Numerical simulation method and system for slurry-water displacement two-phase flow in three-dimensional rough fractures

Abstract

The present application provides a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method and system, which belongs to the field of computer-aided design technology. The method is applied to the analysis of slurry diffusion characteristics during static saturated fracture grouting, including: reconstructing the three-dimensional morphological structure of the fracture using standard rough contour lines and three-dimensional laser scanning technology respectively to obtain a digital model of the 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, carrying out a static water two-phase flow simulation of slurry displacement in the three-dimensional rough fracture; wherein, the slurry-water two-phase flow model includes: control equations and a slurry-water displacement two-phase flow constitutive model, and 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 use of the two-phase flow method to analyze the static saturated fracture grouting process can improve the rationality of the dam foundation fracture grouting design.

Description

Technical Field

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

[0002] Grouting is a key method for improving the shear-slip stability and anti-seepage performance of dams. It displaces water from the fissures and solidifies the grout, thereby strengthening the bonding strength between the fissures. Generally speaking, grouting process design requires comprehensive consideration of geological conditions (such as the development of joints and fissures in the dam foundation), and trial grouting should be conducted before dam construction. Proper grouting process design is crucial for improving grouting efficiency.

[0003] Existing research on dam foundation fissure grouting often considers fissure grouting as a single-phase flow process, ignoring the presence of initial static water in the dam foundation fissures. This provides no accurate guidance for dam foundation fissure grouting engineering practices. Therefore, it is necessary to provide an improved technical solution to address the shortcomings of the above existing technologies. Summary of the Invention

[0004] The purpose of this 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] In order to achieve the above objectives, this application provides the following technical solutions:

[0006] 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 saturated fracture grouting, and includes:

[0007] The three-dimensional morphology of the cracks was reconstructed using standard rough contour lines and three-dimensional laser scanning technology to obtain a digital model of the three-dimensional rough cracks.

[0008] During the grouting process, slurry and water are considered as two phases, and a slurry-water two-phase flow model is established;

[0009] Based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, a simulation of slurry displacement of still water two-phase flow in three-dimensional rough fractures is carried out to obtain simulation results;

[0010] 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 model for describing the flow characteristics of the water phase.

[0011] Optionally, the phase field equation for describing the movement of the phase interface is specifically:

[0012] 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.

[0013] Optionally, the method further includes: verifying the slurry-water two-phase flow model, specifically as follows:

[0014] Based on the slurry-water two-phase flow model, the analytical solution of the Newtonian fluid displaced by the Bingham fluid in the two-dimensional parallel plate is obtained;

[0015] 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;

[0016] The numerical simulation results were 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.

[0017] Alternatively, the analytical solution for a Bingham fluid displacing a Newtonian fluid in a two-dimensional parallel plate is obtained as follows:

[0018] 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;

[0019] Using the velocity continuity condition on the phase interface, the flow rates of the single-phase Newtonian fluid and the single-phase Bingham fluid are integrated in the direction of the opening and averaged to obtain the average flow rates of the water phase and the slurry phase respectively.

[0020] Considering that the hydraulic head in the water phase and the slurry phase are linearly distributed at any time in 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;

[0021] 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.

[0022] Alternatively, in the analytical solution of a Bingham fluid displacing a Newtonian 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:

[0023] Based on the assumption that the hydraulic head on the interface changes continuously, the relationship between the hydraulic head on the interface and the interface position is solved by using the relationship between the slurry phase pressure gradient and the water phase pressure gradient at different times.

[0024] The relationship between the phase interface position and time is obtained by integrating the separated variables using the derivative relationship between the phase interface position and the average flow velocity.

[0025] Optionally, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, a slurry displacement static water two-phase flow simulation in the three-dimensional rough fracture is performed to obtain simulation results, including:

[0026] Under parallel flow conditions, based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, numerical simulations were conducted to analyze the temporal changes in the slurry front's advancement velocity, shape change, and displacement ratio in the three-dimensional rough fractures.

[0027] Under parallel flow conditions, based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, numerical simulation orthogonal experiments were carried out on 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.

[0028] Optionally, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, a slurry displacement static water two-phase flow simulation in the three-dimensional rough fracture is performed to obtain simulation results, including:

[0029] Under the conditions of roughness anisotropy and radiation, based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, the roughness parameters in different directions in the three-dimensional rough fractures are analyzed through numerical simulation. R and the influence of crack morphology on the slurry diffusion direction;

[0030] Under radial flow conditions, based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, the effects of fracture morphology, contact area and surface tension in three-dimensional rough fractures on slurry diffusion were 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 was compared.

[0031] In a second aspect, this embodiment provides a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation system, which is applied to the analysis of slurry diffusion characteristics during static saturated fracture grouting, and includes:

[0032] A rough crack construction unit is used to reconstruct the three-dimensional morphology of the crack using three-dimensional laser scanning technology to obtain a three-dimensional rough crack model;

[0033] Model building unit, used to build slurry-water two-phase flow model;

[0034] A simulation analysis unit is used to perform a slurry displacement still water two-phase flow simulation 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 a simulation result;

[0035] 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 model for describing the flow characteristics of the water phase.

[0036] In a third aspect, this embodiment provides an electronic device, comprising: a memory for storing instructions executed by one or more processors of the electronic device; a processor, which, when the processor executes the instructions in the memory, enables 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.

[0037] In a fourth aspect, this embodiment provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores instructions that, when executed on a computer, 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.

[0038] The technical solution of the embodiment of the present application has the following beneficial effects:

[0039] The technical solution of this embodiment is based on the research background of the reinforcement of saturated hydrostatic fissures in dam foundations. Considering the grouting and water displacement process in real three-dimensional rough fissures, three-dimensional laser scanning technology is used to reconstruct the three-dimensional morphology of the fissures, and a digital model of the three-dimensional rough fissures is obtained to construct a real three-dimensional rough fissure space. The phase field equation (phase field method) is used to capture the movement process of the phase interface. The Bingham-Papanastasiou constitutive model is used to describe the slurry flow characteristics, and the Newtonian fluid model is used to describe the water phase flow characteristics. A slurry-water two-phase flow model is constructed, and a static water two-phase flow simulation of slurry displacement in three-dimensional rough fissures is carried out. This improves the accuracy and rationality of the slurry diffusion characteristic analysis during the grouting process of statically saturated hydrostatic fissures, which is beneficial to provide reasonable guidance for the grouting process design in engineering practice and improves the grouting efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a schematic structural diagram of an electronic device provided according to some embodiments of the present application.

[0041] Figure 2 Schematic diagram of the flow chart of the numerical simulation method for slurry-water displacement two-phase flow in three-dimensional rough fractures.

[0042] Figure 3 Schematic diagram of the digitization process of Barton standard contour line.

[0043] Figure 4 Schematic diagram of a rough disk generated using Barton's standard contour line, where (a) indicates the number JRC = = 2~4 standard contour line generated rough disk; (b) is the number of JRC = 6~8 standard contour line to generate the rough disk, (c) indicates the number JRC = 10~12 standard contour line to generate a rough disk, (d) indicates the number JRC = =14~16 standard contour line to generate a rough disk.

[0044] Figure 5 Schematic diagram of the two-phase flow simulation of Bingham fluid (cement slurry) displacing Newtonian fluid (water) in two-dimensional parallel plates.

[0045] Figure 6 Schematic diagram of the flow velocity distribution of Bingham fluid (slurry) and Newtonian fluid (water) in parallel plates.

[0046] Figure 7 Schematic diagram of using trapezoidal integral accumulation to solve the relationship between time and phase interface position.

[0047] Figure 8Schematic diagram of the simulation of slurry-water displacement two-phase flow in rough disk fractures.

[0048] Figure 9 For different tension coefficients σ Lower displacement ratio I Schematic diagram of the curve of change with time during grouting.

[0049] Figure 10 Schematic diagram of the grouting displacement ratio of different yield stress slurry materials with low plastic viscosity and high plastic viscosity over time, where (a) represents μ g = 0.0025Pa·s, (b) represents μ g =0.25Pa·s.

[0050] Figure 11 Schematic diagram comparing the displacement ratios of the two-phase flow method and the single-phase flow method under low plastic viscosity and high plastic viscosity conditions, where (a) represents μ g = 0.0025Pa·s, (b) shows the comparison results. μ g =0.25Pa·s. DETAILED DESCRIPTION

[0051] In order to better understand the technical solution of this application, the relevant terms involved in this application are explained below.

[0052] (1) Grouting / injection

[0053] Some literatures often use the terms "grouting" and "grouting". The technical description of this embodiment does not distinguish between the two terms and both refer to "grouting". However, the term "grouting" commonly used in engineering is used to describe the problem in the text.

[0054] Grouting, a common technique for blocking and reinforcing fractured rock, is essential for addressing dam leakage and shear slip. Grouting effectively reduces the water content in fractures and blocks the permeation pathways for fracture water. Furthermore, the intrusion and solidification of the grout further strengthens the bonding between fractures, thereby improving the integrity and mechanical properties of the fractured rock mass at the dam foundation.

[0055] Currently, a significant portion of the budget for dam reinforcement and dam repair at hazardous reservoirs is allocated to dam foundation grouting. Grouting can improve the strength and sealing of the dam foundation, reducing the probability of dam failure under adverse conditions (earthquakes, heavy rains). However, the dam grouting process is concealed, and its efficiency is highly uncertain. Generally speaking, grouting process design requires comprehensive consideration of geological conditions (such as the development of joints and fissures in the dam foundation), and trial grouting must be conducted prior to dam construction.

[0056] Existing research on fracture grouting (excluding porous media grouting based on homogenization theory) mainly analyzes the slurry diffusion process from two aspects. First, it assumes that the slurry diffuses in the fracture cavity, that is, the fracture grouting is regarded as a single-phase flow process; under ideal conditions, fracture grouting is simplified to a single-phase flow process of Newtonian fluid (chemical grouting) or Bingham fluid (cement-based grouting) between non-deformable parallel plates. Second, with the dynamic water disasters common in underground projects such as tunnels as the background, a two-phase flow method is used to study the influence of dynamic water on the slurry diffusion process. Existing non-dynamic water grouting research often ignores the existence of initial static water in the fracture and regards fracture grouting as a single-phase Bingham fluid movement process. In the fractures of the dam foundation, there is often nearly static fracture water. However, the inventors found that during fracture grouting, the water phase has a blocking effect on the slurry diffusion process, and the slurry needs to be continuously displaced before it invades the fracture. Therefore, it is of great significance to use a two-phase flow method to analyze the static water grouting process.

[0057] (2) Dynamic water grouting

[0058] In the technical description of this embodiment, dynamic water grouting is a technical term. The research background of dynamic water grouting is adverse geological disasters in tunnel engineering (such as sudden water and mud inrush), and the main focus is on the sealing effect, slurry diffusion and residual morphology. The core issue is whether water drives or affects the flow of slurry.

[0059] It should be noted that while dynamic water grouting and the hydrostatic grouting discussed in this application are both two-phase flow problems, their research objectives and characteristics differ. In this application, the hydrostatic grouting problem is the reinforcement of saturated hydrostatic fissures in dam foundations, focusing on the grouting intrusion length and water displacement effectiveness. The core issue is how the slurry drives the hydrostatic water out of the fissures. While both are two-phase flow problems, they represent different scientific issues.

[0060] In actual engineering, dam foundation fissures exhibit significant three-dimensional morphology, and the slurry diffusion process is affected by factors such as roughness and contact. However, existing research has rarely considered the grouting and water displacement process in real three-dimensional rough fissures. Furthermore, while some studies have constructed slurry-water two-phase flow models in soluble dolomite, these models focus on porous media or porous formations and are not applicable to studying slurry-phase water displacement processes in fractured media (dam foundation fissures). In other words, the mechanism of slurry displacement of static water in fractured media (dam foundation fissures) under real engineering conditions is currently unclear, leading to certain deviations in fracture grouting design under complex conditions.

[0061] In view of this, the present application provides a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method and system. By obtaining a three-dimensional rough surface and constructing a fracture space, a slurry-water displacement two-phase flow model in rough fractures is established, and then a slurry displacement static water two-phase flow simulation in three-dimensional rough fractures is carried out to accurately analyze the slurry phase water displacement mechanism in real three-dimensional rough fracture media (dam foundation fractures), and provide more reasonable guidance for fracture grouting design under complex conditions.

[0062] The embodiments of the present application are described below with reference to the accompanying drawings.

[0063] The embodiments of the present application can be applied to Figure 1 Among the electronic devices shown, the electronic device can be, but is not limited to, mobile terminals such as mobile phones, tablet computers, handheld computers, personal digital assistants (PDAs), smart home devices such as smart TVs and smart cameras, wearable devices such as smart bracelets, smart watches, and smart glasses, or other computer devices such as desktops, laptops, notebook computers, ultra-mobile personal computers (UMPCs), netbooks, and smart screens.

[0064] like Figure 1 As shown, 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. The memory 203 may be connected to the processor 201 via 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, and the like.

[0065] The processor 201 may include one or more processing cores. The processor 201 may utilize various interfaces and lines to connect various components within the entire electronic device 200. By running or executing instructions, programs, code sets, or instruction sets stored in the memory 203, and calling data stored in the memory 203, the processor 201 performs various functions of the electronic device 200 and processes data. For example, 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). Among them, the CPU mainly processes the operating system, user interface, and application programs; the GPU is responsible for rendering and drawing the content to be displayed; the NPU is used to implement artificial intelligence (AI) functions; and the modem is used to handle wireless communications. Different processing units can be independent devices or integrated into one or more processors. For example, the multiple processing units shown above are all integrated into a SoC, or the AP is a separate semiconductor chip and the other processing units are integrated into a SoC. This application is not limited to this.

[0066] The memory 203 may include random access memory (RAM), read-only memory (ROM), or non-transitory computer-readable storage medium. The memory 203 may be used to store instructions, programs, codes, code sets, or instruction sets. The memory 203 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system and instructions for at least one function, such as a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method; the data storage area may store data created based on the use of the electronic device 200, such as input data for numerical solutions.

[0067] In addition, those skilled in the art will appreciate that the structure of the electronic device 200 shown in the above figures does not limit the electronic device 200. The electronic device may include more or fewer components than shown, or may combine certain components, or arrange the components differently. For example, the electronic device 200 may also include a microphone, a speaker, a radio frequency circuit, a sensor, an audio circuit, a power supply, a Bluetooth module, and other components, which will not be described in detail here.

[0068] This embodiment 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 saturated fracture grouting. Figure 2 As shown, the method includes:

[0069] Step S101: reconstructing the three-dimensional morphology of the crack using standard rough contour lines and three-dimensional laser scanning technology to obtain a digital model of the three-dimensional rough crack.

[0070] In this embodiment, the digital model of a 3D rough fracture comprises a digital model generated based on standard contours (i.e., a rough disk) and a digital model obtained using 3D laser scanning technology (used to simulate 3D rough fractures under real-world conditions). These two methods are used to generate the digital model of a 3D rough fracture to more accurately simulate the grouting process of the 3D rough fracture and more rationally reveal the slurry-water displacement mechanism of the 3D rough fracture during grouting of statically saturated fractures.

[0071] Firstly, a rough disk generation method based on standard contour line is introduced, which can generate a digital model of Barton standard contour line.

[0072] Due to the presence of rough surface protrusions, fracture grouting is subject to inertial forces, which in turn affects the grouting efficiency. To investigate the effect of roughness on the grouting process, this study used Barton's standard contours to generate a series of standard disks with varying roughness and aperture. The grouting hole was located in the center of the disk, and the slurry diffused simultaneously in all directions. Because the roughness and aperture of the fractures were identical in each diffusion direction, the influence of parameters such as morphology or aperture on the grouting process could be investigated using the controlled variable method.

[0073] In this embodiment, Figure 3As shown, 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 intercepted and saved separately. (2) The intercepted image is 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 in the matrix represents the length of the image, and the number of rows in the matrix represents the height of the image. The size range of each element in the matrix is 0~255, representing the grayscale of the image element. Among them, 0 represents pure black and 255 represents pure white. (3) Find the minimum value in each column element. 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 points with the largest horizontal distance represents the length of the contour line. (5) Interpolate the contour line to a given sampling point distance. Preferably, the sampling point distance is 1mm. (6) Label the obtained standard contour lines, such as JRC=2~4, 6~8, 10~12, 14~16, which are divided into four standard contour line labels. Each contour line is then offset upward or downward by a certain distance to form a crack space, and then a rough disk is generated by rotation. The rough disk generated using the Barton standard contour line is also called the Barton standard contour line digital model. A typical rough disk is as follows Figure 4 shown.

[0074] The above processing steps are based on the grayscale processing function of MATLAB image. It is a simple digital processing method. This method uses a grayscale matrix to store and represent image information, and quickly locates the position of contour line points by finding the minimum value of each column. The crack space is generated through a simple offset operation, and the rough disk is generated by rotation. This simplifies the generation process of the crack space and rough disk, and improves the efficiency of the digital processing of the standard contour line.

[0075] Secondly, the digital model obtained by 3D laser scanning technology includes the following steps:

[0076] The rough surface acquired by 3D laser scanning is used as one side of the crack wall. The crack surface is then shifted horizontally and vertically by a certain distance to simulate the shear disturbance (horizontal shear displacement and normal dilatancy displacement) of the crack, thereby obtaining the other side of the crack wall. Through this offset operation, the upper and lower crack surfaces shift and no longer align, forming a rough crack space with a certain degree of opening and contact.

[0077] Since the two-phase flow model is relatively complex to solve and requires a large amount of calculation, for example, a small-scale model is used in the three-dimensional laser scanning modeling of this embodiment. The length of the fissure is 80 mm, the width is 30 mm, and the average opening is about 2 mm. In the initial state, the fissure is filled with water. Unlike the common water and mud burst disasters (dynamic water conditions) in tunnel construction, the fissure water in this embodiment is mainly stored in the fissures of the dam foundation, and the flow rate 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 slurry 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 upper and lower walls) are impermeable boundaries, forming a parallel flow space. Contact area (opening is 0). The fissure space is meshed using tetrahedral units with a minimum size of 0.3 mm, and the total number of domain units is about 90,000.

[0078] Step S102: During the grouting process, the slurry and water are considered as two phases, and a slurry-water two-phase flow model is established.

[0079] It should be noted that this example studies the grouting of fractures in the dam foundation rock mass, not the grouting of the dam body filling (typically core wall clay grouting, which requires the use of the uniformity assumption in porous media theory to study slurry diffusion). Therefore, two important premises of the technical solution of this example are: (i) The rock mass is a fractured medium, not a porous medium. Therefore, this example does not use the uniformity assumption commonly used in porous media theory. In fractured media, it is important to construct a realistic three-dimensional rough fracture space. Therefore, this example uses three-dimensional laser scanning technology to reconstruct the three-dimensional morphology of the fracture. (ii) It is assumed that the mixing process of the slurry phase and the water phase during the grouting process has little effect on the overall diffusion process of the slurry. The slurry and water can be approximately regarded as two phases. Therefore, the slurry and water fill the three-dimensional rough fracture space (rather than the porous medium space based on the uniformity assumption) and have a certain interface between the two. This is the premise of the research of this example.

[0080] During the grouting process, slurry and water are considered as two phases, and a slurry-water two-phase flow model is established. The slurry-water two-phase flow model includes governing equations and a slurry-water displacement two-phase flow constitutive model. The governing equations include the continuity equation for fluid flow in fractures, the momentum conservation equation for fluid flow in fractures, 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 slurry flow characteristics and the Newtonian fluid model for describing the water phase flow characteristics.

[0081] Specifically, the governing equations of the slurry-water two-phase flow model are obtained as follows:

[0082] (1) Flow field governing equations

[0083] The fracture grouting water displacement process is described using a slurry-water two-phase flow model. The fluid velocity in the fracture is low, the inertial force on the fluid is smaller than the viscous force, and the fluid is incompressible. The continuity equation for fluid flow in the fracture is:

[0084] (1)

[0085] Where: u is the fluid flow rate (m / s).

[0086] The momentum conservation equation (NS equation) for fluid flow in a fracture is:

[0087] (2)

[0088] 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 For time, μ is the fluid dynamic viscosity (Pa·s), g is the gravity acceleration vector (m / s 2 ), F is the body force (N / m 3 ).

[0089] (2) Phase field equation

[0090] Existing literature often uses the level set method to capture phase interface motion. This example describes the motion of the phase interface using the phase field method. The phase field variables represent the volume fractions of the two phases, and the phase interface is captured using the Cahn-Hilliard equation:

[0091] (3)

[0092] In the formula φ is the phase field variable, when φ When it is equal to -1, it is water phase. φ When it is equal to 1, it indicates 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).

[0093] in, ε Generally, it is half of the maximum grid size.

[0094] ψ is the phase field auxiliary variable, which can be expressed as a function of the phase field variable:

[0095] (4)

[0096] According to the phase field variables, the volume fraction of each phase can be expressed as:

[0097] (5)

[0098] (6)

[0099] V 1. V 2 are the volume fractions of water phase and slurry phase, respectively.

[0100] The constitutive model of the slurry-water two-phase flow model is obtained as follows:

[0101] The water phase is a typical Newtonian fluid with no yield strength. Newtonian fluids will produce shear motion regardless of how small the pressure gradient is. Slurry phase materials mainly include cement-based mixtures and chemical mixtures. Commonly used grouting slurries are cement-based materials. Solid particles and water in cement slurry form a suspension, and the solid phase particles give the mixture a cohesive strength. Only after the bond is broken will the liquid phase control the slurry flow. Therefore, the cement slurry commonly used in grouting engineering practice is a typical non-Newtonian fluid, generally described by the Bingham constitutive model. The Bingham model requires two material parameters to describe the fluid characteristics:

[0102] (7)

[0103] 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. τ 0 =0, the Bingham model is simplified to the Newtonian model.

[0104] In viscoplastic flow calculations, only the shear strain rate term (i.e. μ g +τ 0 / (dγ / dt) ), when the shear rate dγ / dtWhen the value changes from 0 (no fluid flow) to a smaller value, numerical discontinuity occurs. Papanastasiou proposed a continuous model to approximate the Bingham model. In actual calculations, the Bingham model is rarely used. Instead, the Bingham-Papanastasiou constitutive model with continuous characteristics is used:

[0105] (8)

[0106] Where: m is the model control parameter. m When is large, the Bingham-Papanastasiou model can be simplified to the Bingham model.

[0107] After constructing the slurry-water two-phase flow model, some embodiments further include: verifying the slurry-water two-phase flow model, specifically as follows:

[0108] Step S1021: Based on the slurry-water two-phase flow model, solve the analytical solution of the Bingham fluid displacing the Newtonian fluid in the two-dimensional parallel plate.

[0109] Because Bingham fluids exhibit yield stress, the shear stress and velocity gradient no longer strictly follow a proportional relationship. Solving the problem of Bingham fluids displacing Newtonian fluids is complex, and analytical solutions are typically only available in simpler scenarios. In this example, the analytical solution of a Bingham fluid displacing a Newtonian fluid in a two-dimensional parallel plate is first used to verify the correctness of the established numerical model for slurry-water displacement two-phase flow.

[0110] Figure 5 The figure is a schematic diagram of the two-phase flow simulation of Bingham fluid (cement slurry) displacing Newtonian fluid (water) in a two-dimensional parallel plate. Figure 5 As shown, the parallel plate opening b Much smaller than the parallel plate length L ( b <L / 100), the pressure (or head) along the opening direction is the same. Before grouting, the parallel plate cracks are 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. Assume that the inlet head is H 0 , outlet head is H L , are all constant head boundaries. Slurry phase invasion length (or phase interface position) x and the water head at the phase interface (or slurry front) H(x(t)) All time t function.

[0111] Furthermore, step S1021 includes:

[0112] Step S1021a: treating the slurry-water phases as single-phase flows, and determining the single-phase Newtonian fluid flow rate and the single-phase Bingham fluid flow rate respectively;

[0113] Step S1021b: Using the velocity continuity condition at the phase interface, the single-phase Newtonian fluid flow rate and the single-phase Bingham fluid flow rate are integrated in the opening direction and averaged to obtain the average flow rates of the water phase and the slurry phase;

[0114] Step S1021c: Considering that the hydraulic heads in the water phase and the slurry phase are linearly distributed at any time in the single-phase flow, determine the relationship between the linear change of the hydraulic heads in the water phase and the slurry phase with the position of the phase interface;

[0115] Step S1021d: Simultaneously solve the relationship between the average flow rate of the water phase and the slurry phase and the linear change of the water head in the water phase and the slurry phase with the position of the phase interface to obtain an analytical solution for the Bingham fluid displacing the Newtonian fluid in the two-dimensional parallel plate.

[0116] Specifically, the field variables (head H , intrusion length x The key to the problem of single-phase flow is to treat the two phases as single-phase flow and then use the velocity continuity condition at the phase interface to obtain the relationship between the variables. The velocity distribution of Bingham fluid (slurry) and Newtonian fluid (water) in a two-dimensional parallel plate under single-phase flow conditions is shown in the figure below. Figure 6 As shown. Among them, the velocity distribution of single-phase flowing water satisfies the Hagen-Poiseuille law:

[0117] (9)

[0118] Where: μ w is the dynamic viscosity of water (Pa·s), P 1 is the water phase pressure (Pa).

[0119] The velocity distribution formula of Bingham fluid (slurry) under single-phase flow conditions is:

[0120] (10)

[0121] Where: μ g is the plastic viscosity of the slurry (Pa·s), P2 is the slurry phase pressure (Pa), y g The half-width of the rigid core is formed due to the existence of the yield stress term, which depends on the yield stress and the hydraulic gradient. It is calculated as follows:

[0122] (11)

[0123] from Figure 6 As can be seen in the figure, the slurry phase velocity is cork-shaped, while the water phase velocity distribution is parabolic. Therefore, the velocity distribution of the slurry phase and the water phase at the phase interface cannot be completely consistent. Similar to the Saint-Venant principle, the boundary condition is approximated by the average slurry phase velocity being equal to the average water phase velocity. Using the boundary condition of velocity continuity at the phase interface, Equations (9) and (10) are integrated in the direction of the opening and averaged, and the average flow velocities of the water phase and the slurry phase are obtained as follows:

[0124] (12)

[0125] (13)

[0126] Considering that the hydraulic head (or pressure) in the slurry phase and the water phase are linearly distributed at any time in single-phase flow, the relationship between the linear change of the hydraulic head in the water phase and the slurry phase with the position of the phase interface is determined respectively, which is:

[0127] (14)

[0128] (15)

[0129] By combining equations (12) to (15), we can obtain the analytical solution of the slurry-water two-phase flow displacement model in parallel plates.

[0130] However, as mentioned in existing studies, H ( x ( t )) is difficult to calculate directly and no explicit analytical solution can be obtained. The above formula does not directly give H ( x ( t )) and time t The relationship between the phase interface and the water head (or pressure) at different times cannot be directly determined.

[0131] In view of this, in the analytical solution of the Bingham fluid displacing the Newtonian 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:

[0132] Based on the assumption that the hydraulic head on the interface changes continuously, the relationship between the hydraulic head on the interface and the interface position is solved by using the relationship between the slurry phase pressure gradient and the water phase pressure gradient at different times.

[0133] The relationship between the phase interface position and time is obtained by integrating the separated variables using the derivative relationship between the phase interface position and the average flow velocity.

[0134] Specifically, based on the assumption that the hydraulic head at the phase interface continuously changes, this example proposes a direct numerical method to solve the analytical solution of slurry-water two-phase flow in parallel plates by first solving the relationship between the phase interface position and pressure, and then solving the time and slurry phase invasion length. That is, in the analytical solution of Bingham fluid displacing Newtonian fluid in two-dimensional parallel plates, the detailed process of the phase interface position and the hydraulic head at the phase interface at different times is described as follows:

[0135] First, based on the assumption that the hydraulic head on the phase interface changes continuously, the relationship between the slurry phase pressure gradient and the water phase pressure gradient at different times is used to solve the hydraulic head on the phase interface. H ( x ( t )) and interface position x ( t ) relationship. The operation steps include: giving a series of slurry phase pressure gradient values, wherein the minimum slurry phase pressure gradient is when the slurry phase displaces all the water phase, and the maximum slurry phase pressure gradient can be given according to research needs. In this embodiment, as an example, 50 times the minimum pressure gradient value is taken (it should be understood that a larger value can be taken). The water phase pressure gradient array is calculated using the slurry phase pressure gradient array. Calculate the phase interface position array and the phase interface water head array under the given slurry phase pressure gradient 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 -Interface pressure P (or interface head H ) relationship.

[0136] Secondly, the interface position is obtained by separating the variables and integrating the derivative relationship between the interface position and the average flow velocity. x ( t ) and time t Specifically including:

[0137] Consider the relationship between the average flow velocity and the position of the phase interface:

[0138] (16)

[0139] Since the only variable on the right side of the equal sign in the above formula is x ( t ), so the right side can be considered as x (t ), recorded as:

[0140] (17)

[0141] f ( x ( t )) describes the composite function f and phase interface position x relationship.

[0142] Using formula (17) and the above-mentioned interface position x -Interface head H The relationship can be calculated f ( x ( t ))- x ( t ) scatter plot.

[0143] By separating the variables in equation (16), the relationship between the phase interface position and time is obtained as follows:

[0144] (18)

[0145] By integrating both sides of equation (18) simultaneously, we can obtain the relationship between the grouting displacement time and the corresponding phase interface position:

[0146] (19)

[0147] Where: T and X ( T ) are the upper limits of the points at the time and intrusion distance respectively.

[0148] because f ( x ( t )) is not a continuous function and has no explicit expression. In this embodiment, the integrand on the right side of equation (19) is accumulated using the trapezoidal integral formula to obtain the relationship between time and phase interface position.

[0149] Step S1022: numerically simulate the slurry-water two-phase flow model in the two-dimensional parallel plate using computer software to obtain numerical simulation results.

[0150] Specifically, the numerical model of Bingham fluid displacing Newtonian fluid in a two-dimensional parallel plate is set up 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 (e.g. Figure 5The slurry phase adopts the Bingham-Papanastasiou rheological model, while the water phase adopts the Newtonian constitutive model.

[0151] Since the slurry flooding process is a transient study, phase initialization is required before starting the calculation. Since the phase field method is similar to a step function in describing the continuous change of the phase interface, in this example, the position where the slurry phase volume fraction is equal to 0.5 is approximately considered to be the phase interface position:

[0152] (20)

[0153] Where: pf.Vf1 represents the volume fraction of the slurry phase.

[0154] Among them, the parameters used in numerical simulation and analytical solution are shown in Table 1. Table 1 is as follows:

[0155] Table 1 Parameters of numerical model and analytical solution model

[0156]

[0157] Step S1023: Compare the numerical simulation results with the analytical solution and the pre-acquired grouting displacement test results respectively to verify the rationality of the slurry-water two-phase flow model.

[0158] The numerical simulation results are compared with the analytical solution in detail, including the comparison of the pressure on the phase interface. P (or head H ) and the interface position x ( t ) relationship, and the two solutions agree well. The numerical simulation results and the analytical solution are analyzed to determine the temporal variation of the phase interface position under different slurry plastic viscosities, as well as the distribution of the slurry-water two-phase volume fractions in the parallel plate at different times. The results show good agreement between the numerical and analytical solutions under various conditions, demonstrating the rationality of using the constructed slurry-water two-phase flow model to study the slurry diffusion mechanism during statically saturated fracture grouting.

[0159] Furthermore, the numerical simulation results were compared with the grouting displacement test results conducted by Håkansson (1987), and the grouting test results and numerical simulation results at different time steps were analyzed. The results showed that the slurry-water two-phase flow model proposed in this embodiment is reasonable.

[0160] Step S103: Based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, a slurry displacement static water two-phase flow simulation is carried out in the three-dimensional rough fracture to obtain simulation results. Specifically including:

[0161] Step S1031: Based on the Barton standard contour line digital model, the influence of roughness (parameters such as morphology or opening) on the grouting water displacement process is studied by using the control variable method.

[0162] (1) The displacement characteristics of slurry-water two-phase flow in rough disk fractures under constant grouting rate conditions are analyzed, and the effects of fracture roughness, aperture, and grouting conditions on the slurry diffusion process are analyzed.

[0163] Figure 8 Schematic diagram of slurry-water displacement two-phase flow simulation in rough disk fractures. Figure 8 As shown in the figure, 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 rough disk radius is 1 m. Simulations were performed on disks of varying roughness (control variables). Based on the simulation results, the distribution of the slurry and water phase volume fractions in each rough disk at different times was analyzed. The results show that at a constant grouting rate, the slurry phase uniformly displaces the water phase in all directions, with the slurry phase volume fraction continuously increasing and the water phase volume fraction continuously decreasing due to displacement. Analysis of the migration characteristics of the phase interface at different times shows that at a constant grouting rate, the phase interface movement rate gradually slows, and the radial displacement velocity gradually decreases. In current grouting process design, fractures are generally simplified to smooth parallel plate models. In this example, the orifice pressure variation over time for disks of varying roughness under the same fracture aperture and grouting rate conditions was plotted and analyzed. The results show that, at a constant grouting rate, the smooth parallel plate model underestimates the effect of roughness on the average orifice pressure. Considering that the shear rates of the slurry phase and the water phase are affected by the distribution of the protrusions, this example also analyzes the radial shear rate distribution characteristics of the fluid in disks with different roughness when the grouting time is 100 s. The results show that roughness will cause the viscous energy consumption of the fluid to increase, and the greater the kinetic energy required to overcome the viscous resistance of the fluid flow.

[0164] (2) The effects of fracture geometry and grouting pressure on the grouting diffusion process under constant grouting pressure.

[0165] Considering that in addition to constant rate grouting, constant pressure grouting is often used in actual projects, in this embodiment, based on the simulation results, JRC = 14~16 as an example to analyze the migration characteristics of the phase interface with grouting time under different grouting pressures. The results show that under constant grouting pressure conditions, the phase interface movement distance does not increase infinitely with time. Under smaller grouting pressures, even if the grouting time is extended, the amount of slurry intrusion in the rock cracks does not increase significantly with time. JRC=14~16 Rough disks with different crack apertures show a curve of the water phase volume fraction changing with grouting time. Analysis of this curve shows that under constant grouting pressure and the same morphology, as the crack aperture increases, the slurry phase displaces the water phase at a significantly faster rate. At the same time, the larger the crack aperture, the greater the distance the phase interface moves, and the higher the displacement efficiency. In addition, for cracks with low aperture, even if the grouting time is extended, the slurry water displacement does not increase significantly. Therefore, in the actual grouting process design, it is necessary to pay attention to the crack aperture characteristics, and increasing the grouting pressure is also a relatively effective means. Since crack morphology is also an important factor affecting the slurry water displacement efficiency, this example also analyzes the migration characteristics of the slurry-water phase interface position over time in disks of different roughness under the same crack aperture and grouting pressure conditions. The results show that crack morphology has a significant impact on the slurry water displacement efficiency, but the grouting water displacement rate does not decrease with increasing crack roughness. To investigate the effect of asperity distribution within a fracture on grouting, comparative simulations were conducted for two fractured disks with identical roughness but different asperity locations. In one case, the asperities were located near the grouting hole, while in the other, they were located near the outlet. The simulation results show that, under identical grouting pressure and aperture conditions, the shear rate perturbation caused by asperities at the inlet is significantly greater than that caused by asperities near the outlet. Despite identical roughness, the viscous energy dissipation caused by the roughness of the fracture in Case 1 is greater than that in Case 2. Therefore, the water displacement efficiency of fracture grouting is related to the distribution of asperities; the grouting efficiency does not decrease with increasing fracture roughness. The impact of asperities near the grouting hole on grouting efficiency is greater than that of asperities far from the grouting hole. In fracture grouting engineering, the distribution of asperities should be considered to rationally design the grouting hole location.

[0166] The above is the process of using standard rough contour lines to simulate the static water two-phase flow of slurry displacement in three-dimensional rough fractures. The rough disk expansion simulation generated by the standard contour lines is conducive to accurately analyzing the influence of fracture geometric characteristics and grouting parameters on the slurry displacement process under radial flow conditions, which in turn helps to reveal the static water mechanism of slurry displacement from the level of various influencing factors and provide a basis for subsequent research on the static water mechanism of slurry displacement under the complex conditions of real three-dimensional rough fractures.

[0167] Step S1032: Utilize the digital model obtained by the three-dimensional laser scanning technology to carry out a slurry displacement and still water two-phase flow simulation in the three-dimensional rough fracture.

[0168] Current non-dynamic grouting design methods mostly ignore the role of the water phase and treat grouting as a single-phase slurry flow process. In reality, many dam foundation fissures are filled with static water, and the slurry continuously displaces water during grouting. A two-phase flow approach is needed to more realistically reflect the slurry diffusion process. The extent to which traditional single-phase flow models overestimate or underestimate the slurry invasion efficiency and under what conditions are they suitable for describing the slurry displacement process in rough fractures are important scientific questions. Currently, existing research has rarely considered this issue. In this example, numerical simulations of slurry-water two-phase flow displacement characteristics in three-dimensional real rough fractures were conducted to explore the differences in slurry invasion efficiency between single-phase and two-phase flow methods for rough fracture grouting, aiming to identify under what conditions the two-phase flow method can be approximately replaced by the single-phase flow method. Based on digital models obtained through 3D laser scanning, the slurry diffusion mechanism under different conditions was studied, revealing the mechanisms by which factors such as fracture roughness, anisotropy, and surface tension affect slurry diffusion behavior, providing scientific guidance for grouting design under different conditions.

[0169] Specifically, the slurry flow process can be divided into parallel flow and radial flow. This example explores the slurry-water displacement characteristics in fractures under these two conditions. The numerical simulation process under these two flow conditions is described below.

[0170] Step S1032a: Under parallel flow conditions, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fracture, the slurry front front advancement speed, shape change and displacement ratio change over time in the three-dimensional rough fracture are analyzed through numerical simulation.

[0171] First, the parallel displacement of the water phase by the slurry phase in a typical three-dimensional rough fracture was analyzed. The results show that in ideal parallel-plate fractures, the slurry front typically advances uniformly. However, in three-dimensional rough fractures, the slurry front advances at different speeds at different points due to the influence of morphology, contact area, and surface tension. During the grouting process, the contact zone is relatively narrow, and the fluid near the contact zone is affected by surface tension, pulling or dragging the phase interface toward the contact zone.

[0172] Secondly, analyze the same displacement conditions and displacement time t =100s when different surface tension coefficients σ The results show that surface tension affects the advancement position of the slurry front, and the position and shape of the slurry front are affected by the surface tension. σ Changes occur with changes, and there is a certain degree of uncertainty.

[0173] In this example, in order to quantitatively describe the slurry phase water displacement efficiency, the displacement ratio is defined as I = I ( t )as follows:

[0174] (twenty one)

[0175] Where: vf 1( t )for t The volume of the slurry phase at the moment V is the total volume of the crack space, I ( t ) characterization t The volume fraction of the slurry injected at any moment in the total fracture space.

[0176] According to the simulation results, the displacement ratio is calculated according to formula (21), and the surface tension coefficients of different σ Lower displacement ratio I The curve changes with grouting time, such as Figure 9 As shown in the figure, the surface tension coefficient is σ It mainly affects the shape of the slurry front, but has a negative impact on the displacement ratio. I The effect is small; as the grouting time increases, the surface tension coefficient σ It also affects the shape of the slurry front and the displacement ratio; σ The larger it is, the greater the displacement ratio is.

[0177] Step S1032b: Under parallel flow conditions, based on the slurry-water two-phase flow model and the digital model of three-dimensional rough fractures, a numerical simulation orthogonal test is 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.

[0178] It should be noted that, when grouting fissures, grouting materials with different physical and chemical properties are often used according to the needs of the project. These materials include cement-based materials, polyurethane, epoxy resin, etc. Among them, cement-based materials are suitable for injecting fissures larger than cement particles, while polyurethane and epoxy resin are suitable for reinforcing fissures that are difficult to inject cement-based materials. 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. These materials are usually also referred to as chemical grouting materials. Based on the previous description, it can be seen that the fissure grouting of dams in actual projects 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 the two design methods (grouting design method under the guidance of single-phase flow and two-phase flow), in this embodiment, numerical simulation orthogonal experiments are carried out, and the influence of the geometric characteristics of the fissures and the properties of the grouting materials on the displacement ratio of single-phase flow and two-phase flow are analyzed.

[0179] Specifically, the yield stress of the slurry phase material is taken as 0Pa, 0.5Pa, and 3Pa, representing Newtonian fluid (part of chemical grouting materials), low yield stress Bingham fluid, and Bingham fluid respectively; the plastic viscosity of the slurry phase material is taken as 0.0025Pa·s, 0.025Pa·s, and 0.25Pa·s, representing materials with a viscosity slightly greater than that of water (the viscosity of water is 0.001Pa·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 by 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 unidirectional flow method. μ g =0.0025Pa·s) and the displacement state of the slurry-water two-phase in the fracture under different yield stress conditions at the 3s. The results show that when the yield stress τ When 0 = 0 Pa, the displacement of the single-phase flow method is significantly greater than that of the two-phase flow method. As the yield stress increases, the slurry phase advancement distance of the single-phase flow method and the two-phase flow method gradually approaches. Therefore, the smaller the slurry phase yield stress, the greater the difference in displacement between the single-phase flow method and the two-phase flow method.

[0180] Figure 10 The curves of grouting displacement ratio of different yield stress slurry materials with low plastic viscosity and high plastic viscosity over time are shown. Among them, (a) is low plastic viscosity ( μ g =0.0025Pa·s), (b) is high plastic viscosity ( μ g =0.25Pa·s). Figure 10 As can be seen from part (a), the lower the yield stress, the greater the difference in displacement ratio 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, 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 is far from filling the fracture space, the single-phase flow method overestimates the grouting efficiency, which is more obvious for slurries with no yield stress (or low yield stress) (such as polyurethane, epoxy resin grouting materials). As the yield stress increases, the difference in displacement ratio between the single-phase flow method and the two-phase flow method gradually decreases. Figure 10 (a) and (b) τ Comparing the case of 0 = 0 Pa, it can be found that the greater the plastic viscosity of the slurry, the smaller the difference in displacement ratio between the single-phase flow method and the two-phase flow method. Therefore, under high plastic viscosity conditions, the difference in displacement ratio between the single-phase flow method and the two-phase flow method further decreases with increasing yield stress. In this case, it is reasonable to simplify the slurry-water displacement two-phase flow process in saturated fractures into a slurry single-phase flow process.

[0181] Furthermore, the time-varying curves of slurry displacement ratio under different yield stress conditions were plotted and analyzed. The analysis results show that when high-yield stress cement slurry is injected into saturated fractures, it is reasonable to simplify the slurry-water two-phase flow displacement process into a slurry single-phase flow process.

[0182] Step S1032c analyzes the roughness parameters in different directions of the three-dimensional rough fractures by numerical simulation based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fractures under the conditions of roughness anisotropy and radiation. R and the influence of crack morphology on the slurry diffusion direction.

[0183] It should be noted that for a standard rough contour disk model with equal aperture, the orientation of slurry diffusion cannot be analyzed because the disk model has the same features in every direction. Therefore, to further analyze the influence of crack morphology on the slurry diffusion direction, this example uses 3D laser technology to obtain 3D rough cracks with equal aperture and conducts numerical simulations.

[0184] Two types of rough surface fractures, one with relatively low anisotropy and one with high anisotropy, were selected. The time-dependent diffusion characteristics of slurry in these three-dimensional rough fractures with equal aperture were simulated and output, respectively. The influence of three-dimensional morphology on the slurry diffusion direction was analyzed when gravity was not considered. Regarding the morphology of the slurry front, for fractures with relatively low anisotropy, the slurry front remained approximately circular at the initial diffusion stage; as diffusion time increased, the slurry front became approximately elliptical. For fractures with high anisotropy, the slurry front remained approximately elliptical at all stages of slurry diffusion. The slurry diffusion direction (long axis) and the direction of less roughness (minor axis) were approximately aligned. The analysis results show that, for both fractures with low and high anisotropy, under conditions of equal aperture, the slurry tends to preferentially diffuse along the direction of less roughness.

[0185] In step S1032d, under the radial flow condition, 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 in the three-dimensional rough fracture 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.

[0186] Under the condition of radiation flow, the upper and lower walls of the crack were obtained by three-dimensional laser scanning. The crack size was 80mm×80mm, and the average opening was about 2mm. During the simulation, the grouting hole was located in the middle of the model, and the slurry was injected at a constant pressure. In the initial state, the crack was filled with water, and the flow of water in the initial state was also not considered. Due to the displacement of the slurry, water was discharged from the four side outlets, and the outlet was a constant pressure boundary. The pressure difference between the inlet and outlet was set to 150Pa, and the rest was an impermeable boundary. In addition, in order to be closer to the actual project, some contact areas (opening of 0) were also set. Tetrahedral units were still used for meshing, and the minimum unit size was about 0.6mm. Approximately 75,000 domain units were obtained after meshing.

[0187] The simulation results show that under radial flow conditions, the plastic viscosity of the slurry phase is 0.0025 Pa·s and the yield stress is 0.5 Pa. The slurry front gradually spreads from the grouting hole to the surrounding area, and the amount of slurry injected into the crack increases with time. The slurry diffusion process is affected by the crack morphology and surface tension, and the advancement speed of each point on the front is inconsistent. Grouting time t = 500s, the slurry phase flows to the outlet and overflows the fracture space. Therefore, in the subsequent long period of time, the increase in the amount of slurry in the fracture space is small, and it continues to overflow from the upper right outlet.

[0188] Similarly, to compare the differences in grouting displacement efficiency calculated using the single-phase flow method and the two-phase flow method for saturated fractures under radial flow conditions, orthogonal numerical simulation experiments were conducted to investigate the influence of grouting material properties on the displacement ratios of single-phase and two-phase flows. The results showed that the difference in slurry injection volume between the single-phase and two-phase flow methods gradually decreased with increasing yield stress.

[0189] The displacement ratio defined in the above embodiment is still used I To describe the efficiency of fracture grouting, the displacement ratio curves of slurries with different yield stresses under low plastic viscosity and high plastic viscosity conditions are plotted and compared. Figure 11 As shown, where (a) is the low plastic viscosity ( μ g =0.0025Pa·s), (b) is high plastic viscosity ( μ g=0.25Pa·s). Analysis of the curve shows that under low plastic viscosity conditions, when the yield stress is 0Pa, the slurry injected into the saturated fracture is a Newtonian fluid, and the displacement ratios of the single-phase flow method and the two-phase flow method are quite different, 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 slurry in the fracture space, the slurry phase gradually bears the main pressure drop, and the difference in displacement ratios between 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=0Pa), at the same time, the displacement ratio of the single-phase flow method is slightly larger than that of the two-phase flow method, but the difference between the two is significantly smaller than that of the low plastic viscosity case ( Figure 11 (a) τ 0=0Pa). As the yield stress increases, the difference between the single-phase flow method and the two-phase flow method at the same time gradually decreases.

[0190] Furthermore, the authors plotted the time-dependent difference in displacement ratio between the single-phase and two-phase flow methods when slurries with varying yield stresses and plastic viscosities were injected into water-saturated fractures under radial flow conditions. The results showed that the difference in displacement ratio between the single-phase and two-phase flow methods was consistently greater than zero under varying yield stresses and plastic viscosities, indicating that the single-phase flow grouting design method overestimates the slurry's water displacement efficiency in fractures.

[0191] In this example, the displacement characteristics of slurry-water two-phase flow in three-dimensional rough fractures under parallel flow and radial flow conditions were analyzed, and the difference in slurry invasion efficiency between the two-phase flow design method and the single-phase flow design method during grouting of saturated fractures was compared and analyzed. Under both conditions, the lower the slurry yield stress, the greater the difference in displacement ratio between the single-phase flow method and the two-phase flow method. As the yield stress increases, the difference in displacement ratio between the single-phase flow method and the two-phase flow method gradually decreases because the slurry phase bears the main pressure drop during the shorter displacement time. The plastic viscosity shows a similar pattern. The greater the plastic viscosity, the smaller the difference in displacement ratio between the single-phase flow method and the two-phase flow method. Therefore, when injecting slurry with high yield stress and high plastic viscosity into saturated fractures, it is reasonable to simplify the slurry-water displacement two-phase flow process into a slurry single-phase flow process. However, when using chemical grouting materials with low plastic viscosity (typical grouting materials include Newtonian fluids such as polyurethane and epoxy resin), the displacement ratios obtained using the single-phase and two-phase flow methods differ significantly. In this case, the two-phase flow method is required to estimate the grouting characteristics. This mechanistic explanation provides more reasonable guidance for the design of grouting in dam foundation fissures filled with saturated static water.

[0192] Based on the same inventive concept, this embodiment also provides a three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation system, which is applied to the analysis of slurry diffusion characteristics during static saturated fracture grouting, and includes:

[0193] A rough crack construction unit is used to reconstruct the three-dimensional morphology of the crack using three-dimensional laser scanning technology to obtain a three-dimensional rough crack model;

[0194] Model building unit, used to build slurry-water two-phase flow model;

[0195] A simulation analysis unit is used to perform a slurry displacement still water two-phase flow simulation 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 a simulation result;

[0196] 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 model for describing the flow characteristics of the water phase.

[0197] The three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation system provided in this embodiment can implement the process and steps of the three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation method provided in any of the above embodiments and achieve the same technical effects, which will not be repeated here.

[0198] The foregoing description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are readily apparent to those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection 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 cracks was reconstructed using standard rough contour lines and three-dimensional laser scanning technology to obtain a digital model of the three-dimensional rough cracks. During the grouting process, slurry and water are considered 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, a 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 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 Newtonian fluid displaced by the Bingham fluid in the two-dimensional parallel plate is obtained; 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 were 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 for the displacement of a Newtonian fluid by a Bingham 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 flow rates of the single-phase Newtonian fluid and the single-phase Bingham fluid are integrated in the direction of the opening and averaged to obtain the average flow rates of the water phase and the slurry phase respectively. Considering that the hydraulic head in the water phase and the slurry phase are linearly distributed at any time in 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 a Bingham fluid displacing a Newtonian 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 that the hydraulic head on the interface changes continuously, the relationship between the hydraulic head on the interface and the position of the 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 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, a simulation of slurry displacement of still water two-phase flow in three-dimensional rough fractures was carried out. The simulation results include: 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, a numerical simulation orthogonal experiment was 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, a simulation of slurry displacement of still water two-phase flow in three-dimensional rough fractures was carried out. The simulation results include: 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 through numerical simulation. R and the influence of crack morphology on the slurry diffusion direction; Under radial flow conditions, based on the slurry-water two-phase flow model and the digital model of the three-dimensional rough fractures, the effects of fracture morphology, contact area and surface tension in the three-dimensional rough fractures on slurry diffusion were 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 was compared.

8. A three-dimensional rough fracture slurry-water displacement two-phase flow numerical simulation system, characterized by: 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 of the crack using three-dimensional laser scanning technology to obtain a three-dimensional rough crack model; Model building unit, used to build slurry-water two-phase flow model; A simulation analysis unit is used to simulate the slurry displacement of still water two-phase flow in three-dimensional rough fractures based on the slurry-water two-phase flow model and the 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 model for describing the flow characteristics of water phase.

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

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

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