Investigation on the Ampacity of AC Submarine Cables in J-Type Conduit Trenchless Installation

Abstract

For the installation of submarine cables at sites with significant elevation differences and non-excavation bases, the J-type conduit represents an emerging installation solution. This study focused on a typical AC submarine cable installed via J-type conduit trenchless installation. A coupled electromagnetic–thermal–fluid finite element model was established to investigate the effect of the burial depth, conduit material, and environmental temperature on the ampacity of the cable. The results indicate that the ampacity of the cable decreases as the burial depth increases due to the deteriorating heat dissipation capacity of the soil. Regarding the internal medium of the conduit, the cable demonstrates superior ampacity performance in muddy water. Additionally, J-type conduits fabricated from non-magnetic metallic materials such as copper and stainless steel exhibit significantly higher cable ampacity compared to polymeric materials like PE and PVC. As the soil’s temperature rises with the increasing environment temperature, its thermal conductivity efficiency decreases, consequently impairing cable heat dissipation and ampacity.

1. Introduction

With the rapid development of offshore wind power and trans-sea transmission projects, submarine cables are playing an increasingly prominent role in offshore power transmission. For submarine cable landing sections installed at seawall dams or other excavation-prohibited grounds, the elevation difference in the construction area often leads to insufficient burial depth after laying. This makes the cables vulnerable to seawater scouring, resulting in localized exposure and potential safety hazards [1]. Moreover, variations in rock mass stress and seepage pressure during excavation can also affect the ampacity of cables [2]. To address this issue, the J-type conduit trenchless installation method can be adopted [3]. Compared with conventional submarine cable-laying methods, the J-type conduit requires no ground excavation and can traverse complex terrains such as shallow waters and tidal zones while offering enhanced protection and safety. This method also reduces construction costs and minimizes disturbances to marine ecosystems. However, due to space constraints and the diverse filling media, the thermal characteristics of the J-type conduit installation environment restrict the ampacity of AC submarine cables [4], with this becoming a critical limiting factor impacting the power transmission efficiency [5].

The ampacity of cables serves as a key indicator in evaluating their current transmission capability [6], which is quantitatively assessed by the maximum current value when the conductor reaches its permissible temperature limit (typically 90 °C) [7]. The cable is constantly subjected to thermal, electrical, and mechanical stresses, thereby affecting its ampacity [8,9]. For conventional submarine cables, the ampacity is critically dependent on multiple environmental and installation factors, including the seawater temperature, cable laying method, burial depth, thermal conductivity of seabed sediments, and seawater flow velocity. Hao et al. [10] investigated the effects of seawater flow and temperature on submarine cable ampacity and simplified the heat transfer mechanism of marine sediments to a single mode. In reality, coarse-grained sediments (e.g., large-diameter gravel) primarily facilitate heat transfer through thermal convection, significantly influencing the temperature distribution around submarine cables [11]. Hughes et al. [12] developed a coupled electromagnetic–thermal–fluid simulation model to analyze how sediment particle size affects cable temperature fields and ampacity. Alsadat et al. [13] proposed a decentralized reinforcement learning algorithm to evaluate the impacts of multiple variables on system states, which can be applied to optimize the ampacity parameters of cables. Through the intelligent load tuning of the distribution system, the voltage security, operational, and economic states of the network can be maximized [14]. Qiao et al. [15] quantified how burial geometry, the thermal conductivity of surrounding media, and cable configuration affect steady-state ampacity and thermal profiles in submarine cable systems.

Conventional submarine cables are frequently threatened by ship anchors, necessitating sufficient burial depth to prevent anchor damage [16]. However, an increased burial depth inevitably compromises heat dissipation, thereby reducing the cable ampacity. Zhang et al. [17] observed that when the burial depth increased from 0.7 m to 2 m, the cable ampacity decreased progressively, though the rate of reduction gradually stabilized. Che et al. [18] demonstrated that the ampacity could be enhanced by increasing the cable spacing, improving the convective heat transfer coefficients, and maintaining lower ambient temperatures. Li and Wang [19] developed a computational model for pipe-type cables backfilled with mixed-filler materials of varying thermal conductivities, revealing that composite fillers significantly improve current-carrying performance. Maximov et al. [20] found that the more realistic modeling of temperature distribution in surrounding media enables more accurate ampacity estimation. During operation, the process of the cable heating the adjacent medium deteriorates heat dissipation conditions, leading to elevated cable temperatures and consequent ampacity reduction. Furthermore, magnetic metal pipes induce eddy-current losses that degrade the current-carrying capacity. Wang et al. [21] identified that cable phase arrangement, pipe dimensions, and inter-cable spacing critically influence the eddy-current loss magnitude of cables. System uncertainties, such as grid interference and voltage fluctuations [22,23], can also affect the power transmission capacity of submarine cables, as well as the conversion efficiency of renewable energy power stations [24].

J-tubes are prefabricated tubular protection devices featuring a J-shaped curved structure. They provide structural protection against wave-induced dynamic loads during cable installation from the seabed to offshore converter platforms. Compared to conventional submarine cables, cables installed in J-tubes face significantly more complex operational environments [25]. Lin et al. [25] described the J-tube segment and landing section as critical ampacity bottlenecks during power transmission through wind turbine cables. Zhang et al. [26] investigated the influences of the air column length within J-tubes, wind velocity, and ambient temperature on the cable current-carrying capacity. It was demonstrated that sidewall openings in J-tubes enhanced heat dissipation, thereby improving the cable ampacity. Du et al. [27] introduced a derating factor to quantify ampacity reduction due to elevated temperatures in J-tubes, formulated as a function of the J-tube length, outer diameter, ambient temperature, wind speed, and solar irradiance. You et al. [28] developed a 3D numerical model of ventilated J-tube systems, comparing their performance with closed configurations. The study revealed the thermal advantages of forced-air cooling, with a 27.5% ampacity increase achieved at 10 m/s ventilation velocity. Wu et al. [29] found that the temperature gradient across the cable insulation layer governs the electric field distribution in J-tubes, while the burial depth and trench dimensions critically influence the ampacity in cable trenches.

It was found that by adapting the strategic optimization of installation environments, the ampacity of submarine cables can be significantly enhanced. Zou et al. [30] integrated gravity heat pipes into the air segment of J-tubes to enhance thermal management. This approach reduced the cable core’s average temperature by over 26%, demonstrating significant cooling efficacy. Li et al. [31] employed both finite element analysis and analytical methods to study DC submarine cables, revealing that the solar radiation intensity and ambient temperature exert greater influence on the ampacity than the J-tube outer diameter. Xia et al. [32] conducted finite element simulations on ±500 kV DC cables in J-tubes, comparing seawater and air as packing media. Notably, cables in seawater-filled J-tubes exhibited approximately 200% higher ampacity than those in air-filled configurations. The impacts of solar radiation, ambient temperature, and wind speed on ±250 kV DC cable ampacity in J-tubes were quantified by Cui et al. [33]. By implementing sidewall openings, the ampacity increased by up to 13.98% compared to sealed J-tube designs.

From the literature review, it can be concluded that the presence of J-type conduits fundamentally alters the thermal characteristics of submarine cables. In such configurations, cable ampacity is constrained not only by the seawater temperature, the thermal conductivity of seafloor sediments, and other conventional factors, but also by the structural properties of the conduit itself. However, the effects of the J-type conduit material properties and burial depth on submarine cable ampacity have not yet been fully elucidated. In this study, a coupled electromagnetic–thermal–fluid finite element model (FEM) was developed for three-core AC submarine cables, incorporating integrated J-type conduit, intertidal, and submarine cable segments. The effects of the burial depth, internal medium, conduit material properties, and environmental temperature on the temperature distribution and ampacity of the cable were investigated. The main novelty and key contribution of this work lie in allowing a deeper understanding of the ampacity characteristics of J-type submarine cables, offering actionable insights for optimized cable design and practical installation applications.

2. Governing Equations

Thermal analysis was performed on trenchless AC submarine cable systems, focusing exclusively on heat generation within the J-type conduit, comprising Joule heating in copper conductors and induction heating in both the alloy lead sheath and copper armor layers. Heat dissipation in submarine cables primarily involves thermal conduction between the cable and the internal medium (air, seawater, or sludge water) within the J-type conduit, thermal conduction through the conduit wall to the surrounding soil, and convective heat transfer between the conduit’s exterior and ambient seawater. Due to the substantial length of submarine cables, the thermal analysis can be simplified using a 2D model.

To investigate the operational characteristics of submarine cables with J-type conduits in different installation environments, a multi-physics coupling approach is required. The governing equation of the electromagnetic field for submarine cables can be expressed as

$$\left\{\begin{array}{l}\nabla \times H=J\\ B=\nabla \times A\\ J=\mathit{\sigma }E+j\omega D\\ E=-j\omega A\end{array}\right.$$

(1)

where H is the magnetic field strength; J is the current density; B is the magnetic flux density; A is the magnetic vector potential; E is the electric field intensity; D is the electric displacement vector; ω is the alternating current angular frequency corresponding to the 50 Hz power frequency; and σ is the material conductivity, which can be written as

$$\mathit{\sigma }={\displaystyle \frac{{\mathit{\sigma }}_{20}}{[1+\alpha (T-293.15 \left)\right]}}$$

(2)

where σ₂₀ is the conductivity of the material at 20 °C, with values of 5.998 × 10⁷ S/m for the copper conductor and copper armor, and 4.673 × 10⁶ S/m for the alloy lead jacket; α is the temperature coefficient of resistance, with values of 0.0039 K⁻¹ for the copper conductor and copper armor and 0.004 K⁻¹ for the alloy lead jacket; and T is the material temperature.

The coupled electromagnetic–thermal governing equations for submarine cables can be described as

$$\left\{\begin{array}{l}\mathit{\rho }{C}_{p}v\nabla T =\nabla \left(k\nabla T\right)+Q_e\\ Q_e=Q_{\mathit{rh}}+Q_{\mathit{ml}}\\ Q_{\mathit{rh}}={\displaystyle \frac{1}{2}}\mathit{Re}\left(J\cdot E^{*}\right)\\ Q_{\mathit{ml}}={\displaystyle \frac{1}{2}}\mathit{Re}\left(i\omega B\cdot H^{*}\right)\end{array}\right.$$

(3)

where ρ is the density of each layer of material; C_p is the constant-pressure heat capacity of the material; v is the velocity vector, with a fixed value for solid materials; k is the material’s thermal conductivity; Q_e is the total electromagnetic losses; Q_rh is the Joule loss of the conductor layer; Q_ml is the hysteresis loss of the alloy lead jacket and armor layer; Re is the real part of the calculation; E* is the conjugated form of electric field intensity; and H* is the conjugated form of the magnetic field strength.

The governing equations for the heat transfer field applicable to air and seawater can be described as

$$\left[{\displaystyle \frac{\partial \rho }{\partial t}}+\left(v\cdot \nabla \right)T\right]+\left(\nabla \cdot q\right)+\mathit{\tau }:v+{\displaystyle \frac{T}{{\rho }_f}}{\left.{\displaystyle \frac{\partial {\rho }_f}{\partial T}}\right|}_p\left[{\displaystyle \frac{\partial p_{\mathrm{A}}}{\partial t}}+\left(v\cdot \nabla \right)p\right]$$

(4)

where Q_f is the heat source of the fluid material; ρ_f is the density of the fluid material; C_pf is the specific heat capacity at constant pressure; τ is the viscous stress tensor; and p is the fluid pressure.

Since the flow velocities of air or seawater inside the J-type conduit are small, the motion of air and seawater is assumed to show laminar flow. The governing equation relating flow velocity and density can be expressed as

$$\left\{\begin{array}{c}{\rho }_f\left(v\cdot \nabla \right)v=\nabla \cdot \left[-\mathit{pI}+K\right]+{\rho }_{f}g\\ \nabla \cdot \left({\rho }_{f}v\right)=0\\ K=\mathit{\mu }\left[\nabla v+{\left(\nabla v\right)}^T\right]-{\displaystyle \frac{2}{3}}\mathit{\mu }\left(\nabla \cdot v\right)I\end{array}\right.$$

(5)

where μ is the dynamic viscosity; K is the viscous stress tensor; I is the identity matrix tensor; and g is gravitational acceleration.

When the conduit is filled with air, the air thermal radiation between the cable outer surface and the inner pipe wall must be considered and can be defined as

$$Q_i={\mathit{\sigma }}_s{\mathit{\epsilon }}_i{F}_{\mathit{ij}}{A}_i\left(T_i^4-T_j^4\right)$$

(6)

where Q_i is the radiative heat transfer rate of the surface element; σ_s is the Stefan–Boltzmann constant; ε_i is the effective thermal emissivity on the surface element; F_ij is the angle coefficient; A_i is the area of the surface element; and T_i and T_j are the temperature values of surface elements i and j.

3. Numerical Model Setup

3.1. Parameters of the Submarine Cable

J-type conduit trenchless installation is typically accomplished using drilling or pipe jacking construction technology, following a J-shaped trajectory from land to sea, with the submarine cable positioned centrally at the bottom of the conduit. This paper focuses on the soil-embedded segment of the J-type conduit installation, with a case study derived from the Zhoushan Beitang 110 kV power transmission project in China. A 2D numerical model was established using coupled electromagnetic–thermal–fluid physics, as illustrated in Figure 1. The J-type conduit comprises three segments—the buried segment, the horizontal segment, and the excavated segment. The horizontal lengths of these three segments are 66.0 m, 34.0 m and 50.0 m, respectively. The vertical elevation of the conduit is 10.0 m. To monitor the ampacity of the submarine cable, 16 monitoring points were deployed along the cable route at equal horizontal intervals.

In the trenchless installation, the HYJQ41-64/110-3×630+4×48B1 cross-linked, polyethylene (XLPE)-insulated, copper tape-armored submarine power cable was selected. In the modeling, the conductor screen and insulation layer were consolidated into a single insulating layer due to the thinness of the conductor screen and its similar thermal properties to the insulation. Similarly, the polyethylene (PE) sheath, filler layer, wrapping tape, and lining layer were collectively treated as a composite filler layer, while the armor layer was simplified as an annular structure. The parameters of the submarine cable after simplification are listed in

Table 1. Geometrical parameters of the cable.

Definition	Symbol	Value
Radius of the copper conductor	R1	15 mm
Radius of the XLPE insulation layer	R2	33.1 mm
Radius of the insulation layer	R3	34.8 mm
Radius of the alloy lead sleeve	R4	37.7 mm
Radius of the filler layer	R5	89.2 mm
Radius of the armor layer	R6	95.6 mm
Radius of the sheath	R7	99.6 mm

.

The thermal conductivity and electrical conductivity of the main components of the submarine cable are presented in

Table 2. Thermal conductivity and electrical conductivity of the cable.

Definition	Symbol	Value
Thermal conductivity of copper conductors and armor layers	λ1	400 W/(m·K)
Thermal conductivity of the XLPE insulation layer	λ2	0.15 W/(m·K)
Thermal conductivity of the insulation layer	λ3	0.29 W/(m·K)
Thermal conductivity of the alloy lead sleeve	λ4	34.8 W/(m·K)
Thermal conductivity of the sheath	λ5	0.15 W/(m·K)
Electrical conductivity of copper conductors and armor layers	σ1	5.998 × 107 S/m
Electrical conductivity of the alloy lead sleeve	σ2	4.673 × 106 S/m

. The J-type conduit was designed with a diameter of 400 mm and wall thickness of 29.4 mm. Since the cable ampacity remains essentially constant at burial depths exceeding 3.0 m, the vertical distance from the conduit top to the seabed surface was set at 2.0 m, 2.5 m, and 3.0 m for parametric analysis. To investigate the material’s effects on ampacity, the conduit materials were selected as polyethylene (PE), polyvinyl chloride (PVC), and non-magnetic metals (copper and stainless steel).

3.2. Model Setup

The numerical model of the J-type conduit system was established in the FEM platform COMSOL 6.1, as shown in Figure 2. The J-type conduit was embedded in a rectangular soil domain at different burial depths of 2.0 m, 2.5 m, and 3.0 m, with 10.0 m clearance from the left, right, and bottom boundaries, as depicted in Figure 2a. The heat flux at the left and right boundaries of the soil domain was set to 0. The bottom boundary maintained a constant temperature of 273.15 K, while the top boundary simulated seawater interaction with a convective heat transfer coefficient of 200 W/(m²·K).

The main computational modules involved in the model include the electromagnetic field module, thermal transfer module, and fluid flow module. For the electromagnetic field simulation, three-phase coil currents with identical amplitude and 120° phase displacement were applied to the conductors. The external boundaries of the model were set as magnetic insulation boundaries.

In the thermal transfer simulation, the internal medium of the conduit was modeled with distinct thermal properties, as follows: (1) muddy water with thermal conductivity of 1.0 W/(m·K); (2) air with conductivity ranging 0.02~0.1 W/(m·K) and including radiation effects, where both the cable surface and pipe interior were treated as semi-reflective boundaries; (3) seawater with a conductivity of 0.6 W/(m·K) modeled as fluid heat transfer. To reflect realistic conditions, two hybrid media cases were additionally considered, as follows: (1) a seawater–mud interface with the upper seawater region showing fluid heat transfer and the lower mud section showing solid conduction; (2) an air–seawater medium with fully fluid heat transfer and with semi-reflective boundaries at both the cable surface and the air–water interface.

As regards the materials of the J-type conduit, both PE and PVC pipes exhibit stable thermodynamic properties. The PE pipe has a thermal conductivity of 0.15 W/(m·K), electrical conductivity of 1 × 10⁻¹⁴ S/m, and relative dielectric constant of 2.5. In comparison, the PVC pipe demonstrates a slightly higher thermal conductivity of 0.1667 W/(m·K), a lower electrical conductivity of 1 × 10⁻¹⁶ S/m, and a higher relative dielectric constant of 8.0. The thermodynamic properties of metallic materials exhibit significant temperature dependence. The copper pipe has a thermal conductivity of 400 W/(m·K) and electrical conductivity of 5.998 × 10⁷ S/m. In contrast, the stainless steel pipes show more stable thermodynamic characteristics, with a thermal conductivity of 16.2 W/(m·K) and electrical conductivity of 1.5 × 10⁶ S/m.

To validate the ampacity accuracy of the numerical model, the equivalent thermal circuit method specified in the IEC-60287 standard was adopted for comparison [34]. For J-type conduits with air as the internal medium at burial depths of 2.0 m, 2.5 m, and 3.0 m, the equivalent thermal circuit method yielded ampacity values of 701.6 A, 663.5 A, and 678.2 A, respectively, while the numerical model showed 653.3 A, 645.5 A, and 643.6 A. The average error is 4.9%, indicating that the numerical model developed in this study provides relatively high accuracy.

4. Results and Discussion

4.1. Effect of Burial Depth on the Cable Ampacity

As the transmission current increases, the submarine cable temperature rises progressively with an accelerating rate. The steady-state ampacity is determined by regulating the internal current until the conductor reaches 90 °C. For the case with soil surrounding the J-type conduit, simulations were conducted at an ambient temperature of 20 °C using PE pipes to investigate burial depth effects. Figure 3 illustrates the variation in cable ampacity for different internal media with conduit burial depths of 2.0 m, 2.5 m, and 3.0 m. The results demonstrate a consistent 4.7~6.3% reduction in ampacity per 0.5 m increase in burial depth. This phenomenon primarily stems from extended heat transfer paths through the surrounding soil at greater depths, which elevate operating temperatures and increase environmental thermal resistance, consequently reducing the capacity of the cables. In addition, the internal materials between the cable and conduit significantly affect ampacity. Under constant burial depth conditions, the ampacity performance follows the trend muddy > seawater > air. Notably, the muddy water medium enhanced ampacity by 22–35% compared to air-filled conditions, attributable to its minimal thermal resistance and superior thermal conductivity, which enabled more efficient heat dissipation and consequently improved the capacity.

The temperature distribution contours of the conduit–cable coupling model at varying burial depths are shown in Figure 4. The internal medium between the cable and conduit was set as air. The temperature field was primarily generated by Joule heating in the cable conductor and electromagnetic induction losses in the alloy lead sheath. It has been found that the maximum temperature concentrated in the cable core region, exhibiting a radially decreasing gradient toward the outer layers. Increasing the burial depth systematically elevated the cable surface temperature; at burial depths of 2.0 m, 2.5 m, and 3.0 m, the cable surface temperatures reached 84 °C, 87 °C, and 88 °C, respectively. This verifies that greater burial depths reduce heat dissipation by prolonging heat conduction paths and enhancing the thermal resistance effect, consequently diminishing the capacity of the cables.

To more intuitively investigate the influence of burial depth on the temperature distribution of cables, temperature variations at different points along a radial line were monitored to represent the thermal profile. As shown in Figure 5a, the radial line originates from the cable center, passes through the center of the upper-right conductor, and extends to the outer wall of the conduit. A total of 19 key points were selected for monitoring, including intersection points, midpoints, and trisection points along this line. Figure 5b presents the radial temperature profiles under three burial depths at 650 A operation. The analysis reveals the cable core functions as the dominant heat source, exhibiting quasi-uniform temperature distribution resulting from high current density, while the surrounding insulation and conductor screens demonstrate symmetrical thermal dissipation with distinct radial temperature gradients. The central region maintains thermal stability under balanced heating from three phase conductors, whereas the lead sheath and copper armor experience eddy-current heating from AC magnetic fields, resulting in flattened temperature decay profiles. After heat dissipates from the cable surface, it transfers through the internal medium within the conduit to the conduit walls, undergoing further temperature reduction.

In the model, 16 capacity monitoring points were arranged along the submarine cable landing section, as illustrated in Figure 1. The burial depths and corresponding maximum ampacity at each monitoring point are shown in Figure 6. The analysis of monitoring points 1 through 7 reveals that when the surface medium is air, the heat dissipation efficiency of the cable becomes significantly constrained. As the burial depth increases from 0 m to 9.34 m, the capacity demonstrates a clear decreasing trend, reaching its minimum value of 608 A at monitoring point 5. This particular monitoring point serves as the ampacity bottleneck for the entire cable system, with its maximum allowable capacity determining the overall power transmission capability of the system. If the operational current exceeds 608 A, then the local cable temperature will surpass the 90 °C threshold, potentially leading to the accelerated thermal aging of the insulation layer and compromising the operational safety of the cable system. Within the monitoring section between points 8 and 16, where the surface medium transitions from air to seawater, the cable capacity shows significant improvement compared to the previous section. This enhancement primarily stems from two factors: (1) the reduced burial depth decreases thermal resistance and (2) the high thermal conductivity of seawater substantially improves heat dissipation efficiency. The comparative analysis of monitoring points 1 and 16 (both at 0 m burial depth) reveals that the capacity under seawater conditions is markedly higher than in an air medium, further demonstrating the beneficial effect of seawater on cable cooling.

4.2. Effect of Conduit Material on the Cable Ampacity

The J-type conduit serves as a critical protective structure for submarine cables, and material selection significantly impacts the cable ampacity while ensuring operational safety. This study investigated four conduit materials, including polymeric materials, PE, PVC, non-magnetic metals, copper, and stainless steel. Furthermore, accounting for the potential presence of mixed media in the 3D J-type conduit structure under engineering conditions, this study extended beyond single-medium analysis to investigate two mixture scenarios: air–seawater and seawater–mud mixtures.

Figure 7 presents the cable ampacity results for J-type conduits under five medium conditions at a burial depth of 2.5 m. It is found that the non-magnetic metals (copper, stainless steel) demonstrate higher ampacity than polymer materials (PE, PVC), attributable to their superior thermal conductivity and reduced eddy current effects due to optimal conductor spacing. The copper conduits can efficiently transfer the heat to the external environment, thereby reducing the cable temperature and enhancing its ampacity, while PVC shows the lowest ampacity due to its insulating properties and low thermal conductivity. In addition, the results reveal a monotonic increasing trend in submarine cable capacity as the internal medium transitions from air to air–seawater, seawater, seawater–mud and muddy water media, with air remaining the least favorable medium for heat dissipation even when considering radiative heat transfer, while the ampacity in the air–seawater mixed medium is only slightly lower than that in pure seawater, further confirming the dominant role of seawater in the heat dissipation process of mixed media systems. The water molecules in the muddy water completely fill the soil cavities, forming a continuous thermal conduction network that substantially enhances the effective thermal conductivity and cable ampacity.

Figure 8 illustrates the temperature distribution of cables in different internal medium conditions. The effect of the internal medium on thermal performance is mainly determined by its thermal conductivity and convective properties. The results reveal that in the air medium, the temperature field exhibits significant non-uniformity and the heat dissipation efficiency and ampacity are limited due to weak thermal conduction and convection. While both the air–seawater mixed medium and the seawater medium demonstrate fundamentally similar radial temperature distribution patterns when the cable reaches its respective ampacity limit, minor differences emerge during heat transfer through the media regions. The inferior thermal conductivity of air leads to elevated temperatures across all cable material layers in the air medium. Furthermore, the combined effects of thermal convection and radiation in air result in a substantially smaller temperature gradient within the medium region compared to other operational conditions.

The radial temperature distribution of submarine cables under four conduit materials at a 650 A input current is presented in Figure 9. The results demonstrate that polymer materials (PE and PVC) exhibit significantly higher internal cable temperatures compared to metallic conduits due to their inferior thermal conductivity. The copper J-type conduit shows optimal thermal performance, ensuring enhanced operational safety. However, considering the substantial disadvantages of copper in installation complexity and cost, a hybrid design strategy is proposed—implementing non-magnetic metal conduits in terminal sections (where heat dissipation is most critical) while utilizing polymer conduits in intermediate segments. The proposed design solution guarantees adherence to technical capacity requirements while simultaneously optimizing cost efficiency.

4.3. Effect of Environmental Temperature on the Cable Ampacity

This section investigates the significant impact of seasonal temperature variations on the ampacity of buried submarine cables, particularly focusing on cable landing sections where environmental temperature fluctuations substantially affect surface soil temperature. Using Zhoushan, China, as a representative case study, three environmental temperature conditions have been analyzed—extreme heat (30 °C), the annual average (20 °C), and a low temperature (10 °C). Figure 10 demonstrates the variation in cable ampacity with surface soil temperature, revealing a consistent 6.2–7.1% decrease in capacity per 10 °C temperature increase. This phenomenon results from the elevated environmental air temperature raising the surface soil temperature, which weakens the internal thermal gradient and lowers the heat dissipation efficiency, ultimately degrading the cable cooling performance. Furthermore, soil thermal conductivity is moisture-dependent, and high temperatures may cause soil desiccation that further reduces its thermal conductivity.

Figure 11 presents the temperature distribution of the cable when reaching its ampacity limit in a PE conduit filled with seawater. Under 10 °C surface soil temperature conditions, the cable exhibits relatively uniform surrounding temperatures with minimal thermal gradients. In contrast, at 30 °C surface temperature, significant thermal gradients develop around the cable, particularly showing pronounced temperature increases near the soil surface layer. The results indicate that the environmental temperature variation substantially impacts the cable ampacity by altering both the thermal gradient and conductivity of the soil. This finding holds important implications for optimizing the design of cable landing sections and improving their operational efficiency under varying environmental conditions. Notably, the cable ampacity demonstrates significant seasonal reduction during summer periods, thus requiring special operational attention.

5. Conclusions

This study developed a coupled electromagnetic–thermal–fluid finite element model to analyze the behavior of submarine cables in J-type conduit trenchless installations. The effects of burial depth, conduit material, and environmental temperature on cable temperature distribution and ampacity are discussed. The main findings of this study can be concluded as follows:

(1)

As the burial depth increases, the surrounding soil impedes cable heat dissipation, negatively affecting ampacity and resulting in a monotonically decreasing trend. Research on the internal medium of the conduit demonstrates that under identical burial depths, submarine cable ampacity follows the hierarchy of muddy water > seawater–mud > seawater > air–seawater > air.

(2)

The conductor region forms a nearly uniform temperature distribution due to significant Joule heating effects, while the insulation layer and conductor shielding layer constitute the primary thermal resistance zone with the most pronounced temperature gradient. The central cable region achieves thermal equilibrium through the superposition of three-phase conductor thermal fields, resulting in stabilized temperature distribution, whereas the unilateral region mainly follows typical attenuation patterns influenced by heat conduction from adjacent conductors.

(3)

Under identical burial depth and internal medium conditions, the J-type conduit made of non-magnetic metals (copper, stainless steel) shows a significantly higher cable ampacity than polymeric materials (PE, PVC). This difference primarily stems from substantial variations in thermal conductivity. Copper conduits exhibit an optimal ampacity performance, while PVC, with the poorest thermal conductivity, shows the lowest ampacity.

(4)

The environmental temperature significantly affects the cable ampacity. When the surface soil temperature rises, the internal soil temperature gradient decreases, reducing the heat transfer efficiency and consequently impairing both cable cooling performance and capacity. Additionally, soil thermal conductivity is moisture-dependent, and elevated temperatures may cause soil desiccation that further diminishes its heat conduction capability.

The present model involves certain simplifications of the actual operating conditions of submarine cables. In future work, the long-term operational characteristics of cables under real marine environmental conditions can be investigated. A comprehensive balance between cable ampacity, structural stability, and economic evaluation should be considered to provide optimized solutions for engineering applications.