A method for analyzing horizontal deformation of pipelines adjacent to deep foundation pits

Abstract

The present invention relates to a method for analyzing the horizontal deformation of pipelines adjacent to deep foundation pits, comprising: based on the unloading equation of the side wall of the flexible support structure, calculating the horizontal additional load of the adjacent pipelines under the unloading of the side wall of the flexible support structure; determining the horizontal shear coefficient and the resistance coefficient of the interaction between the pipeline and the soil through the differential equation of the horizontal deformation flexure of the pipeline; solving the differential equation of the horizontal deformation of the pipeline based on the horizontal additional load of the adjacent pipeline and the horizontal shear coefficient and the resistance coefficient, and obtaining the horizontal deformation value of the pipeline. The present invention mainly considers the influence of the lateral displacement of the flexible support structure on the unloading distribution of the side wall of the foundation pit, and also considers the influence of the lateral unloading stress path on the value of the model parameters, and uses the boundary conditions to perform integral transformation calculations, etc., which can better conform to the actual situation of the project, reduce the calculation error of the horizontal deformation of the pipeline, and ensure the construction safety and the normal use of the pipelines near the foundation pit.

Description

Technical Field

[0001] The invention relates to the technical field of geotechnical engineering calculation methods, and in particular to a method for analyzing horizontal deformation of pipelines adjacent to a deep foundation pit. Background Art

[0002] Pipeline accidents often occur at home and abroad due to incomplete consideration of foundation pit support design or improper operation during excavation construction. Pipelines are sensitive to deformation, and the excavation of subway station foundation pits will cause large deformation of the stratum. Therefore, the impact of station foundation pit excavation on pipeline deformation is an important research topic.

[0003] At present, the main research methods for the impact of deep foundation pit excavation on adjacent pipelines include numerical simulation method, two-stage analytical method, etc. However, the numerical simulation method is complex to model and the calculation takes a long time, while the pipe-soil stress-deformation model established by the two-stage analytical method simplifies the problem in a series of ways. The value of the pipe-soil interaction parameter has a great influence on the reliability of the results, and the interaction relationship between the pipe and the soil is not very clear.

[0004] On the other hand, the current calculation method simplifies the side wall unloading into a triangular distributed load, but in fact the side wall unloading will increase nonlinearly with the increase of the lateral displacement of the supporting structure. For foundation pits with flexible supporting structures such as underground continuous walls, the deformation mode of the supporting structure after the foundation pit excavation is parabolic. Based on the parabolic deformation mode of the flexible supporting structure, it is unreasonable to simplify the side wall unloading into a triangular distributed load. Therefore, it is very important to consider the influence of the deformation mode and lateral displacement of the supporting structure on the side wall unloading.

[0005] At the same time, the research results on pipeline deformation caused by foundation pit excavation at home and abroad are mostly focused on the vertical deformation of pipelines, while there are few studies on the horizontal deformation of pipelines. Therefore, it is very urgent to study the horizontal deformation of adjacent underground pipelines during foundation pit excavation. Summary of the invention

[0006] In order to reduce errors and make the calculation results closer to the actual situation, the present invention proposes a method for analyzing the horizontal deformation of pipelines adjacent to deep foundation pits, which can more accurately calculate the horizontal deformation value of pipelines.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A method for analyzing horizontal deformation of pipelines adjacent to deep foundation pits, comprising:

[0009] Based on the side wall unloading equation of the flexible support structure, the horizontal additional load of the adjacent pipeline under the side wall unloading of the flexible support structure is calculated;

[0010] The horizontal shear coefficient and resistance coefficient of the interaction between the pipeline and the soil are determined through the differential equation of pipeline horizontal deformation and deflection;

[0011] Based on the horizontal additional load of the adjacent pipeline and the horizontal shear coefficient and resistance coefficient, the differential equation of horizontal deformation of the pipeline is solved to obtain the horizontal deformation value of the pipeline.

[0012] Preferably, the unloading equation of the flexible support structure is:

[0013]

[0014] Among them, K0, K a are the static earth pressure coefficient and the Rankine active earth pressure coefficient, γ is the weighted degree of the soil in the foundation pit, z is the depth, H is the excavation depth of the foundation pit, δ max is the maximum lateral displacement of the supporting structure, δ a is the active limit displacement of soil, and c is the cohesion of soil.

[0015] Preferably, the calculation equation for the additional horizontal load on the adjacent pipeline when the side wall of the flexible support structure is unloaded is:

[0016] q(y)=σ x h

[0017] Where h is the height of the rectangular section, σ x is the total additional horizontal stress of the adjacent pipeline under the unloading of the side wall of the flexible support structure, and q(y) is the additional horizontal load of the adjacent pipeline under the unloading of the side wall of the flexible support structure.

[0018] Preferably, the method for calculating the total horizontal additional stress of the adjacent pipeline under the unloading of the side wall of the flexible support structure includes:

[0019] The additional horizontal stress of the rectangular pipeline caused by unloading of the bottom of the foundation pit and the three side walls adjacent to the pipeline is calculated, and the total additional horizontal stress of the adjacent pipeline under the unloading of the side walls of the flexible support structure is obtained through the superposition principle.

[0020] Preferably, the method for establishing the pipeline horizontal deformation and deflection differential equation comprises:

[0021]

[0022] Among them, E p I is the pipeline bending stiffness, G p is the horizontal shear coefficient, K is the resistance coefficient, and w(y) is the horizontal deformation value of the pipeline.

[0023] Preferably, the horizontal shear coefficient G p The calculation method is:

[0024]

[0025] Where E is the elastic modulus of soil, ν is the Poisson's ratio of soil, ξ(x) is the horizontal attenuation function, and T is the load influence width.

[0026] Preferably, the resistance coefficient K is expressed as:

[0027]

[0028] Where E is the elastic modulus of the soil, z0 is the buried depth of the pipeline, ν is the Poisson's ratio of the soil, and E p I is the bending stiffness of the pipeline.

[0029] Preferably, the horizontal deformation deflection differential equation of the pipeline comprises a fourth-order differential equation, wherein the general homogeneous general solution comprises:

[0030] w(y)=e αy [A1cos(βy)+A2sin(βy)]+e -αy [A3cos(βy)+A4sin(βy)]

[0031] Among them, A1, A2, A3, and A4 are the coefficients to be determined;

[0032] K is the resistance coefficient, E p I is the bending stiffness of the pipeline.

[0033] Preferably, the method for obtaining the pipeline horizontal deformation value comprises:

[0034] Based on the fact that the displacement and rotation angle of the pipeline at the pipeline boundary are 0 and the shear force is balanced, the distributed load infinitesimal element is taken at the pipeline to replace the concentrated load, and the horizontal displacement expression of the pipeline under the horizontal additional load is obtained, and the integral transformation is performed. Based on the Gauss-Laguerre numerical integration method, the horizontal deformation value of the pipeline is obtained.

[0035] The beneficial effects of the present invention are as follows: the present invention proposes an analytical method for the horizontal deformation of pipelines adjacent to deep foundation pits, which improves the situation in which the deformation mode of the foundation pit support structure and the influence of the lateral displacement on the side wall unloading are not considered in the conventional deformation calculation method of pipelines adjacent to foundation pits. The obtained analytical solution is closer to the numerical solution and has a high degree of consistency with the measured value. The horizontal deformation of the pipeline can be effectively calculated, and corresponding effective control measures can be taken during construction to ensure the normal operation of the construction and the pipeline, and to ensure the safe and normal use of the pipeline. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0037] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0038] Figure 2 Schematic diagram of the side wall unloading form of the flexible support structure of an embodiment of the present invention, wherein (a) is a top view, (b) is a schematic diagram of the distribution of soil pressure before and after foundation pit excavation, and (c) is a cross-sectional view;

[0039] Figure 3 A top view of the horizontal force of the pipe-soil model pipeline of an embodiment of the present invention;

[0040] Figure 4 It is a horizontal force section diagram of a pipeline of a pipe-soil model according to an embodiment of the present invention;

[0041] Figure 5 Schematic diagram of the horizontal attenuation function ξ(x) and the load influence width T according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0043] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] Reference Figure 1-Figure 5 As shown in the figure, a method for analyzing the horizontal deformation of pipelines adjacent to deep foundation pits is used. The calculation process is as follows: Figure 1 , the specific implementation is as follows:

[0045] 1. Construct the side wall unloading equation of the flexible support structure.

[0046] When the foundation pit has not been excavated, the lateral displacement of the supporting structure is zero, and the soil pressure acting on the supporting structure is static soil pressure. Figure 2 The figure shows the schematic diagram of the side wall unloading form of the flexible support structure, (a) is a top view, (b) is a schematic diagram of the soil pressure distribution before and after foundation pit excavation, and (c) is a cross-sectional view.

[0047] The static earth pressure p0 of the soil at depth z on the supporting structure is:

[0048] p0=K0γz

[0049] Among them, K0 is the static earth pressure coefficient and γ is the soil weight.

[0050] like Figure 2 (b) After the excavation of the foundation pit, the supporting structure produces lateral deformation, and the earth pressure acting on the supporting structure becomes active earth pressure. The Rankine active earth pressure theory is usually used for calculation. The Rankine active earth pressure p of the soil at depth z on the supporting structure is a have:

[0051]

[0052] Where K a is the Rankine active earth pressure coefficient, and c is the soil cohesion.

[0053] The relationship between the sidewall unloading p and the lateral displacement δ of the supporting structure can be expressed by the displacement function F(δ):

[0054] p=F(δ)(p0-p a )

[0055] The displacement function F(δ) has been verified to be a sine function, from which the unloading equation of the foundation pit side wall is obtained:

[0056]

[0057] Among them, δ(z) is the lateral displacement of the foundation pit support structure about the calculation depth z.

[0058] According to a large number of measured data of lateral displacement of foundation pit flexible support structure, the lateral displacement δ(z) of flexible support structure is obtained as follows:

[0059]

[0060] Among them, δ max is the maximum lateral displacement of the supporting structure.

[0061] Substituting the lateral displacement δ(z) of the flexible support structure into the unloading equation of the foundation pit side wall, the unloading equation of the flexible support structure side wall is obtained as follows:

[0062]

[0063] Among them, K0, K a are the static earth pressure coefficient and the Rankine active earth pressure coefficient, γ is the weighted degree of the soil in the foundation pit, z is the depth, H is the excavation depth of the foundation pit, δ max is the maximum lateral displacement of the supporting structure, δa is the active limit displacement of soil and soil properties, and c is the soil cohesion.

[0064] 2. Calculate the horizontal additional load of the adjacent pipeline under the unloading of the side wall of the flexible support structure (such as Figure 3-4 shown).

[0065] The definition of the impact of the side wall unloading of the flexible support structure on the pipeline is as follows:

[0066] The soil in the foundation pit can be regarded as homogeneous soil in an elastic half-space, and the pipeline is regarded as an infinitely long Bernoulli-Euler beam. The influence of the pipeline axial stress on the pipeline deformation is not considered, the influence of the three-dimensional spatial effect of the foundation pit on the side wall unloading is not considered, and the additional stress influence of the pit wall unloading on the side away from the pipeline in the foundation pit is not considered. The existence of the pipeline does not affect the calculation of additional stress in the soil.

[0067] Calculate the additional horizontal stress of pipelines at the bottom of the foundation pit based on the Mindlin solution And the additional horizontal stress of the rectangular pipeline caused by the unloading of the three side walls adjacent to the pipeline The total horizontal additional stress σ of the adjacent pipeline under the unloading of the side wall of the flexible support structure is obtained by the superposition principle. x for:

[0068]

[0069] The additional horizontal load q(y) of the adjacent pipeline under the unloading of the side wall of the flexible support structure is further calculated, and the calculation equation is:

[0070] q(y)=σ x h

[0071] Where h is the height of the rectangular section, σ x Unload the total horizontal additional stress of the adjacent pipeline on the side wall of the flexible support structure.

[0072] 3. Establish the differential equation of pipeline horizontal deformation and deflection.

[0073] Due to the continuous nature of the two-parameter model, the deflection effect caused by the deadweight or uniformly distributed load along the entire length of the beam must be considered. The basic differential equation for the deflection that controls the horizontal deformation of the pipeline is:

[0074]

[0075] Among them, E p I is the bending stiffness of the pipeline, G p is the horizontal shear coefficient, K is the resistance coefficient, and w(y) is the horizontal deformation value of the pipeline.

[0076] 4. Determine the horizontal shear coefficient and resistance coefficient of the interaction between the pipeline and the soil;

[0077] In the established pipeline horizontal deformation equation, the horizontal shear coefficient G p The value of the resistance coefficient K has an important influence on the calculation of horizontal deformation of the pipeline.

[0078] Horizontal shear coefficient G p The calculation equation is:

[0079]

[0080] Where E is the elastic modulus of soil, v is the Poisson's ratio of soil, ξ(x) is the horizontal attenuation function, and T is the load influence width.

[0081] The buried depth z0 of the pipeline will have a certain impact on the resistance coefficient K. For buried pipelines, the buried depth effect of the pipeline needs to be considered. Therefore, the calculation equation of the resistance coefficient K is:

[0082]

[0083] Where E is the elastic modulus of the soil, z0 is the buried depth of the pipeline, v is the Poisson's ratio of the soil, and E p I is the pipeline bending stiffness.

[0084] like Figure 5 Shown is a schematic diagram of the horizontal attenuation function ξ(x) and the load influence width T.

[0085] 5. Solve the differential equation of pipeline horizontal deformation and calculate the value of pipeline horizontal deformation;

[0086] The horizontal deformation equation of the pipeline is a fourth-order differential equation, and its general homogeneous solution is:

[0087] w(y)=e αy [A1cos(βy)+A2sin(βy)]+e -αy [A3cos(βy)+A4sin(βy)]

[0088] Among them, A1, A2, A3, and A4 are the coefficients to be determined;

[0089]

[0090] Note that the point where y=0 of the pipeline is point O'. Assume that a concentrated load Q acts on point O'. At this time, the boundary conditions of the pipeline are:

[0091]

[0092] According to the boundary conditions, the distributed load microelement q(ξ)dξ is taken at the position y=ξ of the pipeline, and the concentrated load Q is replaced by q(ξ)dξ. Then, the horizontal displacement w(y) of the pipeline is obtained by integrating the horizontal additional load q(y) within the range of action:

[0093]

[0094] Perform an integral transformation on the expression. Let m = α(ξ-y), A = 1 / 4E p Iα 2 β(α 2 +β 2 ), we get the expression:

[0095]

[0096] Then order:

[0097] By Gauss-Laguerre numerical integration, we get:

[0098]

[0099] In the formula, m i With m j represents the Gaussian point of the Gauss-Laguerre numerical integral, C i With C j Represents the integral coefficient corresponding to the Gaussian point.

[0100] A Gauss-Laguerre numerical integration calculation program was written, and the analytical solution for the horizontal deformation of the pipeline was obtained as follows:

[0101]

[0102] The present invention proposes an analytical method for the horizontal deformation of pipelines adjacent to deep foundation pits, which improves the situation in which the deformation mode of the foundation pit support structure and the influence of lateral displacement on the side wall unloading are not considered in the conventional deformation calculation method of pipelines adjacent to foundation pits. The analytical solution obtained is closer to the numerical solution and has a high degree of consistency with the measured value. The horizontal deformation of the pipeline can be effectively calculated, and corresponding effective control measures can be taken during construction to ensure the normal operation of the construction and the pipeline, and to ensure the safe and normal use of the pipeline.

[0103] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for analyzing horizontal deformation of pipelines adjacent to deep foundation pits, characterized in that: include: Based on the side wall unloading equation of the flexible support structure, the horizontal additional load of the adjacent pipeline under the side wall unloading of the flexible support structure is calculated; The side wall unloading equation of the flexible support structure is: Among them, K0, K a are the static earth pressure coefficient and the Rankine active earth pressure coefficient, γ is the weighted degree of the soil in the foundation pit, z is the depth, H is the excavation depth of the foundation pit, δ max is the maximum lateral displacement of the supporting structure, δ a is the active limit displacement of soil, c is the cohesion of soil; The horizontal shear coefficient and resistance coefficient of the interaction between the pipeline and the soil are determined through the differential equation of pipeline horizontal deformation and deflection; The pipeline horizontal deformation and deflection differential equation is: Among them, E p I is the pipeline bending stiffness, G p is the horizontal shear coefficient, K is the resistance coefficient, and w(y) is the horizontal deformation value of the pipeline; Based on the horizontal additional load of the adjacent pipeline and the horizontal shear coefficient and resistance coefficient, solving the differential equation of horizontal deformation of the pipeline to obtain the horizontal deformation value of the pipeline; The pipeline horizontal deformation differential equation comprises a fourth-order differential equation, wherein the general homogeneous general solution comprises: w(y)=e αy [A1 cos(βy)+A2 sin(βy)]+e -αy [A3 cos(βy)+A4 sin(βy)] Among them, A1, A2, A3, and A4 are the coefficients to be determined; K is the resistance coefficient, E p I is the bending stiffness of the pipeline.

2. The method for analyzing horizontal deformation of pipelines adjacent to deep foundation pits according to claim 1 is characterized in that: The calculation equation for the additional horizontal load of the adjacent pipeline under the unloading of the side wall of the flexible support structure is: q(y)=σ x h Where h is the height of the rectangular section, σ x is the total additional horizontal stress of the adjacent pipeline under the unloading of the side wall of the flexible support structure, and q(y) is the additional horizontal load of the adjacent pipeline under the unloading of the side wall of the flexible support structure.

3. The method for analyzing horizontal deformation of pipelines adjacent to deep foundation pits according to claim 2 is characterized in that: The calculation method of the total horizontal additional stress of the adjacent pipeline under the unloading of the side wall of the flexible support structure includes: The additional horizontal stress of the rectangular pipeline caused by unloading of the bottom of the foundation pit and the three side walls adjacent to the pipeline is calculated, and the total additional horizontal stress of the adjacent pipeline under the unloading of the side walls of the flexible support structure is obtained through the superposition principle.

4. The method for analyzing horizontal deformation of pipelines adjacent to deep foundation pits according to claim 1 is characterized in that: The horizontal shear coefficient G p The calculation method is: Where E is the elastic modulus of soil, ν is the Poisson's ratio of soil, ξ(x) is the horizontal attenuation function, and T is the load influence width.

5. The method for analyzing horizontal deformation of pipelines adjacent to deep foundation pits according to claim 1 is characterized in that: The expression of the resistance coefficient K is: Where E is the elastic modulus of the soil, z0 is the buried depth of the pipeline, ν is the Poisson's ratio of the soil, and E p I is the bending stiffness of the pipeline.

6. The method for analyzing horizontal deformation of pipelines adjacent to deep foundation pits according to claim 1 is characterized in that: The method for obtaining the horizontal deformation value of the pipeline includes: Based on the fact that the displacement and rotation angle of the pipeline at the pipeline boundary are 0 and the shear force is balanced, the distributed load infinitesimal element is taken at the pipeline to replace the concentrated load, and the horizontal displacement expression of the pipeline under the horizontal additional load is obtained, and the integral transformation is performed. Based on the Gauss-Laguerre numerical integration method, the horizontal deformation value of the pipeline is obtained.

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