Analysis of Three-Core Composite Submarine Cable Damage Due to Ship Anchor

Suspended submarine cables are prone to likely mechanical damages due to ship anchors, which represent a significant threat to the reliability of power transmission and information communication networks. This paper is aimed at presenting a detailed investigation to the dynamic response of a ship anchor impacting the suspended section a submarine cable in order to reduce the risk of cable damage. In this regard, a three-dimensional and dual nonlinear model of the anchor affecting a subsea cable is established using ABAQUS finite element analysis software. The damage effect due to the ship anchor on the suspended and buried-in-soil sections of the cable is studied. Results show that when a ship anchor hits a suspended section of the subsea cable, the mechanical stress is concentrated at the impacted point and is progressing to both sides of the suspended section with a significant cable deformation. On the other hand, the buried section of the cable suffers from a short impact process, and the deformation is relatively small. To reduce this impact effectively, a detailed technical comparison of two common dumping and filling methods is conducted, and the better protection method is proposed.

environment of the seabed and construction factors. In addi-46 tion, the presence of submarine cables and submarine structures can change the existing flow field, which can increase oretical and experimental research has been conducted to 91 investigate the mechanical behavior of submarine pipelines. 92 Huang et al. [22] carried out a numerical simulation study 93 for the impact of a suspended channel on an anchor. The 94 paper analyzed the influence of the anchoring speed and con-95 crete layer on the mechanical stress imposed on a submarine 96 pipeline and used the coupling effect between the pipe and 97 soil to reflect the seabed effect. Luo et al. [23] considered the 98 interaction between the channel and the ground and employed 99 the Docker-Prager model to simulate the seabed to analyze 100 the dynamic impact on a submarine suspended pipeline due 101 to a falling object. The paper also investigated the effect 102 of volume parameters on the pipeline deformation and the 103 amplitude of the dynamic response. Kouretzis et al. [24] 104 considered materials' nonlinear impact and analyzed the 105 buried pipelines' internal forces and strains under surface 106 subsidence and uplift conditions. Kinash et al. [25] simpli-107 fied the thin-walled cylindrical pipe response problem under 108 combined load and internal pressure into a one-dimensional 109 model using the plastic theory of shell and thin-film. Refer-110 ences [26], [27] compared and analyzed the stress of sub-111 marine pipelines in sandy and cohesive soils, respectively. 112 Sudhan et al. [28] improved the effects of buried depth, rel-113 ative slope height, and scattering parameters on the stress of 114 fully buried submarine pipeline through experimental analy-115 sis. Reported results can provide a specific basis for the buried 116 depth of submarine cables. 117 Up till now, research into buried submarine cables has been 118 focused on towed anchors. The depth of the cable's burial is a 119 key factor in preventing its damage from falling anchors and 120 towing. The analysis should therefore include the function 121 of the anchor in the soil. The literature [29] looks into the 122 buried depth protection index of submarine cables, using a 123 combination of physical model tests, numerical simulations 124 and hypothetical analysis. The effects of anchor bottoming 125 speed, sinking energy and anchor mass on the penetration 126 depth of anchor rods are analysed. By establishing the anchor 127 towing analysis model it is demonstrated that in the study 128 area, the burial depth protection index of submarine cables 129 is 3 metres. The literature [30], [31] conducted numerical 130 replications of ship anchor incursion into soil to discover 131 the effect of anchor movement on submarine cables. The 132 conclusion was that it is possible that dragging under the soil 133 can still cause damage to the submarine cable even if there is 134 no direct contact between it and the ship anchor. This is due 135 to the soil movement between the anchor and the submarine 136 cable, and the sidewall pressure of the anchor which indirectly 137 deepens the mechanical damage to the submarine cable.

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Concerning the research on the protection process of 139 suspended submarine cables, both domestic and overseas 140 research largely focuses on the throwing and filling method 141 and the bionic grass protection method. As the research 142 object, the paper [32] uses the sandbag stacking form in the 143 case of submarine cable suspension management in Bohai 144 Sea, along with Fluent software to create a two-dimensional 145 flow field model to analyse the distribution law of surround-146 ing flow field under diverse forms of sandbag stacking, 147 to decrease the likelihood of sandbags being washed away 148 by water movement. In the paper [33] the rockfill-anchor-149 cable discrete element model was constructed on the PFC3D 150 simulation platform. Quantitative evaluation of the resistance 151 of submarine cables to anchorage damage and simulation of 152 the mechanical properties of the rock throw protection layer 153 throughout local lateral intrusion of the anchor rods to present 154 a foundation for the protection of anchor rods from rock 155 throw protection. The literature [34], shows the velocity field 156 distribution of bionic aquatic grass along the vertical plane 157 VOLUME 10, 2022 is measured using typical particle image velocimetry (PIV).
It concluded that the method of bionic grass protection is 159 effective in suppressing the speed of the water and decreasing 160 the likelihood of overhanging the submarine cable pipe. 161 While some studies on the dynamic behavior of subma-162 rine pipelines can be found in the literature, as discussed 163 above, not much attention was given to analyze the dynamic 164 response of submarine composite cables due to ship anchor. 165 This, the main contribution of this paper is to present a 166 detailed analysis to the dynamic response of a three-core AC 167 composite submarine cable due to ship anchors. In this regard,  When the anchor penetrates the soil, the resistance of the earth 195 first increases and then decelerates to zero.

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The anchor is assumed to have a height above the water sur-197 face and an initial velocity of 0. Moreover, it does not consider 198 the reduction in chain-out speed, wind load, and wave factor 199 that the anchor machine reduces. Then the anchor's free-fall 200 kinetic equation in seawater can be written as: When the anchor is released at a height H above the water 203 surface, the speed of the incoming anchor is v=(2gH) 1/2 , The 204 velocity of the descent to a water depth of l is: where m is the mass of the anchor, ρ w is the density of the 208 seawater, V is the discharge volume of the anchor, C D is the 209 drag coefficient, A is the retaining water area of the front face 210 of the anchor, v is the anchor speed, ρ a is the density of the 211 anchor.

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The equilibrium velocity is: The bottoming kinetic energy of the anchor is: Newton's second law equation for the anchor in the inlet 217 section is: The resistance of the soil is related to the quality of the 220 earth. According to [35], the resistance of sandy and clay soils 221 can be respectively calculated from: where p 0 = ρgh, the overlying soil pressure.

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If the anchor penetrates the soil to a depth of h, the energy 226 consumed by the anchor in penetrating the ground can be 227 obtained by integrating the soil resistance: The energy consumed by the anchor due to resistance 230 in the through-soil section in sandy and clay soils, can be 231 respectively calculated from: where C u0 in the undrained shear strength of the mud surface, B is the anchor crown width, and h is the depth of entry.

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The impact energy of the anchor through the water and 240 earth, in contact with the submarine cable, E c is: When the burial depth is large enough, E a is greater than 243 E k , and the cable will not be damaged. The impact energy will 244 likely collapse the submarine cable in case of shallow burial 245 depth.

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It is necessary to model the system in layers to build the 249 structure of the submarine cable. Firstly, SolidWorks is used 250 to draw a plan, stretch and twist, to finally forming an assem- The submarine cable is laid under the soil. After a long period 264 of complex sea conditions, the ground is washed away by 265 waves, and currents, and the submarine cable is gradually 266 exposed and suspended. As shown in Figure 3, the floating 267 phenomenon occurs in actual projects. At the junction of the 268 suspended section and the buried-in-soil section, the seabed 269 level is uneven, and the soil is loose, which will increase the 270 length of the suspended section of the cable in the long run. 271 The impact of the anchor on the submarine cable is a 272 transient dynamic process involving complex nonlinear and 273 contact problems. The model calculation is completed using 274 the dynamics module Explicit in ABAQUS software. The 275 suspended section of the submarine cable is modelled by 276 simulating a concave broken soil model centered by the 277 submarine cable with a suspended height of twice the outer 278 diameter. As shown in Figure 4, the submarine cable spans a 279 kilometer long, which is long enough compared to the impact 280 site, and the soil and submarine cables at both ends are set 281 to be fixed to constrain the displacement in the X, Y, and Z 282 directions. The anchor exerts an initial vertical velocity and is 283 assumed to hit the submarine cable in the suspended section. 284 The soil adopts the Mohr-Coulomb model to construct its 285 ideal elastic-plastic deformation under impact load.

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For the contact setting, the mechanical behavior of the 287 tangent and the contact surface is described with the help 288 of penalty function. Each contact surface is allowed to slip 289 VOLUME 10, 2022 so that the contact relationship between the anchor contact  armor is a crucial structure to protect the broken core of the 329 optical fiber. Optical fiber is responsible for communication 330 transmission and monitoring the temperature and stress on 331 the cable in real-time. The material of optical fiber armor is 332 the same as that of the outer armor: galvanized steel. Since the 333 optical unit is internally spiraled with the copper, the impact 334 angle of the optical fiber armor varies significantly, but it is 335 always inside the outer armor, and its equivalent stress is close 336 to but consistently lower than the outer armor. 337 Figure 6(a) shows the equivalent stress-time history of 338 the submarine cable when the anchor under the suspended 339 section hits the submarine cable. From 0 ms to 4 ms, the 340 anchor has not yet contacted the cable body, and the equiva-341 lent stress is zero. After 4 ms, the two collide and deform elas-342 tically, the equivalent stress increases linearly, and the armor 343 and copper are close to the yield stress of their respective 344 materials. After each layer structure reaches the yield stage, 345 it enters the plastic stage. When the anchor hits the suspended 346 section of the submarine cable, the speed of the anchor does 347 not drop immediately due to its inertia, and the energy trans-348 mitted to the submarine cable is relatively low, so the entire 349 impact process is slow. 350 Figure 6(b) shows the equivalent stress-time history of 351 the same three layers for the submarine cable in the buried-352 in-soil section. It can be seen from the figure that the elastic 353 stage occurs within 0∼0.2 ms, and the yield stress is quickly 354 reached after which the maximum yield stress exceeds to 355 enter the plastic stage. After 5 ms, the equivalent pressure 356 on each layer structure fluctuates with gradually decreased 357 amplitude due to the influence of the overall damping.   Figure 7 shows a cloud diagram of the deformation of the 388 submarine cable section at the impact point under different 389 environmental conditions. As shown in Figure 7(a), in the 390 suspended section, the outer sheath of the submarine cable 391 and the outer armor have been peeled off from each other. 392 Also, the outer sheath of the optical unit and the fiber armor 393 are extruded from each other, and the lead sheath outside the 394 copper conductor is squeezed out from the XLPE Layers. 395 As shown in Figure 7(b), for the buried-in-soil section, the 396 submarine cable's outer sheath and outer armor are squeezed 397 and deformed, while the internal structure is almost intact. 398 These results reveal that when anchors hit the suspended 399 section of the cable, it is easy to lose the ability to protect 400 the inner core of the submarine cable, which results in a 401 significant deformation of the cross-section of the cable body, 402 and the conductor power is significantly attenuated.

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The typical suspended section adopts the throwing method 406 to prevent the submarine cable from being mechanically 407 damaged. The main throwing and filling methods include 408 the throwing and filling sandbag method and the throwing 409 VOLUME 10, 2022  and filling gravel method. The advantages and disadvantages 410 of these two methods are listed in Table 3. The two meth- Generally, the dent value of the submarine cable is used to 418 evaluate the damage. As shown in Figure 8, when a certain 419 mass shoots down the submarine cable at a certain speed, the 420 entire submarine cable will have an irreversible dent depth.

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The change in the outer layer deformation is called the dent 422 value: the larger the dent value, the more severe the damage.

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When the ratio of the dent value to the outer diameter of the 424 submarine cable exceeds 5%, it will threaten the submarine  Figure 9 shows the effect of anchor speed on the dent value 429 when a 2000 kg anchor hits the submarine cable that employs 430 throwing sandbags and gravel methods at its suspended 431 section. When the anchor speed is less than or equal to 2 m/s, 432 the sandbag and gravel methods result in similar cable's dent 433 value.

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Because the impact velocity is small at this time, the influ-435 ence of soil characteristic is not a decisive factor. With the 436 increase of the anchor speed, the dent value of the submarine 437 cable increases exponentially. Because the anchor's speed 438 increases and its mass is constant, the energy of the anchor 439 will increase by the square of the speed. Comparing the two 440 filling methods, the anchor damage of the submarine cable 441 is more serious in sandbag environment. With the increase in 442 speed, the protective effect of the sandbag and gravel environ-443 ments becomes more different. While the elastic modulus of 444 sandbags is low, the elastic modulus of gravel can reach more 445 VOLUME 10, 2022   When the burial depth of the submarine cable 485 is 1.8 times the outer diameter, the damage is almost reduced 486 to zero. The soil in the sandbag environment is more likely 487 to sag when it is impacted than in the gravel environment, 488 and the soil environment with a lower elastic modulus has 489 less influence on the impact of the anchor. Likewise, the 490 shallower the burial depth, the more significant the difference 491 between the sag values of the two methods. When the burial 492 depth exceeds 1.5 times the outer diameter, the dent values in 493 the two throw-fill environments remain the same. Generally 494 speaking, the difference between the dumped soil and the 495 buried depth is slight, and the buried depth has a more appar-496 ent protective effect on the submarine cable, which is much 497 more critical than the dumped environment. Consequently, 498 when the floating submarine cable is abandoned and filled, 499 it is necessary to focus on the buried depth of the submarine 500 cable under the dumped soil.  3) The dumping and filling method is adopted to treat 522 the suspended section. The study found that the more