A polyurethane penetration grouting diffusion simulation method, device, equipment and medium

Abstract

The present application discloses a method, device, equipment and medium for simulating the diffusion of polyurethane permeation grouting. The method includes constructing a geometric model of the diffusion of polyurethane permeation grouting in a porous medium to be injected according to the physical property data of the porous medium to be injected; establishing a physical field of the geometric model by using the Richards equation and the dilute mass transfer equation of the porous medium, and adjusting the geometric model according to the material property parameters of the geometric model obtained from the physical field; setting the boundary conditions and initial values of the adjusted geometric model, and performing mesh division on the adjusted geometric model based on the local refinement method to obtain a permeation grouting diffusion simulation model; and solving the permeation grouting diffusion simulation model according to a transient solver to complete the simulation of the diffusion of polyurethane permeation grouting in the porous medium. The method provided by the present application improves the accuracy of modeling the slurry diffusion process.

Description

Technical Field

[0001] The present application relates to the field of geotechnical engineering, and particularly to a method, device, equipment and medium for simulating the diffusion of polyurethane permeation grouting. Background Art

[0002] Grouting has long been the most effective means for preventing and controlling sudden water inrush in underground engineering. Existing grouting methods can be divided into permeation grouting, fissure grouting, splitting grouting, etc. according to the diffusion form of the grout in the grouted medium. Among them, permeation grouting refers to the permeation form of the grout in the porous medium, and the grout only seeps in the pores. Different from the construction method of traditional cement-based grouting materials, chemical grouting materials need to be mixed evenly through a static mixer. When the grout is injected into the formation, the viscosity begins to change. The viscosity of the previously injected grout has increased for some time, while the viscosity of the just-injected grout has just started to increase, which results in different viscosities of the grout at different positions. Therefore, the spatio-temporal variation characteristics of the grout viscosity need to be considered.

[0003] However, when constructing a permeation grouting diffusion model in the prior art, it is difficult to accurately reflect its complex physical structure and changes, which leads to a deviation between the simulation results and the actual situation. Summary of the Invention

[0004] The present application aims to provide a method, device, equipment and medium for simulating the diffusion of polyurethane permeation grouting, so as to improve the accuracy of modeling the grout diffusion process.

[0005] To solve the above technical problems, an embodiment of the present application provides a method for simulating the diffusion of polyurethane permeation grouting, including the following steps:

[0006] Construct a geometric model of the permeation grouting diffusion of polyurethane in the to-be-injected porous medium according to the physical property data of the to-be-injected porous medium;

[0007] Establish a physical field of the geometric model by using the Richards equation and the dilute mass transfer equation of the porous medium, and adjust the geometric model according to the material property parameters of the geometric model obtained from the physical field, wherein the physical field reflects the influence of the material properties of the polyurethane on the seepage diffusion process;

[0008] Set the boundary conditions and initial values of the adjusted geometric model, and perform mesh division on the adjusted geometric model based on the local refinement method to obtain a permeation grouting diffusion simulation model;

[0009] Solve the permeation grouting diffusion simulation model according to the transient solver to complete the simulation of the permeation grouting diffusion of the polyurethane in the to-be-injected porous medium.

[0010] As one of the preferred solutions, adjusting the geometric model according to the material property parameters of the geometric model obtained from the physical field includes:

[0011] Constructing a diffusion model based on the Newtonian fluid rheological equation and the seepage motion equation;

[0012] Obtaining the permeability function of the polyurethane in the porous medium to be injected in stages according to the diffusion model;

[0013] Obtaining the dynamic viscosity of the polyurethane during the permeation grouting diffusion process in the porous medium to be injected based on rheological experiments;

[0014] Adjusting the geometric model with the permeability function and the dynamic viscosity as the material property parameters of the geometric model.

[0015] As one of the preferred solutions, the permeability function is expressed as:

[0016]

[0017] where pwl(t) represents the permeability, φ represents the porosity, d represents the pore diameter, t represents the penetration time, t1 represents the time when the flow resistance disappears, t2 represents the slurry curing time, δ represents the porosity, ρ represents the slurry density, R represents the radius of the porous medium, is the integral median value corresponding to the function of the dynamic viscosity and the penetration time, and φ0 and K0 are the porosities under the initial effective stress condition.

[0018] As one of the preferred solutions, the dynamic viscosity is expressed as:

[0019] μ(t) = C1·e kt + μ0 0 ≤ t ≤ t2,

[0020] where μ(t) is the function of the dynamic viscosity and time, μ0 is the initial viscosity of the slurry, t is the time, t2 is the slurry flow-solid phase change time, k is the time-varying coefficient, and C1 is a constant.

[0021] As one of the preferred solutions, in constructing the geometric model of the permeation grouting diffusion of the polyurethane in the porous medium to be injected, it includes:

[0022] Two-dimensionally transforming the permeation grouting diffusion process of the polyurethane in the porous medium to be injected based on the sectional method to obtain a two-dimensional model of the permeation grouting;

[0023] Determining the geometric parameters of the two-dimensional model according to the physical property data of the porous medium to be injected;

[0024] Construct a geometric model of the polyurethane in the porous medium to be injected based on the infinite source domain method and the geometric parameters.

[0025] As one of the preferred solutions, perform mesh generation on the adjusted geometric model based on the local refinement method to obtain a seepage grouting diffusion simulation model, including:

[0026] Perform preliminary mesh generation on the adjusted geometric model to obtain a sparse mesh;

[0027] According to the simulation requirements of the geometric model, identify the key regions in the sparse mesh, and the key regions at least include the grouting pipe region and the internal region of the porous medium;

[0028] Perform secondary mesh encryption on the key regions based on the local refinement method to obtain a seepage grouting diffusion simulation model.

[0029] As one of the preferred solutions, solve the seepage grouting diffusion simulation model according to the transient solver to complete the simulation of the seepage grouting diffusion of the polyurethane in the porous medium to be injected, including:

[0030] According to the Newtonian fluid rheological equation and the seepage motion equation, set up a partial differential equation corresponding to the seepage grouting diffusion process of the polyurethane in the porous medium to be injected;

[0031] Use the implicit Euler backward difference method to discretize the time term in the partial differential equation to obtain a discretized partial differential equation;

[0032] Input the discretized partial differential equation into a pre-constructed transient solver for solution, and simulate the seepage grouting diffusion process of the polyurethane in the porous medium by adjusting the iteration times and time step of the transient solver.

[0033] Another embodiment of the present application provides a polyurethane seepage grouting diffusion simulation device, including:

[0034] A construction module for constructing a geometric model of the seepage grouting diffusion of the polyurethane in the porous medium to be injected according to the physical property data of the porous medium to be injected;

[0035] An assignment module for establishing the physical field of the geometric model by using the Richards equation and the dilute mass transfer equation of the porous medium, and adjusting the geometric model according to the material property parameters of the geometric model obtained from the physical field, wherein the physical field reflects the influence of the material properties of the polyurethane on the seepage diffusion process;

[0036] A partitioning module for setting boundary conditions and initial values of the adjusted geometric model, and performing mesh partitioning on the adjusted geometric model based on a local refinement method to obtain a permeation grouting diffusion simulation model;

[0037] A calculation module for solving the permeation grouting diffusion simulation model according to a transient solver to complete the simulation of the permeation grouting diffusion of the polyurethane in the porous medium to be injected.

[0038] Another embodiment of the present application provides a computer device, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, the above-mentioned polyurethane permeation grouting diffusion simulation method is implemented.

[0039] Another embodiment of the present application provides a computer-readable storage medium storing a computer program. When the device where the computer-readable storage medium is located executes the computer program, the above-mentioned polyurethane permeation grouting diffusion simulation method is implemented.

[0040] Compared with the prior art, the beneficial effects of the embodiments of the present application are at least one of the following:

[0041] (1) The present application constructs a geometric model according to the actual physical structure and properties of the porous medium, which can more realistically reflect the complexity and irregularity of the porous medium, thereby improving the accuracy of the simulation; the Richards equation and the dilute mass transfer equation of the porous medium are used to establish the physical field. These two equations respectively describe the unsaturated seepage and mass transfer processes of fluids in the porous medium, and can more accurately reflect the seepage diffusion behavior of polyurethane in the porous medium.

[0042] (2) By simulating the seepage diffusion behavior of different polyurethane materials in the porous medium, the present application can evaluate the performance of the materials such as permeability and diffusivity, providing a basis for the selection and design of the materials.

[0043] (3) Through numerical simulation, the present application can quickly evaluate the advantages and disadvantages of different grouting schemes or material schemes, improving the decision-making efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic flow chart of the polyurethane permeation grouting diffusion simulation method in one embodiment of the present application;

[0045] Figure 2 is a schematic diagram of the mesh partitioning of the grouting geometric model in one embodiment of the present application;

[0046] Figure 3It is a schematic structural diagram of a polyurethane permeation grouting diffusion simulation device in one of the embodiments of the present application;

[0047] Figure 4 It is a schematic diagram of a polyurethane permeation grouting diffusion simulation device in one of the embodiments of the present application. Specific embodiments

[0048] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The purpose of providing these embodiments is to make the disclosure content of the present application more thorough and comprehensive. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present application.

[0049] In the description of the present application, the terms "first", "second", "third", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", "third", etc. may explicitly or implicitly include one or more of such features. In the description of the present application, unless otherwise stated, the meaning of "plurality" is two or more.

[0050] In the description of the present application, it should be noted that, unless otherwise clearly defined and limited, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected, or indirectly connected through an intermediate medium, and it may be the communication inside two elements. The terms "vertical", "horizontal", "left", "right", "up", "down" and similar expressions used in this article are only for the purpose of illustration, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present application. The term "and / or" used in this article includes any and all combinations of one or more of the related listed items. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific circumstances.

[0051] In the description of the present application, it should be noted that, unless otherwise defined, all the technical and scientific terms used in the present application have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs. The terms used in the specification of the present application are only for the purpose of describing specific embodiments, and are not intended to limit the present application. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific circumstances.

[0052] An embodiment of the present application provides a method for simulating the diffusion of polyurethane permeation grouting. Specifically, please refer to Figure 1 , Figure 1 which shows a schematic flow chart of the method for simulating the diffusion of polyurethane permeation grouting provided in one of the embodiments of the present application. It includes steps S1 to S4:

[0053] S1. According to the physical property data of the porous medium to be injected, construct a geometric model for the diffusion of polyurethane permeation grouting in the porous medium to be injected;

[0054] S2. Use the Richards equation and the dilute mass transfer equation for porous media to establish the physical field of the geometric model, and adjust the geometric model according to the material property parameters of the geometric model obtained from the physical field. Among them, the physical field reflects the influence of the material properties of the polyurethane on the seepage diffusion process;

[0055] S3. Set the boundary conditions and initial values of the adjusted geometric model, and perform mesh division on the adjusted geometric model based on the local refinement method to obtain a permeation grouting diffusion simulation model;

[0056] S4. Solve the permeation grouting diffusion simulation model according to the transient solver to complete the simulation of the diffusion of polyurethane permeation grouting in the porous medium to be injected.

[0057] It should be noted that in the prior art, the influence of gravity and the spatio-temporal variation characteristics of the slurry viscosity are not considered when the slurry penetrates the porous medium, and at the same time, the non-uniformity of the seepage channels of the porous medium itself is also ignored. Due to the time-varying viscosity of the slurry, during the grouting process, as the slurry diffuses, solidified particles will gradually form and fill the pores of the porous medium, reducing its original permeability. In view of the above deficiencies, the present application provides a more practical grouting engineering method. In addition, a permeation grouting modeling method is provided.

[0058] Assume that the porous medium is isotropic. The process of slurry penetration and diffusion can be intuitively understood through the formation profile. Therefore, the grouting model can be simplified to a two-dimensional model and in an axisymmetric form. The vertical axis on the left is the axis of symmetry. Add an infinite element domain with a thickness of 0.5*R1 and a cylindrical type on the right and below the profile to enable the polyurethane to freely leave the soil column and reduce the influence of the artificial boundary on the target area. The established geometric model is a spherical diffusion model of polyurethane permeation grouting in the porous medium. Among them, the porous medium is set as a region with a radius of R1 = 1m and a height of H1 = 2m, and the radius of the grouting pipe is r1 = 5cm and the height is h1 = 0.6m.

[0059] Preferably, in an embodiment of the present invention, in the step of constructing a geometric model of the permeation grouting diffusion of polyurethane in the porous medium to be injected according to the physical property data of the porous medium to be injected, it includes:

[0060] Two-dimensionalize the permeation grouting diffusion process of the polyurethane in the porous medium to be injected based on the section method to obtain a two-dimensional model of the permeation grouting;

[0061] Determine the geometric parameters of the two-dimensional model according to the physical property data of the porous medium to be injected;

[0062] Construct the geometric model of the polyurethane in the porous medium to be injected based on the infinite source domain method and the geometric parameters.

[0063] Specifically, the infinite source domain method is a mathematical model used to simulate the flow and diffusion of fluids in porous media. This method assumes that the fluid source is infinite and the flow and diffusion of the fluid in the porous medium are continuous. Using the infinite source domain method and the determined geometric parameters, a geometric model of polyurethane in the porous medium is constructed. In the model, the process of the polyurethane grouting liquid starting from the grouting port and gradually diffusing and permeating in the porous medium should be accurately reflected.

[0064] When polyurethane undergoes permeation and diffusion in an unsaturated porous medium, the Richards equation module and the dilute mass transfer module of the porous medium are used to simulate its seepage and diffusion process. The pressure field in the porous medium during the permeation process can be expressed as:

[0065]

[0066] In the formula, p is the pore water pressure (Pa), S e is the effective saturation (-), S p is the storage coefficient (1 / Pa), C m is the water capacity (1 / m), ρ is the fluid density (kg / m 3 ), g is the acceleration due to gravity (m / s [[ID=3|0]] 2 ), is the Hamiltonian operator, u is the fluid velocity, κ s is the hydraulic conductivity (m 2 ), μ is the dynamic viscosity of the fluid (Pa·s), κ r is the relative permeability (-), Q m is the fluid source term or sink term (kg / (m 3 ·s)).

[0067] The slurry concentration field during the diffusion process can be expressed as:

[0068]

[0069] In the formula, θ is the volumetric water content (m3 / m 3 ), c i is the concentration of each substance in the solution (mol / m 3 ), ρ is the solution density (kg / m 3 ), c p,i is the adsorption concentration of soil particles (mol / kg), u is the fluid velocity (m / s), D D,i is the dispersion tensor (m 2 / s), D e,i is the effective diffusion coefficient (m 2 / s), R i is the physicochemical reaction term (mol / (m 2 ·s)), S i is the source-sink term (mol / (m 2 ·s)).

[0070] Preferably, in an embodiment of the present invention, adjusting the geometric model according to the material property parameters of the geometric model obtained from the physical field includes:

[0071] Constructing a diffusion model based on the Newtonian fluid rheological equation and the seepage motion equation;

[0072] Obtaining the permeability function of the polyurethane in the porous medium to be injected in stages according to the diffusion model;

[0073] Obtaining the dynamic viscosity of the polyurethane during the permeation grouting diffusion process in the porous medium to be injected based on rheological experiments;

[0074] Adjusting the geometric model with the permeability function and the dynamic viscosity as the material property parameters of the geometric model.

[0075] Determine the material properties and parameters to be assigned according to the physical field. Specifically, as described in Table 1 and Table 2.

[0076] Table 1 User-defined diffusion model

[0077]

[0078] Table 2 Material parameters of polyurethane and porous medium

[0079]

[0080] Specifically, assume that during the permeation and diffusion process of polyurethane in the porous medium, the following conditions are met:

[0081] 1) Static pressure grouting is adopted, ignoring the pressure loss from the grouting pipe to the nozzle and the velocity loss during the diffusion process;

[0082] 2) The slurry is an incompressible and isotropic Newtonian fluid, and it satisfies Darcy's law during the diffusion process;

[0083] 3) During the entire penetration process, the slurry penetrates in a laminar flow form and does not mix with groundwater, which is a complete displacement process;

[0084] 4) The porous medium does not displace during the slurry penetration, displacement, and solidification processes;

[0085] 5) The injected porous medium is a homogeneous and isotropic medium.

[0086] The basic rheological equation of Newtonian fluid can be expressed as

[0087] τ = μ·γ (1)

[0088] where τ is the shear force, that is, the internal friction force per unit area of the slurry (Pa), μ is the dynamic viscosity (mPa·s), and γ = -dv / dr is the shear rate (s -1 ), v and r are the seepage velocity of the fluid in the pore channel and the geometric distance perpendicular to the slurry flow direction, respectively. In actual engineering, when the slurry reacts with water, it will gradually solidify, and its viscosity changes with time. Usually, the time-varying law of the viscosity is expressed in the form of an exponential function, that is

[0089] μ(t) = C1·e kt +μ0 0≤t≤t2 (2)

[0090] where μ(t) is the function of dynamic viscosity and time (mPa·s), which can be measured by a rheometer test, μ0 is the initial viscosity of the slurry, t is the time (s), t2 is the slurry flow-solid phase transition time (s), k is the time-varying coefficient, and C1 is a constant. For the convenience of calculation, the viscosity integral median value is adopted to calculate the diffusion radius of the slurry considering the time-variation of viscosity, that is

[0091]

[0092] For the laminar flow state of Newtonian fluid in a porous medium, a microelement is taken for analysis with the tube axis as the axis of symmetry on the flow path. Let the radius of the circular tube be r0, the radius of the microelement r > r0, and the length be dl. The pressures on the left and right cross-sections of the microelement are p and p + dp respectively, and the shear stresses on the upper and lower surfaces of the microelement are τ. Considering the gravity condition, the force balance condition on the microelement is

[0093]

[0094] where θ is the angle between the slurry diffusion direction and the grouting pipe. When the diffusion direction is upward to the horizontal plane, the angle is positive; when the diffusion direction is downward to the horizontal plane, the angle is negative. After arrangement,

[0095]

[0096] Substituting (5) into (1) gives

[0097]

[0098] Now, integrate (6), and substituting the boundary conditions \(r = r_0\) and \(v = 0\) gives

[0099]

[0100] Therefore, when the slurry is in laminar flow in a single circular pipe, the total flow rate in the pipe is

[0101]

[0102] Assume there are \(N\) i capillaries with a radius of \(r\) i in the porous medium. Then the total slurry flow rate in the porous medium is

[0103]

[0104] In the pores of the actual porous medium, the pipes in the capillaries are random and non-uniform. The tortuosity can be used to characterize the tortuous effect of the movement and diffusion of fluid particles. Its definition formula is as follows:

[0105]

[0106] where \(L\) t is the actual length of the slurry flowing through the porous medium channel, \(L_0\) is the diffusion distance between the grouting hole and the slurry front, and \(\chi\) is the physical tortuosity. Therefore, the total slurry flow rate in the porous medium can be transformed into

[0107]

[0108] Based on the Bruggeman model, the relationship between the physical tortuosity and the geometric tortuosity is given as follows

[0109] \(\chi=\chi\) g \(\varphi\) 0.1 (12)

[0110] where \(\chi\) g is the geometric tortuosity, which can be determined by image analysis combined with the pore centroid method. The porosity can be expressed as

[0111]

[0112] where \(A = 4\pi R\) 2 is the area of the porous medium diffusion region. Since the seepage velocity \(V = Q / A\), then

[0113]

[0114] The effective formation permeability is

[0115]

[0116] The seepage motion equation of Newtonian fluid can be obtained

[0117]

[0118] According to the rheological equation of Newtonian fluid and the seepage motion equation, combined with rheological experiments, specific permeability functions and dynamic viscosities are obtained.

[0119] Preferably, in an embodiment of the present invention, the permeability function is expressed as:

[0120]

[0121] Where pwl(t) represents permeability, φ represents porosity, d represents pore diameter, t represents seepage time, t1 represents the time when flow resistance disappears, t2 represents the slurry curing time, δ represents porosity, ρ represents slurry density, R represents the radius of the porous medium, is the integral median value corresponding to the function of dynamic viscosity and seepage time, and φ0 and K0 are porosities under the initial effective stress condition.

[0122] Preferably, in an embodiment of the present invention, the dynamic viscosity is expressed as:

[0123] μ(t) = C1·e kt + μ0 0 ≤ t ≤ t2,

[0124] Where μ(t) is the function of dynamic viscosity and time, μ0 is the initial viscosity of the slurry, t is the time, t2 is the time of slurry flow-solid phase change, k is the time-varying coefficient, and C1 is a constant.

[0125] Specifically, the measured dynamic viscosity via rheological experiments is:

[0126] ant1(t) = 32.51*exp(0.0027*t).

[0127] After setting the material property parameters, boundary conditions and initial values are determined. In this application, pressure boundary conditions are set. Considering the influence of gravity, the initial pressure value is set to -(z + H1), the pressure head is set to rho0 / (1000 [kg / m^2]*(-g_const)), the bottom and right infinite element domain boundaries are set as permeable layers, and the external water head is set to -2m. Then, concentration boundary conditions are set. The initial concentration value is set to 0, the concentration is c0, and the outflow boundary is set to 0.

[0128] Preferably, in one embodiment of the present invention, meshing the adjusted geometric model based on the local refinement method to obtain a penetration grouting diffusion simulation model includes:

[0129] Performing preliminary meshing on the adjusted geometric model to obtain a sparse mesh;

[0130] According to the simulation requirements of the geometric model, a key area in the sparse grid is identified, wherein the key area includes at least a grouting pipe area and an internal area of the porous medium;

[0131] The key area is meshed twice based on a local refinement method to obtain a penetration grouting diffusion simulation model.

[0132] For details, see Figure 2 , Figure 2 A schematic diagram of the meshing of a grouting geometry model in one embodiment of this application is shown. The model is meshed using user-controlled meshing, with free quadrilateral meshing and local refinement. Local refinement involves secondary mesh refinement of the area near the grouting pipe, with the mesh refinement region defined by a specified bounding box, r(0, 0.5*R1) and z(-0.5*H1, 0).

[0133] Preferably, in one embodiment of the present invention, solving the penetration grouting diffusion simulation model according to a transient solver to complete the simulation of the penetration grouting diffusion of the polyurethane in the porous medium to be injected includes:

[0134] According to the rheological equation of Newtonian fluid and the seepage motion equation, a partial differential equation corresponding to the infiltration grouting and diffusion process of the polyurethane in the porous medium to be injected is set;

[0135] Discretizing the time term in the partial differential equation using an implicit Euler backward difference method to obtain a discretized partial differential equation;

[0136] The discretized partial differential equation is input into a pre-built transient solver for solving, and the infiltration grouting diffusion process of the polyurethane in the porous medium is simulated by adjusting the number of iterations and the time step of the transient solver.

[0137] Specifically, a transient solver was used for the calculation, with a step size of 5 seconds and a computation time of 3600 seconds. It should be noted that during the simulation process, by assigning values to the coefficient-type partial differential equations built into the simulation software as needed, partial differential equations with various properties can be obtained. After assigning values to the coefficients of the equations, they can be solved numerically. The time term in the equations is discretized using the implicit Euler backward difference method, and the equations are solved using the nonlinear iterative modified damped Newton method.

[0138] Finally, the data is visualized to complete the permeation grouting diffusion process.

[0139] In addition, the present application also provides a method for determining the diffusion radius of spherical permeation grouting of polyurethane. In the initial stage of grouting, the influence of flow resistance on the slurry is more obvious, and the permeability gradually increases; when the flow rate gradually stabilizes, the slurry is in a pure flow state or a flow-plastic state, and its permeation process can be regarded as diffusion with a constant permeability; when the grouting process gradually progresses, the rheological properties of the slurry gradually change from the flow-solid phase transition stage to the solid state, and a slurry solidification circle gradually forms at the diffusion front. Affected by the grouting pressure, this solidification circle gradually spreads in the porous medium, and the permeability in the porous medium gradually decreases until it becomes 0. Therefore, the present application divides the slurry diffusion in the permeation process into three stages: permeation diffusion, stable grouting, and phase change solidification.

[0140] 1) Permeation diffusion stage

[0141] During the grouting time t, if the diffusion radius of the slurry is R, then the grouting volume is

[0142]

[0143] The grouting volume required during the grouting time t is equal to the slurry volume required for the slurry to flow through the pores in the diffusion area during this period. Then the grouting volume can also be expressed as:

[0144] Q = VA·t (18)

[0145] By combining (16) and (17), the pressure gradient in the polyurethane permeation area is obtained as:

[0146]

[0147] The pressure decay outside the slurry permeation front is much smaller than that inside the slurry permeation front. It can be considered that the pressure outside the slurry permeation front is constant, and the pressure at the front position is continuous with the external pressure p = p0. In the initial stage of grouting, affected by fluid inertia, the permeability in the porous medium changes with the slurry flow rate. Iberall derived the expression for the permeability of the porous medium based on the flow resistance model

[0148]

[0149] where Re is the Reynolds number, ρ is the slurry density, and δ is the initial pore diameter of the porous medium. By combining (17), (18), (20), and (21), the formation permeability can be expressed as

[0150]

[0151] Take the radius of the grouting pipe as r, and consider the boundary conditions of the grouting pressure of the slurry: when p = p0, L0 = r; when p = p1, L0 = R1. Among them, p1 and R1 are the pressure at the grouting point and the diffusion distance of the slurry at the grouting time t0, respectively. Combine (19) and (22), substitute the boundary conditions, and after separation of variables and integration, the diffusion control equation of permeation grouting considering the influence of permeability is obtained as follows:

[0152]

[0153] Among them, p0 is the constant pressure outside the slurry penetration front.

[0154] 2) Stable grouting stage

[0155] As the permeation grouting process gradually stabilizes, the slurry flow rate and the permeability K2 = K0 in the porous medium are constant values.

[0156] Consider the boundary conditions of the grouting pressure of the slurry: when p = p0, L0 = r; when p = p2, L0 = R2. Among them, p2 and R2 are the pressure at the grouting point and the diffusion distance of the slurry at the grouting time t1, respectively. Combine (19) and (22), and after separation of variables and integration, the control equation of the slurry diffusion radius is obtained as follows:

[0157]

[0158] 3) Phase change and solidification stage

[0159] When the grouting time reaches the phase change end time t0, the slurry enters the phase change and solidification stage. During the breakthrough process of the solidification circle of the slurry front, the polyurethane particles formed after solidification gradually fill the pores of the porous medium due to seepage, reducing its original permeability. As the slurry front forms a solidified layer again, the permeability of the porous medium decreases accordingly and gradually approaches 0.

[0160] The change in porosity is the main reason for the change in permeability. The change law of porosity during the grouting process is as follows

[0161]

[0162] Among them, φ0 is the porosity under the initial effective stress condition, φ r is the porosity of the porous medium measured under the condition of consolidated drainage, σ e is the average effective stress (MPa), and α is the compression coefficient (MPa -1 ). The Kozeny-Carman model is used to describe the change in permeability:

[0163]

[0164] Consider the grouting pressure boundary conditions: when p = p0, L0 = r; when p = p3, L0 = R3. Where p3 and R3 are the pressure at the grouting point and the diffusion distance of the slurry at the grouting time t2, respectively. By combining (19) and (22), separating the variables and integrating them, the slurry diffusion radius control equation is:

[0165]

[0166] Compared with the prior art, the embodiments of the present application have the following advantages:

[0167] (1) This application constructs a geometric model based on the actual physical structure and properties of the porous medium, which can more realistically reflect the complexity and irregularity of the porous medium, thereby improving the accuracy of the simulation; the physical field is established using the Richards equation and the porous medium dilute species transport equation. These two equations describe the unsaturated seepage and material transfer processes of the fluid in the porous medium, respectively, and can more accurately reflect the seepage and diffusion behavior of polyurethane in the porous medium.

[0168] (2) This application simulates the seepage and diffusion behavior of different polyurethane materials in porous media to evaluate the permeability, diffusivity and other properties of the materials, providing a basis for material selection and design.

[0169] (3) Through numerical simulation, this application can quickly evaluate the advantages and disadvantages of different grouting schemes or material schemes and improve decision-making efficiency.

[0170] Another embodiment of the present application provides a polyurethane penetration grouting diffusion simulation device. For details, see Figure 3 , Figure 3 The schematic diagram of the structure of the polyurethane penetration grouting diffusion simulation device provided in one embodiment of the present application includes the following modules: a construction module 11, an assignment module 12, a division module 13, and a calculation module 14, wherein

[0171] A construction module 11 is used to construct a geometric model of polyurethane penetration grouting and diffusion in the porous medium to be injected based on physical property data of the porous medium to be injected;

[0172] an assignment module 12, configured to establish a physical field of the geometric model using the Richards equation and the porous media dilute species transport equation, and adjust the geometric model according to material property parameters of the geometric model obtained from the physical field, wherein the physical field reflects the influence of the material properties of the polyurethane on the seepage and diffusion process;

[0173] A partitioning module 13 is configured to set boundary conditions and initial values for the adjusted geometric model, and perform mesh partitioning on the adjusted geometric model based on a local refinement method to obtain a permeation grouting diffusion simulation model.

[0174] A calculation module 14 is configured to solve the permeation grouting diffusion simulation model according to a transient solver to complete the simulation of the permeation grouting diffusion of the polyurethane in the porous medium to be injected.

[0175] Another embodiment of the present application provides a polyurethane permeation grouting diffusion simulation device, including a processor 21, a memory 22, and a computer program stored in the memory 22 and configured to be executed by the processor 21. When the processor 21 executes the computer program, the steps in the embodiments of the above polyurethane permeation grouting diffusion simulation method are implemented, such as Figure 1 the steps S1 to S4 described therein; or, when the processor 21 executes the computer program, the functions of each module in the above device embodiments are implemented, such as the construction module 11.

[0176] Exemplarily, the computer program can be divided into one or more modules. The one or more modules are stored in the memory 22 and executed by the processor 21 to complete the present application. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, and the instruction segments are used to describe the execution process of the computer program in the polyurethane permeation grouting diffusion simulation device. For example, the computer program can be divided into a construction module 11, an assignment module 12, a partitioning module 13, and a calculation module 14.

[0177] The processor 21 can be a central processing unit (CPU), or can also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The processor 21 is the control center of the polyurethane permeation grouting diffusion simulation device, and connects various parts of the entire polyurethane permeation grouting diffusion simulation device through various interfaces and lines.

[0178] The memory 22 can be used to store the computer programs and / or modules. By running or executing the computer programs and / or modules stored in the memory 22, and invoking the data stored in the memory 22, the processor 21 realizes various functions of the polyurethane permeation grouting diffusion simulation device. The memory 22 mainly includes a program storage area and a data storage area. Among them, the program storage area can store an operating system, application programs required for at least one function (such as a sound playback function, an image playback function, etc.); the data storage area can store data created according to the use of the mobile phone (such as audio data, phone book, etc.). In addition, the memory 22 can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, at least one magnetic disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0179] Among them, if the modules integrated in the polyurethane permeation grouting diffusion simulation device are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, to implement all or part of the processes in the above-mentioned embodiment methods of the present application, it can also be completed by instructing relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-mentioned various method embodiments can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file, or some intermediate form, etc. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a mobile hard disk, a magnetic disk, an optical disc, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0180] Those of ordinary skill in the art can understand that to implement all or part of the processes in the above-mentioned embodiment methods, it can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the above-mentioned method embodiments. Among them, the storage medium can be a magnetic disk, an optical disc, a read-only memory (ROM), or a random access memory (RAM), etc.

[0181] Accordingly, an embodiment of the present application provides a computer-readable storage medium, which includes a stored computer program. When the computer program runs, it controls the device where the computer-readable storage medium is located to execute the steps in the polyurethane permeation grouting diffusion simulation method in the above embodiment, such as Figure 1 the steps S1 to S4 described in

[0182] The above embodiments only represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the patent scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A simulation method for polyurethane permeation grouting diffusion, characterized in that, The method includes the following steps: Construct a geometric model of the infiltration grouting diffusion of polyurethane in the porous medium to be injected according to the physical property data of the porous medium to be injected; Establish a physical field of the geometric model by using the Richards equation and the dilute mass transfer equation of the porous medium, and adjust the geometric model according to the material property parameters of the geometric model obtained from the physical field, wherein the physical field reflects the influence of the material properties of the polyurethane on the seepage diffusion process; Set the boundary conditions and initial values of the adjusted geometric model, and perform mesh division on the adjusted geometric model based on the local refinement method to obtain an infiltration grouting diffusion simulation model; Solve the infiltration grouting diffusion simulation model according to the transient solver to complete the simulation of the infiltration grouting diffusion of the polyurethane in the porous medium to be injected; Wherein, the adjusting the geometric model according to the material property parameters of the geometric model obtained from the physical field includes: Construct a diffusion model based on the Newtonian fluid rheological equation and the seepage motion equation; Obtain the permeability function of the polyurethane in the porous medium to be injected in stages according to the diffusion model; Obtain the dynamic viscosity of the polyurethane in the process of infiltration grouting diffusion in the porous medium to be injected based on rheological experiments; Adjust the geometric model with the permeability function and the dynamic viscosity as the material property parameters of the geometric model; Wherein, the permeability function is expressed as: ， Among them, represents the permeability, represents the porosity, represents the pore diameter, represents the penetration time, represents the time when the flow resistance disappears, represents the slurry curing time, represents the void fraction, represents the slurry density, represents the radius of the porous medium, is the integral median value corresponding to the function of the dynamic viscosity and the penetration time, and is the porosity under the initial effective stress condition.

2. The polyurethane permeation grouting diffusion simulation method according to claim 1, wherein The dynamic viscosity is expressed as: ， wherein, is a function of dynamic viscosity and time, is the initial viscosity of the slurry, is the time, is the fluid-solid phase transition time of the slurry, is the time-varying coefficient, is a constant.

3. The polyurethane permeation grouting diffusion simulation method according to claim 1, characterized in that, In the constructing a geometric model of the infiltration grouting diffusion of polyurethane in the porous medium to be injected according to the physical property data of the porous medium to be injected, it includes: Two-dimensionalize the process of infiltration grouting diffusion of the polyurethane in the porous medium to be injected based on the cross-section method to obtain a two-dimensional model of infiltration grouting; Determine the geometric parameters of the two-dimensional model according to the physical property data of the porous medium to be injected; Construct a geometric model of the polyurethane in the porous medium to be injected based on the infinite source domain method and the geometric parameters.

4. The polyurethane permeation grouting diffusion simulation method according to claim 1, characterized in that, The performing mesh division on the adjusted geometric model based on the local refinement method to obtain an infiltration grouting diffusion simulation model includes: Perform preliminary mesh division on the adjusted geometric model to obtain a sparse mesh; Identify the key regions in the sparse mesh according to the simulation requirements of the geometric model, and the key regions at least include the grouting pipe region and the internal region of the porous medium; Perform secondary mesh encryption on the key regions based on the local refinement method to obtain an infiltration grouting diffusion simulation model.

5. The polyurethane permeation grouting diffusion simulation method according to claim 1, characterized in that The solving the infiltration grouting diffusion simulation model according to the transient solver to complete the simulation of the infiltration grouting diffusion of the polyurethane in the porous medium to be injected includes: Set up a partial differential equation corresponding to the process of infiltration grouting diffusion of the polyurethane in the porous medium to be injected according to the Newtonian fluid rheological equation and the seepage motion equation; Discretize the time term in the partial differential equation using the implicit Euler backward difference method to obtain a discretized partial differential equation; Input the discretized partial differential equation into a pre-built transient solver for solution, and simulate the permeation grouting diffusion process of the polyurethane in the porous medium by adjusting the number of iterations and time step of the transient solver.

6. A polyurethane permeation grouting diffusion simulation device, characterized in that It includes the following modules: A construction module, configured to construct a geometric model of the permeation grouting diffusion of the polyurethane in the porous medium to be injected according to the physical property data of the porous medium to be injected. An assignment module, configured to establish a physical field of the geometric model by using the Richards equation and the dilute mass transfer equation of the porous medium, and adjust the geometric model according to the material property parameters of the geometric model obtained from the physical field, wherein the physical field reflects the influence of the material properties of the polyurethane on the seepage diffusion process. A division module, configured to set the boundary conditions and initial values of the adjusted geometric model, and perform mesh division on the adjusted geometric model based on the local refinement method to obtain a permeation grouting diffusion simulation model. A calculation module, configured to solve the permeation grouting diffusion simulation model according to the transient solver to complete the simulation of the permeation grouting diffusion of the polyurethane in the porous medium to be injected. Wherein, adjusting the geometric model according to the material property parameters of the geometric model obtained from the physical field includes: Constructing a diffusion model based on the Newtonian fluid rheological equation and the seepage motion equation. Obtaining the permeability function of the polyurethane in different stages in the porous medium to be injected according to the diffusion model. Obtaining the dynamic viscosity during the permeation grouting diffusion process of the polyurethane in the porous medium to be injected based on rheological experiments. Adjusting the geometric model by using the permeability function and the dynamic viscosity as the material property parameters of the geometric model. Wherein, the permeability function is expressed as: ， Among them, represents the permeability, represents the porosity, represents the pore diameter, represents the penetration time, represents the time when the flow resistance disappears, represents the slurry curing time, represents the void fraction, represents the slurry density, represents the radius of the porous medium, is the integral median value corresponding to the function of the dynamic viscosity and the penetration time, and is the porosity under the initial effective stress condition.

7. A polyurethane permeation grouting diffusion simulation device, characterized in that, It includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, it implements the polyurethane permeation grouting diffusion simulation method according to any one of claims 1-5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the polyurethane permeation grouting diffusion simulation method according to any one of claims 1-5.

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