Calculation method and system for grouting filling extrusion diffusion mechanism in tunneling type tunnel construction

Abstract

The invention relates to the technical field of tunnel construction grouting filling, in particular to a calculation method and system for a tunneling type tunnel construction grouting filling extrusion diffusion mechanism, and the method comprises the following steps: dispersing a slurry diffusion area at a grouting hole to obtain a plurality of fan-shaped units; performing iterative calculation on the grouting flow and the pressure field of the ith fan-shaped unit based on a secant method; according to the pressure difference of the ith fan-shaped unit, the variable quantity of the construction gap thickness is calculated, and the construction gap thickness is updated; in each calculation step, the diffusion radius and the grouting flow corresponding to each fan-shaped unit are recorded, so that the pressure distribution condition of the grout at each discrete point in the diffusion area is obtained, meanwhile, the thickness of the construction gap is dynamically updated according to a pressure change result, and geometric boundary conditions are provided for next iteration. According to the method, disturbance of slurry filling and diffusion to construction gaps is considered, and the method is closer to actual interface change.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel construction grouting filling, in particular to a calculation method and system for tunnel construction grouting filling extrusion diffusion mechanism. BACKGROUND

[0002] Tunnel grouting is an effective means to improve the friction between soil and shell in tunnel construction, while reducing the disturbance to the surrounding soil, controlling surface subsidence, etc. In-depth study of the grouting diffusion mechanism reveals the filling and diffusion rules of the slurry on the outer surface of the pipe wall and the variation characteristics of the pressure field, providing a scientific basis for determining the grouting construction parameter range, guiding the reasonable equipment selection, providing a theoretical reference for tunnel construction design, ensuring the safety and stability of the structure, and effectively promoting the fine control and parameter optimization of grouting technology.

[0003] At present, most of the tunnel synchronous grouting filling diffusion theoretical models simplify the filling and diffusion process, greatly reducing the complexity of the model derivation process, and assuming that the slurry diffusion process is two independent stages of ring and longitudinal: first, the slurry completes three-dimensional ring filling around the outer surface of the pipe wall, and then realizes longitudinal uniform whole diffusion in the whole ring section. In fact, the flow of slurry in space will not be limited in one direction, but will flow in every direction, so the whole fan-shaped diffusion form related to longitudinal ring with the grouting hole as the center is more in line with the actual flow form of slurry diffusion.

[0004] A prior Chinese patent (application number: 202011124607.2, invention name: Large-section rectangular pipe jacking friction-reducing grouting diffusion and pressure space-time analysis system and method) discloses a large-section rectangular pipe jacking friction-reducing grouting diffusion and pressure space-time analysis system and method, which gives a friction-reducing grouting composite diffusion model, and obtains an actual friction-reducing grouting diffusion pressure three-dimensional distribution map combined with the composite diffusion model, and gives the longitudinal ring whole diffusion mechanism of the friction-reducing grouting. In actual engineering application, especially for soft soil layer application, the gap between the pipe joint and the soil will have a bulging effect with the flow of grouting slurry, but in the above large-section rectangular pipe jacking friction-reducing grouting diffusion and pressure space-time analysis system and method, the gap between the pipe joint and the soil is assumed to be a fixed value, so due to the fact that the change of the gap is not considered, it is difficult to truly simulate the diffusion process of the slurry, so the following research needs to further fine the grouting filling and diffusion mode, and explore a more actual model to guide the engineering. SUMMARY

[0005] The present application aims to overcome the defects of the prior art, and provides a calculation method and system for tunnel construction grouting filling extrusion diffusion mechanism, which solves the problem that the existing scheme is difficult to truly simulate the diffusion process of the slurry due to not considering the change of the gap.

[0006] The technical scheme for achieving the above object is:

[0007] The application provides a calculation method for a tunneling tunnel construction grouting filling extrusion diffusion mechanism, comprising the following steps:

[0008] Obtaining actual construction parameters of the tunnel construction;

[0009] Discretizing the slurry diffusion area at each grouting hole to obtain a plurality of fan units, and dividing each fan unit into annular discrete units along the radial direction;

[0010] Based on the secant method, the grouting flow of the i-th fan unit is iteratively calculated, two different initial flow values are selected as the starting point of the calculation, the pressure field of each annular discrete unit in the i-th fan unit is calculated, the slurry pressure difference before and after each annular discrete unit is obtained, the slurry pressure difference before and after each annular discrete unit in the i-th fan unit is accumulated to obtain two corresponding pressure losses, the difference between the two pressure losses is calculated to obtain the pressure difference, and it is judged whether the pressure difference meets the error control standard, if not, the flow value is updated according to the iteration formula of the secant method, and the next round of solving is continued until the error control standard is met;

[0011] According to the pressure difference of the i-th fan unit, the change amount of the construction gap thickness is calculated, and the construction gap thickness is updated according to the change amount of the construction gap thickness;

[0012] According to the grouting flow of the fan unit, the position of the slurry diffusion front is updated, and then the diffusion boundary of the slurry at the current time step is obtained;

[0013] Based on the updated slurry diffusion front position, the next round of cycle iterative calculation is continued, and the iterative calculation and pressure field calculation of the grouting flow are repeatedly performed to dynamically simulate the continuous diffusion process of the slurry in the shield tail gap until the upper limit of the cycle iterative calculation time is reached.

[0014] In each calculation step, the corresponding diffusion radius and grouting flow of each fan unit are recorded, so as to obtain the pressure distribution of each discrete point in the diffusion area, and the thickness of the construction gap is dynamically updated according to the pressure change result to provide the geometric boundary condition for the next iteration.

[0015] The further improvement of the calculation method for the tunneling tunnel construction grouting filling extrusion diffusion mechanism of the application is that when the change amount of the construction gap thickness is calculated according to the pressure difference of the i-th fan unit, and the construction gap thickness is updated according to the change amount of the construction gap thickness, a construction gap thickness control equation is established, comprising the following steps:

[0016] The soil layer is simplified as a semi-infinite space elastic body model, and it is assumed to bear uniform pressure.

[0017] Based on the generalized Hooke's law, the strain of the soil in the z direction can be derived as follows:

[0018]

[0019] In formula 17, ε z represents the strain in the z direction; Δb represents the displacement change of the soil layer in the z direction, σ z represents the vertical stress, E represents the elastic modulus of the soil layer, and μ represents the Poisson's ratio of the soil layer.

[0020] Integrating formula 17, the vertical displacement of the soil layer can be obtained as follows:

[0021]

[0022] In formula 18, D represents an undetermined coefficient.

[0023] According to the buried depth of the tunnel, the effective influence range of the slurry-soil coupling is set as H, H is less than the buried depth of the tunnel, when z=H, Δb=0, the boundary condition is substituted into formula 18, and the following formula can be obtained:

[0024]

[0025] The maximum vertical displacement Δb max of the soil layer is obtained as follows:

[0026]

[0027] Substituting σ z =p-p e into formula 20, the construction gap thickness control equation is obtained as follows:

[0028]

[0029] In formula 21, b0 represents the initial construction gap, p represents the grouting pressure, p e represents the environmental pressure.

[0030] The further improvement of the calculation method of the grouting filling and extrusion diffusion mechanism of the tunneling type tunnel construction lies in that the thickness of the construction gap is dynamically updated according to the pressure change result, and the updating calculation is performed through the following formula:

[0031]

[0032] In formula 29, H represents the set effective influence range of the slurry-soil coupling, μ represents the Poisson's ratio of the soil layer, p represents the grouting pressure, p e represents the environmental pressure, E represents the elastic modulus of the soil layer, and Δp i,k represents the pressure difference of the i-th fan unit at the current calculation step.

[0033] The further improvement of the tunnel construction grouting filling and extrusion diffusion mechanism calculation method lies in that the actual construction parameters of the tunnel construction include an initial construction gap, a tunnel outer diameter, a vertical included angle between a grouting hole and a center line of a section, and a grouting pressure.

[0034] The tunnel construction grouting filling and extrusion diffusion mechanism calculation system also comprises:

[0035] A parameter acquisition unit is configured to acquire actual construction parameters of the tunnel construction.

[0036] A discrete division unit is configured to discretize a slurry diffusion area at each grouting hole to obtain a plurality of fan units, and divide each fan unit along a radial direction to form annular discrete units.

[0037] An iterative calculation unit is connected with the discrete division unit and is configured to perform iterative calculation on grouting flow of the i-th fan unit based on a secant method, select two different initial flow values as a calculation starting point, perform pressure field calculation on each annular discrete unit in the i-th fan unit, obtain slurry pressure difference values before and after each annular discrete unit, accumulate the slurry pressure difference values before and after each annular discrete unit in the i-th fan unit to obtain two corresponding pressure losses, calculate a pressure difference of the two pressure losses, and judge whether the pressure difference value meets an error control standard.

[0038] A parameter updating unit is connected with the iterative calculation unit and is configured to calculate a change amount of a construction gap thickness according to the pressure difference of the i-th fan unit, and update the construction gap thickness according to the change amount of the construction gap thickness, and update a position of a slurry diffusion front according to the grouting flow of the fan unit, and further obtain a diffusion boundary of the slurry at a current time step.

[0039] A processing unit is connected with the parameter updating unit and the iterative calculation unit and is configured to control the iterative calculation unit to continue a next round of cyclic iterative calculation based on the updated slurry diffusion front position, repeatedly perform iterative calculation and pressure field calculation on the grouting flow, dynamically simulate a continuous diffusion process of the slurry in the shield tail gap, and stop until a time upper limit of the cyclic iterative calculation is reached.

[0040] The further improvement of the tunnel construction grouting filling and extrusion diffusion mechanism calculation system of the application lies in that the parameter updating unit is internally provided with a construction gap thickness control equation, and the parameter updating unit updates the construction gap thickness through the construction gap thickness control equation.

[0041]

[0042] In formula 21, b0 represents an initial construction gap, p represents a grouting pressure, p e represents an ambient pressure, E represents an elastic modulus of a soil layer, mu represents a poisson's ratio of the soil layer, and H represents a set effective influence range of slurry-soil coupling.

[0043] The further improvement of the tunnel construction grouting filling and extrusion diffusion mechanism calculation system of the application lies in that the processing unit updates the thickness of the construction gap according to the following formula:

[0044]

[0045] In formula 29, H represents a set effective influence range of slurry-soil coupling, mu represents a poisson's ratio of a soil layer, p represents a grouting pressure, p e represents an ambient pressure, E represents an elastic modulus of a soil layer, and Ap i,k represents a pressure difference of the i-th fan unit at a current calculation step.

[0046] The further improvement of the tunnel construction grouting filling and extrusion diffusion mechanism calculation system of the application lies in that the actual construction parameters of the tunnel construction obtained by the parameter acquisition unit include an initial construction gap, a tunnel outer diameter, a vertical included angle between a grouting hole and a center line of a section, and a grouting pressure.

[0047] The tunnel construction grouting filling and extrusion diffusion mechanism calculation method and system of the application have the following beneficial effects:

[0048] The application considers the disturbance of slurry filling and diffusion to the construction gap, derives a construction gap control equation based on a semi-infinite space deformation body, the construction gap is uplifted to a certain degree with the filling and diffusion of the slurry, the assumed conditions of the grouting filling and diffusion model are improved, and the interface change is closer to the actual interface change.

[0049] The application comprehensively considers the diffusion behavior of the slurry in the construction gap, a pressure transmission process and the interaction with the surrounding stratum, the grouting pressure is used as a driving force to control the initial input strength and diffusion range of the slurry, and the ambient pressure is used as a boundary constraint to limit the stress state of the slurry diffusion front. By introducing the assumption of longitudinal ring coordination diffusion, the spatial pressure distribution of the slurry at different positions can be simulated in combination with the slurry-soil coupling effect, thereby providing a theoretical reference for the design of tunnel grouting construction. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 Flow chart of the calculation method of the grouting filling and extrusion diffusion mechanism of the tunnel construction by excavation of the present application.

[0051] Figure 2 Schematic diagram of the grouting filling and diffusion three-dimensional structure in the calculation method and system of the grouting filling and extrusion diffusion mechanism of the tunnel construction by excavation of the present application.

[0052] Figure 3 Planar development diagram of the grouting filling and diffusion in the calculation method and system of the grouting filling and extrusion diffusion mechanism of the tunnel construction by excavation of the present application.

[0053] Figure 4 Stress analysis diagram of the grouting filling and diffusion microelement in the calculation method and system of the grouting filling and extrusion diffusion mechanism of the tunnel construction by excavation of the present application.

[0054] Figure 5 Principle diagram of the semi-infinite space body deformation calculation in the calculation method and system of the grouting filling and extrusion diffusion mechanism of the tunnel construction by excavation of the present application.

[0055] Figure 6 Schematic diagram of the discrete element division in the grouting filling and diffusion area in the calculation method and system of the grouting filling and extrusion diffusion mechanism of the tunnel construction by excavation of the present application.

[0056] Figure 7 Schematic diagram of the chord intersection method iterative calculation in the calculation method and system of the grouting filling and extrusion diffusion mechanism of the tunnel construction by excavation of the present application.

[0057] Figure 8 Schematic diagram of the grouting filling and diffusion area in the calculation method and system of the grouting filling and extrusion diffusion mechanism of the tunnel construction by excavation of the present application. DETAILED DESCRIPTION

[0058] The present application will be further described below in combination with the drawings and specific embodiments.

[0059] Reference Figure 1The application provides a tunneling tunnel construction grouting filling and extrusion diffusion mechanism calculation method and system, based on a Bingham fluid constitutive model, related theories of fluid mechanics and elasticity mechanics are fused, and filling and diffusion mechanisms of slurry in a shield tail gap in a tunnel synchronous grouting process are analyzed in depth. By introducing slurry-soil interface interaction, pressure distribution characteristics and diffusion boundary evolution law, a theoretical model closer to actual working conditions is established, the coupling effect of the slurry and the soil interface is further discussed, and on this basis, a longitudinal and circumferential overall filling and diffusion theoretical model considering the slurry-soil interface interaction is established, so that the actual mechanical behavior and mutual influence law in the grouting diffusion process are more comprehensively described. The tunneling tunnel construction grouting filling and extrusion diffusion mechanism calculation method and system will be described below with reference to the drawings.

[0060] The tunnel construction grouting filling and extrusion diffusion mechanism calculation system of the application comprises a parameter acquisition unit, a discrete division unit, an iterative calculation unit, a parameter updating unit and a processing unit, wherein the parameter acquisition unit is connected with the discrete division unit, the iterative calculation unit, the parameter updating unit and the processing unit, the discrete division unit is connected with the iterative calculation unit, the iterative calculation unit is connected with the parameter updating unit and the processing unit, and the parameter updating unit is also connected with the processing unit; the parameter acquisition unit is used to acquire the actual construction parameters of the tunnel construction; the discrete division unit is used to discretize the slurry diffusion area at each grouting hole to obtain a plurality of fan units, and each fan unit is divided along the radial direction to form an annular discrete unit; the iterative calculation unit is used to iteratively calculate the grouting flow of the i-th fan unit based on the secant method, select two different initial flow values as the calculation starting point, calculate the pressure field of each annular discrete unit in the i-th fan unit, obtain the slurry pressure difference before and after each annular discrete unit, accumulate the slurry pressure difference before and after each annular discrete unit in the i-th fan unit to obtain two corresponding pressure losses, calculate the difference between the two pressure losses to obtain the pressure difference, and judge whether the pressure difference meets the error control standard; if not, update the flow value according to the iterative formula of the secant method, continue to solve the next round, and stop until the error control standard is met; the parameter updating unit is used to calculate the change amount of the construction gap thickness according to the pressure difference of the i-th fan unit, and update the construction gap thickness according to the change amount of the construction gap thickness; and is also used to update the position of the slurry diffusion front according to the grouting flow of the fan unit, and further obtain the diffusion boundary of the slurry at the current time step; the processing unit is used to control the iterative calculation unit to continue the next round of cyclic iterative calculation based on the updated slurry diffusion front position, repeatedly perform the iterative calculation and pressure field calculation of the grouting flow, dynamically simulate the continuous diffusion process of the slurry in the shield tail gap, and stop until the upper limit of the cyclic iterative calculation time is reached; the processing unit is also used to record the diffusion radius and grouting flow corresponding to each fan unit in each calculation step, so as to obtain the pressure distribution of each discrete point of the slurry in the diffusion area, and dynamically update the thickness of the construction gap according to the pressure change result to provide the geometric boundary condition for the next iteration.

[0061] As Figure 1 shown, the working process of the simulation calculation system of the application is as follows: first, input the required parameters into the parameter acquisition unit, including the actual construction parameters, the geometric parameters, the material parameters and the calculation parameters, wherein the actual construction parameters include the included angle α1 of the grouting hole and the vertical center line of the vertical tunnel section, the grouting hole pressure P0 and the environmental pressure P eThe geometric parameters include the initial construction gap b0, the construction gap b used in the calculation, b = b0 + Δb, where Δb is the thickness change due to deformation of the construction gap thickness under grout pressure, the effective influence range H of the grout-soil coupling, and the tunnel outer diameter Rt. Material parameters include the static shear force τ0 of the grout, the plastic viscosity μ0 of the grout, the density ρ of the grout, the elastic modulus E of the soil, and the Poisson's ratio μ of the soil layer. Calculation parameters include the number of sector elements n-1, the number of annular discrete elements m, the equivalent radius r0 of the grouting hole, the radius R0 of the first grout diffusion front near the grouting hole, and the single-round iteration time Δt. The second step is to set k = 0 and set the upper limit t of the iteration program time. max The upper limit of the iteration program time t max The first step can be preset, or preferably determined through trial calculations, to ensure good filling and diffusion of the grout on the segment surface, forming a good grout sleeve. The second step involves setting i = 1, and incrementing i by 1 in the next calculation, repeating this process until i = n, assigning values ​​from 1 to n to i. The third step is to specify the grouting flow rate Δq. i,k Two initial flow rates, Δq i,k,0 and Δq i,k,1 The initial flow rate value is usually chosen between 0 and 1. For example, one initial flow rate value can be assigned 1, and the other can be assigned 0. In the fifth step, first let j = 1. During the secant method iteration, j is incremented by 1, looping until j = m. That is, the value assigned to j in this step ranges from 1 to m. The sixth step is to calculate B and α. ij The specific calculation formula will be introduced later. Step 7: Calculate the slurry loss before and after the annular discrete element j. Step 8: Accumulate the pressure loss of the sector element i to obtain ΔP. ik0 and ΔP ik1 Step nine: Calculate the pressure value and determine whether the pressure difference is less than the error control standard ε, |ΔP ik0 -ΔP ik1 If |<ε, proceed to step 10 if the result is yes, otherwise return to step 5. Step 10: Calculate the gap change Δb based on the pressure loss at night, and update the construction gap thickness b=b0+Δb. Step 11: Calculate the diffusion radius increment ΔR. i , to obtain R i,k+1 The specific calculation formula will be introduced later. Step 12: Determine if the upper limit of the iterative calculation time has been reached, k·Δt>t. max If not, let k = k + 1; if yes, proceed to step thirteen. Step thirteen: Record and output the diffusion radius R corresponding to each sector unit. i and flow rate Δq i Calculate the pressure distribution within the diffusion area and update the construction gap value b. i,k =b0+Δb i,k .

[0062] Further, the parameter updating unit is internally provided with a construction gap thickness control equation, and the parameter updating unit updates the construction gap thickness through the construction gap thickness control equation, wherein the construction gap thickness control equation is:

[0063]

[0064] In formula 21, b0 represents an initial construction gap, p represents a grouting pressure, p e represents an ambient pressure, E represents an elastic modulus of the soil layer, μ represents a Poisson's ratio of the soil layer, and H represents a set effective influence range of the slurry-soil coupling.

[0065] The derivation process of the construction gap thickness control equation is described as follows:

[0066] After the grouting hole injects the slurry, the slurry flows and diffuses on the construction gap, and vertical pressure is generated on the upper and lower sides of the gap. The lower side of the segment has large rigidity and is basically not affected by the pressure to generate deformation. The soil layer is subjected to the action of the slurry pressure and will have a heave effect to generate a new diffusion space for the filling and diffusion of the slurry. The displacement amount of the soil layer mainly depends on the elastic modulus of the soil layer and the slurry pressure. The soil layer can be simplified as a semi-infinite space elastic body model, and it is assumed that it bears a uniform pressure, as shown in formula 12. Figure 5 The x direction is the slurry diffusion direction, the soil layer displacement in this direction is assumed to be 0, the z direction is the vertical direction of the soil layer, and the soil layer displacement in this direction is also assumed to be 0, and the y direction is the outward normal direction to establish the coordinate system. Figure 5 The change amount Δb of the z direction displacement of the soil layer is seen in the following formula due to the overall correlation of the slurry in the ring longitudinal direction:

[0067] Δb = f (E, p, σ z ) formula 15;

[0068] In formula 15, E is the elastic modulus of the soil, σ z is the vertical stress, and p is the grouting pressure.

[0069] Under the action of the grouting pressure, the surrounding soil will have a certain vertical displacement, causing local deformation and generating a corresponding stress response. Since the soil is regarded as a homogeneous and isotropic material, its vertical deformation behavior can be described by the generalized Hooke's law. Let the stress σ z = p-p e of the soil producing deformation, and the generalized Hooke's law is seen in the following formula:

[0070]

[0071] In formula 16, σ x is the stress in the x direction, σ y is the stress in the y direction, σ z is the stress in the z direction, ε x is the strain in the x direction, and εx = 0, ε y is the strain in the y direction, ε y = 0, ε z is the strain in the z direction, and μ is the Poisson's ratio of the clay.

[0072] Therefore, the strain in the z direction of the soil can be derived as follows:

[0073]

[0074] The soft clay bears the vertical construction gap direction pressure stress and moves to the side. By integrating equation 17, the vertical displacement of the soil layer can be obtained as follows:

[0075]

[0076] In equation 18, σ z is the additional stress, and D is a to-be-determined coefficient.

[0077] The soft clay interface uplift only occurs in a limited range, and the effective influence range of the grout-soil coupling is H = 10 m when the tunnel depth is 15 m. When z = H, Δb = 0, the boundary condition is substituted into equation 18 to obtain:

[0078]

[0079] The maximum vertical displacement Δb max of the soil layer exists on the grout-soil coupling interface, and z = 0 is obtained as equation 20:

[0080]

[0081] Since the deformation of the grout pipe interface is particularly small, it is ignored, that is, σ z = p - p e is substituted into equation 20 to obtain the construction gap width control equation:

[0082]

[0083] In equation 21, μ is the Poisson's ratio of the soil layer, E is the elastic modulus of the soil layer, b0 is the initial top pipe construction gap, p is the grouting pressure, and p e is the environmental pressure.

[0084] In one specific embodiment of the present application, the processing unit updates the thickness of the construction gap according to the following formula:

[0085]

[0086] In equation 29, H represents the set effective influence range of the grout-soil coupling, μ represents the Poisson's ratio of the soil layer, p represents the grouting pressure, p e represents the environmental pressure, E represents the elastic modulus of the soil layer, and Δpi,k represents the pressure difference of the i-th fan unit at the current calculation step.

[0087] When the slurry fills and diffuses, the soil interface of the construction gap is affected by the slurry pressure, and the uplift effect occurs. With the diffusion of the slurry, the thickness of the gap changes with the position of the slurry, the dissipation of the slurry pressure, the position of the slurry diffusion front, and the change of the slurry flow rate. When the construction gap value changes, it will also affect other slurry diffusion parameters at the next time step. Therefore, in the step-by-step algorithm, considering the fluctuation of the soil interface, the solving accuracy of the step-by-step algorithm can be improved.

[0088] The theoretical formula for calculating the width of the construction gap is obtained from equation 21. Since the construction gap changes when the slurry fan diffuses, the fan area is discretized into n-1 fan units, and each fan unit is discretized into m equally spaced ring units along the radial direction. Therefore, the width of the construction gap is updated based on the position of the slurry diffusion front of the discrete unit, the flow rate update, and the pressure update. The construction gap width change control equation is shown in equation 29. In the step-by-step algorithm, the parameters are updated according to the previous iteration, and the solution at the last step of the step-by-step algorithm is obtained.

[0089] The following describes the calculation principle of the simulation calculation system of the present application.

[0090] First, in order to facilitate the calculation and derivation of the grouting filling and diffusion, the following basic assumptions are made:

[0091] (1) On the slurry diffusion path, the slurry is isotropic and incompressible. The constitutive model is selected as Bingham fluid, and the mass loss, flow diffusion water-cement ratio change, and slurry viscosity time variation are not considered.

[0092] (2) The slurry has no slip with the two side contact surfaces, and the slurry flow state is laminar, satisfying the no-slip boundary condition.

[0093] (3) At the initial filling and diffusion stage of the slurry, the shape of the diffusion front can be approximated as a semicircle. As the slurry diffusion continues, the angle between the flow direction of any point inside the slurry and the tunnel segment axis remains constant, i.e., the slurry flow trajectory has stable directionality.

[0094] (4) When establishing the slurry diffusion motion equation, the acceleration effect in the slurry flow process is ignored, and it is assumed that the internal pressure of the slurry at the slurry front is always consistent with the external environment pressure, thereby simplifying the derivation process of the theoretical model.

[0095] (5) The critical pressure of the construction gap deformation is approximately equal to the environmental pressure, and the environmental pressure is approximately equal near the same grouting hole.

[0096] (6) Soft clay is an isotropic elastic medium. The grout pressure acts vertically on the upper and lower walls of the construction gap. Only the bulging of the soft clay layer under the action of grout pressure is considered, and the collapse of the soft clay layer is not considered.

[0097] Fill in the diffusion motion equations, such as Figure 2 As shown, the straight lines represent newly injected and diffusing grout in the current stage, while the grid-filled areas represent previously formed and well-covered mud jackets. Point D in the figure is any point on the grout diffusion front, and point M is located at a point on the line K2D connecting point D and grouting hole K2. t Let M be the point obtained by projecting it onto the tunnel cross-section. Figure 2 In this context, α1 represents the angle between grouting hole K2 and the vertical centerline of the tunnel section along the vertical direction where the grouting hole is located, thus accurately describing the spatial position of the grouting hole relative to the tunnel axis. M It is the angle between a point M on the fan-shaped flow surface of the grout filling diffusion and the vertical centerline of the tunnel section. Assuming that the angle between the flow direction of the grout micro-element and the vertical axis of the tunnel remains constant during the diffusion process, the diffusion trajectory of the grout within the unfolded plane after the outer surface of the tunnel segment is unfolded can be represented more intuitively, as shown below. Figure 3 As shown.

[0098] like Figure 4 As shown, stress analysis is performed at point D on the diffusion front. In the figure, Z, R, and S represent the thickness direction of the tunnel construction gap, the filling and diffusion direction of the grout, and the outward normal direction of the plane, respectively; b0 is the initial value of the tunnel construction gap; Δb is the thickness change value of the construction gap under the action of grout pressure; z p τ is the core radius of the fluid; P is the slurry pressure during diffusion; τ is the shear stress. Force analysis is performed on the micro-element along the slurry filling and diffusion direction to clarify the mechanical equilibrium relationship of the slurry during the diffusion process.

[0099] Pdz+τdr+f dzdr=(P+dP)dz+(τ+dτ)dr Formula 1,

[0100]

[0101] In Equations 1 and 2, f is the component of gravity in the R direction, as shown in Equation 3, ρ is the density of the slurry, and g is the acceleration due to gravity.

[0102] f=ρgsinθ M sina N Formula 3,

[0103] Let B = -dP / dr + f, then dτ = Bdz. Integrating dτ along the Z-direction, given the boundary conditions z = 0 and τ = 0, we have:

[0104] τ = Bz, z > 0 Equation 4,

[0105] The constitutive equation of Bingham fluid is as follows:

[0106]

[0107] In Equation 5, τ0is the static shear stress of the slurry, μ0is the plastic viscosity of the slurry, γ is the shear rate, and v is the slurry velocity.

[0108] Substituting Equation 4 into Equation 5 gives:

[0109]

[0110] Let τ0= Bz p The flow core radius of the Bingham fluid can be obtained as follows:

[0111]

[0112] Integrating Equation 6, according to the flow rule of the Bingham fluid constitutive model, the boundary conditions for the slurry flow diffusion are as follows: z = b / 2, v = 0, b = b0+ Δb, and substituting the boundary conditions gives the velocity distribution of the slurry in the range of |z|≤b / 2: p

[0113]

[0114] The slurry flow velocity along the Z direction is as follows:

[0115]

[0116] Integrating in the thickness direction of the tunnel construction gap, the average flow velocity of the slurry filling diffusion is obtained as follows:

[0117]

[0118] The expression of the slurry micro-unit flow and the flow velocity is established as follows:

[0119]

[0120] Therefore, the monomial cubic equation of B can be obtained as follows:

[0121]

[0122] Using Equation 12 and the constraint condition of Equation 7: z p <b / 2, the value of B can be solved.

[0123] From Equation 6, we have:

[0124] dP = (-B + f)dr Equation 13,

[0125] ​Therefore, the control equation of the slurry filling diffusion movement is:

[0126]

[0127] In formula 14, P0 is the pressure of the grouting hole, P e is the ambient pressure.

[0128] The simulation calculation system of the application realizes numerical simulation and calculation through Matlab software programming, so that the numerical solution and approximate analytical expression of the pressure distribution in the slurry diffusion process are obtained, thereby providing effective theoretical guidance and reference for actual engineering application.

[0129] Discretization of the solution region:

[0130] In order to more accurately simulate the flow of the slurry in the construction gap of the shield tail, the slurry filling diffusion region is discretized into n-1 fan-shaped units, the central angles Δθ of the fan-shaped units are equal, and each fan-shaped region is discretized into m equidistant ring-shaped units along the radial direction, so that a diffusion analysis grid with double discrete structures of radial and angular directions is constructed. The corresponding discrete length Δr i on the side length R i has self-adaptivity, so as to more truly reflect the diffusion characteristics of the slurry, as shown in formula 20. Figure 6 Wherein, r0 is the equivalent radius of the grouting hole, r ij represents the length of the jth discrete point on R i from the center of the grouting hole.

[0131] Based on formula 13, the pressure loss value consumed by the slurry flow filling the discrete unit r i,j r i,j+1 is as follows:

[0132] ΔP i,j =P i,j+1 -P i,j =(-B i,j -ρg sin α i,j sin θ i )Δr i , formula 22.

[0133] In formula 22, B i,j =f(r i,j ,θ i ,Δq).

[0134] The vertical included angle formula of the ring-shaped discrete unit is as follows:

[0135]

[0136] θ i =iΔθ, formula 24,

[0137] In formula 23 and formula 24, R t is the outer diameter of the tunnel.

[0138] The grouting flow is solved:

[0139] The diffusion speed of the grout in the gap between the shield tail and the surrounding environment is mainly affected by the grouting pressure, the grouting rate, and the pressure difference between the grout and the surrounding environment. In particular, at the flow front of the grout, the difference between the internal pressure of the grout and the ambient pressure directly drives the diffusion speed. To accurately describe this process, the diffusion area can be divided into several discrete fan-shaped units, and the grouting flow in each unit is calculated. According to the flow continuity and pressure distribution characteristics, the grouting flow expression Δq i is as follows:

[0140]

[0141] The chordal section method is used to solve the above formula, as shown in Figure 7 The basic iterative formula of the chordal section method is as follows:

[0142]

[0143] A numerical calculation program is written using Matlab to solve the grouting flow in each fan-shaped discrete unit. By constructing an iterative algorithm that meets the boundary conditions and physical constraints, the flow distribution in the real grouting process is gradually approached. The numerical solution process is based on the premise of controlling the calculation error within an acceptable range, and the grouting flow Δq i of each fan-shaped discrete unit that meets the error is solved.

[0144] Diffusion front tracking:

[0145] During the iterative calculation of the grout pressure, the position of the grout diffusion front must be determined first. Since there is a coupling relationship between the position of the diffusion front and the diffusion speed of the grout, and they influence each other, they cannot be directly solved by simple analytical methods. This process is essentially an alternating iterative updating mechanism based on time step discretization: at each time, the local diffusion speed of the grout is calculated according to the current pressure distribution, and the position of the diffusion front is updated accordingly; then, the pressure field is adjusted and the next iteration is entered until the preset convergence accuracy is met. As shown in Figure 8As shown, the initial state T0 is a semicircular area with a radius of R0 from the grouting hole, and the slurry diffusion front can be approximately simplified as a semicircle. Based on the initial diffusion front state, the area is discretized into a plurality of fan-shaped units, and the slurry diffusion velocity is calculated in each unit. According to the slurry diffusion velocity, the slurry flow path increment in the time step is further calculated. After completing the pressure and velocity calculation of the current step, the position of the slurry diffusion front needs to be updated, and then a new round of iteration process is entered. Through continuous iteration and updating in space-time, the real state of the slurry diffusion process is gradually approached. The numerical iteration process can dynamically capture the change trend of the slurry diffusion front with time advancing, and finally obtain the complete space-time evolution path and diffusion form.

[0146] T k+1 The diffusion front calculation formula is as follows:

[0147]

[0148] In the formula, is the average flow velocity of the slurry at the slurry diffusion front of the i-th fan-shaped unit at time step k, ΔR i is the flow path increment of the i-th fan-shaped unit.

[0149] In order to ensure the accuracy of the Matlab numerical calculation program, max(ΔR i )<0.1m, so the time increment ΔT k dynamically changes with the calculation process. By superimposing the diffusion front of the last time step and the calculated flow path increment, the new diffusion front is updated, and the iteration update of the next time step is entered. After all the time steps are completed, after multiple iterations, when the change between the diffusion front and the flow path increment tends to be stable, that is, the convergence condition is reached, the slurry flow diffusion form and the corresponding slurry pressure space-time distribution characteristics of the slurry in the stable state can be obtained.

[0150] The application also provides a calculation method of the grouting filling and extrusion diffusion mechanism of the tunneling tunnel construction, and the simulation calculation method is described below.

[0151] As Figure 1 shown, the simulation calculation method of the application comprises the following steps:

[0152] Obtaining the actual construction parameters of the tunnel construction;

[0153] Discretizing the slurry diffusion area at each grouting hole to obtain a plurality of fan-shaped units, and dividing each fan-shaped unit into annular discrete units along the radial direction;

[0154] Based on the chord intersection method, the grouting flow of the i-th fan-shaped unit is iteratively calculated, two different initial flow values are selected as the starting point of the calculation, the pressure field of each annular discrete unit in the i-th fan-shaped unit is calculated, the pressure difference of each annular discrete unit before and after grouting is obtained, the pressure difference of each annular discrete unit in the i-th fan-shaped unit is accumulated to obtain two corresponding pressure losses, the difference between the two pressure losses is calculated to obtain the pressure difference, and it is judged whether the pressure difference meets the error control standard, if not, the flow value is updated according to the iteration formula of the chord intersection method, and the next round of solution is continued until the error control standard is met;

[0155] According to the pressure difference of the i-th fan-shaped unit, the change amount of the construction gap thickness is calculated, and the construction gap thickness is updated according to the change amount of the construction gap thickness;

[0156] According to the grouting flow of the fan-shaped unit, the position of the grouting diffusion front is updated, and then the diffusion boundary of the grouting at the current time step is obtained;

[0157] Based on the updated grouting diffusion front position, the next round of cycle iterative calculation is continued, and the iterative calculation and pressure field calculation of the grouting flow are repeatedly performed to dynamically simulate the continuous diffusion process of the grouting in the shield tail gap until the upper limit of the cycle iterative calculation time is reached;

[0158] In each calculation step, the corresponding diffusion radius and grouting flow of each fan-shaped unit are recorded, so as to obtain the pressure distribution of each discrete point of the grouting in the diffusion area, and at the same time, the thickness of the construction gap is dynamically updated according to the pressure change result, so as to provide the geometric boundary condition for the next iteration.

[0159] Further, when calculating the change amount of the construction gap thickness according to the pressure difference of the i-th fan-shaped unit, and updating the construction gap thickness according to the change amount of the construction gap thickness, a construction gap thickness control equation is established, including the following steps:

[0160] The soil layer is simplified as a semi-infinite space elastic body model, and it is assumed to bear uniform pressure;

[0161] Based on the generalized Hooke's law, the strain of the soil layer in the z direction can be derived as:

[0162]

[0163] In formula 17, ε z represents the strain in the z direction; Δb represents the displacement change amount of the soil layer in the z direction, σ z represents the vertical stress, E represents the elastic modulus of the soil layer, and μ represents the Poisson's ratio of the soil layer;

[0164] Integrating formula 17, the vertical displacement of the soil layer is:

[0165]

[0166] In formula 18, D represents a to-be-determined coefficient;

[0167] According to the tunnel depth, the effective influence range of the slurry-soil coupling is set as H, H is less than the tunnel depth, when z=H, Δb=0, the boundary condition is substituted into formula 18, and the following can be obtained:

[0168]

[0169] The maximum vertical displacement Δb of the soil layer max On the slurry-soil coupling interface, z=0 is obtained:

[0170]

[0171] Substitute σ z =p-p e into formula 20, and the construction gap thickness control equation is obtained:

[0172]

[0173] In formula 21, b0 represents an initial construction gap, p represents a grouting pressure, p e represents an environmental pressure.

[0174] In one specific embodiment of the present application, the thickness of the construction gap is dynamically updated according to the pressure change result, and the updating calculation is performed through the following formula:

[0175]

[0176] In formula 29, H represents the effective influence range of the slurry-soil coupling, μ represents the Poisson's ratio of the soil layer, p represents a grouting pressure, p e represents an environmental pressure, E represents the elastic modulus of the soil layer, and Δp i,k represents the pressure difference of the i-th fan unit at the current calculation step.

[0177] In one specific embodiment of the present application, the actual construction parameters of the tunnel construction obtained include the included angle between the grouting hole and the vertical center line of the vertical tunnel section, the grouting hole pressure and the environmental pressure.

[0178] The present application fully considers the actual characteristics of the longitudinal and circumferential coupling diffusion of the slurry in the shield tail gap, also considers the coupling change of the slurry-soil interface, more truly reflects the flow path and pressure change of the slurry in the filling process, emphasizes the coupling relationship between the longitudinal and circumferential flows of the slurry in the diffusion process, more comprehensively reflects the grouting diffusion flow process, also considers the slurry-soil coupling effect in the tunnel construction gap, and points out that the slurry filling diffusion will cause the increase of the construction gap.

[0179] The present application is based on Bingham fluid, combines fluid mechanics and elasticity theory, and comprehensively considers the diffusion behavior of slurry in the construction gap, the pressure transmission process and the interaction with the surrounding stratum. The grouting pressure as the driving force controls the initial input intensity and diffusion range of the slurry; the ambient pressure as the boundary constraint limits the stress state of the slurry diffusion front. By introducing the assumption of longitudinal ring direction coordinated diffusion, combined with the slurry-soil coupling effect, the spatial pressure distribution of the slurry at different positions can be simulated, which provides a theoretical reference for the design of tunnel grouting construction.

[0180] On the basis of fully considering the influence of slurry self-weight, the pressure is taken as the boundary condition to carry out numerical solution, and the results show that the diffusion range of the slurry in the construction gap presents the characteristics of asymmetric and irregular ring distribution. This distribution form is mainly affected by multiple factors such as stratum gravity, self-viscosity and boundary constraint. In order to accurately describe the diffusion process, based on the algorithm concept of space-time discretization, the grouting diffusion area is meshed, and the corresponding mechanical equilibrium equation set is established on each discrete unit. By solving these equations, the functional relationship between the grouting pressure and the slurry diffusion radius (i.e. the diffusion front position) is derived, and a numerical calculation method which can be solved by Matlab algorithm is constructed.

[0181] The disturbance of slurry filling diffusion to the construction gap is considered, and the construction gap control equation is derived based on the semi-infinite space deformation body. The construction gap rises to a certain extent with the filling and diffusion of the slurry, which improves the previous assumption of grouting filling and diffusion, and is more close to the actual interface change.

[0182] The slurry pressure presents the trend of small on the whole and large at the bottom dominated by gravity, and the slurry pressure distribution in the local area near the grouting hole is relatively complex. The construction gap near the grouting hole has the maximum uplift value, and the uplift value of the construction gap is different with the change direction of different slurry pressure gradient, among which the construction gap will become larger when flowing in the direction of increasing slurry pressure, and the construction gap will become smaller when flowing in the direction of decreasing slurry pressure, but it is higher than the initial gap value.

[0183] 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 calculating a grouting filling and extrusion diffusion mechanism of a tunneling construction, characterized in that, The method comprises the following steps: obtaining actual construction parameters of tunnel construction; discretizing the slurry diffusion area at each grouting hole to obtain a plurality of fan-shaped units, and dividing each fan-shaped unit into annular discrete units along the radial direction; based on the secant method, iteratively calculating the grouting flow of the i-th fan-shaped unit, selecting two different initial flow values as the starting point of calculation, calculating the pressure field of each annular discrete unit in the i-th fan-shaped unit, obtaining the slurry pressure difference before and after each annular discrete unit, and accumulating the slurry pressure difference before and after each annular discrete unit in the i-th fan-shaped unit to obtain two corresponding pressure losses, calculating the difference between the two pressure losses to obtain a pressure difference, and judging whether the pressure difference meets the error control standard, if not, updating the flow value according to the iterative formula of the secant method, and continuing to solve the next round until the error control standard is met; calculating the change amount of the construction gap thickness based on the pressure difference of the i-th fan-shaped unit, and updating the construction gap thickness based on the change amount of the construction gap thickness; updating the position of the slurry diffusion front based on the grouting flow of the fan-shaped unit, and then obtaining the diffusion boundary of the slurry at the current time step; based on the updated slurry diffusion front position, continue to perform the next round of iterative calculation, repeat the iterative calculation and pressure field calculation of the grouting flow, to dynamically simulate the continuous diffusion process of the slurry in the shield tail gap, until the upper limit of the iterative calculation time is reached; in each calculation step, record the corresponding diffusion radius and grouting flow of each fan-shaped unit, so as to obtain the pressure distribution of each discrete point in the diffusion area, and dynamically update the thickness of the construction gap according to the pressure change result to provide the geometric boundary condition for the next iteration.

2. The method of claim 1, wherein the method is a method of calculating a tunneling construction grouting filling, extrusion, and diffusion mechanism, characterized by, In the step of calculating the change amount of the construction gap thickness based on the pressure difference of the i-th fan-shaped unit, and updating the construction gap thickness based on the change amount of the construction gap thickness, a construction gap thickness control equation is established, comprising the following steps: simplify the soil layer into a semi-infinite space elastic body model, and assume that it bears uniform pressure; based on the generalized Hooke's law, the strain of the soil layer in the z direction can be derived as: In formula 17, ε z represents the strain in the z direction; Δb represents the displacement variation of the soil layer in the z direction, σ z represents the vertical stress, E represents the elastic modulus of the soil layer, and μ represents the Poisson's ratio of the soil layer; integrate formula 17 to obtain the vertical displacement of the soil layer: in formula 18, D represents an undetermined coefficient; according to the tunnel depth, set the effective influence range of slurry-soil coupling as H, which is less than the tunnel depth, when z=H, Δb=0, and the boundary condition is substituted into formula 18 to obtain: Maximum vertical displacement of soil layer Δb max At the interface between the soil and the pile, z = 0, we have: Substituting equation 20 into equation 19, the construction gap thickness control equation is obtained as follows: z = p - p e Substituting equation 20 into equation 19, the construction gap thickness control equation is obtained as follows: In Equation 21, b0represents an initial construction gap, p represents a grouting pressure, and p e represents an ambient pressure.

3. The method of claim 1, wherein the method is a method of calculating a tunneling construction grouting filling, extrusion, and diffusion mechanism, characterized by, update the thickness of the construction gap based on the pressure change result, and update the calculation through the following formula: In Equation 29, H represents the effective influence range of the set slurry-soil coupling, μ represents the Poisson's ratio of the soil layer, p represents the grouting pressure, p e represents the ambient pressure, E represents the elastic modulus of the soil layer, Δp i,k represents the pressure difference of the i-th fan unit at the current calculation step.

4. The method of claim 1, wherein the method is a method of calculating a tunneling construction grouting filling, extrusion, and diffusion mechanism, characterized by, The obtained actual construction parameters of tunnel construction include the angle between the grouting hole and the vertical center line of the vertical tunnel section, the grouting hole pressure and the environmental pressure.

5. A computing system for grouting filling and extrusion diffusion mechanism of tunneling construction, characterized in that, The method comprises the following steps: a parameter acquisition unit for obtaining actual construction parameters of tunnel construction; a discrete division unit for discretizing the slurry diffusion area at each grouting hole to obtain a plurality of fan-shaped units, and dividing each fan-shaped unit into annular discrete units along the radial direction; The iteration calculation unit is connected with the discrete division unit, and is configured to perform iterative calculation on the grouting flow of the i-th fan-shaped unit based on the secant method, select two different initial flow values as a calculation starting point, perform pressure field calculation on each annular discrete unit in the i-th fan-shaped unit, obtain the front and rear slurry pressure difference values of each annular discrete unit, accumulate the front and rear slurry pressure difference values of each annular discrete unit in the i-th fan-shaped unit to obtain two corresponding pressure losses, calculate the difference between the two pressure losses to obtain a pressure difference, and judge whether the pressure difference value meets an error control standard; if not, update the flow value according to an iterative formula of the secant method, and continue to perform next round of solving until the error control standard is met. The parameter updating unit is connected with the iteration calculation unit, and is configured to calculate a change amount of the construction gap thickness according to the pressure difference of the i-th fan-shaped unit, and update the construction gap thickness according to the change amount of the construction gap thickness; and is further configured to update the position of the slurry diffusion front according to the grouting flow of the fan-shaped unit, and then obtain the diffusion boundary of the slurry at the current time step. The processing unit is connected with the parameter updating unit and the iteration calculation unit, and is configured to control the iteration calculation unit to continue to perform next round of cyclic iteration calculation based on the updated position of the slurry diffusion front, and repeatedly perform the iterative calculation of the grouting flow and the pressure field calculation, so as to dynamically simulate the continuous diffusion process of the slurry in the shield tail gap until a time upper limit of the cyclic iteration calculation is reached. The processing unit is further configured to record the diffusion radius and the grouting flow corresponding to each fan-shaped unit in each calculation step, so as to obtain the pressure distribution of each discrete point of the slurry in the diffusion area, and simultaneously dynamically update the thickness of the construction gap according to the pressure change result, to provide a geometric boundary condition for next round of iteration.

6. The computing system for tunneling construction grout filling extrusion diffusion mechanism of claim 5, wherein, The parameter updating unit is provided with a construction gap thickness control equation, and the parameter updating unit updates the construction gap thickness through the construction gap thickness control equation. In Equation 21, b0represents an initial construction gap, p represents a grouting pressure, p e represents an ambient pressure, E represents an elastic modulus of the soil layer, μ represents a Poisson's ratio of the soil layer, and H represents a set effective influence range of the slurry-soil coupling.

7. The computing system for tunneling construction grout filling extrusion diffusion mechanism of claim 5, wherein, The processing unit updates the thickness of the construction gap according to the following formula: In Equation 29, H represents the effective influence range of the set slurry-soil coupling, μ represents the Poisson's ratio of the soil layer, p represents the grouting pressure, p e represents the ambient pressure, E represents the elastic modulus of the soil layer, Δp i,k represents the pressure difference of the i-th fan unit at the current calculation step.

8. The computing system for tunneling construction grout filling extrusion diffusion mechanism of claim 5, wherein, The actual construction parameters of the tunnel construction obtained by the parameter acquisition unit include an included angle between a grouting hole and a vertical center line of a vertical tunnel section, a grouting hole pressure and an environmental pressure.

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