Three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method and system

Abstract

The invention provides a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method and system, and belongs to the technical field of computer aided design. The method is applied to slurry diffusion characteristic analysis during static water-saturated fracture grouting, and comprises the following steps: reconstructing a fracture three-dimensional morphology structure by respectively utilizing a standard rough contour line and a three-dimensional laser scanning technology to obtain a digital model of a three-dimensional rough fracture; establishing a slurry-water two-phase flow model; based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, slurry displacement still water two-phase flow simulation in the three-dimensional rough fracture is carried out; wherein the slurry-water two-phase flow model comprises a control equation and a slurry-water displacement two-phase flow constitutive model, and the control equation comprises a continuity equation of fluid flowing in the fracture, a momentum conservation equation of fluid flowing in the fracture and a phase field equation used for describing phase interface movement. A two-phase flow method is adopted to analyze the static water-saturated fracture grouting process, and the reasonability of dam foundation fracture grouting design can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of computer-aided design, and particularly relates to a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method and system. Background Art

[0002] Grouting is an important means to improve the shear-slip stability and anti-seepage performance of dams. By displacing water in fractures and solidifying the slurry, the bonding force between fractures is enhanced. Generally, the grouting process design needs to comprehensively consider geological conditions (such as the development of joint fractures in the dam foundation), and trial grouting is carried out before dam construction. Reasonable grouting process design is very important for improving grouting efficiency.

[0003] Most of the existing research on dam foundation fracture grouting regards fracture grouting as a single-phase flow process, ignoring the existence of initial static water in the dam foundation fractures, and cannot accurately guide the engineering practice of dam foundation fracture grouting. Therefore, an improved technical solution for the above-mentioned deficiencies in the prior art is needed. Summary of the Invention

[0004] The purpose of the present application is to provide a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method and system to solve or alleviate the problems existing in the above-mentioned prior art.

[0005] To achieve the above purpose, the present application provides the following technical solutions: In a first aspect, the present application provides a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method, which is applied to the analysis of slurry diffusion characteristics during static water-saturated fracture grouting, including: Reconstructing the three-dimensional morphology structure of the fracture by using the standard rough contour line and three-dimensional laser scanning technology respectively to obtain the digital model of the three-dimensional rough fracture; Regarding the slurry and water as two phases during the grouting process to establish a slurry-water two-phase flow model; Based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, carrying out the simulation of the two-phase flow of slurry displacing static water in the three-dimensional rough fracture to obtain the simulation result; Wherein, the slurry-water two-phase flow model includes: a control equation and a slurry-water displacement two-phase flow constitutive model. The control equation includes: the continuity equation of fluid flow in the fracture, the momentum conservation equation of fluid flow in the fracture, and the phase field equation for describing the movement of the phase interface; the slurry-water displacement two-phase flow constitutive model includes: the Bingham-Papanastasiou constitutive model for describing the flow characteristics of the slurry, and the Newtonian model for describing the flow characteristics of the water phase.

[0006] Optionally, the phase field equation for describing the movement of the phase interface is specifically: The phase field variable is used to represent the volume fractions of the slurry-water two-phase, and the phase interface is captured by the Cahn-Hilliard equation.

[0007] Optionally, it further includes: verifying the slurry-water two-phase flow model as follows: Based on the slurry-water two-phase flow model, solve the analytical solution of the displacement of Newtonian fluid by Bingham fluid in a two-dimensional parallel plate; Use computer software to numerically simulate the slurry-water two-phase flow model in a two-dimensional parallel plate to obtain the numerical simulation results; Compare the numerical simulation results with the analytical solution and the grouting displacement test results obtained in advance to verify the rationality of the slurry-water two-phase flow model.

[0008] Optionally, the solution process of the analytical solution of the displacement of Newtonian fluid by Bingham fluid in a two-dimensional parallel plate is as follows: Regard the slurry-water two-phase as single-phase flows respectively, and determine the velocities of the single-phase Newtonian fluid and the single-phase Bingham fluid respectively; Using the definite solution condition of velocity continuity on the phase interface, integrate and average the velocities of the single-phase Newtonian fluid and the single-phase Bingham fluid in the opening direction respectively to obtain the average velocities of the water phase and the slurry phase correspondingly; Considering that the water heads in the water phase and the slurry phase are linearly distributed at any moment in the single-phase flow, determine the relationships between the water heads in the water phase and the slurry phase and the position of the phase interface changing linearly respectively; Simultaneously solve the average velocities of the water phase and the slurry phase and the relationships between the water heads in the water phase and the slurry phase and the position of the phase interface changing linearly to obtain the analytical solution of the displacement of Newtonian fluid by Bingham fluid in a two-dimensional parallel plate.

[0009] Optionally, in the analytical solution of the displacement of Newtonian fluid by Bingham fluid in a two-dimensional parallel plate, the position of the phase interface and the water head on the phase interface at different moments are calculated as follows: Based on the assumption of continuous change of the water head on the phase interface, use the relationship between the pressure gradients of the slurry phase and the water phase at different moments to solve the relationship between the water head on the phase interface and the position of the phase interface; Use the derivative relationship between the position of the phase interface and the average velocity, and obtain the relationship between the position of the phase interface and time by separating variables and integrating.

[0010] Optionally, based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, carry out the simulation of the displacement of slurry by static water two-phase flow in three-dimensional rough fractures to obtain the simulation results, including: Under parallel flow conditions, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, the advancing velocity, shape change of the slurry front front and the change of the displacement ratio with time in the three-dimensional rough fracture are analyzed by numerical simulation; Under parallel flow conditions, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, a numerical simulation orthogonal test is carried out on the three-dimensional rough fracture to analyze the influence of different grouting material properties on the displacement efficiency of the slurry-water two-phase flow model and the traditional single-phase flow model.

[0011] Optionally, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, a simulation of the slurry displacing the static water two-phase flow in the three-dimensional rough fracture is carried out to obtain simulation results, including: Under the conditions of roughness anisotropy and radiation, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, the roughness parameters in different directions in the three-dimensional rough fracture are analyzed by numerical simulation R and the influence of the fracture morphology on the slurry diffusion direction; Under radiation flow conditions, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, the influence of the fracture morphology, contact area and surface tension on the slurry diffusion in the three-dimensional rough fracture is analyzed by numerical simulation, and the difference in displacement efficiency between the slurry-water two-phase flow model and the traditional single-phase flow model is compared.

[0012] In a second aspect, the present embodiment provides a numerical simulation system for slurry-water displacement two-phase flow in a three-dimensional rough fracture. The system is applied to the analysis of slurry diffusion characteristics during static water-saturated fracture grouting, including: A rough fracture construction unit for reconstructing the three-dimensional morphology structure of the fracture by using three-dimensional laser scanning technology to obtain a three-dimensional rough fracture model; A model establishment unit for establishing a slurry-water two-phase flow model; A simulation analysis unit for carrying out a simulation of the slurry displacing the static water two-phase flow in the three-dimensional rough fracture based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture to obtain simulation results; Among them, the slurry-water two-phase flow model includes: a control equation and a slurry-water displacement two-phase flow constitutive model. The control equation includes: a continuity equation for fluid flow in the fracture, a momentum conservation equation for fluid flow in the fracture, and a phase field equation for describing the movement of the phase interface; the slurry-water displacement two-phase flow constitutive model includes: a Bingham-Papanastasiou constitutive model for describing the flow characteristics of the slurry, and a Newtonian model for describing the flow characteristics of the water phase.

[0013] In a third aspect, this embodiment provides an electronic device, including: a memory for storing instructions executed by one or more processors of the electronic device; a processor, when the processor executes the instructions in the memory, enabling the electronic device to implement the steps of the three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method provided in any of the above embodiments.

[0014] In a fourth aspect, this embodiment provides a computer-readable storage medium, characterized in that instructions are stored on the computer-readable storage medium, and when the instructions are executed on a computer, the steps of the three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method provided in any of the above embodiments are implemented.

[0015] The technical solution of the embodiment of the present application has the following beneficial effects: The technical solution of this embodiment takes the reinforcement of saturated hydrostatic fractures in the dam foundation as the research background, considers the grouting water displacement process in real three-dimensional rough fractures, uses three-dimensional laser scanning technology to reconstruct the three-dimensional morphology structure of the fractures, obtains the digital model of the three-dimensional rough fractures, constructs a real three-dimensional rough fracture space, uses the phase field equation (phase field method) to capture the phase interface movement process, uses the Bingham-Papanastasiou constitutive model to describe the slurry flow characteristics, uses the Newtonian model of Newtonian fluid to describe the water phase flow characteristics, constructs a slurry-water two-phase flow model, and conducts the simulation of slurry displacement of hydrostatic two-phase flow in three-dimensional rough fractures, thereby improving the accuracy and rationality of the analysis of slurry diffusion characteristics in the static saturated water fracture grouting process, being conducive to providing reasonable guidance for the grouting process design in engineering practice, and improving the grouting efficiency. Description of the Drawings

[0016] Figure 1 It is a schematic structural diagram of an electronic device according to some embodiments of the present application.

[0017] Figure 2 It is a schematic flowchart of the three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method.

[0018] Figure 3 It is a schematic diagram of the digital processing process of the Barton standard contour line.

[0019] Figure 4 It is a schematic diagram of a rough disk generated using the Barton standard contour line, where (a) represents a rough disk generated using the standard contour lines numbered JRC = 2 to 4; (b) represents a rough disk generated using the standard contour lines numbered JRC = 6 to 8, (c) represents a rough disk generated using the standard contour lines numbered JRC = 10 to 12, and (d) represents a rough disk generated using the standard contour lines numbered JRCRough disk generated by the standard contour line of 14~16.

[0020] Figure 5 It is a schematic diagram of the simulation of two-phase flow of Bingham fluid (cement slurry) displacing Newtonian fluid (water) in a two-dimensional parallel plate.

[0021] Figure 6 It is a schematic diagram of the velocity distribution of Bingham fluid (slurry) and Newtonian fluid (water) in a parallel plate.

[0022] Figure 7 It is a schematic diagram of using trapezoidal integral accumulation to solve the relationship between time and phase interface position.

[0023] Figure 8 It is a schematic diagram of the simulation of slurry-water displacement two-phase flow in the cracks of a rough disk.

[0024] Figure 9 For different tension coefficients σ The displacement ratio I Schematic diagram of the curve changing with time during grouting.

[0025] Figure 10 It is a schematic diagram of the curve of the grouting displacement ratio of slurry-phase materials with different yield stresses changing with time under low plastic viscosity and high plastic viscosity. Among them, (a) represents μ g The curve at = 0.0025 Pa·s, and (b) represents μ g The curve at = 0.25 Pa·s.

[0026] Figure 11 It is a schematic diagram of the comparison of the displacement ratios of the two-phase flow method and the single-phase flow method under the conditions of low plastic viscosity and high plastic viscosity. Among them, (a) represents μ g The comparison result at = 0.0025 Pa·s, and (b) represents μ g The comparison result at = 0.25 Pa·s. Specific implementation mode

[0027] To better understand the technical solution of this application, the relevant terms involved in this application are described below.

[0028] (1) Grouting In some documents, the two terms "grouting" and "injection grouting" are often used. In the technical description of this embodiment, they are not distinguished and both refer to "grouting", but the commonly used term "grouting" in engineering is used to describe the problem in the text.

[0029] As a common water plugging and reinforcement technology for fractured rock masses, grouting is a necessary means to solve the problems of dam leakage and shear slip. Grouting can effectively reduce the water content in fractures and block the seepage path of fracture water. At the same time, the intrusion and solidification of the grout can further enhance the bonding force between fractures, thereby improving the integrity and mechanical properties of the fractured rock mass at the dam foundation.

[0030] Currently, a large part of the budget for the reinforcement of dangerous and defective reservoir dams is used for the grouting reinforcement of the dam foundation. Grouting can improve the strength and sealing performance of the dam foundation and reduce the probability of dam failure under adverse conditions (earthquakes, heavy rains). The dam grouting process is concealed, and the grouting efficiency has a high degree of uncertainty. Generally speaking, the grouting process design needs to comprehensively consider geological conditions (such as the development of joints and fractures in the dam foundation) and conduct trial grouting before dam construction.

[0031] The existing research on fracture grouting (excluding the grouting of porous media based on homogenization theory) mainly analyzes the slurry diffusion process from two aspects. One is to assume that the slurry diffuses in the fracture cavity, that is, the fracture grouting is regarded as a single-phase flow process; under ideal conditions, the fracture grouting is simplified to the single-phase flow process of Newtonian fluid (chemical grouting) or Bingham fluid (cement-based grouting) between non-deformable parallel plates. The other is to take the common water inrush disasters in underground projects such as tunnels as the background and use the two-phase flow method to study the influence of dynamic water on the slurry diffusion process. In the existing non-dynamic water grouting research, the existence of initial static water in fractures is often ignored, and the fracture grouting is regarded as the movement process of a single-phase Bingham fluid. In the dam foundation fractures, there is often fracture water that is approximately static. However, the inventor's research found that during fracture grouting, water has a blocking effect on the slurry diffusion process, and before the slurry invades the fracture, it is necessary to continuously displace the water. Therefore, it is of great significance to use the two-phase flow method to analyze the static water grouting process.

[0032] (2)Dynamic water grouting In the technical description of this embodiment, dynamic water grouting is a proprietary term. The research background of dynamic water grouting is the adverse geological disasters (such as water inrush and mud inrush) in tunnel engineering, mainly focusing on the plugging effect, slurry diffusion and residual morphology, etc. The core problem is the driving or influence of water on the slurry flow.

[0033] It should be noted that although dynamic water grouting and the static water grouting of this application are both two-phase flow problems, their research purposes and characteristics are different. In this application, the background of the static water grouting problem is the reinforcement of saturated static water fractures in the dam foundation, mainly focusing on the grouting intrusion length and the water displacement effect. The core problem is the driving of the slurry to discharge the static water from the fractures. Although both are two-phase flow problems, they belong to different scientific problems.

[0034] In actual engineering, the cracks in the dam foundation have a significant three-dimensional topographical structure. The process of grout diffusion is affected by roughness, contact, etc. However, existing research rarely considers the process of grout-driven water displacement in real three-dimensional rough cracks. In addition, although some studies have constructed a slurry-water two-phase flow model in dissoluble dolomite, the research object of this model is porous media or pore-type formations and cannot yet be used to study the process of slurry-phase water displacement in fractured media (dam foundation cracks). That is to say, under the current real engineering conditions, in fractured media (dam foundation cracks), the mechanism of slurry displacing static water is not clear, resulting in certain deviations in the design of crack grouting under complex conditions.

[0035] In view of this, the present application provides a numerical simulation method and system for slurry-water displacement two-phase flow in three-dimensional rough cracks. By obtaining a three-dimensional rough surface and constructing a crack space, a slurry-water displacement two-phase flow model in rough cracks is established, and then the simulation of slurry displacing static water two-phase flow in three-dimensional rough cracks is carried out to accurately analyze the mechanism of slurry-phase water displacement in real three-dimensional rough crack media (dam foundation cracks), providing more reasonable guidance for the design of crack grouting under complex conditions.

[0036] The embodiments of the present application will be described below with reference to the accompanying drawings.

[0037] The embodiments of the present application can be applied to Figure 1 the electronic device shown in the figure. The electronic device can be, but is not limited to, mobile terminals such as mobile phones, tablet computers, handheld computers, personal digital assistants (PDAs), etc., smart home devices such as smart TVs, smart cameras, wearable devices such as smart bracelets, smart watches, smart glasses, or other computer devices such as desktop, laptop, notebook computers, ultra-mobile personal computers (UMPCs), netbooks, and smart screens.

[0038] As Figure 1 shown in the figure, the electronic device 200 may include one or more of the following components: a processor 201, a memory 203, a communication interface 202, and a communication bus 204. Among them, the memory 203 can be connected to the processor 201 through the bus 204. The bus can transmit data between the processor 201 and the memory 203. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0039] The processor 201 may include one or more processing cores. The processor 201 can connect various parts within the entire electronic device 200 using various interfaces and circuits. By running or executing instructions, programs, code sets, or instruction sets stored in the memory 203, and by invoking the data stored in the memory 203, it performs various functions of the electronic device 200 and processes data. Exemplarily, the processor 201 may include an application processor (AP), a modem processor, a CPU, a graphics processing unit (GPU), an image signal processor (ISP), a controller, a video codec, a digital signal processor (DSP), a field-programmable gate array (FPGA), a programmable logic array (PLA), and / or a neural-network processing unit (NPU), etc. Among them, the CPU mainly processes the operating system, user interface, and application programs, etc.; the GPU is responsible for rendering and drawing the content to be displayed; the NPU is used to implement artificial intelligence (AI) functions; the modem is used to process wireless communication. Different processing units can be independent devices or integrated in one or more processors. For example, the multiple processing units shown above are all integrated in one SoC, or the AP is a separate semiconductor chip and other processing units are integrated in one SoC. This application does not make any limitations in this regard.

[0040] The memory 203 may include a random access memory (RAM), may also include a read-only memory (ROM), and may further include a non-transitory computer-readable storage medium. The memory 203 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 203 may include a program storage area and a data storage area. Among them, the program storage area can store instructions for implementing the operating system, instructions for at least one function, such as the numerical simulation method of three-dimensional rough fracture slurry-water displacement two-phase flow, etc.; the data storage area can store data created according to the use of the electronic device 200, such as the input data for numerical solution, etc.

[0041] In addition, those skilled in the art can understand that the structure of the electronic device 200 shown in the above drawings does not limit the electronic device 200. The electronic device may include more or fewer components than shown in the drawings, or combine some components, or have different component arrangements. For example, the electronic device 200 also includes components such as a microphone, a speaker, a radio frequency circuit, a sensor, an audio circuit, a power supply, and a Bluetooth module, which will not be elaborated here.

[0042] This embodiment provides a numerical simulation method for three-dimensional rough fracture slurry-water displacement two-phase flow, which is applied to the analysis of slurry diffusion characteristics during static water-saturated fracture grouting, such as Figure 2 shown, the method includes: Step S101: Reconstruct the three-dimensional morphology structure of the fracture by using the standard rough contour line and the three-dimensional laser scanning technology respectively to obtain the digital model of the three-dimensional rough fracture.

[0043] In this embodiment, the digital model of the three-dimensional rough fracture includes: a digital model generated based on the standard contour line (i.e., a rough disk) and a digital model obtained by using the three-dimensional laser scanning technology (used to simulate the three-dimensional rough fracture under real conditions). The digital model of the three-dimensional rough fracture is generated in two ways to more accurately simulate the grouting process of the three-dimensional rough fracture and more reasonably reveal the slurry-water displacement mechanism of the three-dimensional rough fracture during static water-saturated fracture grouting.

[0044] First, introduce the generation method of the rough disk based on the standard contour line, which can generate the digital model of the Barton standard contour line.

[0045] Due to the existence of surface rough protrusions, the fracture grouting is affected by inertial force, and the slurry water displacement efficiency is correspondingly affected. In order to study the influence of roughness on the grouting water displacement process, this study uses the Barton standard contour line to generate a series of standard disks with different roughnesses and apertures. The grouting hole is located in the center of the disk, and the slurry diffuses simultaneously in all directions. Since the roughness and aperture of the fracture are the same in each diffusion direction, the influence of parameters such as morphology or aperture on the slurry water displacement process can be studied separately by the method of controlling variables.

[0046] In this embodiment, as Figure 3As shown in the figure, the process of obtaining the digital model of the Barton standard contour line is as follows: (1) Each Barton contour line in the literature is separately intercepted and saved. (2) The intercepted pictures are imported into MATLAB and the image information is converted into grayscale information. The grayscale information is stored and represented in the form of a matrix. The number of columns of the matrix represents the length of the picture, and the number of rows of the matrix represents the height of the picture. The value range of each element in the matrix is 0-255, representing the grayscale of the picture element. Among them, 0 represents pure black and 255 represents pure white. (3) Find the minimum value in each column of elements, and the position of this value is the position of the contour line point element. (4) Convert the position information obtained from the grayscale image into coordinate information. The length between the two point elements with the largest horizontal distance represents the length of the contour line. (5) Interpolate the contour line into a given sampling point distance. Preferably, the sampling point distance is 1 mm. (6) Label the obtained standard contour lines. For example, JRC = 2-4, 6-8, 10-12, 14-16 are the labels of four standard contour lines. Then each contour line is offset upward or downward by a certain distance to form a fracture space, and a rough disk is generated by rotation. The rough disk generated using the Barton standard contour line is also called the digital model of the Barton standard contour line. A typical rough disk is as shown in Figure 4 as shown in the figure.

[0047] The above processing steps are proposed based on the MATLAB image grayscale processing function and are a simple digital processing method. This method stores and represents image information using a grayscale matrix, quickly locates the position of the contour line point element by finding the minimum value in each column, generates a fracture space through a simple offset operation, and generates a rough disk by rotation, simplifying the generation process of the fracture space and the rough disk and improving the efficiency of the digital processing of the standard contour line.

[0048] Secondly, the digital model obtained by the three-dimensional laser scanning technology includes the following steps: Take the rough surface obtained by three-dimensional laser scanning as one side wall surface of the fracture, and then move the fracture surface a certain distance in the horizontal and vertical directions to simulate the shear disturbance of the fracture (horizontal shear displacement and normal dilatancy displacement), so as to obtain the other side wall surface. Through the offset operation, the upper and lower fracture surfaces are displaced and no longer coincide, thus forming a rough fracture space with a certain aperture and contact.

[0049] Since the solution of the two-phase flow model is relatively complex and the computational workload is large, exemplarily, in the three-dimensional laser scanning modeling of this embodiment, a small-scale model is used for modeling. The fracture length is 80 mm, the width is 30 mm, and the average aperture is about 2 mm. In the initial state, the fracture is filled with water. Different from the common water and mud inrush disasters (dynamic water conditions) in tunnel construction, in this embodiment, the fissure water is mainly stored in the fractures of the dam foundation, and the flow velocity is relatively small. Therefore, it is assumed that the fissure water in the dam foundation is static water under the initial conditions. During grouting, the grout is injected from the inlet at a constant pressure, and the water is discharged from the outlet; the outlet is also a pressure boundary condition, with a pressure difference of 300 Pa, and the rest (both sides and the upper and lower walls) are impermeable boundaries, forming a parallel flow space. The contact area (aperture is 0). The fracture space is meshed with tetrahedral elements with a minimum size of 0.3 mm, and the total number of domain elements is about 90,000.

[0050] Step S102: During the grouting process, regard the grout and water as two phases, and establish a grout-water two-phase flow model.

[0051] It should be particularly noted that this embodiment studies the grouting of fractures in the dam foundation rock mass, rather than the dam filling grouting (usually core wall clay grouting, and the uniformity assumption in the porous medium theory needs to be used to study the diffusion of the grout). Therefore, the two important premises of the technical solution of this embodiment are: (i) The rock mass is a fractured medium rather than a porous medium. Therefore, this embodiment does not use the common uniformity assumption in the porous medium theory. In the fractured medium, it is very important to construct a real three-dimensional rough fracture space. Therefore, this embodiment uses three-dimensional laser scanning technology to reconstruct the three-dimensional morphology structure of the fracture. (ii) It is assumed that during the grouting process, the mixing process of the grout phase and the water phase has little influence on the overall diffusion process of the grout. The grout and water can be approximately regarded as two phases. Therefore, the grout and water fill the three-dimensional rough fracture space (rather than the porous medium space based on the uniformity assumption), and there is a certain interface between the two, which is the premise of this embodiment's research.

[0052] During the grouting process, regard the grout and water as two phases, and establish a grout-water two-phase flow model. The grout-water two-phase flow model includes: control equations and a grout-water displacement two-phase flow constitutive model. The control equations include: the continuity equation of fluid flow in the fracture, the momentum conservation equation of fluid flow in the fracture, and the phase field equation for describing the movement of the phase interface; the grout-water displacement two-phase flow constitutive model includes: the Bingham-Papanastasiou constitutive model for describing the flow characteristics of the grout, and the Newtonian model for describing the flow characteristics of the water phase.

[0053] Specifically, the control equations of the grout-water two-phase flow model are obtained as follows: (1) Flow field control equations The process of water displacement by crack grouting is described using a slurry-water two-phase flow model. The fluid velocity in the crack is small, the inertial force acting on the fluid is less than the viscous force, and the fluid is incompressible. The continuity equation for fluid flow in the crack is: (1) where: u is the fluid velocity (m / s).

[0054] The momentum conservation equation (N-S equation) for fluid flow in the crack is: (2) where: ρ is the fluid density (kg / m 3 ), which is a constant value due to the incompressibility of the fluid; p is the pressure (Pa), t is the time, μ is the dynamic viscosity of the fluid (Pa·s), g is the gravitational acceleration vector (m / s 2 ), F is the body force (N / m 3 ).

[0055] (2) Phase field equation In existing literature, the level set method is often used to capture the movement of the phase interface. In this embodiment, the movement of the phase interface is described by the phase field method. The phase field variable represents the volume fraction of the two phases, and the phase interface is captured by the Cahn-Hilliard equation: (3) where φ is the phase field variable. When φ is equal to -1, it represents the water phase, and when φ is equal to 1, it represents the slurry phase; χ is the migration adjustment parameter (m·s / kg), σ is the surface tension coefficient (N / m), ε is the phase interface thickness parameter (m).

[0056] Among them, ε is generally taken as half of the maximum grid size.

[0057] ψ is the phase field auxiliary variable, which can be expressed as a function of the phase field variable: (4) According to the phase field variable, the volume fraction of each phase can be expressed as: (5) (6) V1 , V 2 are the volume fractions of the aqueous phase and the slurry phase, respectively.

[0058] The constitutive model of the slurry-water two-phase flow model is obtained as follows: The aqueous phase is a typical Newtonian fluid without yield strength. No matter how small the pressure gradient is, the Newtonian fluid will produce shear motion. The slurry phase materials mainly include cement-based mixtures and chemical mixtures. The commonly used grouting slurries are cement-based materials. In the cement slurry, solid particles and water form a suspension, and the solid-phase particles make the mixture have cohesive strength. Only after the cohesion is destroyed, the slurry flow will be controlled by the liquid phase. Therefore, the commonly used cement slurry in grouting engineering practice is a typical non-Newtonian fluid, and the Bingham constitutive model is generally used to describe it. The Bingham model requires two material parameters to describe the fluid characteristics: (7) where: τ is the shear stress (Pa), μ g is the shear strain rate coefficient (or plastic viscosity, Pa·s), τ 0 is the yield stress (Pa), dγ / dt is the shear rate. When τ 0 = 0, the Bingham model simplifies to the Newtonian model.

[0059] In the calculation of viscoplastic flow, usually only the shear strain rate term (i.e., μ g +τ 0 / (dγ / dt) ) is defined. When the shear rate d γ / dt changes from 0 (the fluid is not flowing) to a small value, a numerical discontinuity phenomenon will occur. Papanastasiou proposed a continuous model to approximately approximate the Bingham model. In actual calculations, the Bingham model is rarely used, but the Bingham-Papanastasiou constitutive model with continuous characteristics is used: (8) where: m is the model control parameter. When m is large, the Bingham-Papanastasiou model can be simplified to the Bingham model.

[0060] After constructing the slurry-water two-phase flow model, in some embodiments, it further includes: verifying the slurry-water two-phase flow model, specifically as follows: Step S1021: Based on the slurry-water two-phase flow model, solve the analytical solution of Bingham fluid displacing Newtonian fluid in a two-dimensional parallel plate.

[0061] Since there is a yield stress in Bingham fluid, the strict proportional relationship between shear stress and velocity gradient is no longer satisfied. The solution of the problem of Bingham fluid driving Newtonian fluid is relatively complex, and usually only the analytical solution can be obtained in relatively simple cases. In this embodiment, first, the analytical solution of Bingham fluid displacing Newtonian fluid in a two-dimensional parallel plate is used to verify the correctness of the established numerical model of slurry-water displacement two-phase flow.

[0062] Figure 5 It is a schematic diagram of the simulation of the two-phase flow of Bingham fluid (cement slurry) displacing Newtonian fluid (water) in a two-dimensional parallel plate. As Figure 5 shown, the opening b of the parallel plate is much smaller than the length L ( b<L / 100), and the pressure (or water head) along the opening direction is the same. Before grouting to drive water, the parallel plate fissure is filled with static water. The slurry phase enters from the left inlet, and the water phase is displaced and flows out from the right outlet. Assuming the inlet water head is H 0 and the outlet water head is H L , both are constant water head boundaries. The intrusion length of the slurry phase (or the position of the phase interface) x and the water head H(x(t)) on the phase interface (or the front edge of the slurry phase) are both functions of time t .

[0063] Further, step S1021 includes: Step S1021a: Treat the slurry and water phases as single-phase flows respectively, and determine the velocity of the single-phase Newtonian fluid and the velocity of the single-phase Bingham fluid respectively; Step S1021b: Using the definite solution condition of velocity continuity on the phase interface, integrate and average the velocity of the single-phase Newtonian fluid and the velocity of the single-phase Bingham fluid in the opening direction respectively, and correspondingly obtain the average velocities of the water phase and the slurry phase; Step S1021c: Considering that the water heads in the water phase and the slurry phase are linearly distributed at any moment in the single-phase flow, determine the relationship between the water heads in the water phase and the slurry phase changing linearly with the position of the phase interface respectively; Step S1021d: Simultaneously solve the average flow velocities of the aqueous phase and the slurry phase, and the relationship between the water heads in the aqueous phase and the slurry phase varying linearly with the position of the phase interface, to obtain the analytical solution of the displacement of Newtonian fluid by Bingham fluid in a two-dimensional parallel plate.

[0064] Specifically, the key to solving the various field variables (water head H , intrusion length x , etc.) of the displacement of Newtonian fluid by Bingham fluid in a two-dimensional parallel plate is to consider the two phases as single-phase flows respectively, and then use the definite solution condition of velocity continuity at the phase interface to obtain the relationships between the variables. The velocity distributions of Bingham fluid (slurry) and Newtonian fluid (water) in a two-dimensional parallel plate under the single-phase flow condition are as Figure 6 shown. Among them, the velocity distribution of single-phase water satisfies the Hagen-Poiseuille law: (9) In the formula: μ w is the dynamic viscosity of water (Pa·s), P 1 is the aqueous phase pressure (Pa).

[0065] The velocity distribution formula of Bingham fluid (slurry) under the single-phase flow condition: (10) In the formula: μ g is the plastic viscosity of the slurry (Pa·s), P 2 is the slurry phase pressure (Pa), y g is the half-width of the rigid core formed due to the existence of the yield stress term, which depends on the yield stress and the hydraulic gradient, and its calculation formula is as follows: (11) From Figure 6 it can be seen that the slurry phase velocity is in a plug-like shape, while the velocity distribution of the aqueous phase is parabolic. Therefore, the velocity distributions of the slurry phase and the aqueous phase at the phase interface cannot be exactly the same. Similar to the Saint-Venant principle, the definite solution condition is approximately equivalent to the average velocity of the slurry phase being equal to the average velocity of the aqueous phase. Using the definite solution condition of velocity continuity at the phase interface, integrating equations (9) and (10) in the opening direction and taking the average values respectively, the average flow velocities of the aqueous phase and the slurry phase can be obtained as: (12) (13) Considering that the hydraulic head (or pressure) in the slurry phase and the water phase is linearly distributed at any time in single-phase flow, the relationships between the hydraulic head in the water phase and the slurry phase varying linearly with the position of the phase interface are determined respectively, and we have: (14) (15) By combining equations (12) - (15) etc., the analytical solution of the slurry-water two-phase flow displacement model in a parallel plate can be obtained.

[0066] However, as mentioned in existing research, H ( x ( t )) is difficult to calculate directly and an explicit analytical solution cannot be obtained. The above equation does not directly give H ( x ( t )) and the relationship with time t , and the position of the phase interface at different times and the hydraulic head (or pressure) on the phase interface cannot be directly determined.

[0067] In view of this, in the analytical solution of the displacement of Newtonian fluid by Bingham fluid in a two-dimensional parallel plate, the position of the phase interface at different times and the hydraulic head on the phase interface are calculated as follows: Based on the assumption of continuous change of the hydraulic head on the phase interface, using the relationship between the pressure gradients of the slurry phase and the water phase at different times, the relationship between the hydraulic head on the phase interface and the position of the phase interface is solved; Using the derivative relationship between the position of the phase interface and the average flow velocity, the relationship between the position of the phase interface and time is obtained by separating variables and integrating.

[0068] Specifically, based on the assumption of continuous change of the hydraulic head on the phase interface in this embodiment, by first solving the relationship between the position of the phase interface and pressure and then solving the relationship between time and the intrusion length of the slurry phase, a direct numerical method is proposed to solve the analytical solution of the slurry-water two-phase flow in a parallel plate, that is, in the analytical solution of the displacement of Newtonian fluid by Bingham fluid in a two-dimensional parallel plate, the detailed process of the position of the phase interface at different times and the hydraulic head on the phase interface is described as follows: First, based on the assumption of continuous change of the hydraulic head on the phase interface, using the relationship between the pressure gradients of the slurry phase and the water phase at different times, the hydraulic head H ( x ( t )) and the position of the phase interface x ( t) relationship. The operation steps include: Given a series of slurry-phase pressure gradient values, where the minimum slurry-phase pressure gradient is for the slurry to displace all the aqueous phase, and the maximum slurry-phase pressure gradient can be given according to research needs. In this embodiment, as an example, it is taken as 50 times the minimum pressure gradient value (it should be understood that a larger value can be taken). Calculate the aqueous-phase pressure gradient array using the slurry-phase pressure gradient array. Calculate the phase interface position array and the phase interface water head array at the given slurry-phase pressure gradients respectively. Delete the points in the phase interface array where the intrusion length is less than 0 or greater than the maximum intrusion length to obtain a reasonable phase interface position x - Phase interface pressure P (or phase interface water head H ) relationship.

[0069] Secondly, using the derivative relationship between the phase interface position and the average flow velocity, the phase interface position is obtained by separating variables and integrating x ( t ) and time t relationship. Specifically, it includes: Consider the relationship between the average flow velocity and the phase interface position: (16) Since the only variable on the right side of the above equation is x ( t ), so the right side can be regarded as x ( t ) function, denoted as: (17) f ( x ( t )) describes the composite function f and the phase interface position x relationship.

[0070] Using Equation (17) and the aforementioned phase interface position x - Phase interface water head H relationship, the f ( x ( t )) - x ( t ) scatter plot can be calculated.

[0071] Separate variables for Equation (16) to obtain the relationship between the phase interface position and time as follows: (18) Integrate both sides of Equation (18) to obtain the relationship between the grouting displacement time and the corresponding phase interface position: (19) In the formula:T and X ( T ) are the integration upper limits of the time and the intrusion distance respectively.

[0072] Since f ( x ( t )) is not a continuous function and has no explicit expression form, in this embodiment, the trapezoidal integration formula is used to accumulate the integrand on the right side of formula (19) to obtain the relationship between time and the phase interface position.

[0073] Step S1022: Numerically simulate the slurry-water two-phase flow model in the two-dimensional parallel plate by using computer software to obtain the numerical simulation results.

[0074] Specifically, the settings of the numerical model for the displacement of Newtonian fluid by Bingham fluid in the two-dimensional parallel plate are as follows: COMSOL Multiphysics (version 5.6) is used to solve the numerical model. The phase field inlet and outlet boundary conditions are consistent with the flow field (as Figure 5 shown), and the two are separated by the initial interface. The slurry phase adopts the Bingham-Papanastasiou rheological model, and the water phase adopts the Newtonian constitutive model.

[0075] Since the process of slurry displacing water is a transient study, phase initialization needs to be carried out before starting the calculation. Since the phase field method is similar to a step function to describe the continuous change of the phase interface, in this embodiment, it is approximately considered that the position where the volume fraction of the slurry phase is equal to 0.5 is the phase interface position: (20) In the formula: pf.Vf1 represents the volume fraction of the slurry phase.

[0076] Among them, the parameters used in the numerical simulation and the analytical solution are shown in Table 1, and Table 1 is as follows: Table 1 Model parameters of the numerical model and the analytical solution

[0077] Step S1023: Compare the numerical simulation results with the analytical solution and the grouting displacement test results obtained in advance to verify the rationality of the slurry-water two-phase flow model.

[0078] The numerical simulation results are compared in detail with the analytical solution, including: comparing the pressure P (or the water head H ) and the phase interface position x ( t)The numerical solutions and analytical solutions of the relationship are in good agreement. Analyze the variation law of the phase interface position with time under different plastic viscosities of the slurry and the volume fraction distribution of the slurry-water two-phase in the parallel plate at different times in the numerical simulation results and the analytical solutions. The results show that under various conditions, the numerical solutions and analytical solutions are in good agreement, and it is reasonable to use the constructed slurry-water two-phase flow model to study the slurry diffusion mechanism during static water-saturated fracture grouting.

[0079] Furthermore, the numerical simulation results are compared with the grouting displacement test results carried out by Håkansson (1987), and the grouting test results and numerical simulation results at different time steps are analyzed. The results show that the slurry-water two-phase flow model proposed in this embodiment is reasonable.

[0080] Step S103: Based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, carry out the simulation of the two-phase flow of slurry displacing static water in the three-dimensional rough fracture to obtain the simulation results. Specifically, it includes: Step S1031: Based on the digital model of the Barton standard contour line, study the influence of roughness (parameters such as topography or aperture) on the grouting water displacement process by the method of controlling variables.

[0081] (1) The displacement characteristics of the slurry-water two-phase flow in the rough disk fracture under the condition of a constant grouting rate, and analyze the influence of fracture roughness, aperture, and grouting conditions on the slurry diffusion process.

[0082] Figure 8 It is a schematic diagram of the simulation of the two-phase flow of slurry displacement in the rough disk fracture. As Figure 8As shown, the grouting rate of the grouting hole is 0.05 m / s, the outlet pressure is 0, the fracture aperture is 2 mm, and the radius of the rough disc is 1 m. Simulations are carried out on discs with different roughnesses (controlling variables), and according to the simulation results, the volume fraction distributions of the grout phase and the water phase in each rough disc at different times are analyzed. The results show that at a constant grouting rate, the grout phase uniformly displaces the water phase in all directions, the volume fraction of the grout phase continuously increases, and the volume fraction of the water phase continuously decreases under the displacement effect. Analyzing the migration characteristics of the phase interface at different times, the simulation results show that at a constant grouting rate, the moving speed of the phase interface gradually slows down, and the radial displacement speed gradually decreases. In the current grouting process design, the fracture is generally simplified as a smooth parallel plate model. In this embodiment, the curve of the orifice pressure varying with time for discs with different roughnesses under the same fracture aperture and grouting speed is plotted and analyzed. The results show that under the condition of a constant grouting rate, the smooth parallel plate model underestimates the influence of roughness on the average orifice pressure. Considering that the shear rates of the grout phase and the water phase are affected by the distribution of the protrusions, in this embodiment, the distribution characteristics of the radial shear rate of the fluid in discs with different roughnesses at a grouting time of 100 s are also analyzed. The results show that roughness will cause an increase in the viscous energy consumption of the fluid, and the greater the kinetic energy required to overcome the viscous resistance of the fluid flow.

[0083] (2) Influence of fracture geometric characteristics and grouting pressure on the slurry diffusion process under constant grouting pressure.

[0084] Considering that in addition to constant-rate grouting, constant-pressure grouting is also often used in practical engineering. In this embodiment, based on the simulation results, taking JRC rough discs with = 14 - 16 as an example, the migration characteristics of the phase interface with grouting time under different grouting pressures are analyzed. The results show that under the condition of constant grouting pressure, the moving distance of the phase interface does not increase infinitely with time. At a relatively low grouting pressure, even if the grouting time is extended, the intrusion amount of the slurry in the rock fracture does not increase significantly with time. Further, plot JRC=14 - 16 shows the curves of the variation of the aqueous phase volume fraction with the grouting time in rough disks with different fracture apertures. Analyzing these curves, it can be seen that under constant grouting pressure and the same morphology conditions, as the fracture aperture increases, the rate of the slurry phase displacing the aqueous phase significantly accelerates. At the same moment, the larger the fracture aperture, the greater the moving distance of the phase interface and the higher the displacement efficiency. In addition, for fractures with low apertures, even if the grouting time is extended, the amount of water displaced by the slurry does not increase significantly. Therefore, in the actual grouting process design, it is necessary to pay attention to the aperture characteristics of the fractures, and increasing the grouting pressure is also a relatively effective means. Since the fracture morphology is also an important factor affecting the slurry water displacement efficiency, in this embodiment, the migration characteristics of the slurry-aqueous phase interface position with time in different rough disks under the conditions of the same fracture aperture and grouting pressure are also analyzed. The results show that the fracture morphology has an important impact on the slurry water displacement efficiency, but the grouting water displacement speed does not decrease with the increase of the fracture roughness. In order to study the influence of the distribution of rough protrusions in the fractures on grouting, a comparative simulation is carried out for two fracture disks with the same roughness but different positions of rough protrusions. Among them, in one case, the rough protrusions in the fracture are distributed near the grouting hole, and in the other case, the rough protrusions in the fracture are distributed near the outlet. The simulation results show that under the same grouting pressure and aperture conditions, the shear rate disturbance caused by the rough protrusions at the inlet is much greater than that caused by the rough protrusions near the outlet. Although the roughness is the same, the viscous energy dissipation caused by the fracture roughness in Case 1 is greater than that in Case 2. Therefore, the grouting water displacement efficiency in the fracture is related to the distribution of rough protrusions; the grouting water displacement efficiency does not decrease with the increase of the fracture roughness. The rough protrusions near the grouting hole have a greater impact on the grouting efficiency than the rough protrusions in the far field. In the engineering practice of fracture grouting, it is necessary to reasonably design the position of the grouting hole according to the distribution of rough protrusions.

[0085] The above is the process of simulating the two-phase flow of slurry displacing static water in three-dimensional rough fractures using the standard rough contour line. Conducting the simulation through the rough disks generated by the standard contour line is conducive to accurately analyzing the influence of fracture geometric characteristics and grouting parameters on the slurry water displacement process under radiation flow conditions, and further helps to reveal the slurry displacement of static water mechanism from various influencing factor levels, and provides a basis for subsequent research on the slurry displacement of static water mechanism under the complex conditions of real three-dimensional rough fractures.

[0086] Step S1032: Carry out the simulation of the two-phase flow of slurry displacing static water in three-dimensional rough fractures using the digital model obtained by the three-dimensional laser scanning technology.

[0087] Most of the current non-hydrodynamic grouting design methods ignore the role of the water phase and regard grouting as a single-phase flow process of the slurry. In fact, many cracks in the dam foundation are filled with static water. During grouting, the slurry continuously drives the water, and a two-phase flow method is needed to more realistically reflect the slurry diffusion process. To what extent the traditional single-phase flow model overestimates or underestimates the slurry intrusion efficiency, and under what conditions it is applicable to describe the slurry water drive process in rough cracks is an important scientific issue. At present, existing research has rarely considered this point. In this embodiment, a numerical simulation of the displacement characteristics of the slurry-water two-phase flow in a three-dimensional real rough crack is carried out to explore the differences in the slurry intrusion efficiency between the single-phase flow method and the two-phase flow method for rough crack grouting, so as to find out under what conditions the two-phase flow method can be approximately replaced by the single-phase flow method. Based on the digital model obtained by three-dimensional laser scanning, by studying the slurry diffusion mechanism under different conditions, the action mechanism of factors such as crack roughness, anisotropy, and surface tension on the slurry diffusion behavior is revealed, providing scientific guidance for grouting design under different conditions.

[0088] Specifically, the slurry flow process can be divided into parallel flow and radial flow. In this embodiment, the slurry-water displacement characteristics in the crack under these two conditions are explored respectively. The numerical simulation processes under these two flow conditions are introduced below.

[0089] Step S1032a: Under the condition of parallel flow, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough crack, analyze the change of the advancing speed, shape and displacement ratio of the slurry front front in the three-dimensional rough crack with time through numerical simulation.

[0090] First, analyze the process of the slurry phase parallelly displacing the water phase in a typical three-dimensional rough crack. The results show that in an ideal parallel plate crack, the front front of the slurry phase usually advances uniformly forward. For a three-dimensional rough crack, due to the influence of topography, contact part and surface tension, the advancing speeds of each point on the front front of the slurry phase are inconsistent. During grouting, the opening at the edge of the contact area is small, and the fluid is affected by the surface tension near the contact area, pulling or dragging the phase interface towards the contact area.

[0091] Secondly, analyze the characteristics of the slurry phase front under different surface tension coefficients t = 100 s under the same displacement conditions and displacement time σ . The results show that the surface tension affects the advancing position of the front front of the slurry phase, and the position and shape of the front front of the slurry phase change with σ change, showing a certain degree of uncertainty.

[0092] In this embodiment, in order to quantitatively describe the slurry water drive efficiency, the displacement ratio I = I ( t ) is defined as follows: (21) In the formula: vf 1 ( t ) is t the slurry phase volume at a certain moment, V is the total volume of the fracture space, I ( t ) represents t the volume fraction of the slurry injected at a certain moment in the total fracture space.

[0093] According to the simulation results, the displacement ratio is calculated according to formula (21), and the curves of the displacement ratio σ under different surface tension coefficients I changing with the grouting time are plotted, as shown in Figure 9 . Analyzing this curve, it can be seen that in the initial stage of grouting (0 - 30 s), the surface tension coefficient σ mainly affects the shape of the front front of the slurry phase, and has little effect on the displacement ratio I ; as the grouting time increases, the surface tension coefficient σ affects both the shape of the front front of the slurry phase and the displacement ratio at the same time; σ the larger it is, the larger the displacement ratio is.

[0094] Step S1032b: Under parallel flow conditions, based on the slurry - water two - phase flow model and the digital model of the three - dimensional rough fracture, conduct a numerical simulation orthogonal test on the three - dimensional rough fracture, and analyze the influence of different grouting material properties on the displacement efficiency of the slurry - water two - phase flow model and the traditional single - phase flow model.

[0095] It should be noted that during fracture grouting, grouting materials with different physical and chemical properties are often used according to engineering needs. These materials include cement - based materials, polyurethane, epoxy resin, etc. Among them, cement - based materials are suitable for injecting fractures larger than cement particles, while polyurethane and epoxy resin are suitable for strengthening fractures that are difficult for cement - based materials to inject. In terms of physical properties, cement - based materials are typical Bingham fluids; while polyurethane and epoxy resin are Newtonian fluids with a yield stress of 0, and these materials are usually also called chemical grouting materials. Based on the previous description, the dam fracture grouting in actual engineering is a two - phase flow process, while current research mostly regards it as a single - phase flow process. In order to explore the difference in grouting displacement efficiency under two design methods (single - phase flow, grouting design method guided by two - phase flow), in this embodiment, a numerical simulation orthogonal test is carried out, and the influence of fracture geometric characteristics and grouting material properties on the displacement ratios of single - phase flow and two - phase flow is analyzed.

[0096] Specifically, the yield stress of the slurry-phase material is taken as 0 Pa, 0.5 Pa, and 3 Pa, representing Newtonian fluid (some chemical grouting materials), low-yield-stress Bingham fluid, and Bingham fluid, respectively; the plastic viscosity of the slurry-phase material is taken as 0.0025 Pa·s, 0.025 Pa·s, and 0.25 Pa·s, representing materials with a viscosity slightly greater than that of water (the viscosity of water is 0.001 Pa·s), materials with a viscosity close to that of ordinary cement slurry, and high-viscosity materials, respectively. A total of 9 working conditions are obtained through pairwise combination. When the plastic viscosity of the water phase in the two-phase flow is set to a minimum value, the two-phase flow method can be regarded as a single-phase flow method. In this embodiment, the plastic viscosity is set to 10 -5 Pa·s to simulate the single-phase flow method. The displacement states of the slurry-water two-phase in the fracture under different yield stress conditions with low plastic viscosity ( μ g = 0.0025 Pa·s) at the 3rd second are simulated respectively. The results show that when the yield stress τ 0 = 0 Pa, the displacement volume of the single-phase flow method is significantly greater than that of the two-phase flow method; when the yield stress increases, the advancing distances of the slurry phase of the single-phase flow method and the two-phase flow method gradually approach. Therefore, the smaller the yield stress of the slurry phase, the greater the displacement difference between the single-phase flow method and the two-phase flow method.

[0097] Figure 10 Curves of the grouting displacement ratio of the slurry-phase material with different yield stresses under low plastic viscosity and high plastic viscosity changing with time are shown. Among them, (a) is for low plastic viscosity ( μ g = 0.0025 Pa·s), and (b) is for high plastic viscosity ( μ g = 0.25 Pa·s). It can be seen from Figure 10 part (a) that the lower the yield stress, the greater the displacement ratio difference between the single-phase flow method and the two-phase flow method. As the displacement time increases, the fracture space is gradually filled with the injected slurry, and the slurry phase bears the main pressure drop, and the displacement ratios of the single-phase flow method and the two-phase flow method gradually become the same. Therefore, when the slurry far from fills the fracture space, the single-phase flow method overestimates the grouting efficiency, which is more obvious for slurries without yield stress (or low yield stress) such as polyurethane and epoxy resin grouting materials. As the yield stress increases, the displacement ratio difference between the single-phase flow method and the two-phase flow method gradually decreases. Comparing Figure 10 part (a) with part (b) in τ 0 the case of = 0 Pa, it can be found that the greater the plastic viscosity of the slurry, the smaller the displacement ratio difference between the single-phase flow method and the two-phase flow method. Therefore, under the condition of high plastic viscosity, the displacement ratio difference between the single-phase flow method and the two-phase flow method further decreases with the increase of the yield stress. At this time, it is reasonable to simplify the slurry-water displacement two-phase flow process in the water-saturated fracture into a single-phase flow process of the slurry.

[0098] Furthermore, draw and analyze the curve of the slurry displacement ratio varying with time under different yield stress conditions. The analysis results show that when injecting high-yield stress cement slurry into water-saturated fractures, it is reasonable to simplify the displacement process of the slurry-water two-phase flow into a single-phase slurry flow process.

[0099] Step S1032c analyzes the roughness parameters in different directions in a three-dimensional rough fracture based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture under the conditions of roughness anisotropy and radiation conditions. R and the influence of the fracture morphology on the slurry diffusion direction.

[0100] It should be noted that for the standard rough contour disk model with equal aperture, since the characteristics of the disk model are the same in each direction, the orientation of slurry diffusion cannot be analyzed. Therefore, in order to further analyze the influence of the fracture morphology on the slurry diffusion direction, this embodiment uses three-dimensional laser technology to obtain three-dimensional rough fractures with equal aperture and conducts numerical simulations.

[0101] Select two rough surface fractures with relatively small anisotropy and obvious anisotropy, respectively simulate and output the characteristics of slurry diffusion with time in the three-dimensional rough fracture with equal aperture, and analyze the influence of the three-dimensional morphology on the slurry diffusion direction without considering gravity. From the perspective of the shape of the slurry front, for the fracture with relatively small anisotropy, the slurry front is still approximately circular at the initial stage of diffusion; as the diffusion time increases, the slurry front is approximately elliptical. For the fracture with significant anisotropy of fracture roughness, the slurry front is approximately elliptical at all stages of slurry diffusion; the direction where the slurry diffuses farther (major axis) is approximately the same as the direction with smaller roughness (minor axis). The analysis results show that for fractures with either small or significant anisotropy, the slurry tends to preferentially diffuse along the direction with smaller roughness under the condition of equal aperture.

[0102] Step S1032d analyzes the influence of the fracture morphology, contact area, and surface tension on the slurry diffusion in a three-dimensional rough fracture based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture under the radiation flow condition, and compares the displacement efficiency difference between the slurry-water two-phase flow model and the traditional single-phase flow model.

[0103] Under the condition of radial flow, the upper and lower walls of the fracture are obtained by three-dimensional laser scanning. The fracture size is 80mm×80mm, and the average aperture is about 2mm. During the simulation, the grouting hole is located in the middle of the model, and the slurry is injected at a constant pressure. Initially, the fracture is filled with water, and the flow of water in the initial state is not considered. Due to the displacement effect of the slurry, the water is discharged from the four-side outlets, and the outlets are constant-pressure boundaries. The pressure difference between the inlet and the outlet is set to 150Pa, and the rest is an impermeable boundary. In addition, to be closer to the actual project, some contact areas (aperture is 0) are also set. When meshing, tetrahedral elements are still used, and the minimum element size is about 0.6mm. After meshing, about 75,000 domain elements are obtained.

[0104] The simulation results show that in the process of slurry-water displacement two-phase flow under the condition of radial flow, the plastic viscosity of the slurry phase is 0.0025Pa·s, and the yield stress is 0.5Pa. The front front of the slurry phase gradually spreads from the grouting hole to the surrounding. The injection volume of the slurry in the fracture gradually increases with time. The slurry diffusion process is affected by the fracture morphology and surface tension, and the advancing speeds of each point on the front are inconsistent. The grouting time t =500s, the slurry phase flows to the water outlet and overflows the fracture space. Therefore, in the subsequent long time, the increase in the slurry in the fracture space is small, and it continuously overflows from the upper right outlet.

[0105] Similarly, in order to compare the differences in the grouting displacement efficiency calculated by the single-phase flow method and the two-phase flow method in a water-saturated fracture under the condition of radial flow, a numerical simulation orthogonal experiment was also carried out to study the influence of the properties of the grouting material on the displacement ratios of the single-phase flow and the two-phase flow. The results show that as the yield stress increases, the difference in the slurry injection volume between the single-phase flow method and the two-phase flow method gradually decreases.

[0106] The displacement ratio defined in the foregoing embodiment is still used I To describe the water displacement efficiency of fracture grouting, the curves of the displacement ratio varying with time during the water displacement of the slurry with different yield stresses under the conditions of low plastic viscosity and high plastic viscosity are respectively plotted and compared, as Figure 11 shown, where (a) is the low plastic viscosity ( μ g =0.0025Pa·s), (b) is the high plastic viscosity ( μ g= 0.25 Pa·s). Analyzing this curve shows that under low plastic viscosity conditions, when the yield stress is 0 Pa, the grout injected into the water-saturated fracture is a Newtonian fluid. The displacement ratios of the single-phase flow method and the two-phase flow method differ significantly, and at the same moment, the displacement ratio of the single-phase flow method is always greater than that of the two-phase flow method. As the displacement time increases, there is more grout in the fracture space, and the grout phase gradually bears the main pressure drop. The difference in the displacement ratios of the single-phase flow method and the two-phase flow method gradually decreases. When the yield stress gradually increases, the difference between the single-phase flow method and the two-phase flow method gradually decreases. Under high plastic viscosity conditions, when the grouting material is a Newtonian fluid ( τ 0 = 0 Pa), at the same moment, the displacement ratio of the single-phase flow method is slightly greater than that of the two-phase flow method, but the difference between the two is significantly smaller than that in the case of low plastic viscosity ( Figure 11 in (a) of τ 0 = 0 Pa). When the yield stress increases, the difference between the single-phase flow method and the two-phase flow method at the same moment also gradually decreases.

[0107] Furthermore, a curve showing the variation of the difference in the displacement ratios of the single-phase flow method and the two-phase flow method with time when grouts with different yield stresses and plastic viscosities are injected into water-saturated fractures under radiation flow conditions is plotted. The results show that under different yield stress and plastic viscosity conditions, the difference in the displacement ratios of the single-phase flow method and the two-phase flow method is always greater than 0. Therefore, the single-phase flow grouting design method overestimates the water displacement efficiency of the grout in the fracture.

[0108] In this embodiment, by analyzing the displacement characteristics of the grout-water two-phase flow in three-dimensional rough fractures under parallel flow and radiation flow conditions, and by comparing and analyzing the differences in the grout intrusion efficiencies of the two-phase flow design method and the single-phase flow design method during water-saturated fracture grouting. Under both conditions, the lower the yield stress of the grout, the greater the difference in the displacement ratios of the single-phase flow method and the two-phase flow method. As the yield stress increases, since the grout phase bears the main pressure drop within a shorter displacement time, the difference in the displacement ratios of the single-phase flow method and the two-phase flow method gradually decreases. The plastic viscosity shows a similar pattern. The greater the plastic viscosity, the smaller the difference in the displacement ratios of the single-phase flow method and the two-phase flow method. Therefore, when injecting grouts with high yield stress and high plastic viscosity into water-saturated fractures, it is reasonable to simplify the grout-water displacement two-phase flow process to a single-phase flow process of the grout. When using chemical grouting materials with low plastic viscosity (typical grouting materials include Newtonian fluids such as polyurethane and epoxy resin), the difference in the displacement ratios of the single-phase flow method and the two-phase flow method is large, and at this time, it is necessary to estimate the grout intrusion characteristics according to the two-phase flow method. Through the above mechanism explanation, it provides more reasonable guidance for the design of grouting for the fractures in the dam foundation filled with saturated static water.

[0109] Based on the same inventive concept, this embodiment also provides a numerical simulation system for three-dimensional rough fracture slurry-water displacement two-phase flow, which is applied to the analysis of slurry diffusion characteristics during static water-saturated fracture grouting, and includes: A rough fracture construction unit for reconstructing the three-dimensional morphology structure of the fracture by using three-dimensional laser scanning technology to obtain a three-dimensional rough fracture model; A model establishment unit for establishing a slurry-water two-phase flow model; A simulation analysis unit for carrying out the simulation of slurry displacement of static water two-phase flow in the three-dimensional rough fracture based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture to obtain simulation results; Among them, the slurry-water two-phase flow model includes: a control equation and a constitutive model of slurry-water displacement two-phase flow. The control equation includes: a continuity equation for fluid flow in the fracture, a momentum conservation equation for fluid flow in the fracture, and a phase field equation for describing the movement of the phase interface; the constitutive model of slurry-water displacement two-phase flow includes: a Bingham-Papanastasiou constitutive model for describing the flow characteristics of the slurry, and a Newtonian model for describing the flow characteristics of the water phase.

[0110] The numerical simulation system for three-dimensional rough fracture slurry-water displacement two-phase flow provided in this embodiment can implement the processes and steps of the numerical simulation method for three-dimensional rough fracture slurry-water displacement two-phase flow provided in any of the above embodiments and achieve the same technical effects, which will not be elaborated here one by one.

[0111] The above are only the preferred embodiments of the present application and are not used to limit the present application. For those skilled in the art, the present application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method, characterized in that: The method is applied to the analysis of grout diffusion characteristics during static saturated fracture grouting, including: The three-dimensional morphology of the crack is reconstructed using standard rough contour lines and three-dimensional laser scanning technology to obtain a digital model of the three-dimensional rough crack. In the grouting process, slurry and water are regarded as two phases, and a slurry-water two-phase flow model is established; Based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, the simulation of slurry displacement of still water two-phase flow in three-dimensional rough fractures was carried out and the simulation results were obtained; The slurry-water two-phase flow model includes: a control equation and a slurry-water displacement two-phase flow constitutive model. The control equation includes: a continuity equation for fluid flow in fractures, a momentum conservation equation for fluid flow in fractures, and a phase field equation for describing the movement of phase interfaces. The slurry-water displacement two-phase flow constitutive model includes: a Bingham-Papanastasiou constitutive model for describing the flow characteristics of slurry, and a Newtonian fluid Newtonian model for describing the flow characteristics of water phase.

2. The method according to claim 1, characterized in that The phase field equation describing the movement of the phase interface is specifically: Phase field variables are used to represent the volume fractions of the slurry-water phases, and the phase interface is captured by the Cahn-Hilliard equation.

3. The method according to claim 1, characterized in that: Also includes: The slurry-water two-phase flow model is verified as follows: Based on the slurry-water two-phase flow model, the analytical solution of the Bingham fluid displacing the Newtonian fluid in the two-dimensional parallel plate is solved; The computer software is used to perform numerical simulation on the slurry-water two-phase flow model in the two-dimensional parallel plate to obtain numerical simulation results; The numerical simulation results are compared with the analytical solution and the pre-acquired grouting displacement test results to verify the rationality of the slurry-water two-phase flow model.

4. The method according to claim 3, characterized in that The analytical solution of the Bingham fluid displacing the Newtonian fluid in a two-dimensional parallel plate is obtained as follows: The slurry-water phases are regarded as single-phase flows, and the single-phase Newtonian fluid velocity and single-phase Bingham fluid velocity are determined respectively; Using the velocity continuity condition on the phase interface, the single-phase Newtonian fluid flow rate and the single-phase Bingham fluid flow rate are integrated in the direction of the opening and averaged to obtain the average flow rate of the water phase and the slurry phase. Considering that the hydraulic head in the water phase and the slurry phase are linearly distributed at any time in the single-phase flow, the relationship between the linear change of the hydraulic head in the water phase and the slurry phase and the position of the phase interface is determined respectively; The average flow rates of the water phase and the slurry phase, and the relationship between the linear change of the water head in the water phase and the slurry phase with the position of the phase interface are solved simultaneously to obtain an analytical solution for the Bingham fluid displacing the Newtonian fluid in a two-dimensional parallel plate.

5. The method according to claim 4, characterized in that In the analytical solution of the displacement of Newtonian fluid by Bingham fluid in two-dimensional parallel plates, the position of the phase interface at different times and the hydraulic head on the phase interface are calculated as follows: Based on the assumption that the hydraulic head on the phase interface changes continuously, the relationship between the hydraulic head on the phase interface and the position of the phase interface is solved by using the relationship between the slurry phase pressure gradient and the water phase pressure gradient at different times. The relationship between the phase interface position and the time is obtained by integrating the separated variables using the derivative relationship between the phase interface position and the average flow velocity.

6. The method according to claim 1, characterized in that Based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, the simulation of slurry displacement of still water two-phase flow in three-dimensional rough fractures was carried out, and the simulation results were obtained, including: Under parallel flow conditions, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, the advancement speed, shape change and displacement ratio of the slurry front in the three-dimensional rough fracture are analyzed through numerical simulation; Under parallel flow conditions, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fractures, numerical simulation orthogonal experiments were carried out on the three-dimensional rough fractures to analyze the effects of different grouting material properties on the displacement efficiency of the slurry-water two-phase flow model and the traditional single-phase flow model.

7. The method according to claim 1, characterized in that Based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, the simulation of slurry displacement of still water two-phase flow in three-dimensional rough fractures was carried out, and the simulation results were obtained, including: Under the conditions of roughness anisotropy and radiation, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, the roughness parameters in different directions in the three-dimensional rough fracture are analyzed by numerical simulation. R and the influence of crack morphology on the slurry diffusion direction; Under the condition of radiation flow, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fractures, the influence of fracture morphology, contact area and surface tension in the three-dimensional rough fractures on the slurry diffusion is analyzed through numerical simulation, and the difference in displacement efficiency between the slurry-water two-phase flow model and the traditional single-phase flow model is compared.

8. A three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation system, characterized in that: The system is applied to the analysis of grout diffusion characteristics during static saturated fracture grouting, including: A rough crack construction unit is used to reconstruct the three-dimensional morphology structure of the crack using three-dimensional laser scanning technology to obtain a three-dimensional rough crack model; A model building unit, used to build a slurry-water two-phase flow model; A simulation analysis unit is used to carry out a simulation of slurry displacement of still water two-phase flow in three-dimensional rough fractures based on a slurry-water two-phase flow model and a digital model of three-dimensional rough fractures to obtain simulation results; The slurry-water two-phase flow model includes: a control equation and a slurry-water displacement two-phase flow constitutive model. The control equation includes: a continuity equation for fluid flow in fractures, a momentum conservation equation for fluid flow in fractures, and a phase field equation for describing the movement of phase interfaces. The slurry-water displacement two-phase flow constitutive model includes: a Bingham-Papanastasiou constitutive model for describing the flow characteristics of slurry, and a Newtonian fluid Newtonian model for describing the flow characteristics of water phase.

9. An electronic device, characterized in that: include: a memory for storing instructions executed by one or more processors of the electronic device; The processor, when the processor executes the instructions in the memory, can enable the electronic device to implement the steps of any one of the methods described in claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores instructions, which implement the steps of the method according to any one of claims 1 to 7 when executed on a computer.

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