CN108647441B - Damaged pipeline residual bending moment limit load calculation method under combined load action - Google Patents

Damaged pipeline residual bending moment limit load calculation method under combined load action Download PDF

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CN108647441B
CN108647441B CN201810447972.3A CN201810447972A CN108647441B CN 108647441 B CN108647441 B CN 108647441B CN 201810447972 A CN201810447972 A CN 201810447972A CN 108647441 B CN108647441 B CN 108647441B
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周闻青
陈挺
叶欣
茅振华
周红明
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Zhejiang Province Institute of Metrology
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Abstract

The invention discloses a method for calculating residual bending moment limit load of a damaged pipeline under the action of combined load. The method is divided into the conditions that all the defects of the damaged pipeline fall in a compression zone, most of the defects are in a tension zone in a small part of the compression zone, all the defects are in a tension zone, most of the defects are in the tension zone in a small part of the tension zone in the compression zone, and the bending moment limit load of the damaged pipeline is calculated respectively. The method can accurately evaluate and calculate to obtain the ultimate bending moment load calculation result, improves the calculation precision, and has wider application value in the field of safety evaluation of damaged pipelines.

Description

Damaged pipeline residual bending moment limit load calculation method under combined load action
Technical Field
The invention relates to a method for calculating a limit load of a pipeline, in particular to a method for calculating a residual bending moment limit load of a damaged pipeline under the action of combined load.
Background
Subsea pipelines are an important component of offshore oil and gas development, are the primary means of oil and gas transport, and are considered life lines in marine oil and gas production systems. The seabed environment is comparatively complicated, and the pipeline is under different environmental condition, and the load that receives is different, and under general condition, what the pipeline bore is the effect of pressure load, and when the pipeline received seabed deformation, debris flow etc. and influences, the phenomenon of hanging over of pipeline can make the pipeline have more a moment of flexure load. At present, the key point of domestic and foreign research is the ultimate bearing capacity of the pipeline under the independent action of single load, Hauch and the like are convenient to calculate, the pipeline defect is simplified into the equal-depth defect, and the residual strength expression of the damaged pipeline is obtained; related experiments are carried out by Ahn and the like, and the failure mode of the damaged pipeline under the most used bending load is researched; kim et al experimentally obtained the remaining strength of the damaged pipe under bending load. However, the research on the ultimate bearing capacity under the combined action of various loads is lacked.
Therefore, the prior art lacks a safety evaluation calculation method for determining the ultimate bending moment load of the pipeline under the combined load to the submarine pipeline.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a method for calculating the residual bending moment ultimate load of the damaged pipeline under the combined load effect, and the method for evaluating and calculating the safety of the ultimate bending moment load of the pipeline under the combined load effect on the submarine pipeline has important engineering significance.
The technical scheme adopted by the invention is as follows:
since under the combined load, the defects on the pipe are possibly in the tension area and also in the compression area, in order to obtain a more comprehensive limit load solution of the damaged pipe, four cases need to be analyzed. The method is divided into the conditions that all the defects of the damaged pipeline fall in a compression zone, most of the defects are in a tension zone in a small part of the compression zone, all the defects are in a tension zone, most of the defects are in the tension zone in a small part of the tension zone in the compression zone, and the bending moment limit load of the damaged pipeline is calculated respectively.
The defect is mostly in the compression zone and is in the tension zone in a small part, namely the sectional area of the defect in the compression zone is larger than or equal to that of the defect in the tension zone, namely 50 percent or more of the sectional area of the defect is in the compression zone and the rest is in the tension zone. The defect is mostly in the tension zone and is in the compression zone in a small part, namely the cross-sectional area of the defect in the tension zone is larger than that of the defect in the compression zone, namely more than 50 percent of the cross-sectional area of the defect is in the tension zone and the defect is remained in the compression zone.
As shown in fig. 1(a) and 1(b), when all the defects of the damaged pipe are in the pressure zone, that is, under the combined load, the damaged pipe has a neutral axis, and the pipe above the neutral axis generates compressive stress and the pipe below the neutral axis generates tensile stress. And (3) calculating the bending moment limit load of the damaged pipeline by adopting the following formula:
Figure GDA0003358665550000021
wherein beta represents a polar angle corresponding to the position of the neutral axis of the pipeline, and RmThe mean diameter of the pipeline is represented, t represents the wall thickness of the pipeline, a (xi) represents a change function of the depth of the defect along the circumferential direction of the pipeline, xi represents the angle of the specific position of the depth of the defect at the center of the pipeline, and sigma representsfRepresenting the cross-sectional tensile stress, σ, of the pipe under combined loadingaThe cross section compressive stress of the pipeline under the combined load action is represented, and theta represents a half of the angle of the center of the pipeline occupied by the defect;
the polar angle β corresponding to the position of the neutral axis of the pipe is calculated by the following formula:
Figure GDA0003358665550000022
the polar angle beta is taken with respect to the parameter t, sigmaa,σfAnd a (ξ) can be expressed as β ═ f (t, σ)a,σfA (#)). In the specific calculation process, a discrete calculation mode is adopted to solve the value of the beta.
Cross-sectional tensile stress sigma of the above-mentioned pipe under the combined loadfAnd compressive stress σa：
Figure GDA0003358665550000023
Figure GDA0003358665550000024
Wherein σbIndicating the strength limit of the material used for the pipe, p being the work of the pipeAs a pressure, pLThe limit internal pressure which can be borne under the condition that the pipeline is not damaged.
As shown in fig. 2(a) and 2(b), when the defect of the damaged pipe is mostly in the tension zone in the compression zone and the small part is in the tension zone, i.e. under the combined load, the damaged pipe has a neutral axis and is bounded by the neutral axis, the pipe above the neutral axis generates the compression stress, and the part below the neutral axis generates the tension stress. Most of the defects fall into a pressure stress area of the pipeline, and the rest of the defects fall into a tensile stress area of the pipeline, namely most of the cross section areas of the defects are located above a neutral axis, and the cross section areas of the small parts of the defects are located below the neutral axis, the problem is reanalyzed, and the bending moment limit load of the damaged pipeline is calculated by adopting the following formula:
Figure GDA0003358665550000025
wherein beta represents a polar angle corresponding to the position of the neutral axis of the pipeline, and RmThe mean diameter of the pipeline is represented, t represents the wall thickness of the pipeline, a (xi) represents a change function of the depth of the defect along the circumferential direction of the pipeline, xi represents the angle of the specific position of the depth of the defect at the center of the pipeline, and sigma representsfRepresenting the cross-sectional tensile stress, σ, of the pipe under combined loadingaThe cross section compressive stress of the pipeline under the combined load action is represented, and theta represents a half of the angle of the center of the pipeline occupied by the defect;
the polar angle β corresponding to the position of the neutral axis of the pipe is calculated by the following formula:
Figure GDA0003358665550000031
cross-sectional tensile stress sigma of the above-mentioned pipe under the combined loadfAnd compressive stress σaThe following formulas are adopted for calculation:
Figure GDA0003358665550000032
Figure GDA0003358665550000033
wherein σbRepresenting the strength limit of the material used for the pipe, p being the working pressure of the pipe, pLThe limit internal pressure which can be borne under the condition that the pipeline is not damaged.
As shown in fig. 3(a) and 3(b), when the defects of the damaged pipe are all in the tension zone, that is, under the combined load, the damaged pipe has a neutral axis, and the pipe above the neutral axis generates compressive stress and the pipe below the neutral axis generates tensile stress. And (3) re-analyzing the problem when all the defects fall in the tension area, namely the defects are all positioned below the neutral axis, and calculating the bending moment limit load of the damaged pipeline by adopting the following formula:
Figure GDA0003358665550000034
wherein beta represents a polar angle corresponding to the position of the neutral axis of the pipeline, and RmThe mean diameter of the pipeline is represented, t represents the wall thickness of the pipeline, a (xi) represents a change function of the depth of the defect along the circumferential direction of the pipeline, xi represents the angle of the specific position of the depth of the defect at the center of the pipeline, and sigma representsfRepresenting the cross-sectional tensile stress, σ, of the pipe under combined loadingaThe cross section compressive stress of the pipeline under the combined load action is represented, and theta represents a half of the angle of the center of the pipeline occupied by the defect;
the polar angle β corresponding to the position of the neutral axis of the pipe is calculated by the following formula:
Figure GDA0003358665550000035
cross-sectional tensile stress sigma of the above-mentioned pipe under the combined loadfAnd compressive stress σaThe following formulas are adopted for calculation:
Figure GDA0003358665550000041
Figure GDA0003358665550000042
wherein σbRepresenting the strength limit of the material used for the pipe, p being the working pressure of the pipe, pLThe limit internal pressure which can be borne under the condition that the pipeline is not damaged.
As shown in fig. 4(a) and 4(b), when the defect of the damaged pipe is mostly in the tension zone and the small part is in the compression zone, i.e. under the combined load, the damaged pipe has a neutral axis, and is bounded by the neutral axis, the pipe above the neutral axis generates compressive stress, and the part below the neutral axis generates tensile stress. Most of the defects fall into a tensile stress area of the pipeline, and the other part of the defects fall into a compressive stress area of the pipeline, namely the cross section area of the small part of the defects is located above a neutral axis, the cross section area of the large part of the defects is located below the neutral axis, the problem is reanalyzed, and the bending moment limit load of the damaged pipeline is calculated by adopting the following formula:
Figure GDA0003358665550000043
wherein beta represents a polar angle corresponding to the position of the neutral axis of the pipeline, and RmThe mean diameter of the pipeline is represented, t represents the wall thickness of the pipeline, a (xi) represents a change function of the depth of the defect along the circumferential direction of the pipeline, xi represents the angle of the specific position of the depth of the defect at the center of the pipeline, and sigma representsfRepresenting the cross-sectional tensile stress, σ, of the pipe under combined loadingaThe cross section compressive stress of the pipeline under the combined load action is represented, and theta represents a half of the angle of the center of the pipeline occupied by the defect;
the polar angle β corresponding to the position of the neutral axis of the pipe is calculated by the following formula:
Figure GDA0003358665550000044
cross-sectional tensile stress sigma of the above-mentioned pipe under the combined loadfAnd compressive stress σaThe following formulas are adopted for calculation:
Figure GDA0003358665550000045
Figure GDA0003358665550000046
wherein σbRepresenting the strength limit of the material used for the pipe, p being the working pressure of the pipe, pLThe limit internal pressure which can be borne under the condition that the pipeline is not damaged.
In specific implementation, in order to facilitate implementation on a computer subsequently, in a specific calculation process, the expression of the bending moment limit load can be discretized to implement.
The invention can particularly aim at the complex environment of the seabed, and the bearing capacity of the pipeline can be reduced after corrosion defects are generated on the submarine pipeline under the complex environment of the seabed, thereby influencing the safe operation of the pipeline.
The method can accurately calculate the residual strength (ultimate bending moment load) of the damaged pipeline under the joint action of various loads such as internal pressure, bending moment and the like of the pipeline in the complex environment of the seabed, obtain more reliable analysis results and have wide application value.
The invention has the beneficial effects that:
the invention provides a calculation mode of the ultimate bending moment load borne by the damaged pipeline under the action of combined load working pressure based on the failure mechanism of materials, compared with some existing evaluation methods, the calculation result given by the method is matched with the experiment result through experimental verification, the ultimate bending moment load calculation result can be accurately evaluated and calculated, the calculation precision is improved, and the method has a wide application value in the field of safety evaluation of the damaged pipeline.
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FIG. 1 is a schematic view of an embodiment in which the defects all fall in the pressurized area of the pipe. FIG. 1(a) shows a defect placement diagram for a pipe section, and FIG. 1(b) shows a cross-sectional defect compressive and tensile stress profile for a pipe side.
FIG. 2 is a schematic view of an embodiment in which the defect is mostly located in the pressurized area of the pipe. Fig. 2(a) shows a defect layout diagram in a cross section of a pipe, and fig. 2(b) shows a cross-sectional defect compressive and tensile stress distribution diagram in a side surface of the pipe.
FIG. 3 is a schematic diagram of an embodiment in which the defects all fall in the tensioned region of the pipe. Fig. 3(a) shows a defect layout diagram in a cross section of a pipe, and fig. 3(b) shows a cross-sectional defect compressive and tensile stress distribution diagram in a side surface of the pipe.
FIG. 4 is a schematic view of an embodiment in which the defect is mostly located in the tension zone of the pipe. Fig. 4(a) shows a defect layout diagram in a cross section of a pipe, and fig. 4(b) shows a cross-sectional defect compressive and tensile stress distribution diagram in a side surface of the pipe.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
The case of a fully implemented embodiment of the method according to the invention is as follows:
in order to verify the reliability of the present evaluation method, it is necessary to compare the evaluation result with the existing evaluation method.
The existing bending moment evaluation methods mainly comprise the following methods,
1) ASME Cross-sectional method
In the evaluation method defined by ASME, the defects detected by the pipeline defect detection system are usually treated equivalently, and irregular defects are equivalent to a defect of equal depth, and the depth value is equal to the maximum value of the depth of the detected defect:
aeq＝maxa(ξ)
therefore, the evaluation calculation result can excessively exaggerate the influence of the defect on the ultimate bending moment load, and particularly when the depth of the defect changes greatly, the evaluation result is conservative.
2) Equivalent cross-sectional area method
In order to overcome the defects of the ASME cross section method, researchers propose a new equivalent cross section method, and the main idea of the method is to require that the cross section area of an actually measured defect is equal to the cross section area of an equivalent defect.
The concrete material of the Zea's warrior pipeline in the embodiment of the invention is X60 steel, the shape of the defect is parabolic, and the concrete defect parameters of the damaged pipeline are shown in Table 1.
TABLE 1 damaged pipe geometry parameters
Figure GDA0003358665550000061
Table 1 lists the ultimate bending moment loads of the damaged pipe obtained by the various methods and the error of the experimental results. The error obtained by calculation of the ASME section method is the largest, the mean error reaches 25.15%, the error obtained by calculation of the method is smaller than that obtained by calculation of other methods, the mean error is only 7.92%, and the standard deviation is also the smallest, so that the method not only has higher calculation precision, but also has higher reliability of the calculation result.
TABLE 2 ultimate bending moment load error comparison
Figure GDA0003358665550000062
Therefore, the calculation result is consistent with the experiment result, the accuracy of the calculation result is improved, and the method has the remarkable technical effect.

Claims (1)

1. A method for calculating residual bending moment limit load of a damaged pipeline under the action of combined load is characterized by comprising the following steps: the method comprises the steps of respectively calculating the bending moment limit load of the damaged pipeline under the conditions that all the defects of the damaged pipeline fall into a compression zone, most of the defects are in a tension zone in a small part of the compression zone, all the defects are in a tension zone, most of the defects are in a tension zone in a small part of the tension zone in the compression zone;
the majority of the defects are in the compression zone and the minority of the defects are in the tension zone, which means that the sectional area of the defects in the compression zone is larger than or equal to that of the defects in the tension zone; the defect is mostly in the tension zone and the small part is in the compression zone, which means that the sectional area of the defect in the tension zone is larger than that of the defect in the compression zone;
and when the defects of the damaged pipeline all fall into the compression zone, calculating the bending moment limit load of the damaged pipeline by adopting the following formula:
Figure FDA0003358665540000011
wherein beta represents a polar angle corresponding to the position of the neutral axis of the pipeline, and RmThe mean diameter of the pipeline is represented, t represents the wall thickness of the pipeline, a (xi) represents a change function of the depth of the defect along the circumferential direction of the pipeline, xi represents the angle of the specific position of the depth of the defect at the center of the pipeline, and sigma representsfRepresenting the cross-sectional tensile stress, σ, of the pipe under combined loadingaThe cross section compressive stress of the pipeline under the combined load action is represented, and theta represents a half of the angle of the center of the pipeline occupied by the defect;
the polar angle β corresponding to the position of the neutral axis of the pipe is calculated by the following formula:
Figure FDA0003358665540000012
cross-sectional tensile stress sigma of the above-mentioned pipe under the combined loadfAnd compressive stress σa：
Figure FDA0003358665540000013
Figure FDA0003358665540000014
Wherein σbRepresenting the strength limit of the material used for the pipe, p being the working pressure of the pipe, pLIs a pipeThe limit internal pressure which can be borne under the condition of no damage;
when the defect of the damaged pipe is mostly in the compression zone and the defect of the damaged pipe is mostly in the tension zone, the bending moment limit load of the damaged pipe is calculated by adopting the following formula:
Figure FDA0003358665540000015
wherein beta represents a polar angle corresponding to the position of the neutral axis of the pipeline, and RmThe mean diameter of the pipeline is represented, t represents the wall thickness of the pipeline, a (xi) represents a change function of the depth of the defect along the circumferential direction of the pipeline, xi represents the angle of the specific position of the depth of the defect at the center of the pipeline, and sigma representsfRepresenting the cross-sectional tensile stress, σ, of the pipe under combined loadingaThe cross section compressive stress of the pipeline under the combined load action is represented, and theta represents a half of the angle of the center of the pipeline occupied by the defect;
the polar angle β corresponding to the position of the neutral axis of the pipe is calculated by the following formula:
Figure FDA0003358665540000021
cross-sectional tensile stress sigma of the above-mentioned pipe under the combined loadfAnd compressive stress σaThe following formulas are adopted for calculation:
Figure FDA0003358665540000022
Figure FDA0003358665540000023
wherein σbRepresenting the strength limit of the material used for the pipe, p being the working pressure of the pipe, pLThe limit internal pressure can be borne under the condition that the pipeline is not damaged;
in the case that the defects of the damaged pipe are all in the tension zone, the bending moment limit load of the damaged pipe is calculated by adopting the following formula:
Figure FDA0003358665540000024
wherein beta represents a polar angle corresponding to the position of the neutral axis of the pipeline, and RmThe mean diameter of the pipeline is represented, t represents the wall thickness of the pipeline, a (xi) represents a change function of the depth of the defect along the circumferential direction of the pipeline, xi represents the angle of the specific position of the depth of the defect at the center of the pipeline, and sigma representsfRepresenting the cross-sectional tensile stress, σ, of the pipe under combined loadingaThe cross section compressive stress of the pipeline under the combined load action is represented, and theta represents a half of the angle of the center of the pipeline occupied by the defect;
the polar angle β corresponding to the position of the neutral axis of the pipe is calculated by the following formula:
Figure FDA0003358665540000025
cross-sectional tensile stress sigma of the above-mentioned pipe under the combined loadfAnd compressive stress σaThe following formulas are adopted for calculation:
Figure FDA0003358665540000026
Figure FDA0003358665540000031
wherein σbRepresenting the strength limit of the material used for the pipe, p being the working pressure of the pipe, pLThe limit internal pressure can be borne under the condition that the pipeline is not damaged;
when the defect of the damaged pipe is mostly in the tension zone and the defect of the damaged pipe is mostly in the compression zone, the bending moment limit load of the damaged pipe is calculated by adopting the following formula:
Figure FDA0003358665540000032
wherein beta represents a polar angle corresponding to the position of the neutral axis of the pipeline, and RmThe mean diameter of the pipeline is represented, t represents the wall thickness of the pipeline, a (xi) represents a change function of the depth of the defect along the circumferential direction of the pipeline, xi represents the angle of the specific position of the depth of the defect at the center of the pipeline, and sigma representsfRepresenting the cross-sectional tensile stress, σ, of the pipe under combined loadingaThe cross section compressive stress of the pipeline under the combined load action is represented, and theta represents a half of the angle of the center of the pipeline occupied by the defect;
the polar angle β corresponding to the position of the neutral axis of the pipe is calculated by the following formula:
Figure FDA0003358665540000033
cross-sectional tensile stress sigma of the above-mentioned pipe under the combined loadfAnd compressive stress σaThe following formulas are adopted for calculation:
Figure FDA0003358665540000034
Figure FDA0003358665540000035
wherein σbRepresenting the strength limit of the material used for the pipe, p being the working pressure of the pipe, pLThe limit internal pressure which can be borne under the condition that the pipeline is not damaged.
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