Efficient analysis method for embedding motion trail of dragging anchor in clay sand soil seabed

Abstract

The invention discloses an efficient analysis method for embedding motion trail of a towing anchor in a clay sand soil seabed, and relates to the technical field of ocean engineering and geotechnical engineering.The efficient analysis method comprises the steps that environmental parameters of the towing anchor and the seabed are obtained; based on the towing anchor embedding mechanism, a kinematic model of the towing anchor is established, and the real-time position of the anchor plate is described through the kinematic model; establishing a dragging track prediction equation; equivalent motion parameters are determined, and a motion trail equation of the dragging anchor in homogeneous soil and linear soil is established; and establishing a critical state trajectory prediction method of the towing anchor in the linear soil, and outputting a prediction result. According to the efficient analysis method for the embedding motion trail of the towing anchor in the clay sand soil seabed, the complete motion trail of the anchor plate embedded from the initial position to the limit depth can be accurately described based on the kinematics model obtained through circular motion and motion synthesis derivation, and the motion characteristics of the anchor plate in the actual embedding process are effectively reflected.

Description

Technical Field

[0001] This invention relates to the fields of marine engineering and geotechnical engineering, and in particular to an efficient analysis method for the motion trajectory of towed anchors embedded in clay sand seabeds. Background Technology

[0002] As a widely used anchoring structure in marine engineering, the embedding trajectory and final positioning of towed anchors during installation have a crucial impact on the positioning accuracy, reliability, and safety of marine floating structures and mooring systems. Existing prediction methods mainly suffer from the following technical bottlenecks: In terms of theoretical prediction, existing methods mostly rely on complex numerical incremental calculations, generally falling into two categories: limit equilibrium methods and plastic limit analysis methods. The use of numerical incremental methods to predict trajectories still carries uncertainty, exhibiting low computational efficiency and difficulty in guaranteeing convergence. Classical methods, represented by Neubecker and Randolph (1995-1996), propose closed-loop solutions for estimating the trajectory of towed anchors, but these are only applicable to specific soil conditions (such as clay with strength exhibiting power-law variations), and have poor adaptability to linear soils (soils whose shear strength increases linearly with depth) or homogeneous soils (soils whose strength does not change with depth) commonly found in engineering. Murff et al. (2005), through comparative analysis of multiple research institutions, showed that different prediction methods yielded significantly different calculation results for the same working condition, reflecting the lack of a unified theoretical analysis framework and standards for existing prediction methods.

[0003] Regarding engineering applicability, existing methods lack sufficient accuracy in predicting the actual anchor position, fail to effectively consider the characteristics of soil strength variation with depth, and cannot accurately capture the continuous changes in the cable anti-chain morphology as the towed anchor continues to embed, and the measurements are not accurate enough. In practical engineering, the towed cable length often cannot reach the theoretically limit embedment depth, especially in linear strength soils. In common working conditions where the towed cable length is limited, the lack of accurate descriptions and prediction methods for critical states, such as clear definitions and calculation methods for critical cable length and critical towing distance, makes it difficult to accurately determine the final embedment position of the anchor in engineering practice.

[0004] In the field of motion models, scholars such as Xiao Zhijian (2008) and Yang Hanting (2009) pioneered the kinematic analytical method, aiming to derive the analytical form of the trajectory equation entirely through theoretical formulas, and proposed a trajectory model based on geometric relationships. However, due to the limitations of the research work in the initial stage, it failed to establish a systematic theoretical framework, and there are many areas that need to be revised and improved.

[0005] Therefore, there is an urgent need to establish a theoretically rigorous, widely applicable, and engineeringly practical method for analyzing and predicting the motion trajectory of towed anchors. This method should be able to accurately describe the motion characteristics of anchors under different soil conditions (applicable to both clay and sandy seabeds), effectively handle practical working conditions such as limited tow cable length, and provide reliable technical support for the design and construction of marine anchoring projects. Summary of the Invention

[0006] The purpose of this invention is to provide an efficient analysis method for the motion trajectory of towed anchors embedded in clay sand seabeds, thereby solving the problems mentioned in the background art.

[0007] To achieve the above objectives, this invention provides an efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed, comprising the following steps: Step S1: Obtain the towed anchor and seabed environmental parameters; Step S2: Based on the embedding mechanism of the towed anchor, establish a kinematic model of the towed anchor and describe the real-time position of the anchor plate through the kinematic model; Step S3: Based on the principle of velocity synthesis, establish the relationship between the horizontal motion velocity of the towing point and the circular motion velocity of the anchor plate, derive the analytical expression between the towing distance and the azimuth angle of the anchor plate, and combine the kinematic model to establish the prediction equation of the towing trajectory under ideal conditions. Step S4: Determine the equivalent motion parameters and establish the motion trajectory equations of the towed anchor in homogeneous and linear soils; Step S5: Establish a method for predicting the critical state trajectory of a towed anchor in linear soil and output the prediction results.

[0008] Preferably, the towing anchor and seabed environmental parameters in step S1 include: the geometric dimensions and weight of the towing anchor, the diameter and length of the towing cable, the type and strength parameters of the seabed soil, the speed of movement at the towing point, and the towing angle at the mooring point.

[0009] Preferably, step S2 includes: The motion of the anchor plate is decomposed into two components: circular motion with the drag point as the center and horizontal motion of the drag point itself. The kinematic model describes the real-time position of the anchor plate through circle equations and line equations. The equation of the circle is shown below: ; The equation of the line is shown below: ; The horizontal position of the drag point is shown in the following formula: ; In the formula, Indicates the direction along the seabed. Indicates the direction of gravity. Let the horizontal coordinates of the drag point be... This refers to the length of the tow cable. This is the drag distance. Represents a variable function, and .

[0010] Preferably, the drag trajectory prediction equation under ideal conditions in step S3 is as follows: ; In the formula, Represents a variable function, and , This represents the drag angle of the anchor plate.

[0011] Preferably, the equivalent motion parameters in step S4 include: Equivalent cable length : The distance between the mooring point and the towing point; Effective cable length : The length of the embedded cable; Equivalent angle : The angle between the equivalent cable length and the horizontal plane; tow cable length : The minimum cable length required for the anchor plate to reach its maximum embedment depth.

[0012] Preferably, the more accurate equation for the motion trajectory of the towed anchor in homogeneous soil under actual conditions in step S4 is shown below: ; Based on the embedding characteristics of the anchor plate, the above equation satisfies conditions; In the formula, As the independent variable, and , It is a constant under specific anchor plate types and towing techniques. Indicates the embedding depth.

[0013] Preferably, the trajectory equation of the towed anchor in linear soil in step S4 is as follows: ; In the formula, As the independent variable, and ; It is determined by the specific type of anchor plate and the towing technology.

[0014] Preferably, the method for predicting the critical state trajectory of the towed anchor in linear soil in step S5 includes: introducing a critical cable length to address the practical situation of limited cable length in engineering projects. and critical drag distance The critical cable length and critical towing distance are calculated. When the towing process reaches the critical state, the embedding point coincides with the towing point. The towing equation under ideal conditions is used to describe the motion trajectory of the towing anchor after the critical state. When the initial conditions are limited and changed, the main parameters in the towing equation are extracted from the parameters when the critical state occurs.

[0015] Preferably, in step S5, the critical cable length and critical towing distance are calculated using the following formula: Critical cable length: ; Critical drag distance: ; In the formula, This is a dimensionless quantity, representing the relative embedment depth of the anchor plate relative to the entire towing process. Indicates the maximum embedding depth. Indicates the diameter of the cable.

[0016] Preferably, in step S5, when the towing process reaches a critical state, the motion trajectory of the towing anchor after the critical state is as follows: ; In the formula, It is a variable function, and .

[0017] Therefore, this invention employs an efficient analysis method for the embedding trajectory of towed anchors in clay-sand seabeds. Based on the kinematic model derived from circular motion and motion synthesis, it accurately describes the complete motion trajectory of the anchor plate from initial embedding to its ultimate depth, effectively reflecting the motion characteristics of the anchor plate during the actual embedding process. By establishing an equivalent motion parameter system and a critical state prediction method, it can adapt to different soil conditions and engineering scenarios, providing full-process trajectory prediction for the installation and positioning of towed anchors. The analytical relationship established based on the velocity synthesis principle reveals the intrinsic connection between towing parameters and the motion trajectory, providing theoretical guidance for the optimal selection of towing parameters in engineering practice. This method, by establishing a complete motion trajectory prediction theoretical system, achieves accurate analysis and prediction of the embedding trajectory of towed anchors.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the motion model of the towed anchor under ideal conditions, which is the efficient analysis method for the motion trajectory of the towed anchor embedded in the clay sand seabed of the present invention. Figure 2This is a schematic diagram of the velocity decomposition of the towed anchor, which is part of the efficient analysis method for the motion trajectory of the towed anchor embedded in the clay sand seabed of the present invention. Figure 3 This is a schematic diagram of the motion model under actual conditions for the efficient analysis method of the motion trajectory of the towed anchor embedded in the clay sand seabed of the present invention; Figure 4 A comparison of motion trajector-free motion trajector in Example 1 of the efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to the present invention. Figure 1 ; Figure 5 A comparison of motion trajector-free motion trajector in Example 1 of the efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to the present invention. Figure 2 ; Figure 6 Example 2 of this invention provides a comparison of trajectories using different methods for the efficient analysis of the motion trajectory of a towed anchor embedded in a clay-sand seabed. Figure 1 ; Figure 7 Example 2 of this invention provides a comparison of trajectories using different methods for the efficient analysis of the motion trajectory of a towed anchor embedded in a clay-sand seabed. Figure 2 . Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0022] Example Please see Figures 1-7 This invention provides an efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed, comprising the following steps: Step S1: Obtain the towing anchor and seabed environmental parameters. These include: the geometry and weight of the towing anchor, the diameter and length of the towing cable, the type of seabed soil and its strength parameters (undrained shear strength, strength gradient, etc.), the speed of movement at the towing point, and the towing angle at the mooring point.

[0023] Step S2: Based on the towed anchor embedding mechanism, establish a kinematic model of the towed anchor to describe the real-time position of the anchor plate. The motion of the anchor plate is decomposed into two components: circular motion centered on the tow point and horizontal motion of the tow point itself. A schematic diagram of the kinematic model of the towed anchor is shown below. Figure 1 As shown, the real-time position of the anchor plate is described by the equations of a circle and a line.

[0024] The equation of the circle is shown below: (1) The equation of the line is shown below: (2) The horizontal position of the drag point is shown in the following formula: (3) In the formula, Indicates the direction along the seabed. Indicates the direction of gravity. Let the horizontal coordinates of the drag point be... This refers to the length of the tow cable. This is the drag distance. Represents a variable function, and .

[0025] Assumptions are made about the motion model: During towing, the towing angle of the towing cable at the mooring point is constant, from which we can obtain: (4) in, Represents the azimuth angle of the anchor plate. This represents the drag angle of the anchor plate.

[0026] Step S3: Based on the principle of velocity synthesis, establish the relationship between the horizontal motion velocity of the towing point and the circumferential motion velocity of the anchor plate, derive the analytical expression between the towing distance and the azimuth angle of the anchor plate, and combine it with the kinematic model to form the towing trajectory prediction equation under ideal conditions, which is used to describe the motion path of the anchor plate from the initial embedment to the limit depth.

[0027] The actual speed of the towing anchor Decompose into horizontal velocity at the center of the circle and the speed of circular motion around the center The vector sum, such as Figure 2 As shown, the expression is as follows: (5) Wherein, the speed of the center of the circle is The magnitude along the positive x-axis is The anchor plate is affected by the horizontal movement of the center of the circle, and its horizontal velocity will include a magnitude of Velocity components; velocity of the anchor plate when it makes circular motion around the center. Size is Its angle with the y-axis and the embedded cable and x The included angle of the axis is can exist x and y Direction decomposed into and The actual speed of the anchor plate is Size is If the anchor moves along the plane of the anchor plate, then the direction of the tangent at any point on the trajectory is the direction of the anchor's movement, and the angle between the tangent and the horizontal plane is the azimuth angle of the anchor plate. The velocity components are in x and y The directions are superimposed as follows: (6) Suppose a small time variable The corresponding angle of rotation of the anchor around the center is Then the arc length corresponding to this time period is: (7) From formulas (4), (6), and (7), we can obtain: (8) From 0 to Integrate and with respect to variables From 0 points to And substitute the initial conditions hour, Then the drag distance can be expressed as: (9) From equations (1), (2), (3), and (9), it can be seen that the expression for the embedded motion trajectory of the towed anchor can be expressed as: (10) in, It is a variable function ( ); and Determined by the specific anchor plate type and towing technique. And based on the specific embedding properties of the anchor plate, it always satisfies... .

[0028] Formula (10) is called the drag equation under ideal conditions, and the trajectory represented by formula (10) is called the drag curve under ideal conditions. The drag equation and drag curve under ideal conditions are applicable to drag embedding conditions where the anti-chain effect of the drag cable is not obvious, such as when the embedded cable pole is shallowly buried.

[0029] Step S4: Determine the equivalent motion parameters and establish the motion trajectory equations of the towed anchor in homogeneous and linear soils. The equivalent motion parameters include: Equivalent cable length : The distance between the mooring point and the towing point; Effective cable length : The length of the embedded cable; Equivalent angle : The angle between the equivalent cable length and the horizontal plane; tow cable length : The minimum cable length required for the anchor plate to reach its maximum embedment depth.

[0030] The actual towing and embedding problem is more complex: firstly, soil resistance causes the embedding cable to have an anti-catenary shape (not an ideal straight line); secondly, the embedding point and the towing point usually do not coincide, and the towing cable is divided into two sections: the embedding cable and the bottom cable. The length of the towing cable is defined as the anchor plate retention... The minimum cable length required to reach the ultimate embedding depth is defined at this point, where the embedding point coincides with the dragging point, the horizontal submerged cable length is zero, the effective cable length equals the dragging cable length, and the virtual straight line between the dragging point and the anchor plate represents the equivalent cable length. Based on this, the actual motion model of the anchor can be described as follows: the anchor moves in a circle with the dragging point as the center and the equivalent length of the dragging cable as the diameter, while the dragging point moves horizontally at a uniform speed. Figure 3 As shown.

[0031] The theoretical expression for the anchor embedding trajectory in actual conditions is similar to the dragging equation (10) in ideal conditions, but the independent variable is... And its value changes from 0 to 0 during the dragging process. ,have: (11) in, The drag angle at the mooring point. The angle between the tow cable at the mooring point and the horizontal plane.

[0032] To express the effective length, the anti-catcher equation must be known. Integrating along the curve from the mooring point to the anchor, the effective length can be expressed as: (12) For homogeneous soils, a new anti-catenette equation for towing cables is obtained: (13) Substituting formula (13) into formula (12), the effective length can be expressed as: (14) in, It is about The function is of the form: (15) Introducing variables With variables The relationship, the effective length can be further expressed as: (16) in, This represents the maximum embedding depth.

[0033] At any given time, and The following relationship is satisfied between them: (17) From the equation of the circle and formulas (14) and (17), the equivalent length can be expressed as: (18) From the linear equation, we can obtain the following expression: (19) Substituting formulas (14) and (18) into formula (13), the equivalent angle can be expressed as: (20) At the maximum embedding depth , ,and Substituting these conditions into equation (14), the tow cable length can be expressed as: (twenty one) Formula (21) shows that when the embedding depth When the tow cable length is known, it is fixed.

[0034] The analysis of motion models under actual conditions includes: (twenty two) Based on the above expression, and assuming For small angles, the drag distance formula can be expressed as: (twenty three) Based on the motion model framework, the trajectory of homogeneous soil in actual conditions can be represented by the following equation: (twenty four) in, For independent variable ( ); It is a constant under specific anchor plate types and towing techniques; , , and It can be calculated using formulas (15), (16), (21), and (23) respectively. Based on the embedding characteristics of the anchor plate, It must be satisfied. Formula (24) is called the drag equation in the actual state, and the trajectory curve it represents is called the drag curve in the actual state.

[0035] All the limiting embedment depths involved in the above equations are calculated using existing methods in the art, and the resulting limiting embedment depths can be used in formula (21) to calculate the tow cable length. .

[0036] The drag equation in homogeneous soil still follows the analytical framework under actual conditions. Based on the motion model of the drag anchor, a more accurate equation for the motion trajectory of the drag anchor in homogeneous soil can be derived: (25) in, For independent variable ( ), It is a constant under specific anchor plate types and towing techniques. , and They can be calculated using the following formulas: (26) Based on the embedding characteristics of the anchor plate, the following must be satisfied: The conditions. Formula (25) is the drag equation of the drag anchor in homogeneous soil, and the trajectory curve it represents is called the drag curve of the drag anchor in homogeneous soil.

[0037] If the embedded cable is tangent to the theoretical seabed surface, that is, at the embedding point, When the towing anchor drags the cable in linear soil, the anti-catenary equation (hereinafter referred to as the linear soil anti-catenary equation) can be expressed as: (27) in, .

[0038] The effective cable length equation is: (28) The equation for the length of the tow cable is: (29) According to the definition of the motion model, the equivalent cable length is the distance between the mooring point and the anchor plate. From the linear soil anti-catenette equation (27) and combined with equation (28), This can be deduced as: (30) From the above equation (30), the equivalent angle can be expressed as: (31) Formula (30) differs from the equivalent cable length equation for towed anchors in homogeneous soil, but it can still be considered that its change during towing is small, and therefore it can be approximated as... It is a constant. Assume... For small angles, integrating equation (22) yields the equation for the drag distance of the dragging anchor in linear soil: (32) Based on the motion model framework, the trajectory equation of the towed anchor in linear soil can be expressed as follows: (33) In the formula, For independent variable ( ); Determined by specific anchor plate type and towing technology. In sandy soil, The value represents the initial embedment depth of the cable; in clay, . , and The results are obtained by calculation using equations (28), (29), and (32), respectively. Based on the drag-and-embed characteristics, the following must be satisfied: The conditions. Equation (33) is called the dragging equation of the dragging anchor in linear soil, and the trajectory curve it depicts is called the dragging curve of the dragging anchor in linear soil.

[0039] As the theoretical seabed surface ( z =0), the shear strength of general linear clay can be used It indicates that: In clay ; In sandy soil .

[0040] In the formula, The shear strength of the seabed surface. This represents the undrained shear strength gradient. For soils with linear strength, if the bearing capacity of the seabed is less than the weight of the tow cable, the horizontal bottom-laying cable will embed itself into the seabed until it reaches a depth below the soil surface. place, This represents the initial embedding depth of the cable.

[0041] For linear strength clay ; For non-cohesive soil, .

[0042] In the formula, and This is the load-bearing capacity coefficient of the tow cable. The weight per unit cable length. The buoyant unit weight of the soil. For the effective load-bearing width of the embedded cable, The base width, in this context, refers to the cable diameter.

[0043] The complete motion trajectory of the anchor plate reaching its theoretical limit embedment depth can be predicted according to the drag equation (33). However, in engineering practice, the anchor plate usually does not need to be embedded to the theoretical limit depth. This means that the length of the drag cable or the initial horizontal bottom cable used in actual engineering is often much smaller than the theoretical drag cable length. The actual required length of the tow cable is determined by the required embedment depth of the anchor plate.

[0044] Step S5: Establish a method for predicting the critical trajectory of a towed anchor in linear soil and output the prediction results. Considering the limited length of the towed cable in engineering projects, a critical cable length is introduced. and critical drag distance The critical cable length and critical towing distance are calculated. When the towing process reaches the critical state, the embedding point coincides with the towing point. The towing equation under ideal conditions is used to describe the motion trajectory of the towing anchor after the critical state. When the initial conditions are limited and changed, the main parameters in the towing equation are extracted from the parameters when the critical state occurs.

[0045] For a diameter of The actual installation cable, if the required embedding depth Determined and The critical cable length required to reach this depth can be calculated using the following equation. and the corresponding critical drag distance .

[0046] Critical cable length: (34) Critical drag distance: (35) In the formula, This is a dimensionless quantity, representing the relative embedment depth of the anchor plate relative to the entire towing process. Indicates the maximum embedding depth. Indicates the diameter of the cable.

[0047] In practical engineering, if the required embedment depth is known, equations (34) and (35) can be used to determine the required tow cable length and the required towing distance. The trajectory before reaching the required embedment depth can be determined by equation (33), after which the engineering requirements are met. If towing continues after the critical point, the state after the critical point closely matches the ideal tow anchor motion model, but the main parameters in the towing equations need to be extracted from the parameters at the time of the critical point.

[0048] When the critical condition occurs, the unconstrained drag equation provides the following known conditions: , , , , as well as Accordingly, the initial conditions for the constrained ideal state are: , , , The trajectory of the towed anchor after the critical point can be determined by the following formula: (36) In the formula, It is a variable function, and .

[0049] Example 1: Comparison and verification with existing technologies To verify the prediction accuracy of the method of this invention under linear soil conditions, a hypothetical working condition published in the prior art was used for verification. This study compiled the prediction results of five different institutions or individuals for the same working condition. In this embodiment, a simplified anchor plate is used, the soil is homogeneous clay, and its undrained shear strength is... The effective width of the towing cable is 1.5 z kPa. The buoyant density per unit length is 0.05m. It is 10.3 kg / m, bearing capacity coefficient The values ​​are taken as 11.87 and 7.6 respectively. Based on existing technology, the drag angle... A value between 53° and 55° is considered reasonable. Based on the above parameters, the ultimate embedment depth of the anchor is first calculated using the formula for ultimate embedment depth in existing technologies. ,when At 53°, Between 44.8m and 57.7m; when = At 55°, The length is between 50.3m and 64.9m. The corresponding tow cable length is then calculated using the effective cable length equation (29). ,in The value can be obtained from the formula The above parameters are calculated. Substituting these parameters into the dragging equation (33), the anchor embedding trajectory can be calculated.

[0050] Figure 4 The paper presents a comparison between the motion trajectory curve predicted by the method of this invention and the prediction results of five other institutions. It can be seen that when... When the angle is 53°, the trajectory predicted by this method lies entirely within the distribution range of the prediction curves from the five institutions, and its average value is very close to the average value of the prediction results from the five institutions; when At 55°, the trajectory predicted by this method is also within the distribution range of the comparison curve. Its average value is slightly higher than the average value of the five predicted values, but it is still within a reasonable error range.

[0051] Example 2: Comparison and verification with existing technologies To further verify the predictive capability of the method of this invention, comparative analysis was conducted using experimental data from a drum centrifuge, a technique employed in the prior art. This experiment directly measured the trajectory of the towed anchor in normally consolidated clay using a precise physical model. A Vryhof Stevpris anchor with a scale of 1:16 was used as the research object, corresponding to a prototype anchor plate with a self-weight of 32 tons. The anchor shank angle was investigated. Two working conditions were described, one at 32° and the other at 50°. Some parameters of the prototype anchor plate, towing cable, and soil were known, including the motion direction angle of the anchor plate. The angle is 9.7°, and the anchor length is [missing information]. The effective load-bearing width of the tow cable is 4.97m. The undrained shear strength of the soil is 0.24m. The bearing capacity coefficient is 1.0 z kPa. The value is 9. When applying the method of this invention, the key input parameters are... A three-dimensional model of the prototype anchor plate was established, and an analytical method from the existing technology was used to determine the anchor plate's center of mass. This method assumes the direction of the drag force at the mooring point passes through the anchor plate's centroid. Another key parameter is the limiting embedment depth. It is calculated according to existing technical methods. According to the rules of this field, Take an average value of 0.4. Substitute the determined parameters into the dragging equation (33) to calculate the anchor embedding trajectory.

[0052] A comparison of the predicted trajectory, the measured trajectory of a drum centrifuge, and the numerical simulation results accompanying this study is shown below. Figure 5 As shown in the figure, the drag curve predicted by this method basically matches the experimental measurement curve and the numerical simulation curve for both 32° and 50° anchor angle conditions. In particular, by appropriately adjusting the viscosity coefficient... (For example, if we take 0.32), the prediction results of the method of the present invention are closer to the experimental data.

[0053] The comparison of the results of the method of the present invention with those of the two specific embodiments shows that the method of the present invention exhibits excellent predictive performance, has wide applicability, reliable predictive accuracy and good engineering application value, and provides an effective theoretical tool for the optimized design and construction control of towed anchors.

[0054] Therefore, the present invention adopts the above-mentioned efficient analysis method for the embedding motion trajectory of the towed anchor in the clay sand seabed. Based on the kinematic model derived from circular motion and motion synthesis, it can accurately describe the complete motion trajectory of the anchor plate from the initial embedding to the ultimate depth, and effectively reflect the motion characteristics of the anchor plate in the actual embedding process.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed, characterized in that, Includes the following steps: Step S1: Obtain the towed anchor and seabed environmental parameters; Step S2: Based on the embedding mechanism of the towed anchor, establish a kinematic model of the towed anchor and describe the real-time position of the anchor plate through the kinematic model; Step S3: Based on the principle of velocity synthesis, establish the relationship between the horizontal motion velocity of the towing point and the circular motion velocity of the anchor plate, derive the analytical expression between the towing distance and the azimuth angle of the anchor plate, and combine the kinematic model to establish the prediction equation of the towing trajectory under ideal conditions. Step S4: Determine the equivalent motion parameters and establish the motion trajectory equations of the towed anchor in homogeneous and linear soils; Step S5: Establish a method for predicting the critical state trajectory of a towed anchor in linear soil and output the prediction results.

2. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 1, characterized in that, The towing anchor and seabed environmental parameters in step S1 include: the geometric dimensions and weight of the towing anchor, the diameter and length of the towing cable, the type and strength parameters of the seabed soil, the speed of movement at the towing point, and the towing angle at the mooring point.

3. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 2, characterized in that, Step S2 includes: The motion of the anchor plate is decomposed into two components: circular motion with the drag point as the center and horizontal motion of the drag point itself. The kinematic model describes the real-time position of the anchor plate through circle equations and line equations. The equation of the circle is shown below: ； The equation of the line is shown below: ； The horizontal position of the drag point is shown in the following formula: ； In the formula, Indicates the direction along the seabed. Indicates the direction of gravity. Let the horizontal coordinates of the drag point be... This refers to the length of the tow cable. This is the drag distance. Represents a variable function, and .

4. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 3, characterized in that, The ideal drag trajectory prediction equation in step S3 is as follows: ； In the formula, Represents a variable function, and , This represents the drag angle of the anchor plate.

5. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 4, characterized in that, The equivalent motion parameters in step S4 include: Equivalent cable length : The distance between the mooring point and the towing point; Effective cable length : The length of the embedded cable; Equivalent angle : The angle between the equivalent cable length and the horizontal plane; tow cable length : The minimum cable length required for the anchor plate to reach its maximum embedment depth.

6. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 5, characterized in that, The more accurate equation for the motion trajectory of the towed anchor in homogeneous soil under actual conditions in step S4 is shown below: ； Based on the embedding characteristics of the anchor plate, the above equation satisfies conditions; In the formula, As the independent variable, and , It is a constant under specific anchor plate types and towing techniques. Indicates the embedding depth.

7. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 6, characterized in that, The equation of motion trajectory of the towed anchor in linear soil in step S4 is as follows: ； In the formula, As the independent variable, and ; It is determined by the specific type of anchor plate and towing technology.

8. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 7, characterized in that, The method for predicting the critical state trajectory of the towed anchor in linear soil in step S5 includes: considering the limited length of the towed cable in engineering projects, a critical cable length is introduced. and critical drag distance The critical cable length and critical towing distance are calculated. When the towing process reaches the critical state, the embedding point coincides with the towing point. The towing equation under ideal conditions is used to describe the motion trajectory of the towing anchor after the critical state. When the initial conditions are limited and changed, the main parameters in the towing equation are extracted from the parameters when the critical state occurs.

9. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 8, characterized in that, In step S5, the critical cable length and critical drag distance are calculated using the following formulas: Critical cable length: ； Critical drag distance: ； In the formula, This is a dimensionless quantity, representing the relative embedment depth of the anchor plate relative to the entire towing process. Indicates the maximum embedding depth. Indicates the diameter of the cable.

10. The efficient analysis method for the motion trajectory of a towed anchor embedded in a clay-sand seabed according to claim 9, characterized in that, In step S5, when the towing process reaches a critical state, the trajectory of the towing anchor after the critical state is as follows: ； In the formula, It is a variable function, and .

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