A calculation method for considering the deformation of adjacent pipelines induced by soil deformation unloading

Abstract

The present invention discloses a calculation method for considering the deformation of adjacent pipelines induced by the unloading of soil mass deformation. The steps of the method are as follows: (1) Determine the curve of the lateral deformation of the retaining wall along the depth; (2) Determine the soil mass unloading caused by the deformation of the retaining wall induced by the excavation of the foundation pit; (3) Use the Pasternak foundation and Euler-Bernoulli beam model to determine the deformation control equation of the adjacent pipeline. Using the method of the present invention, the influence of the deformation of the retaining structure caused by the excavation of the foundation pit on the adjacent pipeline can be analyzed before the excavation of the foundation pit. Moreover, the method of the present invention considers that there are significant differences in the change of the soil displacement caused by the excavation of the foundation pit with the depth, and can accurately predict the pipeline deformation, which has guiding significance for the design of the foundation pit.

Description

Technical Field

[0001] The present invention relates to the field of underground structure design, and particularly to a calculation method for considering the deformation of adjacent pipelines induced by soil deformation unloading. Background Art

[0002] With the advancement of the urbanization process, the urban population is becoming increasingly concentrated, and urban land is becoming increasingly tense. While promoting the continuous development of buildings towards high-rise, it also promotes the development of underground space. Pipelines are densely distributed in cities. Generally, the buried depth of underground pipelines is within the range of 0 - 6m, usually within the depth range of foundation pit excavation. The unloading of foundation pit excavation will cause additional deformation of adjacent underground pipelines, resulting in relatively large additional stresses in the pipelines, and in severe cases, it will affect the normal use of the pipelines. When there are sensitive structures such as pipelines around the foundation pit, the foundation pit design should be based on deformation control design, with the standard of not affecting the normal use of the pipelines. Therefore, it is necessary to analyze the influence of the deformation of the retaining structure caused by foundation pit excavation on adjacent pipelines.

[0003] Currently, the main method for predicting the influence of foundation pit excavation on adjacent pipelines is the numerical simulation method. The numerical simulation method can simulate the entire process of foundation pit excavation, and the deformation laws of the retaining structure and underground pipelines are more in line with actual engineering. However, the reliability of its results depends on the rationality of the selected parameters. The theoretical method has great advantages because of its clear principle and fast calculation. When the existing theoretical method considers the soil unloading induced by foundation pit excavation, it does not consider the actual displacement of the soil, and considers the unloading caused by soil displacement through the stress release coefficient. In fact, the soil displacement caused by foundation pit excavation varies greatly with depth. Therefore, the present invention considers the difference in soil deformation-induced unloading along the depth and proposes a calculation method for the deformation of adjacent pipelines induced by foundation pit excavation. Summary of the Invention

[0004] In view of the defects existing in the above background art, the present invention provides a calculation method for considering the deformation of adjacent pipelines induced by soil deformation unloading. This method considers the difference in soil deformation-induced unloading along the depth and can accurately predict pipeline deformation.

[0005] The present invention is realized by the following technical solutions:

[0006] A calculation method for considering the deformation of adjacent pipelines induced by soil deformation unloading, comprising the following steps:

[0007] (1) Determine the curve of the lateral deformation of the retaining wall along the depth;

[0008] (2) Determine the unloading caused by the deformation of the retaining wall induced by foundation pit excavation;

[0009] (3) Use the Pasternak foundation and Euler - Bernoulli beam model to determine the deformation control equation of adjacent pipelines.

[0010] In the above technical solution, further, in the step (1), the spatial distribution equation of the lateral deformation of the retaining wall is:

[0011]

[0012] 0 ≤ z ≤ H + D

[0013] In the formula: y0 represents the direction along the length of the foundation pit; z0 represents the direction along the depth of the foundation pit; f max is the maximum value of the lateral deformation of the retaining wall; z is the buried depth of the calculation point; H is the excavation depth of the foundation pit; D is the insertion depth of the retaining wall; H max is the buried depth where the maximum value of the lateral deformation of the retaining wall is located.

[0014] Further, the step (2) is specifically:

[0015] Establish the relationship between the unloading of lateral earth pressure and displacement:

[0016] p u = k u · p m

[0017] p m = p0 - p a

[0018]

[0019] In the formula, p m is the maximum value of the earth pressure that can be unloaded outside the pit, p0 is the static earth pressure, p a is the active earth pressure, p u is the unloading induced by soil displacement, k u is the unloading coefficient related to soil displacement, S is the soil displacement, S acr is the ultimate displacement of the active soil mass;

[0020] The expression of the unloading of the soil mass outside the pit (x, y, z) induced by the deformation of the retaining structure is:

[0021]

[0022] R1 = [x 2 + (y - y0) 2 + (z - z0) 2 1 / 2

[0023] R2 = [x 2 + (y - y0) 2 + (z + z0) 2 1 / 2 ​​

[0024] In the formula, L is the length of the retaining wall along the wall direction, and v is the Poisson's ratio.

[0025] Furthermore, the specific content of the step (3) is as follows:

[0026] Regarding the adjacent pipeline as an Euler - Bernoulli beam on a Pasternak foundation, when the soil is unloaded by σ(y), the differential equation of the horizontal deformation of the pipeline is:

[0027]

[0028] In the formula, E p I p is the flexural rigidity of the pipeline, G s is the shear stiffness of the foundation, D p is the outer diameter of the pipeline, and w(y) is the horizontal deformation of the pipeline;

[0029] The modulus of subgrade reaction k:

[0030]

[0031] Among them, k Vesic is the expression of the modulus of subgrade reaction proposed by Vesic;

[0032] The shear layer stiffness G s :

[0033]

[0034] In the formula, E s is the elastic modulus of the foundation soil, t is the influence range of the pipeline deformation, and ν is the Poisson's ratio;

[0035] Using the finite - difference method, the pipeline is divided into n equal parts, each part has a length of l, and there are n + 1 nodes; then the finite - difference form of the differential equation of the pipeline deformation is:

[0036]

[0037] w i is the deformation of the i - th pipeline node, q i is the load applied to the i - th pipeline node;

[0038] Assume that both ends of the pipeline are free, that is, the shear forces Q0 and Q n , the bending moments M0 and M n are all 0:

[0039]

[0040] Each node \(i\) has a deformation control equation. Writing \(n + 1\) deformation control equations as a system of equations and rewriting it in matrix form, the matrix expression is as follows:

[0041] (K1 - K2 + K3)w = P

[0042] Where: \(K1\) is the pipeline deformation stiffness matrix, \(K2\) is the foundation shear stiffness matrix, \(K3\) is the foundation stiffness matrix, \(w\) is the pipeline deformation column vector; \(P\) is the additional load column vector caused by the excavation of the foundation pit; the matrix expressions are as follows:

[0043]

[0044] w = [w0 w1 w2 … w n-2 w n-1 w n T (n+1)

[0045] P = D p [q0 q1 q2 … q n-2 q n-1 q n T (n+1) 。

[0046] The beneficial effects of the present invention are:

[0047] The method of the present invention takes the calculation method of the retaining wall varying with depth into the calculation model of soil unloading outside the foundation pit, adopts the Pasternak foundation, considers the continuity of foundation deformation, and determines the calculation method of pipeline deformation. The method of the present invention can fully consider the differences in soil unloading coefficients at different positions and the continuity of soil deformation, and further optimizes the calculation model of the influence of foundation pit excavation on pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is the comparison result between the method of the present invention and the measured data. DETAILED DESCRIPTION OF THE INVENTION

[0049] A calculation method for considering the deformation of adjacent pipelines induced by soil deformation unloading of the present invention is as follows:

[0050] 1) Determine the spatial distribution of the lateral deformation of the retaining wall

[0051]

[0052] 0 ≤ z ≤ H + D

[0053] Where: \(y0\) represents the direction along the length of the foundation pit; \(z0\) represents the direction along the depth of the foundation pit; \(f max ​​is the maximum value of the lateral deformation of the retaining wall; z is the depth of the calculation point; H is the excavation depth of the foundation pit; D is the insertion depth of the retaining wall; H max is the depth where the maximum value of the lateral deformation of the retaining wall is located. f max and H max can be analyzed using the design calculation value or the measured value of the supporting structure according to different stages of the project.

[0054] 2) Determine the soil unloading caused by the deformation of the retaining wall induced by the excavation of the foundation pit

[0055] Establish the relationship between the lateral soil pressure unloading and the displacement:

[0056] p u = k u · p m

[0057] p m = p0 - p a

[0058]

[0059] In the formula, p m is the maximum value of the soil that can be unloaded outside the pit, p0 is the static earth pressure, p a is the active earth pressure, p u is the unloading induced by the soil displacement, k u is the unloading coefficient related to the soil displacement, S is the soil displacement, S acr is the ultimate displacement of the active soil mass.

[0060] Determine the soil unloading induced by the deformation of the retaining structure

[0061] From the Mindlin solution, the expression for the soil unloading at the point (x, y, z) outside the pit induced by the deformation of the retaining wall is:

[0062] R1 = [x 2 + (y - y0) 2 + (z - z0) 2 ] 1 / 2

[0063] R2 = [x 2 + (y - y0) 2 + (z + z0) 2 ] 1 / 2

[0064] In the formula, L is the length of the retaining wall along the wall direction, v is the Poisson's ratio, and f(0, y0, z0) is the deformation of the retaining wall at the point (0, y0, z0).

[0065] 3) Determine the deformation control equation of adjacent pipelines by adopting the Pasternak foundation and Euler-Bernoulli beam model

[0066] Regarding the adjacent pipeline as an Euler-Bernoulli beam on the Pasternak foundation, when the soil is unloaded by σ(y), the differential equation of the horizontal deformation of the pipeline is as follows:

[0067]

[0068] In the formula, E p I p is the flexural rigidity of the pipeline, G s is the shear stiffness of the foundation, D p is the outer diameter of the pipeline, and w(y) is the horizontal deformation of the pipeline; since in σ(x, y, z), x and z are the distance from the tunnel axis to the foundation pit and the buried depth respectively, which can be determined in advance, it can be abbreviated as σ(y);

[0069] The foundation reaction modulus k:

[0070]

[0071] Among them, k Vesic is the expression of the foundation reaction modulus proposed by Vesic;

[0072] The shear layer stiffness G s :

[0073]

[0074] In the formula, E s is the elastic modulus of the foundation soil, t is the influence range of the pipeline deformation, which can be taken as 2.5D p , and ν is the Poisson's ratio.

[0075] Using the finite difference method, the pipeline is divided into n equal parts, and the length of each part is l. Then the finite difference form of the pipeline deformation differential equation is:

[0076]

[0077] w i is the deformation of the i-th pipeline node, and q i is the load applied to the i-th pipeline node;

[0078] Assume that both ends of the pipeline are free, that is, the shear force and bending moment are 0:

[0079]

[0080] Each node i has a deformation control equation. Write the n + 1 deformation control equations as a system of equations and rewrite them in matrix form:

[0081] (K1 - K2 + K3)w = P

[0082] Where: K1 is the pipeline deformation stiffness matrix, K2 is the foundation shear stiffness matrix, K3 is the foundation stiffness matrix, w is the pipeline deformation column vector; P is the additional load column vector caused by foundation pit excavation. The expressions of each matrix are as follows:

[0083]

[0084] w = [w0 w1 w2 … w n-2 w n-1 w n T (n+1)

[0085] P = D p [q0 q1 q2 … q n-2 q n-1 q n T (n+1) Specific embodiments

[0087] The length L of the foundation pit is 20m, the excavation depth H and the insertion depth D of the retaining wall are 5m and 5m respectively, the distance d between the adjacent tunnel and the foundation pit edge is 5m, the buried depth h of the tunnel axis is 2m, and the flexural stiffness E t I t is 123.5 MN·m 2 , the maximum deformation f max of the retaining wall is 7.5mm, and its occurrence position H max is 4m, the elastic modulus E s of the foundation soil is 6MPa, the Poisson's ratio is 0.3, and the ultimate displacement S acr of the soil mass is 40mm.

[0088] It can be seen from the comparison between the calculation method of the present invention and the measured numerical results (as shown in Figure 1 ), the calculation method of the present invention and the measured numerical results have achieved good consistency.​​

Claims

1. A calculation method for considering the deformation of adjacent pipelines induced by the unloading of soil mass deformation, characterized in that, The steps are as follows: (1) Determine the curve of the lateral deformation of the retaining wall varying with depth; (2) Determine the soil unloading caused by the deformation of the retaining wall induced by the foundation pit excavation; (3) Use the Pasternak foundation and Euler-Bernoulli beam model to determine the deformation control equation of adjacent pipelines; The specific content of step (3) is as follows: Regard the adjacent pipeline as an Euler-Bernoulli beam on the Pasternak foundation. When subjected to soil unloading σ(y), the differential equation of the horizontal deformation of the pipeline is: where, E p I p is the flexural rigidity of the pipeline, G s is the shear stiffness of the foundation, D p is the outer diameter of the pipeline, and w(y) is the horizontal deformation of the pipeline; The foundation reaction modulus k: where k Vesic is the expression of the modulus of subgrade reaction proposed by Vesic; Shearing layer stiffness G s : where E s is the elastic modulus of foundation soil, t is the influence range of pipeline deformation, and ν is the Poisson's ratio; Using the finite difference method, divide the pipeline into n equal parts, each part with a length of l, and there are n + 1 nodes in total; then the finite difference form of the pipeline deformation differential equation is: w i is the deformation of the i-th pipeline node, q i is the load on the i-th pipeline node; Assume that both ends of the pipeline are free, that is, the shear forces Q0 and Q n and the bending moments M0 and M n are all 0: Each node i has a deformation control equation. Write the n + 1 deformation control equations as a system of equations and rewrite it in matrix form. Then the matrix expression is as follows: (K1 - K2 + K3)w = P In the formula: K1 is the pipeline deformation stiffness matrix, K2 is the foundation shear stiffness matrix, K3 is the foundation stiffness matrix, w is the pipeline deformation column vector; P is the additional load column vector caused by the foundation pit excavation; the expressions of each matrix are as follows: w = [w0 w1 w2…w n-2 w n-1 w n T (n+1) ​ P = D p [q0 q1 q2…q n-2 q n-1 q n T (n+1) 。​ 2. The calculation method for considering the deformation of adjacent pipelines induced by soil deformation unloading according to claim 1, characterized in that In step (1), the spatial distribution equation of the lateral deformation of the retaining wall is: 0 ≤ z ≤ H + D where: y0 represents the direction along the length of the foundation pit; z0 represents the direction along the depth of the foundation pit; f max is the maximum value of the lateral deformation of the retaining wall; z is the buried depth of the calculation point; H is the excavation depth of the foundation pit; D is the insertion depth of the retaining wall; H max is the buried depth where the maximum value of the lateral deformation of the retaining wall is located.

3. The calculation method for considering the deformation of adjacent pipelines induced by soil deformation unloading according to claim 2, wherein The specific content of step (2) is as follows: Establish the relationship between the lateral soil pressure unloading and displacement: p u = k u · p m p m = p0 - p a where p m is the maximum value of the soil that can be unloaded outside the pit, p0 is the earth pressure at rest, p a is the active earth pressure, p u is the unloading induced by soil displacement, k u is the unloading coefficient related to soil displacement, S is the soil displacement, S acr is the ultimate displacement of the active soil mass; The expression of the soil unloading at the outside of the retaining structure (x, y, z) induced by the deformation is: R1 = [x 2 +(y - y0) 2 +(z - z0) 2 1 / 2 ​ R2 = [x 2 +(y - y0) 2 +(z + z0) 2 1 / 2 ​ In the formula, L is the length of the retaining wall along the wall direction, and v is the Poisson's ratio.

Images