Method and system for determining the column hemispherical penetration radius of the bingham plug flow path

Abstract

The present application relates to the field of environmental protection and ecological restoration, specifically to a method and system for determining the column hemispherical permeation radius of the Bingham slurry diffusion path, the steps of which are as follows: obtaining the physical and mechanical information of the rock-soil body through a rock-soil body mechanics experiment and establishing a rock-soil body porosity calculation model to determine the rock-soil body porosity according to the calculation model; establishing a pore channel length ratio analysis model according to the rock-soil body porosity and physical and mechanical information to analyze the length ratio of the pore channels in the rock-soil body; introducing rheological test information and obtaining Bingham fluid characteristic information, and setting the grouting parameters of the Bingham cement slurry according to the grouting requirements; and constructing a Bingham cement slurry diffusion path column hemispherical permeation radius determination model based on the rock-soil body porosity, length ratio, Bingham fluid characteristic information, and grouting parameters. The present application realizes accurate evaluation of the column hemispherical permeation radius of the Bingham slurry diffusion path based on the porosity and particle size distribution factors of the rock-soil body.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of environmental protection and ecological restoration, in particular to a method and system for determining the column hemispherical permeation radius of a Bingham slurry diffusion path. BACKGROUND

[0002] The current Bingham cement slurry permeation grouting technology considers the influence of the weight of the Bingham cement slurry itself and the laying angle of the grouting pipe on the permeation grouting range, as well as the influence on the column hemispherical permeation grouting range, and analyzes the calculation method of the weight of the power-law fluid and the grouting pipe burial angle on the diffusion effect of the tunnel advanced pre-grouting.

[0003] However, the existing Bingham cement slurry permeation grouting technology has not considered and analyzed the method for determining the column hemispherical permeation radius of the Bingham cement slurry diffusion path. In actual engineering applications, the column hemispherical permeation grouting diffusion form can be used to reinforce rock-soil bodies, and the diffusion path of the Bingham cement slurry in the rock-soil body has an important influence on the permeation and diffusion results of the slurry. Different diffusion paths will lead to significant differences in the distribution and flow characteristics of the slurry in the rock-soil body, and thus affect the grouting reinforcement effect. However, the existing technology lacks an effective method for determining the column hemispherical permeation radius, making it difficult to accurately grasp the diffusion range and degree of the slurry in the rock-soil body, and unable to provide technical support for engineering practice. This makes it difficult to accurately control the grouting effect, ensure the engineering quality and safety requirements in grouting engineering practice. SUMMARY

[0004] In view of the defects of the existing method and the insufficient practical application, the existing Bingham slurry infiltration grouting technology lacks a method for determining the column hemispherical infiltration radius, cannot accurately grasp the diffusion range and degree of the slurry in the rock-soil body, and is difficult to meet the needs of grouting engineering practice, cannot effectively guarantee the engineering quality and safety requirements. The present application provides a method and system for determining the column hemispherical infiltration radius of the Bingham slurry diffusion path. In a first aspect, the present application provides a method for determining the column hemispherical infiltration radius of the Bingham slurry diffusion path, which comprises the following steps: obtaining the physical and mechanical information of the rock-soil body through a rock-soil mechanical experiment, establishing a rock-soil porosity calculation model based on the physical and mechanical information, and determining the rock-soil porosity according to the rock-soil porosity calculation model; establishing a pore channel length ratio analysis model based on the rock-soil porosity and the physical and mechanical information, and analyzing the length ratio of the pore channel in the rock-soil body according to the pore channel length ratio analysis model; introducing rheological test information, obtaining Bingham fluid characteristic information based on the rheological test information, and setting the grouting parameters of the Bingham cement slurry according to the grouting requirements; and constructing a Bingham cement slurry diffusion path column hemispherical infiltration radius determination model based on the rock-soil porosity, the length ratio, the Bingham fluid characteristic information and the grouting parameters, to realize accurate analysis of the column hemispherical infiltration radius of the Bingham slurry diffusion path. The method for determining the column hemispherical infiltration radius of the Bingham slurry diffusion path of the present application has the advantages of accurate simulation, optimized design, improved engineering quality and enhanced method adaptability, etc., and provides technical support for grouting engineering practice, meets the needs of engineering practice, and guarantees the engineering quality and safety requirements.

[0005] Optionally, the obtaining the physical and mechanical information of the rock-soil body through a rock-soil mechanical experiment, establishing a rock-soil porosity calculation model based on the physical and mechanical information, and determining the rock-soil porosity according to the rock-soil porosity calculation model comprises: obtaining the physical and mechanical information of the rock-soil body according to the rock-soil mechanical theory and the rock-soil mechanical experiment, wherein the physical and mechanical information includes the density information, the mass water content information, the specific gravity information, the permeability coefficient information and the average particle size information of the rock-soil body; establishing a rock-soil porosity calculation model based on the density information, the mass water content information, the specific gravity information, the permeability coefficient information and the average particle size information; and determining the rock-soil porosity by using the rock-soil porosity calculation model. The present application comprehensively considers the physical and mechanical parameters of the rock-soil body to establish the porosity calculation model, which can more comprehensively and accurately reflect the internal structure and characteristics of the rock-soil body.

[0006] Optionally, the establishing a rock-soil porosity calculation model based on the density information, the mass water content information, the specific gravity information, the permeability coefficient information and the average particle size information comprises:

[0007] The rock-soil porosity calculation model satisfies the following relationship:

[0008] wherein, represents porosity of the rock-soil body, represents density of the rock-soil body, represents specific gravity of the rock-soil body, represents density of pure distilled water, represents mass water content.

[0009] The rock-soil body porosity calculation model of the application comprehensively considers key parameters of the rock-soil body and can accurately reflect the porosity characteristics of the rock-soil body.

[0010] Optionally, the establishing of the pore channel length ratio analysis model according to the rock-soil body porosity and the physical and mechanical information comprises: analyzing the slurry flow condition through the rock-soil body pores per unit time based on the physical and mechanical information; establishing a length ratio preliminary analysis function according to the rock-soil body porosity and the slurry flow condition; obtaining analysis results of the rock-soil body porosity and the fractal dimension according to the fractal theory method, the radius ratio and the minimum particle size relationship and the length ratio preliminary analysis function; and obtaining the pore channel length ratio analysis model in combination with the radius ratio and the minimum particle size relationship, the analysis results and the rock-soil body porosity. The pore channel length ratio analysis model of the application fuses multi-dimensional information such as the rock-soil body porosity, the physical and mechanical information, the slurry flow condition and the fractal theory method, can reflect the characteristics of the rock-soil body and the distribution characteristics of the pore channel from different angles, and can more comprehensively and accurately reveal the internal law of the pore channel length ratio.

[0011] Optionally, the slurry flow condition satisfies the following relationship:

[0012] ,

[0013] wherein, represents total volume flow per unit time through the unit body, represents the number of pore channels in the unit body, represents the ratio of the circumference to the diameter, represents the pressure gradient of the fluid along the diffusion path direction, represents the pore channel radius, represents the fluid viscosity;

[0014] The length ratio preliminary analysis function satisfies the following relationship:

[0015] ,

[0016] wherein, represents the actual length of the fluid flowing along the diffusion path direction, represents the reference length, represents a pore channel radius, represents a porosity of the rock-soil body, represents a permeability;

[0017] The analysis result of the porosity and the fractal dimension in the rock-soil body satisfies the following relationship:

[0018] ,

[0019] wherein, represents a length ratio of the pore channel in the rock-soil body, represents a pore fractal dimension, represents a porosity of the rock-soil body, represents a circular constant, represents a minimum radius of the pore channel, represents a maximum radius of the pore channel.

[0020] The slurry flow relationship of the present application quantifies the relationship between the total volume flow through a unit body per unit time and key factors, provides parameter information for the analysis of the length ratio of the pore channel, and is beneficial to the effective calculation of the length ratio of the pore channel.

[0021] Optionally, the obtaining of the pore channel length ratio analysis model by combining the relationship between the radius ratio and the minimum particle diameter, the analysis result and the porosity of the rock-soil body comprises:

[0022] The pore channel length ratio analysis model satisfies the following relationship:

[0023] ,

[0024] wherein, represents a length ratio of the pore channel in the rock-soil body, represents an average particle diameter, represents a porosity of the rock-soil body, represents a circular constant.

[0025] The model of the present application combines fluid mechanics, fractal theory and mechanical theory in the model establishment process, and can better understand the pore structure characteristics of the rock-soil body and the flow rule of the slurry in the pore.

[0026] Optionally, the introducing rheological test information, obtaining Bingham fluid characteristic information based on the rheological test information, and setting grouting parameters of the Bingham cement slurry according to grouting requirements comprises: obtaining rheological test information through a designed rheological test; analyzing water viscosity information, Bingham fluid plastic viscosity information, and yield stress information through the rheological test information; obtaining Bingham fluid characteristic information in combination with the water viscosity information, the Bingham fluid plastic viscosity information, and the yield stress information; setting grouting parameters of the Bingham cement slurry according to grouting requirements, wherein the grouting parameters comprise water-cement ratio, grouting time, and grouting pressure; and setting grouting boundary conditions based on the grouting requirements and the grouting parameters, wherein the grouting boundary conditions comprise groundwater pressure at a grouting point.

[0027] The present application comprehensively considers Bingham fluid characteristic information, and sets grouting parameters and boundary conditions of the Bingham cement slurry, which is beneficial to understanding rheological characteristics of the Bingham cement slurry.

[0028] Optionally, the constructing the Bingham cement slurry diffusion path column hemispherical permeation radius determination model based on the rock-soil porosity, the length ratio, the Bingham fluid characteristic information, and the grouting parameters comprises: analyzing average flow velocity of the Bingham cement slurry in combination with a Bingham slurry basic rheological equation and the rheological test information; obtaining a seepage flow motion equation of the diffusion path Bingham cement slurry according to a slurry permeation velocity relationship and the average flow velocity; obtaining a pressure gradient equation based on the grouting boundary conditions and the seepage flow motion equation; and deforming the pressure gradient equation according to the rock-soil porosity, the length ratio, the Bingham fluid characteristic information, the grouting parameters, and the grouting boundary conditions, and obtaining the Bingham cement slurry diffusion path column hemispherical permeation radius determination model.

[0029] The present application comprehensively considers rock-soil porosity, length ratio, Bingham fluid characteristic information, grouting parameters, and grouting boundary conditions when constructing the Bingham cement slurry diffusion path column hemispherical permeation radius determination model, which is beneficial to improving accuracy of a prediction result.

[0030] Optionally, the Bingham cement slurry diffusion path column hemispherical permeation radius determination model satisfies the following relationship:

[0031] ,

[0032] wherein represents the column hemispherical permeation radius, represents a side opening of a grouting pipe, represents plastic viscosity of the Bingham fluid, represents grouting time, represents rock-soil porosity, represents density of water, represents gravitational acceleration, Indicates the permeability coefficient. Indicates the viscosity of water. This represents the ratio of the lengths of pore channels within the soil or rock mass. This indicates the radius of the diffusion pattern of Bingham cement grout in a columnar hemispherical permeation grouting space within the rock and soil mass. This represents the yield stress of the Bingham fluid. This indicates the radius of the grouting hole.

[0033] The radius determination model of this invention comprehensively considers multiple key factors. These factors interact and jointly affect the diffusion path and range of Bingham cement grout, and can more comprehensively and accurately reflect the actual situation in the grouting process.

[0034] Secondly, this invention also provides a system for determining the columnar hemispherical permeation radius of Bingham slurry diffusion paths, capable of efficiently executing the method for determining the columnar hemispherical permeation radius of Bingham 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 columnar hemispherical permeation radius of Bingham slurry diffusion paths provided by this invention has a compact structure, strong applicability, and greatly improves operating efficiency. Attached Figure Description

[0035] Figure 1 Flowchart of the method for determining the columnar hemispherical permeation radius of Bingham slurry diffusion path according to the present invention;

[0036] Figure 2 This is a schematic diagram of a permeation grouting experiment in one embodiment of the method for determining the columnar hemispherical permeation radius of the Bingham slurry diffusion path according to the present invention.

[0037] Figure 3 This is a schematic diagram of a permeation grouting experiment in another embodiment of the method for determining the columnar hemispherical permeation radius of the Bingham slurry diffusion path of the present invention.

[0038] Figure 4 This is a comparative schematic diagram of the permeation radius calculation results in the method for determining the columnar hemispherical permeation radius of the Bingham slurry diffusion path of the present invention.

[0039] Figure 5 This is a schematic diagram of the columnar hemispherical permeation radius determination system for the Bingham slurry diffusion path according to the present invention. Detailed Implementation

[0040] Specific embodiments of the present application will now be described in detail by way of example with reference to the drawings. A detailed description of the application is provided below along with examples, demonstrations, and numerous specific details. However, it should be understood that there is no desire on the inventor's part to limit the application to the precise details set forth and the application extends to other embodiments apparent to those skilled in the art in light of this disclosure. In the description below, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one skilled in the art that the present application can be practiced without these specific details. In other instances, well-known methods, procedures, components, and circuits have not been described in detail so as not to unnecessarily obscure aspects of the present application.

[0041] Reference throughout this specification to "one embodiment", "an embodiment", "one example", or "an example", means that a particular feature, structure, or characteristic described in connection with the embodiment or example is included in at least one embodiment of the application. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" or "one example" or "an example" in various places throughout this specification are not necessarily referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics can be combined in any suitable

[0042] Reference throughout this specification to "one embodiment", "an embodiment", "one example", or "an example", means that a particular feature, structure, or characteristic described in connection with the embodiment or example is included in at least one embodiment of the application. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" or "one example" or "an example" in various places throughout this specification are not necessarily referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics can be combined in any suitable Figure 1 In view of the limitations and deficiencies in the current determination method of the column hemispherical permeation radius of the Bingham slurry diffusion path, the present application proposes a determination method of the column hemispherical permeation radius of the Bingham slurry diffusion path based on the Bingham slurry diffusion path information, which is helpful for analyzing and controlling the diffusion range and degree of the slurry in the rock-soil body, providing theoretical support for the permeation grouting practice engineering of the rock-soil body, and ensuring the engineering quality and safety in practical application. The present application provides a determination method of the column hemispherical permeation radius of the Bingham slurry diffusion path, which comprises the following steps:

[0043] S1, obtaining the physical and mechanical information of the rock-soil body through a rock-soil body mechanics experiment, establishing a rock-soil body porosity calculation model based on the physical and mechanical information, and determining the rock-soil body porosity according to the rock-soil body porosity calculation model, the implementation steps and specific contents of which are as follows:

[0044] Firstly, the physical and mechanical information of the rock-soil body is obtained according to the rock-soil mechanics theory and the rock-soil body mechanics experiment, and the above-mentioned physical and mechanical information in the embodiment mainly includes the density information, the mass water content information, the specific gravity information, the permeability coefficient information and the average particle size information of the rock-soil body.

[0045] Density The measurement can be performed by one or more methods in the density test, including but not limited to the water replacement method, the sand replacement method, and the cutting ring method, etc. The water replacement method is suitable for the in-situ density measurement of large-volume rock-soil bodies; the sand replacement method is used for the density measurement of soil base materials such as roadbeds and pavements on site; and the cutting ring method is more suitable for the density measurement of fine-grained soils in the laboratory. In the embodiments, a suitable measurement method can be selected according to the actual situation and the rock-soil body mechanical test, to further ensure the accuracy and feasibility of the density measurement results.

[0046] Mass water content The drying method is used for the measurement. The rock-soil body sample is dried in an oven at a specific temperature until a constant weight is obtained. The mass water content of the rock-soil body is calculated by using the change in the sample mass before and after drying.

[0047] Specific gravity The specific gravity bottle method and the siphon cylinder method are combined for the measurement. The specific gravity bottle method is suitable for the measurement of the specific gravity of fine-grained soils, and the siphon cylinder method is more suitable for the measurement of the specific gravity of coarse-grained soils. The effective combination of the above two methods can accurately measure the specific gravity of rock-soil bodies with different particle size distributions.

[0048] Permeability coefficient The measurement is obtained by using the field water injection test or the indoor permeation test method. The field water injection test can truly reflect the permeability of the rock-soil body under actual engineering conditions, and the indoor permeation test can test the permeability of the rock-soil body sample under controlled conditions. The reliable permeability coefficient information is obtained by using the above two test methods for mutual verification.

[0049] Average particle size The particle size analysis test is mainly used to obtain the particle size distribution curve of the rock-soil body. Then, a point on the ordinate of the curve is selected, and the corresponding abscissa value is the average particle size of the rock-soil body. The particle size analysis test can be performed by using the sieve method, the sedimentation analysis method, etc. In the embodiments, a suitable particle size analysis method can be selected according to the size and properties of the rock-soil body particles.

[0050] Then, a rock-soil body porosity calculation model is established based on the density information, the mass water content information, the specific gravity information, the permeability coefficient information, and the average particle size information. The rock-soil body porosity is determined by using the rock-soil body porosity calculation model.

[0051] Based on the rock-soil body density, the mass water content, the specific gravity, the permeability coefficient, and the average particle size, a rock-soil body porosity calculation model is constructed. The rock-soil body porosity can be accurately calculated based on the above key parameter information, which provides a data basis for the subsequent permeation radius analysis.

[0052] The rock-soil body porosity calculation model satisfies the following relationship: ​

[0053] ,

[0054] wherein, represents the porosity of the rock-soil body, represents the density of the rock-soil body, represents the specific gravity of the rock-soil body, represents the density of pure distilled water, represents the mass water content.

[0055] In order to ensure the accuracy and consistency of the calculation results in the embodiment, the following conditions are set: 1000 .

[0056] Based on the rock-soil body density, mass water content, specific gravity, permeability coefficient, and average particle size, and other physical and mechanical information, a rock-soil body porosity calculation model is constructed, which can more comprehensively reflect the inherent characteristics of the rock-soil body and provide a theoretical basis for the analysis of the mechanical behavior and permeability characteristics of the rock-soil body.

[0057] Further, in the embodiment, the rock-soil body porosity analysis method is only an optional condition of the present application, and in other one or some embodiments, the rock-soil body porosity analysis method can be optimized according to the information characteristics of the physical and mechanical properties of the rock-soil body and the rock-soil body porosity calculation requirements, which can enhance the model adaptability, make the model better adapt to different types of rock-soil bodies, and obtain more accurate porosity calculation results.

[0058] S2, a pore channel length ratio analysis model is established according to the rock-soil body porosity and the physical and mechanical information, and the length ratio of the pore channel in the rock-soil body is analyzed according to the pore channel length ratio analysis model, and the specific steps and implementation contents are as follows:

[0059] In the field of geotechnical engineering technology, it is of great significance to study the flow characteristics of slurry in the rock-soil body pores, and the slurry flow rate through the rock-soil body pores per unit time is one of the key analysis indicators, which is analyzed in the embodiment based on the physical and mechanical information of the rock-soil body.

[0060] First, the slurry flow rate through the rock-soil body pores per unit time is analyzed based on the physical and mechanical information.

[0061] In the embodiment, the pore channel in the rock-soil body is set as a circular tube structure, and according to the Hagen-Poiseuille formula, the slurry flow rate through a single pore per unit time can be obtained, and thus the slurry flow rate through the rock-soil body pores per unit time can be effectively analyzed. The slurry flow rate through a single pore per unit time needs to satisfy the following relationship:

[0062] ,

[0063] wherein, represents the flow rate of the slurry through a single pore per unit time, represents the constant pi, represents the pressure gradient of the fluid along the diffusion path direction, represents the pore channel radius, represents the fluid viscosity.

[0064] The pressure gradient of the fluid along the diffusion path direction reflects the pressure change of the fluid when flowing in the pore;

[0065] The pore channel radius is one of the important factors affecting the fluid flow;

[0066] The flow characteristics of fluids with different viscosities in the pore are significantly different.

[0067] To more comprehensively describe the flow of the slurry in the rock-soil body, a micro-volume unit is selected in the rock-soil body for analysis, and it is assumed that there are pore channels in the unit body. According to the flow rate expression of a single pore, the total volume flow rate through the unit body can be obtained, that is, the slurry flow rate can be analyzed.

[0068] The above slurry flow rate in the embodiment needs to satisfy the following relationship:

[0069] ,

[0070] wherein, represents the total volume flow rate through the unit body per unit time, represents the number of pore channels in the unit body, represents the constant pi, represents the pressure gradient of the fluid along the diffusion path direction, represents the pore channel radius, represents the fluid viscosity.

[0071] The Darcy's law is also introduced in the embodiment, and the slurry flow rate analysis process can be further compared and analyzed. Based on the Darcy's law, the total volume flow rate through the unit body per unit time also satisfies the following relationship:

[0072] ,

[0073] wherein, represents the total volume flow rate through the unit body per unit time, represents the permeability, represents the cross-sectional area, represents the pressure gradient of the fluid along the diffusion path direction, represents the fluid viscosity.

[0074] Permeability is an important parameter reflecting the ability of fluid to pass through the rock-soil mass;

[0075] Cross-sectional area is the cross-sectional area of fluid passing through.

[0076] Further comparison of the slurry flow condition expression derived based on the Hagen-Poiseuille formula with the Darcy's law total volume flow expression can find that the above expressions consider the influence of pressure gradient, fluid viscosity and other factors on slurry flow, but the Hagen-Poiseuille formula focuses more on the analysis from the microscopic pore structure, such as pore channel radius, while the Darcy's law is described from the macroscopic permeability. The above multi-angle analysis method helps to more comprehensively and deeply understand the flow mechanism of slurry in the rock-soil mass pores and the slurry flow condition of the rock-soil mass pores.

[0077] Then, the length ratio preliminary analysis function is established according to the above rock-soil mass porosity and slurry flow condition.

[0078] Based on the above implementation content and related calculation expressions, the rock-soil mass pore structure is analyzed, and the porosity of the unit body can further satisfy the following relationship:

[0079] ,

[0080] Wherein, represents the porosity of the rock-soil mass, represents the pore volume, represents the total volume of the rock-soil mass;

[0081] Where the pore volume element satisfies the following relationship:

[0082] ,

[0083] Wherein, represents the pore volume element, represents the number of pore channels in the unit body, represents the circumference ratio, represents the pore channel radius, represents the element length along the pore channel direction.

[0084] Further, the total volume element satisfies the following relationship:

[0085] ,

[0086] Wherein, represents the total volume element result, represents the cross-sectional area, represents the element length along a certain reference direction.

[0087] Combining the porosity expression of the unit cell, the slurry flow condition expression, and the Darcy law bulk flow rate expression, the length ratio preliminary analysis function can be derived by simultaneously solving the related equations and performing integral operations.

[0088] The length ratio preliminary analysis function satisfies the following relationship:

[0089]

[0090] wherein, represents the actual length of the fluid flowing along the diffusion path direction, represents the reference length, represents the pore channel radius, represents the porosity of the rock-soil body, represents the permeability;

[0091] The length ratio preliminary analysis function reflects the relationship between the pore channel radius, the porosity, and the physical and mechanical parameters in the pore structure parameters of the rock-soil body, as well as the influence of the related parameters on the length ratio. The length ratio preliminary analysis function is helpful for in-depth study of the permeability characteristics of the rock-soil body and provides scientific support for engineering decision-making.

[0092] Then, the analysis results of the porosity and the fractal dimension in the rock-soil body can be obtained by combining the fractal theory method, the relationship between the radius ratio and the minimum particle size, and the length ratio preliminary analysis function.

[0093] Based on the fractal theory framework, the complexity and self-similarity of the pore structure inside the rock-soil body can be analyzed and characterized by the quantitative relationship between the porosity and the fractal dimension. The porosity and the fractal dimension in the rock-soil body satisfy the following relationship:

[0094] wherein, represents the porosity of the rock-soil body, represents the minimum radius of the pore channel, represents the maximum radius of the pore channel, represents the pore fractal dimension.

[0095] The above dimension relationship expression reflects the fractal characteristic dimension of the pore structure and reveals the internal law that the porosity changes with the distribution of the pore size, which is conducive to in-depth understanding of the fractal characteristics of the pore structure of the rock-soil body.

[0096] Further derivation can be performed by combining the definition of the length ratio of the pore channel and the double dispersion model. The length ratio of the pore channel in the rock-soil body can be defined as the ratio of the equivalent length of the pore channel to its radius, i.e., the length ratio of the pore channel in the rock-soil body satisfies the following relationship: ​​

[0097] ,

[0098] wherein, represents the length ratio of the pore channel in the rock-soil body, represents the equivalent length of the pore channel, represents the radius of the pore channel.

[0099] Based on the bimodal distribution model, considering the non-uniform distribution characteristics of the pore channel size in the rock-soil body, there is a specific functional relationship between the length ratio of the pore channel and the porosity, combined with the fractal theory method, the relationship between the radius ratio and the minimum particle size, and the preliminary analysis function of the length ratio, the analysis results of the porosity and the fractal dimension in the rock-soil body are further derived, which satisfy the following relationship:

[0100] ,

[0101] wherein, represents the length ratio of the pore channel in the rock-soil body, represents the pore fractal dimension, represents the porosity of the rock-soil body, represents the ratio of the circumference to the diameter, represents the minimum radius of the pore channel, represents the maximum radius of the pore channel.

[0102] The above analysis results not only reveal the internal relationship between the fractal characteristics of the pore structure of the rock-soil body and the porosity, but also clearly show the key role of the length ratio of the pore channel in the bimodal distribution model. Through this model, the influence mechanism of different pore structure parameters on the permeability of the rock-soil body can be further explored, which provides a reference for optimizing the engineering design scheme and improving the safety and stability of the engineering.

[0103] Finally, the analysis model of the length ratio of the pore channel is obtained by combining the relationship between the radius ratio and the minimum particle size, the analysis results, and the porosity of the rock-soil body.

[0104] The relationship between the radius ratio and the minimum particle size in the embodiment needs to satisfy the following relationship:

[0105] ,

[0106] wherein, represents the minimum radius of the pore channel, represents the maximum radius of the pore channel, represents the average particle size of the rock-soil body and the ratio of the minimum particle size obtained by using the sieve analysis method when carrying out the particle analysis test of the rock-soil body , represents the porosity of the rock-soil body.

[0107] The above the average particle size of the rock-soil body the ratio of the average particle size of the rock-soil body to the minimum particle size obtained by using the sieve analysis method when carrying out the particle analysis test of the rock-soil body and satisfies the following relationship:

[0108]

[0109] wherein, the average particle size of the rock-soil body the ratio of the average particle size of the rock-soil body to the minimum particle size obtained by using the sieve analysis method when carrying out the particle analysis test of the rock-soil body the average particle size the minimum particle size.

[0110] According to the soil saturated permeability coefficient relationship formula and the calculation formula, the minimum particle size satisfies the following relationship:

[0111]

[0112] wherein, the minimum particle size the minimum particle size of the sieve selected by using the sieve analysis method when carrying out the particle analysis test of the rock-soil body.

[0113] In the process of carrying out the particle analysis test of the rock-soil body, when using the sieve analysis method for operation, the minimum particle size of the selected sieve is set to , and in the embodiment, the minimum particle size calculation formula can obtain .

[0114] Finally, the pore channel length ratio analysis model is constructed in combination with the relationship between the radius ratio and the minimum particle size, the analysis results and the porosity of the rock-soil body, and the pore channel length ratio analysis model in the embodiment satisfies the following relationship:

[0115]

[0116] wherein, the length ratio of the pore channel in the rock-soil body the average particle size the porosity of the rock-soil body the ratio of the circumference of a circle to its diameter.

[0117] The Bingham fluid has rheological properties, and behaves as a plastic fluid at a low shear rate, and requires a certain shear stress to start flowing. The column-hemisphere-shaped permeation radius determination method of the embodiment fully considers the related motion characteristics, and through theoretical derivation, expression conversion and model construction, the pore channel length ratio analysis model can more accurately describe the diffusion behavior of the Bingham fluid in the rock-soil body.​​​​​

[0118] The analysis model of the length ratio of the pore channel is constructed in combination with the relationship between the radius ratio and the minimum particle size, analysis results, and the porosity of the rock-soil body, which is beneficial to subsequent determination of the penetration radius. Based on this, various influences on the diffusion process of the slurry can be more comprehensively reflected, and the accuracy of the prediction result of the column hemispherical penetration radius is further improved.

[0119] Further, in the embodiment, the analysis method of the length ratio of the pore channel in the rock-soil body is only an optional condition of the present application. In other one or some embodiments, the analysis method of the length ratio of the pore channel in the rock-soil body can be optimized according to the actual situation of the physical and mechanical information and the analysis requirement of the length ratio. Different rock-soil bodies have different physical and mechanical characteristic information. In actual engineering, the analysis method of the length ratio is adjusted according to different stress states of the rock-soil body, which helps to ensure the practicability and feasibility of the method for determining the column hemispherical penetration radius.

[0120] S3, rheological test information is introduced, Bingham fluid characteristic information is obtained based on the above rheological test information, and meanwhile, the grouting parameters of the Bingham cement slurry are set according to the grouting requirement, and the specific implementation steps and related contents are as follows:

[0121] In the embodiment, the rheological test is designed to obtain the rheological test information, and then the water viscosity information, the Bingham fluid plastic viscosity information and the yield stress information are analyzed through the rheological test information; the Bingham fluid characteristic information can be obtained by combining the water viscosity information, the Bingham fluid plastic viscosity information and the yield stress information.

[0122] In order to accurately analyze the mechanical characteristics of the fluid in the field of geotechnical engineering, a rheological test is designed and carried out, aiming to comprehensively obtain rheological test information, which mainly covers the response characteristics of the fluid under different stress states and flow conditions.

[0123] In an optional embodiment, the rheological test information is analyzed and processed by using a mathematical model and an analysis method, and the water viscosity information ( ), the Bingham fluid plastic viscosity information ( ) and the yield stress information ( ) are obtained. The water viscosity information reflects the size of the internal friction between water molecules, which is an important indicator for evaluating the flow resistance of the fluid. The Bingham fluid plastic viscosity information reflects the energy required for the Bingham fluid to overcome plastic deformation during flow, which plays an important role in understanding the viscous behavior of the fluid. The yield stress information reveals the minimum stress required for the Bingham fluid to start flowing, which is a key parameter for judging the flow characteristics of the fluid.

[0124] Further integration and analysis of the above water viscosity information, Bingham fluid plastic viscosity information and yield stress information ultimately obtains comprehensive and accurate Bingham fluid characteristic information, which provides an information base for subsequent fluid transport simulation in geotechnical engineering, structure stability evaluation and engineering scheme optimization.

[0125] In the embodiment, the grouting parameters of the Bingham cement grout are set according to the grouting requirements, and the grouting parameters mainly include the water-cement ratio, the grouting time and the grouting pressure; meanwhile, the grouting boundary conditions are set based on the grouting requirements and the grouting parameters, and the grouting boundary conditions mainly include the underground water pressure at the grouting point.

[0126] In order to meet the specific requirements of grouting engineering, the grouting parameters of the Bingham cement grout are set, which are the key factors for the smooth development of grouting operation and the achievement of the expected effect. In the embodiment, the water-cement ratio, the grouting time and the grouting pressure are mainly covered, in which the water-cement ratio as the core index of grout proportioning directly affects the fluidity of grout and the strength after hardening; the grouting time determines the residence time of grout in the grouting hole, which plays an important role in the diffusion range and filling effect of grout; the grouting pressure is the power source for driving grout to flow in the rock-soil medium, and its size and stability are related to the success or failure of grouting.

[0127] Meanwhile, the grouting boundary conditions are further defined according to the grouting requirements and the grouting parameters. The grouting boundary conditions are important constraints for the interaction between grout and the surrounding environment during grouting, and the underground water pressure at the grouting point is a key factor. The underground water pressure has a significant impact on the diffusion and solidification of grout, and too high or too low underground water pressure may lead to poor grouting effect.

[0128] According to the actual requirements of grouting engineering, the water-cement ratio (a) ), the grouting time (b ), the grouting pressure (c ) and the grouting hole radius (d ) and other parameters of the Bingham cement grout are designed. In the design process, the characteristics of rock-soil medium, the purpose of grouting and engineering safety and other factors need to be fully considered to ensure the rationality and effectiveness of the grouting parameters. At the same time, in order to accurately obtain the underground water pressure (p ) at the grouting point, the method of burying pore water pressure sensors on site is used to measure it, which can reflect the change of underground water pressure at the grouting point in real time and accurately, providing data support for grouting operation.

[0129] Further, the calculation method of the water-cement ratio of the Bingham cement grout is defined, and it satisfies the following relationship:

[0130] ,

[0131] wherein, represents the water-cement ratio of the Bingham cement slurry, represents the mass of water required to configure the Bingham cement slurry, represents the mass of cement required to configure the Bingham cement slurry.

[0132] The above water-cement ratio calculation method provides a calculation basis for slurry proportioning. When measuring the mass of water and the mass of cement required to configure the Bingham cement slurry, a balance device is used to measure them, which can ensure the accuracy of the measurement results and provide information basis for subsequent slurry proportioning and grouting operation.

[0133] Further, in the embodiment, the setting method of the Bingham fluid characteristic information and the grouting parameter is only an optional condition of the present application. In other one or some embodiments, the setting method of the Bingham fluid characteristic information and the grouting parameter can be optimized according to the rheological test information and the actual needs of the grouting engineering, more accurate fluid characteristic data can be obtained, and more reliable parameter information can be provided for the determination method of the column hemispherical permeation radius of the Bingham slurry diffusion path.

[0134] S4, based on the porosity of the rock-soil body, the length ratio, the Bingham fluid characteristic information and the grouting parameter, a column hemispherical permeation radius determination model of the Bingham cement slurry diffusion path is constructed to realize accurate analysis of the column hemispherical permeation radius of the Bingham slurry diffusion path, and the specific steps and related contents are as follows:

[0135] Firstly, the average flow rate of the Bingham cement slurry is analyzed based on the basic rheological equation of the Bingham slurry and the rheological test information.

[0136] According to the seepage mechanics theory, the basic rheological equation of the Bingham slurry satisfies the following relationship:

[0137] ,

[0138] wherein, represents the basic rheological equation of the Bingham slurry, represents the yield stress of the Bingham fluid, represents the plastic viscosity of the Bingham fluid, represents the porosity of the rock-soil body, represents the shear rate.

[0139] The above shear rate also satisfies the following relationship:

[0140] ,

[0141] wherein, represents the shear rate, represents the velocity difference, represents the distance difference.

[0142] Shear rate represents the magnitude of velocity gradient in shear flow, reflecting the degree of change in the relative motion between fluid layers, and is one of the important parameters to describe the flow characteristics of fluid.

[0143] The velocity difference refers to the change in velocity between two adjacent layers in the fluid. In practical applications, the difference in fluid velocity at two different positions perpendicular to the flow direction (i.e., the shear direction) is used.

[0144] The distance difference refers to the distance between two adjacent layers where the velocity changes, and is measured perpendicular to the flow direction, which can be used to determine the spatial range of the velocity gradient.

[0145] In the example, the pore channel of the rock-soil body is simplified as a circular pipe model. Based on the theory of seepage mechanics, a micro-flow unit column is selected to analyze the actual flow conditions of the Bingham cement slurry inside it. The radius of the micro-flow unit column is set to , and the pressures at the left and right ends are and , respectively.

[0146] Under the condition of ignoring other external forces, the force relationship of the micro-flow unit column in the pore of the rock-soil body can be expressed as:

[0147] ,

[0148] where represents the circumference ratio, represents the distance from the center of the circular pipe to any radius position, represents the pressure difference between the left and right ends of the micro-flow unit column, represents the shear stress, represents the small length segment of the micro-flow unit column in the flow direction.

[0149] During integration or analysis, all radius values from 0 to (the actual radius of the micro-flow unit column) will be considered.

[0150] The pressure difference between the left and right ends of the micro-flow unit column, i.e., the pressure gradient, further represents the amount of change in pressure in the length direction of the micro-flow unit column.

[0151] Shear stress refers to the internal friction force generated by the velocity gradient during fluid flow. For Bingham fluid, when the shear stress is less than the yield stress, the fluid does not flow; when the shear stress is greater than the yield stress, the fluid begins to flow and exhibits certain viscosity.

[0152] The small length segment of the micro-flow unit column in the flow direction, which is usually considered in seepage mechanics, is a small length unit that can be used to analyze the flow characteristics of fluid in a fixed length segment.

[0153] It can be deduced from the above that the shear stress also satisfies the following relationship:

[0154] ,

[0155] wherein, represents the shear stress, represents the pore channel radius, represents the pressure gradient of the fluid along the diffusion path direction.

[0156] It can be known from the above formula that the shear stress and the radial distance of the pore channel are in linear relationship. When approaching the center of the circular tube ( tends to 0), the shear stress also tends to 0. For Bingham cement slurry, when the shear stress received does not reach the yield stress, that is, , the fluid will not flow relatively, at this time there is a radial distance , the slurry within the range of and the adjacent layer of slurry remain relatively static, the fluid is in piston motion, and the velocity ; the slurry within the range of is in motion relative to the adjacent fluid.

[0157] Further analysis shows that , the shear stress received by the cement slurry , according to the above formula, the radial distance satisfies the following relationship:

[0158] ,

[0159] wherein, represents the radial distance, represents the yield stress of the Bingham fluid, represents the pressure gradient of the fluid along the diffusion path direction.

[0160] Substitute the above content and analysis results into the basic rheological equation of Bingham slurry, and integrate the solution combined with the boundary condition of the underground water pressure at the grouting point, and then the flow velocity distribution formula satisfies the following relationship:

[0161] ,

[0162] wherein, represents the flow velocity of the Bingham slurry in the pore of the rock-soil body, represents the plastic viscosity of the Bingham fluid, represents the pressure gradient of the fluid along the diffusion path direction, represents the maximum radius of the pore channel, represents the pore channel radius, represents the yield stress of Bingham fluid, represents the radial distance.

[0163] In the fluid in the range keeps relative static with the adjacent fluid, and the part of fluid presents piston movement relative to the peripheral fluid, and the substituting the above flow rate distribution formula into the piston movement velocity formula, and combining them, the fluid velocity in the range can be obtained and satisfies the following relationship:

[0164] ,

[0165] wherein, represents the flow velocity of Bingham slurry in the soil pore in the range.

[0166] The velocity distribution of slurry in the soil pore channel presents a truncated parabolic shape, and the flow rate of Bingham cement slurry through a single pore channel with a radius of is the sum of the flow rates of the piston area ( ) and the shear area ( ), that is, it satisfies the following relationship:

[0167] ,

[0168] wherein, represents the flow rate of a single pore channel, represents the maximum radius of the pore channel, represents the radial distance, represents the circular constant, represents the radius of the pore channel, represents the flow velocity of Bingham slurry in the soil pore, represents the distance difference, represents the flow velocity of Bingham slurry in the soil pore in the range.

[0169] Integrating the above flow rate sum formula can obtain the flow rate of Bingham cement slurry through a single pore channel with a radius of , and it satisfies the following relationship:

[0170] ,

[0171] wherein, represents the flow rate of a single pore channel.

[0172] Combining the above analysis formula and theoretical information, it can be obtained that the flow velocity of Bingham cement slurry in the soil pore with a radius of the average flow velocity of the Bingham cement slurry in a single pore channel in laminar flow, satisfies the following relationship:

[0173] ,

[0174] wherein, V represents the average flow velocity of the Bingham cement slurry, R represents the maximum radius of the pore channel, η represents the plastic viscosity of the Bingham fluid, dP / dL represents the pressure gradient of the fluid in the direction of the diffusion path, σ represents the yield stress of the Bingham fluid.

[0175] Then, the percolation motion equation of the Bingham cement slurry in the diffusion path is obtained according to the slurry penetration velocity relationship and the average flow velocity.

[0176] The slurry flow condition and the start-up gradient pressure are analyzed. In order to make the Bingham cement slurry flow in the pore channel, the yield stress thereof must be overcome. When the flow rate of the single pore channel is the relationship between the pressure gradient and the yield stress satisfies the following relationship:

[0177] ,

[0178] Thus, the start-up gradient pressure of the Bingham cement slurry when the flow is about to start is and the above start-up gradient pressure is further denoted as and further satisfies the following relationship:

[0179] ,

[0180] wherein, P represents the start-up gradient pressure.

[0181] The average flow velocity of the Bingham cement slurry is transformed, and further the average flow velocity of the Bingham cement slurry can satisfy the following relationship:

[0182] ,

[0183] wherein, V represents the average flow velocity of the Bingham cement slurry, P represents the start-up gradient pressure.

[0184] Since the start-up gradient pressure in order to simplify the calculation, the average flow velocity of the above Bingham cement slurry can be approximately satisfied with the following relationship:

[0185] ,

[0186] Next, the seepage motion equation is derived, and the permeation velocity of the slurry in the porous medium is determined. With average flow velocity The following relationship must be satisfied:

[0187] ,

[0188] in, Indicates the permeation rate in porous media. Indicates porosity. This indicates the average flow rate of Bingham cement grout.

[0189] Pore ​​radius With penetration rate The following relationship must be satisfied:

[0190] ,

[0191] Combining the above relationships, we can obtain the seepage motion equation for Bingham cement grout, which satisfies the following relationship:

[0192] ,

[0193] in, This indicates the seepage velocity of Bingham cement grout in the soil and rock mass. This indicates the permeability of the soil and rock mass.

[0194] The seepage motion equation of Bingham cement grout comprehensively considers factors such as the yield stress, pressure gradient, porosity and permeability of the grout. By initiating gradient pressure, average flow velocity transformation and seepage velocity, the equation of seepage velocity of grout in rock and soil is obtained, which provides technical support for the flow characteristics of Bingham cement grout in porous media.

[0195] Then, the pressure gradient equation is obtained based on the grouting boundary conditions and the seepage motion equation.

[0196] During the grouting process, the flow of grout in the rock and soil mass is affected by a variety of factors, including the physical properties of the grout, the pore structure of the rock and soil mass, and the grouting pressure. In order to describe the above-mentioned flow relationship, the seepage motion equation is rearranged, and the pressure gradient and the ratio of pore channel length are correlated and analyzed by combining the chain method.

[0197] Combining the flow characteristics of the slurry and the pore structure of the soil and rock mass, the pressure gradient is considered. Ratio of pore channel length A correlation analysis was performed, and the results satisfy the following relationship:

[0198] ,

[0199] in, a pressure gradient representing the pressure gradient of the fluid along the direction of the diffusion path, a porosity representing the porosity of the rock-soil mass, a length parameter representing the diffusion length of the slurry, a permeability coefficient, a length ratio representing the length ratio of the pore channel in the rock-soil mass, a plastic viscosity representing the plastic viscosity of the slurry, a volume flow rate representing the volume flow rate of the slurry, a start-up gradient pressure.

[0200] the pressure gradient further satisfies the following relationship:

[0201] ,

[0202] wherein, an intermediate length parameter representing the flow of the slurry in the rock-soil mass.

[0203] In the grouting process, the grouting amount of the slurry the grouting time and the grouting speed satisfy the following relationship:

[0204] ,

[0205] wherein, the grouting amount of the slurry, the volume flow rate of the slurry, a total diffusion surface area, the grouting time.

[0206] The Bingham cement slurry is in the form of a column-hemisphere diffusion in the rock-soil mass, and the total diffusion surface area of the column-hemisphere diffusion satisfies the following relationship:

[0207] ,

[0208] wherein, the total diffusion surface area, a constant representing the ratio of the circumference to the diameter, a diffusion height of the column part, a diffusion radius of the hemisphere part.

[0209] According to the relationship between the diffusion height of the column part and the diffusion radius of the hemisphere part, the total diffusion surface area and the diffusion height of the column part further satisfy the following relationship:

[0210] ,

[0211] wherein, the diffusion height of the column part, Represents pi (π). This represents the diffusion radius of the hemispherical portion.

[0212] Combining the above analysis results and relationships, the pressure gradient relationship can be obtained, which satisfies the following relationship:

[0213] ,

[0214] Considering the grouting boundary condition where Bingham cement grout diffuses in a columnar hemispherical shape within the soil and rock mass, i.e. when hour, ;when hour, In the embodiment, the separation of variables integration method is used to... The calculation formula is solved to obtain the pressure gradient equation, which satisfies the following relationship:

[0215] ,

[0216] in, Indicates the permeability radius of the columnar hemispherical shape. 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 rock and soil. 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 grouting time. Indicates the initiation of gradient pressure. This indicates the radius of the diffusion pattern of Bingham cement grout in a columnar hemispherical permeation grouting space within the rock and soil mass. This indicates the radius of the grouting hole.

[0217] The pressure gradient equation described above describes the pressure difference between the grouting pressure and the groundwater pressure when Bingham cement grout diffuses in a columnar hemispherical shape within the soil mass. The relationship between grouting volume, grouting time, porosity of soil and rock, permeability coefficient, ratio of pore channel length, diffusion morphology radius and grouting hole radius.

[0218] Finally, the pressure gradient equation was deformed based on the porosity, length ratio, Bingham fluid characteristics, grouting parameters, and grouting boundary conditions of the soil and rock mass, and a model for determining the hemispherical permeability radius of the Bingham cement grout diffusion path column was obtained.

[0219] In the process of grouting in geotechnical engineering, the diffusion behavior of Bingham cement slurry is influenced by many factors. In order to accurately describe the diffusion path, a model for determining the column-hemisphere penetration radius is constructed, which takes into account the porosity of the rock-soil mass, the length ratio of the pore channel, the plastic viscosity and yield stress of the Bingham fluid, and the grouting parameters such as grouting time and grouting amount. At the same time, the model also considers the boundary conditions of grouting, i.e. the difference between grouting pressure and groundwater pressure.

[0220] The relationship between grouting amount and diffusion radius is analyzed, and the grouting amount at the t-th moment and the diffusion radius is related, that is, the grouting amount at different moments satisfies the following relationship:

[0221] ,

[0222] wherein, represents the grouting amount of the slurry, represents the grouting rate, represents the column-hemisphere penetration grouting space diffusion shape radius of Bingham cement slurry in the rock-soil mass, which further illustrates that the grouting amount increases with the increase of the diffusion radius, and is proportional to the grouting time.

[0223] The pressure gradient equation is derived by combining the seepage motion equation and the chain rule, which also satisfies the following relationship:

[0224] ,

[0225] which further describes the relationship between the pressure gradient and the diffusion radius, the grouting time, the porosity of the rock-soil mass, the permeability coefficient and the length ratio of the pore channel.

[0226] The conversion relationship between the permeability coefficient and the permeability is substituted into the above pressure gradient equation to obtain the pressure gradient equation considering the physical properties of water.

[0227] wherein the permeability coefficient and the permeability satisfy the following relationship:

[0228] ,

[0229] wherein, represents the permeability, represents the permeability coefficient, represents the viscosity of water, represents the density of water, represents the acceleration of gravity.

[0230] Through further mathematical derivation and arrangement, the Bingham cement slurry diffusion path column hemispherical permeation radius determination model can be obtained, which not only considers the physical properties of the slurry and the grouting conditions, but also considers the influence of the pore structure of the rock-soil body and the physical properties of water on the slurry diffusion.

[0231] In the embodiment, the Bingham cement slurry diffusion path column hemispherical permeation radius determination model is obtained by combining the average flow velocity, the seepage motion equation and the pressure gradient equation, and meets the following relationship:

[0232] ,

[0233] wherein represents the column hemispherical permeation radius, represents the side opening of the grouting pipe, represents the plastic viscosity of the Bingham fluid, represents the grouting time, represents the porosity of the rock-soil body, represents the density of water, represents the gravitational acceleration, represents the permeability coefficient, represents the viscosity of water, represents the length ratio of the pore channel in the rock-soil body, represents the column hemispherical permeation grouting space diffusion form radius of the Bingham cement slurry in the rock-soil body, represents the yield stress of the Bingham fluid, represents the grouting hole radius.

[0234] The model comprehensively considers the porosity of the rock-soil body, the length ratio of the pore channel, the physical properties such as the plastic viscosity and the yield stress of the Bingham fluid, and the grouting parameters such as the grouting time and the grouting amount, and the related factors jointly affect the diffusion behavior of the slurry.

[0235] The model assumes that the slurry is in a column hemispherical diffusion in the rock-soil body, which is more in line with the grouting situation in actual engineering, and the model determined by the embodiment can more accurately predict the diffusion range and the penetration depth of the slurry, thereby providing a scientific basis and technical support for determining the column hemispherical permeation radius.

[0236] In summary, the Bingham cement slurry diffusion path column hemispherical permeation radius determination model comprehensively considers various factors and can accurately reflect the actual diffusion form, thereby providing technical support for decision-making and having a wide application prospect and practical value in the grouting practice of geotechnical engineering.

[0237] In an optional embodiment, a column hemispherical permeation radius determination method considering the diffusion path of the Bingham cement slurry is described, and the specific implementation steps are as follows:

[0238] Obtaining the mechanical parameters of the rock-soil body

[0239] Determination of key physical parameters of geotechnical mass by system through geotechnical mass mechanics experiment, wherein the density of geotechnical mass , mass water content , specific gravity , permeability coefficient and average particle size .

[0240] Calculation of porosity of geotechnical mass

[0241] Based on the experimentally determined density, mass water content and specific gravity of geotechnical mass, the porosity is calculated by using the standard formula:

[0242] ,

[0243] wherein, represents the porosity of geotechnical mass, represents the density of geotechnical mass, represents the specific gravity of geotechnical mass, represents the density of pure distilled water at , represents the mass water content.

[0244] wherein, , the calculation is .

[0245] Calculation of pore channel length ratio

[0246] Combined with the porosity of geotechnical mass and the average particle size , the pore channel length ratio is calculated by the pore channel length ratio analysis model .

[0247] ,

[0248] Acquisition of fluid characteristic parameters

[0249] Determination of key fluid parameters by rheological test: viscosity of water , plastic viscosity of Bingham fluid , yield stress .

[0250] Design of grouting parameters

[0251] According to the actual needs of the project, the water-cement ratio of Bingham cement slurry , grouting time , grouting pressure , grouting hole radius are designed, and the underground water pressure at the grouting point is measured .

[0252] Theoretical calculation of the penetration radius

[0253] Based on the Bingham cement slurry diffusion path column hemispherical penetration radius determination model:

[0254] ,

[0255] Through iterative solution, the theoretical value of the penetration radius is .

[0256] Through comparative analysis, the theoretical value of the Bingham cement slurry diffusion path column hemispherical penetration radius determination model proposed in this embodiment is 0.0644m, while the theoretical value of the traditional method (without considering porosity and particle size distribution) is 2.3419m. Combined with the penetration grouting experimental data (actual penetration radius 0.0553m) of this embodiment, please see Figure 2 .

[0257] In another optional embodiment, a column hemispherical penetration radius determination method considering the diffusion path of Bingham cement slurry is described, and the specific implementation steps are as follows:

[0258] Obtaining mechanical parameters of rock-soil mass

[0259] Through systematic development of rock-soil mass mechanical experiment to determine key physical parameters, the rock-soil mass density , mass water content , specific gravity , permeability coefficient and average particle size .

[0260] Calculation of porosity of rock-soil mass

[0261] Based on the experimentally determined rock-soil mass density, mass water content and specific gravity, the porosity is calculated by using the standard formula:

[0262] ,

[0263] wherein, represents the porosity of the rock-soil mass, represents the density of the rock-soil mass, represents the specific gravity of the rock-soil mass, represents the density of pure distilled water when , represents the mass water content.

[0264] wherein, , the calculation result is .

[0265] Calculation of pore channel length ratio

[0266] Combined with the porosity of the rock-soil mass The average particle size The pore channel length ratio is calculated by a pore channel length ratio analysis model .

[0267] ,

[0268] Fluid property parameter acquisition

[0269] Key fluid parameters are determined by rheological tests: viscosity of water , plastic viscosity of Bingham fluid , yield stress .

[0270] Grouting parameter design

[0271] According to the actual needs of the project, the water-cement ratio of the Bingham cement slurry is designed , grouting time , grouting pressure , grouting hole radius , and the underground water pressure at the grouting point is measured .

[0272] Theoretical calculation of the penetration radius

[0273] Based on the Bingham cement slurry diffusion path column hemispherical penetration radius determination model:

[0274] ,

[0275] Through iterative solution, the theoretical value of the penetration radius is obtained .

[0276] Through comparative analysis, it is found that the theoretical calculation value of the Bingham cement slurry diffusion path column hemispherical penetration radius determination model proposed in this embodiment is 0.0958 m, while the theoretical value of the traditional method (without considering porosity and particle size distribution) is 2.6194 m. Combined with the penetration grouting experimental data of this embodiment (actual penetration radius 0.0629 m, ), the penetration grouting experimental graph of this embodiment is shown in Figure 3 .

[0277] The error of the Bingham cement slurry diffusion path column hemispherical penetration radius determination model in this embodiment is , compared with the error of the traditional method, the Bingham slurry diffusion path column hemispherical penetration radius determination method is closer to the experimental value.

[0278] The calculation results of the above two specific embodiments and the radius theoretical value of the existing analysis method are compared, and the specific comparison is shown in Figure 4 , based on Figure 4The information indicates that the determination method and related models in this embodiment provide more reliable technical support for grouting projects. Please refer to [link / reference]. Figure 5 In an optional embodiment, the present invention also provides a columnar hemispherical permeation radius determination system for Bingham slurry diffusion paths, the system comprising a processor, an input...

[0279] The device, output device, and memory are interconnected. The processor, input device, output device, and memory are interconnected. The memory is used to store computer programs, which include program instructions. The processor is configured to call the program instructions and execute the specific steps of the method for determining the columnar hemispherical permeation radius of the Bingham slurry diffusion path and related embodiments provided by the present invention. The system for determining the columnar hemispherical permeation radius of the Bingham slurry diffusion path of the present invention has a complete structure and is objective and stable.

[0280] 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 column hemispherical penetration radius of the Bingham slurry flow path, characterized by, The method comprises the following steps: Obtaining physical and mechanical information of the rock-soil body through a rock-soil body mechanical experiment, establishing a rock-soil body porosity calculation model based on the physical and mechanical information, and determining the rock-soil body porosity according to the rock-soil body porosity calculation model; Establishing a pore channel length ratio analysis model according to the rock-soil body porosity and the physical and mechanical information, and analyzing the length ratio of pore channels in the rock-soil body according to the pore channel length ratio analysis model; Introducing rheological test information, obtaining Bingham fluid characteristic information based on the rheological test information, and setting grouting parameters of the Bingham cement grout according to grouting requirements; Based on the rock-soil body porosity, the length ratio, the Bingham fluid characteristic information and the grouting parameters, a Bingham cement grout diffusion path column hemispherical permeation radius determination model is constructed to realize accurate analysis of the Bingham grout diffusion path column hemispherical permeation radius; The construction of the Bingham cement grout diffusion path column hemispherical permeation radius determination model based on the rock-soil body porosity, the length ratio, the Bingham fluid characteristic information and the grouting parameters comprises: Combining the Bingham grout basic rheological equation and the rheological test information to analyze the average flow rate of the Bingham cement grout; Obtaining a seepage flow motion equation of the diffusion path Bingham cement grout according to the grout permeation velocity relationship and the average flow rate; Obtaining a pressure gradient equation based on grouting boundary conditions and the seepage flow motion equation; According to the rock-soil body porosity, the length ratio, the Bingham fluid characteristic information, the grouting parameters and the grouting boundary conditions, the pressure gradient equation is deformed to obtain the Bingham cement grout diffusion path column hemispherical permeation radius determination model; The Bingham cement grout diffusion path column hemispherical permeation radius determination model satisfies the following relationship: ， wherein represents a cylindrical hemispherical permeation radius, represents a side opening of a grouting pipe, represents a plastic viscosity of a Bingham fluid, represents a grouting time, represents a porosity of a rock-soil body, represents a density of water, represents a gravitational acceleration, represents a permeability coefficient, represents a viscosity of water, represents a length ratio of a pore passage in a rock-soil body, represents a cylindrical hemispherical permeation radius of a Bingham cement grout in a rock-soil body, represents a yield stress of a Bingham fluid, represents a grouting hole radius.

2. The method for determining the column hemispherical penetration radius of a Bingham slurry flow path according to claim 1, wherein, The obtaining of the physical and mechanical information of the rock-soil body through the rock-soil body mechanical experiment, the establishment of the rock-soil body porosity calculation model based on the physical and mechanical information, and the determination of the rock-soil body porosity according to the rock-soil body porosity calculation model comprise: Obtaining the physical and mechanical information of the rock-soil body according to rock-soil mechanics theory and the rock-soil body mechanical experiment, wherein the physical and mechanical information comprises density information, mass water content information, specific gravity information, permeability coefficient information and average particle size information of the rock-soil body; Establishing the rock-soil body porosity calculation model based on the density information, the mass water content information, the specific gravity information, the permeability coefficient information and the average particle size information; Determining the rock-soil body porosity by using the rock-soil body porosity calculation model.

3. The method for determining the column hemispherical penetration radius of Bingham slurry flow paths according to claim 2, characterized in that, The establishment of the rock-soil body porosity calculation model based on the density information, the mass water content information, the specific gravity information, the permeability coefficient information and the average particle size information comprises: The rock-soil body porosity calculation model satisfies the following relationship; ， wherein, represents the porosity of the rock-soil body, represents the density of the rock-soil body, represents the specific gravity of the rock-soil body, represents the density of pure distilled water at the time, represents the mass water content.

4. The method for determining the column hemispherical penetration radius of Bingham slurry flow paths according to claim 1, wherein, The establishment of the pore channel length ratio analysis model according to the rock-soil body porosity and the physical and mechanical information comprises: Analyzing the grout flow rate through the rock-soil body pores per unit time based on the physical and mechanical information; Establishing a length ratio preliminary analysis function according to the rock-soil body porosity and the grout flow rate. The analysis result of the porosity and the fractal dimension in the rock-soil mass is obtained according to a fractal theory method, a radius ratio and a minimum particle diameter relationship and a length ratio preliminary analysis function; A pore channel length ratio analysis model is obtained in combination of the radius ratio and the minimum particle diameter relationship, the analysis result and the porosity of the rock-soil mass.

5. The method for determining the column hemispherical penetration radius of Bingham slurry flow paths according to claim 4, characterized in that, The slurry flow condition satisfies the following relationship: ， wherein, represents the total volumetric flow rate through the unit volume per unit time, represents the number of pore channels in the unit volume, represents the ratio of the circumference of a circle to its diameter, represents the pressure gradient of the fluid along the direction of the diffusion path, represents the radius of the pore channel, represents the viscosity of the fluid; The length ratio preliminary analysis function satisfies the following relationship: ， wherein, represents the actual length of the fluid flow along the diffusion path direction, represents the reference length, represents the pore channel radius, represents the porosity of the rock-soil body, represents the permeability; The analysis result of the porosity and the fractal dimension in the rock-soil mass satisfies the following relationship: ， wherein, represents a length ratio of a pore channel in a geotechnical body, represents a pore fractal dimension, represents a porosity of a geotechnical body, represents a circumference ratio, represents a minimum radius of a pore channel, represents a maximum radius of a pore channel.

6. The method for determining the column hemispherical penetration radius of Bingham slurry flow paths according to claim 4, wherein, The pore channel length ratio analysis model obtained in combination of the radius ratio and the minimum particle diameter relationship, the analysis result and the porosity of the rock-soil mass includes: The pore channel length ratio analysis model satisfies the following relationship: ， wherein, represents a length ratio of a pore channel in a rock-soil body, represents an average particle diameter, represents a porosity of a rock-soil body, represents a circular constant.

7. The method for determining the column hemispherical penetration radius of Bingham slurry flow paths according to claim 1, wherein, The rheological test information is introduced, Bingham fluid characteristic information is obtained based on the rheological test information, and grouting parameters of the Bingham cement slurry are set according to grouting requirements, including: Designing a rheological test to obtain rheological test information; Analyzing water viscosity information, Bingham fluid plastic viscosity information and yield stress information through the rheological test information; Obtaining Bingham fluid characteristic information in combination of the water viscosity information, the Bingham fluid plastic viscosity information and the yield stress information; Setting grouting parameters of the Bingham cement slurry according to grouting requirements, including water-cement ratio, grouting time and grouting pressure; Setting grouting boundary conditions based on the grouting requirements and the grouting parameters, including underground water pressure at a grouting point.

8. A system for determining the column hemispherical penetration radius of the Bingham plug flow regime, characterized by, The system comprises a processor, an input device, an output device and a memory, which are connected to each other, wherein the memory is used to store a computer program, the computer program comprises program instructions, and the processor is configured to call the program instructions to execute the method for determining the column hemispherical percolation radius of the Bingham slurry diffusion path according to any one of claims 1-7.

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