A method for predicting the settlement of a shield tunnel under a pipeline

Abstract

The present invention relates to a method for predicting the settlement of a pipeline under a shield tunnel, comprising the following steps: estimating the soil settlement caused by shield tunnel excavation; applying the estimated soil settlement to a pipeline to establish a load balance differential equation of the pipeline, wherein the pipeline is regarded as a Timoshenko beam on a Vlasov foundation; and obtaining the pipeline settlement by solving the load balance differential equation of the pipeline. The present invention belongs to the field of urban underground space engineering calculation methods.

Description

Technical Field

[0001] The invention relates to the field of underground space engineering calculation methods, and in particular to a method for predicting the settlement of a shield tunnel underpass. Background Art

[0002] During shield tunnel excavation, stratum loss will cause deformation of the surrounding strata. Since the pipelines immediately above the tunnel will inevitably settle due to the influence of stratum deformation, pipeline settlement is one of the key points of pipeline stability control and is also a key issue in subway tunnel construction.

[0003] At present, in order to simplify the calculation, most of the calculation methods for the settlement of pipelines under shield tunnels simplify the pipelines into Euler-Bernouli beams. However, in actual tunnel excavation projects, the pipelines bear a certain amount of additional soil load. Especially when the shield tunnel excavation radius is large, treating the pipeline as an Euler-Bernouli beam will seriously affect the accuracy of the calculation. On the other hand, the current calculation method will also simplify the foundation around the pipeline into a Winkler foundation or a Pasternak foundation. However, these two foundations cannot accurately reflect the uneven distribution of foundation parameters along the vertical direction caused by tunnel excavation. The above-mentioned disadvantages may cause large calculation errors and pose safety hazards to the implementation of the project. Summary of the invention

[0004] In view of the technical problems existing in the prior art, according to one aspect of the present invention, a method for predicting the settlement of a pipeline under a shield tunnel is provided, comprising estimating the soil settlement caused by shield tunnel excavation; applying the estimated soil settlement to the pipeline to establish a load balance differential equation of the pipeline, wherein the pipeline is regarded as a Timoshenko beam on a Vlasov foundation; and obtaining the pipeline settlement by solving the load balance differential equation of the pipeline.

[0005] According to another aspect of the present invention, a method for estimating the settlement of a pipeline under a shield tunnel is provided, comprising providing an estimated amount of settlement of the pipeline under the shield tunnel based on a pipeline settlement prediction obtained through a pipeline stress analysis; wherein, in the pipeline stress analysis, the pipeline is regarded as a Timoshenko beam; and the foundation around the pipeline is simplified to a Vlasov foundation model.

[0006] According to another aspect of the present invention, a method for estimating the settlement of a pipeline under a shield tunnel is provided, which further includes estimating the settlement of a pipeline under a shield tunnel using the following formula:

[0007]

[0008] Where ω(x) is the settlement of the pipeline, q(ξ)dξ is the distributed load element on the pipeline axis, ξ is the distance of the load element from O, x is the horizontal distance from the centerline of the tunnel, EI is the bending stiffness of the pipeline; ψ is the equivalent modified shear stiffness of the pipeline, D is the diameter of the pipeline,

[0009] Among them, ψ=κGA, κ is the equivalent section coefficient of the pipeline, which is 0.5; G is the shear modulus of the pipeline, G=E p / 2(1+υ p ), E P , p is the Poisson’s ratio of the pipe; A is the cross-sectional area of ​​the pipe. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The preferred embodiments of the present invention will be further described in detail below with reference to the accompanying drawings, wherein:

[0011] Figure 1 A flowchart of a method for estimating settlement of a pipeline under a shield tunnel according to an embodiment of the present invention is shown;

[0012] Figure 2 The calculation model of the pipeline under the tunnel according to the embodiment of the present invention is shown;

[0013] Figure 3 A schematic diagram of coordinates when a pipeline and a tunnel are obliquely intersected according to an embodiment of the present invention is shown;

[0014] Figure 4 A schematic diagram showing the load of the surrounding soil on the pipeline according to an embodiment of the present invention is shown;

[0015] Figure 5 A schematic diagram of a Timoshenko beam before and after deformation according to an embodiment of the present invention is shown;

[0016] Figure 6 A method for estimating the settlement of a pipeline under a shield tunnel according to an embodiment of the present invention is shown; and

[0017] Figure 7 The measured and calculated values ​​of pipeline settlement according to the embodiment of the present invention are shown. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] In the following detailed description, reference may be made to the various specification drawings that are part of the present application and are used to illustrate specific embodiments of the present application. In the accompanying drawings, similar reference numerals describe substantially similar components in different figures. The various specific embodiments of the present application are described below in sufficient detail so that a person of ordinary skill in the art with relevant knowledge and skills in the art can implement the technical solutions of the present application. It should be understood that other embodiments may also be used or structural, logical or electrical changes may be made to the embodiments of the present application.

[0020] At present, the method for calculating the settlement of the pipeline under the shield tunnel is the two-stage displacement method. The idea of ​​this method is that in the first stage, based on the Winkler foundation model, the pipeline is regarded as an Euler-Bernouli beam to calculate the soil settlement at the position of the pipeline axis; and in the second stage, the soil settlement is converted into an additional load form and applied to the pipeline, and the analytical expression of the pipeline settlement is obtained. Therefore, the basic model of the two-stage displacement method is the WE model. However, the Winkler foundation model cannot consider the continuity of foundation deformation and ignores the influence of soil shear force on the calculation results. Furthermore, the applicable condition of the Euler-Bernouli beam is the situation where the ratio of beam diameter to beam length is very small. With the development in recent years, the diameter of underground pipelines in some parts of the country has reached 3m, and the ratio of diameter to length has been greatly reduced. It is obviously inappropriate to still use the Euler-Bernouli beam. In the scheme of the present invention, the pipeline is regarded as a Timoshenko beam on the Vlasov foundation, so as to obtain a more accurate calculation result of the pipeline settlement.

[0021] Figure 1 The flowchart of a method for estimating the settlement of a shield tunnel under a pipeline provided in an embodiment of the present application is shown. As shown in the figure, the method comprises the following steps: In step 110, the soil settlement caused by the excavation of the shield tunnel is estimated. Figure 2 When the tunnel axis is perpendicular to the adjacent pipeline axis, according to the Loganathan formula (1), the soil settlement u(x) caused by shield tunnel excavation can be expressed as:

[0022]

[0023] In the formula, ε 0 is the average formation loss ratio; R is the tunnel radius; Z 0 is the depth of the existing pipeline axis; H is the depth of the tunnel axis; υ is the Poisson's ratio of the soil; x is the horizontal distance from the center line of the tunnel.

[0024] In some embodiments, when the tunnel axis is oblique to the adjacent pipeline axis, such as Figure 3The tunnel and pipeline are obliquely intersected at an angle θ. The horizontal distance from any point A on the pipeline to the centerline of the tunnel on the XOY projection is xsinθ, and x in formula (1) is the horizontal distance from the centerline of the tunnel. Therefore, replacing x in formula (1) with xsinθ yields formula (2):

[0025]

[0026] In step 120, the estimated soil settlement is applied to the pipeline to establish a load balance differential equation for the pipeline. In this embodiment, the pipeline is regarded as a Timoshenko beam on a Vlasov foundation. Figure 4 , assuming that the pipeline is always in contact with the surrounding strata, when the tunnel is excavated, the vertical external load on the pipeline is the additional soil load caused by the soil settlement on the pipeline. According to the Vlasov foundation model, the relationship between the soil settlement u(x,θ) and the additional soil load q(x) is expressed as formula (3):

[0027]

[0028] Where k is the spring coefficient and t is the shear coefficient of the soil layer.

[0029] refer to Figure 5 The pipeline is a Timoshenko beam before and after deformation. The beam section is perpendicular to the neutral axis before deformation, and the beam section is perpendicular to the normal direction of the neutral axis after deformation. Angle, no longer vertical.

[0030] Furthermore, according to the Vlasov foundation model, formula (3) is obtained to obtain the functional relationship between land settlement and additional soil load.

[0031]

[0032] Furthermore, according to the Vlasov foundation model, the relationship between pipeline deflection ω(x) and foundation reaction force is obtained by formula (4):

[0033]

[0034] Furthermore, according to the pipeline stress analysis, the relationship between the pipeline settlement and the soil additional load and foundation reaction force is expressed according to formula (5) and formula (6):

[0035]

[0036]

[0037] Furthermore, according to the pipeline stress analysis, formula (3), (4), (5) and (6) are combined to obtain formula (7), which is the differential equation of the relationship between the pipeline settlement and the soil additional load and foundation reaction force:

[0038]

[0039] In step 130, the pipeline settlement is obtained by solving the load balance differential equation of the pipeline.

[0040] As those skilled in the art will appreciate, pipeline settlement can be obtained through a variety of solutions. The following is a preferred solution proposed in this embodiment.

[0041] First, let q(x) = 0 and solve the general solution of the equilibrium differential equation, thereby transforming the equilibrium differential equation into formula (8);

[0042]

[0043] Furthermore, by using symmetry, we study the part where x>0 and simplify the equilibrium differential equation to formula (9):

[0044] ω(x)=e -αx (B 1 cosβx+B 2 sinβx)(9)

[0045] Furthermore, the following boundary condition (10) is:

[0046]

[0047] Substituting into formula (9), we get the solution of formula (11) when the pipeline is subjected to concentrated load:

[0048]

[0049] Take the distributed load microelement q(ξ)dξ on the pipeline axis, the distance between the load microelement and O is ξ, and use q(ξ)dξ to replace the concentrated load P to obtain the pipeline settlement ω(x) under the additional soil load in formula (12):

[0050]

[0051] According to the above embodiment, when the shield tunnel obliquely passes under the pipeline, the pipeline is regarded as a Timoshenko beam, and the influence of the bending stiffness and shear stiffness of the beam itself during the force process and the attenuation deformation of the foundation soil around the pipeline along the deformation direction are considered at the same time, so that the calculated value of the pipeline settlement is closer to the actual project situation, the error in the calculation process of the pipeline settlement is reduced, and a strong guarantee is provided for safe construction.

[0052] In the above embodiments, the process of obtaining the pipeline settlement prediction is described in detail. As can be understood by those skilled in the art, after obtaining the pipeline settlement expression of formula (12), the formula can be directly used to predict the pipeline settlement.

[0053] According to one embodiment of the present invention, the following formula is used to estimate the settlement of the shield tunnel under the pipeline:

[0054]

[0055] As can be understood, those skilled in the art can obtain other technical solutions based on the above embodiments of the present invention without departing from the concept of the present invention, based on the above embodiments.

[0056] Figure 6 The present invention is a method for estimating the settlement of a pipeline under a shield tunnel according to an embodiment of the present invention. As shown in the figure, the method includes: in step 510, when the pipeline is regarded as a Timoshenko beam on a Vlasov foundation, a pipeline settlement prediction is obtained based on a pipeline stress analysis. In step 520, an estimated amount of settlement of a pipeline under a shield tunnel is provided based on actual measurement results.

[0057] In some embodiments, in the pipeline analysis, soil settlement is calculated based on the following formula (1):

[0058]

[0059] In some embodiments, when the axis of the shield tunnel is oblique to the axis of the pipeline, the soil settlement is estimated according to the following formula (2):

[0060]

[0061] In some embodiments, the soil additional load function q(x) acting on the pipeline axis is determined according to the following formula (3):

[0062]

[0063] Among them, k is the spring coefficient and t is the shear coefficient of the soil layer.

[0064] In some embodiments, the beam cross section of the pipeline Timoshenko beam is perpendicular to the neutral axis before deformation; after deformation, the beam cross section is perpendicular to the normal direction of the neutral axis. Angle, where The angle is not equal to 90°.

[0065] In some embodiments, the pipeline load balance differential equation is determined according to formula (7):

[0066]

[0067] Among them, ω(x) is the pipeline settlement; EI is the pipeline bending stiffness; Ψ is the pipeline equivalent modified shear stiffness; D is the pipeline diameter.

[0068] In some embodiments, distributed load elements are used instead of concentrated loads to calculate pipeline settlement.

[0069] In some embodiments: a distributed load microelement q(ξ)dξ is taken on the pipeline axis, the distance between the load microelement and O is ξ, and q(ξ)dξ is used to replace the concentrated load P. Under the additional load of the soil, the pipeline settlement ω(x) is calculated using the following formula (11):

[0070]

[0071] in,

[0072] Among them, ψ=κGA, κ is the equivalent section coefficient of the pipeline, which is 0.5; G is the shear modulus of the pipeline, G=E p / 2(1+υ p ), E P is the elastic modulus of the pipe, υ p is the Poisson’s ratio of the pipe; A is the cross-sectional area of ​​the pipe.

[0073] The above embodiments describe the specific contents of the present invention in detail. The following engineering examples verify the settlement prediction method for a pipe under a shield tunnel provided by the present invention. The settlement monitoring data of a concrete water pipe above the tunnel of Shanghai Metro Line 11 are used to verify the method proposed by the present invention.

[0074] The tunnel was constructed using the shield method. A concrete water pipe with a diameter of D = 1.0m was vertically passed underneath. The pipe wall thickness was tp = 0.12m, and the axis buried depth was Z0 = 3m. The other parameters are shown in Table 1.

[0075] Table 1 Water pipe calculation parameters

[0076]

[0077] Figure 7 The comparison results of pipeline settlement curves calculated by engineering monitoring data, existing elastic foundation beam method (Winkler-Euler model is denoted as WE model, Pasternak-Euler model is denoted as PE model) and this paper’s method are shown in Figure 2. Figure 7It can be seen that the calculation method of the Vlasov foundation model and the Timoshenko beam model used in this paper has higher accuracy in pipeline settlement and is closer to the actual monitoring data. Compared with the calculated value of the PE model, the calculated value of the WE model has a larger error. This is because the Winkler foundation model ignores the shear force between the foundation springs, which leads to a larger pipeline settlement value. In contrast, the error between the calculated value of the PE model and the calculated value of the method in this paper is much smaller, but there is still a significant difference.

[0078] The above embodiments are only used to illustrate the present invention, but not to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the scope of the present invention. Therefore, all equivalent technical solutions should also fall within the scope of the present invention.

Claims

1. A method for predicting the settlement of a pipeline under a shield tunnel, comprising: Estimate soil settlement caused by shield tunneling; Applying the estimated soil settlement to the pipeline to establish a load balance differential equation for the pipeline, wherein the pipeline is regarded as a Timoshenko beam on a Vlasov foundation; and Obtaining pipeline settlement by solving the load balance differential equation of the pipeline; When the axis of the shield tunnel is oblique to the axis of the pipeline, the soil settlement is estimated according to the following formula (2): Among them, ε0 is the average formation loss ratio; R is the tunnel radius; Z0 is the depth of the existing pipeline axis; H is the depth of the tunnel axis; υ is the Poisson's ratio of the soil; x is the horizontal distance from the center line of the tunnel; θ is the oblique angle between the pipeline and the tunnel; The pipeline load balance differential equation is determined according to formula (7): Wherein, ω(x) is the settlement of the pipeline; EI is the bending stiffness of the pipeline; Ψ is the equivalent modified shear stiffness of the pipeline; D is the diameter of the pipeline, t is the shear coefficient of the soil layer, q(x) is the additional load of the soil, and k is the spring coefficient; Among them, ψ=κGA: κ is the equivalent section coefficient of the pipeline, which is 0.5; G is the shear modulus of the pipeline, G=E p / 2(1+υ p ), E P is the elastic modulus of the pipe, υ p is the Poisson's ratio of the pipeline; A is the cross-sectional area of ​​the pipeline; Use distributed load micro-element instead of concentrated load to calculate pipeline settlement; Take the distributed load microelement q(ξ)dξ on the pipeline axis. The distance between the load microelement and the intersection of the pipeline and tunnel projection is ξ. q (ξ) d ξ replaces the concentrated load P, and under the additional load of the soil, the pipeline settlement ω(x) is calculated using the following formula (11): in, In the process of solving the differential equation, the boundary conditions (10) are defined as follows: Where P is the concentrated load.

2. The method according to claim 1, further comprising: When the tunnel axis is perpendicular to the adjacent pipeline axis, the soil settlement is estimated according to the following formula (1) based on Loganathan: Among them, ε0 is the average formation loss ratio; R is the tunnel radius; Z0 is the depth of the existing pipeline axis; H is the depth of the tunnel axis; υ is the Poisson's ratio of the soil; and x is the horizontal distance from the centerline of the tunnel.

3. The method according to claim 1, further comprising: The additional soil load function q(x) acting on the pipeline axis is determined according to the following formula (3): Among them, k is the spring coefficient and t is the shear coefficient of the soil layer.

4. The method according to claim 1, wherein the beam cross section of the pipeline Timoshenko beam is perpendicular to the neutral axis before deformation; after deformation, the beam cross section is perpendicular to the normal direction of the neutral axis. Angle, where The angle is not equal to 90°.

5. A method for estimating the settlement of a pipeline under a shield tunnel, comprising: According to the pipeline settlement prediction obtained by the pipeline stress analysis, an estimated amount of settlement of the pipeline under the shield tunnel is provided; wherein, in the pipeline stress analysis, the pipeline is regarded as a Timoshenko beam; and the foundation around the pipeline is simplified to a Vlasov foundation model; According to formula (12), the distributed load microelement is used to replace the concentrated load to calculate the pipeline settlement: Where D is the pipeline diameter, EI is the pipeline bending stiffness, ω(x) is the pipeline settlement, q(ξ)dξ is the distributed load microelement on the pipeline axis, ξ is the distance between the load microelement and the intersection of the pipeline and tunnel projection, t is the soil shear coefficient, ψ is the equivalent modified shear stiffness of the pipeline; Among them, ψ=κGA, κ is the equivalent section coefficient of the pipeline, which is 0.5; G is the shear modulus of the pipeline, G=E p / 2(1+υ p ), E P is the elastic modulus of the pipe, υ p is the Poisson’s ratio of the pipe; A is the cross-sectional area of ​​the pipe.

6. The method according to claim 5, further comprising: When the tunnel axis is perpendicular to the adjacent pipeline axis, in the pipeline analysis, the soil settlement is calculated based on the following formula (1): Among them, ε0 is the average formation loss ratio, R is the tunnel radius, Z0 is the depth of the existing pipeline axis, H is the depth of the tunnel axis, υ is the Poisson's ratio of the soil, and x is the horizontal distance from the center line of the tunnel.

7. The method according to claim 6, wherein when the axis of the shield tunnel is oblique to the axis of the pipeline, the soil settlement is estimated according to the following formula (2): in, θ is the oblique intersection angle between the pipeline and the tunnel.

8. The method according to claim 5, further comprising: According to the Vlasov foundation model, the relationship between soil settlement u(x,θ) and soil additional load q(x) is determined according to formula (3): Among them, k is the spring coefficient, t is the shear coefficient of the soil layer, and θ is the oblique angle between the pipeline and the tunnel.

9. The method according to claim 8, further comprising: According to the Vlasov foundation model, the relationship between pipeline settlement ω(x) and foundation reaction force p(x) is as follows according to formula (4):

10. The method according to claim 9, further comprising: According to the pipeline stress analysis, the relationship between the pipeline settlement and the soil additional load and foundation reaction force is expressed by formula (5) and formula (6): Where D is the pipeline diameter, EI is the pipeline bending stiffness, M is the pipeline bending moment, and ψ is the pipeline equivalent modified shear stiffness; Among them, ψ=κGA, κ is the equivalent section coefficient of the pipeline, which is 0.5; G is the shear modulus of the pipeline, G=E p / 2(1+υ p ), E P is the elastic modulus of the pipe, υ p is the Poisson’s ratio of the pipe; A is the cross-sectional area of ​​the pipe.

11. The method according to claim 10 further comprises: according to the pipeline stress analysis, the relationship between the pipeline settlement and the soil additional load and the foundation reaction force is a differential equation (7):

12. The method according to claim 11 further comprises converting the equilibrium differential equation into formula (8) by solving the general solution of the differential equation: in, A1, A2, B1, B2 are unknown coefficients.

13. The method according to claim 12 further comprises simplifying the equilibrium differential equation to formula (9) by symmetry: ω(x)=e -αx (B1 cosβx+B2 sinβx)(9)。 14. The method according to claim 13 further comprises, in the process of solving the differential equation, defining boundary conditions (10) as follows: in, P is the concentrated load.

15. The method according to claim 14 further comprises substituting the boundary condition (10) into the formula (9) to obtain the solution (11) when the pipeline is subjected to the concentrated load:

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