A method for constructing an empirical formula for the ultimate embedment depth of a high-holding force anchor group

Abstract

The present invention relates to a method for constructing an empirical formula for the ultimate embedding depth of a large-holding anchor group. The method comprises the following steps: S1, establishing a solid model of a finite element model of the large-holding anchor group; S2, designing the working conditions of the finite element model in groups, and analyzing the influence of the seabed mooring chain loading angle #imgabs0#, the mooring chain dragging speed #imgabs1#, the undrained shear strength of the seabed soil surface #imgabs2#, and the undrained shear strength gradient #imgabs3# of the soil on the ultimate embedding depth of the large-holding anchor group; S3, obtaining the ultimate embedding depth of the large-holding anchor group based on the analysis results of all working conditions of the finite element model, and deriving the empirical formula #imgabs4# for the ultimate embedding depth of the large-holding anchor group through multivariate function fitting; and S4, setting verification working conditions through an orthogonal test method, comparing the empirical formula with the results of the finite element analysis, and verifying the reliability of the empirical formula.

Description

Technical Field

[0001] The present invention relates to the field of deep-sea anchoring technology design, and in particular to a method for constructing an empirical formula for the ultimate embedding depth of a large-holding-force anchor group. Background Art

[0002] As a drag-embedded plate anchor, the high-holding anchor is a key anchoring structure in deepwater mooring systems. Relying on the anchor plate to be dragged on the seabed and embedded in the soil to provide resistance, it can provide a reliable bottom-level positioning foundation for upper floating structures such as semi-submersible offshore platforms, floating offshore wind power platforms, deep-sea oil and gas production platforms, offshore airports, artificial floating islands, etc. It has excellent horizontal bearing capacity (up to 10,000 kN) and economic advantages.

[0003] In terms of their specific working mechanism, high-hold anchor systems are typically installed by towing mooring chains. Driven by the inverse catenary effect, they gradually embed into the seabed until they reach their designed embedment depth. This embedment depth directly determines whether the anchor can provide sufficient positioning bearing capacity for the floating superstructure. However, as modern offshore platforms continue to grow in size and depth, engineering applications are rapidly increasing the requirements for the bearing performance and deepwater installation performance of anchor structures. Traditional high-hold anchor systems face numerous practical bottlenecks, including: 1) In terms of anchor body motion characteristics, the accuracy of embedment trajectory prediction is insufficient, making it difficult to accurately determine the ultimate penetration depth; 2) In terms of bearing performance assessment, there is a lack of reliable bearing capacity prediction models, resulting in insufficient means to verify engineering reliability; 3) In terms of experimental research, the size effect of prototype anchors is significant, making field testing expensive and difficult to implement; and 4) In terms of numerical simulation, the soil-anchor interaction modeling is complex, making it difficult to accurately simulate dynamic anchor chain loads. These issues severely restrict the accuracy of performance prediction and assessment of high-hold anchor systems during the engineering design phase. Summary of the Invention

[0004] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is to provide a method for constructing an empirical formula for the ultimate embedding depth of a large-grip anchor group. According to the empirical formula, the ultimate embedding depth of a large-grip anchor group can be quickly predicted, the design process of the large-grip anchor group can be simplified, and the design cycle can be shortened.

[0005] To achieve the above object, the present invention provides a method for constructing an empirical formula for the ultimate embedding depth of a high-holding force anchor group, the method comprising the following steps:

[0006] S1. Establishing a solid model of a finite element model of a high-holding-power anchor assembly, wherein the high-holding-power anchor assembly includes a front high-holding-power anchor, a rear high-holding-power anchor, a mooring chain, and a connecting chain. The mooring chain and the connecting chain each include multiple anchor chains. The mooring chain is connected to the front end of the front high-holding-power anchor, one end of the connecting chain is connected to the rear end of the front high-holding-power anchor, and the other end is connected to the front end of the rear high-holding-power anchor.

[0007] S2. Design the finite element model in groups and analyze the loading angle of the mooring chain on the seabed , mooring chain drag speed , Undrained shear strength of seabed soil surface and undrained shear strength gradient of soil Impact on the ultimate embedment depth of high holding force anchor groups;

[0008] S3. Based on the analysis results of all working conditions of the finite element model, the ultimate embedment depth of the large holding force anchor group is obtained, and the empirical formula of the ultimate embedment depth of the large holding force anchor group is obtained through multivariate function fitting. ;

[0009] S4. Use the orthogonal test method to set up verification conditions, compare the empirical formula with the results of finite element analysis, and verify the reliability of the empirical formula.

[0010] Furthermore, the S1 specifically includes the following steps:

[0011] S11. Import the solid geometric models of the front and rear large holding anchors, mesh the solid geometric models of the front and rear large holding anchors, assign material properties to the solid geometric models, set a connecting component at the rear end of the front large holding anchor, set mooring points at the front ends of the front and rear large holding anchors, and set rigid body constraints using the mooring points as reference points.

[0012] S12. Construct simplified models of mooring chain and connecting chain: In the finite element model, construct The anchor chain solid geometry model of a mooring chain and The anchor chain solid geometry model is constrained by rigid body conditions, and binding constraint points and rigid body reference points are set at the front and rear ends respectively to construct The anchor chain solid geometric model of the mooring chain is connected in sequence by discrete line segments to form a simplified model of the mooring chain. The discrete line segments connect the anchor chain solid geometric models of the connection chain in sequence to form a simplified model of the connection chain, and give the discrete line segments connection properties;

[0013] S13. Connect the mooring chain and the front high-holding anchor: construct a new discrete line segment starting from the rear end of the rearmost discrete line segment in the simplified mooring chain model and connect it to the mooring point at the front end of the front high-holding anchor;

[0014] S14. Connect the front large holding anchor and the rear large holding anchor via a connecting chain: construct a new discrete line segment with the frontmost discrete line segment in the simplified model of the connecting chain as the starting point, and connect it to the connecting component at the rear end of the front large holding anchor. Then, construct a new discrete line segment with the rearmost discrete line segment in the simplified model of the connecting chain as the starting point, and connect it to the mooring point at the front end of the rear large holding anchor.

[0015] S15. Calculate the cable load angle of the mooring chain : Connect the anchor chain solid geometry model at the front end of the mooring chain simplified model to the cable. The connection point is the point where the mooring chain cable load is applied, and the cable load angle of the mooring chain is iteratively calculated through the cable equation. , the cable equation is given by:

[0016] (1)

[0017] Where, is the vertical depth coordinate of the point where the mooring chain cable load is applied; is the vertical coordinate of the seabed surface; is the normal soil resistance of the cable per unit length, ,in, is the bearing capacity coefficient of the cable in the soil, To correspond to the soil pressure at the cable burial depth, is the effective width of the cable; is the tension of the mooring chain; is the friction coefficient between the cable and the soil; is the seabed mooring chain loading angle, which is the angle between the tension of the mooring chain at the seabed and the horizontal plane;

[0018] S16. Apply cable load to the mooring chain: Load the mooring chain according to the cable load angle. , apply cable load to the anchor chain at the front end of the mooring chain, and calculate the mooring chain dragging speed through the horizontal coordinate increment and vertical depth coordinate increment of the mooring chain cable load application point at each time step By monitoring the coordinates of the mooring points of the large holding anchor group, the horizontal and vertical displacements of the large holding anchor group are obtained, thereby obtaining the embedding depth of the large holding anchor group;

[0019] S17, according to the tension of the mooring chain Recalculate the cable load angle of the mooring chain : According to the mooring chain drag speed Determining the tension in the mooring chain , if the mooring chain drag speed Greater than control speed , then reduce the tension of the mooring chain , and put it into formula (1) to recalculate the cable load angle of the mooring chain As the initial value of the next cable equation iteration calculation, if the mooring chain drag speed Less than control speed , then increase the tension of the mooring chain , and put it into formula (1) to recalculate the cable load angle of the mooring chain As the initial value for the next iterative calculation of the cable equation;

[0020] S18. Obtain the ultimate embedment depth of the high-holding anchor group :Cycle S15-S17 to simulate the dragging process of the large holding force anchor group until the maximum embedding depth of the large holding force anchor group is obtained .

[0021] Furthermore, the step S2 specifically includes the following steps:

[0022] S21. Working condition analysis: Set up four groups of working conditions in an orderly manner, and analyze the loading angle of the mooring chain on the seabed through the four groups of working conditions. , mooring chain drag speed , Undrained shear strength of seabed soil surface and undrained shear strength gradient of soil Impact on the ultimate embedment depth of high holding force anchor groups;

[0023] S22. Analysis of the first and second working conditions: Calculate the ultimate embedment depth of the high-holding anchor group under the first working condition and analyze the loading angle of the mooring chain on the seabed The influence of the maximum embedment depth of the large holding force anchor group is calculated, and the maximum embedment depth of the large holding force anchor group under the second working condition is analyzed, and the mooring chain drag speed is analyzed. Regarding the influence of the ultimate embedment depth of the high-holding anchor group, the seabed soil strength characteristics set in the first and second working conditions remain constant and serve as the reference conditions for the third and fourth working conditions;

[0024] S23, Analysis of the third and fourth working conditions: Calculate the ultimate embedment depth of the high-holding anchor group under the third working condition and analyze the undrained shear strength of the seabed soil surface The third working condition is set with the first and second working conditions as the benchmark working conditions. The ultimate embedment depth of the large holding force anchor group under the fourth working condition is calculated, and the undrained shear strength gradient of the soil is analyzed. The fourth group of working conditions is set based on the first, second and third groups of working conditions as the benchmark working conditions for the influence of the maximum embedment depth of the large holding force anchor group.

[0025] Furthermore, the step S3 specifically includes the following steps:

[0026] S31. Obtain analysis results for four groups of working conditions: Taking the embedment depth at which the dragging trajectory of the large holding force anchor group reaches a stable stage as its limit embedment depth, obtain analysis results for all working conditions;

[0027] S32. Fitting base surface: Based on the mooring chain loading angle on the seabed and mooring chain towing speed The analytical results are expressed using the binary Taylor series rational function The surface function of the maximum embedment depth of the large holding force anchor group is fitted. This surface function is used as the base surface of the empirical formula. The explicit expression of the surface function is as follows:

[0028] (2)

[0029] Where, is the normalized maximum embedment depth of the large holding force anchor group, which is given by The ratio of is obtained, where is the maximum embedment depth of the large holding force anchor group, is the anchor plate length of the high holding force anchor group; 、 、 、 、 、 、 、 、 and All are fitting coefficients;

[0030] S33. Factors affecting the calculation of undrained shear strength of seabed soil surface : It is the ratio of the ultimate embedment depth of the high holding force anchor group under the third group of working conditions to the ultimate embedment depth results of the corresponding benchmark working conditions in the first and second groups;

[0031] S34. Influencing factors of undrained shear strength of seabed soil surface fitted with high holding force anchor group :The influencing factors of undrained shear strength of seabed soil surface by fitting high holding force anchor groups through multivariate function The functional form is as follows:

[0032] (3)

[0033] Where, is the reference value of the undrained shear strength of the seabed surface, which is the undrained shear strength value of the seabed surface in the first group of working conditions and the second group of working conditions; is the fitting coefficient; The undrained shear strength of the seabed soil surface and is a two-variable Taylor series rational function of the variable;

[0034] S35. Factors affecting the calculation of undrained shear strength gradient of seabed soil : It is the ratio of the ultimate embedment depth of the large holding force anchor group under the fourth working condition to the ultimate embedment depth results of the corresponding benchmark working conditions in the first, second and third groups;

[0035] S36. Influencing factors of the undrained shear strength gradient of the seabed soil surface fitted with high holding force anchors :The influencing factors of undrained shear strength gradient of seabed soil surface for large holding force anchor group by multivariate function fitting , The functional form is as follows:

[0036] {F}_{k}\left ( {k,{s}_{u0},v,{\theta}_{e}} \right )=1+\left [ {{F}_{Taylor}\left ( {{\theta}_{e},k} \right )+A{s}^{2}_{u0}+B\left ( {k{\theta}_{e}{s}_{u0}+{C}^{2}} \right )+D\left ( {k{s}_{uo}{\theta}_{e}v+E} \right )} \right ]\left ( {k-{k}_{r}} \right ) (4)

[0037] Where k r is the reference value of the undrained shear strength gradient of the seabed surface, which is obtained by taking the undrained shear strength gradient values ​​of the seabed surface in the first, second and third groups of working conditions; 、 、 、 and All are fitting coefficients; Therefore and undrained shear strength gradient of soil is a two-variable Taylor series rational function of the variable;

[0038] S37. Obtain the normalized empirical formula for the ultimate embedment depth of the high-holding anchor group: Based on the base surface (Formula (2)), the influencing factor of the undrained shear strength of the seabed soil surface (Formula (3)) and the influencing factor of the gradient of undrained shear strength of seabed soil (Formula (4)), obtain the normalized empirical formula for the ultimate embedding depth of the large holding force anchor group: , The functional form is as follows:

[0039] (5).

[0040] Furthermore, the S4 includes: Orthogonal table, take 、 、 and Four factors are set with three parameter levels respectively. The results are obtained according to the empirical formula and compared with the results of finite element analysis to verify the reliability of the empirical formula.

[0041] Furthermore, the front high holding power anchor, the rear high holding power anchor, the mooring chain and the connecting chain are all constructed using Lagrangian units.

[0042] As described above, the method for constructing the empirical formula for the ultimate embedding depth of a high-holding force anchor group according to the present invention has the following beneficial effects:

[0043] 1. A database of the ultimate embedment depth of high-holding anchor groups is established based on coupled Euler-Lagrange large-deformation finite element analysis. Compared with small-deformation finite element simulation, this method can more accurately capture the complete drag trajectory of high-holding anchor groups. Compared with experimental methods, it can obtain large-scale, high-quality data at significantly reduced costs, providing reliable data support for engineering applications. Compared with traditional methods, it achieves efficient prediction of the ultimate embedment depth of high-holding anchor groups, significantly shortening the design cycle, simplifying the design process, and reducing design costs, with high engineering application value.

[0044] 2. The proposed empirical formula innovatively takes into account the loading angle of the mooring chain on the seabed , mooring chain drag speed , Undrained shear strength of seabed soil surface and undrained shear strength gradient of soil The main influencing factors of the BP neural network have wider engineering applicability and better prediction accuracy;

[0045] 3. The binary Taylor series rational function is used to construct the basis surface, so that the empirical formula has a concise mathematical expression while ensuring the calculation accuracy, which is convenient for application and promotion in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the process of constructing the empirical formula for the ultimate embedding depth of a high-holding-force anchor group in the present invention.

[0047] Figure 2 It is a structural schematic diagram of the high holding force anchor group in the present invention.

[0048] Figure 3It is a structural schematic diagram of the front high-holding force anchor in the present invention.

[0049] Figure 4 It is a structural schematic diagram of the rear high-holding force anchor in the present invention.

[0050] Figure 5 Schematic diagram of the connection between the anchor chain entity geometric model and the discrete line segments in the present invention.

[0051] Figure 6 This is a schematic diagram of the drag trajectory curve of the high-holding force anchor group analyzed by finite element analysis in the present invention.

[0052] Explanation of Figure Numbers

[0053] 10. Rear high-holding anchor, 11. Rear high-holding anchor mooring point, 20. Front high-holding anchor, 21. Front high-holding anchor mooring point, 22. Connecting components, 30. Connecting chain, 40. Mooring chain, 50. Anchor chain solid geometry model, 51. Binding constraint point, 52. Rigid body reference point, 60. Discrete line segment. DETAILED DESCRIPTION

[0054] The following is a further detailed description of the specific embodiments of the present invention in conjunction with the accompanying drawings. These embodiments are only used to illustrate the present invention, and are not intended to limit the present invention.

[0055] In the description of the present invention, it should be noted that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "back," "left," "right," "vertical," "horizontal," "top," "bottom," "inside," and "outside" and the like, indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate the description of the present invention and simplify the description. They do not indicate or imply that the devices or components referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0056] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0057] Furthermore, in the description of the present invention, unless otherwise specified, “plurality” means two or more.

[0058] See also Figures 1 to 6The present invention provides a method for constructing an empirical formula for the ultimate embedding depth of a large holding force anchor group, comprising the following steps:

[0059] S1. Establish a solid model of a finite element model of a large holding anchor group, wherein the large holding anchor group includes a front large holding anchor 20, a rear large holding anchor 10, a mooring chain 40, and a connecting chain 30. Preferably, the front large holding anchor 20 and the rear large holding anchor 10 are spaced apart in front and back; the mooring chain 40 and the connecting chain 30 each include multiple anchor chains, one end of the mooring chain 40 is connected to the front end of the front large holding anchor 20, and the other end is connected to the upper floating structure; one end of the connecting chain 30 is connected to the rear end of the front large holding anchor 20, and the other end is connected to the front end of the rear large holding anchor 10. Preferably, the front large holding anchor 20 is configured as a Delta anchor, and the rear large holding anchor 10 is configured as a Mk5 anchor; the seabed soil is regarded as homogeneous saturated clay, assumed to meet the Tresca yield criterion, and described using an Euler body;

[0060] S2. Design the finite element model in groups and analyze the loading angle of the mooring chain on the seabed , mooring chain drag speed , Undrained shear strength of seabed soil surface and undrained shear strength gradient of soil Impact on the ultimate embedment depth of high holding force anchor groups;

[0061] S3. Based on the analysis results of all working conditions of the finite element model, the ultimate embedment depth of the large holding force anchor group is obtained, and the empirical formula of the ultimate embedment depth of the large holding force anchor group is obtained through multivariate function fitting. ;

[0062] S4. Use the orthogonal test method to set up verification conditions, compare the empirical formula with the results of finite element analysis, and verify the reliability of the empirical formula.

[0063] The basic working principle of the method for constructing an empirical formula for the ultimate embedment depth of a large-holding anchor group involved in the present invention is as follows: by establishing a solid model of the finite element model of the large-holding anchor group, based on the coupled Euler-Lagrange large deformation finite element analysis method, the anchor-soil interaction mechanism can be accurately simulated; by grouping the working conditions of the finite element model, a numerical model considering the influence of multiple coupling factors can be established; by using a multivariate function to fit the empirical formula for the ultimate embedment depth of the large-holding anchor group, explicit expressions for the ultimate embedment depth of the front large-holding anchor 20 and the rear large-holding anchor 10 are respectively established, which can quickly predict the ultimate embedment depth of the large-holding anchor group, simplify the design process of the large-holding anchor group, and shorten the design cycle;

[0064] See also Figures 1 to 6 The present invention will be further described below with reference to a specific embodiment:

[0065] In this embodiment, see Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 and Figure 5 As a preferred design, S1 specifically includes the following steps:

[0066] S11. Importing the solid geometric models of the front large holding force anchor 20 and the rear large holding force anchor 10, meshing the solid geometric models of the front large holding force anchor 20 and the rear large holding force anchor 10, assigning material properties to the solid geometric models, providing a connecting component 22 at the rear end of the front large holding force anchor 20, providing mooring points at the front ends of the front large holding force anchor 20 and the front ends of the rear large holding force anchor 10, and setting rigid body constraints using the mooring points as reference points.

[0067] S12. Construct simplified models of the mooring chain 40 and the connecting chain 30: In the finite element model, construct Anchor chain solid geometry model 50 of a mooring chain 40 and The anchor chain solid geometric model 50 of the connecting chain 30 is preferably set as a cylinder with a length of 1.0m and a diameter of 0.2m. The anchor chain solid geometric model 50 is constrained by rigid body conditions, and binding constraint points 51 and rigid body reference points 52 are set at the front and rear ends respectively to construct The discrete line segments 60 connect the anchor chain solid geometric model 50 of the mooring chain 40 in sequence to form a simplified model of the mooring chain 40. The discrete line segments 60 sequentially connect the anchor chain solid geometric models 50 of the connection chain 30 to form a simplified model of the connection chain 30, and give the discrete line segments 60 connection properties;

[0068] S13. Connecting the mooring chain 40 and the front high-holding anchor 20: A new discrete line segment 60 is constructed with the rear end of the rearmost discrete line segment 60 in the simplified mooring chain model as the starting point, and connected to the mooring point at the front end of the front high-holding anchor 20. That is, the rigid reference point 52 on the rearmost anchor chain solid geometric model 50 in the simplified mooring chain model is connected to the mooring point at the front end of the front high-holding anchor 20 via the new discrete line segment 60.

[0069] S14. Connect the front large holding power anchor 20 and the rear large holding power anchor 10 through the connecting chain 30: construct a new discrete line segment 60 with the front end of the discrete line segment 60 in the simplified model of the connecting chain as the starting point, and connect it to the connecting component 22 at the rear end of the front large holding power anchor 20. Then, construct a new discrete line segment 60 with the rear end of the discrete line segment 60 in the simplified model of the connecting chain as the starting point, and connect it to the mooring point at the front end of the rear large holding power anchor 10. That is, connect the binding constraint point 51 on the anchor chain solid geometric model 50 at the front end of the simplified model of the connecting chain to the connecting component 22 at the rear end of the front large holding power anchor 20 through a new discrete line segment 60, and connect the rigid reference point 52 on the anchor chain solid geometric model 50 at the rear end of the simplified model of the connecting chain to the mooring point at the front end of the rear large holding power anchor 10 through a new discrete line segment 60.

[0070] S15. Calculate the cable load angle of the mooring chain : Connect the anchor chain solid geometry model 50 at the front end of the mooring chain simplified model to the cable. The connection point is the cable load application point of the mooring chain 40, and the cable load loading angle of the mooring chain is calculated iteratively through the cable equation. , the cable equation is given by:

[0071] (1)

[0072] Where, is the vertical depth coordinate of the point where the cable load of mooring chain 40 is applied; is the vertical coordinate of the seabed surface; is the normal soil resistance of the cable per unit length, ,in, is the bearing capacity coefficient of the cable in the soil, To correspond to the soil pressure at the cable burial depth, is the effective width of the cable, Take 0.2m; is the tension of the mooring chain 40; is the friction coefficient between the cable and the soil, and the value range for marine clay is 0.1~0.6; is the seabed mooring chain loading angle, which is the angle between the tension of the mooring chain 40 at the seabed and the horizontal plane;

[0073] S16, applying cable load to the mooring chain 40: applying cable load angle according to the mooring chain , apply a cable load to the anchor chain at the front end of the mooring chain 40, and calculate the mooring chain dragging speed by the horizontal coordinate increment and vertical depth coordinate increment of the cable load application point of the mooring chain 40 at each time step By monitoring the coordinates of the mooring points of the large holding anchor group, the horizontal and vertical displacements of the large holding anchor group are obtained, thereby obtaining the embedding depth of the large holding anchor group;

[0074] S17, according to the tension of the mooring chain 40 Recalculate the cable load angle of the mooring chain : According to the mooring chain drag speed Determine the tension in the mooring chain 40 , if the mooring chain drag speed Greater than control speed , preferably, =0.6m / s; then reduce the tension of the mooring chain 40 , update the soil stress and strain and structural motion state through finite element analysis, and bring it into formula (1) to recalculate the cable load angle of the mooring chain As the initial value of the next cable equation iteration calculation, if the mooring chain drag speed Less than control speed , preferably, =0.6m / s; then increase the tension of the mooring chain 40 , update the soil stress and strain and structural motion state through finite element analysis, and bring it into formula (1) to recalculate the cable load angle of the mooring chain As the initial value for the next iterative calculation of the cable equation;

[0075] S18. Obtain the ultimate embedment depth of the high-holding anchor group :Cycle S15-S17 to simulate the dragging process of the large holding force anchor group until the maximum embedding depth of the large holding force anchor group is obtained .

[0076] In this embodiment, see Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 and Figure 5 As a preferred design, S2 specifically includes the following steps:

[0077] S21. Working condition analysis: Set up four groups of working conditions in an orderly manner, and analyze the loading angle of the mooring chain on the seabed through the four groups of working conditions. , mooring chain drag speed , Undrained shear strength of seabed soil surface and undrained shear strength gradient of soil The influence on the ultimate embedment depth of the high holding force anchor group is shown in Table 1. Table 1 is as follows:

[0078] Table 1 Working condition analysis table

[0079]

[0080] In this embodiment, see Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 and Figure 6 As a preferred design, S3 specifically includes the following steps:

[0081] S31. Obtain analysis results for four groups of working conditions: Taking the embedment depth at which the dragging trajectory of the large holding force anchor group reaches a stable stage as its limit embedment depth, obtain analysis results for all working conditions;

[0082] S32. Fitting base surface: Based on the mooring chain loading angle on the seabed and mooring chain towing speed The analytical results are expressed using the binary Taylor series rational function Fit the surface function of the ultimate embedding depth of the large holding force anchor group. Specifically, use a binary Taylor series rational function to fit the explicit expression of the surface function of the ultimate embedding depth of the front large holding force anchor 20 and the rear large holding force anchor 10. The surface function serves as the base surface of the empirical formula. The explicit expression of the surface function is as follows:

[0083] (2)

[0084] Where, is the normalized maximum embedment depth of the large holding force anchor group, which is given by The ratio of is obtained, where is the maximum embedment depth of the large holding force anchor group, is the anchor plate length of the high holding force anchor group; 、 、 、 、 、 、 、 、 and All are fitting coefficients. The fitting coefficient values ​​are shown in Table 2. Table 2 is as follows:

[0085] Table 2 Empirical formula coefficient value table

[0086]

[0087]

[0088] S33. Factors affecting the calculation of undrained shear strength of seabed soil surface : It is the ratio of the ultimate embedment depth of the high holding force anchor group under the third group of working conditions to the ultimate embedment depth results of the corresponding benchmark working conditions in the first and second groups;

[0089] S34. Influencing factors of undrained shear strength of seabed soil surface fitted with high holding force anchor group :The influencing factors of undrained shear strength of seabed soil surface by fitting high holding force anchor groups through multivariate function That is, the influencing factors of the undrained shear strength of the seabed soil surface of the front large holding anchor 20 and the rear large holding anchor 10 are fitted by multivariate functions. , The functional form is as follows:

[0090] (3)

[0091] Where, is the reference value of the undrained shear strength of the seabed surface, which is the undrained shear strength value of the seabed surface in the first group of working conditions and the second group of working conditions; is the fitting coefficient, and the fitting coefficient values ​​are shown in Table 2; The undrained shear strength of the seabed soil surface and is a two-variable Taylor series rational function of the variable;

[0092] S35. Factors affecting the calculation of undrained shear strength gradient of seabed soil : It is the ratio of the ultimate embedment depth of the large holding force anchor group under the fourth working condition to the ultimate embedment depth results of the corresponding benchmark working conditions in the first, second and third groups;

[0093] S36. Influencing factors of the undrained shear strength gradient of the seabed soil surface fitted with high holding force anchors :The influencing factors of undrained shear strength gradient of seabed soil surface for large holding force anchor group by multivariate function fitting That is, the influencing factors of the undrained shear strength gradient of the seabed soil surface of the front large holding anchor 20 and the rear large holding anchor 10 are fitted by multivariate functions. , The functional form is as follows:

[0094] {F}_{k}\left ( {k,{s}_{u0},v,{\theta}_{e}} \right )=1+\left [ {{F}_{Taylor}\left ( {{\theta}_{e},k} \right )+A{s}^{2}_{u0}+B\left ( {k{\theta}_{e}{s}_{u0}+{C}^{2}} \right )+D\left ( {k{s}_{uo}{\theta}_{e}v+E} \right )} \right ]\left ( {k-{k}_{r}} \right ) (4)

[0095] Where, is the reference value of the undrained shear strength gradient of the seabed surface, which is obtained by taking the undrained shear strength gradient values ​​of the seabed surface in the first, second and third groups of working conditions; 、 、 、 and All are fitting coefficients, and the values ​​of fitting coefficients are shown in Table 2; Therefore and undrained shear strength gradient of soil is a two-variable Taylor series rational function of the variable;

[0096] S37. Obtain the normalized empirical formula for the ultimate embedment depth of a high-holding anchor group: Based on the base surface formula 2, the influencing factor of the undrained shear strength of the seabed soil surface Formula 3 and the influencing factor of the gradient of undrained shear strength of seabed soil Formula 4, obtain the normalized empirical formula for the maximum embedment depth of the large holding force anchor group , The functional form is as follows:

[0097] (5).

[0098] In this embodiment, see Figure 1 As a preferred design, S4 includes: Orthogonal table, as shown in Table 3, Table 3 is as follows, take 、 、 and Four factors, three parameter levels are set for each of the four factors, and the results are obtained according to the empirical formula. The results are compared with the results of finite element analysis to verify the reliability of the empirical formula. Settings are 0°, 5°, and 10°; Set to 0.1 , 0.5 and 1.0 ,in, Indicates the length of the anchor plate traveled per second; Settings are 3kPa, 9kPa and 15kPa; When the pressures are set to 0.5 kPa / m, 1.5 kPa / m, and 3 kPa / m, the average deviations between the predicted ultimate embedment depths of the front high-holding anchor 20 and the rear high-holding anchor 10 by the empirical formula and the finite element analysis results are 1.25% and 4.55%, respectively.

[0099] Table 3 Orthogonal array

[0100]

[0101] In this embodiment, see Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 and Figure 5 As a preferred design, the front high-holding anchor 20, the rear high-holding anchor 10, the mooring chain 40, and the connecting chain 30 are all constructed using Lagrangian units.

[0102] As described above, the method for constructing the empirical formula for the ultimate embedding depth of a high-holding force anchor group according to the present invention has the following beneficial effects:

[0103] 1. A database of the ultimate embedment depth of high-holding anchor groups is established based on coupled Euler-Lagrange large-deformation finite element analysis. Compared with small-deformation finite element simulation, this method can more accurately capture the complete drag trajectory of high-holding anchor groups. Compared with experimental methods, it can obtain large-scale, high-quality data at significantly reduced costs, providing reliable data support for engineering applications. Compared with traditional methods, it achieves efficient prediction of the ultimate embedment depth of high-holding anchor groups, significantly shortening the design cycle, simplifying the design process, and reducing design costs, with high engineering application value.

[0104] 2. The proposed empirical formula innovatively takes into account the loading angle of the mooring chain on the seabed , mooring chain drag speed , Undrained shear strength of seabed soil surface and undrained shear strength gradient of soil The main influencing factors of the BP neural network have wider engineering applicability and better prediction accuracy;

[0105] 3. The binary Taylor series rational function is used to construct the basis surface, so that the empirical formula has a concise mathematical expression while ensuring the calculation accuracy, which is convenient for application and promotion in engineering practice.

[0106] In summary, the present invention effectively overcomes various shortcomings in the prior art and has high industrial utilization value.

[0107] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Anyone skilled in the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by one of ordinary skill in the art without departing from the spirit and technical principles disclosed herein are intended to be covered by the claims of the present invention.

Claims

1. A method for constructing an empirical formula for the ultimate embedment depth of a high-holding anchor group, characterized by: The following steps are involved: S1. Establishing a solid model of a finite element model of a large holding power anchor group, wherein the large holding power anchor group comprises a front large holding power anchor (20), a rear large holding power anchor (10), a mooring chain (40), and a connecting chain (30), wherein the mooring chain (40) and the connecting chain (30) each comprise a plurality of anchor chains, wherein the mooring chain (40) is connected to the front end of the front large holding power anchor (20), one end of the connecting chain (30) is connected to the rear end of the front large holding power anchor (20), and the other end is connected to the front end of the rear large holding power anchor (10); S2. Design the finite element model in groups and analyze the loading angle of the mooring chain on the seabed , mooring chain drag speed , Undrained shear strength of seabed soil surface and undrained shear strength gradient of soil Impact on the ultimate embedment depth of high holding force anchor groups; S3. Based on the analysis results of all working conditions of the finite element model, the ultimate embedment depth of the large holding force anchor group is obtained, and the empirical formula of the ultimate embedment depth of the large holding force anchor group is obtained through multivariate function fitting. ; S31. Obtain analysis results for four groups of working conditions: Taking the embedment depth at which the dragging trajectory of the large holding force anchor group reaches a stable stage as its limit embedment depth, obtain analysis results for all working conditions; S32. Fitting base surface: Based on the mooring chain loading angle on the seabed and mooring chain towing speed The analytical results are expressed using the binary Taylor series rational function The surface function of the maximum embedment depth of the large holding force anchor group is fitted. This surface function is used as the base surface of the empirical formula. The explicit expression of the surface function is as follows: (2) Where, is the normalized maximum embedment depth of the large holding force anchor group, which is given by The ratio of is obtained, where is the maximum embedment depth of the large holding force anchor group, is the anchor plate length of the high holding force anchor group; 、 、 、 、 、 、 、 、 and All are fitting coefficients; S33. Factors affecting the calculation of undrained shear strength of seabed soil surface : It is the ratio of the ultimate embedment depth of the high holding force anchor group under the third group of working conditions to the ultimate embedment depth results of the corresponding benchmark working conditions in the first and second groups; S34. Influencing factors of undrained shear strength of seabed soil surface fitted with high holding force anchor group :The influencing factors of undrained shear strength of seabed soil surface by fitting high holding force anchor groups through multivariate function , The functional form is as follows: (3) Where, is the reference value of the undrained shear strength of the seabed surface, which is the undrained shear strength value of the seabed surface in the first group of working conditions and the second group of working conditions; is the fitting coefficient; The undrained shear strength of the seabed soil surface and is a two-variable Taylor series rational function of the variable; S35. Factors affecting the calculation of undrained shear strength gradient of seabed soil : It is the ratio of the ultimate embedment depth of the large holding force anchor group under the fourth working condition to the ultimate embedment depth results of the corresponding benchmark working conditions in the first, second and third groups; S36. Influencing factors of the undrained shear strength gradient of the seabed soil surface fitted with high holding force anchors :The influencing factors of undrained shear strength gradient of seabed soil surface for large holding force anchor group by multivariate function fitting , The functional form is as follows: (4) Where k r is the reference value of the undrained shear strength gradient of the seabed surface, which is obtained by taking the undrained shear strength gradient values ​​of the seabed surface in the first, second and third groups of working conditions; 、 、 、 and All are fitting coefficients; The loading angle of the mooring chain on the seabed is and undrained shear strength gradient of soil is a two-variable Taylor series rational function of the variable; S37. Obtain the normalized empirical formula for the ultimate embedment depth of the high-holding anchor group: Based on the base surface (Formula (2)), the influencing factor of the undrained shear strength of the seabed soil surface (Formula (3)) and the influencing factor of the gradient of undrained shear strength of seabed soil (Formula (4)), obtain the normalized empirical formula for the ultimate embedding depth of the large holding force anchor group: , The functional form is as follows: (5)； S4. Use the orthogonal test method to set up verification conditions, compare the empirical formula with the results of finite element analysis, and verify the reliability of the empirical formula.

2. The method for constructing the empirical formula for the ultimate embedment depth of a high-holding-power anchor assembly according to claim 1, characterized in that: Said S1 specifically comprises the following steps: S11, importing the solid geometric models of the front large grip anchor (20) and the rear large grip anchor (10), meshing the solid geometric models of the front large grip anchor (20) and the rear large grip anchor (10), and assigning material properties to the solid geometric models, setting a connecting component (22) at the rear end of the front large grip anchor (20), setting mooring points at the front end of the front large grip anchor (20) and the front end of the rear large grip anchor (10), and setting rigid body constraints with the mooring points as reference points; S12. Construct simplified models of the mooring chain (40) and the connecting chain (30): In the finite element model, construct The anchor chain solid geometry model (50) of the mooring chain (40) and The anchor chain solid geometric model (50) of the connecting chain (30) is constrained by rigid body conditions, and the binding constraint points (51) and rigid body reference points (52) are set at the front and rear ends respectively to construct The anchor chain solid geometric model (50) of the mooring chain (40) is connected in sequence by discrete line segments (60) to form a simplified model of the mooring chain (40). The discrete line segments (60) sequentially connect the anchor chain solid geometric models (50) of the connection chain (30) front to back to form a simplified model of the connection chain (30), and give the discrete line segments (60) connection properties; S13, connecting the mooring chain (40) and the front large holding power anchor (20): constructing a new discrete line segment (60) starting from the rear end of the rearmost discrete line segment (60) in the simplified mooring chain model, and connecting it to the mooring point at the front end of the front large holding power anchor (20); S14, connecting the front large holding power anchor (20) and the rear large holding power anchor (10) through the connecting chain (30): constructing a new discrete line segment (60) with the front end of the most front discrete line segment (60) in the simplified model of the connecting chain as the starting point, and connecting it to the connecting component (22) at the rear end of the front large holding power anchor (20); then constructing a new discrete line segment (60) with the rear end of the most rear discrete line segment (60) in the simplified model of the connecting chain as the starting point, and connecting it to the mooring point at the front end of the rear large holding power anchor (10); S15. Calculate the cable load angle of the mooring chain :Connect the anchor chain solid geometry model (50) at the front end of the mooring chain simplified model with the cable. The connection point is the cable load application point of the mooring chain (40). The cable load loading angle of the mooring chain is calculated iteratively through the cable equation. , the cable equation is given by: (1) Where, is the vertical depth coordinate of the point where the cable load of the mooring chain (40) is applied; is the vertical coordinate of the seabed surface; is the normal soil resistance of the cable per unit length, ,in, is the bearing capacity coefficient of the cable in the soil, To correspond to the soil pressure at the cable burial depth, is the effective width of the cable; is the tension of the mooring chain (40); is the friction coefficient between the cable and the soil; is the seabed mooring chain loading angle, which is the angle between the tension of the mooring chain (40) at the seabed and the horizontal plane; S16. Apply cable load to the mooring chain (40): Apply cable load angle according to the mooring chain , apply a cable load to the anchor chain at the front end of the mooring chain (40), and calculate the mooring chain dragging speed by the horizontal coordinate increment and vertical depth coordinate increment of the cable load application point of the mooring chain (40) at each time step By monitoring the coordinates of the mooring points of the large holding anchor group, the horizontal and vertical displacements of the large holding anchor group are obtained, thereby obtaining the embedding depth of the large holding anchor group; S17, according to the tension of the mooring chain (40) Recalculate the cable load angle of the mooring chain : According to the mooring chain drag speed Determine the tension in the mooring chain (40) , if the mooring chain drag speed Greater than control speed , then reduce the tension of the mooring chain (40) , and put it into formula (1) to recalculate the cable load angle of the mooring chain As the initial value of the next cable equation iteration calculation, if the mooring chain drag speed Less than control speed , then increase the tension of the mooring chain (40) , and put it into formula (1) to recalculate the cable load angle of the mooring chain As the initial value for the next iterative calculation of the cable equation; S18. Obtain the ultimate embedment depth of the high-holding anchor group :Cycle S15-S17 to simulate the dragging process of the large holding force anchor group until the maximum embedding depth of the large holding force anchor group is obtained .

3. The method for constructing the empirical formula for the ultimate embedment depth of a high-holding-power anchor assembly according to claim 2, characterized in that: Said S2 specifically comprises the following steps: S21. Working condition analysis: Set up four groups of working conditions in an orderly manner, and analyze the loading angle of the mooring chain on the seabed through the four groups of working conditions. , mooring chain drag speed , Undrained shear strength of seabed soil surface and undrained shear strength gradient of soil Impact on the ultimate embedment depth of high holding force anchor groups; S22. Analysis of the first and second working conditions: Calculate the ultimate embedment depth of the high-holding anchor group under the first working condition and analyze the loading angle of the mooring chain on the seabed The influence of the maximum embedment depth of the large holding force anchor group is calculated, and the maximum embedment depth of the large holding force anchor group under the second working condition is analyzed, and the mooring chain drag speed is analyzed. Regarding the influence of the ultimate embedment depth of the high-holding anchor group, the seabed soil strength characteristics set in the first and second working conditions remain unchanged and serve as the reference conditions for the third and fourth working conditions; S23, Analysis of the third and fourth working conditions: Calculate the ultimate embedment depth of the high-holding anchor group under the third working condition and analyze the undrained shear strength of the seabed soil surface The third working condition is set with the first and second working conditions as the benchmark working conditions. The ultimate embedment depth of the large holding force anchor group under the fourth working condition is calculated, and the undrained shear strength gradient of the soil is analyzed. In order to determine the influence of the ultimate embedment depth of the large holding force anchor group, the fourth group of working conditions is set with the first group of working conditions, the second group of working conditions and the third group of working conditions as the benchmark working conditions.

4. The method for constructing an empirical formula for the ultimate embedment depth of a high-holding-power anchor assembly according to claim 3, characterized in that: The S4 includes: Orthogonal table, take 、 、 and Four factors are set at three parameter levels respectively. The results are obtained according to the empirical formula and compared with the results of finite element analysis to verify the reliability of the empirical formula.

5. The method for constructing the empirical formula for the ultimate embedment depth of a high-holding-power anchor assembly according to claim 4 is characterized by: The front high-holding power anchor (20), the rear high-holding power anchor (10), the mooring chain (40), and the connecting chain (30) are all constructed using Lagrangian units.

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