Comprehensive evaluation method and system for longitudinal deformation of shield tunnel

Abstract

The invention relates to the technical field of tunnel engineering design, and discloses a comprehensive evaluation method and system for longitudinal deformation of a shield tunnel, and the method comprises the steps: obtaining a target shield tunnel analysis calculation parameter; based on the target shield tunnel analytical calculation parameters and the target shield soil analytical calculation parameters, constructing a first shield tunnel stress calculation model to calculate additional stress at the axis of the target shield tunnel; constructing an additional stress work equation at the axis of the target shield tunnel to obtain the total work of the target shield tunnel under stress; constructing a second shield tunnel longitudinal deformation calculation model based on an energy method to obtain a longitudinal displacement field at the axis of the target shield tunnel; constructing a third shield lining performance nonlinear degradation model to obtain an evaluation index of the longitudinal deformation of the target shield tunnel; evaluating the longitudinal deformation of the target shield tunnel based on the evaluation index; the tunnel longitudinal deformation evaluation method solves the problems that an existing tunnel longitudinal deformation evaluation method is single in consideration of influence factors and poor in evaluation accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel engineering design, and particularly to a comprehensive evaluation method and system for longitudinal deformation of shield tunnels. Background Art

[0002] With the rapid development of shield tunnel technology, the density of underground projects in coastal areas has increased significantly in recent years. However, the geological and hydrogeological conditions in these areas are complex, especially in water-rich strata, which pose significant challenges to underground projects. These conditions make tunnels extremely vulnerable to interference, including seasonal water level changes and nearby construction activities, resulting in excessive additional deformations. These deformations trigger a series of related problems, such as segment cracking, water leakage, and joint opening, ultimately accelerating the degradation of structural performance. Given the increasing complexity of underground projects in coastal areas, it is of great significance to evaluate the structural performance of shield tunnels and ensure long-term safety and reliability. Therefore, it is necessary to determine the longitudinal deformation of existing shield tunnels during construction, and then determine that the degradation of the lining performance of shield tunnels is within a reasonable range, so as to ensure the safety of existing shield tunnels during surrounding construction. Currently, in the method for determining the longitudinal deformation of existing shield tunnels caused by water level changes and surrounding environment construction, compared with numerical simulation, indoor model tests, and field tests, the theoretical analysis method is faster, more accurate, and convenient for researchers and engineers to use. However, for the longitudinal deformation of shield tunnels, usually only the influencing factors in a single case are considered, and the change of the lining performance of shield tunnels is not further analyzed. It can be seen that the existing evaluation methods for tunnel longitudinal deformation have problems of single consideration of influencing factors and poor evaluation accuracy. Summary of the Invention

[0003] The present invention provides a comprehensive evaluation method and system for longitudinal deformation of shield tunnels to solve the problems of single consideration of influencing factors and poor evaluation accuracy in the existing evaluation methods for tunnel longitudinal deformation.

[0004] To achieve the above object, the present invention is implemented through the following technical solutions: In the first aspect, the present invention provides a comprehensive evaluation method for longitudinal deformation of shield tunnels, including: S1. Obtain the analytical calculation parameters of the target shield tunnel, the analytical calculation parameters of the target shield soil body, the allowable maximum deformation and initial deformation of the target shield tunnel lining, the characteristics of the surface soil cover load, and the analytical calculation parameters of the water level; S2. Construct a first force calculation model for the shield tunnel based on the analytical calculation parameters of the target shield tunnel, the analytical calculation parameters of the target shield soil body, the characteristics of the surface soil cover load, and the analytical calculation parameters of the water level, and calculate the additional stress at the axis of the target shield tunnel based on the first force calculation model for the shield tunnel; S3. Construct the additional stress work equation at the axis of the target shield tunnel, and solve the additional stress work equation based on the additional stress at the axis of the target shield tunnel to obtain the total work done by the force on the target shield tunnel; S4. Based on the energy method, construct a longitudinal deformation calculation model for the second shield tunnel, and solve the longitudinal deformation calculation model of the second shield tunnel based on the total work done by the force on the target shield tunnel to obtain the longitudinal displacement field at the axis of the target shield tunnel; S5. Based on the allowable maximum deformation and initial deformation of the lining of the target shield tunnel, construct a non-linear degradation model for the performance of the third shield lining, and solve the non-linear degradation model for the performance of the third shield lining according to the longitudinal displacement field at the axis of the target shield tunnel to obtain the evaluation index of the longitudinal deformation of the target shield tunnel; S6. Evaluate the longitudinal deformation of the target shield tunnel based on the evaluation index.

[0005] Optionally, the analytical calculation parameters of the target shield tunnel in S1 include: the buried depth of the axis of the shield tunnel; The analytical calculation parameters of the target shield soil include: the Poisson's ratio of the soil and the elastic modulus of the soil; The characteristics of the overburden load on the ground surface include: the unit weight of the overburden load, the length of the overburden load, the width of the overburden load, and the depth of the overburden load; The analytical calculation parameters of the water level, including: the initial water level height and the dynamically changing water level height.

[0006] Optionally, S2 includes: Construct a force calculation model for the first shield tunnel according to the characteristics of the target shield tunnel to calculate the additional stress at the axis of the target shield tunnel, where the additional stress includes: the formation reaction force, the external water pressure on the lining of the shield tunnel, and the additional stress of the overburden load; Substitute the analytical calculation parameters of the target shield tunnel, the analytical calculation parameters of the target shield soil, the characteristics of the overburden load on the ground surface, and the analytical calculation parameters of the water level into the force calculation model of the first shield tunnel to solve the formation reaction force, the external water pressure on the lining of the shield tunnel, and the additional stress of the overburden load at the axis of the target shield tunnel, where the force calculation model of the first shield tunnel satisfies the following relational expressions: ; ; ; ; ; ; ; ; ; ; ; ; ; ; where: σ q ( x ) is the vertical stress caused by the overburden load at a certain point on the tunnel axis, q is the unit weight of the overburden load, taking a negative value under loading conditions and a positive value under unloading conditions, R 1, R 2 are respectively the distances from the load application point to the target point and from its mirror point with respect to the ground to the target point, B is the width of the overburden load, L is the length of the topsoil overburden load, h is half of the height of the overburden load, P ( y , z ) is the water pressure at any position outside the lining, P r0 is the water pressure inside the lining, taking 0, h w is the ground water head, c is the tunnel burial depth, r is the lining radius, Z ( x ) is the foundation reaction force, w ( x ) is the foundation deformation, k is the foundation stiffness coefficient, g is the foundation shear coefficient, r g is the grouting circle thickness, k r , k g is the permeability coefficient of the stratum and the grouting circle, R ( x ) is the total additional stress at a certain point on the tunnel axis, γ w is the unit weight of water, E S is the equivalent elastic modulus of the stratum, EI is the segment stiffness, h 1 is the thickness of the shear layer, taking 2.5 D , h 2 is the height of the groundwater level after the water level change, D is the tunnel diameter, F t ,F c , F s are the circumferential tensile stress, circumferential compressive stress, and circumferential shear stress respectively, γ 1 is the natural unit weight of the soil mass, γ 2 is the saturated unit weight of the soil mass, G is the gravity of the segment per unit length, γ c is the unit weight of the lining, r 0 is the inner diameter of the lining, k s is the shear stiffness between segments, k t is the tensile stiffness between segments, k c is the compressive stiffness between segments, θ m is the angle between adjacent rings, Δ w m is the displacement between adjacent rings, θ j is per unit area P and the angle with the vertical direction, ξ is the correction coefficient, κ b , κ s are the shear coefficients of the bolt and the segment ring Timoshenko, l b is the length of the bolt, E b , E s are the elastic moduli of the concrete and the bolt, μ b , μ s are the Poisson's ratios of the concrete and the bolt, A b is the cross-sectional area of a single bolt, n b is the number of bolts, A s is the cross-sectional area of the segment concrete, k b is the average line stiffness of the bolt, A ] is the intermediate parameter in the corresponding calculation formula, is the partial derivative symbol, x is the longitudinal coordinate of the stress point to be calculated, y is the transverse coordinate of the stress point to be calculated, z is the vertical coordinate of the stress point to be calculated, is the additional stress of the soil mass caused by the water level change, is the proportionality coefficient of the tensile area between two lining rings, is the vertical resultant force of the external water pressure on the lining, is the horizontal resultant force of the external water pressure on the lining, P is the external water pressure on the lining, μ is the Poisson's ratio of the soil, z 0 is the longitudinal coordinate of the stress at the point to be determined, h 0 is the vertical coordinate of the vertical point load, Pv is the vertical resultant force of the external water pressure on the lining, y ( θ j ) is the representation form of the longitudinal coordinate in the form of spatial coordinates, z ( θ j ) is the representation form of the vertical coordinate in the form of spatial coordinates, σ 1 is the total stress of the soil after the water level changes, u 1 is the pore water pressure of the soil after the water level changes, σ 0 is the total stress of the soil under the initial water level, u 0 is the pore water pressure of the soil after the water level changes, r 1 is the outer diameter of the tunnel; Obtained through the above calculation formula σ q ( x )、 Pv 、 Z ( x )、 R ( x )、 F t 、 F c 、 F s 、 G are all the forces at the axis of the target shield tunnel.

[0007] Optionally, the S3 includes: Construct an additional stress work equation based on the formation reaction force, the external water pressure on the shield tunnel lining, and the additional stress of the overburden load. Among them, the additional stress work equation includes: the work equation for overcoming the formation reaction force, the work equation for overcoming the shear force between rings, the work equation for overcoming the tensile stress between rings, and the work equation for the vertical component of the lining water pressure; Based on the work equation for overcoming formation reaction force, the work equation for overcoming shear force between rings, the work equation for overcoming tensile stress between rings, and the work equation for the vertical component of lining water pressure, a total calculation model for a specific ring of the target shield tunnel is constructed, and the formation reaction force, external water pressure on the shield tunnel lining, and additional stress of overburden load are substituted into the total calculation model for the specific ring of the target shield tunnel to solve the total work done by the target shield tunnel under force. Among them, the total work calculation model for the specific ring of the target shield tunnel satisfies the following relationship: ; ; ; ; ; ; ; ; ; In the formula: W R is the work done by the additional stress, W k is the work done to overcome the formation reaction force, W S is the work done to overcome the shear force between rings, W t is the work done to overcome the tensile force between rings, W c is the work done to overcome the compressive stress between rings, W P is the work done by the vertical water pressure outside the lining, W G is the work done by the weight of the lining ring, W is the total work done by the target shield tunnel under force, N is the number of segment rings taken for calculation, m is the number of segment rings to be calculated.

[0008] Optionally, the S4 includes: Based on the energy variational method and the principle of minimum potential energy, a longitudinal deformation calculation model for the second shield tunnel is constructed, and the total work done by the target shield tunnel under force is substituted into the longitudinal deformation calculation model for the second shield tunnel to solve the longitudinal displacement field at the axis of the target shield tunnel. Among them, the longitudinal deformation calculation model for the second shield tunnel satisfies the following relationship: ; ; ; ; ; ; ; ; ; ; ; ; ; In the formula: K s is the formation reaction stiffness matrix, K G is the gravity action matrix, K t is the stiffness matrix between tunnel rings, P T is the action effect of water pressure and the tunnel lining ring, G T is the gravity action effect, σ ′] T is the action effect of the additional stress in the formation caused by the water level, R T is the interaction effect between the free displacement of the soil mass and the tunnel lining ring, a n are the Fourier expansion coefficients, n is the number of Fourier expansion terms, T n ( x ) is the Fourier expansion formula matrix, A is the Fourier expansion coefficient matrix, ξ i are different numbers of Fourier expansion terms, T is the matrix transpose symbol.

[0009] Optionally, the S5 includes: Construct a non - linear degradation model of the performance of the third shield lining, substitute the longitudinal displacement field at the axis of the target shield tunnel into the non - linear degradation model of the performance of the third shield lining to solve the lining structure performance, and use the lining structure performance as the evaluation index of the longitudinal deformation of the target shield tunnel. Among them, the non - linear degradation model of the performance of the third shield lining satisfies the following relational formula: ; In the formula: Q is the lining structure performance, Δ w max is when the tunnel structure fails ( Q ( t ​​​) = 0), the maximum allowable longitudinal deformation, Δ w 0 is the initial deformation, Δ w ( t ) is the longitudinal deformation output by the longitudinal deformation calculation model of the second shield tunnel.

[0010] Optionally, the S6 includes: Determine the preset index threshold based on the construction characteristics of the target shield tunnel. When the evaluation index of the longitudinal deformation of the target shield tunnel is greater than or equal to the preset index threshold, evaluate the performance of the current lining structure as high performance; When the evaluation index of the longitudinal deformation of the target shield tunnel is less than the preset index threshold but greater than or equal to 0.75 times the preset index threshold, evaluate the performance of the current lining structure as medium performance; When the evaluation index of the longitudinal deformation of the target shield tunnel is less than 0.75 times the preset index threshold but greater than or equal to 0.5 times the preset index threshold, evaluate the performance of the current lining structure as low performance; When the evaluation index of the longitudinal deformation of the target shield tunnel is less than 0.5 times the preset index threshold but greater than or equal to 0.25 times the preset index threshold, evaluate the performance of the current lining structure as non-performance; And 0.25 times the preset index threshold is the index critical value of non-performance, and the situation less than 0.25 times the preset index threshold is not evaluated.

[0011] In a second aspect, an embodiment of the present application provides a comprehensive evaluation system for the longitudinal deformation of a shield tunnel, including a processor and a memory; The memory is used to store a computer program; The processor, when executing the program stored on the memory, implements any of the method steps in the first aspect.

[0012] Beneficial effects: The comprehensive evaluation method for the longitudinal deformation of a shield tunnel provided by the present invention constructs a force calculation model at the axis of the shield tunnel caused by water level change and overburden load through the target shield tunnel, shield soil body, allowable maximum and initial deformations of the shield tunnel lining, characteristics of overburden load on the ground surface, and water level analysis calculation parameters, and calculates the force on the shield tunnel; then, based on the energy variational method and the principle of minimum potential energy, a longitudinal deformation control equation of the shield tunnel considering the foundation shear effect is derived; according to the longitudinal deformation control equation of the shield tunnel and the established performance degradation model of the shield lining, the performance of the shield tunnel lining is calculated, and the performance is used as an evaluation index for the shield tunnel under the action of water level change and overburden load; It should be noted that the present invention constructs a first calculation model for the force of the shield tunnel caused by water level changes and overburden loads, combines the energy variational method and the principle of minimum potential energy to establish a second calculation model reflecting the longitudinal deformation of the shield tunnel, and then based on the longitudinal deformation of the shield tunnel of the second model and the non-linear degradation of the performance of the shield lining of the third model, an evaluation index of the shield tunnel under the action of water level changes and overburden loads with high innovation and overall systematization is obtained. Compared with the finite element method, the finite difference method, the indoor model test and the field test, this method is more simple, fast and accurate, and has high engineering application and popularization value. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flowchart of the comprehensive evaluation method for the longitudinal deformation of the shield tunnel according to the preferred embodiment of the present invention; Figure 2 It is a calculation model diagram of the comprehensive evaluation method for the longitudinal deformation of the shield tunnel according to the preferred embodiment of the present invention, wherein (a) is a schematic diagram of the physical and mechanical parameters of the shield tunnel under the action of foundation pit excavation construction, and (b) is a schematic diagram of the physical and mechanical parameters of the shield tunnel under the water level change; Figure 3 It is a longitudinal force model diagram of the shield tunnel provided by the preferred embodiment of the present invention; Figure 4 It is a transverse force model diagram of the shield tunnel provided by the preferred embodiment of the present invention; Figure 5 It is a schematic diagram of the longitudinal deformation of the shield tunnel provided by the preferred embodiment of the present invention; Figure 6 It is a schematic diagram of the change in the performance of the lining provided by the preferred embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0014] The technical solutions of the present invention will be described clearly and completely below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative work shall fall within the protection scope of the present invention.

[0015] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the art to which the present invention pertains. The "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. Similarly, terms such as "a" or "an" do not denote a quantity limitation, but mean that there is at least one. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left" and "right" are only used to indicate relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship also changes accordingly.

[0016] Please refer to Figures 1 - 6 , the selected embodiment of the present application provides a comprehensive evaluation method for the longitudinal deformation of a shield tunnel, and the specific steps are as Figure 1 shown, including: Obtain the allowable maximum and initial deformations of the target shield tunnel, shield soil body, and shield tunnel lining, the characteristics of the overburden load on the ground surface, and the analytical calculation parameters of the water level; Based on the analytical calculation parameters, construct a first shield tunnel stress calculation model, a second shield tunnel longitudinal deformation calculation model, and a third shield tunnel lining performance non-linear degradation model. Among them, the first shield tunnel stress calculation model is used to calculate the additional stress at the axis of the shield tunnel caused by water level changes and overburden load, the second shield tunnel longitudinal deformation calculation model is used to calculate the longitudinal deformation of the shield tunnel, and the third shield tunnel lining performance non-linear degradation model is used to calculate the degradation of the lining performance caused by the deformation of the shield tunnel; Based on the first shield tunnel stress calculation model, calculate the stress at the axis of the shield tunnel, based on the second shield tunnel longitudinal deformation calculation model, calculate the longitudinal deformation at the axis of the shield tunnel, and based on the third shield tunnel lining performance non-linear degradation model, calculate the lining performance of the shield tunnel; Based on the energy method, deduce and construct a longitudinal deformation control equation for the shield tunnel. Among them, the longitudinal deformation control equation for the shield tunnel is used to reflect the bending effect and shear effect of the stratum; According to the tunnel longitudinal deformation control equation and the principle of minimum potential energy, construct an analytical formula reflecting the tunnel longitudinal deformation; According to the calculation results of the analytical formula of the tunnel longitudinal deformation and the third shield tunnel lining performance non-linear degradation model, calculate the performance of the segments of the shield tunnel, and use the performance of the segments of the shield tunnel as the evaluation index of the shield tunnel.

[0017] In the above embodiments, a mechanical calculation model of the shield tunnel is constructed by using the target shield tunnel, shield soil mass, allowable maximum and initial deformations of the shield tunnel lining, characteristics of the overburden load on the ground surface, and water level analysis calculation parameters. Then, a longitudinal deformation control equation of the shield tunnel is derived and constructed based on the energy method. Among them, the longitudinal deformation control equation of the shield tunnel is used to reflect the bending effect and shear effect of the stratum. An analytical formula reflecting the longitudinal deformation of the tunnel is constructed according to the longitudinal deformation control equation of the tunnel and the principle of minimum potential energy. Then, a longitudinal deformation control equation of the shield tunnel considering the shear effect of the foundation is derived based on the energy variational method and the principle of minimum potential energy. The performance of the shield tunnel lining is calculated according to the longitudinal deformation control equation of the shield tunnel and the established shield tunnel lining degradation model, and the performance is used as an evaluation index of the shield tunnel under the action of water level change and overburden load.

[0018] The specific steps of its embodiments are as follows: (1) Determine the analytical calculation parameters of the existing shield and soil mass under the action of water level change and overburden load.

[0019] As Figure 2 shown, the physical and mechanical parameters of the shield tunnel under the action of water level change and foundation pit excavation construction in a certain project. Among them, Figure 2 in (a) is a schematic diagram of the physical and mechanical parameters of the shield tunnel under the action of foundation pit excavation construction. Under the action of foundation pit excavation construction, loading will be applied to the ground surface and soil layer. The soil layer will have corresponding unloading based on the applied loading. Under the action of loading and unloading, additional stresses will be generated on the shield tunnel, causing tunnel heave and settlement. Figure 2 in (b) is a schematic diagram of the physical and mechanical parameters of the shield tunnel under the water level change. Under the influence of rising and falling water levels, additional stresses will also be generated on the shield tunnel, thereby causing tunnel heave and settlement. The specific physical and mechanical parameters are as follows: a) Shield tunnel: The unit weight of the shield segment is 25 kN / m 3 , the buried depth is 6 m, the outer diameter of the shield is 3 m, the inner diameter of the shield is 2.7 m, the elastic modulus of the segment is 3.45×10 4 MPa, the shear modulus of the segment is 14.375 MPa, the flexural rigidity of the segment is 754.8 GPa, the tensile stiffness between segments is 9.28×10 4 MPa, the compressive stiffness between segments is 1.48×10 8 MPa, the tensile stiffness between segments is 3.06×10 6 MPa, the Poisson's ratio is 0.2; the unit weight of the grouting layer is 22 kN / m 3 , the inner diameter of the grouting layer is 3.1 m, and the outer diameter is 3 m.

[0020] b) Overburden load: The width is 10 m, the length is 10 m, the depth is 1 m, and the unit weight of the overburden load is 18 kN / m 3 .

[0021] c) Soil layer parameters: Elastic modulus is 15 MPa, unit weight is 18 kN / m 3 , Poisson's ratio is 0.3.

[0022] d) Water level: Unit weight of water is 10 kN / m 3 , water level is 12 m.

[0023] e) Allowable maximum and initial deformations of the shield tunnel lining: Maximum allowable deformation is 20 mm, initial deformation is 0.5 mm.

[0024] After obtaining the input parameters, first calculate the forces on the shield tunnel and the lining performance degradation model. The calculated forces on the shield can be further used to calculate the total work done by the forces, and then based on the energy method and the principle of minimum potential energy, establish the longitudinal deformation equation of the shield tunnel, so as to obtain the longitudinal displacement of the shield tunnel. Then, calculate the performance index of the lining based on the lining performance degradation model.

[0025] After obtaining the input parameters, first calculate the forces on the shield tunnel. After calculating the forces on the shield, the total work done by the forces on the shield tunnel can be calculated. Then, based on the energy method and the principle of minimum potential energy, establish the control equation for the tunnel deformation, so as to solve the deformation of the shield tunnel, and combine the established lining performance degradation model to calculate the performance of the lining and classify the lining performance according to the lining performance; Finally, output the final segment performance and the lining performance grade.

[0026] In the above embodiments, the parameters are all analytically calculated by constructing a mechanical model of the shield tunnel, a deformation model of the shield tunnel, and a lining performance degradation model of the shield tunnel. The analytical calculation model of the mechanical model of the shield tunnel is as Figure 3 、 Figure 4 shown, where Figure 3 is the longitudinal force model diagram of the shield tunnel, Figure 4 is the transverse force model diagram of the shield tunnel.

[0027] In this embodiment, the specific numerical values of the parameters are only for demonstration and are not limited.

[0028] Substitute the required calculation parameters into equations (1)-(13) to calculate the forces at the axis of the shield tunnel under the action of water level change and overburden load.

[0029] (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) In the formula: σ q ( x ) is the vertical stress caused by the overburden load at a certain point on the tunnel axis; q is the unit weight of the overburden load, taking a negative value under the loading condition and a positive value under the unloading condition; R 1, R 2 are respectively the distances from the load application point to the target point and from its mirror point with respect to the ground to the target point, and , ; B is the width of the overburden load; L is the length of the topsoil overburden load; h is half of the height of the overburden load; P ( y , z ) is the water pressure at any position outside the lining; P r0 is the water pressure inside the lining, taking 0; h w is the surface water head; c is the tunnel burial depth; r is the lining radius; Z ( x ) is the foundation reaction force; w ( x ) is the foundation deformation; k is the foundation stiffness coefficient; G is the foundation shear coefficient; r g is the thickness of the grouting ring; k r , k g are the permeability coefficients of the stratum and the grouting ring; R ( x ) is the total additional stress at a certain point on the tunnel axis; γ w is the unit weight of water; E S is the equivalent elastic modulus of the stratum; EI is the segment stiffness; h1 is the thickness of the shear layer, taking 2.5 D , D is the tunnel diameter; F t , F c , F s are the circumferential tensile stress, circumferential compressive stress, and circumferential shear stress respectively; γ 1 is the natural unit weight of the soil; γ 2 is the saturated unit weight of the soil; G is the gravity of the lining per unit length; γ c is the unit weight of the lining; r 0 is the inner diameter of the lining; k s is the shear stiffness between segments; k t is the tensile stiffness between segments; k c is the compressive stiffness between segments; θ m is the angle between adjacent rings; Δ w m is the displacement between adjacent rings; θ j is on the unit area P and the vertical angle; ξ is the correction coefficient; κ b , κ s are the shear coefficients of the bolt and the Timoshenko of the segment ring; l b is the length of the bolt; E b , E s are the elastic moduli of the concrete and the bolt; μ b , μ s are the Poisson's ratios of the concrete and the bolt; A b is the cross-sectional area of a single bolt; n b is the number of bolts; A s is the cross-sectional area of the segment concrete; k b is the average line stiffness of the bolt; A are the intermediate parameters in the corresponding calculation formula.

[0030] In the above calculations, through the vertical stress formula of overburden load, the foundation reaction formula, etc., combined with the tunnel burial depth and soil parameters, such as Poisson's ratio, elastic modulus, overburden load, such as unit weight, width, depth, and water level parameters, such as water head height, dynamic change, the formation reaction, external water pressure, and additional stress of overburden load are calculated. Through the above calculations of forces, multiple factors such as overburden load, water pressure, and foundation shear effect can be comprehensively incorporated, avoiding the limitations of the simplified model with a single factor. At the same time, the foundation reaction formula combined with stiffness and shear coefficient can more realistically reflect the interaction between the soil and the tunnel, improving the physical rationality of the additional stress calculation.

[0031] Substitute the forces acting on the tunnel obtained from the above calculations into equations (14)-(22) (14) (15) (16) (17) (18) (19) (20) (21) (22) Where: W R The work done by the additional stress; W Z The work done to overcome the formation reaction; W S The work done to overcome the establishment between rings; W t The work done to overcome the tensile force between rings; W c The work done to overcome the compressive stress between rings; W P The work done by the vertical water pressure outside the lining; W G The work done by the gravity of the lining ring; N is the number of lining rings taken for the calculation. In this example N Take 60.

[0032] In the above calculations, by constructing a work equation that overcomes the formation reaction force, inter-ring shear force, tensile stress, and the component force of water pressure, and by superimposing the work of each component, the total work W can be obtained. By calculating the work in this way, the complex stress is transformed into an energy form, providing input for the subsequent energy method and ensuring the strict application of the principle of energy conservation. At the same time, by quantifying the work of each component, the contribution weight of each factor to the total deformation is clarified, facilitating targeted optimization design.

[0033] After obtaining the total work done by the tunnel force, based on the energy method and the principle of minimum potential energy, substitute the assumed tunnel deformation equation into the energy equation to obtain the control equation for the longitudinal deformation of the tunnel. The calculation formulas are shown in Eqs. (23)-(36) as follows: (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) In the formulas: K s is the stiffness matrix of the formation reaction force, K t is the inter-ring stiffness matrix of the tunnel, P T is the action effect of water pressure on the tunnel lining ring, G T is the action effect of gravity, σ ′] T is the action effect of the additional stress in the formation caused by the water level, R T is the interaction effect between the free displacement of the soil and the tunnel lining ring.

[0034] ​​​In the above calculations, based on the energy variational method and the principle of minimum potential energy, the stiffness matrix and Fourier expansion are constructed to solve the longitudinal displacement field. By combining the total work and the Fourier coefficient matrix, the longitudinal deformation distribution of the tunnel is analyzed. Through the above calculations of the displacement field, the continuum problem is discretized into a matrix equation, which simplifies the computational complexity and improves the numerical solution efficiency. At the same time, the stiffness matrix can reflect the coupling effects of different deformation modes (such as bending and shear), accurately capturing the spatial distribution characteristics of tunnel deformation.

[0035] According to the above calculations, the longitudinal deformation of the tunnel can be obtained, such as Figure 5 shown Figure 5 is a schematic diagram of the longitudinal deformation of the shield tunnel. Figure 5 The settlement distance of the tunnel caused by the longitudinal deformation of the tunnel in (37) In the formula: Q is the lining structure performance, Δ w max is the maximum allowable longitudinal deformation when the tunnel structure fails ( Q ( t ) = 0), taking 20 mm; Δ w 0 is the initial deformation, taking 0.5 mm; Δ w ( t ) is the longitudinal deformation output by the longitudinal deformation calculation model of the second shield tunnel.

[0036] Among them, the lining performance obtained from the non - linear degradation model of the lining of the third shield tunnel satisfies the following indicators. Q 0, Q 1 = 0.75 Q 0, Q 2 = 0.50 Q 0, Q 3 = 0.25 Q 0 respectively meet the critical values of the indicators for high performance, medium performance, low performance, and no performance. The schematic diagram of the performance index results is as Figure 6 shown Figure 6 is a schematic diagram of the change in lining performance. The larger the lining performance Q obtained through calculation, the higher the structural performance of the shield tunnel.

[0037] In the above calculations, quantifying the lining performance through non - linear formulas can make the non - linear model more in line with the actual material degradation laws (such as concrete cracking and joint failure), avoiding the errors of linear assumptions. At the same time, through the normalized index Q, the degree of structural performance degradation can be intuitively reflected, providing a quantitative basis for maintenance decisions.

[0038] The embodiment of the present application further provides a comprehensive evaluation system for the longitudinal deformation of a shield tunnel, including a processor and a memory; The memory is used for storing a computer program; The processor is configured to implement any of the method steps in the comprehensive evaluation method for the longitudinal deformation of a shield tunnel when executing the program stored in the memory.

[0039] The above-mentioned comprehensive evaluation system for the longitudinal deformation of a shield tunnel can implement each embodiment of the above-mentioned comprehensive evaluation method for the longitudinal deformation of a shield tunnel and can achieve the same beneficial effects, which will not be elaborated here.

[0040] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A comprehensive evaluation method for the longitudinal deformation of shield tunnels, characterized in that Including: S1. Obtain the analytical calculation parameters of the target shield tunnel, the analytical calculation parameters of the target shield soil body, the allowable maximum deformation and initial deformation of the target shield tunnel lining, the characteristics of the overburden load on the ground surface, and the analytical calculation parameters of the water level; S2. Based on the analytical calculation parameters of the target shield tunnel, the analytical calculation parameters of the target shield soil body, the characteristics of the overburden load on the ground surface, and the analytical calculation parameters of the water level, construct a first force calculation model for the shield tunnel, and calculate the additional stress at the axis of the target shield tunnel based on the first force calculation model for the shield tunnel; S3. Construct an additional stress work equation at the axis of the target shield tunnel, and solve the additional stress work equation based on the additional stress at the axis of the target shield to obtain the total work done by the force on the target shield tunnel; S4. Based on the energy method, construct a second longitudinal deformation calculation model for the shield tunnel, and solve the second longitudinal deformation calculation model for the shield tunnel based on the total work done by the force on the target shield tunnel to obtain the longitudinal displacement field at the axis of the target shield tunnel; S5. Based on the allowable maximum deformation and initial deformation of the target shield tunnel lining, construct a third non-linear degradation model for the performance of the shield tunnel lining, and solve the third non-linear degradation model for the performance of the shield tunnel lining according to the longitudinal displacement field at the axis of the target shield tunnel to obtain the evaluation index of the longitudinal deformation of the target shield tunnel; S6. Evaluate the longitudinal deformation of the target shield tunnel based on the evaluation index.

2. The comprehensive evaluation method for the longitudinal deformation of a shield tunnel according to claim 1, wherein The analytical calculation parameters of the target shield tunnel in S1 include: the buried depth of the axis of the shield tunnel; The analytical calculation parameters of the target shield soil body include: the Poisson's ratio of the soil body and the elastic modulus of the soil body; The characteristics of the overburden load on the ground surface include: the unit weight of the overburden load, the length of the overburden load, the width of the overburden load, and the depth of the overburden load; The analytical calculation parameters of the water level include: the initial water level height and the dynamically changing water level height.

3. The comprehensive evaluation method for the longitudinal deformation of a shield tunnel according to claim 2, wherein, The S2 includes: Construct a first force calculation model for the shield tunnel according to the characteristics of the target shield tunnel to calculate the additional stress at the axis of the target shield tunnel, where the additional stress includes: the formation reaction force, the external water pressure on the shield tunnel lining, and the additional stress of the overburden load; Substitute the analytical calculation parameters of the target shield tunnel, the analytical calculation parameters of the target shield soil body, the characteristics of the overburden load on the ground surface, and the analytical calculation parameters of the water level into the first force calculation model for the shield tunnel to solve the formation reaction force, the external water pressure on the shield tunnel lining, and the additional stress of the overburden load at the axis of the target shield tunnel, where the first force calculation model for the shield tunnel satisfies the following relational expressions: ； ； ； ； ； ； ； ； ； ； ； ； ； ； In the formula: σ q ( x ) is the vertical stress caused by the overburden load at a certain point on the tunnel axis, q is the unit weight of the overburden load, taking a negative value under the loading condition and a positive value under the unloading condition, R 1, R 2 are respectively the distances from the load application point to the target point and from its mirror point with respect to the ground to the target point, B is the width of the overburden load, L is the length of the topsoil overburden load, h is half of the height of the overburden load, P ( y , z ) is the water pressure at any position outside the lining, P r0 is the water pressure inside the lining, taking 0, h w is the ground water head, c is the tunnel burial depth, r is the lining radius, Z ( x ) is the foundation reaction force, w ( x ) is the foundation deformation, k is the foundation stiffness coefficient, g is the foundation shear coefficient, r g is the grouting ring thickness, k r , k g is the permeability coefficient of the formation and the grouting ring, R ( x ) is the total additional stress at a certain point on the tunnel axis, γ w is the unit weight of water, E S is the equivalent elastic modulus of the formation, EI is the segment stiffness, h 1 is the thickness of the shear layer, taking 2.5 D , h 2 is the height of the groundwater level after the water level change, D is the tunnel diameter, F t 、 F c 、 F s are respectively the circumferential tensile stress, circumferential compressive stress, and circumferential shear stress, γ 1 is the natural unit weight of the soil, γ 2 is the saturated unit weight of the soil, G is the gravity of the segment per unit length, γ c is the unit weight of the lining, r 0 is the inner diameter of the lining, k s is the shear stiffness between segments, k t is the tensile stiffness between segments, k c is the compressive stiffness between segments, θ m is the included angle between adjacent rings, Δ w m is the displacement between adjacent rings, θ j is on the unit area P the included angle with the vertical direction, ξ is the correction coefficient, κ b 、 κ s are the shear coefficients of the bolt and the Timoshenko of the segment ring, l b is the length of the bolt, E b 、 E s are the elastic moduli of the concrete and the bolt, μ b 、 μ s are the Poisson's ratios of the concrete and the bolt, A b is the cross-sectional area of a single bolt, n b is the number of bolts, A s is the cross-sectional area of the segment concrete, k b is the average line stiffness of the bolt, A is the intermediate parameter in the corresponding calculation formula, is the partial derivative symbol, x is the longitudinal coordinate of the stress point to be calculated, y is the transverse coordinate of the stress point to be calculated, z is the vertical coordinate of the stress point to be calculated, is the additional soil stress caused by the water level change, is the proportional coefficient of the tensile area between two lining rings, is the vertical resultant force of the external water pressure on the lining, is the horizontal resultant force of the external water pressure on the lining, P is the external water pressure on the lining, μ is the Poisson's ratio of the soil, z 0 is the longitudinal coordinate of the stress of the point to be calculated, h 0 is the vertical coordinate of the vertical point load, Pv is the vertical resultant force of the external water pressure on the lining, y ( θ j ) is the representation form of the longitudinal coordinate in the form of spatial coordinates, z ( θ j ) is the representation form of the vertical coordinate in the form of spatial coordinates, σ 1 is the total stress of the soil mass after the water level change, u 1 is the pore water pressure of the soil mass after the water level change, σ 0 is the total stress of the soil mass under the initial water level, u 0 is the pore water pressure of the soil mass after the water level change, r 1 is the outer diameter of the tunnel; Obtained through the above calculation formula σ q ( x )、 Pv 、 Z ( x )、 R ( x )、 F t 、 F c 、 F s 、 G are all the forces at the axis of the target shield tunnel.

4. The comprehensive evaluation method for the longitudinal deformation of a shield tunnel according to claim 3, characterized in that The S3 includes: Based on the formation reaction force, the external water pressure on the shield tunnel lining, and the additional stress of the overburden load, construct an additional stress work equation, where the additional stress work equation includes: the work equation for overcoming the formation reaction force, the work equation for overcoming the shear force between rings, the work equation for overcoming the tensile stress between rings, and the work equation for the vertical component of the lining water pressure. Based on the work equation for overcoming formation reaction force, the work equation for overcoming shear force between rings, the work equation for overcoming tensile stress between rings, and the work equation for the vertical component of lining water pressure, a total calculation model for a specific ring of the target shield tunnel is constructed. The formation reaction force, external water pressure on the shield tunnel lining, and additional stress of overburden load are substituted into the total calculation model for a specific ring of the target shield tunnel to solve the total work done by the target shield tunnel under stress. Among them, the total work calculation model for a specific ring of the target shield tunnel satisfies the following relationship: ； ； ； ； ； ； ； ； ； Wherein: W R The work done by the additional stress W k The work done to overcome the formation reaction force W S The work done to overcome the establishment between rings W t The work done to overcome the tensile force between rings W c The work done to overcome the compressive stress between rings W P The work done by the vertical water pressure outside the lining W G The work done by the gravity of the lining ring W The total work done on the target shield tunnel N The number of segment rings taken for calculation m The required number of segment rings for calculation 5. The comprehensive evaluation method for the longitudinal deformation of a shield tunnel according to claim 4, wherein The S4 includes: Based on the energy variational method and the principle of minimum potential energy, a longitudinal deformation calculation model for the second shield tunnel is constructed. The total work done by the target shield tunnel under stress is substituted into the longitudinal deformation calculation model for the second shield tunnel to solve the longitudinal displacement field at the axis of the target shield tunnel. Among them, the longitudinal deformation calculation model for the second shield tunnel satisfies the following relationship: ； ； ； ； ； ； ； ； ； ； ； ； ； In the formula: K s is the formation reaction stiffness matrix, K G is the gravity action matrix, K t is the stiffness matrix between tunnel rings, P T is the action effect of water pressure and the tunnel lining ring, G T is the gravity action effect, σ ′] T is the action effect of the additional stress in the formation caused by the water level, R T is the interaction effect between the free displacement of the soil mass and the tunnel lining ring, a n are the Fourier expansion coefficients, n is the number of Fourier expansion terms, T n ( x ) is the Fourier expansion formula matrix, A is the Fourier expansion coefficient matrix, ξ i are different numbers of Fourier expansion terms, T is the matrix transpose symbol.​​​ 6. The comprehensive evaluation method for the longitudinal deformation of a shield tunnel according to claim 5, characterized in that The S5 includes: A non-linear degradation model for the performance of the third shield lining is constructed. The longitudinal displacement field at the axis of the target shield tunnel is substituted into the non-linear degradation model for the performance of the third shield lining to solve the lining structure performance, and the lining structure performance is used as an evaluation index for the longitudinal deformation of the target shield tunnel. Among them, the non-linear degradation model for the performance of the third shield lining satisfies the following relationship: ； In the formula: Q is the lining structure performance, Δ w max When the tunnel structure fails ( Q ( t ) = 0), the maximum allowable longitudinal deformation, Δ w 0 is the initial deformation, Δ w ( t ) is the longitudinal deformation output by the longitudinal deformation calculation model of the second shield tunnel.

7. The comprehensive evaluation method for the longitudinal deformation of a shield tunnel according to any one of claims 1-6, characterized in that The S6 includes: Based on the construction characteristics of the target shield tunnel, a preset index threshold is determined. When the evaluation index of the longitudinal deformation of the target shield tunnel is greater than or equal to the preset index threshold, the current lining structure performance is evaluated as high performance; When the evaluation index of the longitudinal deformation of the target shield tunnel is less than the preset index threshold but greater than or equal to 0.75 times the preset index threshold, the current lining structure performance is evaluated as medium performance; When the evaluation index of the longitudinal deformation of the target shield tunnel is less than 0.75 times the preset index threshold but greater than or equal to 0.5 times the preset index threshold, the current lining structure performance is evaluated as low performance; When the evaluation index of the longitudinal deformation of the target shield tunnel is less than 0.5 times the preset index threshold but greater than or equal to 0.25 times the preset index threshold, the current lining structure performance is evaluated as non-performance; And 0.25 times the preset index threshold is the index critical value of non-performance, and the case less than 0.25 times the preset index threshold is not evaluated.

8. An integrated evaluation system for longitudinal deformation of shield tunnels, characterized in that, Including a processor and a memory; The memory is used to store a computer program; The processor is used to implement the method steps described in any one of claims 1-7 when executing the program stored on the memory.

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