Submarine pipeline stability analysis method based on mathematical optimization particle finite element method

Abstract

The invention provides a submarine pipeline stability analysis method based on a mathematical optimization particle finite element method, which is used for specially building a set of novel submarine pipeline stability analysis architecture and reflecting the novel submarine pipeline stability analysis architecture by a corresponding numerical model, and can accurately simulate the interaction of wave-pipeline-soil body, so that the stability of the submarine pipeline is improved. Therefore, the stability of the submarine pipeline can be accurately analyzed, high-quality data support is provided for evaluating the stability of the submarine pipeline in a real marine environment, and then work in the aspects of analysis, construction, maintenance and the like of the submarine pipeline can be better carried out.

Description

Technical Field

[0001] This application relates to the field of marine engineering, specifically to a method for analyzing the stability of subsea pipelines based on the mathematically optimized particle finite element method. Background Technology

[0002] In marine engineering operations, there may be a need for stability analysis of a specific object such as a subsea pipeline.

[0003] In response to the need for stability analysis of subsea pipelines, the inventors of this application have found that, on the one hand, existing methods for analyzing soil and rock stability typically use the limit theorems of classical plasticity theory to calculate the ultimate load. However, this method cannot predict changes in soil resistance caused by variations in boundary and load conditions. On the other hand, they have also found that common large deformation calculation techniques used to analyze pipeline-soil interactions, such as arbitrary Lagrange-Euler methods, coupled Euler-Lagrange methods, small strain re-meshing and interpolation techniques, and sequential limit analysis, also have the problem of not being well adapted to the stability analysis scenario of subsea pipelines.

[0004] In other words, existing stability analysis schemes for subsea pipelines have limitations in analytical accuracy, which hinders the analysis, construction, and maintenance of subsea pipelines. Summary of the Invention

[0005] This application provides a method for analyzing the stability of subsea pipelines based on the mathematically optimized particle finite element method. A novel stability analysis framework for subsea pipelines is specifically built and represented by a corresponding numerical model. This model can accurately simulate the interaction between waves, pipelines, and soil, and thus accurately analyze the stability of subsea pipelines. It provides high-quality data support for assessing the stability of subsea pipelines in real marine environments, thereby enabling better work in the analysis, construction, and maintenance of subsea pipelines.

[0006] Firstly, this application provides a method for stability analysis of subsea pipelines based on the mathematically optimized particle finite element method, the method comprising: After identifying the target subsea pipeline object for which stability analysis is required, the model input data is obtained for the pre-configured numerical model. Specifically, the numerical model is a dynamic saturated particle finite element model used to simulate the interaction between waves, pipelines, and soil. The model input data is input into the numerical model to simulate the interaction between waves, pipes, and soil. For the numerical model, under the set condition that a two-dimensional region is composed of saturated porous media and the boundary is defined by a closed surface, dynamic equilibrium equations, strain-displacement relationships, Darcy's law, mass conservation equations, boundary conditions, and elastoplastic relationships are pre-configured. Time and space discretization is performed, and a calculation framework based on the hybrid variational principle is adopted. The simulation results of the four consecutive stages of pipe penetration, consolidation, operation and wave loading are extracted from the numerical model output and output as the stability analysis results.

[0007] Secondly, this application provides a device for analyzing the stability of subsea pipelines based on the mathematically optimized particle finite element method. The device includes: The acquisition unit is used to acquire model input data corresponding to a pre-configured numerical model after the target subsea pipeline object for which stability analysis is required has been determined. Specifically, the numerical model is a dynamic saturated particle finite element model used to simulate the interaction between waves, pipeline and soil. The simulation unit is used to input model input data into the numerical model for simulation of wave-pipe-soil interaction. For the numerical model, under the set conditions of a two-dimensional region composed of saturated porous medium and the boundary defined by a closed surface, dynamic equilibrium equations, strain-displacement relationship, Darcy's law, mass conservation equation, boundary conditions and elastoplastic relationship are pre-configured, and time and space discretization is performed. A calculation framework based on the hybrid variational principle is adopted. The extraction unit is used to extract the simulation results of the four consecutive stages of pipe penetration, consolidation, operation and wave loading from the numerical model output, and output them as stability analysis results through the output unit.

[0008] Thirdly, this application provides a processing device, including a processor and a memory, wherein a computer program is stored in the memory, and the processor executes the method provided in the first aspect of this application when it invokes the computer program in the memory.

[0009] Fourthly, this application provides a computer-readable storage medium storing a plurality of instructions adapted for loading by a processor to execute the method provided in the first aspect of this application.

[0010] From the above, it can be concluded that this application has the following beneficial effects: Under the objective of subsea pipeline stability analysis, this application specifically constructs a novel subsea pipeline stability analysis framework and embodies it with a corresponding numerical model. It can accurately simulate the interaction between waves, pipelines, and soil, and thus accurately analyze the stability of subsea pipelines. This provides high-quality data support for assessing the stability of subsea pipelines in real marine environments, thereby enabling better work in the analysis, construction, and maintenance of subsea pipelines. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a schematic diagram of a method for analyzing the stability of subsea pipelines based on the mathematical optimization particle finite element method, as described in this application. Figure 2 This is a schematic diagram illustrating the region and boundary division of the saturated medium in this application. Figure 3 This is a schematic diagram of a node-based smoothing unit according to this application; Figure 4 For this application, from the time step arrive An example diagram of a PFEM program is used; Figure 5 This is a schematic diagram of a subsea pipeline stability analysis device based on the mathematical optimization particle finite element method of this application. Figure 6 This is a schematic diagram of one type of processing equipment used in this application. Detailed Implementation

[0013] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0014] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or modules is not necessarily limited to those explicitly listed, but may include other steps or modules not explicitly listed or inherent to such processes, methods, products, or devices. The naming or numbering of steps appearing in this application does not imply that the steps in the method flow must be performed in the chronological / logical order indicated by the naming or numbering. The execution order of named or numbered process steps can be changed according to the desired technical purpose, as long as the same or similar technical effect is achieved.

[0015] The module division described in this application is a logical division. In practical applications, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. In addition, the coupling or direct coupling or communication connection between modules shown or discussed may be through some interfaces, and the indirect coupling or communication connection between modules may be electrical or other similar forms, none of which are limited in this application. Furthermore, the modules or sub-modules described as separate components may or may not be physically separated, may or may not be physical modules, or may be distributed in multiple circuit modules. Some or all of the modules may be selected to achieve the purpose of the solution in this application according to actual needs.

[0016] Before introducing the stability analysis method for subsea pipelines based on mathematically optimized particle finite element method provided in this application, we will first introduce the background content involved in this application.

[0017] The method, apparatus, and computer-readable storage medium for analyzing the stability of subsea pipelines based on the mathematically optimized particle finite element method provided in this application can be applied to processing equipment. A novel stability analysis framework for subsea pipelines is specifically built and embodied in a corresponding numerical model. It can accurately simulate the interaction between waves, pipelines, and soil, and thus accurately analyze the stability of subsea pipelines. This provides high-quality data support for assessing the stability of subsea pipelines in real marine environments, thereby enabling better work in the analysis, construction, and maintenance of subsea pipelines.

[0018] The subsea pipeline stability analysis method based on the mathematically optimized particle finite element method mentioned in this application can be implemented by a subsea pipeline stability analysis device based on the mathematically optimized particle finite element method, or by different types of processing devices such as servers, physical hosts, or user equipment (UE) that integrate the subsea pipeline stability analysis device based on the mathematically optimized particle finite element method. The subsea pipeline stability analysis device based on the mathematically optimized particle finite element method can be implemented in hardware or software. The UE can specifically be a terminal device such as a smartphone, tablet, laptop, desktop computer, or personal digital assistant (PDA). The processing devices can be configured in a device cluster.

[0019] It is understandable that the proposed solution is usually based on existing data or data that has already been collected. Therefore, the processing equipment that executes the submarine pipeline stability analysis method based on the mathematically optimized particle finite element method of this application, or that carries the corresponding application service of the submarine pipeline stability analysis method based on the mathematically optimized particle finite element method of this application, usually only needs to meet the required data processing capabilities. The specific equipment type and equipment deployment form are quite flexible.

[0020] If the direct collection of existing data mentioned above is involved, then further hardware and software adaptation configurations are needed for the processing equipment to enable it to acquire data. For example, if the existing data mentioned above needs to be collected in real time, the corresponding acquisition equipment can be incorporated into the equipment cluster of the processing equipment, or the processing equipment itself can be the control part of the acquisition equipment. Alternatively, a third-party call can be used to trigger the acquisition equipment outside the processing equipment to perform real-time data acquisition operations.

[0021] In addition, if there is a need to display the processing progress (including the processing results), the processing device itself can be configured with the required display screen (including touch screen) to display the specific content. Of course, the processing device can also display the specific content through an external display device or other devices with a display screen.

[0022] The following section introduces the stability analysis method for subsea pipelines based on the mathematically optimized particle finite element method provided in this application.

[0023] First, refer to Figure 1 , Figure 1This paper presents a flowchart illustrating a subsea pipeline stability analysis method based on the mathematically optimized particle finite element method of this application. The subsea pipeline stability analysis method based on the mathematically optimized particle finite element method provided in this application may specifically include the following steps S101 to S103: Step S101: After determining the target subsea pipeline object for which stability analysis is required, model input data is obtained corresponding to the pre-configured numerical model. Specifically, the numerical model is a dynamic saturated particle finite element model used to simulate the interaction between waves, pipeline and soil. Understandably, this application has specifically built a novel subsea pipeline stability analysis framework to meet the needs of subsea pipeline stability analysis, and it is represented by a corresponding numerical model. In the actual use of this numerical model, after determining the target subsea pipeline object for which stability analysis processing is required, the corresponding model input data can be obtained.

[0024] The acquisition and processing of model input data can involve manual entry of existing data, local / remote extraction of existing data, or real-time acquisition. As can be seen, the initial data acquisition process is quite flexible and can be configured according to the actual situation.

[0025] In practical applications, the proposed solution typically initiates stability analysis work on the target subsea pipeline object that needs to be processed, in the form of relevant work tasks or stability analysis tasks.

[0026] The specific methods for obtaining tasks can be manual initiation, automatic initiation by the system under the corresponding automatic initiation strategy, or receiving tasks sent / assigned by other devices.

[0027] For some or all of the model input data, it can either be included directly in the task information or obtained according to the instructions in the task information.

[0028] The numerical model constructed in this application can be understood to be a dynamic saturated particle finite element model used to simulate the interaction between waves, pipes, and soil. During the simulation process, the numerical model can process the corresponding stability analysis content and finally form and output the corresponding stability analysis results.

[0029] As an exemplary embodiment, for each target subsea pipeline object that will be updated or changed as the scheme is applied, the model input data obtained in step S101 may specifically include soil material property data, pipeline property parameter data, and multi-stage load and boundary condition data. Soil material property data may specifically include mechanical and hydraulic parameters, strain rate parameters describing the strength degradation behavior of soil under cyclic loading, and strain softening parameters describing the strength degradation behavior of soil under cyclic loading. Mechanical and hydraulic parameters may specifically include saturated density, elastic modulus, permeability coefficient, cohesion, and internal friction angle. Pipeline attribute parameters may specifically include parameters such as pipeline diameter, pipeline-soil interface roughness coefficient, initial burial depth of pipeline, and initial penetration depth of pipeline; The multi-stage load and boundary condition data specifically include parameters such as the initial gravity field, the vertical velocity of the pipeline during the penetration stage, the lateral motion path of the pipeline during the operation stage, the constant vertical load of the pipeline during the operation stage, and wave parameters, including wave height and wave period acting on the seabed surface during the wave load stage.

[0030] Furthermore, it should be noted that the aforementioned series of parameters are not directly reflected in the model content configured for the numerical model below. It can be understood that the numerical model of this application is a simulation process performed by substituting the aforementioned series of parameters of the target subsea pipeline object under the current conditions, based on the model content configuration specifically designed in this application.

[0031] Furthermore, regarding the above series of model input data, this application believes that, in addition to involving actual measurements, manual settings, or engineering defaults / fixed situations, simulation settings for encountering extreme situations can also be introduced in actual situations. This allows for attention to the impact of rare extreme situations under actual conditions during the solution processing, so as to better cope with and respond to them.

[0032] For example, the potential impacts of vertical displacement, seafloor uplift, or seafloor subsidence caused by sudden earthquakes can be considered. In addition to considering the basic time factor, the potential impacts of seabed soil and / or seawater on climate, season, marine biological activity, human activities, additional / extra seabed engineering, marine pollution, etc. can also be considered. The potential impacts of abnormal operations during the processing, transportation, penetration, and operation of subsea pipelines can also be considered. Furthermore, the possibility of misjudgment or false alarms during the data acquisition process itself can be taken into account.

[0033] Understandably, the simulation of extreme cases here can be further modified based on the initial model input data to obtain the final model input data.

[0034] Furthermore, the transformation process can involve manual operation, manual operation within the system's prompts for selectable simulation ranges (as guidance), and automatic system operation. For the latter, it is understandable that, in addition to operating in a sequential or random manner within the preset simulation settings, it can also be combined with other types of numerical models or machine learning models to perform more refined extreme condition generation processing, thereby applying more flexible transformations to the model input data that are better able to capture extreme situations.

[0035] For potential data modifications, corresponding identifiers can be used to indicate that the content of the current data item has been modified. This allows the model to highlight, view, or process the simulation results output or processed by the model. Alternatively, the original model input data and the modified model input data can be configured separately in the dataset, allowing subsequent models to perform simulation processing separately in the same data processing task. This provides a more intuitive way to view, compare, and analyze the simulation results under the two states.

[0036] Step S102: Input the model input data into the numerical model to simulate the interaction between waves, pipes, and soil. For the numerical model, under the set condition that a two-dimensional region is composed of saturated porous media and the boundary is defined by a closed surface, dynamic equilibrium equations, strain-displacement relationships, Darcy's law, mass conservation equations, boundary conditions, and elastoplastic relationships are pre-configured. Time and space discretization is performed, and a calculation framework based on the hybrid variational principle is adopted. Understandably, after obtaining the model input data corresponding to the numerical model of the current subsea pipeline stability analysis object, the model can be input to allow it to carry out the simulation of wave-pipeline-soil interaction (i.e., the interaction between waves, pipeline and soil) in order to achieve the goal of subsea pipeline stability analysis.

[0037] Among them, the simulation of the interaction between the three factors of waves, pipes and soil can involve the simulation of the interaction between the three factors at the same time, or it can involve the simulation of the interaction between two factors, such as the interaction between pipes and soil, or the interaction between waves and pipes.

[0038] Regarding the simulation processing that this numerical model can perform, which can accurately reproduce the actual situation, this application specifically includes several aspects of the model content, mainly: Under the given conditions that a two-dimensional region (V) is composed of a saturated porous medium and its boundary is defined by a closed surface (S), dynamic equilibrium equations, strain-displacement relationships, Darcy's law, mass conservation equations, boundary conditions, and elastoplastic relationships are pre-configured. The system is discretized in time and space and uses a computational framework based on the principle of mixed variation.

[0039] These aspects of the model lay a solid foundation for high-precision simulation. The following sections will elaborate on these aspects of the model in more detail: 1) For a two-dimensional region (V) consisting of a saturated porous medium, whose boundary is defined by a closed surface (S), the dynamic elastoplastic analysis can involve the following set of equations by adopting a simplified “up” form.

[0040] 1.1) The dynamic equilibrium equation can be specifically expressed as: , in, This represents the differential operator, and the superscript T indicates transpose. Indicates effective stress. Let [1; 1; 0] represent the vector. It is pore water pressure. Represents volume force. Indicates density, The derivative of acceleration, i.e., velocity (v), This represents a two-dimensional region (as mentioned in the settings above).

[0041] 1.2) The strain-displacement relationship can be specifically expressed as: , in, Indicates strain, Indicates displacement.

[0042] The model employs the small strain assumption at each time step, neglecting nonlinear second-order terms.

[0043] 1.3) Darcy's Law can be specifically expressed as: , in, , and These represent the fluid's density, unit weight, and volumetric force, respectively. Darcy's hydraulic conductivity is represented by his coefficient of performance. This indicates the apparent flow rate.

[0044] 1.4) The mass conservation equation can be specifically expressed as: , The above Substituted here This further eliminates the [something] within it. The corresponding ones are: .

[0045] 1.5) The boundary conditions can be specifically expressed as: , , , , in, This represents a matrix containing the components of the boundary outward normal vector. , , and These represent the specified traction force, displacement, pore pressure, and fluid flux, respectively. Indicates the boundary of external forces. Indicates the displacement boundary. Indicates the pore water pressure boundary. Indicates the fluid flux boundary; Here you can also refer to Figure 2 The diagram shown illustrates a region of saturated medium and its boundary delineation in this application.

[0046] In the numerical model, wave load conditions are applied by specifying pore water pressure at the top surface, and a sine function is used to simulate the effect of propagating sine waves on the seabed, corresponding to: , , in, Indicates pore water pressure, Indicates the given wave pressure amplitude. Indicates wave number, Represents the horizontal coordinate. Indicates wave frequency. Indicates time, This indicates the unit weight of water. represents the wave height, Indicates water depth.

[0047] It is also worth noting that when simulating soil completely submerged in water, if the presence of a water layer is not considered, the effective vertical normal stress on the top surface will be zero. Correspondingly, according to the above formula... This boundary condition can be achieved in the following two ways: Apply a traction force to the top surface , making , Add an additional item at the same time , making .

[0048] As can be seen from the boundary condition settings here, in terms of boundary condition processing, this application ensures that physically realistic results can be obtained regardless of the input method, thereby improving the reliability of input conditions.

[0049] 1.5) The elastoplastic relationship can be specifically expressed as: , , in, Represents the yield function. Indicates elastic strain. Indicates plastic strain, Represents the flexibility matrix. Indicates plastic multiplier, It represents plastic potential.

[0050] Furthermore, for the elastoplastic relationship, the corresponding flow rules assume... The two equations above the elastoplastic relationship are... and The complementary condition is expressed by the following formula: , Here, △ represents the change operation symbol.

[0051] The above governing equations take into account the dynamic analysis of saturated media, and can be further simplified to total stress analysis under undrained conditions and effective stress analysis neglecting seepage effects.

[0052] Therefore, by simplifying the dynamic analysis that originally considered the saturated medium into a total stress analysis under undrained conditions and an effective stress analysis that neglects seepage effects, the governing equations for the effective stress analysis can omit the expression for Darcy's law (i.e., ), and replace the expression of the mass conservation equation with the following formula (i.e. To restore: , in, The bulk modulus of a pore fluid corresponds to, or in other words means, the condition of complete incompressibility. .

[0053] 2) Time and space discretization 2.1) Time Discretization Processing Time discretization can be specifically implemented using... The Theta method for effective stress ( ),speed( ) and pore water pressure ( Discretization is performed, and the corresponding methods are: , , , Where the subscript n represents the known state, and the subscript n+1 represents the unknown state. Indicates the time step. , and This represents different numerical parameters, with values ​​ranging from 0 to 1.

[0054] Substitute the three discretized equations above into the previous equilibrium equation. Boundary condition equations and boundary condition equations Therefore, the time discretization process here can be further expressed as: , , , , , , In this model, the superscript Inter indicates intermediate terms. These field variables are discretized using a backward Euler scheme. .

[0055] 2.2) Spatial Discretization Processing Spatial discretization can be achieved using efficient three-node triangular elements for finite element discretization. A nodal integration scheme is then applied to the constructed smooth element. Using standard finite element notation, the displacement field is approximated as follows: , Where u represents the displacement field, and the cap symbol ˆ represents the field variable at the grid node. This represents a matrix containing linear interpolation shape functions.

[0056] Strain tensor on finite element method Further expressed as: , The linear shape function used can generate a uniform strain tensor within each three-node triangular element. strain tensor This is further used to evaluate the so-called smoothed strain at each mesh node by calculating the strain-weighted average within the smoothed element, such as... Figure 3As shown in the schematic diagram of a node-based smoothing element of this application, the centroid of each triangle is connected to the midpoint nodes of its three sides, forming a smoothing element. (That is, a triangle will be divided into three smooth units based on the midpoints of its three sides and its centroid.) Therefore, the smooth strain at the k-th node (or the strain within the k-th smooth element) can be expressed as: , in, This represents the smooth strain at the k-th node, where k represents the k-th smoothing element. Area, smoothing unit It is formed by connecting the centroid of the corresponding triangle and its three midpoint nodes. This indicates the number of cells used to construct the smooth element. , and They represent the first The first smoothing unit involved in the The area, strain gradient matrix, and nodal displacement of a linear triangular element.

[0057] The above formula can be further expressed as: , in, This is the smoothed strain gradient matrix.

[0058] Other home-field variables, including effective stress pore water pressure and inertial force It is also assumed that it is uniform within each smooth unit, that is, we have: , The overline represents the average value at the smoothing cell (i.e., the value at the grid node associated with that smoothing cell). For simplicity, the numerical model also introduces an intermediate variable. .

[0059] 3) Computational Framework The computational framework based on the Hellinger-Reissner variational principle integrates the governing equations into a single function, and the relevant Lagrangian function is expressed as follows: , In terms of details, the Lagrange functional described above can be verified by deriving the Carlow-Kun-Tucker (KKT) conditions.

[0060] 3.1) Optimization problem In terms of specific solutions, the hybrid variational principle, i.e., the above computational framework, can be reformulated as a minimax optimization problem, which can be specifically expressed as: , In this application, considering the node-based smoothing technique employed, all matrices in the above minimax problem expression are evaluated on smoothing units, and the expressions for these matrices and vectors can be represented as: , in, Represents the identity matrix; The computational framework based on the hybrid variational principle also maps the yield condition to a cone constraint, which is then efficiently solved using the interior point method, as follows: , The underlined items are equivalent to standard rotational quadratic constraints and yield functions. It can also be reformulated as cone constraints with different criteria. Then, the discretized control equations involved in the above time and space discretization process can be solved using the interior point algorithm available in the optimization solver.

[0061] In this way, by uniformly expressing the complex elastoplastic constitutive relations as mathematical "cone constraints" within the framework of second-order cone programming, users only need to input parameters according to their physical meaning without worrying about complex iterative convergence problems. This ensures the numerical stability and computational efficiency of the output results in multi-timescale analysis and greatly enhances the robustness when using complex constitutive models.

[0062] 3.2) Particle Finite Element Method (PFEM) The computational framework based on the hybrid variational principle can specifically employ the particle finite element method to solve the mesh distortion problem encountered by the classical Lagrange finite element method in large deformation problems.

[0063] In practice, the α-shape method is used to identify the evolutionary boundaries of the computational domain. Boundary identification is performed by removing unnecessary cells from the mesh generated by Delauna triangulation using updated mesh nodes. During this process, the improved α-shape method also generates a new mesh.

[0064] It should be noted that the quality of the obtained mesh may not meet the requirements of finite element analysis. Therefore, this application can also perform a re-meshing operation on the identified region to generate a high-quality mesh; or, the typical smoothing technique in the smooth finite element method can be used to reduce the requirements for mesh quality and avoid repeated meshing operations. This greatly reduces the stringent requirements for the quality of the initial mesh, and the model will automatically handle the mesh distortion problem during the calculation process, so that the user does not need to spend a lot of effort to generate a perfect mesh.

[0065] Understandably, the numerical model employs node-based smoothing techniques (i.e., spatial discretization) to construct the particle finite element method (PFEM) framework. In each step of the PFEM analysis, reference... Figure 4 The present application is shown from the time step arrive The example diagram of the PFEM program used includes the following calculation steps: (i) Corresponding Figure 4 In part a, the computational domain is represented using a node cloud (particle); (ii) Corresponding Figure 4 In part b, the α-shape method is used to identify the computational domain, thereby obtaining a triangular cell mesh; (iii) Corresponding Figure 4 In part c, construct smooth units; (iv) Perform optimization-based finite element analysis, i.e., solve the minimax problem mentioned above; (v) Corresponding Figure 4 In the d part, update the field variables of all grid nodes, for example, update the grid node positions using the solved incremental displacements.

[0066] In this model, large deformation analysis is achieved through a series of small deformation analyses, i.e., using a Lagrangian description and applying the micro-strain assumption (i.e., the previous formula) by updating the geometry. ).

[0067] Furthermore, calibrated strain rate and strain softening relationships can be incorporated into the numerical model to update the undrained shear strength during remodeling. The corresponding empirical expression is as follows: , , , , in, Indicates strain rate effect; Used to account for strain softening effect Indicates the reference shear strain rate before any softening occurs. Undrained shear strength This represents the rate of increase in shear strength per logarithmic cycle. Indicates the maximum shear strain rate. Indicates incremental principal strain. Indicates secondary principal strain. Indicates incremental displacement. Indicates the pipe penetration rate. This represents the ratio of complete remodeling to initial shear strength (i.e., remodeling sensitivity). (the reciprocal of) Represents the cumulative absolute plastic shear strain. This indicates that the reshaping resulted in When reduced by 95% value.

[0068] Step S103: Extract the simulation results of the four consecutive stages of pipe penetration, consolidation, operation and wave loading from the numerical model output, and output them as stability analysis results.

[0069] Understandably, a numerical model used to simulate the interaction between waves, pipes, and soil can output four consecutive stages formed during the simulation process: pipe penetration, consolidation, operation, and wave loading. In this case, the simulation results of these four consecutive stages can be extracted, and the corresponding output processing can be performed according to the specific application requirements of the scheme.

[0070] In the output stage, the model can simultaneously output multi-physics field data such as displacement, strain, pore pressure, and stress. It can also continue to dynamically visualize the evolution of free surfaces through the particle finite element method, intuitively displaying the entire process of pipe penetration, lateral movement, and seabed deformation.

[0071] Specifically, as an exemplary embodiment, the simulation results output by the model for the four consecutive stages of pipe penetration, consolidation, operation, and wave loading can include macroscopic mechanical response, soil condition visualization results, dynamic response of pore water pressure, and full life cycle time history diagrams. Correspondingly, these include: The macroscopic mechanical response can specifically include the curve of vertical resistance as a function of depth during pipe penetration, as well as the evolution of horizontal resistance as a function of lateral displacement and time under operational and wave loads. These curves are the direct evidence of pipe stability. The visualization results of soil conditions can specifically include equivalent plastic strain cloud maps, which can clearly show the formation and development of soil shear zones around the pipeline and reveal potential instability modes. The dynamic response of pore water pressure can specifically include the spatial distribution of excess pore water pressure and its dissipation over time, which is key to judging soil drainage conditions and predicting liquefaction or strength softening. The full life cycle time history diagram is specifically displayed on a logarithmic time axis spanning from seconds to years, integrating and showing the changes in soil resistance throughout the entire process from rapid penetration and long-term consolidation operation to instantaneous wave loading, thus intuitively reflecting the coupling effect of physical processes at different time scales.

[0072] In specific output processing, specific actions can be taken such as local storage, off-site storage, result display, result push, output completion prompts, or further data analysis.

[0073] It is understandable that the specific output processing can be flexibly adjusted according to the pre-configured and real-time output settings.

[0074] As is easy to understand, submarine pipelines refer to pipeline systems laid on the seabed for transporting liquids, gases or solid particles, and are widely used in offshore oil and gas extraction, submarine cable protection, seawater desalination and cross-sea bridge construction.

[0075] In terms of further applications, it is understood that this could involve the analysis, construction, and maintenance of submarine pipeline projects.

[0076] As an example, after obtaining the stability analysis results of the current target subsea pipeline, the daily maintenance work of the subsea pipeline can be carried out based on the stability analysis results, combined with the corresponding alarm thresholds or alarm change characteristics, to monitor / determine whether the current situation meets the alarm triggering conditions. If it does, obviously, the alarm can be output immediately according to the preset alarm output scheme, so that relevant systems or personnel can respond in a timely manner to avoid losses or effectively reduce losses.

[0077] In the specific alarm output mechanism, multi-level alarm output can also be involved to adapt the alarm output to different severity situations, thereby helping to promote a more appropriate response in the first time in actual situations.

[0078] In conclusion, regarding the above-mentioned solutions, under the objective of subsea pipeline stability analysis, this application has specifically constructed a novel subsea pipeline stability analysis framework and embodied it with a corresponding numerical model. This framework can accurately simulate the interaction between waves, pipelines, and soil, thereby accurately analyzing the stability of subsea pipelines. It provides high-quality data support for assessing the stability of subsea pipelines in real marine environments, and thus better facilitates the analysis, construction, and maintenance of subsea pipelines.

[0079] In terms of details, the specific beneficial effects of this application are as follows: 1. The pipeline lifecycle involves a huge time span from seconds (wave loading, rapid penetration) to years (consolidation, slow lateral creep), and the model can dynamically adjust the calculation step size to adapt to the speed of different physical processes.

[0080] 2. The model is a fully coupled hydrodynamic framework that naturally reflects the transition of the drainage state by solving the generation and dissipation of pore water pressure (Darcy's law and the mass conservation equation). The empirical strain rate and softening model enables the model to dynamically update the soil strength and simulate the evolution of material properties.

[0081] 3. Pipe penetration and lateral sliding can cause soil flow, heave, and even the formation of scour gullies, involving severe mesh distortion and free surface changes. To achieve large deformation analysis, mesh distortion is handled by moving nodes and re-meshing, ensuring the robustness of the calculation. At the solution level, the model incorporates node-based smooth strain technology to improve accuracy and avoid lock-up.

[0082] 4. During the pipeline's lifecycle, boundary conditions can change drastically, such as the sudden application of periodic wave loads from hydrostatic pressure. A hybrid variational principle is used to simultaneously and accurately solve for displacement and stress fields, and the problem is ultimately reconstructed into an optimization problem based on implicit second-order cone programming. An interior-point algorithm is used for efficient and stable solution. This implicit scheme allows for a large time step, thus ensuring computational efficiency.

[0083] The above is an introduction to the subsea pipeline stability analysis method based on the mathematically optimized particle finite element method provided in this application. To facilitate better implementation of the subsea pipeline stability analysis method based on the mathematically optimized particle finite element method provided in this application, this application also provides a subsea pipeline stability analysis device based on the mathematically optimized particle finite element method from the perspective of functional modules.

[0084] See Figure 5 , Figure 5 This is a schematic diagram of a subsea pipeline stability analysis device based on the mathematically optimized particle finite element method of this application. In this application, the subsea pipeline stability analysis device 500 based on the mathematically optimized particle finite element method may specifically include the following structure: The acquisition unit 501 is used to acquire model input data corresponding to a pre-configured numerical model after the target subsea pipeline object for which stability analysis processing is required has been determined. Specifically, the numerical model is a dynamic saturated particle finite element model used to simulate the interaction between waves, pipeline and soil. Simulation unit 502 is used to input model input data into the numerical model for simulation of wave-pipe-soil interaction. The numerical model is pre-configured with dynamic equilibrium equations, strain-displacement relationships, Darcy's law, mass conservation equations, boundary conditions, and elastoplastic relationships in a two-dimensional region composed of saturated porous media and defined by closed surfaces. It is discretized in time and space and adopts a computational framework based on the hybrid variational principle. Extraction unit 503 is used to extract the simulation results of the four consecutive stages of pipe penetration, consolidation, operation and wave loading from the numerical model output, and output them as stability analysis results through output unit 504.

[0085] In one exemplary embodiment, the model input data may specifically include soil material property data, pipeline property parameter data, and multi-stage loads and boundary conditions. Soil material property data include mechanical and hydraulic parameters, strain rate parameters describing the strength degradation behavior of soil under cyclic loading, and strain softening parameters describing the strength degradation behavior of soil under cyclic loading. The mechanical and hydraulic parameters include saturated density, elastic modulus, permeability coefficient, cohesion, and internal friction angle. Pipeline attribute parameters may specifically include pipeline diameter, pipeline-soil interface roughness coefficient, initial burial depth of pipeline, and initial penetration depth of pipeline. The multi-stage load and boundary condition data specifically include the initial gravity field, the vertical velocity of the pipeline during the penetration stage, the lateral motion path of the pipeline during the operation stage, the constant vertical load of the pipeline during the operation stage, and wave parameters, including the wave height and wave period acting on the seabed surface during the wave load stage.

[0086] In yet another exemplary embodiment, the dynamic equilibrium equation is expressed as: , in, This represents the differential operator, and the superscript T indicates transpose. Indicates effective stress. Let [1; 1; 0] represent the vector. It is pore water pressure. Represents volume force. Indicates density, Indicates acceleration. Represents a two-dimensional region; The strain-displacement relationship is expressed as: , in, Indicates strain, Indicates displacement; Darcy's Law is expressed as: , in, , and These represent the fluid's density, unit weight, and volumetric force, respectively. Darcy's hydraulic conductivity is represented by his coefficient of performance. Indicates apparent flow rate; The mass conservation equation is expressed as: ; The boundary conditions are expressed as follows: , , , , in, This represents a matrix containing the components of the boundary outward normal vector. , , and These represent the specified traction force, displacement, pore pressure, and fluid flux, respectively. Indicates the boundary of external forces. Indicates the displacement boundary. Indicates the pore water pressure boundary. Indicates the fluid flux boundary; Wave loading conditions are applied by specifying pore water pressure on the top surface, and the effect of propagating sine waves on the seabed is simulated using a sine function, corresponding to: , , in, Indicates pore water pressure, Indicates the given wave pressure amplitude. Indicates wave number, Represents the horizontal coordinate. Indicates wave frequency. Indicates time, This indicates the unit weight of water. represents the wave height, Indicates water depth. Apply a traction force to the top surface , making At the same time, add an extra item , making , The elastic-plastic relationship is expressed as: , , in, Represents the yield function. Indicates elastic strain. Indicates plastic strain, Represents the flexibility matrix. Indicates plastic multiplier, It represents plastic potential.

[0087] In yet another exemplary embodiment, for an elastoplastic relationship, it is assumed that... The complementary condition is expressed by the following formula: , Here, △ represents the change operation symbol.

[0088] In yet another exemplary embodiment, by simplifying the dynamic analysis that originally considered the saturated medium into a total stress analysis under undrained conditions and an effective stress analysis that ignores seepage effects, the expression for Darcy's law is omitted, and the expression for the mass conservation equation is replaced with the following equation to restore the original expression: , in, The bulk modulus of a pore fluid corresponds to the condition of complete incompressibility. .

[0089] In yet another exemplary embodiment, the time discretization process employs... The method discretizes the effective stress, velocity, and pore water pressure. Spatial discretization is performed using three-node triangular elements for finite element discretization, and nodal integration is applied to the constructed smooth elements. , and inertial force It is assumed that the smoothing is uniform within each smoothing unit; The computational framework based on the hybrid variational principle is reformulated as a minimax optimization problem; The computational framework based on the hybrid variational principle maps the yield condition to a cone constraint and finally solves it efficiently using the interior point method. The computational framework based on the hybrid variational principle uses the particle finite element method to solve the mesh distortion problem encountered by the classical Lagrange finite element method in large deformation problems.

[0090] In yet another exemplary embodiment, the simulation results for the four stages include macroscopic mechanical response, soil condition visualization results, dynamic response of pore water pressure, and full life cycle time history. The macroscopic mechanical response includes the curve of vertical resistance as a function of depth during pipe penetration, as well as the evolution of horizontal resistance as a function of lateral displacement and time under operational and wave loads. Soil condition visualization results can include equivalent plastic strain contour maps; The dynamic response of pore water pressure includes the spatial distribution of excess pore water pressure and the process of excess pore water pressure dissipating over time. The full life cycle time history diagram integrates and displays the changes in soil resistance throughout the entire process, from rapid penetration and long-term consolidation operation to instantaneous wave loading, on a logarithmic time axis spanning from seconds to years.

[0091] This application also provides a processing device from a hardware architecture perspective, see [link / reference]. Figure 6 , Figure 6 This diagram illustrates a structural schematic of the processing device of this application. Specifically, the processing device may include a processor 601, a memory 602, and an input / output device 603. The processor 601 executes the computer program stored in the memory 602 to implement, for example... Figure 1 The corresponding embodiments describe the steps of the subsea pipeline stability analysis method based on the mathematically optimized particle finite element method; or, when the processor 601 executes the computer program stored in the memory 602, it implements the following: Figure 5 Corresponding to the functions of each unit in the embodiment, the memory 602 is used to store the functions executed by the processor 601 as described above. Figure 1 The computer program required for the stability analysis method of subsea pipelines based on the mathematically optimized particle finite element method in the corresponding embodiment.

[0092] For example, a computer program may be divided into one or more modules / units, one or more of which are stored in memory 602 and executed by processor 601 to complete this application. One or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in a computer device.

[0093] The processing device may include, but is not limited to, processor 601, memory 602, and input / output device 603. Those skilled in the art will understand that the illustrations are merely examples of the processing device and do not constitute a limitation on the processing device. It may include more or fewer components than illustrated, or combine certain components, or different components. For example, the processing device may also include network access devices, buses, etc., and processor 601, memory 602, input / output device 603, etc., are connected via a bus.

[0094] Processor 601 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. Processor 601 is the control center of the processing device, connecting various parts of the entire device through various interfaces and lines.

[0095] The memory 602 can be used to store computer programs and / or modules. The processor 601 implements various functions of the computer device by running or executing the computer programs and / or modules stored in the memory 602 and by calling data stored in the memory 602. The memory 602 may mainly include a program storage area and a data storage area. The program storage area may store the operating system, application programs required for at least one function, etc.; the data storage area may store data created according to the use of the processing device, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, RAM, plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0096] When processor 601 executes a computer program stored in memory 602, it can specifically perform the following functions: After identifying the target subsea pipeline object for which stability analysis is required, the model input data is obtained for the pre-configured numerical model. Specifically, the numerical model is a dynamic saturated particle finite element model used to simulate the interaction between waves, pipelines, and soil. The model input data is input into the numerical model to simulate the interaction between waves, pipes, and soil. For the numerical model, under the set condition that a two-dimensional region is composed of saturated porous media and the boundary is defined by a closed surface, dynamic equilibrium equations, strain-displacement relationships, Darcy's law, mass conservation equations, boundary conditions, and elastoplastic relationships are pre-configured. Time and space discretization is performed, and a calculation framework based on the hybrid variational principle is adopted. The simulation results of the four consecutive stages of pipe penetration, consolidation, operation and wave loading are extracted from the numerical model output and output as the stability analysis results.

[0097] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the subsea pipeline stability analysis device, processing equipment, and its corresponding units based on the mathematically optimized particle finite element method described above can be found in the following reference: Figure 1 The description of the stability analysis method for subsea pipelines based on the mathematically optimized particle finite element method in the corresponding embodiment will not be repeated here.

[0098] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be performed by instructions, or by instructions controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor.

[0099] Therefore, this application provides a computer-readable storage medium storing a plurality of instructions that can be loaded by a processor to execute the present application. Figure 1 The steps of the subsea pipeline stability analysis method based on the mathematically optimized particle finite element method in the corresponding embodiment can be referred to as follows for specific operations. Figure 1 The description of the stability analysis method for subsea pipelines based on the mathematically optimized particle finite element method in the corresponding embodiment will not be repeated here.

[0100] The computer-readable storage medium may include: read-only memory (ROM), random access memory (RAM), disk or optical disk, etc.

[0101] Because of the instructions stored in the computer-readable storage medium, the present application can be executed as described above. Figure 1 The steps of the subsea pipeline stability analysis method based on the mathematically optimized particle finite element method in the corresponding embodiment can therefore achieve the results of this application. Figure 1 The beneficial effects that the subsea pipeline stability analysis method based on the mathematically optimized particle finite element method can achieve in the corresponding embodiment are detailed in the preceding description and will not be repeated here.

[0102] The above provides a detailed description of the method, apparatus, processing equipment, and computer-readable storage medium for stability analysis of subsea pipelines based on the mathematically optimized particle finite element method provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for stability analysis of subsea pipelines based on mathematically optimized particle finite element method, characterized in that, The method includes: After identifying the target subsea pipeline object for which stability analysis is required, model input data is obtained corresponding to the pre-configured numerical model, wherein the numerical model is specifically a dynamic saturated particle finite element model for simulating wave-pipe-soil interaction. The model input data is input into the numerical model to simulate the wave-pipe-soil interaction. The numerical model is pre-configured with dynamic equilibrium equations, strain-displacement relationships, Darcy's law, mass conservation equations, boundary conditions, and elastoplastic relationships in a two-dimensional region composed of saturated porous media and defined by closed surfaces. It is discretized in time and space and uses a computational framework based on the hybrid variational principle. The simulation results of the four consecutive stages of pipe penetration, consolidation, operation and wave loading output by the numerical model are extracted and output as the stability analysis results.

2. The method according to claim 1, characterized in that, The model input data includes soil material property data, pipeline property parameter data, and multi-stage loads and boundary conditions. The soil material property data includes mechanical and hydraulic parameters, strain rate parameters describing the strength degradation behavior of the soil under cyclic loading, and strain softening parameters describing the strength degradation behavior of the soil under cyclic loading. The mechanical and hydraulic parameters include saturated density, elastic modulus, permeability coefficient, cohesion, and internal friction angle. The pipeline attribute parameter data includes pipeline diameter, pipeline-soil interface roughness coefficient, initial burial depth of pipeline, and initial penetration depth of pipeline. The multi-stage load and boundary condition data include the initial gravity field, the vertical velocity of the pipeline during the penetration stage, the lateral motion path of the pipeline during the operation stage, the constant vertical load of the pipeline during the operation stage, and wave parameters, including the wave height and wave period acting on the seabed surface during the wave load stage.

3. The method according to claim 1, characterized in that, The dynamic equilibrium equation is expressed as: ， in, This represents the differential operator, and the superscript T indicates transpose. Indicates effective stress. Let [1; 1; 0] represent the vector. It is pore water pressure. Represents volume force. Indicates density, Indicates acceleration. This represents the two-dimensional region; The strain-displacement relationship is expressed as follows: ， in, Indicates strain, Indicates displacement; Darcy's law is expressed as follows: ， in, , and These represent the fluid's density, unit weight, and volumetric force, respectively. Darcy's hydraulic conductivity is represented by his coefficient of performance. Indicates apparent flow rate; The mass conservation equation is expressed as: ； The boundary conditions are expressed as follows: ， ， ， ， in, This represents a matrix containing the components of the boundary outward normal vector. , , and These represent the specified traction force, displacement, pore pressure, and fluid flux, respectively. Indicates the boundary of external forces. Indicates the displacement boundary. Indicates the pore water pressure boundary. Indicates the fluid flux boundary; Wave loading conditions are applied by specifying pore water pressure on the top surface, and the effect of propagating sine waves on the seabed is simulated using a sine function, corresponding to: ， ， in, This represents the pore water pressure. Indicates the given wave pressure amplitude. Indicates wave number, Represents the horizontal coordinate. Indicates wave frequency. Indicates time, This indicates the unit weight of water. represents the wave height, Indicates water depth. Apply a traction force to the top surface , making At the same time, add an extra item , making , The elastic-plastic relationship is expressed as: ， ， in, Represents the yield function. Indicates elastic strain. Indicates plastic strain, Represents the flexibility matrix. Indicates plastic multiplier, It represents plastic potential.

4. The method according to claim 3, characterized in that, For the aforementioned elastoplastic relationship, it is assumed that... The complementary condition is expressed by the following formula: ， Here, △ represents the change operation symbol.

5. The method according to claim 4, characterized in that, By simplifying the dynamic analysis that originally considered the saturated medium into a total stress analysis under undrained conditions and an effective stress analysis that ignores seepage effects, the expression for Darcy's law is omitted, and the expression for the mass conservation equation is replaced by the following equation for restoration: ， in, The bulk modulus of a pore fluid corresponds to the condition of complete incompressibility. .

6. The method according to claim 3, characterized in that, Time discretization processing adopts The method discretizes the effective stress, velocity, and pore water pressure. Spatial discretization is performed using three-node triangular elements for finite element discretization, and nodal integration is applied to the constructed smooth elements. , and inertial force It is assumed that the smoothing is uniform within each of the smoothing units; The computational framework based on the aforementioned hybrid variational principle is reformulated as a minimax optimization problem; The computational framework based on the aforementioned hybrid variational principle maps the yield condition to a cone constraint and ultimately solves it efficiently using the interior point method. The computational framework based on the hybrid variational principle employs the particle finite element method to solve the mesh distortion problem encountered by the classical Lagrange finite element method in large deformation problems.

7. The method according to claim 1, characterized in that, The simulation results for the four stages include macroscopic mechanical response, soil condition visualization results, dynamic response of pore water pressure, and full life cycle time history diagram; The macroscopic mechanical response includes the curve of vertical resistance as a function of depth during pipe penetration, and also includes the evolution of horizontal resistance as a function of lateral displacement and time under the loads of the operation and the waves. The soil condition visualization results may include an equivalent plastic strain cloud map; The dynamic response of pore water pressure includes the spatial distribution of excess pore water pressure and the process of the excess pore water pressure dissipating over time. The full life cycle time history diagram integrates and displays the changes in soil resistance throughout the entire process, from rapid penetration and long-term consolidation operation to instantaneous wave loading, on a logarithmic time axis spanning from seconds to years.

8. A device for analyzing the stability of subsea pipelines based on the mathematically optimized particle finite element method, characterized in that, The device includes: The acquisition unit is used to acquire model input data corresponding to a pre-configured numerical model after determining the target subsea pipeline object for which stability analysis is required. Specifically, the numerical model is a dynamic saturated particle finite element model used to simulate the interaction between waves, pipelines, and soil. The simulation unit is used to input the model input data into the numerical model to simulate the wave-pipe-soil interaction. The numerical model is configured with dynamic equilibrium equations, strain-displacement relationships, Darcy's law, mass conservation equations, boundary conditions, and elastoplastic relationships in a two-dimensional region composed of saturated porous media and defined by closed surfaces. It is discretized in time and space and adopts a calculation framework based on the hybrid variational principle. The extraction unit is used to extract the simulation results of the four consecutive stages of pipe penetration, consolidation, operation and wave loading from the numerical model, and output them as stability analysis results through the output unit.

9. A processing device, characterized in that, The method includes a processor and a memory, wherein the memory stores a computer program, and the processor executes the method as described in any one of claims 1 to 7 when it invokes the computer program in the memory.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a plurality of instructions adapted for loading by a processor to perform the method of any one of claims 1 to 7.

Images