A method for calculating dynamic tension in an anchor cable mooring state

Abstract

The application discloses a kind of dynamic tension calculation methods under the state of anchor cable mooring, applied to immersed tube-anchor cable system, comprising the following steps: step 1: based on the constraint condition that immersed tube-anchor cable is in mooring state and considers that anchor cable generates tensile force to immersed tube, establish the motion equation of immersed tube in wave;Step 2: based on the motion equation, the roll, surge, yaw, sway, pitch, heave six degrees of freedom displacement of immersed tube is solved;Step 3: based on the displacement of six degrees of freedom, the motion vector corresponding to the three coordinate axes direction under the coordinate system of immersed tube gravity center based on the connection endpoint of anchor cable and immersed tube is solved;Step 4: based on motion vector, the displacement vector of tangential and normal of anchor cable dynamic tension respectively is calculated.This application can accurately calculate the dynamic tension of anchor cable under the state of mooring under the action of wave, and the subsequent anchor cable fracture prediction can be applied based on the calculated dynamic tension, and data support guidance is provided.

Description

Technical Field

[0001] This invention relates to the field of immersed tunnel construction technology, specifically a method for calculating dynamic tension under anchor cable mooring conditions. Background Technology

[0002] During the sinking and mooring of the immersed tunnel section, anchor cables are required for positioning, forming a tunnel-cable system. The cables are the main structural component of the anchor cables and can therefore be considered as anchor cables themselves. Under wave action, the immersed tunnel section experiences periodic swaying, causing alternating periods of relaxation and tension in the anchor cables, resulting in sudden changes in dynamic tension. The peak value of this dynamic tension can be many times that of the normal tension. In extremely short periods, excessive dynamic tension can cause the anchor cables to break, leading to safety risks such as tunnel section displacement. Therefore, for engineering safety, it is necessary to calculate the dynamic tension of the anchor cables to provide data guidance and to predict anchor cable breakage based on this dynamic tension. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method for calculating dynamic tension under anchor cable mooring conditions, which can solve the problems described in the background art.

[0004] The technical solution to achieve the objective of this invention is: a method for calculating dynamic tension under anchor cable mooring conditions, applied to immersed tube-anchor cable systems, comprising the following steps:

[0005] Step 1: Based on the mooring state of the immersed tube and anchor cable, and considering the constraint of the tension force exerted by the anchor cable on the immersed tube, establish the motion equation of the immersed tube in the waves.

[0006] Step 2: Based on the aforementioned equations of motion, solve for the displacements of the immersed tube in six degrees of freedom: roll, sway, head roll, roll, pitch, and heave.

[0007] Step 3: Based on the displacements of the immersed tube in six degrees of freedom (roll, sway, pitch, heave, roll, and heave), solve for the motion vectors (D) at the connection points between the anchor cables and the immersed tube in the x, y, and z coordinate axes of the immersed tube's centroid coordinate system. lx D ly D lz );

[0008] Step 4: Based on motion vectors (D) lx D ly D lz ), calculate the displacement vector y of the anchor cable dynamic tension in the tangential direction. t The displacement vector y in the normal direction r .

[0009] Furthermore, the equation of motion of the immersed tube in the waves is as shown in formula ①:

[0010]

[0011] In the formula, m jk A is the element in the j-th row and k-th column of the generalized mass matrix. jk It is the element in the j-th row and k-th column of the additional quality coefficient, B jk It is the element in the j-th row and k-th column of the damping coefficient, C jk It is the element in the j-th row and k-th column of the generalized restoring force coefficient. It is the Froude-Krylov force under wave w in the j-th degree of freedom. E is the diffraction force under wave w in the j-th degree of freedom. eq This is the equivalent elastic modulus of the anchor cable, where A is the cross-sectional area of ​​the anchor cable, ε is the dynamic strain of the anchor cable, L is the length of the anchor cable, and μ is the dynamic strain of the anchor cable. k The displacements of the immersed tunnel section are in six degrees of freedom: lateral roll, sway, head roll, lateral roll, sway, and heave. μ k The second derivative, μ k The first derivative, e represents the integral of the dynamic strain of the anchor cable along the length of the anchor cable. iωt Indicates the time component.

[0012] Furthermore, the motion vector (D) is calculated according to formula ②. lx D ly D lz ):

[0013]

[0014] In the formula, (x l y l z1) is the coordinate of the connection end of the anchor cable and the immersed tube in the centroid coordinate system of the immersed tube.

[0015] Furthermore, the displacement vectors y of the anchor cable dynamic tension in the tangential direction are calculated according to formula ③. t The displacement vector y in the normal direction r :

[0016]

[0017] In the formula, ρ w ρ m These represent the density of the anchor cable and the density of the water, respectively; T0 is the static tension of the anchor cable; α represents the angle between the anchor cable and the bottom of the water; g represents the acceleration due to gravity; and F... w It is the force F exerted on the anchor cable in the water. a It is the force ε exerted on the anchor cable in the air.m It is a dynamic response.

[0018] Furthermore, F w The result is obtained through formula ④:

[0019]

[0020] In the formula, C Dw C is the drag coefficient of the anchor cable in water. mw It is the additional mass coefficient of the anchor cable in the water.

[0021] Furthermore, F a Calculated using formula ⑤:

[0022]

[0023] In the formula, C aw ρ is the drag coefficient of the anchor cable in the air. a It is air density, u a It's air speed.

[0024] Furthermore, ε m Calculated using formula ⑥:

[0025]

[0026] The beneficial effects of this invention are: This invention can accurately calculate the dynamic tension of the anchor cable in the immersed tube-anchor cable system under wave action in the moored state. Based on the calculated dynamic tension, it can be applied to subsequent anchor cable fracture prediction, providing data support and guidance. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating a preferred embodiment of the present invention;

[0028] Figure 2 This is a schematic diagram of the dynamic tension-time curve of the anchor cable under excitation with a wave height of 0.6 m and a wave period of 5 s, where the water flow velocity is 0.5 m / s and the wind speed is 9.5 m / s.

[0029] Figure 3 This is a schematic diagram of the dynamic tension-time curve of the anchor cable under excitation with a wave height of 0.6 m and a wave period of 9 s. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0031] like Figures 1-3 As shown, a method for calculating dynamic tension under anchor cable mooring conditions, applied to a immersed tube-anchor cable system, includes the following steps:

[0032] Step 1: Based on the mooring state of the immersed tube and anchor cable, and considering the constraint of the tension force exerted by the anchor cable on the immersed tube, establish the motion equation of the immersed tube in the waves.

[0033] In this step, the anchor cables, including the tension cables, exert tension on the immersed tunnel section. These cables are typically made of steel wire rope; therefore, it is the steel wire rope that exerts tension on the immersed tunnel section. Thus, considering the constraint of the steel wire rope tension, the influence of waves on the movement of the immersed tunnel section is considered.

[0034] In an optional implementation, the equation of motion of the immersed tube in the waves is as described in formula ①:

[0035]

[0036] In the formula, m jk A is the element in the j-th row and k-th column of the generalized mass matrix. jk It is the element in the j-th row and k-th column of the additional quality coefficient, B jk It is the element in the j-th row and k-th column of the damping coefficient, C jk It is the element in the j-th row and k-th column of the generalized restoring force coefficient. It is the Froude-Krylov force under wave w in the j-th degree of freedom. E is the diffraction force under wave w in the j-th degree of freedom. eq This is the equivalent elastic modulus of the anchor cable, where A is the cross-sectional area of ​​the anchor cable, ε is the dynamic strain of the anchor cable, L is the length of the anchor cable, and μ is the dynamic strain of the anchor cable. k The displacements of the immersed tunnel section are in six degrees of freedom: lateral roll, sway, head roll, lateral roll, sway, and heave. μ k The second derivative, μ k The first derivative, e represents the integral of the dynamic strain of the anchor cable along the length of the anchor cable. iωt Indicates the time component.

[0037] in, This represents the tension force exerted by the wire rope on the immersed tube. Therefore, formula ① takes into account the constraint condition of the tension force exerted by the anchor cable on the immersed tube.

[0038] Step 2: Based on the aforementioned equation of motion, solve for the displacements of the immersed tube in six degrees of freedom: roll, sway, head roll, roll, pitch, and heave.

[0039] In this step, the displacements in the six degrees of freedom can be solved by using formula ① for the equation of motion.

[0040] Step 3: Solve for the motion vector (D) at the connection point between the anchor cable and the immersed tube in the x, y, and z coordinate axes based on the centroid coordinate system of the immersed tube, according to formula ②. lx D ly D lz ), D lx D represents the motion vector along the x-axis. ly D represents the motion vector along the y-axis. lz This represents the motion vector along the z-axis. The origin of the immersed tunnel's centroid coordinate system is the centroid of the immersed tunnel itself. Formula ② is as follows:

[0041]

[0042] In the formula, (x l y l , z l ) is the coordinate of the connection point between the anchor cable and the immersed tube in the centroid coordinate system of the immersed tube.

[0043] Formula ② can be used to determine the motion vectors in three directions at the connection point between the anchor cable and the immersed tube.

[0044] Step 4: Calculate the displacement vector y of the anchor cable dynamic tension in the tangential direction according to formula ③. t The displacement vector y in the normal direction r :

[0045]

[0046] In the formula, ρ w ρ m These represent the density of the anchor cable and the density of the water, respectively; T0 is the static tension of the anchor cable; α represents the angle between the anchor cable and the bottom of the water; g represents the acceleration due to gravity; and F... w This is the force exerted on the anchor cable in the water, which can be calculated using formula ④, F. a It is the force exerted on the anchor cable in the air, which can be calculated using formula ⑤, ε. m It is dynamic strain, which can be calculated using formula ⑥:

[0047]

[0048] In the formula, C Dw C is the drag coefficient of the anchor cable in water. mw C is the additional mass coefficient of the anchor cable in water. aw ρ is the drag coefficient of the anchor cable in the air. a It is air density, u a d1 represents the air velocity and the anchor cable diameter.

[0049] The above formulas can be used to calculate the vectors of the tangent and normal directions of the anchor cable dynamic tension. Formula ⑥ can be used to obtain the anchor cable dynamic tension, thereby solving for the anchor cable dynamic tension and generating a dynamic tension-time curve. The dynamic tension-time curve can be used to determine whether a tension-relaxation phenomenon has occurred.

[0050] refer to Figures 2-3 , Figure 2 This is a schematic diagram of the dynamic tension-time curve of the anchor cable under excitation with a wave height of 0.6 m and a wave period of 5 s, where the water flow velocity is 0.5 m / s and the wind speed is 9.5 m / s. Figure 3 This is a schematic diagram of the dynamic tension-time curve of an anchor cable under wave excitation with a wave height of 0.6 m and a wave period of 9 s. The water flow velocity is 0.5 m / s, and the wind speed is 9.5 m / s. The tension shown in the graph refers to dynamic tension. Figure 2 As can be seen, the maximum dynamic tension of the anchor cable is 73.794.5 N (Newtons), and the minimum is 7036 N. Since the minimum value is greater than 0, it indicates that the anchor cable remains taut. From Figure 3 It can be seen that the maximum value of the dynamic tension of the anchor cable is 83225.4N and the minimum value is 0N. Since the minimum value is ≤0, the dynamic tension changes from the maximum value to 0 and then back to the positive value >0, indicating that the anchor cable exhibits frequent alternation between tension and relaxation.

[0051] By determining whether a tension-relaxation effect (phenomenon) occurs and combining this with dynamic tension, it is possible to predict in advance whether the anchor cable will break, or to predict the level of breakage risk, thereby ensuring mooring and positioning safety. For example, when a tension-relaxation effect occurs, and the maximum or average value of the dynamic tension exceeds a preset threshold, it can be considered that a breakage risk will occur, and the greater the exceedance of the preset threshold, the greater the breakage risk.

[0052] This invention can accurately calculate the dynamic tension of anchor cables when moored and subjected to wave action. Based on the calculated dynamic tension, it can be applied to subsequent anchor cable fracture prediction, providing data support and guidance.

[0053] The embodiments disclosed in this specification are merely illustrative of one aspect of the invention, and the scope of protection of the invention is not limited to these embodiments. Any other functionally equivalent embodiments fall within the scope of protection of the invention. Those skilled in the art can make various other corresponding changes and modifications based on the technical solutions and concepts described above, and all such changes and modifications should fall within the scope of protection of the claims of this invention.

Claims

1. A method for calculating dynamic tension under anchor cable mooring conditions, characterized in that, Applied to immersed tube-anchor cable systems, the following steps are included: Step 1: Based on the mooring state of the immersed tube and anchor cable, and considering the constraint of the tension force exerted by the anchor cable on the immersed tube, establish the motion equation of the immersed tube in the waves. Step 2: Based on the aforementioned equations of motion, solve for the displacements of the immersed tube in six degrees of freedom: roll, sway, head roll, roll, pitch, and heave. Step 3: Based on the displacements of the six degrees of freedom of the immersed tunnel segment (roll, sway, pitch, heave, roll, and heave), solve for the motion vectors at the connection points between the anchor cables and the immersed tunnel segment in the x, y, and z coordinate axes of the immersed tunnel segment's centroid coordinate system. ; Step 4: Based on motion vectors Calculate the displacement vectors of the anchor cable dynamic tension in the tangential direction. displacement vector and normal direction ; Step 5: Dynamic Strain Calculated using formula ⑥: ------⑥ 2. The method for calculating dynamic tension under anchor cable mooring conditions according to claim 1, characterized in that, The equation of motion of the immersed tube in the waves is as shown in formula ①: ，k=1~6------① In the formula, It is the element in the j-th row and k-th column of the generalized mass matrix. It is the element in the j-th row and k-th column of the additional quality coefficient. It is the element in the j-th row and k-th column of the damping coefficient. It is the element in the j-th row and k-th column of the generalized restoring force coefficient. It is the Froude-Krylov force under wave w in the j-th degree of freedom. It is the diffraction force under wave w in the j-th degree of freedom. It is the equivalent elastic modulus of the anchor cable. The cross-sectional area of ​​the anchor cable. Let L be the dynamic strain of the anchor cable, and L be the length of the anchor cable. The displacements of the immersed tunnel section are in six degrees of freedom: lateral roll, sway, head roll, lateral roll, sway, and heave. express The second derivative, express The first derivative, This represents the integral of the dynamic strain of the anchor cable along its length. Indicates the time component.

3. The method for calculating dynamic tension under anchor cable mooring conditions according to claim 2, characterized in that, Calculate the motion vector using formula ②. : ------② In the formula, ( , ) is the coordinate of the connection point between the anchor cable and the immersed tube in the centroid coordinate system of the immersed tube.

4. The method for calculating dynamic tension under anchor cable mooring conditions according to claim 3, characterized in that, The displacement vectors of the anchor cable dynamic tension in the tangential direction are calculated using formula ③. displacement vector and normal direction : ------③ In the formula, These are the densities of the anchor cable and the water, respectively. It is the tension of the anchor cable in its static state. The angle between the anchor cable and the seabed is represented by , and g represents the acceleration due to gravity. It is the force exerted on the anchor cable in the water. It is the force exerted on the anchor cable in the air.

5. The method for calculating dynamic tension under anchor cable mooring conditions according to claim 4, characterized in that, The result is obtained through formula ④: ------④ In the formula, It is the drag coefficient of the anchor cable in water. It is the additional mass coefficient of the anchor cable in the water. Indicates the diameter of the anchor cable.

6. The method for calculating dynamic tension under anchor cable mooring conditions according to claim 5, characterized in that, Calculated using formula ⑤: ------⑤ In the formula, It is the drag coefficient of the anchor cable in the air. It is air density. It's air speed.

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