Unstable slurry diffusion process simulation method and system considering slurry-rock coupling effect

Abstract

The invention discloses an unsteady slurry diffusion process simulation method and system considering a slurry-rock coupling effect, and belongs to the technical field of rock mass engineering grouting, and the method comprises the following steps: step 1, defining basic assumptions of slurry and fractures; step 2, establishing a slurry flow control equation and a fracture deformation control equation based on basic assumptions of slurry and fractures; step 3, based on the slurry flow control equation and the fracture deformation control equation, establishing an unsteady slurry-rock coupling pressure control equation; 4, initial conditions, boundary conditions and grouting conditions are established based on basic assumptions of grout and fractures, and an unsteady grout diffusion model considering the grout-rock coupling effect is established in combination with an unsteady grout-rock coupling pressure control equation; and 5, carrying out numerical solution on the unstable slurry diffusion model by adopting a finite volume method. The method is suitable for grouting design and optimization in the fields of tunnel engineering, mine engineering, geological disaster prevention and control and the like, and theoretical support and technical guidance can be provided for engineering practice.

Description

Technical Field

[0001] The present invention belongs to the technical field of rock engineering grouting, and in particular relates to a method and system for simulating a non-steady-state slurry diffusion process taking into account a slurry-rock coupling effect. Background Art

[0002] Grouting technology is an important reinforcement and anti-seepage method in rock mass engineering, widely used in tunneling, mining, and geological disaster prevention. Grouting injects slurry into rock mass fissures, filling them and forming a consolidated mass, thereby improving the strength and stability of the rock mass and preventing groundwater seepage. However, the diffusion behavior of slurry in fractures during grouting is influenced by multiple factors, including the rheological properties of the slurry, the geometry of the fractures, the mechanical properties of the rock mass, grouting pressure instability, and the mechanical coupling effect between the slurry and the rock mass. Traditional grouting models are often based on simplified assumptions and fail to accurately describe the diffusion behavior of slurry in fractures. The rheological properties of slurries are a key factor in grouting theory research. Traditional models typically assume that the slurry is a Newtonian fluid, ignoring the slurry's yield stress and the time-varying properties of its yield stress and viscosity. However, cement-water glass rapid-setting grouts commonly used in practical engineering exhibit distinct non-Newtonian fluid properties, with their yield stress and viscosity varying significantly over time. This characteristic makes the diffusion behavior of slurry in fractures more complex, making it difficult to accurately describe the traditional Newtonian fluid model. In addition, the geometry of the fracture and the mechanical properties of the rock mass also have a significant impact on the slurry diffusion behavior. Traditional grouting models usually assume that the fracture aperture is constant and ignore the effect of slurry pressure on the fracture aperture. However, during the actual grouting process, slurry pressure can cause the fracture aperture to change, thereby affecting the diffusion range and pressure distribution of the slurry. This coupling effect between slurry and rock mass is often ignored in traditional models, resulting in large deviations between simulation results and actual engineering.

[0003] In recent years, with the continuous development of grouting technology, the non-Newtonian fluid properties of slurries, the elastic deformation of fractures, and the slurry-rock coupling effect have gradually become research hotspots. Some scholars have proposed grouting models that consider the time-varying properties of slurry yield stress and viscosity. However, these models are mostly based on steady-state assumptions and ignore the non-steady-state effects of slurry pressure changes over time.

[0004] Therefore, it is necessary to design a simulation method and system for the unsteady slurry diffusion process that takes into account the slurry-rock coupling effect to address the above problems. Summary of the Invention

[0005] The purpose of the present invention is to address the problem that the model is based on the steady-state assumption and ignores the non-steady-state effect of slurry pressure changing with time. A method and system for simulating the non-steady-state slurry diffusion process considering the slurry-rock coupling effect is provided. Based on the fracture flow theory, combined with slurry flow, fracture deformation and non-steady-state effects, a slurry diffusion model in fractured rock mass is constructed, and numerically solved by the finite volume method (FVM). It can accurately simulate the slurry diffusion process in the fracture, predict the slurry pressure distribution, fracture aperture changes, and capture the slurry diffusion range at all times.

[0006] According to one aspect of the present specification, a method for simulating an unsteady-state slurry diffusion process taking into account the slurry-rock coupling effect is provided, comprising:

[0007] Based on fracture flow theory, define the basic assumptions of slurry and fractures;

[0008] Based on the basic assumptions of slurry and fractures, the governing equations of slurry flow and fracture deformation are established;

[0009] Based on the slurry flow control equation and the fracture deformation control equation, the unsteady slurry-rock coupling pressure control equation is established;

[0010] Based on the basic assumptions of slurry and fractures, initial conditions, boundary conditions, and grouting conditions are established. Combined with the unsteady slurry-rock coupling pressure control equation, an unsteady slurry diffusion model considering the slurry-rock coupling effect is constructed.

[0011] The finite volume method is used to numerically solve the unsteady slurry diffusion model to simulate the unsteady slurry diffusion process considering the slurry-rock coupling effect.

[0012] Furthermore, basic assumptions about grout and fractures are defined, including:

[0013] (1) Assume that the slurry is an incompressible, homogeneous, isotropic Bingham fluid;

[0014] (2) Assume that the slurry flow velocity on the upper and lower side walls of the fracture is 0;

[0015] (3) Assuming that the slurry diffuses only in the cracks;

[0016] (4) Assume that the cracks are distributed horizontally;

[0017] (5) Assume that the movement mode of slurry in the fracture is laminar flow;

[0018] (6) Assume that the rock mass on both sides of the crack undergoes only elastic deformation;

[0019] (7) Assume that the pressure at the slurry diffusion front is always equal to the static pressure.

[0020] Furthermore, the slurry flow control equation and the fracture deformation control equation are established, including:

[0021] The slurry flow control equation is expressed as:

[0022]

[0023] in, represents the average flow of slurry diffusion along the crack direction, b represents the crack opening, represents the time-varying function of slurry viscosity, represents the real variable function of slurry yield stress, represents the slurry pressure gradient, represents the critical pressure gradient for Bingham fluid to flow;

[0024] The crack deformation control equation is expressed as:

[0025]

[0026] Where b0 is the initial crack opening, P is the slurry pressure, and P s is the crack deformation threshold pressure, K n is the normal elastic coefficient, where K n =D / E, D is the grouting influence range, and E is the elastic modulus of rock mass.

[0027] Furthermore, the unsteady-state magma-rock coupling pressure control equation is established, including:

[0028]

[0029] in, is the distance between any position in the crack and the grouting port, is the time rate of change of slurry pressure at any position in the fracture, is the rate of change along the slurry radiation diffusion direction, represents the slurry flow rate at any position in the fracture, where Indicates the crack opening, Indicates the slurry flow rate.

[0030] Furthermore, the initial conditions, boundary conditions and grouting volume conservation conditions are established, including:

[0031] The pressure at each position of the crack at the initial moment is the crack hydrostatic pressure;

[0032] At the grouting port, the grouting pressure is set as the boundary condition, and at the slurry diffusion front, the fracture hydrostatic pressure is set as the boundary condition;

[0033] During the process of slurry displacing fractured media, the volume of slurry injected from the grouting port and the volume of slurry retained in the fracture are set to be conservative.

[0034] Furthermore, the finite volume method is used to numerically solve the unsteady slurry diffusion model, including:

[0035] Polar coordinate system is used to mesh and spatially discretize the computational domain of the unsteady slurry diffusion model.

[0036] Discretize the slurry flow control equation and the unsteady slurry-rock coupling pressure control equation, and construct discrete equations;

[0037] The grouting volume conservation condition is discretized to obtain the real-time representation of the slurry diffusion front radius;

[0038] The slurry reaction degree time at the grid space nodes within the slurry range is captured by spatial mapping;

[0039] The pressure and crack aperture distributions are iteratively modified until the convergence conditions are met, and finally the slurry pressure distribution, crack aperture change and slurry diffusion range are obtained.

[0040] According to one aspect of the present specification, a system for simulating an unsteady-state slurry diffusion process taking into account a slurry-rock coupling effect is provided, comprising:

[0041] Basic assumption setting module, used to define the basic assumptions of slurry and fractures based on fracture flow theory;

[0042] A control equation establishment module is used to establish the slurry flow control equation and the fracture deformation control equation based on the basic assumptions of slurry and fractures;

[0043] The coupling control equation establishment module is used to establish the unsteady-state slurry-rock coupling pressure control equation based on the slurry flow control equation and the fracture deformation control equation;

[0044] The diffusion model establishment module is used to establish initial conditions, boundary conditions, and grouting conditions based on the basic assumptions of slurry and fractures. It combines the unsteady slurry-rock coupling pressure control equation to build an unsteady slurry diffusion model that considers the slurry-rock coupling effect.

[0045] The model solving module is used to numerically solve the unsteady slurry diffusion model using the finite volume method, and to simulate the unsteady slurry diffusion process considering the slurry-rock coupling effect.

[0046] According to one aspect of the present specification, an electronic device is provided, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect are implemented.

[0047] According to one aspect of the present specification, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect are implemented.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] 1. By defining the basic assumptions of slurry and fractures and establishing the unsteady-state slurry-rock coupled pressure control equation, the present invention can more comprehensively consider the temporal changes of slurry pressure and the dynamic adjustment of fracture aperture, thereby more accurately describing the unsteady-state effects of slurry diffusion.

[0050] 2. The present invention can accurately simulate the diffusion process of slurry in cracks by building a non-steady-state slurry diffusion model that takes into account the slurry-rock coupling effect. The finite volume method is used to numerically solve the non-steady-state slurry diffusion model, predict the slurry pressure distribution, the change in crack aperture, and capture the slurry diffusion range at all times. It can efficiently and accurately simulate the diffusion process of slurry in cracks, significantly improving the calculation efficiency. In addition, the present invention can provide theoretical support and technical guidance for engineering practice, optimize grouting parameters, improve grouting effects and engineering safety, reduce engineering costs, and significantly improve the scientificity and reliability of engineering design. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0052] Figure 1 Calculation flow chart of the overall method of an embodiment of the present invention;

[0053] Figure 2 Schematic diagram of force analysis of slurry flow in cracks in an embodiment of the present invention;

[0054] Figure 3 A schematic diagram of crack opening driven by grouting pressure and a curve diagram of crack opening varying with grouting pressure in an embodiment of the present invention;

[0055] Figure 4 Schematic diagram of crack opening and closing under unsteady grouting pressure in an embodiment of the present invention;

[0056] Figure 5 A schematic diagram of control volume establishment and meshing according to an embodiment of the present invention;

[0057] Figure 6 Schematic diagram of the time-space mapping strategy for slurry reaction degree in an embodiment of the present invention;

[0058] Figure 7 Graphs showing the slurry diffusion front radius curve and the slurry flow velocity time-varying curve of the grouting port under different working conditions in an embodiment of the present invention;

[0059] Figure 8 Schematic diagram of the distribution of slurry pressure and crack aperture along the grouting process under different working conditions at a grouting time of 10s in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0061] like Figure 1 As shown, an embodiment of the present invention provides a method for simulating an unsteady-state slurry diffusion process taking into account the slurry-rock coupling effect, comprising: Step 1, based on the fracture flow theory, defining the basic assumptions of slurry and fractures. Step 2, based on the basic assumptions of slurry and fractures, establishing the slurry flow control equation and the fracture deformation control equation, and then establishing the unsteady-state slurry-rock coupling pressure control equation. Step 3, based on the basic assumptions of slurry and fractures, establishing initial conditions, boundary conditions and grouting body conditions, combining the unsteady-state slurry-rock coupling pressure control equation, and building an unsteady-state slurry diffusion model taking into account the slurry-rock coupling effect. Step 4, using the finite volume method to numerically solve the unsteady-state slurry diffusion model to achieve the simulation of the unsteady-state slurry diffusion process taking into account the slurry-rock coupling effect.

[0062] Specifically, the embodiment of the present invention also provides the specific content of step 1: 1. Assume that the slurry is an incompressible, homogeneous, isotropic Bingham fluid. 2. Assume that the upper and lower side walls of the crack meet the no-slip boundary condition, that is, the flow velocity of the slurry on the upper and lower side walls of the crack is 0. 3. Ignore the slurry loss caused by the slurry penetrating into the rock mass on both sides of the crack, and assume that the slurry only diffuses in the crack. 4. The cracks are assumed to be horizontally distributed, and their initial crack openings are uniformly distributed. The influence of gravity on the grouting diffusion process is not considered, and it is assumed that the movement mode of the slurry in the cracks is laminar flow. 5. Assume that the rock mass on both sides of the crack only undergoes elastic deformation. 6. In the process of slurry diffusion, the flow of the slurry dispersing medium is not considered, that is, it is assumed that the pressure at the slurry diffusion front is always equal to the static pressure.

[0063] Specifically, the embodiment of the present invention also provides the specific content of step 2: Figure 2-3As shown in the figure, the slurry flow control equation and the fracture deformation control equation are introduced respectively, as shown in the figure. Figure 4 As shown in the figure, the unsteady-state slurry-rock coupling pressure control equation is established. The time-varying characteristics of the slurry yield stress and viscosity and the influence of the slurry pressure on the fracture aperture are considered. At the same time, the unsteady-state characteristics of the slurry pressure changing with time, which leads to the dynamic adjustment of the fracture aperture, are considered as follows:

[0064] Step 2.1, establish the slurry flow control equation:

[0065] (1)

[0066] in, represents the average flow velocity of the slurry diffusing along the crack direction; b represents the crack opening; represents the time-varying function of slurry viscosity; represents the real variable function of slurry yield stress; represents the slurry pressure gradient; The critical pressure gradient at which a Bingham fluid begins to flow is primarily controlled by the yield stress of the slurry. When the pressure gradient along a fracture is less than this critical pressure gradient, the slurry is considered to be non-flowing.

[0067] Step 2.2: Establish the crack deformation control equation:

[0068] (2)

[0069] Where b0 is the initial crack opening; P is the slurry pressure; P s is the crack deformation threshold pressure; K n =D / E, which represents the normal elastic coefficient, D is the grouting influence range, and E is the rock mass elastic modulus.

[0070] Step 2.3: Establish the unsteady-state magma-rock coupling pressure control equation:

[0071] (3)

[0072] in, is the distance between any position in the crack and the grouting port, is the time rate of change of slurry pressure at any position in the fracture, is the rate of change (gradient) along the slurry radiation diffusion direction, represents the slurry flow rate at any position in the fracture, where Indicates the crack opening, Indicates the slurry flow rate.

[0073] Specifically, the embodiment of the present invention further provides the specific content of step 3:

[0074] Step 3.1: Establish initial conditions, boundary conditions, and grouting volume conservation conditions:

[0075] 1. At the initial moment, the crack is filled with water, and the pressure at each position is the hydrostatic pressure of the crack :

[0076] (4)

[0077] Where r represents the position (with the grouting port as the coordinate origin), t represents the grouting time, and formula (4) represents the initial time t=0.

[0078] 2. At the grouting port At the grouting point, the pressure is used to control the grouting, that is, the grouting pressure is set as the boundary condition at the grouting port, and the injection pressure It is known that its value can change with time, but at the initial moment it remains consistent with the hydrostatic pressure in the fracture:

[0079] (5)

[0080] in, is the grouting port radius, Indicates grouting time, Indicates the injection pressure at the grouting port when grouting time t=0.

[0081] 3. At the slurry diffusion front (i.e. slurry-water interface), the influence of water flow is not considered, that is, the position is always the fracture hydrostatic pressure :

[0082] (6)

[0083] in, Represents the radius of the slurry diffusion front.

[0084] 4. During the process of slurry displacing fractured media, the diffusion range of the slurry in the fracture changes with time. It is necessary to satisfy the conservation of the slurry volume injected from the grouting start time to a certain time and the slurry volume retained in the fracture:

[0085] (7)

[0086] in, It represents the change of grouting volume with grouting time t, The crack at the grouting port is opened. is the slurry flow rate at the grouting port.

[0087] Step 3.2: Give the model parameters that need to be calculated. In order to realize the non-steady-state effect of slurry diffusion during the grouting process, define the grouting port to adopt the sinusoidal pulse pressure grouting form. The analytical expression of the grouting pressure at the grouting port is:

[0088] (8)

[0089] Among them, f z , P1 and P2 represent the oscillation frequency, average pressure and amplitude pressure of the sinusoidal pulse pressure respectively; t up represents the grouting pressure rise time. Six working conditions were designed using three different rock fracture apertures and two different grouting pressure pulse frequencies. The model parameters are summarized in Table 1, and the calculation conditions are summarized in Table 2.

[0090] Table 1 Model parameters under all working conditions

[0091]

[0092] Table 2 Calculation conditions

[0093]

[0094] Specifically, the embodiment of the present invention further provides the specific content of step 4:

[0095] Step 4.1, such as Figure 5 As shown, the computational area is divided into grids and the polar coordinate system is used for spatial discretization:

[0096] Polar coordinates are used for grid division, with a time step of 0.01s and a space step of 0.01m. Each grid cell corresponds to an independent control volume. The boundary of each control volume is defined by adjacent grid nodes and their connecting segments, and a staggered grid arrangement is used, that is, the crack opening data b is defined as i and slurry flow velocity data v i Stored at the control volume boundary (i.e., grid node), the slurry pressure P i The data is stored in the center of the control volume. Through this setting, n grid space nodes and n-1 pressure space nodes can be formed, and the grid space nodes within the slurry diffusion front are defined as effective space nodes, and the pressure space nodes are defined as effective pressure space nodes.

[0097] In terms of time advancement, a progressive time-stepping strategy is adopted, defining the superscript of the physical quantity as the time step and the subscript as the space step. This approach effectively captures the dynamic behavior and characteristics of the fluid, accurately simulating complex physical processes while ensuring numerical stability.

[0098] Step 4.2: Discretize the slurry flow control equation and the unsteady slurry-rock coupled pressure control equation and construct the discrete equations:

[0099] The slurry flow control equation (1) and the unsteady slurry-rock coupling pressure control equation (3) in the simultaneous model, and the spatial mapping of the slurry reaction time, can be obtained as the pressure-velocity coupling control equation:

[0100] (9)

[0101] in, is the normal elastic coefficient of rock, Time-space mapping showing the extent of grout reaction at different locations within the fracture.

[0102] Formula (9) can be used to solve the slurry pressure within the slurry diffusion range. According to the divided control volume and grid, the left side of Formula (9) is discretized to obtain:

[0103] (10)

[0104] The slurry reaction time at all valid grid space nodes at time step j is recorded as , discretizing the right side of equation (10) yields:

[0105] (11)

[0106] The crack opening b, slurry viscosity u and yield stress τ0 all change with time along the slurry radiation diffusion direction. Combining equations (10) and (11) yields the algebraic equation:

[0107] (12)

[0108] The number of valid grid space nodes within the slurry diffusion front range at the current time step j is defined as , which can be used to store slurry flow rate and fracture opening data; after adopting staggered grid arrangement, -1 pressure space node, recorded as the number of effective pressure space nodes = -1, where valid grid space nodes The quantitative solution will be introduced in detail in step 3. For each effective pressure space node i (i=1,2,……, ), can satisfy the above algebraic equation, so the coefficient matrix can be extracted from formula (12) and the right vector , where the assembly coefficient matrix Can be assembled into The order banded symmetric matrix can be expressed as:

[0109] (13)

[0110] Assemble the elements of the coefficient matrix and They can be expressed as:

[0111] (14)

[0112] (15)

[0113] Right vector The result obtained by the source term and the pressure at the previous time step The vector composition format and its elements can be expressed as:

[0114] (16)

[0115] (17)

[0116] (18)

[0117] (19)

[0118] In the formula and They are the grouting pressure at the grouting port and the hydrostatic pressure at the slurry diffusion front, where the grouting port pressure is a known parameter that changes with time, and the hydrostatic pressure Known. In summary, the discrete equation can be formed:

[0119] (20)

[0120] Step 4.3: Discretize the grouting volume conservation condition to obtain a real-time representation of the slurry diffusion front radius; when calculating time step j after completing the calculation of time step j-1, the data at the first pressure space node of time step j-1 needs to be used. Calculate the discrete form of formula (1) to obtain the slurry flow rate at the grouting port at the current time step:

[0121] (twenty one)

[0122] The discrete equation of the total slurry flow at the jth time step is:

[0123] (twenty two)

[0124] The number of spatial nodes within the slurry diffusion front when entering the jth time step calculation is an unknown quantity. In order to calculate this value, it is necessary to solve Equation (22) by a cumulative method. Assuming that the cumulative amount of slurry in the crack is obtained by k times of calculation, the amount is:

[0125] (twenty three)

[0126] until Stop accumulation and get the number of valid grid space nodes =k-1, and the number of effective pressure space nodes can be obtained at the same time , thus the slurry diffusion front radius can be obtained:

[0127] (twenty four)

[0128] Step 4.4, such as Figure 6 As shown, the slurry reaction degree time at the grid space nodes within the slurry range is captured by spatial mapping;

[0129] It is known that a check valve is added at the grouting port to prevent slurry backflow, that is, the slurry flow rate at each time step is not less than 0, and the slurry flow rate from the grouting port into the crack at each time step is recorded ,set up is the grouting port radius, then:

[0130] (25)

[0131] Since the spatial distribution of crack openings is different, it is impossible to solve Equation (25) directly by integration. The diffusion radius can be obtained by using a successive accumulation method similar to that in Equation (23): Adjacent grid space nodes near the grouting port :

[0132] (26)

[0133] Obtain the diffusion range of the slurry entering the crack at different times :

[0134] (27)

[0135] (28)

[0136] in, It represents the total amount of slurry discharged from time step j-l+1 to time step j and the effective grid nodes 1~ The difference in the total amount of slurry within the grid space node ~ The remaining slurry within the range of +1. Further, the slurry range of the effective grid space nodes can be captured one by one starting from the grouting port position, and then the corresponding slurry reaction time can be calculated by linear interpolation method. (i=1,2,…, ):

[0137] (29)

[0138] Step 4.5: Iterate and modify the pressure and crack aperture distribution until the convergence condition is met. Finally, output the slurry pressure distribution, crack aperture change, and slurry diffusion range.

[0139] Since it is impossible to directly obtain the fracture opening distribution vector corresponding to time step j, it is necessary to iteratively update the number of effective pressure space nodes and the pressure distribution vector by adjusting the fracture opening distribution. Specifically, when entering the jth time step calculation, first the fracture opening distribution vector of the previous time step j-1 is obtained. As the initial iteration value, denoted as , the effective grid space nodes are calculated by equations (22) and (23) and the number of effective pressure space nodes , and the assembly matrix is ​​obtained according to the number of effective pressure space nodes and the right vector (The second superscript indicates the number of iterations). Then use formula (20) to calculate the pressure distribution vector in the first iteration process: :

[0140] (30)

[0141] Furthermore, the pressure distribution vector And Goodman model (2) to correct the crack opening of the next iteration Since a staggered grid arrangement is used in the discretization process, when performing crack correction, the pressure data at the effective grid space node must be calculated based on the data of its adjacent effective pressure space node. If the pressure distribution between adjacent effective space nodes satisfies the linear relationship, then the grid node The pressure at can be expressed as:

[0142] (31)

[0143] After recalculating the effective grid space nodes and effective pressure space nodes using the iterative crack opening distribution vector, the pressure distribution vector along the path of the next iteration is calculated again using formula (30): Repeat the above steps until the error between the two results before and after the nth iteration falls within an acceptable range, at which point the iteration is stopped. The final result is the pressure and crack opening distribution along the current time step. The relative error of pressure and the relative error of crack opening distribution between the two iteration results are defined as and :

[0144] (32)

[0145] (33)

[0146] in, and are expressed as the difference vector formed by the two iterations before and after -norm. When and When , it can be considered that the convergence condition is met, and finally the pressure and crack opening distribution along the j-th time step as well as the number of effective grid and pressure space nodes are output. The slurry diffusion front radius at the j-th time step is obtained by formula (24).

[0147] Step 4.6: When entering the next time step, repeat steps 4.1 to 4.5 until the calculation end time is reached. The program automatically stops the calculation and outputs the results.

[0148] Specifically, the embodiment of the present invention also provides the specific content of step 5. According to the calculation results of all the above steps, the slurry diffusion front radius curve and the slurry flow rate curve of the grouting port under various working conditions can be finally obtained, such as Figure 7 As shown in the figure, the grouting pressure and crack opening distribution curves along the grouting process at a grouting time of 10s are shown in the figure. Figure 8 shown.

[0149] The implementation of each embodiment of the present invention is based on programmed processing performed by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functionalities of each embodiment of the present invention are packaged into various modules. Based on this reality, and in addition to the aforementioned embodiments, an embodiment of the present invention provides a system for simulating an unsteady slurry diffusion process that considers magma-rock coupling effects. This system is used to implement a method for simulating an unsteady slurry diffusion process that considers magma-rock coupling effects, as described in the aforementioned method embodiments.

[0150] The system includes: a basic assumption setting module, which is used to define the basic assumptions of slurry and fractures based on fracture flow theory; a control equation establishment module, which is used to establish the slurry flow control equation and the fracture deformation control equation based on the basic assumptions of slurry and fractures; a coupling control equation establishment module, which is used to establish the unsteady-state slurry-rock coupling pressure control equation based on the slurry flow control equation and the fracture deformation control equation; a diffusion model establishment module, which is used to establish initial conditions, boundary conditions and grouting body conditions based on the basic assumptions of slurry and fractures, and to build an unsteady-state slurry diffusion model considering the slurry-rock coupling effect in combination with the unsteady-state slurry-rock coupling pressure control equation; a model solving module, which is used to numerically solve the unsteady-state slurry diffusion model using the finite volume method, so as to realize the simulation of the unsteady-state slurry diffusion process considering the slurry-rock coupling effect.

[0151] The embodiment of the present invention provides a system for simulating the unsteady-state slurry diffusion process that takes into account the slurry-rock coupling effect. In the prior art, the model is based on a steady-state assumption and ignores the unsteady-state effect of the slurry pressure changing with time. The system adopts several modules and, based on the fracture flow theory, combines slurry flow, fracture deformation, and unsteady-state effects to construct a slurry diffusion model in a fractured rock mass. The model is numerically solved using the finite volume method (FVM). This system can accurately simulate the slurry diffusion process in the fracture, predict the slurry pressure distribution, fracture aperture changes, and constantly capture the slurry diffusion range.

[0152] Based on the same inventive concept as the aforementioned embodiment, an embodiment of the present invention further provides an electronic device, including a memory and a processor, wherein the memory is used to store computer-executable instructions, and the processor is used to execute computer-executable instructions, thereby implementing a method for simulating a non-steady-state slurry diffusion process taking into account the slurry-rock coupling effect as proposed in the aforementioned embodiment.

[0153] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When executed by a processor, this program overcomes the problem of neglecting the non-steady-state effect of time-varying slurry pressure in traditional models. It can efficiently and accurately simulate the diffusion process of slurry in fractures, significantly improving computational efficiency. The program is applicable to grouting design and optimization in fields such as tunnel engineering, mining engineering, and geological disaster prevention and control. It can provide theoretical support and technical guidance for engineering practice, optimize grouting parameters, improve grouting effects and engineering safety, reduce engineering costs, and significantly enhance the scientific nature and reliability of engineering design.

[0154] The storage medium can be any non-volatile storage device such as a hard disk, a solid-state drive, a flash drive, an optical disk, etc., which is used to store computer program code and necessary data files. The stored computer program includes: a basic assumption setting module, a control equation establishment module, a coupled control equation establishment module, a diffusion model establishment module, and a model solving module.

[0155] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and is susceptible to numerous variations. Any simple modifications, equivalent variations, and modifications to the above specific embodiments based on the technical essence of the present invention shall be deemed to fall within the scope of protection of the present invention.

Claims

1. A method for simulating the unsteady slurry diffusion process considering the slurry-rock coupling effect, characterized in that: include: Based on fracture flow theory, define the basic assumptions of slurry and fractures; Based on the basic assumptions of slurry and fractures, the governing equations of slurry flow and fracture deformation are established; Based on the slurry flow control equation and the fracture deformation control equation, the unsteady slurry-rock coupling pressure control equation is established; Based on the basic assumptions of slurry and fractures, initial conditions, boundary conditions, and grouting conditions are established. Combined with the unsteady slurry-rock coupling pressure control equation, an unsteady slurry diffusion model considering the slurry-rock coupling effect is constructed. The finite volume method is used to numerically solve the unsteady slurry diffusion model to simulate the unsteady slurry diffusion process considering the slurry-rock coupling effect.

2. The method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect according to claim 1, characterized in that: Basic assumptions defining grout and fractures include: (1) Assume that the slurry is an incompressible, homogeneous, isotropic Bingham fluid; (2) Assume that the slurry flow velocity on the upper and lower side walls of the fracture is 0; (3) Assuming that the slurry diffuses only in the cracks; (4) Assume that the cracks are distributed horizontally; (5) Assume that the movement mode of slurry in the fracture is laminar flow; (6) Assume that the rock mass on both sides of the crack undergoes only elastic deformation; (7) Assume that the pressure at the slurry diffusion front is always equal to the static pressure.

3. The method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect according to claim 1, characterized in that: Establish the slurry flow control equation and fracture deformation control equation, including: The slurry flow control equation is expressed as: , in, represents the average flow of slurry diffusion along the crack direction, b represents the crack opening, represents the time-varying function of slurry viscosity, represents the real variable function of slurry yield stress, represents the slurry pressure gradient, represents the critical pressure gradient for Bingham fluid to flow; The crack deformation control equation is expressed as: , Where b0 is the initial crack opening, P is the slurry pressure, and P s is the crack deformation threshold pressure, K n is the normal elastic coefficient, where K n =D / E, D is the grouting influence range, and E is the elastic modulus of rock mass.

4. The method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect according to claim 1, characterized in that: Establish the unsteady-state magma-rock coupling pressure control equation, including: , in, is the distance between any position in the crack and the grouting port, is the time rate of change of slurry pressure at any position in the fracture, is the rate of change along the slurry radiation diffusion direction, represents the slurry flow rate at any position in the fracture, where Indicates the crack opening, Indicates the slurry flow rate.

5. The method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect according to claim 1, characterized in that: Establish initial conditions, boundary conditions, and grouting volume conservation conditions, including: The pressure at each position of the crack at the initial moment is the crack hydrostatic pressure; At the grouting port, the grouting pressure is set as the boundary condition, and at the slurry diffusion front, the fracture hydrostatic pressure is set as the boundary condition; During the process of slurry displacing fractured media, the volume of slurry injected from the grouting port and the volume of slurry retained in the fracture are set to be conservative.

6. The method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect according to claim 1, characterized in that: The finite volume method is used to numerically solve the unsteady slurry diffusion model, including: Polar coordinate system is used to mesh and spatially discretize the computational domain of the unsteady slurry diffusion model. Discretize the slurry flow control equation and the unsteady slurry-rock coupling pressure control equation, and construct discrete equations; The grouting volume conservation condition is discretized to obtain the real-time representation of the slurry diffusion front radius; The slurry reaction degree time at the grid space nodes within the slurry range is captured by spatial mapping; The pressure and crack aperture distributions are iteratively modified until the convergence conditions are met, and finally the slurry pressure distribution, crack aperture change and slurry diffusion range are obtained.

7. A simulation system for unsteady slurry diffusion process considering slurry-rock coupling effect, characterized by: include: Basic assumption setting module, used to define the basic assumptions of slurry and fractures based on fracture flow theory; A control equation establishment module is used to establish the slurry flow control equation and the fracture deformation control equation based on the basic assumptions of slurry and fractures; The coupling control equation establishment module is used to establish the unsteady-state slurry-rock coupling pressure control equation based on the slurry flow control equation and the fracture deformation control equation; The diffusion model establishment module is used to establish initial conditions, boundary conditions, and grouting conditions based on the basic assumptions of slurry and fractures. It combines the unsteady slurry-rock coupling pressure control equation to build an unsteady slurry diffusion model that considers the slurry-rock coupling effect. The model solving module is used to numerically solve the unsteady slurry diffusion model using the finite volume method, and to simulate the unsteady slurry diffusion process considering the slurry-rock coupling effect.

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for simulating an unsteady-state slurry diffusion process considering the slurry-rock coupling effect according to any one of claims 1 to 6 are implemented.

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