Calculation method of grout loss in synchronous grouting of shield tunnel based on finite element analysis

Abstract

The present invention proposes a method for calculating the loss of slurry in synchronous grouting of a shield tunnel based on finite element analysis, and relates to the technical field of shield grouting. It includes establishing a group of nonlinear partial differential equations of slurry migration and clogging in the soil, and determining the numerical solution through the finite element method to obtain relevant material parameters; establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on soil layer distribution, tunnel geometric characteristics and relevant material parameters; simulating the tunnel excavation and grouting process based on the finite element simulation model; wherein the grouting process includes the process from the beginning of grouting to the end of grouting and the continuous penetration and clogging of slurry into the surrounding soil after the end of grouting; determining the slurry loss volume based on the slurry diffusion range and relevant material parameters. The present invention is completely based on mathematical formula description, is objective, does not rely on empirical judgment, can analyze the real diffusion process of slurry in uneven strata, and the obtained slurry loss coefficient is more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of shield grouting, and in particular to a method for calculating slurry loss during synchronous grouting of a shield tunnel based on finite element analysis. Background Art

[0002] Mechanized excavation using shield machines is common in the construction of deep buried tunnels and underwater tunnels. As the shield machine advances, due to the over-excavation of the shield, an annular gap of up to 20 cm can be formed between the shield tail lining and the surrounding soil. In order to control surface settlement, maintain the stability of the lining and the waterproofness of the tunnel, the shield machine uses synchronous grouting behind the wall to fill the gap at the shield tail during excavation. However, after the grouting material is injected into the gap at the shield tail, the slurry tends to penetrate and diffuse into the surrounding soil layer under the action of the grouting pressure, and after the grouting is completed and the grouting port is closed, as the pressure of the grouting layer dissipates, it continues to penetrate and diffuse into the surrounding soil, thus causing slurry loss and displacement of the surrounding strata. Therefore, accurately determining the amount of slurry lost from synchronous grouting of shield tunnels under different strata and different grouting parameters is of great significance to controlling stratum disturbance and construction costs. At present, the research on synchronous grouting of shield tunnels mainly includes the following categories:

[0003] (1) Empirical method

[0004] In engineering practice, the permeability coefficient of the strata around the tunnel can be obtained from the preliminary exploration results. The empirical method is to estimate the grout loss coefficient based on the grouting materials given by experience when the permeability coefficient of the strata around the tunnel is known. However, since this coefficient is determined artificially based on experience, it is highly subjective and often has certain discrepancies with the actual situation.

[0005] (2) Analytical method

[0006] Some scholars have determined the slurry diffusion distance by the balance between the slurry diffusion pressure and the groundwater pressure based on different geometric diffusion assumptions. This method mainly focuses on the influence of the ideal diffusion of slurry on the tunnel lining pressure. Its limitation is that it cannot truly consider the infiltration and diffusion process of slurry into the surrounding soil, and cannot calculate the diffusion of slurry in mixed strata, which is inconsistent with the actual situation.

[0007] The existing calculation methods have the following two main problems: 1. Relying on experience, the loss of slurry needs to be roughly judged based on the permeability of the slurry in different soil layers before calculation, and there is a certain error between the estimated result and the actual situation. 2. It is impossible to consider the actual process of the slurry's penetration and diffusion into the surrounding soil (slurry migration and siltation), and can only consider the ideal diffusion of the slurry in a single soil layer. The results obtained by these two methods have a certain error from their true values, which will have a certain impact on the determination of the shield tunnel synchronous grouting parameters and slurry dosage in the design stage, as well as the deformation control of the stratum and tunnel in the construction stage. Therefore, correctly determining the loss of slurry from the synchronous grouting of the shield tunnel is of great significance for guiding reasonable design and construction.

[0008] In view of the shortcomings of the prior art, it is necessary to provide a method for calculating the loss of grouting slurry in synchronous grouting of a shield tunnel based on finite element analysis, which can solve the problems raised in the above background technology. Summary of the invention

[0009] The purpose of the present invention is to provide a method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis, which can propose solutions to the deficiencies in the prior art and has the characteristics of simple structure, being able to effectively coarsely crush and dry biomass raw materials, and being conducive to subsequent fine crushing operations.

[0010] The embodiment of the present invention is achieved as follows:

[0011] The calculation method of grout loss in synchronous grouting of shield tunnel based on finite element analysis includes the following steps:

[0012] A set of nonlinear partial differential equations for slurry migration and clogging in soil is established, and the numerical solutions are determined by finite element method to obtain relevant material parameters;

[0013] According to the tunnel soil layer distribution, tunnel geometric characteristics and the relevant material parameters, a finite element simulation model for shield tunnel excavation and grouting simulation is established;

[0014] The tunnel excavation and grouting process is simulated according to the finite element simulation model; wherein the grouting process includes the process from the beginning of grouting to the end of grouting and the process in which the slurry continues to penetrate into the surrounding soil and clog after the end of grouting;

[0015] The slurry loss volume is determined based on the slurry diffusion range and the relevant material parameters.

[0016] In some embodiments of the present invention, the step of establishing a set of nonlinear partial differential equations for slurry migration and clogging in the soil and determining the numerical solution of material parameters by finite element method comprises:

[0017] The first set of nonlinear partial differential equations for slurry migration and clogging in soil is established:

[0018]

[0019]

[0020] μ=μ g c+μ w (1-c);

[0021]

[0022]

[0023] Where: k0 is the initial intrinsic permeability; ρg and ρw are the densities of the slurry and pure water, respectively; μ is the dynamic viscosity of the fluid, where μg and μw are the dynamic viscosities of the slurry and pure water, respectively, and μg0 is the initial viscosity of the slurry; ξ is the material constant determined by the dynamic viscosity test; λ f is a parameter of the clogging rate of slurry in granular material determined by indoor grouting tests, wherein the clogging of the slurry in the soil increases with the increase of grouting flow rate and concentration;

[0024] The numerical solution of the first set of equations is determined by the finite element method to obtain first relevant material parameters, wherein the first relevant material parameters include: soil inherent permeability k; liquid mixture density ρ; fluid dynamic viscosity μ; slurry clogging rate n.

[0025] In some embodiments of the present invention, the step of establishing a set of nonlinear partial differential equations for slurry migration and clogging in the soil and determining numerical solutions of material parameters by finite element method further includes:

[0026] The second set of nonlinear partial differential equations for slurry migration and clogging in soil is established:

[0027] (σ′ ij -p w ) ,j +w j =0;

[0028] div(v s )+div(q w )=0;

[0029]

[0030]

[0031]

[0032] Where: σij' is the effective stress of the soil determined by the soil constitutive model, w is the gravity per unit volume of the system; u is the displacement of the soil skeleton, Vs is the velocity of the soil skeleton displacement, Pw is the pore pressure, is the porosity, C is the slurry concentration, qw is the slurry flow rate;

[0033] According to the first relevant material parameters, the numerical solution of the second equation group is determined by the finite element method to obtain the second relevant material parameters, wherein the second relevant material parameters include: soil skeleton displacement u, soil skeleton displacement speed Vs, pore pressure Pw, porosity Slurry concentration C, slurry flow rate qw.

[0034] In some embodiments of the present invention, the step of establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on the tunnel soil layer distribution, tunnel geometric characteristics and the relevant material parameters includes:

[0035] Determining the distribution of tunnel soil layers and the geometry of the tunnel, wherein the geometry includes the distance between the tunnel and the ground surface and the dimensions of the tunnel and the lining;

[0036] According to the soil layer distribution of the tunnel, the geometric relationship of the tunnel and the relevant material parameters, a finite element simulation model for shield tunnel excavation and grouting simulation is established.

[0037] In some embodiments of the present invention, the step of establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on the tunnel soil layer distribution, the tunnel geometry and the relevant material parameters includes: wherein the finite element simulation model includes a soil layer model, a grouting layer model and a lining layer model;

[0038] Establish a tunnel lining model based on linear elastic materials;

[0039] Establishing a soil layer model and a grouting layer model according to the second related material parameters determined by the second set of equations;

[0040] The tunnel lining layer model, the soil layer model and the grouting layer model are meshed and given material properties.

[0041] In some embodiments of the present invention, the step of establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on the tunnel soil layer distribution, the tunnel geometry and the relevant material parameters further includes:

[0042] Setting the normal contact between the grouting layer and the lining layer to be rigid contact;

[0043] The tangential contact between the grouting layer and the lining layer is set to be rough contact.

[0044] In some embodiments of the present invention, the step of simulating the tunnel excavation and grouting process according to the finite element simulation model includes:

[0045] Stress initialization is simulated according to the finite element simulation model.

[0046] In some embodiments of the present invention, the step of simulating stress initialization according to the finite element simulation model comprises: wherein the soil layer model, the grouting layer model and the lining layer model respectively comprise a soil layer unit, a grouting layer unit and a lining layer unit;

[0047] The corresponding initial stress field is generated according to the groundwater level and the self-weight of the soil in the target domain, wherein in the stress initialization stage, the deformation of the soil layer unit is reset to 0, and the grouting layer unit and the lining layer unit are not activated.

[0048] In some embodiments of the present invention, the step of simulating the tunnel excavation and grouting process according to the finite element simulation model includes:

[0049] Deleting the soil layer unit, and activating the grouting layer unit and the lining layer unit;

[0050] The filling process of the slurry is converted into a grouting pressure change and a slurry concentration change; wherein the grouting pressure change is a linear increase of the grouting pressure at the grouting port over time, and the slurry concentration change is a linear increase of the slurry concentration in the grouting layer unit over time;

[0051] When the grouting pressure and the slurry concentration reach the target value and remain constant for a period of time, the grouting port is closed;

[0052] The grouting pressure boundary condition at the grouting port is deleted to allow the slurry to continue to penetrate and clog the surrounding soil.

[0053] In some embodiments of the present invention, the step of determining the slurry loss volume based on the slurry diffusion range and the relevant material parameters includes:

[0054] Get the slurry diffusion range S A ;

[0055] According to the slurry diffusion range and the second related material parameter, the slurry loss volume V is calculated. Loss , wherein the second related material parameters include: porosity Slurry concentration C; where the calculation method is:

[0056]

[0057] Compared with the prior art, the embodiments of the present invention have at least the following advantages or beneficial effects:

[0058] The present invention establishes a nonlinear partial differential equation group of slurry migration and clogging in the soil, and determines the numerical solution through the finite element method to obtain relevant material parameters; according to the soil layer distribution, tunnel geometric characteristics and the relevant material parameters, a finite element simulation model of shield tunnel excavation and grouting simulation is established; according to the finite element simulation model, the tunnel excavation and grouting process is simulated; wherein, the grouting process includes the process from the beginning of grouting to the end of grouting and the continuous penetration and clogging of slurry into the surrounding soil after the end of grouting; according to the slurry diffusion range and the relevant material parameters, the slurry loss volume is determined. The present invention is completely based on mathematical formula description, has objectivity, does not rely on empirical judgment, can analyze the real diffusion process of slurry in uneven strata, and the obtained slurry loss coefficient is more accurate, which has positive significance for correctly designing the grouting amount, analyzing the deformation of tunnels and strata, and guiding the design and construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0060] Figure 1 It is a flowchart of the steps of a method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to an embodiment of the present invention;

[0061] Figure 2 Schematic diagram of the change of pressure in the grouting layer over time in an embodiment of the present invention;

[0062] Figure 3 The mesh and schematic diagram of the numerical model of the example in the embodiment of the present invention;

[0063] Figure 4 Schematic diagram of the relationship between elastic modulus and Poisson's ratio of relevant material parameters and time in an embodiment of the present invention;

[0064] Figure 5 1 is a grouting pressure distribution diagram at different times in an embodiment of the present invention;

[0065] Figure 6 A graph showing the variation of the slurry penetration and diffusion distance in the top, left center line and bottom soil of the tunnel with time in an embodiment of the present invention;

[0066] Figure 7 is a spatial distribution diagram of the porosity of the soil at the bottom of the tunnel at different times in an embodiment of the present invention;

[0067] Figure 8 Graph showing the grouting ratio changing with time in an embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0069] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0071] In the description of the embodiments of the present invention, it should be noted that if the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. appear, the orientation or position relationship indicated is based on the orientation or position relationship shown in the drawings, or the orientation or position relationship in which the invented product is usually placed when used. It is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", "third", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0072] In addition, the terms "horizontal", "vertical", "overhanging" and the like do not mean that the components must be absolutely horizontal or overhanging, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0073] In the description of the embodiments of the present invention, "plurality" means at least 2.

[0074] In the description of the embodiments of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal connection of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0075] Example

[0076] Please refer to Figure 1 ,like Figure 1 It is a flowchart of the steps of a method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to an embodiment of the present invention;

[0077] In an embodiment of the present application, a method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis specifically includes:

[0078] S110, establishing a nonlinear partial differential equation group of slurry migration and clogging in the soil, and determining a numerical solution by a finite element method to obtain relevant material parameters; wherein the relevant material parameters include material parameters of the soil, lining and grouting material;

[0079] S120, establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on soil layer distribution, tunnel geometric characteristics and the relevant material parameters;

[0080] S130, simulating the tunnel excavation and grouting process according to the finite element simulation model; wherein the grouting process includes the process from the beginning of grouting to the end of grouting and the process in which the slurry continues to penetrate into the surrounding soil and clog after the end of grouting;

[0081] S140, determining the slurry loss volume according to the slurry diffusion range and the relevant material parameters.

[0082] The present invention establishes a nonlinear partial differential equation group of slurry migration and clogging in the soil, and determines the numerical solution through the finite element method to obtain relevant material parameters; wherein the relevant material parameters include material parameters of the soil, lining and grouting materials; according to the soil layer distribution, tunnel geometric characteristics and the relevant material parameters, a finite element simulation model of shield tunnel excavation and grouting simulation is established; according to the finite element simulation model, the tunnel excavation and grouting process is simulated; wherein the grouting process includes the process from the beginning of grouting to the end of grouting and the continuous penetration and clogging of slurry into the surrounding soil after the end of grouting; according to the slurry diffusion range and the relevant material parameters, the slurry loss volume is determined. The present invention is completely based on mathematical formula description, has objectivity, does not rely on empirical judgment, can analyze the real diffusion process of slurry in uneven strata, and the obtained slurry loss coefficient is more accurate, which has positive significance for correctly designing the grouting amount, analyzing the deformation of tunnels and strata, and guiding the design and construction.

[0083] Next, the calculation method of slurry loss in synchronous grouting of a shield tunnel based on finite element analysis in this exemplary embodiment will be further described.

[0084] As described in step S110, a nonlinear partial differential equation group of slurry migration and clogging in the soil is established, and a numerical solution is determined by a finite element method to obtain relevant material parameters;

[0085] It should be noted that the relevant material parameters include the material parameters of soil, lining and grouting materials, specifically including: soil inherent permeability k; liquid mixture density ρ; fluid dynamic viscosity μ; slurry clogging rate n; soil skeleton displacement u, soil skeleton displacement speed Vs, pore pressure Pw, porosity The slurry concentration C, slurry flow rate qw, etc., are obtained by solving the partial differential equations using the finite element method to obtain the data of the above-mentioned related material parameters; among them, the finite element method (finite element method) is a high-efficiency and commonly used numerical calculation method. In the field of scientific computing, it is often necessary to solve various differential equations, and the analytical solutions of many differential equations are generally difficult to obtain. After the differential equations are discretized using the finite element method, a program can be compiled and a computer-assisted solution can be used.

[0086] In one embodiment of the present application, the specific process of "establishing a set of nonlinear partial differential equations for slurry migration and clogging in the soil, and determining the numerical solution through the finite element method to obtain relevant material parameters" described in step S110 can be further explained in combination with the following description.

[0087] It should be noted that the establishment of a set of nonlinear partial differential equations for slurry migration and clogging in soil is based on the principles of conservation of mass and momentum of the mixture system, wherein the mixture system includes a system in which the elements involved in the entire process of synchronous grouting of a shield tunnel are mixed together, and in the embodiments of the present application, it is a mixed system of elements such as slurry, soil, and lining.

[0088] As an example, based on the principles of conservation of mass and momentum of the mixture system, the first set of nonlinear partial differential equations for slurry migration and clogging in the soil is established:

[0089]

[0090]

[0091] μ=μ g c+μ w (1-c);

[0092]

[0093]

[0094] Wherein: k0 is the initial intrinsic permeability; ρg and ρw are the densities of the slurry and pure water, respectively; μ(x, t) is the dynamic viscosity of the fluid, wherein μg and μw are the dynamic viscosities of the slurry and pure water, respectively. The viscosity of the slurry will also gradually increase with the hardening of the slurry. In the embodiment of the present application, it is assumed that the slurry viscosity μg(t) changes exponentially with time, and μg0 is the initial viscosity of the slurry; ξ is a material constant determined by a dynamic viscosity test; λ f is the clogging rate parameter of the slurry in the granular material determined by the indoor grouting test, wherein the clogging of the slurry in the soil increases with the grouting flow rate and concentration (c|q w |) increases.

[0095] The numerical solution of the first set of equations is determined by the finite element method to obtain the first relevant material parameters, wherein the first relevant material parameters include: the inherent permeability k(x, t) of the soil; the density ρ(x, t) of the liquid mixture; the dynamic viscosity μ(x, t) of the fluid; and the slurry clogging rate n.

[0096] As an example, based on the principles of mass conservation and momentum conservation of the mixture system, the second set of nonlinear partial differential equations for slurry migration and clogging in the soil is established:

[0097] (σ′ ij -p w ) ,j +w j =0;

[0098] div(vs )+div(q w )=0;

[0099]

[0100]

[0101]

[0102] Where: σij' is the effective stress of the soil determined by the soil constitutive model, w is the gravity per unit volume of the system; u(x, t) is the displacement of the soil skeleton, Vs(x, t) is the velocity of the soil skeleton displacement, that is, the first-order derivative of the soil skeleton displacement with respect to time, Pw(x, t) is the pore pressure, is the porosity, C(x, t) is the slurry concentration, qw(x, t) is the slurry flow rate;

[0103] According to the first relevant material parameters, the numerical solution of the second equation group is determined by the finite element method to obtain the second relevant material parameters, wherein the second relevant material parameters include: soil skeleton displacement u, soil skeleton displacement speed Vs, pore pressure Pw, porosity Slurry concentration C, slurry flow rate qw.

[0104] In a specific embodiment, known quantities are substituted into the first set of equations to solve the unknown first-related material parameters, and the numerical solutions of the first-related material parameters are obtained. The numerical solutions of the first-related material parameters are substituted into the second set of equations, and the unknown second-related material parameters in the second set of equations are solved based on the remaining known quantities to obtain the numerical solutions of the second-related material parameters. A finite element simulation model of shield tunnel excavation and grouting simulation is established based on the numerical solutions of the second-related materials.

[0105] As described in step S120, a finite element simulation model for shield tunnel excavation and grouting simulation is established based on the tunnel soil layer distribution, tunnel geometric characteristics and the relevant material parameters.

[0106] In one embodiment of the present application, the specific process of "establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on the tunnel soil layer distribution, tunnel geometric characteristics and the relevant material parameters" in step S120 can be further explained in combination with the following description.

[0107] As an example, the distribution of tunnel soil layers and the tunnel geometry are determined.

[0108] It should be noted that the above-mentioned tunnel soil layer distribution includes soil layer properties, soil layer structure, soil layer distribution, soil layer self-weight and soil layer thickness and other related conditions, which provide data support for the soil layer model for the above-mentioned finite element simulation model for shield tunnel excavation and grouting simulation; the above-mentioned tunnel geometric relationship includes relevant geometric data such as the distance between the tunnel and the ground surface and the dimensions of the tunnel and lining, which provides data support for the grouting layer model and the lining layer model for the above-mentioned finite element simulation model for shield tunnel excavation and grouting simulation.

[0109] As an example, a finite element simulation model of shield tunnel excavation and grouting simulation is established based on the distribution of soil layers in the tunnel, the geometric relationship of the tunnel and the relevant material parameters.

[0110] In a specific embodiment, a finite element simulation model is established by finite element simulation software, such as ABAQUS, COMSOL; specifically, a tunnel lining layer model is established based on a linear elastic material. It should be noted that the constitutive relationship of the linear elastic material obeys the generalized Hooke's law, that is, the stress and strain are linearly related during loading and unloading, and there is no residual strain in the material after unloading. When the stress level of the concrete material is low, the stress-strain relationship calculated according to the model basically conforms to the actual situation. Therefore, the tunnel lining layer model is established based on the linear elastic material to provide accurate data support for the subsequent calculation of the loss; the soil layer model and the grouting layer model are established based on the second related material parameters determined by the second set of equations, specifically the first related material parameters and the second related material parameters calculated based on the above-mentioned first set of equations and the second set of equations: soil inherent permeability k, liquid mixture density ρ, fluid dynamic viscosity μ, slurry clogging rate n, soil skeleton displacement u, soil skeleton displacement velocity Vs, pore pressure Pw, porosity Slurry concentration C, slurry flow rate qw, establish a soil layer model and a grouting layer model according to the above-mentioned relevant material parameters; divide the tunnel lining layer model, the soil layer model and the grouting layer model into grids and assign material properties;

[0111] Furthermore, the normal contact between the grouting layer and the lining layer is set as rigid contact; and the tangential contact between the grouting layer and the lining layer is set as rough contact.

[0112] It should be noted that the interaction between the lining and the slurry depends on the contact characteristics of the normal and tangential directions of the contact surface; in the normal direction, the contact between the lining and the slurry is rigid contact, that is, no penetration or separation is allowed; in the tangential direction, the contact between the lining and the slurry is rough contact, that is, no relative sliding movement is allowed on the contact surface.

[0113] As described in step S130, the tunnel excavation and grouting process is simulated according to the finite element simulation model; wherein the grouting process includes the process from the start of grouting to the end of grouting and the process in which the slurry continues to penetrate into the surrounding soil and clog after the end of grouting.

[0114] In one embodiment of the present application, the specific process of "simulating the tunnel excavation and grouting process based on the finite element simulation model; wherein the grouting process includes the process from the start of grouting to the end of grouting and the continuous penetration and clogging of the slurry into the surrounding soil after the end of grouting" described in step S130 can be further explained in combination with the following description.

[0115] As an example, stress initialization is simulated according to the finite element simulation model.

[0116] It should be noted that the soil layer model, the grouting layer model and the lining layer model include a soil layer unit, a grouting layer unit and a lining layer unit respectively.

[0117] In a specific embodiment, under the action of gravity, an initial stress field corresponding to the groundwater level and the deadweight of the soil in the analysis domain is generated. In the stress initialization stage, the grouting layer unit and the lining layer unit are not activated, and the deformation of the soil is reset to 0 after the stress initialization; the soil layer unit is deleted, and the grouting layer unit and the lining layer unit are activated; the filling process of the slurry is converted into a grouting pressure change and a slurry concentration change; wherein the grouting pressure change is a linear increase of the grouting pressure at the grouting port with time, and the slurry concentration change is a linear increase of the grouting layer The slurry concentration in the unit increases linearly with time; the grouting pressure and grouting time are observed. When the grouting pressure and the slurry concentration reach the target value and remain constant for a period of time, it can be considered that the slurry has filled the initial shield tail gap and the grouting port is closed; the grouting pressure boundary condition at the grouting port is deleted to allow the slurry to continue to penetrate and clog the surrounding soil. The grouting pressure in the grouting layer unit and the excess pore water pressure in the soil layer unit dissipate with time. During the pressure dissipation process during and after grouting, the slurry will continue to penetrate and clog the surrounding soil.

[0118] As described in step S140, the slurry loss volume is determined according to the slurry diffusion range and the relevant material parameters.

[0119] In a specific embodiment, the slurry diffusion range S is obtained. A Calculate the slurry loss volume V according to the slurry diffusion range and the second related material parameters Loss , wherein the second related material parameters include: porosity Slurry concentration C; where the calculation method is:

[0120] In order to establish a more accurate calculation method for the loss of synchronous grouting slurry in shield tunnels, the present invention theoretically derives a group of nonlinear partial differential equations of slurry migration and clogging in soil, and solves them using the finite element method. According to the formation conditions and the basic geometric parameters of the tunnel, a finite element model is established to simulate the diffusion process of slurry in the formation during and after grouting, so as to determine the slurry diffusion range and calculate the synchronous grouting slurry loss coefficient. Compared with other analysis methods of slurry loss, the present invention has the following characteristics:

[0121] The slurry penetration and diffusion process is completely described by mathematical formulas, which is objective, independent of empirical judgment, and avoids subjective influence in the calculation process.

[0122] The diffusion control equation can be solved by numerical methods. The calculation procedure is fixed and the amount of calculation is moderate. It can be used for secondary development of commercial software.

[0123] It can truly simulate the properties of the stratum, taking into account the heterogeneity of the stratum and the uneven diffusion of the slurry. The synchronous grouting slurry loss calculated using this method is more accurate, which is of positive significance for correctly calculating the designed grouting volume, tunnel and stratum deformation, and guiding reasonable design and construction.

[0124] Below, in conjunction with a specific embodiment, a method for calculating slurry loss during synchronous grouting in a shield tunnel based on finite element analysis in an embodiment of the present application is further explained.

[0125] Reference Figure 2 , showing a schematic diagram of the pressure change over time in the grouting layer in an embodiment of the present invention. The top of a shield tunnel is 15m from the ground surface, the stratum is fully saturated, and the groundwater level is on the ground. The cross-sectional outer diameter of the tunnel is 6.2m, the inner diameter is 5.5m, the lining thickness is 0.35m, and the over-excavation annular gap between the outer side of the lining and the soil is 12cm. The grouting points of synchronous grouting are located at 45° to the left and right of the top and bottom of the tunnel. Considering the two-dimensional conditions of plane symmetry, only half of the area to be analyzed is modeled, and the model area is a rectangle of 40×50m in length and height. The vertical boundary surface of the model is a plane symmetric boundary (roller boundary), and the bottom boundary of the model is a fully fixed boundary.

[0126] In this analysis, the soil model adopts the Mohr-Coulomb model. The grouting layer and lining layer adopt the linear elastic model, and the hardening of the grouting material is simplified by using the time-dependent Young's modulus and Poisson's ratio, such as Figure 3 The Young's modulus of the linear elastic lining unit is 20 GPa, the Poisson's ratio is 0.25, and the bulk density is 25 KN / m3. The remaining material parameters are shown in Table 1 Shield Tunnel Excavation Simulation Parameters:

[0127]

[0128]

[0129] Simulate the grouting process:

[0130] Stress initialization is performed based on the groundwater level and soil self-weight in the analysis domain. During the stress initialization stage, the initial grouting layer and tunnel lining unit are not activated. After stress initialization, the deformation of the soil is reset to 0;

[0131] Then, the soil elements in the tunnel are deleted, and the grouting layer and tunnel lining elements are activated. Within one minute of activating the grouting layer, the grouting pressure at the grouting point increases linearly from 0 to 220 kPa;

[0132] After keeping the grouting pressure constant for 10 minutes, close the grouting port and delete the grouting pressure boundary condition at the grouting point. The slurry pressure in the grouting layer and the excess pore water pressure in the soil will dissipate over time. The schematic diagram of the pressure change over time in the grouting layer is shown in Figure 4 shown.

[0133] During the grouting process and the process of pressure dissipation after grouting, the slurry will continue to penetrate and block the surrounding soil. A , porosity and slurry concentration C to determine the slurry loss volume V Loss :

[0134] Simulation results:

[0135] Figure 5 The figure shows the grouting pressure at the interface between the soil and the grouting layer at different times. During the grouting process, the grouting pressure applied to the top and bottom grouting points of the tunnel is the same, while the hydrostatic pressure varies along the depth, resulting in a greater pressure difference in the upper part of the tunnel. The results show that the penetration expansion distance of the slurry in the upper part of the tunnel is greater than that in the lower part. However, after the grouting point is closed, the slurry pressure in the upper part of the tunnel will gradually decrease to the hydrostatic pressure at the corresponding depth, and the slurry moves under the action of gravity, which reduces the slurry penetration distance in the upper part of the tunnel. At the same time, the slurry in the lower part of the tunnel continues to penetrate under the action of the slurry's own weight and the dissipation of the grouting pressure.

[0136] Figure 6 The variation of grout penetration distance over time in the top, left centerline and bottom soil of the tunnel is plotted, where the thickness of the shield tail gap is not included in the grouting penetration distance. For the bottom of the tunnel, the grout penetration diffusion distance increases with time to 0.25m and then remains basically stable due to the hardening of the grout, the dissipation of the grouting pressure and the clogging of the grout in the soil. Similar variation of grout penetration diffusion distance over time was also observed on the left side of the tunnel. In contrast, the grout penetration diffusion distance at the top of the tunnel gradually increased to 0.14m during the grouting process. When the grouting pressure was removed, the slurry moved downward under the action of gravity, resulting in a decrease in the grout diffusion distance at the top of the tunnel.

[0137] Along with the convection diffusion of the slurry, the clogging of the slurry in the soil layer will lead to a decrease in the porosity of the surrounding soil. Figure 7 The spatial distribution of soil porosity at different times in the vertical downward direction of the tunnel bottom is plotted, where the solid line represents the grouting process and the dashed line represents after grouting. When the lining and grouting layer are just activated (T = 1min), the porosity in the soil around the tunnel increases slightly due to the application of grouting pressure. After that, as the slurry is blocked in the soil, the porosity in the soil around the tunnel gradually decreases, making the slurry penetration gradually stable and preventing further loss of slurry.

[0138] Figure 8 The variation of the grouting ratio (i.e., the ratio of the total injected slurry volume to the initial annular void volume) over time is shown, and it can be seen that at a constant grouting pressure, the grouting ratio increases from 1.0 to 1.82.

[0139] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the loss of synchronous grouting slurry in shield tunnels based on finite element analysis, characterized in that: The steps include: The nonlinear partial differential equations for slurry migration and clogging in soil are established, and the numerical solutions are determined by finite element method to obtain relevant material parameters; including: The first set of nonlinear partial differential equations for slurry migration and clogging in soil is established: μ=μ g c+m w (1-c); m g (t)=μ g0 e ξt ; Where: k is the inherent permeability of the soil; k0 is the initial inherent permeability; is the density of the liquid mixture; c is the relative concentration of the slurry; ρ g and ρ w are the densities of slurry and pure water respectively; μ is the dynamic viscosity of the fluid, where μ g and μ w are the dynamic viscosities of the slurry and pure water, μ g0 is the initial viscosity of the slurry; ξ is the material constant determined by the dynamic viscosity test; t is the time; λ f is the clogging rate parameter of the slurry in the granular material determined by the indoor grouting test, q w is the seepage velocity of the slurry suspension; wherein the clogging of the slurry in the soil increases with the increase of the grouting flow rate and concentration; The numerical solution of the first set of equations is determined by the finite element method to obtain the first relevant material parameters, wherein the first relevant material parameters include: the inherent permeability k of the soil, the density of the liquid mixture Dynamic viscosity μ of the fluid, slurry clogging rate The second set of nonlinear partial differential equations for slurry migration and clogging in soil is established: (in ij -p w ) ,j +w j =0; div(v s )+div(q w )=0; Where: σ′ ij is the effective stress of the soil determined by the soil constitutive model, wj is the gravity per unit volume of the system; v s is the velocity of soil skeleton displacement, p w is the pore pressure, φ is the porosity; Determine the numerical solution of the second set of equations by the finite element method according to the first related material parameters to obtain the second related material parameters, wherein the second related material parameters include: the velocity v of the soil skeleton displacement s , pore pressure p w , porosity φ, slurry concentration c, slurry flow rate q w ; According to the tunnel soil layer distribution, tunnel geometric characteristics and the relevant material parameters, a finite element simulation model for shield tunnel excavation and grouting simulation is established; The tunnel excavation and grouting process is simulated according to the finite element simulation model; wherein the grouting process includes the process from the beginning of grouting to the end of grouting and the process in which the slurry continues to penetrate into the surrounding soil and clog after the end of grouting; The slurry loss volume is determined based on the slurry diffusion range and the relevant material parameters.

2. The method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to claim 1 is characterized in that: The step of establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on tunnel soil layer distribution, tunnel geometric characteristics and the relevant material parameters includes: Determine the distribution of tunnel soil layers and tunnel geometry; According to the distribution of the tunnel soil layer, the geometric relationship of the tunnel and the relevant material parameters, a finite element simulation model for shield tunnel excavation and grouting simulation is established.

3. The method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to claim 2 is characterized in that: The step of establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on the tunnel soil layer distribution, the tunnel geometry and the relevant material parameters comprises: wherein the finite element simulation model comprises a soil layer model, a grouting layer model and a lining layer model; Establish a tunnel lining model based on linear elastic materials; Establishing a soil layer model and a grouting layer model according to the second related material parameters determined by the second set of equations; The tunnel lining layer model, the soil layer model and the grouting layer model are meshed and given material properties.

4. The method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to claim 3 is characterized in that: The step of establishing a finite element simulation model for shield tunnel excavation and grouting simulation based on the tunnel soil layer distribution, the tunnel geometric relationship and the relevant material parameters also includes: Setting the normal contact between the grouting layer and the lining layer to be rigid contact; The tangential contact between the grouting layer and the lining layer is set to be rough contact.

5. The method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to claim 3 is characterized in that: The step of simulating the tunnel excavation and grouting process according to the finite element simulation model comprises: Stress initialization is simulated according to the finite element simulation model.

6. The method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to claim 5 is characterized in that: The step of simulating stress initialization according to the finite element simulation model comprises: wherein the soil layer model, the grouting layer model and the lining layer model respectively comprise a soil layer unit, a grouting layer unit and a lining layer unit; The corresponding initial stress field is generated according to the groundwater level and the self-weight of the soil in the target domain, wherein in the stress initialization stage, the deformation of the soil layer unit is reset to 0, and the grouting layer unit and the lining layer unit are not activated.

7. The method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to claim 6 is characterized in that: The step of simulating the tunnel excavation and grouting process according to the finite element simulation model comprises: Deleting the soil layer unit, and activating the grouting layer unit and the lining layer unit; The filling process of the slurry is converted into a grouting pressure change and a slurry concentration change; wherein the grouting pressure change is a linear increase of the grouting pressure at the grouting port over time, and the slurry concentration change is a linear increase of the slurry concentration in the grouting layer unit over time; When the grouting pressure and the slurry concentration reach the target value and remain constant for a period of time, the grouting port is closed; The grouting pressure boundary condition at the grouting port is deleted to allow the slurry to continue to penetrate and clog the surrounding soil.

8. The method for calculating the loss of synchronous grouting slurry in a shield tunnel based on finite element analysis according to claim 1 is characterized in that: The step of determining the slurry loss volume according to the slurry diffusion range and the relevant material parameters comprises: Get the slurry diffusion range S A ; According to the slurry diffusion range and the second related material parameter, the slurry loss volume V is calculated. Loss , wherein the second related material parameters include: porosity Slurry concentration c; where the calculation method is:

Images