A method of dynamic response of laying a cable on an undersea undulating terrain

Abstract

The present application relates to the technical field of submarine cable laying, in particular to a dynamic response method for laying cable on submarine undulating terrain. A numerical dynamic model based on the coupling of cable-laying ship, submarine cable and submarine slope is established by combining catenary theory and lumped mass method, which is used to simulate the laying process of the cable on the undulating submarine section. The influences of laying speed, speed adjustment position, submarine slope and swing distance on the cable-submarine adhesion, maximum effective tension and minimum bending radius are analyzed. The final cable laying strategy is determined as the research result, which provides a theoretical basis for selecting appropriate cable laying scheme in complex submarine environment.

Description

Technical Field

[0001] This invention relates to the field of submarine cable laying technology, and in particular to a dynamic response method for laying cables on undulating submarine terrain. Background Technology

[0002] The ocean holds abundant renewable energy resources, and their large-scale development relies on efficient 24 / 7 power transmission systems. Submarine cable laying is a crucial component of offshore energy network construction; therefore, its design and analysis are essential for achieving reliable long-distance power transmission and the large-scale development of marine renewable energy.

[0003] Dynamic response during cable laying is a key issue in design and construction control. Excessive tension can lead to structural damage, while insufficient tension can cause cable accumulation or entanglement. Meanwhile, irregular seabed topography can also affect the bending deformation and bottom-contact behavior of cables (Drissi-Habti et al., 2022a, 2022b). To address this issue, previous studies have systematically analyzed the tension distribution during cable laying from both static and dynamic perspectives (Drissi-Habti et al., 2022b; Zhang et al., 2023). Among these, the classic catenary model proposed by Zajac (1957) and the improved model by Yoshizawa and Yabuta (1983) remain important foundations for static tension analysis of cables. Yang et al. (2013) and Mamatsopoulos et al. (2020a, 2020b) further incorporated factors such as water depth, current velocity, and cable weight. It is worth noting that Yan et al. (2013) analyzed the umbilical cable recovery load and explored the catenary morphology, contact point (TDP), and seabed contact behavior, pointing out that contact boundary conditions significantly affect the cable's stress and geometry. These research findings provide important references for the mechanical analysis of submarine cable laying under complex seabed conditions.

[0004] However, in actual offshore operations, ideal static assumptions often do not hold. Therefore, the lumped mass method has gradually become the main method for describing the nonlinear dynamic behavior of flexible cables (Chen et al., 2021). Hu et al. (2020) showed that wave-current coupling amplifies the peak tension of submarine cables; while Zhang et al. (2020) found that the tension extremes usually occur near the connection area between the laying vessel and the cable. With the continuous development of this field, cable dynamics research has gone beyond the traditional static analysis and single-factor dynamic analysis. Current research increasingly focuses on multi-field coupling modeling that includes curvature evolution, internal flow effects, and environmental excitation. Li et al. (2025a) established a nonlinear dynamic model of cable-stayed risers considering different curvatures, while incorporating internal flow and external current effects (47), revealing the response mechanism of slender structures with variable curvature under complex excitations. Zhou et al. (2025) further studied the adaptive vibration control problem of flexible risers with internal flow coupling, emphasizing the impact of fluid-structure interaction vibration on the safety of flexible marine structures.

[0005] The complex marine loading environment has also driven the development of numerical simulation towards multiphysics coupling. Xie et al. (2015) found that deep-water S-shaped laying operations may induce significant plastic deformation and reduce the structure's resistance to collapse. Huang et al. (2023) revealed the nonlinear coupling relationship between ship motion and pipeline tension through experiments and simulations. Lu et al. (2024) focused on the contact problem between the umbilical cable and the overflow guide channel and clarified the stress concentration effect during deep-water S-shaped laying. Liang et al. (2018, 2019) established a more accurate support force model through roller contact state analysis; simulation results based on DNV standard verification showed that the model significantly improved the prediction accuracy of pipeline strain distribution. Yin et al. (2025) developed a multi-parameter coupled simulation and optimization framework applicable to the dynamic response of steel catenary risers on semi-submersible platforms, confirming that the structural response under extreme sea conditions is jointly determined by platform motion, environmental loads, and structural parameters.

[0006] Research based on professional simulation platforms such as OrcaFlex has clarified how key engineering parameters regulate the mechanical properties of cables. Existing research shows that water depth, laying length, and ship motion characteristics (such as acceleration and release rate) are the core variables affecting cable tension and minimum bending radius. Zhang et al. (2019) pointed out that motion parameters at different stages of ship operation significantly affect cable safety and established engineering optimization criteria based on maximum effective tension and minimum bending radius. Yang et al. (2013) proposed a two-dimensional semi-analytical model that comprehensively considers water flow, ship motion, release rate, water depth, and material properties; the results show that cable tension is significantly reduced after considering dynamic loads, reflecting the stress relief effect generated by motion coupling. Wang et al. (2010) found a near-linear relationship between water depth and cable tension through full-process simulation. Okkerstrom et al. (2021) and Wang (2019) pointed out that extending the laying length can increase cable tension and reduce the minimum bending radius, especially in deep water environments. Zhang et al. (2020) quantified the positive correlation between suspension distance and tension, while Gong and Xu (2016) determined that wave height and period are key input parameters affecting the dynamic response during the laying process. In fatigue studies, Zhu et al. (2024) pointed out that eddy current-induced vibration is one of the main causes of cable fatigue failure; Kuang et al. (2022) confirmed that when the water depth is below the critical value, damaged cable segments may cause large errors in tension calculation, thus requiring the use of correction coefficients; Zhang et al. (2026) further revealed the evolution of failure modes of reinforced thermoplastic pipes under the combined action of external pressure and torsion during the laying process.

[0007] Submarine cables are mainly laid in three ways: direct laying, laying followed by burial, and simultaneous laying and burial. The specific method used depends on the line conditions. In burial-related research, Shen et al. (2024) found through 3D modeling that the peak tension of the cable increases linearly with the burial depth, and established a prediction model combining water depth and self-weight based on a genetic programming algorithm. Lyu et al. (2024) used the random forest method to analyze construction data and determined that water depth, cable length, and laying tension are the main factors affecting burial depth. When laying directly, excessive cable suspension distance in the water should be avoided; once exposed to water flow, the cable may undergo lateral displacement, leading to structural instability or damage (Wang et al., 2025). Summary of the Invention

[0008] The purpose of this invention is to overcome the limitations of existing technologies, where most dynamic studies on submarine cable laying assume a flat seabed surface. This assumption restricts the applicability of these studies to wave-swept seabed conditions. This invention provides a dynamic response method for laying cables on undulating seabed terrain.

[0009] In a first aspect, the present invention provides a dynamic response method for laying cables on undulating seabed terrain, comprising:

[0010] S1. A coupled numerical dynamic model of cable-laying vessel-submarine cable-submarine slope is established by combining the lumped mass method with the catenary theory. Based on the coupled numerical dynamic model of cable-laying vessel-submarine cable-submarine slope, the bending radius, tension and suspension distance during the cable laying process are analyzed to obtain the suspension distance, maximum effective tension and minimum bending radius. The laying conditions of the coupled numerical dynamic model of cable-laying vessel-submarine cable-submarine slope cover both downhill and uphill laying conditions. S2. Using suspension distance, maximum effective tension, and minimum bending radius as key dynamic response evaluation indicators, the influence of cable lowering speed-related parameters and acceleration distance on dynamic response evaluation indicators during the laying process is analyzed based on the fully coupled dynamic model, and optimization strategies for lowering speed-related parameters and acceleration distance under different slope-swing distance combinations are obtained. S3. Evaluate the impact of wave load, current load, and wave-current coupling on the lowering speed-related parameters and acceleration-distance optimization strategy to determine the final cable lowering strategy.

[0011] Preferably, the parameters related to the lowering speed include the duration of acceleration during cable release and the lowering speed of the cable.

[0012] Preferably, based on the fully coupled dynamic model, the influence of cable lowering speed-related parameters on dynamic response evaluation indicators during the laying process is analyzed, and optimization strategies for lowering speed-related parameters under different slope-swing distance combinations are obtained, as follows: S201. Obtain the maximum seabed slope of the target sea area and set the initial ship speed of the cable-laying vessel and the initial cable lowering speed; S202. Based on the initial ship speed and the initial cable lowering speed, a constant laying speed condition is formed. Under the constant laying speed condition, the influence of slope and swing distance on the dynamic response evaluation index during the cable laying process is analyzed based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope. S203. Based on the initial cable lowering speed, increase the cable lowering speed to obtain the acceleration duration. Based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope, analyze the impact of different acceleration durations on the dynamic response evaluation index under different slope-swing distance combinations, and compare this impact with the impact on the dynamic response evaluation index in S202 to formulate an optimization strategy for the acceleration duration. S204. Based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope, analyze the impact of different cable lowering speeds on dynamic response evaluation indicators under different slope-swing distance combinations, and obtain recommended cable exit speeds under different slope-swing distance combinations by combining the negative factors of cable lowering speed, as a recommended strategy for cable lowering speeds under different slope-swing distance combinations.

[0013] Preferably, in step S202, the following analysis is performed based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope: S2021: Comparative analysis of key dynamic response indicators for constant speed paving under different slope conditions in downhill and uphill configurations; S2022: Under fixed seabed slope conditions, a comparative analysis of key dynamic response indicators for constant-speed laying under different swing distance values ​​in downhill and uphill configurations.

[0014] Preferably, in step S203, the following analysis is performed based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope: S2031: Under different slopes, a comparative analysis of the impact of acceleration duration on key dynamic responses during slope paving was conducted, and it was found that: under accelerated paving conditions, a slope threshold still exists, and changing the acceleration duration will not change the slope threshold. S2032: A comparative analysis of the impact of acceleration duration on key dynamic responses during slope laying under different swing distances shows that: compared with the constant speed cable laying method, the accelerated cable laying method is more conducive to the cable's adhesion to the seabed. Based on S2031-S2032, an optimized strategy for the duration of the acceleration is obtained.

[0015] Preferably, in step S204, the following analysis is performed based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope: S2041: Under at least three different downslope conditions, a comparative analysis of the suspended distance during variable-speed laying using different swing distances was conducted to obtain the recommended cable laying speed under different combinations of slope and swing. S2042: Under the conditions of fixed downhill slope and different swing distances, a comparative analysis of the effective tension time variation curves of variable speed laying was conducted, and it was found that different cable laying speeds will produce different fluctuation amplitudes and stable tension values. S2043: Comparative analysis of the maximum effective tension values ​​of submarine cables laid at different speeds and swing lengths under at least three different slope conditions; S2044: Analysis of the maximum reduction rate of effective tension in variable speed paving under different slopes and swing distances; S2045: Comparative analysis of the minimum bending radius of submarine cables laid under at least three different slope conditions, using different laying methods and laying speeds; S2046: Analysis of key dynamic response characteristics of submarine cables at different laying speeds when laid at a fixed downslope angle; S2047: Under the condition of variable speed paving with a fixed slope, the key dynamic response characteristic value analysis of acceleration-displacement relationship under different swing distances is carried out. S2048: Analysis of the maximum effective tension and minimum bending radius of variable speed paving under the conditions of fixed downhill slope, fixed acceleration distance and variable swing distance; S2049: Analysis of key dynamic response curves of acceleration-distance during variable-speed paving on a fixed downhill slope; Based on S2041-S2049, a recommended strategy for cable lowering speed under different combinations of slope and swing distance is obtained.

[0016] Preferably, the optimization strategy for the duration of the acceleration includes: Compared with constant speed laying, increasing the cable lowering speed can shorten the suspension distance, reduce the maximum effective tension value and reduce the minimum bending radius; Under the same swing distance, increasing the cable lowering speed can improve the laying performance of submarine cables under different slopes, and the shorter the acceleration duration, the more significant the improvement in laying performance. Preferably, when the seabed slope is ≥15°, the cable lowering speed should be increased; When the swing distance is ≥100 meters, the laying performance should be improved by increasing the cable laying speed.

[0017] Preferably, the negative factors affecting the cable lowering speed include cable stacking and / or cable entanglement.

[0018] Preferably, the influence of the acceleration distance of the cable under different slope-swing distance combinations on the dynamic response evaluation index is analyzed based on the fully coupled dynamic model during the laying process, and the optimization strategy for acceleration distance under different swing distances is obtained, as follows; S211. Determine a certain slope, and based on the fully coupled dynamic model, analyze the influence of the acceleration distance of the cable under different combinations of slope and swing distance on the dynamic response evaluation index during the laying process, and find the recommended value of acceleration distance under the slope based on the influence. S212. Based on the recommended value of the acceleration distance, expand to both sides to obtain at least three acceleration distance values. Analyze the maximum effective tension and minimum bending radius corresponding to different swing distance values ​​under each acceleration distance value, and determine whether all minimum bending radii meet the limit requirements. If not, adjust the cable laying speed, and then repeat steps S211 and S212 until all minimum bending radii meet the limit requirements. S213. Based on all the minimum bending radii and maximum effective tensions that ultimately meet the limit requirements, obtain the acceleration distance value that can be used as the equilibrium threshold, and use it as the optimization strategy for acceleration distance.

[0019] Preferably, the effects of wave load, current load, and wave-current coupling on the recommended cable delivery speed and its corresponding gradient and swing distance are evaluated to determine the final cable laying strategy.

[0020] Preferably, the final cable laying strategy is as follows: under constant speed laying conditions, the seabed slope has a more sensitive impact on the dynamic response of the cable when laying downhill than when laying uphill; when the slope is ≥15°, the suspension distance increases rapidly and the fit between the cable and the seabed decreases; the increase in swing distance will further increase the suspension distance and cable tension. Preferably, the final cable-laying strategy is as follows: with a fixed speed of the laying vessel, increasing the cable-laying speed can shorten the suspension distance and reduce the maximum effective tension; however, excessively fast laying speed will reduce the minimum bending radius and increase the risk of cable accumulation at the contact point with the seabed. Preferably, the final cable laying strategy is as follows: under steep slope conditions, an appropriate acceleration distance can effectively shorten the suspension distance and maintain the maximum effective tension stability; however, when the slope is extremely steep, simply increasing the acceleration distance is not enough to meet the requirements, and the cable laying speed also needs to be adjusted to meet the bending radius limit. Preferably, the final cable laying strategy is as follows: the direction of wave load and current load has a significant impact on cable laying performance. Alignment with the dominant ocean current can improve the cable's fit with the seabed and reduce tension; while the wave-ocean current coupling effect will produce the strongest overall dynamic response.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: (only the beneficial effects of the invention are listed) 1. This invention provides a dynamic response method for laying cables on undulating seabed terrain. Combining catenary theory and the lumped mass method, a coupled numerical dynamic model based on the cable-laying vessel, submarine cable, and seabed slope is established to simulate the cable laying process on wave-undulating seabed sections. The study systematically analyzes the effects of laying speed, speed adjustment position, seabed slope, and layback distance on the cable-seabed fit, maximum effective tension, and minimum bending radius. The research results provide a theoretical basis for selecting appropriate cable laying schemes in complex seabed environments. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the general unit model of the lumped mass method in this application; Figure 2 This is a schematic diagram illustrating the forces acting on a submarine cable based on the catenary theory of this application.

[0023] Figure 3 This is a schematic diagram of the uphill and downhill laying of the submarine cable in this application.

[0024] Figure 4 This is a schematic diagram comparing the key dynamic response indicators of constant speed paving under different slope conditions in the downhill and uphill configurations of this application.

[0025] Figure 5 This is a schematic diagram comparing the key dynamic response indicators of constant-speed paving under different swing distance values ​​in the downhill and uphill configurations of this application.

[0026] Figure 6 This is a schematic diagram comparing the impact of acceleration duration on key dynamic responses during downhill paving at different slopes in this application.

[0027] Figure 7 This is a schematic diagram comparing the impact of acceleration duration on key dynamic responses during downhill paving at different swing distances in this application.

[0028] Figure 8 This is a schematic diagram comparing the suspension distance of the submarine cable under different swing conditions using a variable speed laying method under downslope conditions of 15°, 20° and 30°.

[0029] Figure 9 This is a schematic diagram comparing the effective tension-time variation curves of the variable-speed paving under different conditions of a 15° downhill slope and different swing distances.

[0030] Figure 10 This is a schematic diagram comparing the maximum effective tension values ​​of submarine cables laid at different speeds and swing lengths under three different slopes (15°, 20° and 30°, a total of 290 downhill sections) according to this application.

[0031] Figure 11 This diagram illustrates the maximum reduction rate of effective tension in variable-speed paving under different slopes and swing distances according to this application.

[0032] Figure 12 This is a comparative diagram showing the minimum bending radius of submarine cables laid under different laying methods and at different laying speeds under slope conditions of 15°, 20° and 30°.

[0033] Figure 13 This is a schematic diagram showing the key dynamic response characteristics of the submarine cable at different laying speeds when laid at a 30° downhill angle, as per this application.

[0034] Figure 14 These are the key dynamic response characteristic values ​​of the acceleration-displacement relationship under different swing distances under the variable speed paving conditions with a slope of 20°, as presented in this application.

[0035] Figure 15 This is a schematic diagram illustrating the maximum effective tension and minimum bending radius of the variable-speed paving under the conditions of a 30° downhill slope, an acceleration distance of 360 meters over a distance of 300 meters, and a variable swing distance.

[0036] Figure 16 This is a schematic diagram of the key dynamic response curve of acceleration-distance when performing variable-speed paving on a 30° downhill slope, as described in this application.

[0037] Figure 17 This is a schematic diagram showing the laying direction and environmental load direction for this application.

[0038] Figure 18 This is a schematic diagram of the key dynamic response values ​​of the submarine cable laid under wave load according to this application.

[0039] Figure 19 This is a schematic diagram of the key dynamic response values ​​of the submarine cable laid under the current load of this application.

[0040] Figure 20 This is a schematic diagram of the key dynamic response under the combined wave-current load of this application. Detailed Implementation

[0042] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0043] Unless otherwise specified, the terms "upper," "lower," "left," "right," "center," "inner," and "outer," etc., used in the description of specific embodiments of the present invention to indicate orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, and for enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0044] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," "parallel," and "coaxial" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, parallel, or coaxial. Slight tilt or deviation is permissible, as long as it does not affect the normal function of the relevant component. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," not that the structure must be perfectly horizontal; a slight tilt is acceptable. "Coaxial" means that two components are arranged as coaxially as possible, allowing them to move coaxially or approximately coaxially when their relative positions change. Alternatively, it can be simplified to mean that the corresponding device / component / element, when arranged in "horizontal," "vertical," "suspended," "parallel," or "coaxial" directions, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. For example, the deviation in the "coaxial" direction is controlled within 0.2-1mm, preferably within 0.2-0.5mm. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the solution of the present invention.

[0045] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0046] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as two, three, four, five, six, seven, eight, or nine, and can even exceed nine.

[0047] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to connection methods commonly used in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0048] Example 1 This embodiment provides a dynamic response method for laying cables on undulating seabed terrain, including the following: 1. Theoretical basis.

[0049] like Figure 1 As shown, submarine cables are typical slender marine structures. Their overall mechanical behavior exhibits the typical characteristics of slender structural systems. The lumped mass method models the cable as a nonlinear spring system and discretizes it into a series of massless line segments and lumped nodes. The governing equations of a typical element can be expressed in the following form:

[0050] Where: M is the nodal mass matrix, C is the nodal damping coefficient matrix, and K is the stiffness matrix. F(t) Let be the external force at time t, where t is time. For the nodal acceleration vector, For the node velocity vector, X is the nodal displacement vector.

[0051] like Figure 2 As shown, considering the force balance of cable components, the catenary theory is adopted ( Figure 2 The directions correspond to the tangent direction (t) and the normal direction (p) respectively.

[0052]

[0053] Where T represents the tension at the i-th point; W is the immersion weight per unit length; ΔT and Δα These represent the tension difference and height difference between point i and point i+1, respectively. ΔL It is the arc length; D t and D n These are tangential resistance and normal resistance, respectively.

[0054] When the length of the element approaches infinity:

[0055] The tangential and normal drag per unit length are given by the Morrison equation:

[0056] in C t and C n The drag coefficient (depends on the Reynolds number and cable roughness). ρ W The density of seawater, D The effective diameter of the cable. V t and V n These are the relative velocity components perpendicular to the cable and parallel to the cable, respectively.

[0057] In the initial tension calculation, the tangential resistance is usually negligible, thus simplifying equation (3):

[0058] Where φ1 represents the tension when the elevation angle is θ.

[0059]

[0060] Where T1 is the tension at the landing point (TDP) and α1 is the angle at the landing point (TDP).

[0061] Tension is related to water depth H:

[0062] The final tensile force distribution is determined by the following factors: (11) 2. Numerical Model This application constructs a coupled numerical dynamic model of a cable-laying vessel, a submarine cable, and a seabed slope to analyze the bending radius, tension, and suspension distance characteristics during the laying process. The cable is laid using an S-shaped laying method, with the cable forming an "S"-shaped curve when it contacts the seabed. Figure 3 The diagram illustrates the laying of submarine cables uphill and downhill: a specific tension is applied by a tensioning device, driving the cable from the stern of the cable-laying vessel (LOP) to the seabed contact point (TDP), thus naturally forming a catenary shape. The cable-laying vessel is also called a cable-laying vessel.

[0063]

[0064] Table 1. Main design parameters of the model 3. The impact of cable lowering speed on dynamic response during installation 3.1 Analysis of cable laying response characteristics under constant pay-out speed: The maximum seabed slope of the target sea area was obtained, and the ship speed of the cable-laying vessel and the cable lowering speed were set. Based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope, the influence of slope and swing distance on the dynamic response evaluation index during the cable laying process was analyzed.

[0065] Taking a certain strait as an example: the maximum seabed slope of this strait is approximately 22° to 24°. In this application, the speed of the cable-laying vessel and the cable lowering speed are both set to 0.20 m / s, and the influence of slope and swing distance on cable laying is analyzed.

[0066] like Figure 4 As shown, slope changes significantly affect the mechanical response and laying posture of the cable. The trends differ significantly between uphill and downhill laying: in downhill laying, the suspension distance increases with the slope from 5° to 30°; the rate of increase accelerates significantly after the slope exceeds 10° (reaching a maximum of 0.48 m / °). The maximum effective tension (MET) initially rises rapidly, then the rate of increase slows; the minimum bending radius (MBR) continuously decreases, with the rate of decrease weakening when the slope exceeds 15°. For uphill laying, the suspension distance remains essentially 0 meters when the slope is between 5° and 15°; it begins to increase after the slope exceeds 15°, increasing significantly at a rate of 0.32 m / ° at 30°; within the range of 5° to 15°, the minimum bending radius first rises and then falls, with the turning point at 15°; while the maximum effective tension is largely unaffected by the slope.

[0067] These results indicate that when the slope exceeds 15°, the overhang distance is the most significantly affected response parameter by slope changes, while the minimum bending radius and maximum effective tension are relatively less sensitive. Compared to uphill paving, downhill paving exhibits a much stronger dependence on slope changes in both mechanical response and paving posture.

[0068] The swing distance also has a significant impact on the maximum effective tension. Figure 5 Dynamic response data under different swing distances at a seabed slope of 15° are presented. The results show that both the suspension distance and the maximum effective tension increase synchronously with the increase of the swing distance; when the swing distance exceeds the critical values ​​(100 meters for downhill and 150 meters for uphill), the rate of increase accelerates significantly. The variation pattern of the minimum bending radius differs between the two cases: the minimum bending radius changes gradually downhill, while it tends to stabilize uphill after the swing distance exceeds 150 meters.

[0069] These results demonstrate that swayback significantly reduces the flatness of the submarine cable's seabed contact surface. This is achieved by altering the geometry of the suspension cable segment. Compared to uphill laying, submarine cables exhibit more sensitive dynamic responses under downhill laying conditions. Therefore, the following discussion will focus on downhill laying scenarios.

[0070] Evaluate the effect of acceleration duration on laying performance: When there are significant undulations in the seabed topography, the length of the released cable can be increased by adjusting the relative difference between the cable release speed and the ship speed; then the resulting changes in cable stress, cable morphology and seabed contact state can be analyzed.

[0071] Considering that the acceleration during cable release may affect the laying performance, this application sets the initial cable release speed to 0.20 m / s, and then increases it to 0.22 m / s by adjusting the acceleration duration. A systematic analysis was conducted for different downhill conditions (initial swing distance of 150 m) and different swing conditions under a 15° downhill slope.

[0072] like Figure 6 As shown, compared with constant-speed laying, accelerated cable laying (also called installation) can shorten the suspension distance, reduce the maximum effective tension value, and decrease the minimum bending radius. The dynamic response curves at different acceleration stages show similar patterns: the increase is smaller at low slopes (10°-15°), while it rises more rapidly at high slopes (15°-30°). This indicates that under accelerated laying conditions, the slope still has a significant threshold effect, with the critical slope remaining at 15°. Changing the acceleration duration does not change this threshold; when the slope is 10°, the acceleration duration has a relatively significant impact on the minimum bending radius—the reduction rates of the minimum bending radius for the three acceleration durations are 52.4%, 45.1%, and 36.2%, respectively. When the slope reaches 15°, the curve tends to converge and then gradually decreases, while the difference between constant-speed and accelerated laying methods gradually narrows. Furthermore, under different acceleration durations and slope conditions, the maximum effective tension value remains basically unchanged, indicating that the tension is not sensitive to changes in these two parameters.

[0073] like Figure 7As shown, compared with the constant speed cable lowering method, the accelerated cable lowering method is more conducive to the fit between the cable and the seabed. When the cable swing distance is less than 100 meters, the accelerated cable lowering only causes a small change in the suspension distance, and the magnitude of this change remains at a low level, indicating a better fit. However, when the swing distance exceeds 150 meters, the suspension distance begins to gradually increase, and the longer the acceleration duration, the more significant the increase in suspension distance.

[0074] Under constant-speed laying conditions, the maximum effective tension value is significantly higher than that under accelerated laying conditions. During accelerated cable laying, as the swing distance increases, the maximum effective tension values ​​corresponding to different acceleration durations gradually converge, and their growth rate is significantly lower than that under constant-speed laying conditions. The minimum bending radius value initially rises rapidly and then gradually stabilizes; when the swing distance is less than 100 meters, the minimum bending radius value rises rapidly; once the swing distance exceeds 150 meters, the results under different acceleration durations gradually converge. This indicates that under large swing conditions, the difference in minimum bending radius caused by different acceleration durations gradually decreases.

[0075] In general, under the same swing distance, accelerating the cable lowering speed can improve the laying performance of submarine cables under different slope conditions; and the effect is more significant as the acceleration duration decreases. When the seabed slope exceeds 15°, the cable lowering speed should be appropriately increased. Under specific slope conditions, if the swing distance is small (50–100 meters), the cable suspension distance during accelerated lowering is still close to 0 meters, indicating good laying effect; conversely, when the swing distance exceeds 100 meters, the acceleration duration has a relatively limited impact on the maximum extension length (maximum effective tension) and maximum elongation (minimum bending radius), but the suspension distance increases significantly, and the cable's fit with the seabed decreases accordingly. Therefore, under small swing conditions, the selection of acceleration duration is relatively flexible; when the cable swing distance is greater than 100 meters, the acceleration duration should be increased by increasing the cable lowering speed to improve laying performance.

[0076] Analysis of the effect of cable pay-out speed on dynamic laying response: The above analysis shows that increasing the cable lowering speed can mitigate the adverse effects of slope changes on submarine cable laying to some extent. However, if the cable lowering speed is too high, cable accumulation or entanglement may occur in the seabed contact area. Therefore, it is still necessary to reasonably control the cable lowering speed during actual installation. To this end, this application further studies the simulated effects of cable laying under different combinations of slope and swing distance.

[0077] like Figure 8As shown, the suspended distance of the submarine cable under different swing conditions was compared when using a variable-speed laying method at downslope angles of 15°, 20°, and 30°, thus characterizing the degree of cable contact with the seabed. To meet the requirement of avoiding excessive suspended distance during submarine cable laying, recommended cable laying speeds for different slope and swing combinations were further obtained (Table 2). Table 3 lists the suspended distances corresponding to different swing distances under different slope conditions and using the recommended cable laying speeds.

[0078] Table 2: Recommended cable laying speed and corresponding recommended cable suspension distance for submarine cables with different slopes and swing distances.

[0079] Swing distance 100m 150m 200m 100m 150m 200m 100m 150m 200m Recommended cable laying speed (ms) 0.22 0.24 0.26 0.26 0.28 0.32 0.34 0.4 0.58 Suspension distance m -0.00187 -0.00545 -0.00603 -0.00902 -0.01232 -0.00454 -0.00157 -0.00355 -0.00096 like Figure 9 As shown, this diagram illustrates the time history curves of effective cable tension during variable-speed laying under a 15° slope and different layback conditions. In all cases, the effective tension initially fluctuates before stabilizing or increasing. Longer layback distances result in higher stable tension levels. Different cable laying speeds also produce different fluctuation amplitudes and stable tension values. When the cable laying speed is 0.20 m / s (equal to ship speed), the effective tension remains relatively stable during the flat seabed phase; it then rises rapidly along the downhill section; and gradually stabilizes again as the cable reaches the bottom of the slope and re-enters the flat seabed area. In contrast, at laying speeds of 0.26 m / s and 0.30 m / s, the effective tension of the submarine cable first decreases, then increases, and finally decreases again. During the initial flat seabed laying phase, the tension continuously decreases as the layback distance gradually shortens; as the cable enters the downhill section, the increased suspension distance causes the tension to rise and peak near the bottom of the slope, subsequently decreasing again as the cable continues to be laid on the flat seabed.

[0080] like Figure 10 As shown, this diagram illustrates the relationship between cable release speed and maximum effective tension (MPT) under different slope conditions, with three different swing distances of 100 meters, 150 meters, and 200 meters. At slopes of 15° and 20°, the MPT initially drops sharply and then stabilizes. When the cable release speed exceeds 10% of the ship's speed, the MPT changes very little with further increases in speed. In all cases, longer swing distances result in higher MPT values. At a slope of 30°, the effect of cable release speed on tension is more widespread: as the release speed increases, the tension initially drops sharply and then gradually stabilizes; larger swing distances also correspond to higher initial tension.

[0081] like Figure 11As shown, it further demonstrates the maximum rate of decrease after the tension reaches a stable stage under different slope conditions. It can be seen that when the swing distance is 150 meters, the decrease in the maximum effective tension is the most significant.

[0082] Therefore, the slope and swing distance together determine the variation of cable tension. The steeper the slope, the wider the range by which the cable release speed affects the maximum energy loss (maximum effective tension). Under the conditions considered in this application, a swing distance of 150 meters is more conducive to reducing the maximum effective tension value.

[0083] like Figure 12 As shown, the minimum bending radius generally decreases with increasing cable laying speed. The shorter the swing distance, the smaller the minimum bending radius and the more pronounced the decrease. When both the slope and swing distance increase simultaneously, the decreasing trend of the minimum bending radius gradually approaches a linear relationship. With increasing slope and swing distance, the cable laying speed, which causes a sharp decrease in the minimum bending radius, also gradually increases. Combined with the results in Table 3, it can be seen that when the slope exceeds 15°, the effect of cable laying speed on the bending radius is more significant.

[0084] Table 3: Recommended cable laying speeds for sharp decreases in minimum bending radius Swing distance 100m 150m 200m 100m 150m 200m 100m 150m 200m Cable laying speed (m / s) 0.22 0.24 0.26 0.24 0.26 0.3 0.28 0.34 0.54 Coordination and adjustment of ship speed and cable laying speed: For high-risk conditions with a slope of 30°, a ship speed of 0.20 m / s, and a swing distance of 200 m, the optimized cable laying speed is 0.58 m / s, approximately three times the ship speed. Considering the potential risks of excessively high cable laying speeds, the speed difference was fixed at 0.38 m / s, and the ship speed and cable laying speed were coordinated and adjusted. Subsequently, the resulting submarine cable laying performance, stress state, and landing configuration were analyzed.

[0085] like Figure 13 As shown, with the increase in cable laying speed (and the synchronous increase in ship speed), the fit between the cable and the seabed decreases, which is reflected in the increased suspension distance. At the same time, the laying effect improves: the minimum bending radius of the submarine cable in water gradually increases, and the cable profile becomes smoother; furthermore, the cable tension remains stable. Therefore, in situations with a steep slope and a long laying distance, the cable laying speed and ship speed can be appropriately reduced. During this adjustment process, the minimum bending radius must be closely monitored to ensure compliance with relevant specifications and to avoid excessive bending damage to the cable.

[0086] 4. The Influence of Acceleration Distance on Dynamic Response During Laying Response characteristics under a 20° downhill slope: The location of the acceleration setting is crucial during the accelerated laying of submarine cables. When the target velocity remains constant while the length of the acceleration segment varies, the acceleration distance is negatively correlated with the swing distance at the beginning of the slope segment. In other words, the longer the acceleration segment, the smaller the swing distance. This relationship directly affects the quality of cable laying.

[0087] like Figure 14 As shown, under a 20° slope, the cable lowering speed of this application was simulated for different swing distances. When the swing distance is 100 meters, the suspension distance remains close to 0 meters and is almost unaffected by changes in acceleration distance. When the swing distance reaches 150 meters or 200 meters, the suspension distance rapidly decreases to zero as the acceleration distance increases from 100 meters to 200 meters. Under different swing conditions, the maximum effective tension value remains stable as the acceleration distance increases. The response of the bending radius shows different trends: when the swing distance is 100 meters, once the acceleration distance exceeds 200 meters, the bending radius stabilizes at about 20 meters; when the swing distance is 150 meters, the bending radius continues to decrease with increasing acceleration distance; and when the swing distance is 200 meters, this decreasing trend becomes more significant.

[0088] A comprehensive comparison shows that for a 20° slope, an acceleration distance of 200 meters is recommended. This acceleration distance eliminates the risk of free span caused by excessive swing distance, keeps the maximum effective tension within a stable range, and maintains a controllable bending radius even with a relatively small swing distance.

[0089] Response characteristics under a 30° downhill slope condition: like Figure 16 As shown, this diagram illustrates the maximum effective tension and minimum bending radius corresponding to different swing distances under variable-speed laying conditions with a 30° downhill slope and an acceleration distance of 300 meters. The results indicate that as the cable laying speed increases, the maximum effective tension remains relatively stable, while the minimum bending radius decreases significantly. If the cable laying speed is directly calculated based on the initial laying speed, the minimum bending radius in some cases will fail to meet the allowable limit of 3.975 meters. Therefore, further adjustments to the cable laying speed are necessary. After adjustment, the recommended cable laying speeds for swing distances of 100 meters, 150 meters, and 200 meters are 0.30 m / s, 0.36 m / s, and 0.42 m / s, respectively.

[0090] The submarine cable was laid using the adjusted recommended cable laying speed, and the corresponding dynamic response data were evaluated.

[0091] like Figure 16As shown: when the acceleration distance is 100 meters, the suspension distance increases with the swing distance; when the acceleration distance exceeds 200 meters, the suspension distance rapidly decreases to near zero under all swing conditions. The maximum effective tension parameter changes little, while the minimum bending radius continues to decrease. Under a 30° slope, the acceleration distance mainly affects the free span and bending response, but has a limited impact on its tension.

[0092] Overall, an acceleration distance of 200 meters can be considered a balancing threshold between safety and construction feasibility. Under this condition, submarine cables have virtually no risk of free span, the maximum effective tension parameter remains stable, and the minimum bending radius meets requirements under most swing distance conditions.

[0093] 5. The impact of environmental parameters on the dynamic response of submarine cable laying This application investigates the effects of wave load, current load, and wave-current coupling on three key response indicators: suspension distance, maximum effective tension, and minimum bending radius. The preferred case uses a seabed slope of 20°, a swing distance of 200 meters, an acceleration distance of 200 meters, a recommended cable delivery speed of 0.32 m / s, and a ship laying heading of 0°.

[0094] like Figure 17 As shown, it clearly defines the laying direction and the direction of environmental load.

[0095] Influence of wave parameters: The environmental load under wave conditions is adopted (wave exchange factor jonswap, significant wave height Hs: 1.0–2.0 m, spectral peak value 387, period Tp: 3.0–7.0 s), and the load direction range is 0°–180° (where the laying direction is defined as 0°).

[0096] like Figure 18As shown, a larger spectral peak period and significantly higher wave height generally improve cable-submarine fit compared to the waveless condition. However, when the wave direction is 0°, Hs = 1.0 m, and Tp = 3.0 s, the suspension distance is greater than that under the waveless condition. This result indicates that when the wave direction is aligned with the laying direction, low-frequency waves with short periods and high wave heights may adversely affect cable-submarine fit. Wave loads significantly increase the metallic elastic tension (maximum effective tension) of the submarine cable, with the increase becoming more pronounced as the spectral peak period increases. The maximum effective tension reaches its lowest value at a wave direction of 180°, closest to the value under the waveless condition; in most cases, the maximum effective tension reaches its maximum value at a wave direction of 45° or 90°. When Hs = 2.0 m and Tp = 5.0 s, the peak maximum effective tension is approximately 300 kN under a 90° wave direction, indicating a potential risk of cable breakage. The elastic tensile strength of the metal (minimum bending radius) reaches a significant minimum at the 90° wave direction, while remaining at a relatively high level in other wave directions; however, at the 180° wave direction, the minimum bending radius is usually closest to the value under non-wave conditions. Overall, wave action exacerbates the reduction in cable bending radius, and this effect intensifies with increasing spectral peak period.

[0097] Influence of current parameters: Current velocity and current direction are key environmental variables determining cable laying performance. In this application, uniform flow velocities of 0.5, 0.7, and 1.0 m / s were considered, with current direction ranging from 4090° to 180°, while the laying direction was fixed at 0°. The dynamic responses of suspension distance, maximum effective tension, and minimum bending radius were analyzed and compared with results under no-current conditions.

[0098] like Figure 19As shown, current load significantly affects the dynamic response of submarine cables, and this effect becomes more pronounced with increasing current velocity. For the overhang distance, at a current velocity of 1.0 m / s, the value reaches a peak of 0.036 m at 0° current direction; it then decreases significantly with changing direction, approaching zero current level after 90°. The maximum effective tension exhibits a clear directional variation. Under all current velocity conditions, the tension peak occurs near 0°. Under a current of 1.0 m / s, the maximum effective tension peaks at 0° current direction, reaching approximately 240 kN. These results indicate that current load significantly increases cable tension, and the peak tension increases with increasing current velocity; in contrast, the maximum effective tension is lowest at 180° current direction. The minimum bending radius remains relatively large at 0° current direction; for example, it is approximately 40 m under a current of 1.0 m / s. However, when the current direction changes to 420°, the bending radius decreases sharply; at the same current velocity, the bending radius at 180° drops to approximately 15 m. This result indicates that current load significantly reduces the bending radius of the cable, and this reduction effect becomes more pronounced with increasing current velocity. It also highlights the adverse effects of a 180° current direction on the bending performance of submarine cables.

[0099] Overall, as the current direction changes from 0° (co-current) to 180° (counter-current), the suspension distance, maximum effective tension, and minimum bending radius all gradually decrease; the decreasing trend becomes more pronounced with increasing current velocity. At a current direction of 90°, these three indicators are closest to those under no-current conditions. Laying cables in the co-current direction may result in excessive suspension distance and excessive cable tension, thus increasing the risk of breakage; conversely, counter-current laying improves the cable's fit with the seabed and reduces the maximum effective tension. However, the risk of excessive cable bending still needs to be considered.

[0100] Response characteristics under wave-current coupling: This application further simulated a complex wave-current environment, taking the wave conditions of Hs=1.5 m, Tp=437.5 s and a uniform flow velocity of 0.7 m / s as an example, and compared the results with the simulation results under the conditions of only wave action and only fluid action.

[0101] like Figure 20As shown, under wave-current coupling, the suspension distance in the 0° to 90° direction falls between the results of wave-only and water-only conditions. At 90°, the three conditions exhibit similar performance. Within the 90° to 180° range, the suspension distance is smallest under wave-current coupling, indicating improved cable-submarine adhesion. The maximum internal force (maximum effective tension) under wave-current coupling initially increases with the wave-current direction and then decreases, reaching a peak of approximately 301 kN at 90°; however, it drops below 270 kN at 135° and 180°, lower than the value under wave-only conditions at 135°. In contrast, the overall maximum effective tension value is lowest under water-only conditions. The minimum bending radius of the maximum internal force under wave-current coupling drops to a minimum of 20 m at 180°, significantly lower than the water-only conditions (23 m) and wave-only conditions (32 m). At 0° and 45°, the minimum bending radius remains at approximately 35 m, which is comparable to the value under conditions of water flow load only.

[0102] Overall, wave-current coupling significantly alters the cable's fit with the seabed, stress state, and laying pattern compared to when subjected to wave or water flow loads alone. Consequently, the overall response of the cable becomes more complex.

[0103] In summary, this application investigated the dynamic response characteristics of submarine cables laid on undulating seabed topography under different operating and environmental conditions. The main conclusions are as follows: (1) Under constant speed laying conditions, the seabed slope has a significant impact on cable response, and laying on a downhill slope is more sensitive than laying on an uphill slope. When the slope exceeds 15°, the suspension distance increases rapidly and the fit between the cable and the seabed decreases; a larger swing distance will further increase the suspension distance and cable tension.

[0104] (2) When the ship speed is fixed, appropriately increasing the cable release speed can shorten the suspension distance and reduce the maximum effective tension; this effect is more obvious when the acceleration duration is short; however, excessively fast release speed will reduce the minimum bending radius and increase the risk of cable accumulation at the contact with the seabed.

[0105] (3) Under steep slope conditions, an appropriate acceleration distance can effectively shorten the suspension distance and maintain the maximum effective tension stability; however, when the slope is extremely steep, simply increasing the acceleration distance is not enough to meet the requirements, and the cable release speed also needs to be adjusted to meet the bending radius limit.

[0106] (4) The direction of environmental load has a significant impact on laying performance. In general, aligning with the dominant ocean current can improve the fit between the cable and the seabed and reduce tension; while the wave-ocean current coupling effect will produce the strongest overall dynamic response, so the most conservative control measures need to be taken.

[0107] This embodiment provides a dynamic response method for laying cables on undulating seabed terrain. Combining catenary theory and the lumped mass method, a coupled numerical dynamic model of the cable-laying vessel, submarine cable, and seabed slope based on OrcaFlex software was established to simulate the cable laying process on a wave-undulating seabed. The study systematically analyzed the effects of laying speed, speed adjustment position, seabed slope, and layback distance on the cable-seabed fit, maximum effective tension, and minimum bending radius. The research results provide a theoretical basis for selecting appropriate cable laying schemes in complex seabed environments.

[0108] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A dynamic response method for laying cables on undulating seabed terrain, characterized in that, include: S1. A coupled numerical dynamic model of cable-laying vessel-submarine cable-submarine slope is established by combining the lumped mass method with the catenary theory. Based on the coupled numerical dynamic model of cable-laying vessel-submarine cable-submarine slope, the bending radius, tension and suspension distance during the cable laying process are analyzed to obtain the suspension distance, maximum effective tension and minimum bending radius. The laying conditions of the coupled numerical dynamic model of cable-laying vessel-submarine cable-submarine slope cover both downhill and uphill laying conditions. S2. Using suspension distance, maximum effective tension, and minimum bending radius as key dynamic response evaluation indicators, the influence of cable lowering speed-related parameters and acceleration distance on dynamic response evaluation indicators during the laying process is analyzed based on the fully coupled dynamic model, and optimization strategies for lowering speed-related parameters and acceleration distance under different slope-swing distance combinations are obtained. S3. Evaluate the impact of wave load, current load, and wave-current coupling on the lowering speed-related parameters and acceleration-distance optimization strategy to determine the final cable lowering strategy.

2. The dynamic response method for laying cables on undulating seabed terrain according to claim 1, characterized in that, The parameters related to the lowering speed include the duration of acceleration during cable release and the cable lowering speed.

3. The dynamic response method for laying cables on undulating seabed terrain according to claim 2, characterized in that, Based on the fully coupled dynamic model, the influence of cable lowering speed-related parameters on dynamic response evaluation indicators during the laying process is analyzed, and optimization strategies for lowering speed-related parameters under different slope-swing distance combinations are obtained, as follows: S201. Obtain the maximum seabed slope of the target sea area and set the initial ship speed of the cable-laying vessel and the initial cable lowering speed; S202. Based on the initial ship speed and the initial cable lowering speed, a constant laying speed condition is formed. Under the constant laying speed condition, the influence of slope and swing distance on the dynamic response evaluation index during the cable laying process is analyzed based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope. S203. Based on the initial cable lowering speed, increase the cable lowering speed to obtain the acceleration duration. Based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope, analyze the impact of different acceleration durations on the dynamic response evaluation index under different slope-swing distance combinations, and compare this impact with the impact on the dynamic response evaluation index in S202 to formulate an optimization strategy for the acceleration duration. S204. Based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope, analyze the impact of different cable lowering speeds on dynamic response evaluation indicators under different slope-swing distance combinations, and obtain recommended cable exit speeds under different slope-swing distance combinations by combining the negative factors of cable lowering speed, as a recommended strategy for cable lowering speeds under different slope-swing distance combinations.

4. The dynamic response method for laying cables on undulating seabed terrain according to claim 3, characterized in that, In step S202, the following analysis is performed based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope: S2021: Comparative analysis of key dynamic response indicators for constant speed paving under different slope conditions in downhill and uphill configurations; S2022: Comparative analysis of key dynamic response indicators for constant-speed laying under different swing distance values ​​in downhill and uphill configurations under fixed seabed slope conditions; And / or, In step S203, the following analysis is performed based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope: S2031: Under different slopes, a comparative analysis of the impact of acceleration duration on key dynamic responses during slope paving was conducted, and it was found that: under accelerated paving conditions, a slope threshold still exists, and changing the acceleration duration will not change the slope threshold. S2032: A comparative analysis of the impact of acceleration duration on key dynamic responses during slope laying under different swing distances shows that: compared with the constant speed cable laying method, the accelerated cable laying method is more conducive to the cable's adhesion to the seabed. Based on S2031-S2032, an optimization strategy for the duration of the acceleration is obtained; And / or, In step S204, the following analysis is performed based on the coupled numerical dynamic model of the cable-laying vessel-submarine cable-submarine slope: S2041: Under at least three different downslope conditions, a comparative analysis of the suspended distance during variable-speed laying using different swing distances was conducted to obtain the recommended cable laying speed under different combinations of slope and swing. S2042: Under the conditions of fixed downhill slope and different swing distances, a comparative analysis of the effective tension time variation curves of variable speed laying was conducted, and it was found that different cable laying speeds will produce different fluctuation amplitudes and stable tension values. S2043: Comparative analysis of the maximum effective tension values ​​of submarine cables laid at different speeds and swing lengths under at least three different slope conditions; S2044: Analysis of the maximum reduction rate of effective tension in variable speed paving under different slopes and swing distances; S2045: Comparative analysis of the minimum bending radius of submarine cables laid under at least three different slope conditions, using different laying methods and laying speeds; S2046: Analysis of key dynamic response characteristics of submarine cables at different laying speeds when laid at a fixed downslope angle; S2047: Under the condition of variable speed paving with a fixed slope, the key dynamic response characteristic value analysis of acceleration-displacement relationship under different swing distances is carried out. S2048: Analysis of the maximum effective tension and minimum bending radius of variable speed paving under the conditions of fixed downhill slope, fixed acceleration distance and variable swing distance; S2049: Analysis of key dynamic response curves of acceleration-distance during variable-speed paving on a fixed downhill slope; Based on S2041-S2049, a recommended strategy for cable lowering speed under different combinations of slope and swing distance is obtained.

5. The dynamic response method for laying cables on undulating seabed terrain according to claim 3, characterized in that, The optimization strategies for the duration of the acceleration include: Compared with constant speed laying, increasing the cable lowering speed can shorten the suspension distance, reduce the maximum effective tension value and reduce the minimum bending radius; At the same swing distance, increasing the cable lowering speed can improve the laying performance of submarine cables under different slopes, and the shorter the acceleration duration, the more significant the improvement in laying performance.

6. A dynamic response method for laying cables on undulating seabed terrain according to claim 4, characterized in that, When the seabed slope is ≥15°, increase the cable lowering speed; When the swing distance is ≥100 meters, the laying performance should be improved by increasing the cable laying speed.

7. The dynamic response method for laying cables on undulating seabed terrain according to claim 3, characterized in that, Negative factors affecting cable lowering speed include cable accumulation and / or cable entanglement.

8. A dynamic response method for laying cables on undulating seabed terrain according to claim 3, characterized in that, Based on the fully coupled dynamic model, the influence of the cable acceleration distance on the dynamic response evaluation index under different slope-swing distance combinations during the laying process is analyzed, and the optimization strategy for acceleration distance under different swing distances is obtained as follows; S211. Determine a certain slope, and based on the fully coupled dynamic model, analyze the influence of the acceleration distance of the cable under different combinations of slope and swing distance on the dynamic response evaluation index during the laying process, and find the recommended value of acceleration distance under the slope based on the influence. S212. Based on the recommended value of the acceleration distance, expand to both sides to obtain at least three acceleration distance values. Analyze the maximum effective tension and minimum bending radius corresponding to different swing distance values ​​under each acceleration distance value, and determine whether all minimum bending radii meet the limit requirements. If not, adjust the cable laying speed, and then repeat steps S211 and S212 until all minimum bending radii meet the limit requirements. S213. Based on all the minimum bending radii and maximum effective tensions that ultimately meet the limit requirements, obtain the acceleration distance value that can be used as the equilibrium threshold, and use it as the optimization strategy for acceleration distance.

9. A dynamic response method for laying cables on undulating seabed terrain according to claim 7, characterized in that, The effects of wave load, current load, and wave-current coupling on the recommended cable delivery speed and its corresponding gradient and swing distance are evaluated to determine the final cable laying strategy.

10. A dynamic response method for laying cables on undulating seabed terrain according to claim 1, characterized in that, The final cable-laying strategy is as follows: Under constant speed laying conditions, the submarine slope has a more sensitive effect on the dynamic response of the cable than the uphill laying condition. When the slope is ≥15°, the suspension distance increases rapidly and the fit between the cable and the submarine decreases. The increase in swing distance will further increase the suspension distance and cable tension. And / or, With a fixed cable-laying vessel speed, increasing the cable release speed can shorten the suspension distance and reduce the maximum effective tension; however, excessively fast release speed will reduce the minimum bending radius and increase the risk of cable accumulation at the contact point with the seabed. And / or, Under steep slope conditions, an appropriate acceleration distance can effectively shorten the suspension distance and maintain maximum effective tension stability; however, when the slope is extremely steep, simply increasing the acceleration distance is not enough to meet the requirements, and the cable release speed also needs to be adjusted to meet the bending radius limit. And / or, The direction of wave loads and current loads has a significant impact on cable laying performance. Alignment with the dominant ocean current can improve the cable's fit to the seabed and reduce tension; while wave-current coupling will produce the strongest overall dynamic response.

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