Underground structure compaction grouting permeation filtration diffusion time-varying analysis system and method

Abstract

The invention relates to the technical field of shield tunnel construction, in particular to an underground structure compaction grouting permeation filtration diffusion time-varying analysis system and method.The method comprises the following steps that a grouting pressure and grouting time relation calculation model is built, and construction parameters are obtained; inputting the obtained construction parameters into a constructed grouting pressure and grouting time relation calculation model; the situation that the grouting pressure changes along with the grouting time and considering the deep percolation effect and the slurry viscosity time-varying characteristic at the same time, the situation that the grouting pressure changes along with the grouting time and considering the deep percolation effect independently and the situation that the grouting pressure changes along with the grouting time and considering the viscosity time-varying characteristic independently are obtained through calculation and output. According to the method, the pore blocking effect caused by particle deposition of the slurry in the soil body and the dynamic change of the slurry viscosity along with time are coupled, and the influence of the deep percolation effect and the time-varying property of the slurry viscosity on the permeation and diffusion of the slurry is considered at the same time.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of shield tunnel construction, in particular to an underground structure densification grouting permeation filtration diffusion time-varying analysis system and method. BACKGROUND

[0002] Densification grouting is a common technique for enhancing the stability of soil around underground structure excavation engineering and reducing construction risks. The main purpose is to achieve the purpose of filling soil voids, stabilizing surrounding rock, controlling ground settlement, and improving the integrity and waterproof performance of the structure through grouting process. The core of this technology lies in selecting grouting materials and precisely controlling grouting parameters.

[0003] The key technology of construction mainly reflects the following aspects: first, the preparation of slurry to ensure that its performance meets the engineering requirements, and second, construction control. Both of them jointly determine the grouting effect, which plays an important role in the stability of underground structure and ground deformation control. In terms of grouting construction, grouting pressure and grouting quantity are the two most important parameters. The size of grouting pressure directly determines the quality of grouting effect, and the grouting pressure should be adjusted to the appropriate range during construction. Precise control of grouting quantity is often difficult, which requires construction personnel to consider the comprehensive influence of factors such as stratum permeability and different types of slurry when formulating the scheme.

[0004] Under the driving of grouting pressure, the slurry flows along the pore channel in the soil pore, which is called permeation and diffusion of slurry. Then, by extruding the water in the soil pore, the purpose of effective filling and reinforcement of the pore is achieved. However, due to the difficulty of observing the permeation and diffusion process of slurry in soil, and the complexity of factors affecting the diffusion mechanism, current permeation grouting work mainly relies on engineering experience, lacking theoretical support. Therefore, many scholars have carried out a lot of research on the permeation and diffusion mechanism of grouting slurry.

[0005] The formation of traditional permeation grouting theory is mainly based on Darcy's law, and it is continuously expanded and improved under this theoretical framework. According to the diffusion form of slurry under the driving of grouting pressure, it is divided into spherical permeation diffusion, cylindrical diffusion permeation, and hemispherical permeation diffusion. The foundational research of spherical permeation diffusion theory can be traced back to 1938. Maag first established a mathematical model to describe the permeation behavior of slurry based on the spherical diffusion hypothesis, which is still widely used today. On this basis, many scholars have also conducted research on the permeation and diffusion mechanism of slurry.

[0006] However, the traditional slurry infiltration diffusion theory is more applied to grouting engineering and insufficiently explored for underground structure pressure grouting. Moreover, most of the researches excessively simplify the hypothesis system, resulting in that the research on grouting diffusion mechanism is long-term stayed at the macro scale and difficult to realize the fine characterization of multi-field coupling and micro mechanism. In addition, the slurry in actual underground structure engineering such as tunnel and foundation pit is generally non-Newtonian fluid, and the slurry infiltration diffusion behavior is affected by complex factors such as deep percolation effect and time-varying characteristics of slurry viscosity. Therefore, it is necessary to propose a new technical solution. SUMMARY

[0007] The underground structure pressure grouting infiltration filtration diffusion time-varying analysis system and method provided by the present application can overcome the defects of the prior art and solve the problem that the existing slurry infiltration diffusion research excessively simplifies the hypothesis system and is difficult to realize the fine characterization of multi-field coupling and micro mechanism.

[0008] The technical solution for realizing the above-mentioned purpose is as follows:

[0009] The underground structure pressure grouting infiltration filtration diffusion time-varying analysis method provided by the present application comprises the following steps:

[0010] A grouting pressure and grouting time relationship calculation model is constructed, and the constructed grouting pressure and grouting time relationship calculation model comprises the following expressions:

[0011]

[0012] In formula 2-41, formula 2-46 and formula 2-50, p0 is the grouting pressure, r0 is the grouting pipe radius, r t is the penetration range of the slurry in the soil at time t1, Q is the grouting flow, n'0 is the initial equivalent porosity of the soil, ρ p is the suspended particle density, ρ is the slurry density, δ is the volume proportion of the suspended particles in the solid part of the slurry, g is the gravitational acceleration, μ s is the slurry viscosity, ρ w is the density of water, μ s0 is the initial viscosity of the slurry, K0 is the permeability coefficient of the soil layer in the initial state, K w is the permeability coefficient of water in the stratum, μ w is the viscosity of water, t is the grouting time, R is the slurry diffusion radius, a is the percolation coefficient, is the soil permeability coefficient change parameter, r is the diffusion front radius, v0 is the speed of the slurry before being injected into the stratum pore, p s is the hydrostatic pressure;

[0013] The construction parameters of the underground structure are obtained;

[0014] The obtained construction parameters are input into the built grouting pressure and grouting time relationship calculation model, and through calculation, the grouting pressure change condition with grouting time considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, the grouting pressure change condition with grouting time considering the deep percolation effect alone, and the grouting pressure change condition with grouting time considering the viscosity time-varying characteristics alone are obtained and output.

[0015] The underground structure pressure consolidation grouting permeation filtration diffusion time-varying analysis system also provides an underground structure pressure consolidation grouting permeation filtration diffusion time-varying analysis method.

[0016] The grouting pressure and grouting time relationship calculation model comprises the following expressions.

[0017]

[0018] In formula 2-41, formula 2-46 and formula 2-50, p0 is the grouting pressure, r0 is the grouting pipe radius, r t is the penetration range of the slurry in the soil at time t1, Q is the grouting flow, n'0 is the initial equivalent porosity of the soil, ρ p is the suspended particle density, ρ is the slurry density, δ is the volume proportion of the suspended particles in the solid part of the slurry, g is the gravity acceleration, μ s is the slurry viscosity, ρ w is the water density, μ s0 is the initial viscosity of the slurry, K0 is the permeability coefficient of the soil layer in the initial state, K w is the permeability coefficient of water in the stratum, μ w is the water viscosity, t is the grouting time, R is the slurry diffusion radius, a is the percolation coefficient, is the soil permeability coefficient change parameter, r is the diffusion front radius, v0 is the speed of the slurry before being injected into the stratum pores, p s is the hydrostatic pressure.

[0019] The obtaining unit is configured to obtain construction parameters of the underground structure.

[0020] The processing unit is connected with the obtaining unit and the grouting pressure and grouting time relationship calculation model, and is configured to input the obtained construction parameters into the grouting pressure and grouting time relationship calculation model, and through calculation, obtain the grouting pressure change condition with grouting time considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, the grouting pressure change condition with grouting time considering the deep percolation effect alone, and the grouting pressure change condition with grouting time considering the viscosity time-varying characteristics alone, and output.

[0021] The underground structure pressure consolidation grouting permeation filtration diffusion time-varying analysis system and method have the following beneficial effects:

[0022] The analysis system and method of the present application establish a calculation model considering deep percolation effect and time-varying viscosity of slurry simultaneously, couple the pore blockage effect caused by particle deposition of slurry in soil and the dynamic change of slurry viscosity with time, and realize the influence of deep percolation effect and time-varying viscosity of slurry on slurry penetration and diffusion simultaneously.

[0023] The analysis system and method of the present application construct a calculation model of relationship between grouting pressure and grouting time, can calculate the change of grouting pressure with grouting time under the conditions of considering deep percolation effect and time-varying viscosity of slurry simultaneously, considering deep percolation effect only, and considering time-varying viscosity of slurry only, and can obtain the influence of deep percolation effect and time-varying viscosity of slurry on grouting pressure by analyzing the change of grouting pressure under the three conditions, thereby providing guidance for construction control of synchronous grouting.

[0024] The analysis system and method of the present application construct a calculation model of relationship between diffusion radius and grouting pressure, can calculate the change of diffusion radius with grouting pressure under the conditions of considering deep percolation effect and time-varying viscosity of slurry simultaneously, considering deep percolation effect only, and considering time-varying viscosity of slurry only, and can obtain the influence of deep percolation effect and time-varying viscosity of slurry on diffusion range of slurry by analyzing the change of diffusion radius under the three conditions, thereby providing guidance for construction control of synchronous grouting.

[0025] The analysis system and method of the present application also construct a penetration and diffusion model of slurry in the direction of flow and counterflow, clarify the internal mechanism of influence of tortuosity effect and disturbance of groundwater flow on penetration and diffusion of slurry, and have important theoretical research value and practical engineering guiding significance. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 It is a deep percolation effect principle schematic diagram in the present application.

[0027] Figure 2 It is a unit volume of soil schematic diagram in the present application.

[0028] Figure 3 It is a slurry penetration and diffusion model elevation schematic diagram in the present application.

[0029] Figure 4 It is a slurry penetration and diffusion model plane schematic diagram in the present application.

[0030] Figure 5 It is a slurry viscosity change rule curve diagram under different conditions of an example in the present application.

[0031] Figure 6 A variation curve of grouting pressure with grouting time under different conditions for an example in the application.

[0032] Figure 7 A variation curve of diffusion radius with grouting pressure under different conditions for an example in the application.

[0033] Figure 8 A variation curve of grouting pressure with distance from grouting hole under different conditions for an example in the application.

[0034] Figure 9 A variation curve of grouting pressure distance from grouting hole at different times for an example in the application.

[0035] Figure 10 A flow schematic diagram of grouting slurry in soil for the application.

[0036] Figure 11 A grouting slurry penetration diffusion model and stress analysis for the application.

[0037] Figure 12 A Bingham fluid flow velocity distribution schematic diagram for the application.

[0038] Figure 13 A principle diagram of a test device. DETAILED DESCRIPTION

[0039] The application will be further described below in combination with the drawings and specific embodiments.

[0040] The application provides a time-varying analysis system and method for underground structure pressure consolidation grouting penetration filtration diffusion, which, through in-depth research on the coupling mechanism of deep filtration effect and viscosity time-varying characteristics of grouting slurry on penetration diffusion, derives theoretical formulas of variation of grouting pressure with grouting time and diffusion radius according to mass conservation, momentum conservation, linear filtration and Darcy's law, and establishes a theoretical model of grouting slurry penetration diffusion. Based on the Bingham fluid constitutive model and fluid mechanics principles, the application further researches around two key factors of tortuosity effect and groundwater flow disturbance, establishes a theoretical model of grouting slurry penetration diffusion considering the tortuosity effect and groundwater flow conditions, and clarifies the internal mechanism of the influence of the tortuosity effect and groundwater flow disturbance on grouting slurry penetration diffusion, which has important theoretical research value and practical engineering guiding significance. The time-varying analysis system and method for underground structure pressure consolidation grouting penetration filtration diffusion of the application will be described below in combination with the drawings.

[0041] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0042] The application provides a time-varying analysis system for underground structure compaction grouting permeation filtration diffusion, which comprises a grouting pressure and grouting time relationship calculation model, an acquisition unit and a processing unit, wherein the grouting pressure and grouting time relationship calculation model comprises the following expression:

[0043]

[0044]

[0045] In formula 2-41, formula 2-46 and formula 2-50, p0 is grouting pressure, r0 is grouting pipe radius, r t is the penetration range of slurry in the soil at time t1, Q is grouting flow, n'0 is initial equivalent porosity of the soil, ρ p is suspended particle density, ρ is slurry density, δ is the volume proportion of suspended particles in the solid part of the slurry, g is gravitational acceleration, μ s is slurry viscosity, ρ w is water density, μ s0 is initial viscosity of the slurry, K0 is the permeability coefficient of the soil layer in the initial state, K w is the permeability coefficient of water in the stratum, μ w is water viscosity, t is grouting time, R is slurry diffusion radius, a is filtration coefficient, is the permeability coefficient change parameter of the soil, r is diffusion front radius, v0 is the speed of slurry before being injected into the stratum pore, p s is hydrostatic pressure;

[0046] The acquisition unit is used for acquiring construction parameters; the processing unit is connected with the acquisition unit and the grouting pressure and grouting time relationship calculation model, the processing unit is used for inputting the acquired construction parameters into the grouting pressure and grouting time relationship calculation model, obtaining the conditions of grouting pressure change with grouting time considering the deep filtration effect and the viscosity time-varying characteristics of slurry at the same time, the condition of grouting pressure change with grouting time considering the deep filtration effect alone and the condition of grouting pressure change with grouting time considering the viscosity time-varying characteristics alone and outputting.

[0047] Further, the acquisition unit acquires construction parameters of the underground structure, which can be obtained by manual input. The construction parameters acquired by the acquisition unit include grouting hole parameters, grouting flow parameters, filtration coefficient parameters, soil permeability coefficient variation parameters, soil initial porosity parameters, grout filling rate parameters (for calculating soil initial equivalent porosity), water-cement ratio parameters, density parameters of grout cement particles, density parameters of water, solid volume fraction of cement particles in grout, grout viscosity time-varying parameters, groundwater pressure parameters, soil permeability coefficient parameters, initial viscosity parameters of grout, viscosity parameters of water, and solid volume fraction parameters of original grout before permeation and diffusion. The processing unit is configured to input the acquired parameters into a grouting pressure and grouting time relationship calculation model, and obtain the variation of grouting pressure with time under three conditions (considering grout viscosity time-varying alone, considering deep filtration effect alone, and considering both) by calculation.

[0048] In one specific embodiment of the present application, the analysis system further includes a diffusion radius and grouting pressure relationship calculation model, which includes the following expression:

[0049]

[0050]

[0051] The processing unit is connected to the diffusion radius and grouting pressure relationship calculation model, and is configured to input the acquired construction parameters into the diffusion radius and grouting pressure relationship calculation model, and output the variation of diffusion radius with grouting pressure considering both deep filtration effect and grout viscosity time-varying, the variation of diffusion radius with grouting pressure considering deep filtration effect alone, and the variation of diffusion radius with grouting pressure considering viscosity time-varying alone by calculation.

[0052] In one specific embodiment of the present application, the analysis system further includes a grout pressure and diffusion distance relationship calculation model, which includes the following expression:

[0053]

[0054] In formula 2-43, formula 2-48, and formula 2-52, p r is the grout pressure at r0;

[0055] The processing unit connected with the slurry pressure and diffusion distance relationship calculation model is used for inputting the obtained construction parameters into the slurry pressure and diffusion distance relationship calculation model, obtaining the slurry pressure change with the distance from the grouting hole by considering the deep percolation effect and the viscosity time-varying characteristics of the slurry at the same time, the slurry pressure change with the distance from the grouting hole by considering the deep percolation effect alone, and the slurry pressure change with the distance from the grouting hole by considering the viscosity time-varying characteristics alone, and outputting.

[0056] In one specific embodiment of the present application, the analysis system further comprises a slurry viscosity change calculation model, which comprises the following expression:

[0057] μ s0 (δ,r,t)=μ s0 (t1) Equation 2-29,

[0058] λ(δ,r,t)=λ(t1) Equation 2-30,

[0059] In Equation 2-29 and Equation 2-30, λ is a viscosity time-varying parameter of the slurry;

[0060] The processing unit connected with the slurry viscosity change calculation model is used for inputting the obtained construction parameters and the set grouting time t1 into the slurry viscosity change calculation model, obtaining the slurry viscosity change at different positions by considering the deep percolation effect and the viscosity time-varying characteristics of the slurry at the same time, and outputting.

[0061] In one specific embodiment of the present application, the analysis system further comprises a slurry pressure and grouting time and distance from grouting hole relationship calculation model, which comprises the following expression:

[0062]

[0063] The processing unit connected with the slurry pressure and grouting time and distance from grouting hole relationship calculation model is used for inputting the set grouting time points and the obtained construction parameters into the constructed slurry pressure and grouting time and distance from grouting hole relationship calculation model, obtaining the slurry pressure change with the distance from the grouting hole corresponding to each grouting time point by calculation, and outputting.

[0064] In one specific embodiment of the present application, the analysis system further comprises a slurry permeation and diffusion model in the downstream and upstream directions, which comprises the following expression:

[0065]

[0066] In formula 3-29 and formula 3-34, t is a grouting time, n is a porosity of the stratum, β is a viscosity ratio of the slurry to water, η is a viscosity of water, χ is tortuosity, l is a flow straight line length of the slurry in the soil, l0 is a grouting hole radius, k is a stratum permeability, p0 is a grouting pressure, ρ w is a density of water, ρ is a slurry density, v is a water flow velocity, θ is an angle formed by a central axis of the capillary and a horizontal direction, τ0 is a yield stress, r0 is a capillary radius, p s is a hydrostatic pressure;

[0067] The obtaining unit is used for obtaining the grouting pressure, the water flow velocity, the hydrostatic pressure, the tortuosity, the grouting hole radius and the grouting time of the shield tunnel;

[0068] The processing unit is used for inputting the parameters obtained by the obtaining unit into a permeation and diffusion model of the slurry in the forward flow and reverse flow directions, so as to obtain the diffusion distances of the slurry in the forward flow and reverse flow directions considering the tortuosity effect and output the diffusion distances.

[0069] The principle of the deep percolation effect is that when the slurry penetrates and diffuses in the sandy soil layer, the suspended particles (such as fly ash, bentonite and cement colloid) in the slurry are carried into the stratum. Since the soil layer is a porous medium composed of irregular particles, part of the particles will be affected by chemical adsorption or physical barrier, resulting in deposition in the pore. The deposited particles no longer diffuse with the slurry, which is called percolation effect. As shown in the formula (1), when the finer particles in the slurry are mixed with water and pass through the pores of the soil layer, if the pressure applied to the slurry does not exceed the yield stress of the mixture, the movement of the fine particles will be blocked and retained inside the soil layer, thereby causing the deep percolation effect. Figure 1

[0070] The permeation and diffusion model of the present application simultaneously considers the deep percolation effect-viscosity time-varying coupling, and is based on the following basic assumptions:

[0071] (1) The slurry is assumed to be incompressible and isotropic, and the volume loss that may occur in the seepage process is ignored;

[0072] (2) The soil is regarded as a homogeneous porous medium, and the aggregate is considered as a rigid material and does not deform due to the seepage of the slurry;

[0073] (3) The densities of the suspended particles and the soil particles satisfy ρ p / ρ s = 1, and the deposited suspended particles can be equivalent to the soil particles;

[0074] (4) During the slurry permeation and diffusion process, the movement speed of the suspended particles is consistent with the flow velocity of the liquid part of the slurry, that is, v p = v w ​= v.

[0075] The present application takes the unit volume of soil in the slurry permeation and diffusion area as the analysis object. As shown in the figure, n Figure 2 s , n p , n w respectively represent the soil particle volume fraction, the slurry non-deposited suspended particle volume fraction and the liquid volume fraction of the unit volume of soil.

[0076] The porosity of the unit volume of soil and the volume fractions of the above components satisfy the following relationship:

[0077] n = n p + n w = 1 - n s Equation 2-1,

[0078] The flow rate η c of the suspended particles in the slurry is:

[0079]

[0080] The flow rate η w of the liquid in the slurry is:

[0081]

[0082] According to the principle of conservation of mass, we can obtain:

[0083] (1) Soil particles

[0084]

[0085] In the formula, ρ s is the soil particle density, kg / m 3 , ζ is the mass exchange parameter, the total mass of the suspended particles deposited in the unit volume of slurry.

[0086] (2) Liquid in the pore

[0087]

[0088] In the formula, v w is the flow velocity of the liquid, cm / s, ρ w is the density of water, kg / m 3 .

[0089] (3) Slurry suspended particles in the pore

[0090]

[0091] In the formula, ρ p is the suspended particle density, kg / m 3 .​

[0092] Based on assumption 3, formula 2-1 and formula 2-4 can be combined to obtain:

[0093]

[0094] Considering multiple influencing factors, the linear filtration law is used to simplify the calculation process:

[0095]

[0096] In the formula, a is the filtration coefficient, and δ is the volume proportion of suspended particles in the slurry in the solid part.

[0097] Formula 2-7 and formula 2-8 can be combined to obtain:

[0098]

[0099] Combining formula 2-1, 2-5, and 2-6, we obtain:

[0100]

[0101] Combining formula 2-7 and 2-10, we find:

[0102]

[0103] During the grouting process, it is generally believed that the slurry first fills the larger voids in the soil near the grouting pipe; when these voids are filled, the slurry spreads outward and penetrates into the surrounding strata under the driving force of the filling pressure, as shown in Figure 3 and Figure 4 .

[0104] According to the law of conservation of flow, the relationship between the seepage velocity v(r, t) of the slurry in the stratum pores in the seepage and diffusion area is as follows:

[0105]

[0106] In the formula, v0 is the velocity of the slurry before it is injected into the stratum pores, cm / s.

[0107] The above formula can be rearranged to obtain:

[0108] Assuming that the injection rate of the slurry remains constant, according to the principle of mass conservation, we obtain:

[0109]

[0110] The above formula can be rearranged to obtain:

[0111] According to the definition of the solid volume ratio δ of the suspended particles in the slurry, we obtain:

[0112] n p = δn Formula 2-16,

[0113] Substituting Formula 2-16 into Formula 2-6, we have:

[0114] After expanding the above Formula 2-17, and combining Formula 2-8, 2-9 and 2-11, we have:

[0115]

[0116] For the penetration and diffusion process of grout in grouting, the following initial conditions and boundary conditions are set:

[0117]

[0118] In the formula, f is the volume proportion of the solid component of the initial grout before penetration and diffusion, n'0 is the initial equivalent porosity of the soil, where n'0 = n0 + (1-n0) / ψ, ψ is the grout injection rate; R is the grout diffusion boundary radius, cm.

[0119] During the pore penetration process of the soil, the relationship between the change of the solid volume fraction of the grout can be represented by the following formula, where r0≤r≤R:

[0120]

[0121] Therefore, the expression of the soil porosity considering the deep effect of grout can be obtained by the above formula: when r0≤r≤R:

[0122] When R < r: n = n'0 Formula 2-22.

[0123] Time-varying viscosity: The grouting process generally uses silicate cement-based grout. Affected by the hydration reaction and thixotropic characteristics, the viscosity of the grout shows significant time dependence. Based on the indoor rheological test data, the viscosity evolution law can be characterized as an exponential function:

[0124] μ s (t) = μ s0 e λt Formula 2-23,

[0125] In the formula, μ s0 is the initial viscosity of the grout, Pa·s, and λ is the viscosity time-varying parameter of the grout.

[0126] According to the law of conservation of mass: the total amount of grout injected into the soil should be equal to the total amount of its penetration and diffusion in the soil, we have:

[0127] where Q is the flow rate of the grout, cm 3 / s, r t is the penetration range of the grout in the soil at time t1, i.e., the diffusion radius, cm.

[0128] Rearranging the above equation, since the radius of the grout hole r0 is much smaller than the diffusion radius of the grout, it can be considered that its influence on the entire diffusion process is negligible, thus determining the diffusion radius of the grout r t :

[0129]

[0130] The time required for the viscosity of the grout to increase corresponds to the diffusion time t of the grout, and when the diffusion radius reaches r, then t is:

[0131]

[0132] At this time, r satisfies the following relationship:

[0133]

[0134] In the process of pressure grouting of underground structures, many scholars have assumed that the concentration of the grout remains constant in order to simplify the calculation, attributing the evolution of the viscosity of the grout to a single factor of time, but the concentration gradient change caused by the seepage of the surrounding rock will affect the dynamic evolution law of its rheological parameters. The solid volume fraction δ of the cement particles in the grout and the water-cement ratio w / c satisfy the following relationship:

[0135]

[0136] where ρ p is the density of the suspended particles in the grout, kg / m 3 , ρ w is the density of water, kg / m 3 , and w / c is the water-cement ratio of the grout, w is the mass of water, kg, and c is the mass of lime, kg.

[0137] According to the results of field tests, combined with equation 2-28 and the viscosity time-varying equation of grout with different water-cement ratios, the relationship between the initial viscosity μ s0 and the time-varying parameter λ and the solid volume fraction δ of the cement particles can be determined.

[0138] According to equation 2-26, the solid volume fraction δ of the cement particles in the grout is related to the diffusion distance r, and the viscosity growth time t of the grout and the diffusion distance r have a space-time coupling relationship. Based on this correlation, when the grouting time is t1, μ s0 and λ at the radius r of the diffusion front can be expressed as:

[0139] μ s0 (δ, r, t) = μs0 (t1) Equation 2-29,

[0140] λ(δ, r, t) = λ(t1) Equation 2-30,

[0141] By combining Equations 2-23, 2-26, 2-29 and 2-30, the equation describing the change in viscosity of the slurry in the slurry infiltration zone can be obtained.

[0142] Simultaneously considering the deep percolation effect and the time-varying characteristics of the viscosity of the slurry, the slurry infiltration diffusion is:

[0143] According to Darcy's law, we have:

[0144] In the formula, Q is the grouting flow, cm 3 / s; A is the slurry infiltration area, A = 2πr 2 , cm 2 ; p is the slurry diffusion pressure, Pa; ρ is the slurry density, kg / m 3 .

[0145] In the formula, the density ρ of the slurry changes during the percolation process, and there is a certain corresponding relationship between this change and the solid volume ratio δ of the cement particles in the slurry, which can be expressed by the following formula: ρ = ρ p δ+ρ w (1-δ) Equation 2-32,

[0146] K w is the permeability coefficient of water in the stratum, which satisfies the following relationship:

[0147] In the formula, β is the ratio of the viscosity of the slurry to the viscosity of water.

[0148] In the formula, μ w is the viscosity of water, Pa·s.

[0149] Substituting Equation 2-34 into 2-33, we have:

[0150] To describe the process of deep percolation effect, a hyperbolic model is introduced, and the corresponding formula is given:

[0151]

[0152] In the formula, K0 is the permeability coefficient of the soil layer in the initial state, cm / s; is the change parameter of the permeability coefficient of the soil.

[0153] Combining Equations 2-21, 2-35 and 2-36, we have:

[0154] Since the grouting speed remains constant, combining equation 2-15, we can obtain:

[0155] Substituting equations 2-32, 2-37, and 2-38 into equation 2-31, we can obtain the slurry diffusion radius. hour:

[0156]

[0157] Let r = r0, and combine the boundary conditions. Integrating the above equation, we get:

[0158]

[0159] In the formula, p s The hydrostatic pressure is expressed in Pa.

[0160] Substituting equation 2-25 into the above equation, we can obtain the expression for the change of grouting pressure p0 with grouting time t:

[0161]

[0162] In the formula, p0 is the grouting pressure, Pa.

[0163] Substituting equation 2-26 into the above equation, we can obtain the grouting pressure p0 as a function of the diffusion radius r. t Expressions of change:

[0164]

[0165] Combined with boundary conditions The expression for the slurry pressure p at a distance r0 can be obtained. r for:

[0166]

[0167] Slurry permeation and diffusion considering deep infiltration effect alone:

[0168] Substituting the time-varying parameter λ=0 of the slurry into Equation 2-23, we get: μ s (t)=μ s0 Equation 2-44,

[0169] Substituting the above equation into Equation 2-40, we can obtain the spatiotemporal distribution equation of slurry pressure:

[0170]

[0171] Substituting equation 2-44 into equation 2-41, we can obtain the relationship between grouting pressure p0 and grouting time t:

[0172]

[0173] Similarly, the grouting pressure p0 as a function of the grout diffusion radius r can be obtained. t The changing relationship:

[0174]

[0175] The slurry pressure p at a distance r0 r The expression is:

[0176]

[0177] Considering viscosity-dependent time-varying slurry penetration and diffusion alone:

[0178] Substituting the permeation coefficient a = 0 into equation 2-23, we get:

[0179] Expression for slurry pressure:

[0180]

[0181] The expression for the change of grouting pressure p0 with grouting time t:

[0182]

[0183] Grouting pressure p0 varies with grout diffusion radius r t Expressions of change:

[0184]

[0185] The slurry pressure p at a distance r0 r The expression is:

[0186]

[0187] The theoretical model of this invention can simultaneously encompass the deep infiltration effect of slurry and the time-varying viscosity, or it can consider either factor individually. The following example illustrates the influence of various parameters on slurry infiltration and diffusion.

[0188] Assuming the underground structure project is a shield tunnel construction, with a grouting hole radius r0 of 0.04m and a grouting flow rate of 0.025m³ / h. 3 / min, the permeability coefficient a is 1.1×10-3, soil permeability coefficient variation parameters Given a soil porosity of -34, an initial soil porosity n0 of 0.38, and a grout filling ratio ψ of 1.5, the initial equivalent soil porosity n'0 can be calculated to be 0.79 according to the above formula. The water-cement ratio w / c is 1, and the density ρ of the grout cement particles is... p It is 3.0×103 kg / m 3 The density of water ρ wis 1.0 x 103kg / m 3 The initial value of the solid volume fraction of cement particles in the slurry is δ0= 0.25, and the viscosity time-varying parameter of the slurry is λ = 1.0 x 10 3 The groundwater pressure p s is taken as 0, and the permeability coefficient of the soil K0is 1.0 x 10 -6 The initial viscosity of the slurry is obtained according to the test results: μ w The viscosity of water is taken as 1.005 x 10 -3 Pa·s, and the solid volume fraction f of the original slurry before the penetration and diffusion occurs is 0.1.

[0189] The grouting time is set as 60 min, and the above parameters are substituted into equations 3-29 and 3-30 to obtain the change of the slurry viscosity at different positions under the conditions of considering the deep percolation effect and viscosity time-varying. On this basis, the viscosity time-varying parameter of the slurry is set as zero to obtain the change of the slurry viscosity at different positions under the condition of considering the deep percolation effect alone. Similarly, the percolation coefficient is set as zero to obtain the change of the slurry viscosity at different positions under the condition of considering the viscosity time-varying alone, and the relationship among the three is shown in the following equation 3-31. Figure 5

[0190] From Figure 5 ​It can be found that the viscosity of the slurry changes little in the initial stage of diffusion, and the curves of the three conditions basically coincide, indicating that the change of the viscosity of the slurry is basically consistent. This also shows that the slurry is in a relatively stable stage of penetration and diffusion, and the slurry is not much affected by the deep percolation effect and viscosity time variation. When the diffusion radius increases to 0.15 m, the curve considering only the deep percolation effect is separated from the other two curves. When the diffusion radius further increases to 0.35 m, the curve considering both the deep percolation effect and the viscosity time variation is separated from the curve considering only the viscosity time variation. Among them, the viscosity of the slurry considering only the viscosity time variation increases the fastest, indicating that the viscosity time variation has the greatest influence on the viscosity of the slurry. The viscosity of the slurry considering only the deep percolation effect gradually decreases with the increase of the diffusion radius, because the deep percolation effect has not been fully formed at the initial stage, and the slurry diffuses freely, so the viscosity of the slurry is basically consistent with that under the other two conditions. With the increase of the diffusion radius, the deep percolation effect will make the particles in the slurry stay and form a filter cake layer, so the concentration of the slurry will decrease, and the viscosity of the slurry will also decrease. Considering both conditions, the viscosity of the slurry increases slowly with the increase of the diffusion radius, especially when the diffusion radius is less than 0.35 m, the viscosity of the slurry is basically consistent with that considering only the viscosity time variation, because the deep percolation effect has not been fully formed at this time, and has little effect on the change of the viscosity of the slurry, and the viscosity of the slurry is mainly affected by the viscosity time variation of the slurry. When the diffusion radius reaches 0.95 m, the growth rate of the viscosity of the slurry tends to zero. This is because the deep percolation effect inhibits the further increase of the viscosity of the slurry with the increase of the diffusion distance.

[0191] The above related parameters are substituted into equations 2-41, 2-46 and 2-50, as shown in Figure 6 The variation of the grouting pressure with time considering only the viscosity time variation of the slurry, only the deep percolation effect, and both can be obtained.

[0192] From Figure 6It can be seen that when the grouting time is 0-3 min, the grouting pressure under the three conditions increases steeply with time, which shows that the slurry rapidly penetrates into the stratum pores in the initial stage, and the stratum resistance also increases rapidly. The difference in grouting pressure is small at this stage, indicating that the time-varying viscosity of the slurry and the deep filtration effect have relatively small influence at this time. With the increase of grouting time, the slurry pressure gradually decreases. Among them, considering the time-varying viscosity of the slurry alone, the growth rate of the grouting pressure is the smallest and the change is relatively the most stable, and the final grouting pressure value is also the lowest, which shows that the time-varying viscosity of the slurry has the smallest effect on the grouting pressure. Under the condition of considering the deep filtration effect alone, the grouting pressure increases with time faster than when considering the time-varying viscosity alone. This is because as the slurry penetrates further in the soil, the deep filtration effect of the stratum increases the resistance of the stratum pores to the fine particles of the slurry, so that the slurry needs to overcome greater resistance, and the grouting pressure will also increase. Considering the deep filtration effect and the time-varying viscosity of the slurry, the growth rate of the grouting pressure is the fastest, and the final pressure reaches the maximum value under the three conditions. This shows that under the coupling effect of the time-varying viscosity of the slurry and the deep filtration effect, the increase of the slurry viscosity and the filtration effect of the stratum pores will further increase the stratum resistance, and the slurry needs to overcome greater penetration resistance and shear resistance, so the slurry penetration and diffusion will be more difficult.

[0193] The above related parameters are substituted into equations 2-42, 2-47 and 2-51. As shown in Figure 1 , the variation of the slurry diffusion radius with grouting pressure under the conditions of considering the deep filtration effect alone, considering the time-varying viscosity of the slurry alone, and considering both can be obtained.

[0194] From Figure 7It can be seen that within the grouting pressure range of 0–1.5 bar, the diffusion radius growth trend under the three different conditions is basically consistent. This indicates that the time-varying viscosity and deep filtration effect have little impact on the diffusion of the grout in the initial stage. When the grouting pressure increases, the diffusion radius of the grout considering only the time-varying viscosity is much larger than the other two cases. This is because the deep filtration effect is ignored, and the influence of the time-varying viscosity on the diffusion radius of the grout is much smaller than that of the deep filtration effect. Therefore, under the same grouting pressure, the grout can diffuse to a greater range. However, when considering the deep filtration effect alone, the deposition of fine particles greatly hinders the penetration and diffusion of the grout, causing the grout diffusion curve to not exhibit the exponential growth characteristic of the diffusion radius with increasing grouting pressure shown by the time-varying viscosity curve, but rather a near-linear growth trend. When considering both the deep infiltration effect and the time-varying viscosity, the influence of grout viscosity on diffusion increases when the pressure exceeds 2 bar. The combined effect of the deep infiltration effect further inhibits the diffusion distance of the grout, minimizing the diffusion radius under the same grouting pressure. This combined effect forces the grout to overcome both the seepage resistance of soil particles and the flow resistance resulting from the increase in grout viscosity over time during diffusion, thus limiting the grout's diffusion range.

[0195] Substituting the aforementioned parameters into equations 2-43, 2-48, and 2-52, we can obtain the laws governing the variation of grout pressure with distance from the grouting hole, considering the deep infiltration effect alone, the time-varying viscosity of the grout alone, and both simultaneously. Figure 8 As shown.

[0196] from Figure 8 It can be seen that the diffusion radius increases similarly under the three conditions, and the grout pressure decreases rapidly with increasing distance from the grouting hole. This is because the resistance of the formation to the grout increases during diffusion, thus reducing the grout pressure. Among these, considering only the time-varying viscosity characteristics of the grout, the grout pressure decreases most slowly, and a significant value is still present at distances greater than 1.0 m. This indicates that when considering only viscosity time-varying characteristics, the grout diffusion resistance is much smaller than the resistance generated by deep filtration in the formation pores. Considering only the deep filtration effect, the grout pressure decreases significantly faster, rapidly dropping to zero. This indicates that the deep filtration effect rapidly increases the resistance of the grout in the formation, limiting long-distance diffusion. Considering both the deep filtration effect and viscosity time-varying characteristics, the grout pressure decreases most rapidly, dropping to zero at a distance of approximately 1.0 m from the grouting hole. This demonstrates that the coupling effect of gradually increasing slurry viscosity and deep infiltration enhances the slurry's permeability resistance in the formation and reduces the slurry diffusion range.

[0197] By taking the grouting time as 10-60 min and substituting the related parameters into equation 2-40, the law of slurry pressure change with diffusion distance can be obtained under the condition of considering deep percolation effect and viscosity time variability, and the specific results are shown in Figure 9

[0198] As can be seen from Figure 9 , with the extension of grouting time from 10 min to 60 min, the slurry pressure decay curve at each time point gradually moves away from the grouting hole. It shows that with the extension of grouting time, the slurry diffusion gradually deepens, the pressure maintains longer in the distance and the slurry diffusion range is larger. When grouting for 10 min, the pressure decays fastest from the grouting hole. With the extension of grouting time, the pressure decay rate gradually decreases and the slurry diffusion slowly stabilizes.

[0199] The viscosity of the slurry is weakly affected by the deep percolation effect and viscosity time variability at the initial stage of diffusion. However, with the increase of slurry diffusion distance, the viscosity change shows obvious difference. When considering the viscosity time variability alone, the viscosity increases rapidly with the diffusion radius; when considering the deep percolation effect alone, the viscosity gradually decreases with the diffusion radius; and when considering both effects, the viscosity shows a slow growth and tends to be stable, which reflects the coupling effect of deep percolation effect and viscosity time variability.

[0200] Under the three conditions (only considering deep percolation, only considering viscosity time variability, and considering both), the grouting pressure increases rapidly at the initial grouting stage. However, with the increase of grouting time, the grouting pressure rise rate gradually decreases and tends to be stable. Among them, the grouting pressure grows fastest when considering both deep percolation effect and viscosity time variability, indicating that the superposition of deep percolation effect and viscosity increase will increase the diffusion resistance of slurry.

[0201] The slurry diffusion radius shows a linear growth trend with the grouting pressure at the stage of small initial grouting pressure, and there is little difference among the three conditions. However, with the further increase of grouting pressure, the slurry diffusion radius considering viscosity time variability alone is significantly larger than that of the other two conditions. When considering deep percolation effect alone, the slurry diffusion radius grows smoothly. And when considering both effects, the slurry diffusion radius growth is inhibited, which reflects the limiting effect of the superposition of the two effects on the slurry diffusion distance.

[0202] Under the three conditions, the slurry pressure decreases rapidly with the increase of slurry diffusion distance. When considering both deep percolation effect and viscosity time variability, the slurry pressure decays fastest. And under the condition of considering viscosity time variability alone, the slurry pressure decays relatively slowly, indicating that the deep percolation effect enhances the resistance in the process of slurry diffusion. In addition, with the extension of grouting time, the slurry pressure distribution expands to a distance as a whole, and the diffusion area gradually stabilizes and expands.

[0203] The principle of tortuosity effect: ​

[0204] When the slurry flows in the soil, its flow path will be tortuous due to the complex pore structure, and the actual flow path will be much longer than the straight-line distance, which is called the tortuosity effect (as shown in Figure 10 In this paper, the concept of tortuosity is introduced to quantify this effect, which is defined as the ratio of the actual flow path length of the slurry in the soil to the straight-line distance, and its calculation formula is:

[0205] Assuming that the formation is isotropic, the relationship between tortuosity and porosity can be expressed as:

[0206]

[0207] In the formula, χ is the tortuosity, l e is the actual flow distance of the slurry in the soil, cm; l is the straight-line distance of the slurry in the soil, cm; n is the porosity of the formation.

[0208] Under the action of external shear force, the fluid will deform due to its own characteristics. Internal friction will inevitably occur between different parts of the fluid, which is the specific manifestation of fluid viscosity.

[0209] According to the specific manifestation of fluid viscosity, the shear stress τ and the velocity gradient du / dy are in a linear positive relationship, which is usually expressed as:

[0210] In the formula, τ is the shear stress, Pa; is the velocity gradient (shear rate), which represents the rate of change of the velocity between fluid layers; μ is the dynamic viscosity (also known as the viscosity coefficient) of the fluid, which reflects the ability of the fluid to resist deformation, Pa·s.

[0211] On the other hand, if the function in formula 3-3 is nonlinear, i.e. the shear stress τ and the shear rate du / dy are not in a proportional relationship, such fluid is defined as a non-Newtonian fluid. Unlike Newtonian fluids, the viscosity behavior of non-Newtonian fluids is more complex, and strictly speaking, only Newtonian fluids have a clear viscosity μ concept, because their viscosity is constant and can be described by only one parameter. The viscosity behavior of non-Newtonian fluids usually needs to be described by two or more parameters. However, in order to facilitate the description of the viscosity characteristics of non-Newtonian fluids, the concept of apparent viscosity η0 is usually introduced, which is expressed as follows:

[0212]

[0213] The apparent viscosity η0 is an important parameter to describe the viscous property of non-Newtonian fluid, but it is not a constant as the viscosity μ of Newtonian fluid. The apparent viscosity depends on the physical properties of the fluid itself, and also has a close relationship with the shear stress τ and shear rate du / dy. This indicates that the internal friction property of non-Newtonian fluid will change with the change of flow conditions. In order to more clearly show the viscous behavior of non-Newtonian fluid, the functional relationship between shear stress τ and shear rate du / dy is usually shown in the form of a curve, which is called the rheological curve. Through the analysis of the rheological curve, the flow characteristics of the fluid under different shear conditions can be understood.

[0214] In the process of shield construction, the single liquid slurry used in synchronous grouting is mainly made of cement, mineral powder, additives and stabilizers, while the double liquid slurry is a grouting material composed of two components. Generally speaking, these slurries belong to non-Newtonian fluid. According to the literature in the field of slurry material research, only Bingham model, power law model and Herschel-Bulkley model can be used to study the rheological properties of cement mortar at present. In addition, many slurries (such as mud, cement slurry, drilling fluid, etc.) also exhibit similar characteristics of Bingham fluid in actual engineering. Through the Bingham fluid model, the diffusion behavior of slurry in porous media or pipeline can be more accurately analyzed, thereby providing theoretical support for engineering practice.

[0215] The mathematical expression of Bingham fluid constitutive model is: τ = τ0 + η p γ formula 3-5,

[0216] In the formula, τ0 is the yield stress, Pa; η p is the plastic viscosity, Pa·s.

[0217] In particular, when the yield stress τ0 is zero, the Bingham fluid is simplified as Newtonian fluid.

[0218] The basic assumptions of the permeation and diffusion model of slurry in the forward and reverse flow directions are:

[0219] (1) The porous medium satisfies the homogeneity and isotropy;

[0220] (2) The slurry is assumed to be an incompressible homogeneous fluid, ignoring the dilution effect of groundwater and keeping the fluid flow pattern consistent;

[0221] (3) The slurry is in laminar flow, ignoring the energy loss of the slurry in the flow process.

[0222] When studying the permeation and diffusion characteristics of grout, a uniform capillary model is typically used for analysis. The effective pore structure in a porous medium can be considered as consisting of several capillaries of the same diameter, simplifying the diffusion process of the grout within the medium into the overall effect of the grout flowing through these capillaries. To investigate the permeation and diffusion characteristics of grout along the tunnel radial direction in the shield tail gap and to study it using a uniform capillary group model, it is necessary to first establish the equations of motion for the grout flow within a single capillary.

[0223] Construct a Cartesian coordinate system by selecting a capillary tube along the radial direction of the tunnel, such as... Figure 11 As shown, the angle between the central axis of the capillary and the horizontal direction is θ, the radius of the capillary is r0, the axis of symmetry is the central axis of the capillary, and a segment of length dl is selected. e An analysis is performed on a Bingham fluid element with radius r. The scouring force of the water flow is p. w The grouting pressure is p, the shear stress of the infinitesimal element is τ, and the pressures at both ends of the infinitesimal element are p+p. w and p+p w +d(p+p w ).

[0224] The fluid element must satisfy the following mechanical equilibrium relationship:

[0225] (p+p w )πr 2 -(p+p w +d(p+p w ))πr 2 -ρgsinθ·πr 2 dl e -τ·2πrdl e =0 Equation 3-6,

[0226] The above equation simplifies to: d(p+p) w )πr 2 +ρgsinθ·πr 2 dl e +τ·2πrdl e =0 Equation 3-7,

[0227] Further analysis revealed:

[0228] The rheological equation for Bingham fluid can be expressed as: τ=τ0+η p γ-form 3-9,

[0229] In the formula, τ is the shear stress (Pa); τ0 is the yield stress (Pa); η p The viscosity is plastic, Pa·s; The shear rate (γ = -dv / dr) represents the rate of change of velocity between fluid layers.

[0230] For Bingham fluid, since the fluid has a yield stress τ0, the relative motion between fluid layers will only occur when the shear stress τ exceeds its yield limit, so the shear stress in equation 3-8 is set as the yield stress, and the slurry flow core radius r p :

[0231] As Figure 12 shown, in the range of 0 < r ≤ r p , the shear stress of the fluid is not enough to break through the yield stress, so there will be no relative shear motion between the fluid layers, and the fluid will remain relatively static and move in a piston-like overall motion, which is defined as the flow core area; when r p < r ≤ r0, the fluid will shear flow, and the fluid layers will be in a non-stationary state, and the overall motion will show a gradient distribution, which is called the gradient area.

[0232] Substitute equation 3-9 into equation 3-8 to get:

[0233] The above equation can be obtained by:

[0234] Integrating the above equation, we get in the range of r p < r ≤ r0:

[0235]

[0236] Where C is a constant.

[0237] Combined with the boundary condition: when r = r0, v = 0, the above equation can be rewritten as:

[0238]

[0239] In the range of 0 < r ≤ r p , the fluid flow rate v p can be replaced by r p in equation 3-11 to get:

[0240] The total flow rate q of the slurry is:

[0241] After solving the above equation, we get:

[0242] The average flow rate in the pipe is:

[0243] According to the theory of seepage mechanics, the flow rate of the slurry can be derived as:

[0244]

[0245] where n is the porosity of the stratum.

[0246] The ratio of the viscosity of the slurry to the viscosity of water is defined as: β = η p / η Formula 3-20,

[0247] where η is the viscosity of water, Pa·s.

[0248] The stratum permeability k, the porosity n, and the capillary radius r0satisfy the following relationship:

[0249]

[0250] Substituting Formula 3-20 and Formula 3-21 into Formula 3-19, we have:

[0251]

[0252] Therefore, the unit flow rate of the slurry is:

[0253]

[0254] Integrating Formula 3-23 during the diffusion of the slurry in the reverse water direction, we have: when l e = l0, p = p0, p w = p w ; when l e = l e , p = 0, p w = 0. Therefore, the above formula can be rewritten as:

[0255]

[0256] Therefore, the unit flow rate in the forward water direction is:

[0257]

[0258] Considering that the volume of the slurry injected in a unit time is exactly equal to the volume of the slurry required for permeation and diffusion, we have:

[0259] Substituting Formula 3-25 into Formula 3-26, we have:

[0260]

[0261] where p w is the dynamic flushing force in the forward water direction, Pa; l e is the diffusion distance of the slurry, cm; l0is the radius of the grouting pipe, cm; and t is the grouting time, s.

[0262] Based on the static pressure energy conversion mechanism of Bernoulli equation to kinetic energy, when the slurry diffusion direction is the same as the water flow direction, there is a relationship as follows:

[0263] In the formula, t is the grouting time, s; l e is the slurry diffusion distance, cm.

[0264] The formula 3-2 and the formula 3-27 are brought into the formula 3-28, and the relationship between the slurry diffusion distance and the grouting time in the water direction is obtained:

[0265]

[0266] In the process of slurry diffusion along the water direction, according to the boundary conditions, when l e = l0, p = p0, p w = p w ; when l e = l e , p = p s , p w = 0. Therefore, the above formula can be rewritten as:

[0267]

[0268] Therefore, the unit flow in the water direction can be obtained as:

[0269]

[0270] Similarly, the grouting time relationship formula in the water direction is established:

[0271]

[0272] In the formula, p w is the dynamic water scouring force in the water direction, Pa; p s is the static water pressure, Pa.

[0273] Based on the static pressure energy conversion mechanism of Bernoulli equation to kinetic energy, when the slurry diffusion direction is opposite to the water flow direction:

[0274] The formula 3-2 and the formula 3-32 are brought into the formula 3-33, and the following formula is obtained:

[0275]

[0276] The formula 3-29 and the formula 3-34 respectively represent the penetration and diffusion model of slurry in the water direction and the water direction under the condition of underground water flow. The diffusion range of slurry can be obtained by grouting pressure p0, water flow velocity v, static water pressure p sThe parameters such as tortuosity χ, grouting hole radius l0 and grouting time t are calculated.

[0277] By comparing formula 3-29 with formula 3-34, it can be concluded that under the condition of convection, the scouring pressure of water flow and the grouting pressure are superimposed, which enhances the driving force of the slurry and expands the diffusion range of the slurry. On the contrary, under the condition of counterflow, the scouring pressure of water flow and the grouting pressure jointly form a counterforce, which requires additional grouting energy to overcome the reverse action, thereby leading to a decrease in the diffusion range of the slurry.

[0278] Due to the characteristics of the shield synchronous grouting slurry that cannot be directly observed during the diffusion process outside the segment, the verification of the theoretical model faces great challenges. In actual shield construction, synchronous grouting slurry first fills the annular gap between the segment and the shield tail, and then penetrates and diffuses along the radial direction of the tunnel to the surrounding stratum under the driving of the grouting pressure. If the physical mechanism of slurry penetration and diffusion is analyzed, this process has high similarity with the slurry diffusion behavior in traditional permeation grouting. In existing research, Zhou Yao et al. (Zhou Yao, Xie Zhiquing, Liu Changyou, et al. Dynamic water grouting model test of water-rich sandy gravel stratum [J]. Chinese Journal of Underground Space and Engineering, 2023, 19(06): 1926-1937) analyzed the influence of the comprehensive action of stratum permeability coefficient, water flow velocity, water-cement ratio and grouting pressure on the diffusion law of slurry in soil through dynamic water grouting model test. The test controls the stratum coefficient by setting different fractal dimensions of sandy gravel layer, controls the underground water flow velocity by using adjustable valve, and controls the grouting pressure by setting different grouting water head height. The test model box is composed of a transparent chocolate plate with a size of 520mm×320mm×310mm, and the model box is divided into grouting area and steady flow area by a perforated partition plate. The stratum material is selected as riverbed sandy gravel, and the specific test device is as shown in Figure 13

[0279] ​According to the experimental conditions and data provided in the reference, the main parameters used in the model test are as follows: the groundwater flow velocity is 6 cm / s, the water-cement ratio of the grout is 1, the corresponding grout viscosity is 0.0096 Pa-s, the yield stress is 1.563 Pa, the grouting pipe radius is 20 mm, the grouting pressure is 28.81 kPa, the angle in the horizontal direction is 0, the formation permeability coefficient is 0.3149 cm / s, the formation fractal dimension is 2.49, the porosity is 0.51 calculated by the formula 3.2, and the tortuosity is 1.245 calculated according to the formula 3.2. By substituting the above parameters into the formula 3-29 and the formula 3-34, the theoretical calculation values of the grout permeation and diffusion under the conditions of considering the tortuosity effect and groundwater flow are obtained. Table 3-1 shows the comparison between the theoretical calculation values and the experimental values.

[0280] Table 3-1 Comparison of grout permeation and diffusion distance between theoretical calculation values and experimental values

[0281]

[0282] According to the comparison between the grout permeation and diffusion theoretical calculation values and the experimental values in the table, the established grout permeation and diffusion theoretical model of synchronous grouting shows good prediction accuracy under the conditions of considering the tortuosity effect and groundwater flow. Among them, the theoretical calculation errors of the grout permeation and diffusion in the water direction and the reverse water direction are 8.8% and 9.5% respectively, which are significantly lower than the corresponding 17.9% and 19.2% without considering the tortuosity effect. This fully reflects the important influence of the tortuosity effect on the actual grout permeation and diffusion process under the condition of groundwater flow, and verifies the rationality and applicability of the theoretical model. In addition, whether the theoretical calculation values or the experimental values, it can be found that the grout permeation and diffusion distance in the water direction is greater than that in the reverse water direction. This shows that under the action of groundwater flow, when the grout flow direction is consistent with the water flow direction, the water flow direction has a boosting effect on the grout diffusion, and the grout is more likely to penetrate and diffuse to a farther range along the water flow path. On the contrary, the reverse water flow will collide with the grout flow, weakening the permeability of the grout, resulting in a significant decrease in the diffusion distance.

[0283] Theoretical prediction error in the water flow direction is slightly larger than that in the opposite direction, because the farther diffusion distance of slurry in the water flow direction makes the seepage path more complex, thus increasing the error of theoretical prediction. In addition, there are still some errors between the predicted values of the theoretical model and the test values, which are mainly caused by the following reasons: 1) The parameters such as soil layer permeability, slurry viscosity and groundwater flow rate used in the theoretical calculation are mostly based on the idealized homogeneous assumption. However, the actual stratum conditions are often characterized by anisotropy and heterogeneity, which will lead to the deviation between the model prediction and the test measurement; 2) The slurry-soil interaction mechanism is complex, and the slurry diffusion process in the actual project not only involves fluid permeation, but also involves complex physical and chemical effects such as particle plugging, consolidation and precipitation. However, the theoretical model is not sufficient to describe these micro effects, resulting in some deviation between the theoretical prediction and the test values; 3) The initial state factors such as the initial water content of the soil and the distribution of the gas in the pore will have an impact on the slurry diffusion path and range. The gas existing in the pore may cause the local occlusion of slurry and channel or the gas entrainment effect, and the theoretical model derived in this paper has not considered this; 4) Although this study has considered the tortuosity effect, the pore structure of the actual stratum is often more complex, and the characteristics such as the branching and confluence phenomenon in the stratum pore, multiple tortuous paths are difficult to completely describe through the theoretical formula, and the simplification in the theoretical formula will bring the gap between the theory and the actual situation.

[0284] The application further provides a time-varying analysis method for permeation, filtration and diffusion of underground structure pressure consolidation grouting.

[0285] The analysis method of the application comprises the following steps:

[0286] A calculation model of the relationship between grouting pressure and grouting time is constructed, and the calculation model of the relationship between grouting pressure and grouting time comprises the following expressions:

[0287]

[0288] In formula 2-41, formula 2-46 and formula 2-50, p0 is grouting pressure, r0 is grouting pipe radius, r t is the permeation range of slurry in the soil at time t1, Q is grouting flow, n'0 is initial equivalent porosity of the soil, ρ p is suspended particle density, ρ is slurry density, δ is the volume proportion of suspended particles in the solid part of the slurry, g is gravitational acceleration, μ s is slurry viscosity, ρ w is water density, μ s0 is initial viscosity of the slurry, K0 is the permeability coefficient of the soil layer in the initial state, K w is the permeability coefficient of water in the stratum, μw viscosity of water, t is grouting time, r is diffusion radius, a is filtration coefficient, viscosity of water, t is grouting time, r is diffusion radius, a is filtration coefficient, s hydrostatic pressure;

[0289] obtaining construction parameters of the underground structure; the obtained construction parameters of the underground structure include grouting hole parameters, grouting flow parameters, filtration coefficient parameters, soil permeability coefficient variation parameters, soil initial porosity parameters, slurry filling rate parameters (for calculating soil initial equivalent porosity), water-cement ratio parameters, density parameters of slurry cement particles, density parameters of water, solid volume fraction of cement particles in the slurry, slurry viscosity time-varying parameters, groundwater pressure parameters, soil permeability coefficient parameters, initial viscosity parameters of the slurry, viscosity parameters of water, and solid volume fraction parameters of the original slurry before permeation and diffusion.

[0290] inputting the obtained construction parameters into the constructed grouting pressure-grouting time relationship calculation model, obtaining, by calculation, the conditions of the grouting pressure varying with the grouting time considering the deep filtration effect and the slurry viscosity time-varying characteristics simultaneously, the grouting pressure varying with the grouting time considering the deep filtration effect only, and the grouting pressure varying with the grouting time considering the viscosity time-varying characteristics only, and outputting.

[0291] In one specific embodiment of the present application, the analysis method further comprises:

[0292] constructing a diffusion radius-grouting pressure relationship calculation model, the constructed diffusion radius-grouting pressure relationship calculation model comprising the following expression:

[0293]

[0294] inputting the obtained construction parameters into the constructed diffusion radius-grouting pressure relationship calculation model, obtaining, by calculation, the conditions of the diffusion radius varying with the grouting pressure considering the deep filtration effect and the slurry viscosity time-varying characteristics simultaneously, the diffusion radius varying with the grouting pressure considering the deep filtration effect only, and the diffusion radius varying with the grouting pressure considering the viscosity time-varying characteristics only, and outputting.

[0295] In one specific embodiment of the present application, the analysis method further comprises:

[0296] constructing a slurry pressure-diffusion distance relationship calculation model, the constructed slurry pressure-diffusion distance relationship calculation model comprising the following expression:

[0297]

[0298] In formula 2-43, formula 2-48, and formula 2-52, p r is the slurry pressure at r0;

[0299] The obtained construction parameters are input into the constructed relationship calculation model of slurry pressure and diffusion distance, and through calculation, the slurry pressure changing with the distance from the grouting hole under the conditions of simultaneously considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, the deep percolation effect alone, and the viscosity time-varying characteristics alone is obtained and output.

[0300] In one specific embodiment of the present application, the analysis method further comprises:

[0301] A slurry viscosity change calculation model is constructed, and the constructed slurry viscosity change calculation model comprises the following expression:

[0302] μ s0 (δ,r,t)=μ s0 (t1) formula 2-29,

[0303] λ(δ,r,t)=λ(t1) formula 2-30,

[0304] In formula 2-29 and formula 2-30, λ is a slurry viscosity time-varying parameter;

[0305] The obtained construction parameters and the set grouting time t1 are input into the constructed slurry viscosity change calculation model, and through calculation, the slurry viscosity changing at different positions under the conditions of simultaneously considering the deep percolation effect and the viscosity time-varying characteristics of the slurry is obtained and output.

[0306] In one specific embodiment of the present application, the analysis method further comprises:

[0307] A relationship calculation model of slurry pressure and grouting time and distance from grouting hole is constructed, and the constructed relationship calculation model of slurry pressure and grouting time and distance from grouting hole comprises the following expression:

[0308]

[0309] A plurality of grouting time points are set, the set grouting time points and the obtained construction parameters are input into the constructed relationship calculation model of slurry pressure and grouting time and distance from grouting hole, and through calculation, the slurry pressure changing with the distance from the grouting hole corresponding to each grouting time point is obtained and output.

[0310] In one specific embodiment of the present application, the analysis method comprises:

[0311] The permeation and diffusion model of the slurry in the forward flow and reverse flow directions is constructed, and the permeation and diffusion model of the slurry in the forward flow and reverse flow directions constructed includes the following expressions:

[0312]

[0313] In formula 3-29 and formula 3-34, t is the grouting time, n is the porosity of the stratum, β is the viscosity ratio of the slurry and water, η is the viscosity of water, χ is the tortuosity, l is the linear length of the slurry flow in the soil, l0 is the grouting hole radius, k is the stratum permeability, p0 is the grouting pressure, ρ w is the density of water, ρ is the slurry density, v is the water flow velocity, θ is the angle formed by the central axis of the capillary and the horizontal direction, τ0 is the yield stress, r0 is the capillary radius, p s is the hydrostatic pressure;

[0314] The grouting pressure, water flow velocity, hydrostatic pressure, tortuosity, grouting hole radius and grouting time of the shield tunnel are obtained and input into the constructed permeation and diffusion model of the slurry in the forward flow and reverse flow directions, so as to obtain the diffusion distance of the slurry in the forward flow direction considering the tortuosity effect and the diffusion distance of the slurry in the reverse flow direction considering the tortuosity effect and output.

[0315] The above embodiments of the present application are described in detail in combination with the drawings, and those skilled in the art can make various changes to the present application according to the above description. Therefore, some details in the embodiments should not constitute a limitation on the present application, and the scope of protection of the present application will be defined by the appended claims.

Claims

1. A method for time-varying analysis of permeation and filtration diffusion of underground structure compaction grouting, characterized in that, The method comprises the following steps: The method comprises the following steps: In Formula 2-41, Formula 2-46, and Formula 2-50, p0 is a grouting pressure, r0 is a grouting pipe radius, r t is a penetration range of the slurry in the soil at time t1, Q is a grouting flow rate, n'0 is an initial equivalent porosity of the soil, p p is a suspended particle density, p is a slurry density, d is a volume ratio of the suspended particles in the slurry to a solid portion, g is a gravitational acceleration, m s is a slurry viscosity, p w is a water density, m s0 is an initial viscosity of the slurry, K0 is a permeability coefficient of the soil layer in an initial state, K w is a permeability coefficient of water in the soil layer, m w is a viscosity of water, t is a grouting time, r is a slurry diffusion radius, a is a filtration coefficient, is a permeability coefficient change parameter of the soil, r is a diffusion front radius, v0 is a velocity of the slurry before being injected into a soil layer, p s is a hydrostatic pressure; Obtain construction parameters of the underground structure; Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation.

2. The method of time-varying analysis of permeation and filtration and diffusion of underground structure compaction grouting according to claim 1, wherein, Further comprising: The method comprises the following steps: Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation.

3. The method of time-varying analysis of permeation and filtration and diffusion of underground structure compaction grouting according to claim 1, wherein, Further comprising: The method comprises the following steps: In formulae 2-43, 2-48, and 2-52, p r is the slurry pressure at r0; Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation.

4. The method of time-varying analysis of permeation and filtration and diffusion of underground structure compaction grouting according to claim 1, wherein, Further comprising: The method comprises the following steps: μ s0 (δ, r, t) = μ s0 (t1) Equation 2-29, Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation. Further comprising: The method comprises the following steps:

5. The method of time-varying analysis of permeation and filtration and diffusion of underground structure compaction grouting according to claim 1, wherein, Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation. Further comprising: The method comprises the following steps:

6. The method of time-varying analysis of permeation and filtration and diffusion of underground structure compaction grouting according to claim 1, wherein, Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation. Further comprising: The method comprises the following steps: Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation. Further comprising: The method comprises the following steps: Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation. Further comprising: The method comprises the following steps: Input the obtained construction parameters into the constructed calculation model of the relationship between the grouting pressure and the grouting time, and obtain and output the changes of the grouting pressure with the grouting time under the conditions of considering the deep percolation effect and the viscosity time-varying characteristics of the slurry, considering only the deep percolation effect, and considering only the viscosity time-varying characteristics by calculation. In Formula 3-29 and Formula 3-34, t is the grouting time, n is the porosity of the stratum, β is the viscosity ratio of the slurry to water, η is the viscosity of water, χ is the tortuosity, l is the linear length of the slurry flow in the soil, l0 is the grouting hole radius, k is the stratum permeability, p0 is the grouting pressure, ρ w is the density of water, ρ is the slurry density, v is the water flow velocity, θ is the angle formed by the central axis of the capillary and the horizontal direction, τ0 is the yield stress, r0 is the capillary radius, p s is the hydrostatic pressure; The grouting pressure, water flow velocity, hydrostatic pressure, tortuosity, grouting hole radius and grouting time of the shield tunnel are obtained and input into the constructed permeation and diffusion model of the slurry in the forward flow and reverse flow directions, so as to obtain the diffusion distance of the slurry in the forward flow direction considering the tortuosity effect and the diffusion distance of the slurry in the reverse flow direction considering the tortuosity effect and output.

7. A system for time-varying analysis of consolidation grouting permeation seepage diffusion of underground structures, characterized by, It comprises: A grouting pressure and grouting time relationship calculation model comprising the following expression: In Formula 2-41, Formula 2-46 and Formula 2-50, p0 is the grouting pressure, r0 is the grouting pipe radius, r t is the penetration range of the slurry in the soil at time t1, Q is the grouting flow, n'0 is the initial equivalent porosity of the soil, p p is the density of the suspended particles, p is the density of the slurry, d is the volume proportion of the suspended particles in the solid part of the slurry, g is the acceleration of gravity, m s is the viscosity of the slurry, p w is the density of water, m s0 is the initial viscosity of the slurry, K0 is the permeability coefficient of the soil layer in the initial state, K w is the permeability coefficient of water in the soil layer, m w is the viscosity of water, t is the grouting time, a is the diffusion radius of the slurry, a is the filtration coefficient, is the permeability coefficient change parameter of the soil, r is the diffusion front radius, v0 is the velocity of the slurry before being injected into the soil layer, p s is the hydrostatic pressure; An acquisition unit for acquiring construction parameters of an underground structure; A processing unit connected with the acquisition unit and the grouting pressure and grouting time relationship calculation model, for inputting the acquired construction parameters into the grouting pressure and grouting time relationship calculation model, and obtaining the change of the grouting pressure with the grouting time considering the deep percolation effect and the viscosity time-varying characteristic of the slurry, the change of the grouting pressure with the grouting time considering the deep percolation effect alone, and the change of the grouting pressure with the grouting time considering the viscosity time-varying characteristic alone, and outputting.

8. The underground structure compaction grouting permeation loss dispersion time-variation analysis system of claim 7, wherein, It further comprises: A diffusion radius and grouting pressure relationship calculation model comprising the following expression: The processing unit is connected with the diffusion radius and grouting pressure relationship calculation model, for inputting the acquired construction parameters into the diffusion radius and grouting pressure relationship calculation model, and obtaining the change of the diffusion radius with the grouting pressure considering the deep percolation effect and the viscosity time-varying characteristic of the slurry, the change of the diffusion radius with the grouting pressure considering the deep percolation effect alone, and the change of the diffusion radius with the grouting pressure considering the viscosity time-varying characteristic alone, and outputting.

9. The underground structure compaction grouting permeation loss dispersion time-variation analysis system of claim 7, wherein, It further comprises: A slurry pressure and diffusion distance relationship calculation model comprising the following expression: In formulae 2-43, 2-48, and 2-52, p r is the slurry pressure at r0; The processing unit is connected with the slurry pressure and diffusion distance relationship calculation model, for inputting the acquired construction parameters into the slurry pressure and diffusion distance relationship calculation model, and obtaining the change of the slurry pressure with the distance from the grouting hole considering the deep percolation effect and the viscosity time-varying characteristic of the slurry, the change of the slurry pressure with the distance from the grouting hole considering the deep percolation effect alone, and the change of the slurry pressure with the distance from the grouting hole considering the viscosity time-varying characteristic alone, and outputting.

10. The underground structure consolidation grouting permeation seepage diffusion time-variation analysis system of claim 7, wherein, It further comprises: A slurry viscosity change calculation model comprising the following expression: μ s0 (δ, r, t) = μ s0 (t1) Equation 2-29, λ(δ, r, t) = λ(t1) Equation 2-30, In Equation 2-29 and Equation 2-30, λ is a viscosity time-varying characteristic parameter of the slurry; The processing unit is connected with the slurry viscosity change calculation model, for inputting the acquired construction parameters and the set grouting time t1 into the slurry viscosity change calculation model, and obtaining the change of the viscosity of the slurry at different positions considering the deep percolation effect and the viscosity time-varying characteristic of the slurry, and outputting.

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