindrical permeation radius under the influence of the diffusion path satisfies the following relationship:

[0056]

[0057] in, Indicates the radius of penetration of the column. Indicates the grouting pressure. This indicates the groundwater pressure at the grouting point. This indicates the plastic viscosity of Bingham fluid. Indicates the grouting time. This indicates the density of water. Indicates the porosity of soil and rock mass. Represents gravitational acceleration. This represents the spherical diffusion radius of Bingham cement grout in soil and rock mass. Indicates the permeability coefficient. Indicates the viscosity of water. This represents the ratio of the lengths of pore channels within soil and rock. Indicates the radius of the grouting hole. This represents the yield stress of the Bingham fluid.

[0058] This invention introduces the relationship between starting gradient pressure, grout volume, and total diffusion surface area, and combines multiple parameters such as soil porosity, length ratio, water viscosity, Bingham fluid plastic viscosity, yield stress, water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure to more comprehensively consider various factors affecting the diffusion path and columnar permeability radius of Bingham cement grout.

[0059] Secondly, this invention also provides a system for determining the cylindrical penetration radius of Bingham cement slurry diffusion paths, capable of efficiently executing the method for determining the cylindrical penetration radius of Bingham cement slurry diffusion paths provided by this invention. The system includes an input device, a processor, an output device, and a memory, wherein the input device, processor, output device, and memory are interconnected. The memory includes a computer-readable storage medium as described in the first aspect of this invention, and is used to store a computer program, which includes program instructions. The processor is configured to call the program instructions. The system for determining the cylindrical penetration radius of Bingham cement slurry diffusion paths provided by this invention has a compact structure, strong applicability, and greatly improves operating efficiency. Attached Figure Description

[0060] Figure 1 This is a flowchart of the method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to the present invention.

[0061] Figure 2 This is a schematic diagram of the columnar permeation grouting stone morphology in the first embodiment of the Bingham cement slurry diffusion path determination method of the present invention.

[0062] Figure 3 This is a schematic diagram of the columnar permeation grouting stone morphology in the second embodiment of the Bingham cement slurry diffusion path determination method of the present invention.

[0063] Figure 4This is a schematic diagram of the columnar permeation grouting stone shape in the third embodiment of the Bingham cement slurry diffusion path determination method of the present invention.

[0064] Figure 5 This is a schematic diagram comparing the calculated value of the cylindrical penetration radius of the Bingham cement slurry diffusion path determined by the present invention with the traditional theoretical value.

[0065] Figure 6 This is a schematic diagram of the cylindrical penetration radius determination system for the diffusion path of Bingham cement slurry according to the present invention. Detailed Implementation

[0066] 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.

[0067] 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.

[0068] Please see Figure 1 To meet the needs of complex geological conditions and practical engineering requirements, this invention aims to accurately predict the columnar penetration radius of Bingham cement grout, improve the effectiveness of grouting projects, and provide technical support for the stability of the mechanical properties of soil and rock. The invention provides a method for determining the columnar penetration radius of the diffusion path of Bingham cement grout, comprising the following steps:

[0069] S1. Obtain the density, water content, specific gravity, permeability coefficient, and average particle size of the soil and rock mass through mechanical experiments. Based on the density, water content, and specific gravity, derive the porosity of the soil and rock mass. The implementation steps and specific details are as follows:

[0070] First, the density, mass water content, specific gravity, permeability coefficient and average particle size of the soil and rock were obtained through soil and rock mechanics experiments.

[0071] The rock and soil mechanics experimental data obtained from the experiments include the rock and soil density, water content, specific gravity, permeability coefficient, and average particle size. The details of how these experimental parameters were obtained are as follows:

[0072] Density of rock and soil Density tests are used for measurement, and any of the following methods can be selected: water filling method, sand filling method, or ring cutter method, to accurately obtain the density value of the soil and rock mass.

[0073] Mass moisture content The main method used is the drying method, which involves drying the soil and rock samples and calculating their mass change to obtain the mass water content.

[0074] proportion A comprehensive measurement combining the specific gravity bottle method and the siphon method is needed to further ensure the accuracy of the specific gravity determination results for soil and rock masses.

[0075] Permeability coefficient The permeability coefficient of the soil and rock mass is obtained by using on-site water injection tests or indoor permeability tests.

[0076] Average particle size The particle size distribution curve of the soil and rock mass is mainly obtained by particle analysis test. The abscissa value corresponding to the 50% point on the vertical axis of the curve is the average particle size of the soil and rock mass.

[0077] The porosity of the soil can be obtained based on its density, water content, and specific gravity.

[0078] Given the specific physical relationship between the density, mass water content and specific gravity of soil and rock, the porosity of soil and rock can be calculated based on the above three parameters, the physical properties of soil and rock, and related theoretical relationships.

[0079] The above porosity results for soil and rock masses satisfy the following relationship;

[0080]

[0081] in, Indicates the porosity of soil and rock mass. Indicates the density of rock and soil mass. Indicates the specific gravity of the rock and soil mass. express The density of pure distilled water, Indicates the water content by mass.

[0082] in, for Density of pure distilled water, as shown in the examples, is [value missing]. .

[0083] Calculations using the three basic parameters of density, mass water content, and specific gravity of soil and rock can more accurately reflect the actual porosity of the soil and rock. Each of these parameters has a clear physical meaning, and the analysis is based on the physical properties of the soil and rock and related theoretical relationships, which makes the calculation results highly reliable.

[0084] Furthermore, the method for analyzing the porosity of soil and rock in this embodiment is merely an optional condition of the present invention. In other embodiments, the method for analyzing the porosity of soil and rock can be optimized based on the physical and mechanical characteristics of the soil and rock and the calculation of the porosity of the soil and rock. This can lead to a deeper understanding of the mechanical properties and physical attributes of the soil and rock, and can more accurately calculate the porosity, laying the foundation for the practical application of the method for determining the cylindrical permeation radius of the diffusion path of Bingham cement slurry.

[0085] S2. Based on the porosity, density, water content, specific gravity, permeability coefficient, and average particle size of the soil and rock mass, the length ratio of pore channels is analyzed, and the length ratio of pore channels within the soil and rock mass is obtained. The specific steps and implementation content are as follows:

[0086] First, based on the Hagen-Poiseuille formula, Darcy's law, porosity-fractal dimension relationship, and porosity results of soil and rock, the expression for the ratio of pore channel length is derived and analyzed.

[0087] In the pore flow analysis, to simplify the analysis process, the pore channels in the soil and rock mass are approximated as circular pipes. Based on this assumption and combined with mathematical derivation, a formula for the flow rate per pore is derived. Furthermore, the intrinsic relationship between flow rate and pore radius, pressure gradient, and fluid viscosity is established. When fluid flows in a circular tubular pore channel, the flow rate of slurry passing through a single pore per unit time must satisfy the following relationship:

[0088]

[0089] in, This represents the flow rate of slurry through a single pore per unit time. Represents pi (π). This represents the pressure gradient of the fluid along the diffusion path. Indicates the radius of the pore channel. This indicates the viscosity of the fluid.

[0090] To further reveal the relationship between the macroscopic seepage characteristics and the microscopic pore structure of porous media, this embodiment arbitrarily selects a micro-volume unit within the soil and rock mass, and assumes that N pore channels exist within this unit. Furthermore, the total volumetric flow rate through this unit can be obtained by superimposing the flow rates of each pore channel; that is, the total volumetric flow rate of the unit satisfies the following relationship:

[0091]

[0092] in, This represents the total volumetric flow rate passing through the unit cell per unit time. Indicates the number of pore channels within a unit cell. Represents pi (π). This represents the pressure gradient of the fluid along the diffusion path. Indicates the radius of the pore channel. This indicates the viscosity of the fluid.

[0093] At the same time, according to Darcy's law, the total volumetric flow rate through the unit cell per unit time It can also be expressed as:

[0094]

[0095] in, This represents the total volumetric flow rate passing through the unit cell per unit time. Indicates penetration rate. Represents the cross-sectional area. Indicates fluid viscosity. This represents the pressure gradient of the fluid along the diffusion path.

[0096] By combining the two expressions above and introducing the permeability parameter, a relationship between the macroscopic seepage characteristics and the microscopic pore structure of porous media was successfully constructed. This is beneficial for analyzing the fluid flow between pores and provides an analytical basis and technical support for the pore flow law.

[0097] Further analysis of the relationship between porosity and particle size parameters, after obtaining the slurry flow rate of individual pores and the total volumetric flow rate of unit cells, as well as the basic calculation formula, further combines fractal dimension and bidispersion model to explore the intrinsic connection between the pore structure and particle characteristics of rock and soil.

[0098] Based on the above content and the basic calculation formula, the porosity of the unit cell satisfies the following relationship:

[0099]

[0100] in, Indicates the porosity of soil and rock mass. Represents pore volume, Represents the total volume of the rock and soil mass. Represents the infinitesimal element of pore volume. Indicates the number of pore channels within a unit cell. Represents pi (π). Indicates the radius of the pore channel. This represents the length of the infinitesimal element along the pore channel direction. This represents the result of the total volume infinitesimal element. Represents the cross-sectional area. It represents the length of a micro-element along a certain reference direction.

[0101] Combining the above analytical formulas with analysis and integration, we find that... The following relationship must be satisfied:

[0102]

[0103] in, Indicates a specific length associated with the pore channel. Indicates the reference length. Indicates the radius of the pore channel. Indicates the porosity of soil and rock mass. Indicates penetration rate;

[0104] Next, it is necessary to analyze the relationship between fractal dimension and porosity. This is mainly based on fractal theory, which analyzes the relationship between porosity and fractal dimension within soil and rock. Fractal dimension reflects the complexity of the pore structure of soil and rock. The aforementioned relationship between porosity and fractal dimension within soil and rock yields the porosity-fractal dimension equation.

[0105] The above porosity-fractal dimension relationship satisfies the following relationship:

[0106]

[0107] in, Indicates the porosity of soil and rock mass. Indicates the minimum radius of the pore channel. Indicates the maximum radius of the pore channel. Represents the fractal dimension of the pores;

[0108] Based on the definition of the ratio of pore channel lengths within soil, a quantitative relationship between the actual and reference lengths of pore channels can be derived by simultaneously solving relevant analytical formulas and performing integration. Specifically, the above expression for the ratio of pore channel lengths must satisfy the following relationship:

[0109]

[0110] in, This represents the ratio of the lengths of pore channels within soil and rock. Indicates the equivalent length of the pore channel. Indicates the radius of the pore channel.

[0111] Furthermore, based on the relationship between the bidispersion model and porosity, and the length ratio expression, the porosity results, density, water content, specific gravity, permeability coefficient, and average particle size of the soil and rock mass are used to derive and transform the length ratio of pore channels, thus obtaining the target expression for the length ratio of pore channels in the soil and rock mass.

[0112] In this embodiment, based on the intrinsic relationship between the bidispersion model and porosity, as well as the length ratio expression, and combined with parameters such as the porosity results of the soil and rock mass, density, mass water content, specific gravity, permeability coefficient, and average particle size, the length ratio of pore channels is derived and transformed, and finally the target expression of the pore channel length ratio in the soil and rock mass is obtained.

[0113] Based on the derivation and analysis of the bidispersion model, the relationship between the length ratio of pore channels and porosity within soil and rock can be clearly defined. The specific expression is as follows:

[0114]

[0115] in, This represents the ratio of the lengths of pore channels within soil and rock. Represents the fractal dimension of the pores. Indicates the porosity of soil and rock mass. Represents pi (π). Indicates the minimum radius of the pore channel. This indicates the maximum radius of the pore channel.

[0116] In the field of geotechnical engineering, length ratio relationships help to more accurately assess the engineering properties of soil and rock masses. Furthermore, by combining fractal dimension and bidispersion models, it is possible to delve into the microstructure of soil and rock masses and predict their mechanical behavior and properties in engineering.

[0117] The calculation of particle size ratio and minimum particle size must satisfy the following relationship:

[0118]

[0119] in, Indicates the minimum radius of the pore channel. Indicates the maximum radius of the pore channel. Indicates the average grain size of the soil and rock mass The minimum particle size obtained by sieve analysis when conducting particle size analysis tests on soil and rock masses The ratio, This indicates the porosity of the soil and rock mass.

[0120] The above-described embodiments The following relationship must be satisfied:

[0121]

[0122] in, Indicates the average grain size of the soil and rock mass The minimum particle size obtained by sieve analysis when conducting particle size analysis tests on soil and rock masses The ratio, Indicates the average particle size. Indicates the minimum particle size.

[0123] Based on the soil saturated permeability coefficient relationship and its variations, the above minimum particle size The following relationship must be satisfied:

[0124]

[0125] in, Indicates the minimum particle size. This indicates the minimum particle size of the sieve selected using the sieve analysis method when conducting particle size analysis tests on soil and rock.

[0126] In practical applications, the minimum particle size of the sieve selected for particle size analysis of soil and rock masses using the sieve separation method is [missing information]. The above formula can be used to calculate the result. The specific value is 4.33.

[0127] The aforementioned particle size ratio and minimum particle size have a significant impact on the pore structure, permeability, and strength of soil and rock masses. Soil and rock masses with smaller particle size ratios have smaller porosity and higher strength. Therefore, accurately measuring and calculating the particle size ratio and minimum particle size during engineering design and construction is beneficial to ensuring the safety and reliability of the project.

[0128] Subsequently, the experimental data of rock and soil mechanics, the results of pore flow burr formation, and the porosity-fractal dimension relationship were jointly analyzed to construct the target expression for the ratio of pore channel length in rock and soil.

[0129] The target expression for the ratio of pore channel lengths in the aforementioned soil and rock mass satisfies the following relationship;

[0130]

[0131] in, This represents the ratio of the lengths of pore channels within soil and rock. Indicates the average particle size. Indicates the porosity of soil and rock mass. It represents pi (π).

[0132] The target expression for the ratio of pore channel lengths within soil and rock can be used to quickly obtain the ratio of pore channel lengths within soil and rock.

[0133] In the study of the relevant properties of soil and rock, based on the intrinsic relationship between the bidispersion model and porosity, and combined with the length ratio expression, the key parameters such as the porosity results, density, mass water content, specific gravity, permeability coefficient and average particle size of soil and rock were analyzed. The length ratio of pore channels was derived and transformed. After a series of mathematical operations and logical derivations, the target expression of the length ratio of pore channels in soil and rock was finally obtained.

[0134] The target expression for the pore channel length ratio within soil and rock masses, as described above, helps to more accurately assess the engineering properties of soil and rock masses. Combined with the porosity-particle size parameter correlation function established using fractal dimension and a bidispersive model, it allows for a deeper exploration of the microstructure of soil and rock masses and the prediction of their mechanical behavior and properties in engineering applications. Compared to traditional methods, the method of this invention can more comprehensively consider various factors, thereby obtaining more accurate analysis results for the pore channel length ratio within soil and rock masses.

[0135] Furthermore, the method for constructing the pore channel length ratio calculation model in this embodiment is merely an optional condition of the present invention. In other embodiments, the method for constructing the pore channel length ratio calculation model can be optimized and adjusted according to the rheological properties of Bingham cement slurry and the construction requirements of the calculation model. This can make the pore channel length ratio calculation model more closely match the rheological properties of the specific slurry and more accurately describe the diffusion of the slurry in the soil and rock mass.

[0136] S3. Based on the rheological test scheme, the water viscosity, Bingham fluid plastic viscosity and Bingham fluid yield stress are obtained. At the same time, according to the grouting requirements, the water-cement ratio of Bingham cement grout, grouting time, grouting pressure, grouting pipe radius and groundwater pressure at the grouting point are obtained.

[0137] To obtain comprehensive key parameters of Bingham cement grout, it is necessary to combine the rheological testing plan with the actual grouting requirements. The specific implementation steps and related content are as follows:

[0138] It is necessary to clarify the testing and grouting requirements. A thorough analysis of the rheological testing scheme is needed to clarify its purpose, scope, and core concerns. Based on practical engineering applications, grouting requirements should be accurately determined, including grouting effects and construction conditions. Based on the rheological testing scheme and grouting requirements, relevant parameters reflecting the characteristics of Bingham cement grout should be selected, including but not limited to water viscosity, Bingham fluid plastic viscosity, and Bingham fluid yield stress.

[0139] Rheological tests and parameter acquisition were conducted. The rheological tests primarily utilized experimental equipment and instruments to systematically test and analyze Bingham cement slurry; the viscosity of water was obtained through these tests. Plastic viscosity of Bingham fluid Yield stress of Bingham fluid Key parameters, etc., need to be verified and supplemented based on existing experimental data to further ensure the accuracy and reliability of the parameter information.

[0140] Furthermore, grouting parameters are designed and groundwater pressure is measured. The grouting parameters need to be designed based on the actual grouting requirements, specifically the water-cement ratio of the Bingham cement grout. Grouting time Grouting pressure Grouting pipe radius The parameters were designed reasonably, and the groundwater pressure at the grouting point was measured. .

[0141] The water-cement ratio is a key factor affecting the performance of grout and needs to be determined by accurately measuring the amount of water and cement required to prepare the grout.

[0142] Grouting time and grouting pressure are key control parameters in the grouting construction process, and they need to be set reasonably by comprehensively considering factors such as the properties of the soil and rock, the requirements of the grouting project, and the construction conditions.

[0143] Measuring groundwater pressure refers to installing pore water pressure sensors at the grouting point to monitor groundwater pressure in real time. The changes in the data require careful consideration of the geological conditions and construction requirements of the grouting point. The appropriate placement and depth of the sensors must be carefully selected to ensure the accuracy and reliability of the measurement data.

[0144] Parameter calculations and verifications were also performed in the examples. The water-cement ratio was calculated primarily by accurately measuring the mass of water and cement required to prepare the Bingham cement slurry using a balance. and The water-cement ratio is calculated according to the formula, which provides an important basis for the preparation and performance control of the slurry.

[0145] The above Bingham cement grout water-cement ratio It satisfies the following relationship:

[0146]

[0147] in, This indicates the water-cement ratio of Bingham cement grout. This indicates the mass of water required to prepare Bingham cement grout. This indicates the mass of cement required to prepare Bingham cement grout. The mass of water required to prepare Bingham cement grout. Cement quality The measurements were obtained using a balance.

[0148] Simultaneously, parameter verification and adjustment are necessary. The acquired parameter information should be comprehensively verified to ensure it meets the requirements of grouting design and construction. Grouting parameters should be adjusted in a timely manner according to actual conditions to guarantee optimal grouting results. Through these steps, key parameters of Bingham cement grout can be obtained comprehensively and accurately, providing strong technical support for grouting design and construction.

[0149] Furthermore, in this embodiment, the method for obtaining information related to Bingham cement slurry is merely an optional condition of the present invention. In other embodiments, the method for obtaining Bingham cement slurry parameter information can be replaced and adjusted according to the actual situation of the rheological test and the actual needs of the project, so as to make the parameter information acquisition method more flexible, ensure effective monitoring and accurate acquisition of information, and improve the adaptability and reliability of the method of the present invention.

[0150] S4. Combining information on the comprehensive effects of particle size distribution, diffusion path influence, soil porosity, length ratio, water viscosity, Bingham fluid plastic viscosity, Bingham fluid yield stress, Bingham cement grout water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure, the columnar permeability radius under the diffusion path of Bingham cement grout is predicted, and the columnar permeability radius analysis results are obtained. The specific steps and related content are as follows:

[0151] First, Bingham's basic rheological equation for slurry and the flow of slurry in pore channels are introduced.

[0152] Based on seepage mechanics theory, combined with the basic analytical equation and the obtained Bingham cement slurry parameter information, the flow characteristics of Bingham cement slurry in the pore channels of soil and rock are analyzed in depth. Through reasoning analysis, the relationship between flow rate and average flow velocity is further derived, and the basic rheological equation of Bingham slurry can be obtained.

[0153] The above Bingham slurry basic rheological equations satisfy the following relationship;

[0154]

[0155] in, The basic rheological equation of Bibbingham slurry This represents the yield stress of the Bingham fluid. This indicates the plastic viscosity of Bingham fluid. Indicates the speed difference, Indicates time difference.

[0156]

[0157] in, The basic rheological equation of Bibbingham slurry This represents the yield stress of the Bingham fluid. This indicates the plastic viscosity of Bingham fluid. Indicates shear rate;

[0158] Among them, shear rate It can be achieved through speed difference and distance difference The ratio of shear rate to shear rate is defined as follows:

[0159]

[0160] in, Indicates shear rate, Indicates the speed difference, Indicates the distance difference.

[0161] In this embodiment, the pore channels of the soil and rock mass are simplified into a circular tube model, and a microfluidic element column is selected for stress analysis. The radius of the microfluidic element column is set to... The pressures at its left and right ends are respectively and Ignoring other external forces, the force equilibrium relationship of the microfluidic unit column in the pores of the soil and rock mass satisfies certain flow conditions, which satisfy the following relationship;

[0162]

[0163] in, Represents pi (π). This represents the distance from the center of the circular tube to any point of arbitrary radius. This represents the pressure difference between the left and right ends of the microfluidic unit column. Represents pi (π). Represents shear stress. This represents a small length segment of a microfluidic unit column in the flow direction.

[0164] Based on this further derivation and analysis, it can be seen that the shear stress satisfies the following relationship:

[0165]

[0166] in, Represents shear stress. Indicates the radius of the pore channel. This represents the pressure gradient of the fluid along the diffusion path.

[0167] Based on the expression for shear stress, it can be found that the shear stress is related to the radial distance within the pore channel. There is a linear relationship. Near the center of the circular tube ( When the shear stress approaches zero, the condition is met for Bingham cement grout when the shear stress is less than the yield stress. At this point, no relative flow will occur between the fluids, meaning there exists a specific radial distance. ,exist Within this region, the slurry remains relatively stationary with the slurry in adjacent layers, exhibiting piston-like motion characteristics, and its velocity... Not exceeding a certain specific value speed , and Within the region, the slurry is in motion relative to the fluid in the adjacent layer.

[0168] By introducing the fundamental rheological equations of Bingham grout, a theoretical basis is provided for analyzing the flow characteristics of Bingham cement grout. These equations accurately describe the rheological behavior of the grout under stress, which is key to understanding the flow and permeation mechanisms of the grout. In this embodiment, the pore channels of the soil and rock mass are simplified into a circular tube model, and a microfluidic column is selected for stress analysis. This retains the essential characteristics of the problem while greatly simplifying the calculation process. Through this simplification, the relevant laws governing grout flow and permeation can be effectively derived. Based on this, the flow characteristics of Bingham cement grout in pore channels can be accurately analyzed, including the relationship between shear stress and radial distance, and the fluid motion state at different radial distances. This is beneficial for subsequent understanding of the grout permeation mechanism, prediction of the grout diffusion path, and determination of the columnar permeation radius.

[0169] Then, based on Bingham's basic rheological equations for slurry, the flow of slurry in pore channels, the plastic viscosity of Bingham fluid, the yield stress of Bingham fluid, and the radius of the grouting pipe, an analysis was conducted to obtain the velocity distribution expressions for the piston zone and the shear zone.

[0170] Based on the above expression for shear stress, it can be seen that the shear stress exhibits a linear relationship with the radial distance *r* within the pore channel. Building upon this, further expressions for the velocity distribution in the piston region and shear region are derived based on the pressure gradient, with respect to the radial distance... satisfy In the region, the flow velocity of Bingham grout in the pores of the rock and soil mass The following relationship must be satisfied, that is, the velocity distribution expressions for the piston region and the shear region are as follows;

[0171]

[0172] in, This indicates the flow velocity of Bingham grout in the pores of the rock and soil mass. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. Indicates the maximum radius of the pore channel. Indicates the radius of the pore channel. This represents the yield stress of the Bingham fluid. Indicates radial distance;

[0173] Next, the average flow velocity of laminar flow in a single pore channel of Bingham cement slurry is calculated based on the velocity distribution expression of the piston zone and the shear zone.

[0174] against The velocity distribution expressions of the piston region and shear region within the area are further analyzed. Within this range, the fluid remains relatively stationary with the fluid in the adjacent layers, exhibiting piston-like motion characteristics. Substitution speed The expression, and with By solving the simultaneous calculation formulas, the velocity of the fluid within this range can be obtained. And the expression satisfies the following relationship:

[0175]

[0176] in, express Within the specified range, the flow velocity of Bingham grout in the pores of the rock and soil mass.

[0177] Based on relevant theoretical knowledge and basic concepts, it is known that the velocity distribution of grout in the pore channels of soil and rock exhibits a truncated parabolic shape. Bingham cement grout passes through a radius of... Flow rate of a single pore channel For the piston area ( ) and shear zone ( The sum of the flow rates, i.e., the flow rate of a single pore channel, satisfies the following relationship:

[0178]

[0179] in, This represents the flow rate of a single pore channel. Indicates the maximum radius of the pore channel. Indicates radial distance. Represents pi (π). Indicates the radius of the pore channel. This indicates the flow velocity of Bingham grout in the pores of the rock and soil mass. Indicates the distance difference. express The flow velocity of Bingham slurry in the pores of the soil and rock within the specified range.

[0180] Integrating the above formula, we can obtain the radius through which Bingham cement slurry passes. The expression for the flow rate of a single pore channel, satisfying the following relationship:

[0181]

[0182] in, This represents the flow rate of a single pore channel. Represents pi (π). Indicates the radius of the pore channel. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. This represents the yield stress of the Bingham fluid;

[0183] The average flow velocity is calculated based on the formula for calculating the flow rate of a single pore channel and the above calculation model. The flow rate of a single pore channel... Bingham cement slurry can be obtained in a radius of The average velocity of laminar flow in a single pore channel, i.e., the average flow velocity, must satisfy the following relationship:

[0184]

[0185] in, This indicates the average flow rate of Bingham cement grout. Indicates the maximum radius of the pore channel. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. This represents the yield stress of the Bingham fluid.

[0186] Finally, the formulas for the relationship between the starting gradient pressure, grout volume, and total diffusion surface area are introduced. Combined with the results of the starting gradient pressure, grout volume, total diffusion surface area, soil porosity, length ratio, water viscosity, Bingham fluid plastic viscosity, Bingham fluid yield stress, Bingham cement grout water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure, the function for determining the cylindrical permeability radius under the influence of the diffusion path is obtained by combining the separation variable integration method.

[0187] The average flow velocity was further investigated in the embodiments, and the starting gradient pressure was analyzed and simplified. To ensure the smooth flow of Bingham cement grout in the pore channels, its yield stress must be overcome. In the embodiments, the flow rate of a single pore channel was set... Traffic in Therefore, it can be deduced that:

[0188]

[0189] Therefore, we can determine the starting gradient pressure at which the Bingham cement slurry is about to begin flowing. The aforementioned initiation gradient pressure satisfies the following relationship:

[0190]

[0191] in, Indicates the initiation of gradient pressure. This represents the yield stress of the Bingham fluid. Indicates the maximum radius of the pore channel;

[0192] Will Substituting these values ​​into the formula for calculating the average flow velocity, we can obtain the result of the average flow velocity calculation, as shown in the following expression:

[0193]

[0194] in, This indicates the average flow rate of Bingham cement grout. Indicates the radius of the pore channel. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. This indicates the initiation of gradient pressure.

[0195] because In this embodiment, to simplify the calculation, the fourth-order terms within the parentheses in the formula can be ignored. Therefore, the above expression for calculating the average flow velocity can be further expressed as:

[0196]

[0197] Then, the seepage motion equation of Bingham cement grout under diffusion was established by combining the flow analysis results and the average flow velocity calculation results.

[0198] Furthermore, based on the correlation between the slurry's permeation velocity in porous media and related parameters, namely the relationship between permeation velocity and the average porosity, flow rate and flow volume analysis results, and average flow velocity calculation results, the seepage motion equation of Bingham cement slurry under diffusion environment was obtained.

[0199] Based on the relevant analytical expression and the seepage characteristics of Bingham cement grout, it is known that the permeation rate of the grout in porous media follows... This relationship, in which Indicates the permeation rate in porous media. Indicates porosity. This indicates the average flow rate of Bingham cement grout.

[0200] at the same time, satisfy This relationship.

[0201] Through joint efforts Relations and The expression can be used to derive the Bingham cement grout seepage motion equation considering the diffusion path, that is, the Bingham cement grout seepage motion equation under diffusion, which satisfies the following relationship.

[0202]

[0203] in, This indicates the seepage velocity of Bingham cement grout in soil and rock. Indicates the permeability of rock and soil. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. Indicates the initiation gradient pressure;

[0204] The seepage motion equations for Bingham cement grout under diffusion conditions were rearranged and applied according to the chain rule. Further, we can obtain The following relationship must be satisfied;

[0205]

[0206] in, This represents the pressure gradient of the fluid along the diffusion path. Indicates the porosity of soil and rock mass. A parameter representing the length of slurry diffusion. Indicates the permeability coefficient. This represents the ratio of the lengths of pore channels within soil and rock. Indicates the plastic viscosity of the slurry. Indicates the volumetric flow rate of the slurry. This indicates the initiation of gradient pressure.

[0207] During the diffusion process of Bingham cement grout, its flow characteristics are affected by various factors, such as the plastic viscosity of the fluid and the permeability of the soil and rock. This embodiment uses the seepage motion equation of Bingham cement grout under diffusion to more accurately describe the flow state of the grout in porous media, and can also further verify and improve the method for determining the columnar permeation radius.

[0208] Subsequently, the relevant information on grouting volume and diffusion surface area, as well as the relationship between permeability coefficient and permeability, were analyzed. During the penetration grouting operation with Bingham cement grout, a certain correlation was found between grouting volume and diffusion surface area, namely the grouting volume relationship, which satisfies the following relationship:

[0209]

[0210] in, Indicates the amount of grout injected. Represents pi (π). This indicates the diffusion radius of Bingham cement grout in soil and rock mass. Indicates the diffusion height. Indicates the porosity of soil and rock mass;

[0211] The formula for calculating the total diffusion surface area satisfies the following relationship:

[0212]

[0213] in, This represents the total surface area of ​​the Bingham cement grout diffusion. Represents pi (π). Indicates the diffusion radius. Indicates the diffusion height;

[0214] By combining the previously derived content and theoretical information, the above can be obtained. The calculation formula satisfies the following relationship:

[0215]

[0216] Considering the columnar diffusion of Bingham cement grout in the soil and rock mass, i.e., when... hour, ;when hour, The above-mentioned method of separation of variables integration is used. The calculation formula is expanded and solved by pre-setting relevant parameters at the initial time and a specific time. After a series of rigorous derivations, the cylindrical permeation radius under the influence of the diffusion path is finally obtained, which satisfies the following relationship:

[0217]

[0218] in, Indicates the radius of penetration of the column. Indicates the grouting pressure. This indicates the groundwater pressure at the grouting point. This indicates the plastic viscosity of Bingham fluid. Indicates the porosity of soil and rock mass. This indicates the amount of grout injected. Indicates penetration rate. Represents pi (π). This represents the ratio of the lengths of pore channels within soil and rock. Indicates the diffusion height. Indicates the grouting time. This indicates the radius of the diffusion morphology of Bingham cement grout in the column-hemispherical permeation grouting space within the rock and soil mass. Indicates the radius of the grouting hole. This indicates the initiation of gradient pressure.

[0219] Among them, penetration rate The following relationship must be satisfied:

[0220]

[0221] The grouting volume at different times satisfies the following relationship:

[0222] Then columnar permeation half That is, the function for determining the cylindrical permeation radius can also satisfy the following relationship:

[0223]

[0224] in, Indicates the radius of penetration of the column. Indicates the grouting pressure. This indicates the groundwater pressure at the grouting point. This indicates the plastic viscosity of Bingham fluid. Indicates the grouting time. This indicates the density of water. Indicates the porosity of soil and rock mass. Represents gravitational acceleration. This represents the spherical diffusion radius of Bingham cement grout in soil and rock mass. Indicates the permeability coefficient. Indicates the viscosity of water. This represents the ratio of the lengths of pore channels within soil and rock. Indicates the radius of the grouting hole. This represents the yield stress of the Bingham fluid.

[0225] Therefore, the cylindrical permeability radius can be predicted using the cylindrical permeability radius determination function, and the cylindrical permeability radius analysis results can be obtained.

[0226] Based on the derived cylindrical penetration radius determination function, the cylindrical penetration radius can be accurately predicted, and the analysis results can be obtained in depth. The cylindrical penetration radius determination method proposed in this embodiment focuses on the implementation steps and analysis methods of the cylindrical penetration radius of Bingham cement slurry diffusion path.

[0227] Analysis based on engineering practice and theoretical research shows that columnar permeation grouting diffusion is a key technical means to reinforce soil and rock and improve their mechanical properties, and it has been widely used in the engineering field. In soil and rock reinforcement projects, columnar permeation grouting can effectively inject cement grout into the pores and fissures of the soil and rock, significantly improving the strength and stability of the soil and rock. The diffusion path of Bingham cement grout in the soil and rock plays a crucial role in the grout penetration and diffusion results. Different diffusion paths will lead to significant differences in the distribution range, filling effect, and reinforcement effect of the grout in the soil and rock.

[0228] Specifically, factors such as the length and tortuosity of the diffusion path, as well as the heterogeneity of the soil and rock mass, all affect the flow and permeability characteristics of Bingham cement grout. When the diffusion path is long and tortuous, the flow resistance of the grout increases, potentially preventing the grout from fully filling the pores and fissures in the soil and rock mass, thus affecting the reinforcement effect. Furthermore, the heterogeneity of the soil and rock mass causes variations in the permeation rate and diffusion range of the grout in different areas, further increasing the complexity of the grout permeation and diffusion process.

[0229] In this embodiment, based on the columnar permeability radius determination function and permeation grouting technology, the needs of grouting engineering practice can be fully met. The above function comprehensively considers a variety of influencing factors, such as grouting pressure, grouting time, porosity of soil and rock, and permeability coefficient. Through accurate calculation and analysis, the permeability radius of Bingham cement grout in soil and rock can be reasonably and effectively determined, taking into account the columnar diffusion pattern of the grout. This not only helps to improve the design accuracy and construction efficiency of grouting engineering, but also ensures that the grouting reinforcement effect achieves the expected goal, providing reliable technical support for soil and rock reinforcement engineering.

[0230] In an optional embodiment, a method for determining the spherical penetration radius considering the diffusion path of Bingham cement grout is provided, with the following specific steps:

[0231] Acquisition of mechanical parameters of soil and rock

[0232] Key physical parameters, including soil density, were determined through systematic rock and soil mechanics experiments. The mass moisture content is ,proportion Permeability coefficient and average particle size .

[0233] Calculation of porosity of soil and rock

[0234] Based on the experimentally determined density, water content, and specific gravity of the soil and rock mass, the porosity was calculated using the standard formula:

[0235]

[0236] in, Indicates the porosity of soil and rock mass. Indicates the density of rock and soil mass. Indicates the specific gravity of the rock and soil mass. express The density of pure distilled water, Indicates the water content by mass.

[0237] in, Calculated .

[0238] Calculation of pore channel length ratio

[0239] Combined with the porosity of soil and rock With average particle size The pore channel length ratio is calculated using a pore channel length ratio analysis model. .

[0240]

[0241] Fluid characteristic parameter acquisition

[0242] Determining key fluid parameters, such as the viscosity of water, through rheological testing. Plastic viscosity of Bingham fluid Yield stress .

[0243] Grouting parameter design

[0244] Based on the actual needs of the project, the water-cement ratio of Bingham cement grout was designed. Grouting time Grouting pressure Grouting hole radius And measure the groundwater pressure at the grouting point. .

[0245] Theoretical calculation of penetration radius

[0246] Based on the Bingham cement slurry diffusion path column-hemispherical penetration radius determination model:

[0247]

[0248] The theoretical value of the permeation radius is obtained through iterative solution. .

[0249] Comparative analysis shows that the Bingham cement grout diffusion path column-hemispherical permeation radius determination model proposed in this embodiment has a theoretical calculated value of 0.1014 m, while the traditional method (without considering porosity and particle size distribution) has a theoretical value of 5.1439 m. Combined with the permeation grouting experimental data of this embodiment (actual permeation radius 0.0725 m), and referring to the column permeation test diagram of the first embodiment, please refer to... Figure 2 .

[0250] In another alternative embodiment, a method for determining the spherical penetration radius considering the diffusion path of Bingham cement slurry is provided, the specific steps of which are as follows:

[0251] Acquisition of mechanical parameters of soil and rock

[0252] Key physical parameters, including soil density, were determined through systematic rock and soil mechanics experiments. The mass moisture content is ,proportion Permeability coefficient and average particle size .

[0253] Calculation of porosity of soil and rock

[0254] Based on the experimentally determined density, water content, and specific gravity of the soil and rock mass, the porosity was calculated using the standard formula:

[0255]

[0256] in, Indicates the porosity of soil and rock mass. Indicates the density of rock and soil mass. Indicates the specific gravity of the rock and soil mass. express The density of pure distilled water, Indicates the water content by mass.

[0257] in, Calculated .

[0258] Calculation of pore channel length ratio

[0259] Combined with the porosity of soil and rock With average particle size The pore channel length ratio is calculated using a pore channel length ratio analysis model. .

[0260]

[0261] Fluid characteristic parameter acquisition

[0262] Determining key fluid parameters, such as the viscosity of water, through rheological testing. Plastic viscosity of Bingham fluid Yield stress .

[0263] Grouting parameter design

[0264] Based on the actual needs of the project, the water-cement ratio of Bingham cement grout was designed. Grouting time Grouting pressure Grouting hole radius And measure the groundwater pressure at the grouting point. .

[0265] Theoretical calculation of penetration radius

[0266] Based on the Bingham cement slurry diffusion path column-hemispherical penetration radius determination model:

[0267]

[0268] The theoretical value of the permeation radius is obtained through iterative solution. .

[0269] Comparative analysis shows that the Bingham cement grout diffusion path column-hemispherical permeation radius determination model proposed in this embodiment has a theoretical calculated value of 0.1305 m, while the traditional method (without considering porosity and particle size distribution) has a theoretical value of 3.8751 m. Combining this with the permeation grouting experimental data of this embodiment (actual permeation radius 0.0772 m), the permeation radius in the second embodiment is... Please refer to the corresponding cylindrical permeation radius diagram. Figure 3 .

[0270] In an optional embodiment, a method for determining the spherical penetration radius considering the diffusion path of Bingham cement grout is provided, with the following specific steps:

[0271] Acquisition of mechanical parameters of soil and rock

[0272] Key physical parameters, including soil density, were determined through systematic rock and soil mechanics experiments. The mass moisture content is ,proportion Permeability coefficient and average particle size .

[0273] Calculation of porosity of soil and rock

[0274] Based on the experimentally determined density, water content, and specific gravity of the soil and rock mass, the porosity was calculated using the standard formula:

[0275]

[0276] in, Indicates the porosity of soil and rock mass. Indicates the density of rock and soil mass. Indicates the specific gravity of the rock and soil mass. express The density of pure distilled water, Indicates the water content by mass.

[0277] in, Calculated .

[0278] Calculation of pore channel length ratio

[0279] Combined with the porosity of soil and rock With average particle size The pore channel length ratio is calculated using a pore channel length ratio analysis model. .

[0280]

[0281] Fluid characteristic parameter acquisition

[0282] Determining key fluid parameters, such as the viscosity of water, through rheological testing. Plastic viscosity of Bingham fluid Yield stress .

[0283] Grouting parameter design

[0284] Based on the actual needs of the project, the water-cement ratio of Bingham cement grout was designed. Grouting time Grouting pressure Grouting hole radius And measure the groundwater pressure at the grouting point. .

[0285] Theoretical calculation of penetration radius

[0286] Based on the Bingham cement slurry diffusion path column-hemispherical penetration radius determination model:

[0287]

[0288] The theoretical value of the permeation radius is obtained through iterative solution. .

[0289] Comparative analysis shows that the Bingham cement grout diffusion path column-hemispherical permeation radius determination model proposed in this embodiment has a theoretical calculated value of 0.2091 m, while the traditional method (without considering porosity and particle size distribution) has a theoretical value of 4.8281 m. Combining this with the permeation grouting experimental data of this embodiment (actual permeation radius 0.0692 m), the permeation radius in the third embodiment is... Please refer to the corresponding cylindrical permeation radius diagram. Figure 4 .

[0290] The numerical values ​​calculated in the above embodiments are compared and analyzed with the theoretical values ​​obtained using traditional methods. For details of the comparison, please refer to [link to relevant documentation]. Figure 5 , Figure 5 The comparison between the calculated values ​​of this embodiment and the theoretical values ​​of traditional methods is clearly shown. Figure 5 The information presented clearly shows that the theoretical value of the penetration radius obtained by using the cylindrical penetration radius of the Bingham cement slurry diffusion path proposed in this invention is closer to the actual experimental value.

[0291] Please see Figure 6 In an optional embodiment, the present invention also provides a system for determining the cylindrical penetration radius of Bingham cement slurry diffusion path. The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to call the program instructions and execute the specific steps of the method for determining the cylindrical penetration radius of Bingham cement slurry diffusion path and related embodiments provided by the present invention. The system for determining the cylindrical penetration radius of Bingham cement slurry diffusion path of the present invention is structurally complete, objective, and stable.

[0292] 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 determining the cylindrical penetration radius of Bingham cement slurry diffusion path, characterized in that, Includes the following steps: The density, mass water content, specific gravity, permeability coefficient and average particle size of the soil and rock mass are obtained through soil and rock mechanics experiments. Based on the density, mass water content and specific gravity of the soil and rock mass, the porosity of the soil and rock mass is obtained. The length ratio of pore channels in the rock and soil is analyzed based on the porosity, density, water content, specific gravity, permeability coefficient, and average particle size, and the length ratio of pore channels in the rock and soil is obtained. Based on the rheological test scheme, the water viscosity, Bingham fluid plastic viscosity and Bingham fluid yield stress were obtained. According to the grouting requirements, the water-cement ratio of Bingham cement grout, grouting time, grouting pressure, grouting pipe radius and groundwater pressure at the grouting point were obtained. By combining information on the comprehensive effect of particle size distribution, the influence of diffusion path, the porosity of the soil and rock mass, the length ratio, the water viscosity, the plastic viscosity of Bingham fluid, the yield stress of Bingham fluid, the water-cement ratio of Bingham cement grout, the grouting time, the grouting pressure, the grouting pipe radius, and the groundwater pressure, the columnar permeability radius under the diffusion path of Bingham cement grout is predicted, and the columnar permeability radius analysis results are obtained. The function for determining the cylindrical permeation radius under the influence of the diffusion path satisfies the following relationship: ， in, Indicates the radius of penetration of the column. Indicates the grouting pressure. This indicates the groundwater pressure at the grouting point. This indicates the plastic viscosity of Bingham fluid. Indicates the grouting time. This indicates the density of water. Indicates the porosity of soil and rock mass. Represents gravitational acceleration. This represents the spherical diffusion radius of Bingham cement grout in soil and rock mass. Indicates the permeability coefficient. Indicates the viscosity of water. This represents the ratio of the lengths of pore channels within soil and rock. Indicates the radius of the grouting hole. This represents the yield stress of Bingham fluid.

2. The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to claim 1, characterized in that, The process of obtaining soil and rock density, water content, specific gravity, permeability coefficient, and average particle size through soil and rock mechanics experiments, and then obtaining the soil and rock porosity results based on the soil and rock density, water content, and specific gravity, includes: The rock and soil mechanics test data obtained based on the aforementioned rock and soil mechanics test data include rock and soil density, mass water content, specific gravity, permeability coefficient and average particle size; The porosity of the soil and rock mass is obtained based on the density, water content, and specific gravity of the soil and rock mass. The porosity results of the soil and rock mass satisfy the following relationship; ， in, Indicates the porosity of soil and rock mass. Indicates the density of rock and soil mass. Indicates the specific gravity of the rock and soil mass. express The density of pure distilled water, Indicates the water content by mass.

3. The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to claim 1, characterized in that, The analysis of the ratio of pore channel length to the porosity, density, water content, specific gravity, permeability coefficient, and average particle size of the soil and rock mass, and the resulting ratio of pore channel length to the soil and rock mass, includes: Based on the Hagen-Poiseuille formula, Darcy's law, porosity-fractal dimension relationship, and the porosity results of the soil and rock mass, the expression for the ratio of pore channel length is derived. Based on the relationship between the bidispersion model and porosity, the length ratio expression, the porosity result of the soil and rock mass, the density of the soil and rock mass, the mass water content, the specific gravity, the permeability coefficient, and the average particle size, the target expression for the length ratio of pore channels in the soil and rock mass is derived and transformed to obtain the target expression for the length ratio of pore channels in the soil and rock mass. The length ratio of pore channels within the soil and rock mass is obtained using the target expression for the ratio of pore channel lengths within the soil and rock mass.

4. The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to claim 3, characterized in that, The expression for the ratio of pore channel lengths derived from the Hagen-Poiseuille formula, Darcy's law, porosity-fractal dimension relationship, and the porosity results of the soil and rock mass includes: The porosity-fractal dimension relationship satisfies the following relationship: ， in, Indicates the porosity of soil and rock mass. Indicates the minimum radius of the pore channel. Indicates the maximum radius of the pore channel. Represents the fractal dimension of the pores; The expression for the ratio of pore channel lengths satisfies the following relationship: ， in, This represents the ratio of the lengths of pore channels within soil and rock. Indicates the equivalent length of the pore channel. Indicates the radius of the pore channel.

5. The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to claim 3, characterized in that, The relationship between the bidispersion model and porosity, the length ratio expression, the porosity result of the soil and rock mass, the density of the soil and rock mass, the mass water content, the specific gravity, the permeability coefficient, and the average particle size are used to derive and transform the length ratio of pore channels to obtain the target expression for the length ratio of pore channels in the soil and rock mass. The target expression for the ratio of pore channel lengths within the soil and rock mass satisfies the following relationship; ， in, This represents the ratio of the lengths of pore channels within soil and rock. Indicates the average particle size. Indicates the porosity of soil and rock mass. It represents pi (π).

6. The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to claim 1, characterized in that, The columnar permeability radius of Bingham cement grout under the diffusion path is predicted by combining information on the comprehensive effect of particle size distribution, diffusion path influence, soil porosity, length ratio, water viscosity, Bingham fluid plastic viscosity, Bingham fluid yield stress, Bingham cement grout water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure. The columnar permeability radius analysis results include: The Bingham basic rheological equation for slurry and the flow of slurry in pore channels are introduced; Based on the Bingham slurry basic rheological equation, the flow of the slurry in the pore channel, the plastic viscosity of the Bingham fluid, the yield stress of the Bingham fluid, and the radius of the grouting pipe, an analysis is conducted to obtain the velocity distribution expressions of the piston zone and the shear zone; The average flow velocity of laminar flow in a single pore channel of Bingham cement slurry is calculated based on the velocity distribution expression of the piston zone and the shear zone. By introducing the formulas for initiating gradient pressure, grout volume, and total diffusion surface area, and combining these with the initiating gradient pressure, grout volume, total diffusion surface area, soil porosity, length ratio, water viscosity, Bingham fluid plastic viscosity, Bingham fluid yield stress, Bingham cement grout water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure, a function for determining the columnar permeability radius under the influence of the diffusion path is derived using the separation of variables integral method. The cylindrical permeability radius is predicted using the aforementioned cylindrical permeability radius determination function, and the cylindrical permeability radius analysis results are obtained.

7. The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to claim 6, characterized in that, The introduction of Bingham's basic rheological equation for slurry and the flow of slurry in pore channels include: The Bingham slurry basic rheological equation satisfies the following relationship; ， in, The basic rheological equation of Bibbingham slurry This represents the yield stress of the Bingham fluid. This indicates the plastic viscosity of Bingham fluid. Indicates shear rate; The flow condition satisfies the following relationship; ， in, Represents pi (π). This represents the distance from the center of the circular tube to any point of arbitrary radius. This represents the pressure difference between the left and right ends of the microfluidic unit column. Represents shear stress. This represents a small length segment of a microfluidic unit column in the flow direction.

8. The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to claim 6, characterized in that, The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path also includes: The velocity distribution expressions of the piston region and the shear region are obtained based on the pressure gradient, and the velocity distribution expressions of the piston region and the shear region satisfy the following relationship; ， in, This indicates the flow velocity of Bingham grout in the pores of the rock and soil mass. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. Indicates the maximum radius of the pore channel. Indicates the radius of the pore channel. This represents the yield stress of the Bingham fluid. Indicates radial distance; The average flow velocity satisfies the following relationship: ， in, This indicates the average flow rate of Bingham cement grout. Indicates the maximum radius of the pore channel. This indicates the plastic viscosity of Bingham fluid. This represents the pressure gradient of the fluid along the diffusion path. This represents the yield stress of Bingham fluid.

9. The method for determining the cylindrical penetration radius of the Bingham cement slurry diffusion path according to claim 6, characterized in that, The introduction of the initiation gradient pressure, grout volume relationship formula, and diffusion total surface area calculation formula, combined with the initiation gradient pressure, grout volume relationship formula, diffusion total surface area calculation formula, soil porosity result, length ratio, water viscosity, Bingham fluid plastic viscosity, Bingham fluid yield stress, Bingham cement grout water-cement ratio, grouting time, grouting pressure, grouting pipe radius, and groundwater pressure, along with the separation of variables integration method, yields the following function for determining the cylindrical permeability radius under the influence of the diffusion path: The initiation gradient pressure satisfies the following relationship: ， in, Indicates the initiation of gradient pressure. This represents the yield stress of the Bingham fluid. Indicates the maximum radius of the pore channel; The formula for slurry volume relationship satisfies the following relationship: ， in, Indicates the amount of grout injected. Represents pi (π). This indicates the diffusion radius of Bingham cement grout in soil and rock mass. Indicates the diffusion height. Indicates the porosity of soil and rock mass; The formula for calculating the total diffusion surface area satisfies the following relationship: ， in, This represents the total surface area of ​​the Bingham cement grout diffusion. Represents pi (π). Indicates the diffusion radius. Indicates the diffusion height.

10. A system for determining the cylindrical penetration radius of Bingham cement slurry diffusion path, characterized in that, The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to invoke the program instructions to execute the method for determining the columnar penetration radius of the Bingham cement slurry diffusion path as described in any one of claims 1-9.

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