Construction method of empirical formula of embedding depth under limit of high holding power anchor group

Abstract

The invention relates to a construction method of an embedded depth empirical formula under the limit of a high holding power anchor group. The construction method comprises the following steps: S1, establishing a solid model of a finite element model of the high holding power anchor group; s2, working conditions of the finite element model are designed in a grouped mode, and the influences of the seabed surface mooring chain loading angle # imgabs0 #, the mooring chain dragging speed # imgabs1 #, the seabed soil surface undrained shear strength # imgabs2 # and the soil body undrained shear strength gradient # imgabs3 # on the embedding depth of the large holding power anchor set under the limit are analyzed; s3, according to all working condition analysis results of the finite element model, the limit embedding depth of the large holding power anchor group is obtained, and an empirical formula # imgabs4 # of the limit embedding depth of the large holding power anchor group is obtained through multivariate function fitting; and S4, setting a verification working condition through an orthogonal test method, comparing the empirical formula with a finite element analysis result, 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 particularly to a method for constructing an empirical formula for the ultimate penetration depth of a large - holding - power anchor group. Background Art

[0002] As a type of drag - embedment plate anchor, the large - holding - power anchor is a key anchoring structure in deep - water mooring systems. It relies on the anchor plate to be dragged and embedded into the seabed to provide resistance, and can provide a reliable bottom - layer positioning foundation for upper floating structures such as semi - submersible offshore platforms, floating offshore wind power platforms, deep - sea oil and gas exploitation platforms, offshore airports, artificial floating islands, etc. It has excellent horizontal bearing capacity (up to the order of 10000 kN) and economic advantages.

[0003] In terms of the specific working mechanism, the large - holding - power anchor group is usually installed by towing with a mooring chain. Under the action of the anti - catenary effect, it can gradually embed into the seabed until it reaches the designed burial depth. This burial depth directly determines whether the anchor body can provide sufficient positioning bearing capacity for the upper floating structure. However, with the continuous development of modern offshore platforms towards large - scale and deep - water, the requirements for the bearing performance and deep - water installation performance of the anchoring structure in engineering applications have rapidly increased. Traditional large - holding - power anchor groups face many bottlenecks in practice, such as: 1) In terms of the motion characteristics of the anchor body: the prediction accuracy of the penetration motion trajectory is insufficient, and it is difficult to accurately determine the ultimate penetration depth; 2) In terms of the bearing performance evaluation: there is a lack of a reliable bearing capacity prediction model, and the means for engineering reliability verification are insufficient; 3) In terms of experimental research: the size effect of the prototype anchor is significant, and the cost of on - site tests is high and difficult to implement; 4) In terms of numerical simulation: the modeling of the soil - anchor interaction is complex, and it is difficult to accurately simulate the dynamic anchor chain load. These problems seriously restrict the performance prediction and evaluation accuracy of large - holding - power anchor groups in the engineering design stage. 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 penetration depth of a large - holding - power anchor group. According to the empirical formula, the ultimate penetration depth of the large - holding - power anchor group can be quickly predicted, the design process of the large - holding - power anchor group can be simplified, and the design cycle can be compressed.

[0005] To achieve the above object, the present invention provides a method for constructing an empirical formula for the ultimate penetration depth of a large - holding - power anchor group. The construction method includes the following steps:

[0006] S1. Establish a solid model of the finite - element model of the large - holding - power anchor group. The large - holding - power anchor group includes a front large - holding - power anchor, a rear large - holding - power anchor, a mooring chain, and a connecting chain. The mooring chain and the connecting chain both include multiple anchor chains. The mooring chain is connected to the front end of the front large - holding - power anchor, and one end of the connecting chain is connected to the rear end of the front large - holding - power anchor, and the other end is connected to the front end of the rear large - holding - power anchor;

[0007] S2. Group the working conditions of the finite element model and analyze the loading angle of the mooring chain on the seabed surface , the towing speed of the mooring chain , the undrained shear strength of the seabed soil surface and the gradient of the undrained shear strength of the soil mass on the ultimate embedment depth of the large drag embedment anchor group;

[0008] S3. According to the analysis results of all working conditions of the finite element model, obtain the ultimate embedment depth of the large drag embedment anchor group, and obtain the empirical formula of the ultimate embedment depth of the large drag embedment anchor group by multi - variable function fitting ;

[0009] S4. Set verification working conditions through the orthogonal test method, compare the results of the empirical formula and the 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 large drag embedment anchor and the rear large drag embedment anchor, perform mesh division on the solid geometric models of both the front large drag embedment anchor and the rear large drag embedment anchor, and assign material properties to both. Set connection components at the rear end of the front large drag embedment anchor, set mooring points at the front end of the front large drag embedment anchor and the front end of the rear large drag embedment anchor respectively, and set rigid body constraints with the mooring points as reference points;

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

[0013] S13. Connect the mooring chain and the front large drag embedment anchor: Construct a new discrete line segment starting from the rear end of the last discrete line segment in the simplified model of the mooring chain and connect it to the mooring point at the front end of the front large drag embedment anchor;

[0014] S14. Connect the front large-claw anchor and the rear large-claw anchor with a connecting chain: Starting from the front end of the discrete line segment at the very front of the connecting chain simplified model, construct a new discrete line segment and connect it to the connecting component at the rear end of the front large-claw anchor. Then, starting from the rear end of the discrete line segment at the very rear of the connecting chain simplified model, construct a new discrete line segment and connect it to the mooring point at the front end of the rear large-claw anchor;

[0015] S15. Calculate the loading angle of the mooring chain cable : Connect the geometric model of the anchor chain entity at the very front of the mooring chain simplified model to the cable. The connection point is the application point of the mooring chain cable load, and iteratively calculate the loading angle of the mooring chain cable through the cable equation , and the formula of the cable equation is as follows:

[0016] (1)

[0017] In the formula, is the vertical depth coordinate of the application point of the mooring chain cable load; is the vertical coordinate of the seabed surface; is the normal soil resistance force on the cable per unit length, , where is the bearing capacity coefficient of the cable in the soil, is the soil pressure corresponding to the cable burial depth, is the effective width borne by the cable; is the tension of the mooring chain; is the friction coefficient between the cable and the soil; is the loading angle of the mooring chain at the seabed surface, which is the angle between the tension of the mooring chain at the seabed surface and the horizontal plane;

[0018] S16. Apply the cable load to the mooring chain: According to the loading angle of the mooring chain cable, apply the cable load to the anchor chain at the very front of the mooring chain. Calculate the towing speed of the mooring chain through the horizontal coordinate increment and vertical depth coordinate increment of the application point of the mooring chain cable load at each time step. By monitoring the coordinates of the mooring points of the large-claw anchor group, obtain the horizontal displacement and vertical displacement of the large-claw anchor group, so as to obtain the embedment depth of the large-claw anchor group;

[0019] S17. Recalculate the loading angle of the mooring chain cable according to the tension of the mooring chain: Determine the tension of the mooring chain according to the towing speed of the mooring chain. If the towing speed of the mooring chain is greater than the control speed , then reduce the tension , and substitute 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 substitute 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 embedding depth of the large holding force anchor group :S15-S17 are cycled 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 S2 specifically comprises the following steps:

[0022] S21. Working condition analysis: Set four groups of working conditions in order, 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 the undrained shear strength gradient of the soil The influence on the ultimate embedment depth of high holding force anchor group;

[0023] S22, Analysis of the first and second working conditions: Calculate the ultimate embedding depth of the large holding force anchor group under the first working condition, and analyze the loading angle of the mooring chain on the seabed The influence of the maximum embedding depth of the large holding force anchor group on the maximum embedding depth of the large holding force anchor group under the second group of working conditions is calculated, and the mooring chain drag speed is analyzed. The influence of the maximum embedment depth of the large holding force 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 embedding depth of the large holding force anchor group under the third working condition, and analyze the undrained shear strength of the seabed soil surface The third group of working conditions is set with the first and second groups of working conditions as the benchmark working conditions. The ultimate embedding depth of the large grip anchor group under the fourth group of working conditions 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 embedding depth of the large holding force anchor group.

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

[0026] S31. Obtain the analysis results of four groups of working conditions: Take the embedment depth at the stable stage of the drag trajectory of the large-claw anchor group as its ultimate embedment depth, and obtain the analysis results of all working conditions;

[0027] S32. Fit the base surface: Based on the analysis results of the loading angle of the mooring chain on the seabed surface and the drag velocity of the mooring chain, use the binary Taylor series rational function

[0028] (2)

[0029] In the formula, is the normalized ultimate embedment depth of the large-claw anchor group, obtained from the ratio of , where is the ultimate embedment depth of the large-claw anchor group, is the anchor plate length of the large-claw anchor group; , , , , , , , , and are all fitting coefficients;

[0030] S33. Calculate the influence factor of the undrained shear strength of the seabed soil surface: is the ratio of the ultimate embedment depth of the large-claw anchor group under the third group of working conditions to the ultimate embedment depth results of the corresponding reference working conditions in the first and second groups;

[0031] S34. Fit the influence factor of the undrained shear strength of the seabed soil surface for the large-claw anchor group: Fit the function form of the influence factor of the undrained shear strength of the seabed soil surface for the large-claw anchor group as follows:

[0032] (3)

[0033] In the formula, is the reference value of the undrained shear strength of the seabed surface, taking the undrained shear strength values of the seabed surface in the first group of working conditions and the second group of working conditions; is the fitting coefficient; is based on the undrained shear strength of the seabed soil surface and A rational function of a binary Taylor series for a variable;

[0034] S35. Calculate the influence factor of the undrained shear strength gradient of the seabed soil : It is the ratio of the ultimate embedment depth of the large-claw anchor group under the fourth working condition to the ultimate embedment depth results of the corresponding reference working conditions in the first, second, and third groups;

[0035] S36. Fit the influence factor of the undrained shear strength gradient of the seabed surface of the large-claw anchor group : Fit the influence factor of the undrained shear strength gradient of the seabed surface of the large-claw anchor group through a multivariate function , 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] Wherein, k r is the reference value of the undrained shear strength gradient of the seabed surface, taking the undrained shear strength gradient values of the seabed surface in the first working condition, the second working condition, and the third working condition; , , , and are all fitting coefficients; is a rational function of a binary Taylor series with and the undrained shear strength gradient of the soil mass as variables;

[0038] S37. Obtain the empirical formula for the normalized ultimate embedment depth of the large-claw anchor group: According to the base surface (formula (2)), the influence factor of the undrained shear strength of the seabed surface (formula (3)) and the influence factor of the undrained shear strength gradient of the seabed soil (formula (4)), obtain the empirical formula for the normalized ultimate embedment depth of the large-claw anchor group , The functional form is as follows:

[0039] (5).

[0040] Further, the S4 includes: According to the orthogonal array, take , , and four factors. Three parameter levels are set for each of the four factors. 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] Further, the front large holding power anchor, the rear large holding power anchor, the mooring chain, and the connecting chain are all constructed using Lagrangian elements.

[0042] As described above, the method for constructing the empirical formula for the ultimate embedment depth of the large holding power anchor group involved in the present invention has the following beneficial effects:

[0043] 1. Based on the coupled Euler-Lagrange large deformation finite element analysis, a database for the ultimate embedment depth of the large holding power anchor group is established. Compared with the small deformation finite element simulation, it can capture the complete dragging trajectory of the large holding power anchor group more accurately. Compared with the test method, it can obtain a large amount of high-quality data under the condition of significantly reducing costs, providing reliable data support for engineering applications. Compared with the traditional method, it realizes the efficient prediction of the ultimate embedment depth of the large holding power anchor group, can greatly shorten the design cycle, simplify the design process, reduce the design cost, and has high engineering application value;

[0044] 2. The proposed empirical formula innovatively comprehensively considers the main influencing factors such as the loading angle of the mooring chain on the seabed surface, the dragging speed of the mooring chain, the undrained shear strength of the seabed soil surface, and the undrained shear strength gradient of the soil mass, and has broader engineering applicability and better prediction accuracy;

[0045] 3. The base surface is constructed using a binary Taylor series rational function, making the empirical formula have a simple mathematical expression form while ensuring the calculation accuracy, which is convenient for application and promotion in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flowchart showing the method for constructing the empirical formula for the ultimate embedment depth of the large holding power anchor group in the present invention.

[0047] Figure 2 is a structural schematic diagram of the large holding power anchor group in the present invention.

[0048] Figure 3This is a schematic diagram of the structure of the front high-holding power anchor in the present invention.

[0049] Figure 4 This is a schematic diagram of the structure of the rear high-holding power anchor in the present invention.

[0050] Figure 5 This is a schematic diagram of the connection between the physical geometric model of the anchor chain and the discrete line segments in the present invention.

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

[0052] Explanation of the reference numerals in the attached drawings

[0053] 10. Rear high-holding power anchor, 11. Mooring point of the rear high-holding power anchor, 20. Front high-holding power anchor, 21. Mooring point of the front high-holding power anchor, 22. Connecting component, 30. Connecting chain, 40. Mooring chain, 50. Physical geometric model of the anchor chain, 51. Binding constraint point, 52. Rigid body reference point, 60. Discrete line segment. Detailed implementation manners

[0054] The following further elaborates on the detailed implementation manners of the present invention in conjunction with the attached drawings. These implementation manners are only for illustrating 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 orientation or positional relationship indicated by the terms "center", "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the attached drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0056] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installed", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0057] In addition, in the description of the present invention, unless otherwise stated, the meaning of "a plurality of" is two or more.

[0058] See Figures 1 to 6, the present invention provides a method for constructing an empirical formula for the ultimate embedment depth of a large-grip anchor group, comprising the following steps:

[0059] S1. Establish a solid model of the finite element model of the large-grip anchor group. The large-grip anchor group includes a front large-grip anchor 20, a rear large-grip anchor 10, a mooring chain 40, and a connecting chain 30. Preferably, the front large-grip anchor 20 and the rear large-grip anchor 10 are arranged at intervals front and rear; both the mooring chain 40 and the connecting chain 30 include a plurality of anchor chains. One end of the mooring chain 40 is connected to the front end of the front large-grip 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-grip anchor 20, and the other end is connected to the front end of the rear large-grip anchor 10. Preferably, the front large-grip anchor 20 is set as a Delta anchor, and the rear large-grip anchor 10 is set as an Mk5 anchor; the seabed soil is regarded as homogeneous saturated clay, assumed to conform to the Tresca yield criterion, and described by the Eulerian body.

[0060] S2. Group and design the working conditions of the finite element model, and analyze the influence of the mooring chain loading angle , the mooring chain dragging speed , the undrained shear strength of the seabed soil surface and the undrained shear strength gradient of the soil body on the ultimate embedment depth of the large-grip anchor group.

[0061] S3. According to the analysis results of all working conditions of the finite element model, obtain the ultimate embedment depth of the large-grip anchor group, and obtain the empirical formula for the ultimate embedment depth of the large-grip anchor group through multivariate function fitting ;

[0062] S4. Set verification working conditions through the orthogonal test method, compare the results of the empirical formula and the finite element analysis, and verify the reliability of the empirical formula.

[0063] The basic working principle of the method for constructing the empirical formula for the ultimate embedment depth of the large-grip anchor group involved in the present invention is as follows: By establishing a solid model of the finite element model of the large-grip 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 and designing the working conditions of the finite element model, a numerical model considering the coupling influence of multiple factors can be established. By using multivariate function fitting for the empirical formula of the ultimate embedment depth of the large-grip anchor group, explicit expressions for the ultimate embedment depth of the front large-grip anchor 20 and the rear large-grip anchor 10 are respectively established, which can quickly predict the ultimate embedment depth of the large-grip anchor group, simplify the design process of the large-grip anchor group, and compress the design cycle;

[0064] See Figures 1 to 6 , the following further illustrates the present invention with a specific embodiment:

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

[0066] S11. Import the solid geometric models of the front large-grip anchor 20 and the rear large-grip anchor 10, perform mesh division on the solid geometric models of the front large-grip anchor 20 and the rear large-grip anchor 10, allocate material properties to both, set a connecting component 22 at the rear end of the front large-grip anchor 20, set mooring points at the front ends of the front large-grip anchor 20 and the rear large-grip anchor 10 respectively, and set rigid body constraints with 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 solid geometric models 50 of the anchor chains of the mooring chain 40 and solid geometric models 50 of the anchor chains of the connecting chain 30. Preferably, the solid geometric model 50 of the anchor chain is set as a cylinder, the length of the cylinder is 1.0 m, and the diameter of the cylinder is 0.2 m; The solid geometric model 50 of the anchor chain is constrained by rigid body conditions, and binding constraint points 51 and rigid body reference points 52 are set at its front and rear ends respectively. Construct discrete line segments 60 to connect the solid geometric models 50 of the anchor chains of the mooring chain 40 in sequence front and back to form a simplified model of the mooring chain 40, and construct discrete line segments 60 to connect the solid geometric models 50 of the anchor chains of the connecting chain 30 in sequence front and back to form a simplified model of the connecting chain 30, and endow the discrete line segments 60 with connection attributes;

[0068] S13. Connect the mooring chain 40 and the front large-grip anchor 20: Construct a new discrete line segment 60 starting from the rear end of the discrete line segment 60 at the rearmost end of the simplified mooring chain model and connect it to the mooring point at the front end of the front large-grip anchor 20. That is, connect the rigid body reference point 52 on the solid geometric model 50 of the anchor chain at the rearmost end of the simplified mooring chain model to the mooring point at the front end of the front large-grip anchor 20 through a 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: Starting from the front end of the discrete line segment 60 at the very front end in the simplified model of the connecting chain, construct a new discrete line segment 60 at one end and connect it to the connecting component 22 at the rear end of the front large holding power anchor 20. Then, starting from the rear end of the discrete line segment 60 at the very rear end in the simplified model of the connecting chain, construct a new discrete line segment 60 at one end 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 entity geometric model 50 at the very front end in 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 body reference point 52 on the anchor chain entity geometric model 50 at the very rear end in 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 loading angle of the mooring chain cable : Connect the anchor chain entity geometric model 50 at the very front end in the simplified model of the mooring chain to the cable, with the connection point being the cable load application point of the mooring chain 40, and calculate the loading angle of the mooring chain cable through cable equation iteration , and the formula of the cable equation is as follows:

[0071] (1)

[0072] In the formula, is the vertical depth coordinate of the cable load application point of the mooring chain 40; is the vertical coordinate of the seabed surface; is the normal soil resistance force on the cable per unit length, , where is the bearing capacity coefficient of the cable in the soil, is the soil pressure corresponding to the cable burial depth, is the effective width borne by the cable, Take 0.2 m; 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 loading angle of the mooring chain at the seabed surface, which is the angle between the tension of the mooring chain 40 at the seabed surface and the horizontal plane;

[0073] S16. Apply the cable load to the mooring chain 40: According to the loading angle of the mooring chain cable , apply the cable load to the anchor chain at the very front end of the mooring chain 40, and calculate the towing speed of the mooring chain through 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 power anchor group, the horizontal displacement and vertical displacement of the large holding power anchor group are obtained, so as to obtain the embedded depth of the large holding power anchor group;

[0074] S17. According to the tension of the mooring chain 40 Recalculate the loading angle of the mooring cable load of the mooring chain : According to the towing speed of the mooring chain Determine the tension of the mooring chain 40 , if the towing speed of the mooring chain is greater than the control speed , preferably, = 0.6 m / s; then reduce the tension of the mooring chain 40 , update the soil stress-strain and structural motion state through finite element analysis, and substitute into formula (1) to recalculate the loading angle of the mooring cable load of the mooring chain as the initial value for the next iteration calculation of the mooring cable equation. If the towing speed of the mooring chain is less than the control speed , preferably, = 0.6 m / s; then increase the tension of the mooring chain 40 , update the soil stress-strain and structural motion state through finite element analysis, and substitute into formula (1) to recalculate the loading angle of the mooring cable load of the mooring chain as the initial value for the next iteration calculation of the mooring cable equation;

[0075] S18. Obtain the ultimate embedded depth of the large holding power anchor group : Loop S15 - S17 to simulate the towing process of the large holding power anchor group until the ultimate embedded depth of the large holding power anchor group is obtained .

[0076] In this embodiment, referring to 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: Four groups of working conditions are set in an orderly manner, and the influence of the mooring chain loading angle , the towing speed of the mooring chain , the undrained shear strength of the seabed soil surface and the undrained shear strength gradient of the soil body on the ultimate embedded depth of the large holding power anchor group is analyzed, as shown in Table 1. Table 1 is as follows:

[0078] Table 1 Working condition analysis table

[0079]

[0080] In this embodiment, referring to 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 the analysis results of four groups of working conditions: Take the penetration depth at the stable stage of the towing trajectory of the large-grip anchor group as its ultimate penetration depth, and obtain the analysis results of all working conditions;

[0082] S32. Fit the base surface: Based on the analysis results of the loading angle of the mooring chain on the seabed surface and the towing speed of the mooring chain, use the binary Taylor series rational function to fit the surface function of the ultimate penetration depth of the large-grip anchor group. Specifically, use the binary Taylor series rational function to fit the explicit expressions of the surface functions of the ultimate penetration depths of the front large-grip anchor 20 and the rear large-grip anchor 10 respectively. This surface function serves as the base surface of the empirical formula, and the explicit expression of the surface function is as follows:

[0083] (2)

[0084] In the formula, is the normalized ultimate penetration depth of the large-grip anchor group, obtained from the ratio of . Among them, is the ultimate penetration depth of the large-grip anchor group, and is the anchor plate length of the large-grip anchor group; , , , , , , , , and are all fitting coefficients, and the values of the fitting coefficients are shown in Table 2. Table 2 is as follows:

[0085] Table 2 Value Table of Empirical Formula Coefficients

[0086]

[0087]

[0088] S33. Calculate the influence factor of the undrained shear strength of the seabed soil surface: is the ratio of the ultimate embedment depth of the large holding power anchor group under the third group of working conditions to the ultimate embedment depth results of the corresponding reference working conditions in the first and second groups;

[0089] S34. Fitting the influencing factor of the undrained shear strength of the seabed soil surface for the large holding power anchor group : Fitting the influencing factor of the undrained shear strength of the seabed soil surface for the large holding power anchor group through a multivariate function , that is, fitting the influencing factors of the undrained shear strength of the seabed soil surface for the front large holding power anchor 20 and the rear large holding power anchor 10 respectively through a multivariate function , The functional form of

[0090] (3)

[0091] In the formula, is the reference value of the undrained shear strength of the seabed surface, taking the undrained shear strength values of the seabed surface in the first group of working conditions and the second group of working conditions; is the fitting coefficient, and the values of the fitting coefficient are shown in Table 2; is a binary Taylor series rational function with the undrained shear strength and of the seabed soil surface as variables;

[0092] S35. Calculating the influencing factor of the undrained shear strength gradient of the seabed soil : is the ratio of the ultimate embedment depth of the large holding power anchor group under the fourth group of working conditions to the ultimate embedment depth results of the corresponding reference working conditions in the first, second, and third groups;

[0093] S36. Fitting the influencing factor of the undrained shear strength gradient of the seabed soil surface for the large holding power anchor group : Fitting the influencing factor of the undrained shear strength gradient of the seabed soil surface for the large holding power anchor group through a multivariate function , that is, fitting the influencing factors of the undrained shear strength gradient of the seabed soil surface for the front large holding power anchor 20 and the rear large holding power anchor 10 respectively through a multivariate function , The functional form of

[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] In the formula, is the reference value of the undrained shear strength gradient of the seabed surface, and the undrained shear strength gradient values of the seabed surface in the first working condition, the second working condition, and the third working condition are taken; 、 、 、 and are all fitting coefficients, and the values of the fitting coefficients are shown in Table 2; is a binary Taylor series rational function with and the undrained shear strength gradient of the soil mass as variables;

[0096] S37. Obtain the empirical formula for the ultimate embedment depth of the large drag embedment anchor group after normalization: According to the base surface formula 2, the influence factor of the undrained shear strength of the seabed soil surface, formula 3, and the influence factor of the undrained shear strength gradient of the seabed soil, formula 4, obtain the empirical formula for the ultimate embedment depth of the large drag embedment anchor group after normalization , The functional form of is as follows:

[0097] (5).

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

[0099] Table 3 Orthogonal table

[0100]

[0101] In this embodiment, referring to Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 and Figure 5 , as a preferred design, the front large-claw anchor 20, the rear large-claw anchor 10, the mooring chain 40, and the connecting chain 30 are all constructed using Lagrangian elements.

[0102] As described above, the method for constructing the empirical formula for the ultimate embedment depth of the large-claw anchor group involved in the present invention has the following beneficial effects:

[0103] 1. Based on the coupled Euler-Lagrange large deformation finite element analysis, a database of the ultimate embedment depth of the large-claw anchor group is established. Compared with the small deformation finite element simulation, it can capture the complete dragging trajectory of the large-claw anchor group more accurately. Compared with the test method, it can obtain a large amount of high-quality data under the condition of significantly reducing costs, providing reliable data support for engineering applications. Compared with the traditional method, it realizes the efficient prediction of the ultimate embedment depth of the large-claw anchor group, can greatly shorten the design cycle, simplify the design process, and reduce the design cost, and has high engineering application value;

[0104] 2. The proposed empirical formula innovatively comprehensively considers the main influencing factors such as the loading angle of the mooring chain on the seabed surface , the dragging speed of the mooring chain , the undrained shear strength of the seabed soil surface and the gradient of the undrained shear strength of the soil mass , and has broader engineering applicability and better prediction accuracy;

[0105] 3. The base surface is constructed using a binary Taylor series rational function, making the empirical formula have a simple mathematical expression form while ensuring the calculation accuracy, which is convenient for application and popularization in engineering practice.

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

[0107] The above embodiments are only illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Any person familiar with this technology can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical idea disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A method for constructing an empirical formula for the ultimate embedded depth of a large-grip anchor group, characterized in that: It includes the following steps: S1. Establish a solid model of the finite element model of the large holding power anchor group. The large holding power anchor group includes a front large holding power anchor (20), a rear large holding power anchor (10), a mooring chain (40), and a connecting chain (30). Both the mooring chain (40) and the connecting chain (30) include multiple anchor chains. 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. Group the working conditions of the finite element model and analyze the loading angle of the mooring chain on the seabed surface , the towing speed of the mooring chain , the undrained shear strength of the seabed soil surface and the gradient of the undrained shear strength of the soil mass on the ultimate embedment depth of the large-claw anchor group; S3. Obtain the ultimate embedment depth of the large holding power anchor group based on the analysis results of all working conditions of the finite element model, and obtain the empirical formula for the ultimate embedment depth of the large holding power anchor group through multivariate function fitting ; S4. Set verification working conditions through the orthogonal test method, compare the results of the empirical formula and the finite element analysis, and verify the reliability of the empirical formula.

2. The construction method of the empirical formula for the ultimate embedded depth of the large-grip anchor group according to claim 1, characterized in that: The S1 specifically includes the following steps: S11. Import the solid geometric models of the front large holding power anchor (20) and the rear large holding power anchor (10), perform mesh division on the solid geometric models of the front large holding power anchor (20) and the rear large holding power anchor (10), and assign material properties to both. Set a connecting component (22) at the rear end of the front large holding power anchor (20), set mooring points at the front end of the front large holding power anchor (20) and the front end of the rear large holding power anchor (10) respectively, and set rigid body constraints with the mooring points as reference points; S12. Construct a simplified model of the mooring chain (40) and the connecting chain (30): In the finite element model, respectively construct the geometric model (50) of the anchor chain entity of the mooring chain (40) and the geometric model (50) of the anchor chain entity of the connecting chain (30). The geometric model (50) of the anchor chain is constrained by rigid body conditions, and binding constraint points (51) and rigid body reference points (52) are respectively set at its front and rear ends. Construct discrete line segments (60) to connect the geometric models (50) of the anchor chain entities of the mooring chain (40) successively from front to back to form a simplified model of the mooring chain (40). Construct discrete line segments (60) to connect the geometric models (50) of the anchor chain entities of the connecting chain (30) successively from front to back to form a simplified model of the connecting chain (30), and endow the discrete line segments (60) with connection attributes; S13. Connect the mooring chain (40) and the front large holding power anchor (20): Construct a new discrete line segment (60) starting from the rear end of the last discrete line segment (60) in the simplified model of the mooring chain, and connect it to the mooring point at the front end of the front large holding power anchor (20); 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) starting from the front end of the most front discrete line segment (60) in the simplified model of the connecting chain, 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) starting from the rear end of the last discrete line segment (60) in the simplified model of the connecting chain, and connect it to the mooring point at the front end of the rear large holding power anchor (10); S15. Calculate the loading angle of the mooring chain cable : Connect the geometric model of the anchor chain entity (50) at the very front in the simplified model of the mooring chain to the cable. The connection point is the application point of the cable load of the mooring chain (40), and iteratively calculate the loading angle of the mooring chain cable through the cable equation , and the formula of the cable equation is as follows: (1) Wherein, is the vertical depth coordinate of the cable load application point of the mooring chain (40); is the vertical coordinate of the seabed surface; is the normal soil resistance force on the cable per unit length, , where, is the bearing capacity coefficient of the cable in the soil, is the earth pressure corresponding to the cable burial depth, is the effective width borne by the cable; is the tension of the mooring chain (40); is the friction coefficient between the cable and the soil; is the mooring chain loading angle at the seabed surface, which is the angle between the tension of the mooring chain (40) at the seabed surface and the horizontal plane; S16. Apply a mooring line load to the mooring chain (40): According to the loading angle of the mooring line load of the mooring chain , apply a mooring line load to the anchor chain at the foremost end of the mooring chain (40), and calculate the mooring chain dragging speed through the horizontal coordinate increment and the vertical depth coordinate increment of the mooring line load application point of the mooring chain (40) at each time step , by monitoring the coordinates of the mooring point of the large holding power anchor group, obtain the horizontal displacement and the vertical displacement of the large holding power anchor group, so as to obtain the embedment depth of the large holding power 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 towing speed Determine the tension in the mooring chain (40) , if the mooring chain drag speed Greater than control speed , then the tension of the mooring chain (40) is reduced , and substitute 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 the tension of the mooring chain (40) is increased. , and substitute 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 embedding depth of the large-grip anchor group : Simulate the dragging process of the large-grip anchor group by looping S15 - S17 until the ultimate embedding depth of the large-grip anchor group is obtained .

3. The construction method of the empirical formula for the ultimate embedded depth of the large-grip anchor group according to claim 2, characterized in that: The S2 specifically includes the following steps: S21. Working condition analysis: Four groups of working conditions are set orderly, and the loading angle of the mooring chain on the seabed surface, , the dragging speed of the mooring chain, , the undrained shear strength of the seabed soil surface, and the gradient of the undrained shear strength of the soil mass on the ultimate embedment depth of the large-claw anchor group are analyzed through the four groups of working conditions; S22. Analysis of the first and second groups of working conditions: Calculate the ultimate embedment depth of the large-claw anchor group under the first group of working conditions, and analyze the loading angle of the mooring chain on the seabed surface Effect on the ultimate embedment depth of the large-claw anchor group, calculate the ultimate embedment depth of the large-claw anchor group under the second group of working conditions, and analyze the dragging speed of the mooring chain Effect on the ultimate embedment depth of the large-claw anchor group. The seabed soil strength characteristics set in the first group of working conditions and the second group of working conditions remain constant and are used as the reference conditions for the third group of working conditions and the fourth group of working conditions; S23. Analysis of the third and fourth groups of working conditions: Calculate the ultimate embedment depth of the large-claw anchor group under the third group of working conditions, and analyze the undrained shear strength of the seabed soil surface. Regarding the influence on the ultimate embedment depth of the large-claw anchor group, the third group of working conditions is set with the first and second groups of working conditions as the reference working conditions. Calculate the ultimate embedment depth of the large-claw anchor group under the fourth group of working conditions, and analyze the undrained shear strength gradient of the soil. Regarding the influence on the ultimate embedment depth of the large-claw anchor group, the fourth group of working conditions is set with the first, second, and third groups of working conditions as the reference working conditions.

4. The construction method of the empirical formula for the ultimate downward embedding depth of the large holding power anchor group according to claim 3, characterized in that: The S3 specifically includes the following steps: S31. Obtain the analysis results of four groups of working conditions: Take the embedment depth at the stable stage of the dragging trajectory of the large holding power anchor group as its ultimate embedment depth, and obtain the analysis results of all working conditions; S32. Fitting the base surface: Based on the mooring chain loading angle of the seabed surface and the mooring chain dragging speed Analysis results, use the binary Taylor series rational function to fit the surface function of the ultimate embedment depth of the large holding power anchor group. This surface function is used as the base surface of the empirical formula, and the explicit expression of the surface function is as follows: (2) In the formula, is the normalized ultimate embedment depth of the large drag embedment anchor group, obtained from the ratio of . Among them, is the ultimate embedment depth of the large drag embedment anchor group, and is the anchor plate length of the large drag embedment anchor group; , , , , , , , , and are all fitting coefficients; S33. Calculate the influence factor of the undrained shear strength of the seabed soil surface : is the ratio of the ultimate penetration depth of the large-grip anchor group under the third group of working conditions to the ultimate penetration depth of the corresponding reference working conditions in the first and second groups; S34. Fitting the influencing factor of undrained shear strength of seabed soil for large-claw anchor group : Fitting the influencing factor of undrained shear strength of seabed soil for large-claw anchor group through multivariate function , The functional form is as follows: (3) In the formula, is the reference value of the undrained shear strength of the seabed surface, taking the undrained shear strength values of the seabed surface in the first working condition and the second working condition; is the fitting coefficient; is a binary Taylor series rational function with the undrained shear strength and of the seabed soil surface as variables; S35. Calculate the influence factor of the undrained shear strength gradient of seabed soil : It is the ratio of the ultimate penetration depth of the large grab anchor group under the fourth working condition to the ultimate penetration depth of the corresponding reference working conditions in the first, second, and third groups. S36. Fitting the influence factor of the undrained shear strength gradient of the seabed soil surface for the large-claw anchor group : Fitting the influence factor of the undrained shear strength gradient of the seabed soil surface for the large-claw anchor group by a multivariate function , The functional form is as follows: (4) where k r is the reference value of the undrained shear strength gradient of the seabed surface, taking the undrained shear strength gradient values of the seabed surface in the first working condition, the second working condition, and the third working condition; , , , and are all fitting coefficients; is a binary Taylor series rational function with the loading angle of the mooring chain on the seabed surface and the undrained shear strength gradient of the soil as variables; S37. Obtain the empirical formula for the ultimate penetration depth of the normalized large-grip anchor group: Based on the base surface (Equation (2)), the influence factor of the undrained shear strength of the seabed soil surface (Equation (3)) and the influence factor of the undrained shear strength gradient of the seabed soil (Equation (4)), obtain the empirical formula for the ultimate penetration depth of the normalized large-grip anchor group , The functional form of which is as follows: (5)。 5. The method for constructing the empirical formula for the ultimate embedded depth of the large-grip anchor group according to claim 4, characterized in that: The said S4 includes: According to the orthogonal array, taking , , and four factors, three parameter levels are set for each of the four factors, 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.

6. The construction method of the empirical formula for the ultimate embedded depth of the large grip anchor group according to claim 5, characterized in that: Both the front large holding power anchor (20), the rear large holding power anchor (10), the mooring chain (40), and the connecting chain (30) are constructed using Lagrange elements.

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