A method and system for calculating the penetration and diffusion radius of grouting outside the tunnel pressure relief drainage ring

Abstract

The present invention relates to the field of tunnel engineering technology, and in particular to a method and system for calculating the seepage diffusion radius of grouting outside the tunnel pressure relief drainage ring. The method comprises the following steps: constructing a partial differential equation for the porosity of a sand layer; obtaining a function expression for the porosity of the sand layer based on the partial differential equation; establishing a grouting positive pressure spatial distribution equation for slurry seepage diffusion; constructing a drainage negative pressure spatial distribution equation for slurry seepage diffusion; and obtaining a calculation expression for the seepage diffusion radius of grouting outside the ring based on the grouting positive pressure spatial distribution equation and the drainage negative pressure spatial distribution equation. The present invention substitutes relevant grouting parameters and geological parameters into the calculation expression to obtain the theoretical value of the seepage diffusion radius of grouting outside the ring under pressure relief drainage conditions, and takes into account the influence of pressure relief drainage factors on the seepage diffusion of slurry in actual engineering, reduces errors, solves the problem of blindness in the control of grouting time and grouting amount in engineering applications, and provides a reference for practical applications.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel engineering, and in particular to a method and system for calculating the penetration and diffusion radius of grouting outside a tunnel pressure relief drainage ring. Background Art

[0002] In the rapid development of modern transportation networks, tunnels, as key buildings that pass through complex geological structures, have attracted widespread attention for their long-term operational safety. As the completion time increases, problems such as slight deformation and water leakage will inevitably occur in the tunnel structure. These problems not only affect the main structure of the tunnel and weaken its bearing capacity, but are also directly related to the smoothness and safety of traffic. In order to solve the above problems, the tunnel outer ring grouting reinforcement technology came into being and became an important means to improve the stability and durability of the tunnel structure.

[0003] The tunnel ring grouting reinforcement technology uses a precisely designed grouting hole or drilling system to inject the prepared slurry into the soil outside the tunnel ring under controlled pressure. During the penetration and solidification process, the slurry can significantly improve the physical and mechanical properties of the soil, such as increasing density, enhancing impermeability and reducing deformation, thereby achieving the purpose of reinforcing the soil around the tunnel, alleviating tunnel deformation and blocking the leakage path. However, under the geological conditions of water-rich sand layers, the mechanism of slurry penetration and diffusion is particularly complex. In particular, how to achieve effective pressure relief and drainage while ensuring that the grouting pressure does not damage the tunnel structure, and accurately predict and control the penetration and diffusion radius of the slurry, has become a difficulty and hot spot in current research.

[0004] Therefore, a tunnel pressure relief drainage ring grouting permeation and diffusion model is established according to the characteristics of water-rich sand layers. The flow law, pressure transmission mechanism and consolidation and hardening process of slurry in complex geological environments are theoretically analyzed, and the model parameters are verified and optimized by combining field tests and numerical simulation technology. On this basis, a scientific and reasonable permeation and diffusion radius calculation method is proposed, which has important reference value for guiding the design of actual engineering grouting schemes, optimizing grouting parameters, improving reinforcement effects and ensuring long-term safe operation of tunnels. Summary of the invention

[0005] In view of the defects in the prior art, the present invention provides a method and system for calculating the penetration and diffusion radius of grouting outside the tunnel pressure relief drainage ring.

[0006] In order to achieve the above-mentioned purpose, in the first aspect, the present invention provides a method for calculating the seepage and diffusion radius of grouting outside the tunnel pressure relief drainage ring, the method comprising the following steps: constructing a partial differential equation for the porosity of the sand layer; obtaining a function expression for the porosity of the sand layer based on the partial differential equation; establishing a spatial distribution equation for the grouting positive pressure of the slurry seepage and diffusion; constructing a spatial distribution equation for the drainage negative pressure of the slurry seepage and diffusion; and obtaining a calculation expression for the seepage and diffusion radius of grouting outside the ring based on the spatial distribution equation for the grouting positive pressure and the spatial distribution equation for the drainage negative pressure. The present invention proposes a method for calculating the seepage diffusion radius of outer-annular grouting, obtains relevant grouting parameters and geological parameters, substitutes them into the calculation expression to obtain the theoretical value of the seepage diffusion radius of outer-annular grouting under the condition of pressure relief and drainage, and takes into account the influence of pressure relief and drainage factors on the seepage and diffusion of slurry in actual projects, so that the result is more in line with reality, reduces the error between theory and practice, and solves the problem of blindness in controlling the grouting time and grouting amount in the grouting process due to the inability to observe the real-time diffusion process of the slurry in the soil in actual projects. The proposed method for calculating the seepage diffusion radius of outer-annular grouting is used to calculate the theoretical diffusion radius that changes with the grouting time after grouting, and the total grouting time is controlled according to the diffusion range, which provides a reference for actual grouting and improves the efficiency.

[0007] Optionally, the partial differential equation for constructing the porosity of the sand layer includes: expanding the material derivative of the mass of a particle using a Taylor series; obtaining a first sand skeleton mass balance equation, a water mass balance equation and a first slurry solid particle mass balance equation based on the material derivative; constructing a relationship between the porosity of the sand layer and the volume percentage of the sand skeleton; obtaining a second sand skeleton mass balance equation based on the first sand skeleton mass balance equation; obtaining a first partial differential equation for the porosity of the sand layer based on the relationship between the porosity of the sand layer and the volume percentage of the sand skeleton and the second sand skeleton mass balance equation; obtaining a second partial differential equation for the porosity of the sand layer based on the first partial differential equation combined with an expression of the linear filtration law of the mass exchange coefficient. The present invention uses Taylor series to expand the mass derivative of a particle, and then derives the mass balance equation. According to the relationship between the porosity of a sand layer and its skeleton, the sand skeleton mass balance equation is used to obtain the first partial differential equation of the porosity of the sand layer. The second partial differential equation of the porosity of the sand layer is obtained by combining the mass exchange law. The dynamic changes of the sand layer are accurately simulated, the accuracy of geological engineering prediction and design is improved, and data support is provided for constructing a functional expression of the porosity of the sand layer.

[0008] Optionally, the functional expression of the porosity of the sand layer obtained based on the partial differential equation includes: obtaining a first functional equation between the slurry flow rate and the porosity of the sand layer according to the flow conservation principle; converting the first slurry solid particle mass balance equation according to the volume fraction definition of solid particles in the slurry to obtain a second slurry solid particle mass balance equation; substituting the linear filtration law expression, the second partial differential equation and the first functional equation into the second slurry solid particle mass balance equation to obtain a second functional equation of the porosity of the sand layer; based on the second functional equation, combining the boundary condition equation and the initial condition equation of the hemispherical penetration of the outer ring grouting slurry to obtain the functional expression of the porosity of the sand layer. The present invention derives the relationship between the slurry flow rate and the porosity based on the flow conservation and the volume fraction of solid particles, constructs a porosity dynamic equation in combination with mass balance and filtration law, and obtains the functional expression of the porosity of the sand layer in combination with the hemispherical penetration boundary condition equation and the initial condition equation, thereby improving the simulation accuracy of the grouting project and the grouting control effect.

[0009] Optionally, the establishment of the spatial distribution equation of the grouting positive pressure for slurry penetration and diffusion includes: obtaining the relationship between the grouting volume and the permeability coefficient per unit time according to the Darcy's law expression; constructing an expression for the viscosity of the cement slurry according to the time-varying viscosity of the slurry; substituting the viscosity expression into the first permeability coefficient expression to obtain the second permeability coefficient expression; substituting the permeability coefficient expression of the soil medium into the second permeability coefficient expression to obtain the third permeability coefficient expression; obtaining an expression for the grouting volume per unit time according to the Darcy's law expression, the third permeability coefficient expression and the boundary condition equation for the hemispherical penetration of the outer ring grouting slurry; integrating the grouting volume expression per unit time to obtain an expression for the total flow rate of the grouting slurry; constructing an expression for the diffusion volume of the slurry based on the law of hemispherical diffusion of the slurry in the soil medium; and establishing the spatial distribution equation of the grouting positive pressure for slurry penetration and diffusion according to the total flow rate expression of the grouting slurry and the diffusion volume expression of the slurry. The present invention calculates the relationship between the grouting volume and the permeability coefficient through Darcy's law, obtains the permeability coefficient expression according to the time-varying property of the slurry viscosity and the permeability coefficient, derives the grouting volume and diffusion volume formula in combination with the hemispherical permeability model, and then establishes the grouting positive pressure spatial distribution equation, which improves the scientific nature of the grouting engineering design and the accuracy of the grouting effect prediction.

[0010] Optionally, the grouting positive pressure spatial distribution equation for slurry penetration and diffusion includes:

[0011]

[0012] in, is the slurry diffusion pressure, is the grouting pressure, is the initial porosity of the sand layer, is the bulk density of the slurry, is the specific surface area of ​​soil particles, is the dynamic viscosity of water, is the ratio of the initial viscosity of the slurry to the viscosity of water, is the penetration and diffusion radius of the outer ring grouting, is a coefficient related to the particle shape and the actual flow direction of water, is the water density, The present invention constructs an expression for the permeability coefficient and then constructs an expression for the total flow rate of the grouting slurry, and finally obtains the spatial distribution equation of the grouting positive pressure of the slurry penetration and diffusion; the slurry diffusion pressure is quantified through the expression, which more intuitively reflects the spatial distribution of the grouting positive pressure and provides data support for the subsequent construction of the calculation expression for the outer ring grouting penetration and diffusion radius.

[0013] Optionally, the construction of the drainage negative pressure spatial distribution equation for the infiltration and diffusion of the slurry includes: obtaining a water flow expression under drainage negative pressure conditions based on the Darcy's law expression; integrating the water flow expression to obtain a preliminary drainage negative pressure spatial distribution equation; substituting the boundary conditions of pressure relief drainage into the preliminary drainage negative pressure spatial distribution equation to construct the drainage negative pressure spatial distribution equation for the infiltration and diffusion of the slurry. The present invention derives the water flow expression under drainage negative pressure conditions through Darcy's law, integrates the water flow expression to obtain a preliminary negative pressure spatial distribution equation, and then combines the boundary condition optimization equation to obtain the drainage negative pressure spatial distribution equation to describe the infiltration and diffusion behavior of the slurry during the negative pressure drainage process, which provides a scientific theoretical basis and technical reference for grouting reinforcement in engineering, helps to improve the efficiency and effect of pressure relief drainage, and reduces uncertainty risks.

[0014] Optionally, the drainage negative pressure spatial distribution equation of the slurry penetration diffusion includes:

[0015]

[0016] in, For drainage negative pressure, is the diffusion radius of the outer ring grouting penetration, is the discharge pressure, is the water flow rate, is the specific gravity of water, is the permeability coefficient of water in sand, For time, The present invention obtains the water flow expression under drainage negative pressure conditions based on Darcy's law, and then integrates the water flow expression to obtain the preliminary negative pressure spatial distribution equation, and then combines the boundary conditions to obtain the drainage negative pressure spatial distribution equation. The drainage negative pressure of the slurry during the pressure relief and drainage process is quantified using the expression, and data support is provided for the subsequent construction of the calculation expression for the penetration and diffusion radius of the outer ring grouting.

[0017] Optionally, the calculation expression for the permeability diffusion radius of the outer-annular grouting is obtained based on the grouting positive pressure spatial distribution equation and the drainage negative pressure spatial distribution equation, including: summing the grouting positive pressure spatial distribution equation and the drainage negative pressure spatial distribution equation to obtain the slurry pressure spatial distribution equation under pressure relief and drainage conditions; simplifying the slurry pressure spatial distribution equation to obtain a simplified slurry pressure spatial distribution equation; and obtaining the calculation expression for the permeability diffusion radius of the outer-annular grouting according to the simplified slurry pressure spatial distribution equation. The present invention sums the grouting positive pressure spatial distribution equation and the drainage negative pressure spatial distribution equation to obtain the slurry pressure spatial distribution equation, simplifies the slurry pressure spatial distribution equation, and then derives the calculation expression for the permeability diffusion radius of the outer-annular grouting. This process simplifies the analysis of the spatial distribution of grouting pressure under complex geological conditions, improves the accuracy of the prediction of the permeability diffusion radius of the outer-annular grouting, and has important reference value for actual engineering design and construction.

[0018] Optionally, the calculation expression of the outer ring grouting penetration diffusion radius includes:

[0019]

[0020] in, is the diffusion radius of the outer ring grouting penetration, is the hydrostatic pressure, is the grouting pressure, is the discharge pressure, The invention expresses the diffusion radius of the outer ring grouting penetration with a clear expression through rigorous formula deduction, and each step is linked to each other and progressive, making the method of the invention more rigorous and reliable, greatly improving the operability and practicality of the method of the invention, and providing a solid theoretical basis for practical engineering applications.

[0021] In the second aspect, the present invention provides a system for calculating the penetration and diffusion radius of grouting outside the ring for tunnel pressure relief drainage. The system executes the method for calculating the penetration and diffusion radius of grouting outside the ring for tunnel pressure relief drainage provided by the present invention. The system includes an input device, an output device, a processor and a memory. Its gain lies in: the hardware facilities integrated by the present invention have excellent performance, the input device, the output device, the processor and the memory are interconnected, and the information transmission between the various components is smooth. Through the interaction of multiple hardware facilities, an efficient information processing system is constructed. The present invention proposes a method for calculating the penetration and diffusion radius of grouting outside the ring, which takes into account the influence of pressure relief drainage factors on the penetration and diffusion of slurry in actual projects, makes the results more in line with reality, reduces the error between theory and practice, solves the problem of blindness in the control of grouting time and grouting amount in actual projects, and provides a reference for actual grouting. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A flow chart of a method for calculating the penetration and diffusion radius of grouting outside a tunnel pressure relief drainage ring according to an embodiment of the present invention;

[0023] Figure 2 It is a schematic diagram of hemispherical infiltration and diffusion outside the ring under pressure relief and drainage conditions of an embodiment of the present invention;

[0024] Figure 3 This is a framework diagram of a system for calculating the penetration and diffusion radius of grouting outside the tunnel pressure relief drainage ring according to an embodiment of the present invention. DETAILED DESCRIPTION

[0025] The specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are only for illustration and are not intended to limit the present invention. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details do not need to be adopted to implement the present invention. In other examples, in order to avoid confusing the present invention, known circuits, software or methods are not specifically described.

[0026] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "in one embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or subcombination. In addition, it should be understood by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale.

[0027] In an embodiment of the present invention, the following assumptions are made for a method and system for calculating the penetration and diffusion radius of grouting outside a tunnel pressure relief drainage ring proposed by the present invention:

[0028] 1. The sand layer into which the slurry is injected is homogeneous and isotropic, and no soil structure changes will occur during the grouting process;

[0029] 2. During the grouting process, the slurry diffusion and pressure relief drainage are both spherical diffusion, which conforms to Darcy's law;

[0030] 3. The slurry is incompressible, homogeneous and isotropic, and the diffusion effect of free water on the slurry is not considered;

[0031] 4. The movement speed of solid particles in the slurry is equal to the flow rate of water in the slurry;

[0032] 5. The density of solid particles in the slurry is considered to be equal to that of soil particles, and the solid particles in the slurry are regarded as soil particles after they are deposited in the soil;

[0033] 6. Considering that the radius of the shield segment is much larger than the radius of the grouting sphere, the influence of the curvature of the shield segment on the grouting process is ignored, and the outer edge of the shield segment is regarded as a plane.

[0034] S1. Construct the partial differential equation for the porosity of the sand layer.

[0035] Among them, S1 specifically includes the following steps:

[0036] S11. Use Taylor series to expand the material derivative of the mass of a particle.

[0037] Specifically, the mass of a certain particle is taken as the research object, and the material derivative of the mass of the particle is expanded according to the Taylor series.

[0038] More specifically, the material derivatives include:

[0039]

[0040] in, is the mass of the particle, For time, For speed, is the Hamiltonian operator.

[0041] S12. Obtaining a first sand skeleton mass balance equation, a water mass balance equation and a first slurry solid particle mass balance equation based on the material derivatives.

[0042] Specifically, according to the percolation effect, cement particles in the suspension are adsorbed to the medium skeleton or filtered out of the pores of the sand layer. Assuming that the retained cement particles are considered as sand particles, the percolation effect can be regarded as the mass exchange between cement particles and the medium skeleton.

[0043] More specifically, the first sand skeleton mass balance equation is obtained according to the material derivative of the mass of the particle, including:

[0044]

[0045] in, is the mass exchange coefficient, is the density of the sand skeleton, is the volume percentage of sand skeleton in unit volume, For time, is the velocity of the sand skeleton, is the Hamiltonian operator.

[0046] More specifically, the water mass balance equation is obtained based on the material derivative of the mass of the particle, including:

[0047]

[0048] in, is the density of water, is the volume percentage of water per unit volume, For time, is the speed of water, is the Hamiltonian operator.

[0049] More specifically, the mass balance equation of the solid particles in the first slurry is obtained according to the material derivative of the mass of the particle, including:

[0050]

[0051] in, is the mass exchange coefficient, is the density of cement particles, is the volume percentage of cement particles per unit volume, For time, is the velocity of cement particles, is the Hamiltonian operator.

[0052] S13, constructing a relationship between the porosity of the sand layer and the volume percentage of the sand skeleton.

[0053] Specifically, since the pores of the sand layer are completely filled with slurry, the relationship between the porosity of the sand layer and the volume percentage of the sand skeleton is obtained, including:

[0054]

[0055] in, is the porosity of the sand layer, is the volume percentage of cement particles per unit volume, is the volume percentage of water per unit volume, It is the volume percentage of sand skeleton in unit volume.

[0056] S14. Obtain a second sand skeleton mass balance equation based on the first sand skeleton mass balance equation.

[0057] Specifically, in the fifth assumption of the embodiment of the present invention, it is assumed that the density of solid particles in the slurry is equal to the density of soil particles, that is, the density of cement particles is equal to the density of sand particles, and then the first sand skeleton mass balance equation is transformed to obtain the second sand skeleton mass balance equation.

[0058] More specifically, the second sand skeleton mass balance equation includes:

[0059]

[0060] in, is the mass exchange coefficient, is the density of cement particles, is the volume percentage of sand skeleton in unit volume, For time.

[0061] S15. Obtain a first partial differential equation for the porosity of the sand layer according to a relationship between the porosity of the sand layer and the volume percentage of the sand skeleton and a second sand skeleton mass balance equation.

[0062] Specifically, the first partial differential equation includes:

[0063]

[0064] in, is the porosity of the sand layer, For time, is the mass exchange coefficient, is the density of cement particles.

[0065] S16. Based on the first partial differential equation and the linear filtration law expression of the mass exchange coefficient, a second partial differential equation for the porosity of the sand layer is obtained.

[0066] Specifically, the linear filtration law expression of the mass exchange coefficient includes:

[0067]

[0068] in, is the mass exchange coefficient, is the density of cement particles, is the percolation coefficient, is the volume percentage of cement particles per unit volume, Initial porosity of sand layer, is the cement particle content of the slurry in the pores.

[0069] More specifically, the second partial differential equation of the porosity of the sand layer includes:

[0070]

[0071] in, is the porosity of the sand layer, For time, is the percolation coefficient, is the cement particle content of the slurry in the pores.

[0072] S2. Obtaining a functional expression for the porosity of the sand layer based on the partial differential equation.

[0073] Among them, S2 specifically includes the following steps:

[0074] S21. Obtain a first functional equation between the slurry flow rate and the porosity of the sand layer according to the flow conservation principle.

[0075] Specifically, the first functional equation between the slurry flow rate and the porosity of the sand layer includes:

[0076]

[0077]

[0078] in, is the radius of the grouting hole, is the velocity of the slurry before it enters the sand, is the function of slurry flow rate and sand layer porosity with respect to grouting hole radius and time, For time, is the diffusion radius of the outer ring grouting penetration, It is a function of the slurry flow rate and the porosity of the sand layer with respect to the external grouting penetration diffusion radius and time.

[0079] S22. According to the definition formula of the volume fraction of solid particles in the slurry, the first slurry solid particle mass balance equation is transformed to obtain a second slurry solid particle mass balance equation.

[0080] Specifically, the definition formula of the volume fraction of solid particles in the slurry includes:

[0081]

[0082] in, is the volume percentage of cement particles per unit volume, is the cement particle content of the slurry in the pores, is the porosity of the sand layer.

[0083] More specifically, the second slurry solid particle mass balance equation includes:

[0084]

[0085] in, is the cement particle content of the slurry in the pores, is the porosity of the sand layer, For time, is the velocity of cement particles, is the mass exchange coefficient, is the density of cement particles.

[0086] S23. Substitute the linear filtration law expression, the second partial differential equation and the first functional equation into the second slurry solid particle mass balance equation to obtain the second functional equation for the porosity of the sand layer.

[0087] Specifically, the second functional equation of the porosity of the sand layer includes:

[0088]

[0089] in, is the porosity of the sand layer, is the cement particle content of the slurry in the pores, For time, is the velocity of the slurry before it enters the sand, is the radius of the grouting hole, is the penetration and diffusion radius of the outer ring grouting, is the percolation coefficient.

[0090] S24. Based on the second functional equation, a boundary condition equation and an initial condition equation for hemispherical penetration of the outer ring grouting slurry are combined to obtain a functional expression for the porosity of the sand layer.

[0091] Specifically, the boundary condition equation and initial condition equation of the hemispherical penetration of the outer ring grouting slurry include:

[0092]

[0093] in, is the cement particle content of the slurry in the pores, is the radius of the grouting hole, For time, is the volume fraction of cement particles before the slurry is injected into the soil, is the porosity of the sand layer, is the diffusion radius of the outer ring grouting penetration, is the slurry diffusion boundary radius, Initial porosity of sand layer.

[0094] More specifically, the functional expression of the porosity of the sand layer includes:

[0095]

[0096] in, is the porosity of the sand layer, is the diffusion radius of the outer ring grouting penetration, For time, is the initial porosity of the sand layer, is the percolation coefficient, is the radius of the grouting hole, is the velocity of the slurry before it enters the sand, is the slurry diffusion boundary radius, It is the volume fraction of cement particles before the slurry is injected into the soil.

[0097] S3. Establish the spatial distribution equation of grouting positive pressure for slurry penetration and diffusion.

[0098] Among them, S3 specifically includes the following steps:

[0099] S31. According to Darcy's law expression, the relationship between the grouting volume per unit time and the permeability coefficient is obtained.

[0100] Specifically, the Darcy's law expression includes:

[0101]

[0102] in, is the grouting volume per unit time, is the hemispherical diffusion area, is the permeability coefficient of slurry in the formation, For water head, is the diffusion radius of the outer ring grouting penetration, is the slurry diffusion pressure, is the bulk density of slurry.

[0103] S32. Construct an expression for the viscosity of cement slurry based on the time-varying viscosity of the slurry.

[0104] Specifically, the viscosity expression of the cement slurry includes:

[0105]

[0106] in, is the viscosity of cement slurry, is the initial viscosity of cement slurry, is the cement slurry viscosity correlation coefficient, For time.

[0107] S33. Substitute the viscosity expression into the first permeability coefficient expression to obtain a second permeability coefficient expression.

[0108] Specifically, the first permeability coefficient expression includes:

[0109]

[0110]

[0111] in, is the permeability coefficient of slurry in the formation, is the soil permeability coefficient, is the viscosity ratio of cement slurry to water, is the viscosity of cement slurry, is the viscosity of water.

[0112] More specifically, the second permeability coefficient expression includes:

[0113]

[0114] in, is the permeability coefficient of slurry in the formation, is the soil permeability coefficient, is the viscosity of water, is the initial viscosity of cement slurry, is the cement slurry viscosity correlation coefficient, For time, It is the ratio of the initial viscosity of cement slurry to the viscosity of water.

[0115] S34. Substitute the permeability coefficient expression of the soil medium into the second permeability coefficient expression to obtain a third permeability coefficient expression.

[0116] Specifically, the permeability coefficient expression of the soil medium includes:

[0117]

[0118] in, is the soil permeability coefficient, is a coefficient related to the particle shape and the actual flow direction of water, is the density of water, is the porosity of the sand layer, is the specific surface area of ​​soil particles, is the dynamic viscosity of water.

[0119] More specifically, the third permeability coefficient expression includes:

[0120]

[0121] in, is the permeability coefficient of slurry in the formation, is a coefficient related to the particle shape and the actual flow direction of water, is the density of water, is the porosity of the sand layer, is the specific surface area of ​​soil particles, is the dynamic viscosity of water, is the ratio of the initial viscosity of cement slurry to the viscosity of water, is the cement slurry viscosity correlation coefficient, For time.

[0122] S35. According to the Darcy's law expression, the third permeability coefficient expression and the boundary condition equation of hemispherical penetration of the outer ring grouting slurry, an expression for the grouting volume per unit time is obtained.

[0123] Specifically, the expression of the grouting volume per unit time includes:

[0124]

[0125]

[0126] in, is the grouting volume per unit time, is a coefficient related to the particle shape and the actual flow direction of water, is the density of water, is the cement slurry viscosity correlation coefficient, For time, is the grouting pressure, is the slurry diffusion pressure, is the bulk density of the slurry, is the specific surface area of ​​soil particles, is the dynamic viscosity of water, is the ratio of the initial viscosity of cement slurry to the viscosity of water, is the diffusion radius of the outer ring grouting penetration, is the radius of the grouting hole, is the porosity of the sand layer.

[0127] S36. Integrate the expression of the grouting volume per unit time to obtain the expression of the total flow rate of the grouting slurry.

[0128] Specifically, the expression of grouting volume per unit time is integrated to obtain The total flow rate expression of the grouting slurry at the moment, the total flow rate expression of the grouting slurry includes:

[0129]

[0130] in, is the total flow rate of grouting slurry, For time, is the grouting volume per unit time, is the grouting pressure, is the slurry diffusion pressure, is a coefficient related to the particle shape and the actual flow direction of water, is the density of water, is the bulk density of the slurry, is the specific surface area of ​​soil particles, is the dynamic viscosity of water, is the ratio of the initial viscosity of cement slurry to the viscosity of water, is the diffusion radius of the outer ring grouting penetration, is the viscosity correlation coefficient of cement slurry.

[0131] S37. Construct an expression for the slurry diffusion volume based on the law of hemispherical diffusion of slurry in soil medium.

[0132] Specifically, the slurry diffusion volume expression is obtained based on the hemispherical diffusion of the slurry. In the numerical dimension of the calculation, the slurry diffusion volume is equal to the total flow rate of the grouting slurry. The slurry diffusion volume expression includes:

[0133]

[0134] in, is the slurry diffusion volume, is the diffusion radius of the outer ring grouting penetration, is the initial porosity of the sand layer.

[0135] For more details, see Figure 2 The figure is a schematic diagram of the hemispherical infiltration diffusion outside the ring under pressure relief drainage conditions. It intuitively reflects the hemispherical diffusion state of the slurry after being injected into the sand layer, and intuitively shows the position distribution of the shield segments, grouting pipes and pressure relief drainage pipes.

[0136] S38. Establish a grouting positive pressure spatial distribution equation for slurry penetration and diffusion based on the grouting slurry total flow expression and the slurry diffusion volume expression.

[0137] Specifically, the grouting positive pressure spatial distribution equation includes:

[0138]

[0139]

[0140] in, is the slurry diffusion pressure, is the grouting pressure, is the initial porosity of the sand layer, is the bulk density of the slurry, is the specific surface area of ​​soil particles, is the dynamic viscosity of water, is the ratio of the initial viscosity of cement slurry to the viscosity of water, is the diffusion radius of the outer ring grouting penetration, is a coefficient related to the particle shape and the actual flow direction of water, is the density of water, For time, is the viscosity correlation coefficient of cement slurry.

[0141] S4. Construct a spatial distribution equation of the drainage negative pressure of the slurry penetration and diffusion.

[0142] Wherein, S4 specifically includes the following steps:

[0143] S41. Based on the Darcy's law expression, an expression for water flow under drainage negative pressure conditions is obtained.

[0144] Specifically, the water flow expression includes:

[0145]

[0146] in, is the water flow rate, is the permeability coefficient of water in sand, is the hemispherical diffusion area, is the hydraulic gradient, For time, is the diffusion radius of the outer ring grouting penetration, For drainage negative pressure, is the specific gravity of water.

[0147] S42. Integrate the slurry flow expression to obtain a preliminary drainage negative pressure spatial distribution equation.

[0148] Specifically, the preliminary drainage negative pressure spatial distribution equation includes:

[0149]

[0150] in, For drainage negative pressure, is the diffusion radius of the outer ring grouting penetration, is the water flow rate, is the specific gravity of water, is the permeability coefficient of water in sand, For time, is a constant.

[0151] S43. Substitute the boundary conditions of pressure relief and drainage into the preliminary drainage negative pressure spatial distribution equation to construct the drainage negative pressure spatial distribution equation of the slurry penetration and diffusion.

[0152] Specifically, the boundary conditions for pressure relief and drainage include:

[0153] hour,

[0154] in, is the diffusion radius of the outer ring grouting penetration, is the radius of the grouting hole, For drainage negative pressure, For the water discharge pressure.

[0155] Further, the boundary conditions are substituted into the preliminary drainage negative pressure spatial distribution equation to obtain the drainage negative pressure spatial distribution equation, and the drainage negative pressure spatial distribution equation includes:

[0156]

[0157] in, For drainage negative pressure, is the diffusion radius of the outer ring grouting penetration, is the discharge pressure, is the water flow rate, is the specific gravity of water, is the permeability coefficient of water in sand, For time, is the radius of the grouting hole.

[0158] S5. According to the grouting positive pressure spatial distribution equation and the drainage negative pressure spatial distribution equation, a calculation expression for the outer ring grouting penetration and diffusion radius is obtained.

[0159] Among them, S5 specifically includes the following steps:

[0160] S51. Summing the grouting positive pressure spatial distribution equation and the drainage negative pressure spatial distribution equation, obtain the slurry pressure spatial distribution equation under pressure relief and drainage conditions.

[0161] Specifically, the slurry pressure spatial distribution equation includes:

[0162]

[0163] in, is the slurry pressure, is the slurry diffusion pressure, For drainage negative pressure, is the distance between the grouting hole and the pressure relief hole, is the diffusion radius of the outer ring grouting penetration, is the grouting pressure, is the discharge pressure, is the initial porosity of the sand layer, is the bulk density of the slurry, is the specific surface area of ​​soil particles, is the dynamic viscosity of water, is the ratio of the initial viscosity of cement slurry to the viscosity of water, is a coefficient related to the particle shape and the actual flow direction of water, is the density of water, For time, is the water flow rate, is the specific gravity of water, is the permeability coefficient of water in sand, is the radius of the grouting hole.

[0164] S52. Simplify the slurry pressure spatial distribution equation to obtain a simplified slurry pressure spatial distribution equation.

[0165] Specifically, the simplified equation for the spatial distribution of slurry pressure includes:

[0166]

[0167]

[0168]

[0169] in, is the slurry pressure, is the diffusion radius of the outer ring grouting penetration, is the grouting pressure, is the discharge pressure, For time, is the initial porosity of the sand layer, is the bulk density of the slurry, is the specific surface area of ​​soil particles, is the dynamic viscosity of water, is the ratio of the initial viscosity of cement slurry to the viscosity of water, is a coefficient related to the particle shape and the actual flow direction of water, is the density of water, is the specific gravity of water, is the permeability coefficient of water in sand, is the radius of the grouting hole, is the distance between the grouting hole and the pressure relief hole.

[0170] S53. Obtain a calculation expression for the outer ring grouting penetration and diffusion radius based on the simplified equation for the spatial distribution of the slurry pressure.

[0171] Specifically, the slurry pressure is set equal to the hydrostatic pressure, and then the calculation expression of the permeation diffusion radius of the outer ring grouting is obtained. The calculation expression of the permeation diffusion radius of the outer ring grouting includes:

[0172]

[0173] in, is the diffusion radius of the outer ring grouting penetration, is the hydrostatic pressure, is the grouting pressure, is the discharge pressure, For time.

[0174] See also Figure 3 In an optional embodiment, in order to be able to efficiently execute the method for calculating the penetration diffusion radius of the grouting outside the tunnel pressure relief drainage ring provided by the present invention, the present invention provides a system for calculating the penetration diffusion radius of the grouting outside the tunnel pressure relief drainage ring provided by the present invention, the system includes an input device, an output device, a processor and a memory, and the hardware facilities are interconnected, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions to execute the specific steps of the relevant embodiments of the method for calculating the penetration diffusion radius of the grouting outside the tunnel pressure relief drainage ring provided by the present invention. The system for calculating the penetration diffusion radius of the grouting outside the tunnel pressure relief drainage ring provided by the present invention has a complete structure, is objective and stable, and can efficiently execute the method for calculating the penetration diffusion radius of the grouting outside the tunnel pressure relief drainage ring provided by the present invention, thereby improving the overall applicability and practical application capabilities of the present invention.

[0175] In summary, the method and system for calculating the penetration and diffusion radius of grouting outside the tunnel pressure relief drainage ring provided by the method of the present invention take into account the influence of pressure relief drainage factors on the penetration and diffusion of slurry in actual engineering, making the results more practical, reducing the error between theory and practice, and solving the problem of blindness in the control of grouting time and grouting amount in actual engineering, providing a reference for actual engineering applications. The method of the present invention is easy to understand, simple to calculate, and has a small workload, providing a theoretical basis and technical support for the further development of the field of grouting technology in tunnel engineering.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for calculating the penetration and diffusion radius of grouting outside the tunnel pressure relief drainage ring. It is characterized in that The steps include: Construct the partial differential equation for the porosity of the sand layer; Obtaining a functional expression of the porosity of the sand layer based on the partial differential equation; Establish the spatial distribution equation of grouting positive pressure for slurry penetration and diffusion; Constructing a spatial distribution equation of drainage negative pressure for slurry penetration and diffusion; According to the grouting positive pressure spatial distribution equation and the drainage negative pressure spatial distribution equation, a calculation expression for the outer ring grouting penetration and diffusion radius is obtained; The partial differential equation for constructing the porosity of the sand layer includes: Use Taylor series to expand the material derivative of particle mass; A first sand skeleton mass balance equation, a water mass balance equation and a first slurry solid particle mass balance equation are obtained according to the material derivatives; Constructing a relationship between the porosity of the sand layer and the volume percentage of the sand skeleton; Obtaining a second sand skeleton mass balance equation based on the first sand skeleton mass balance equation; Obtaining a first partial differential equation of the porosity of the sand layer according to a relationship between the porosity of the sand layer and the volume percentage of the sand skeleton and a second sand skeleton mass balance equation; Based on the first partial differential equation combined with the linear filtration law expression of the mass exchange coefficient, a second partial differential equation for the porosity of the sand layer is obtained; The functional expression for obtaining the porosity of the sand layer based on the partial differential equation includes: According to the flow conservation principle, a first functional equation between the slurry flow rate and the porosity of the sand layer is obtained; According to the definition of the volume fraction of solid particles in the slurry, the first slurry solid particle mass balance equation is transformed to obtain a second slurry solid particle mass balance equation; Substituting the linear filtration law expression, the second partial differential equation and the first functional equation into the second slurry solid particle mass balance equation to obtain the second functional equation for the porosity of the sand layer; Based on the second functional equation and the boundary condition equation and initial condition equation of the hemispherical penetration of the outer ring grouting slurry, a functional expression for the porosity of the sand layer is obtained.

2. According to the method for calculating the penetration and diffusion radius of the tunnel pressure relief drainage ring outer grouting according to claim 1, It is characterized in that The method of establishing the grouting positive pressure spatial distribution equation for slurry penetration and diffusion includes: The relationship between the grouting volume per unit time and the permeability coefficient is obtained according to the Darcy's law expression; The viscosity expression of cement slurry is constructed based on the time-varying property of slurry viscosity; Substituting the viscosity expression into the first permeability coefficient expression to obtain a second permeability coefficient expression; Substituting the permeability coefficient expression of the soil medium into the second permeability coefficient expression to obtain a third permeability coefficient expression; The expression of grouting volume per unit time is obtained according to the expression of Darcy's law, the expression of the third permeability coefficient and the boundary condition equation of hemispherical permeation of the outer ring grouting slurry; Integrating the expression of the grouting volume per unit time to obtain the expression of the total flow rate of the grouting slurry; Based on the law of hemispherical diffusion of slurry in soil medium, the expression of slurry diffusion volume is constructed; The grouting positive pressure spatial distribution equation of grouting penetration and diffusion is established based on the grouting slurry total flow expression and the slurry diffusion volume expression.

3. The calculation method of the penetration and diffusion radius of the outer grouting of the tunnel pressure relief drainage ring according to claim 2, It is characterized in that The grouting positive pressure spatial distribution equation for the slurry penetration and diffusion includes: in, is the slurry diffusion pressure, is the grouting pressure, is the initial porosity of the sand layer, is the bulk density of the slurry, is the specific surface area of ​​soil particles, is the dynamic viscosity of water, is the ratio of the initial viscosity of the slurry to the viscosity of water, is the diffusion radius of the outer ring grouting penetration, is a coefficient related to the particle shape and the actual flow direction of water, is the water density, For time.

4. The method for calculating the penetration and diffusion radius of the grouting outside the tunnel pressure relief drainage ring according to claim 2, It is characterized in that The construction of the drainage negative pressure spatial distribution equation for the slurry penetration and diffusion includes: Based on the Darcy's law expression, the water flow expression under the drainage negative pressure condition is obtained; Integrating the water flow expression to obtain a preliminary drainage negative pressure spatial distribution equation; Substituting the boundary conditions of pressure relief drainage into the preliminary drainage negative pressure spatial distribution equation, the drainage negative pressure spatial distribution equation of slurry penetration and diffusion is constructed.

5. According to the method for calculating the penetration and diffusion radius of the tunnel pressure relief drainage ring outer grouting according to claim 4, It is characterized in that The drainage negative pressure spatial distribution equation of the slurry penetration diffusion includes: in, To drain negative pressure, is the diffusion radius of the outer ring grouting penetration, is the discharge pressure, is the water flow rate, is the specific gravity of water, is the permeability coefficient of water in sand, For time, is the radius of the grouting hole.

6. The method for calculating the penetration and diffusion radius of the grouting outside the tunnel pressure relief drainage ring according to claim 4, It is characterized in that The calculation expression for the outer ring grouting penetration and diffusion radius obtained based on the grouting positive pressure spatial distribution equation and the drainage negative pressure spatial distribution equation includes: The spatial distribution equation of grouting positive pressure and the spatial distribution equation of drainage negative pressure are summed to obtain the spatial distribution equation of slurry pressure under pressure relief and drainage conditions; Simplifying the slurry pressure spatial distribution equation to obtain a simplified slurry pressure spatial distribution equation; The calculation expression of the outer ring grouting penetration and diffusion radius is obtained based on the simplified equation of the spatial distribution of slurry pressure.

7. The method for calculating the penetration and diffusion radius of the grouting outside the tunnel pressure relief drainage ring according to claim 6, It is characterized in that The calculation expression of the permeation and diffusion radius of the outer ring grouting includes: in, is the diffusion radius of the outer ring grouting penetration, is the hydrostatic pressure, is the grouting pressure, is the discharge pressure, For time.

8. A tunnel pressure relief drainage ring outer grouting penetration and diffusion radius calculation system, It is characterized in that The system includes an input device, an output device, a processor and a memory, and the input device, the output device, the processor and the memory are interconnected, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions to execute the method for calculating the penetration and diffusion radius of grouting outside the tunnel pressure relief drainage ring as described in any one of claims 1-7.

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