CN116244978B - Pipeline landslide influence calculation method based on Timoshenko Liang Moxing - Google Patents
Pipeline landslide influence calculation method based on Timoshenko Liang Moxing Download PDFInfo
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- 238000004364 calculation method Methods 0.000 title claims abstract description 24
- 238000004458 analytical method Methods 0.000 claims abstract description 32
- 238000005452 bending Methods 0.000 claims abstract description 23
- 238000000034 method Methods 0.000 claims abstract description 23
- 238000010008 shearing Methods 0.000 claims abstract description 20
- 238000006073 displacement reaction Methods 0.000 claims description 13
- 239000011159 matrix material Substances 0.000 claims description 6
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 2
- 239000002689 soil Substances 0.000 abstract description 8
- 230000007812 deficiency Effects 0.000 abstract 1
- 238000010586 diagram Methods 0.000 description 3
- 230000007547 defect Effects 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000012271 agricultural production Methods 0.000 description 1
- 230000004075 alteration Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000005520 cutting process Methods 0.000 description 1
- 230000001066 destructive effect Effects 0.000 description 1
- 230000005484 gravity Effects 0.000 description 1
- 239000003673 groundwater Substances 0.000 description 1
- 238000009776 industrial production Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000007935 neutral effect Effects 0.000 description 1
- 239000011435 rock Substances 0.000 description 1
- 238000009991 scouring Methods 0.000 description 1
- 238000002791 soaking Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/14—Pipes
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention discloses a calculation method for the influence of landslide on a pipeline based on Timoshenko Liang Moxing, which comprises the following steps of S1: carrying out stress analysis on the longitudinal direction of the pipeline and taking a deformation differential equation of the length unit, and S2: t imoshenko beam model deformation analysis is carried out on the differential equation after S1 deformation, and S3: dividing a solution domain of a differential equation obtained after S2 deformation to replace a continuous solution domain, and carrying out deformation analysis by utilizing a finite difference method and additional boundary conditions; according to the pipeline landslide influence calculating method based on the T imoshenko Liang Moxing, the disturbance of the landslide soil body is considered, the acting force of the landslide soil body on the pipeline is reduced to a certain extent, and the problems that in the landslide and pipeline influence research, the shearing deformation influence of the beam in the deformation process cannot be considered in the analysis process by the existing Eu er-Bernoul i beam theory are solved, so that the problem of certain deficiency exists, the influence of the landslide soil body on the pipeline is not calculated by adopting any theoretical calculation method at present, and the indexes such as deflection, bending moment and shearing force of the pipeline influenced by the landslide cannot be calculated are solved.
Description
Technical Field
The invention relates to the technical field of pipeline engineering, in particular to a calculation method for the influence of landslide on a pipeline based on Timoshenko Liang Moxing.
Background
Landslide refers to the natural phenomenon that soil or rock mass on a slope is influenced by river scouring, groundwater movement, rainwater soaking, earthquakes, manual slope cutting and other factors, and slides downwards along a certain weak surface or a weak belt integrally or dispersedly under the action of gravity.
Landslide often causes huge losses, some and even destructive disasters for industrial and agricultural production and people life and property, the most serious hazard of landslide is to destroy infrastructure such as factory schools, institutions, road and bridge, agricultural machinery facilities, water conservancy and hydropower, and the like, pipelines are inevitably influenced by landslide as life lines of cities, in the research of influence of landslide on pipelines, the shearing deformation influence of the beams in the deformation process cannot be considered in the analysis process of the existing Euler-Bernoulli beam theory, so that certain defects exist, in addition, at present, no theoretical calculation method is adopted to calculate the influence of landslide soil on the pipelines, and indexes such as deflection, bending moment, shearing force and the like of the pipelines influenced by the landslide cannot be calculated.
Disclosure of Invention
The invention aims to provide a calculation method for the influence of landslide on a pipeline based on Timoshenko Liang Moxing.
In order to achieve the above purpose, the present invention provides the following technical solutions: a calculation method for the influence of landslide on a pipeline based on Timoshenko Liang Moxing comprises the following specific calculation steps:
s1: carrying out stress analysis on the longitudinal direction of the pipeline and taking a deformation differential equation of the length unit;
s2: performing Timoshenko beam model deformation analysis on the differential equation after S1 deformation;
s3: dividing a solution domain of a differential equation obtained after S2 deformation to replace a continuous solution domain, and carrying out deformation analysis by utilizing a finite difference method and additional boundary conditions;
the specific calculation steps of the S1 are as follows:
and (3) carrying out stress and deformation analysis on a unit with the length dx, wherein the stress and deformation analysis is obtained by balancing the vertical stress of the infinitesimal:
Q+k 1 w(x)Ddx＝Q+dQ+k 2 u(x)Ddx (1)；
in the formula (1): q is the section shear force, dQ is the increment of the shear force of infinitesimal, w (x) is the longitudinal displacement of the pipeline, k (x) is the foundation coefficient of a Winkler, u (x) is the displacement caused by landslide, and the formula is simplified to obtain:
the bending moment balance of the hogels is as follows:
in the formula (3): m is a bending moment, dM is a infinitesimal bending moment increment;
the expression is simplified, and the high-order trace is omitted, so that the method is obtained:
the specific calculation step of the S2 is as follows:
deforming Timoshenko Liang Moxing to obtain a relation of the shearing force Q, the bending moment M, the deflection w, the rotation angle theta and the shearing angle i of the beam:
in formula (5): kappa GA is the shear stiffness of the pipe gallery, kappa is the Timoshenko shear coefficient of the pipe, G is the shear modulus of the pipe, and A is the cross-sectional area of the pipe;
obtaining the relationship between the shearing force Q, the bending moment M and the deflection w of the pipeline by the pipeline infinitesimal from the (5):
obtaining the derivative (7):
substituting the formula (8) into the formula (2), and obtaining a differential equation only related to the vertical displacement omega (x) after finishing, wherein the differential equation is as follows:
the specific calculation step of the S3 is as follows:
the pipe gallery is longitudinally discretized into n units with equal intervals by utilizing a finite difference method, in addition, two virtual differential nodes are respectively constructed at two ends of the pipe gallery to construct differential equations of endpoints, and the finite difference forms of first, second, third and fourth-order differential terms are respectively obtained by utilizing a standard finite difference principle:
in the formula (10): w (w) i 、w i-1 、w i+1 、w i+2 W i-2 Horizontal displacement of pipe lanes at the i < th >, i-1, i+1, i+2 and i-2 nodes respectively;
substituting the differential form of the w (x) differential to obtain a finite differential expression of the pipeline deflection differential equation:
similarly, the bending moment and the shearing force at any node i obtained by the formulas (6) and (7) are expressed as:
the two ends of the pipe are subjected to forces, whereby the boundary conditions are:
the equations relating the virtual node deflection are obtained by combining equations (12) - (14) as follows:
substituting i=0, 1,2 … n-2, n-1, n into formula (11) and combining with formula (15) to obtain a linear algebraic equation set consisting of n+5 equations, the matrix form of which is expressed as:
(K 1 +K 2 +K 3 )W＝(K 4 +K 5 )U (16)。
preferably, the (K 1 +K 2 +K 3 )W＝(K 4 +K 5 ) Each matrix expression of U is as follows:
according to the technical scheme, the invention has the following beneficial effects:
according to the calculation method for the influence of the landslide on the pipeline based on Timoshenko Liang Moxing, the disturbance of the landslide soil body is considered, the acting force of the landslide soil body on the pipeline is reduced to a certain extent, the stress analysis is carried out on the pipeline in the longitudinal direction, a length unit deformation differential equation is taken, the deformation analysis is carried out on the deformed differential equation by using the Timoshenko beam model type deformation analysis, the solving domain of the differential equation obtained after the deformation is replaced by the continuous solving domain, the deformation analysis is carried out by using the finite difference method for additional boundary conditions, the influence of the pipeline on the landslide is calculated theoretically, the problem that the influence of the landslide on the pipeline cannot be considered in the analysis process by the existing Eulter-Bernoulli beam theory is solved, and therefore the problem that the influence of the landslide soil body on the pipeline cannot be calculated by any theoretical calculation method at present, and the problems of indexes such as deflection, bending moment and shearing force of the pipeline influence cannot be calculated by the landslide are solved.
Drawings
Fig. 1 is a schematic flow chart of a calculation method of landslide influence of a pipeline based on Timoshenko Liang Moxing;
FIG. 2 is a graph showing the stress analysis of the shearing and rotation effects of the beam section during the deformation of the Timoshenko beam model according to the present invention;
FIG. 3 is a schematic diagram of the differential equation of the longitudinal deformation of the pipeline according to the present invention;
FIG. 4 is a schematic diagram of a discretization analysis of a pipeline according to the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1 and fig. 2, a calculation method for calculating the influence of landslide on a pipeline based on Timoshenko Liang Moxing specifically includes the following steps:
step one: force analysis and deformation differential equation were performed for the longitudinal direction of the pipe, resulting in:
step two: and carrying out deformation analysis on the differential equation subjected to the stress analysis and deformation in the first step by using a Timoshenko beam model to obtain a fourth-order differential equation only related to the vertical displacement omega (x):
step three: dividing the solution domain of the four differential equations obtained by the deformation analysis in the second step, replacing the continuous solution domain, and then carrying out deformation analysis by utilizing a finite difference method and adding boundary conditions.
The Euler-Bernoulli beam theory cannot consider shear deformation in the beam deformation process, so that certain defects exist, the Timoshenko beam model is based on the traditional theory, the assumption that the cross section of the beam keeps a plane in the bending process is reserved, and meanwhile, the shearing and rotation effects of the beam in the deformation process are considered, so that the method is more suitable for deformation calculation of a pipeline.
As shown in fig. 3, the specific analysis for step one is as follows: assuming that the Winker foundation is affected by landslide, arbitrarily taking a unit with length dx to perform vertical stress analysis and deformation, and obtaining the following equation according to the vertical stress balance of the infinitesimal:
Q+k 1 w(x)Ddx＝Q+dQ+k 2 u(x)Ddx (1)；
wherein: q is the section shear force, dQ is the increment of the shear force of infinitesimal, w (x) is the longitudinal displacement of the pipeline, k (x) is the foundation coefficient of a Winkler, u (x) is the displacement caused by landslide, and the formula is simplified to obtain:
the bending moment balance of the infinitesimal can be obtained:
wherein: m is a bending moment, dM is a infinitesimal bending moment increment; simplifying the formula and omitting the higher-order trace can obtain:
as shown in fig. 2 and 3, the specific analysis for the second step is as follows: different from an Euler-Bernoulli beam model, for a deformation mode of a Timoshenko beam model, the section of the beam rotates relative to the normal line direction of a neutral axis under the shearing force, and the rotation angle θ of the beam deforms Timoshenko Liang Moxing to obtain a relation among the shearing force Q, the bending moment M, the deflection w, the rotation angle θ and the shearing angle i of the beam:
wherein: kappa GA is the shear stiffness of the pipe gallery, kappa is the Timoshenko shear coefficient of the pipe, G is the shear modulus of the pipe, and A is the cross-sectional area of the pipe;
the relation between the shearing force Q, the bending moment M and the pipe deflection w of the pipe infinitesimal can be obtained by the formula (5):
the derivative formula (7) can be obtained:
substituting formula (8) into formula (2), the following fourth-order differential equation only related to vertical displacement ω (x) can be obtained after finishing:
as shown in fig. 4, the specific analysis for step two is as follows: the deformation of the pipeline under the action of the tensile force can be obtained by solving the differential equation, but the above equation is a fourth-order differential equation, so that the mathematical solution is difficult to directly solve, and the solution domain is divided into a limited grid to replace the continuous solution domain for simplifying the calculation. The method is characterized in that a finite difference method is adopted to longitudinally disperse a pipe gallery into n units with equal intervals, the number of finite difference nodes is n+1, in addition, in order to construct a difference equation of end points, two virtual difference nodes are respectively constructed at two ends of the pipe gallery, n+5 nodes are total, fig. 4 is a schematic diagram of discretization analysis of the pipe gallery, and the finite difference forms of first-order, second-order, third-order and fourth-order differential terms can be respectively obtained by utilizing a standard finite difference principle:
wherein: w (w) i 、w i-1 、w i+1 、w i+2 W i-2 Horizontal displacement of pipe lanes at the i < th >, i-1, i+1, i+2 and i-2 nodes respectively;
substituting the differential form of the w (x) differential to obtain a finite differential expression of the pipeline deflection differential equation:
similarly, the bending moment and shear force at any node i obtainable according to equations (6), (7) can be expressed as:
from the forces acting on the two ends of the pipe, the boundary conditions can be obtained:
by combining equations (12) - (14), the equation relating the virtual node deflection can be found as follows:
substituting i=0, 1,2 … n-2, n-1, n into formula (11) and combining with formula (15) can result in a linear algebraic system of n+5 equations, the matrix form of which can be expressed as:
(K 1 +K 2 +K 3 )W＝(K 4 +K 5 )U (16)；
wherein each matrix expression of the above formula is respectively:
in the embodiment, a differential method is adopted to solve the fourth-order differential equation, and the deflection, the bending moment and the shearing force of the pipeline can be obtained by combining boundary conditions, so that the influence of landslide on the theoretical calculation pipeline is realized.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (2)
1. A calculation method for the influence of landslide on a pipeline based on Timoshenko Liang Moxing is characterized by comprising the following specific calculation steps:
s1: carrying out stress analysis on the longitudinal direction of the pipeline and taking a deformation differential equation of the length unit;
s2: performing Timoshenko beam model deformation analysis on the differential equation after S1 deformation;
s3: dividing a solution domain of a differential equation obtained after S2 deformation to replace a continuous solution domain, and carrying out deformation analysis by utilizing a finite difference method and additional boundary conditions;
the specific calculation steps of the S1 are as follows:
and (3) carrying out stress and deformation analysis on a unit with the length dx, wherein the stress and deformation analysis is obtained by balancing the vertical stress of the infinitesimal:
Q+k 1 w(x)Ddx＝Q+dQ+k 2 u(x)Ddx (1)；
in the formula (1): q is the section shear force, dQ is the increment of the shear force of infinitesimal, w (x) is the longitudinal displacement of the pipeline, k (x) is the foundation coefficient of a Winkler, u (x) is the displacement caused by landslide, and the formula is simplified to obtain:
the bending moment balance of the hogels is as follows:
in the formula (3): m is a bending moment, dM is a infinitesimal bending moment increment;
the expression is simplified, and the high-order trace is omitted, so that the method is obtained:
the specific calculation step of the S2 is as follows:
deforming Timoshenko Liang Moxing to obtain a relation of the shearing force Q, the bending moment M, the deflection w, the rotation angle theta and the shearing angle i of the beam:
in formula (5): kappa GA is the shear stiffness of the pipe gallery, kappa is the Timoshenko shear coefficient of the pipe, G is the shear modulus of the pipe, and A is the cross-sectional area of the pipe;
obtaining the relationship between the shearing force Q, the bending moment M and the deflection w of the pipeline by the pipeline infinitesimal from the (5):
obtaining the derivative (7):
substituting the formula (8) into the formula (2), and obtaining a differential equation only related to the vertical displacement omega (x) after finishing, wherein the differential equation is as follows:
the specific calculation step of the S3 is as follows:
the pipe gallery is longitudinally discretized into n units with equal intervals by utilizing a finite difference method, in addition, two virtual differential nodes are respectively constructed at two ends of the pipe gallery to construct differential equations of endpoints, and the finite difference forms of first, second, third and fourth-order differential terms are respectively obtained by utilizing a standard finite difference principle:
in the formula (10): w (w) i 、w i-1 、w i+1 、w i+2 W i-2 Horizontal displacement of pipe lanes at the i < th >, i-1, i+1, i+2 and i-2 nodes respectively;
substituting the differential form of the w (x) differential to obtain a finite differential expression of the pipeline deflection differential equation:
similarly, the bending moment and the shearing force at any node i obtained by the formulas (6) and (7) are expressed as:
the two ends of the pipe are subjected to forces, whereby the boundary conditions are:
the equations relating the virtual node deflection are obtained by combining equations (12) - (14) as follows:
substituting i=0, 1,2 … n-2, n-1, n into formula (11) and combining with formula (15) to obtain a linear algebraic equation set consisting of n+5 equations, the matrix form of which is expressed as:
(K 1 +K 2 +K 3 )W＝(K 4 +K 5 )U (16)。
2. a pipeline landslide influence calculating method based on Timoshenko Liang Moxing in accordance with claim 1, wherein the (K 1 +K 2 +K 3 )W＝(K 4 +K 5 ) Each matrix expression of U is as follows:
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| CN112307545A (en) * | 2020-10-30 | 2021-02-02 | 大连海事大学 | Large-diameter single pile horizontal vibration analysis method considering axial force action |
| CN113361169A (en) * | 2021-06-10 | 2021-09-07 | 安徽省建筑科学研究设计院 | Efficient prediction method for longitudinal deformation of shield tunnel caused by surface burst loading |
| CN114357575A (en) * | 2021-12-21 | 2022-04-15 | 中国矿业大学(北京) | Method for predicting settlement of downward-passing pipeline of shield tunnel |
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| CN112307545A (en) * | 2020-10-30 | 2021-02-02 | 大连海事大学 | Large-diameter single pile horizontal vibration analysis method considering axial force action |
| CN113361169A (en) * | 2021-06-10 | 2021-09-07 | 安徽省建筑科学研究设计院 | Efficient prediction method for longitudinal deformation of shield tunnel caused by surface burst loading |
| CN114357575A (en) * | 2021-12-21 | 2022-04-15 | 中国矿业大学(北京) | Method for predicting settlement of downward-passing pipeline of shield tunnel |
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| 考虑隧道剪切效应的隧道下穿对既有盾构隧道的纵向影响;梁荣柱;宗梦繁;康成;吴文兵;方宇翔;夏唐代;程康;;浙江大学学报(工学版)(03);第420-429页 * |
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