### 1. Introduction

### 2. Experimental Analysis

### 3. Theoretical Analysis

### 3.1 Theoretical Analysis of a Cylindrical Element

*M*; pressures on the inner and outer surfaces, respectively (

_{t}*q*,

_{in}*q*); and the stress components within the element when the cylindrical element is subjected to a constant axial load

_{out}*F*are expressed as follows:

*∊*= strain in the longitudinal direction_{x}*∊*= strain in the circumferential direction_{θ}*∊*= strain in the radial direction_{r}*γ*= shear strain in the plane of the element*L*= length of the cylinder*ΔL*= longitudinal deformation of the cylinder*ΔR*= constriction of the cylinder*Δt*= variation in the thickness of the cylinder*ϕ*= twisting angle per unit length

*σ*

_{r}can be expressed as Eq. (8):

### 3.2 Theoretical Analysis of Helical Elements

*∊*can be derived as a function of

_{a}*∊*as follows:

_{x}*a*

_{1}can be expressed as a function of ∆

*R*,

*∊*, and ϕ:

_{x}*L*= initial pitch length of the helical strip

*q*−

_{out}*q*=

_{in}*X*/

*b*. Here,

*b*is the effective width of the helical element. From Eqs. (27) and (28), the pressure difference between the outer and inner surfaces of the helical element is rearranged and derived as Eq. (34):

### 3.3 Theoretical Analysis of Structural Characteristics of Subsea Power Cables Based on Composite Hierarchical Integration

*∊*) and twisting angle (ϕ) per unit length. The respective layers constituting the composite hierarchical structure interact with each other while undergoing different variations in radius or thickness under the action of an arbitrary external force. Furthermore, a governing equation is required to derive the expressions for the interactions of the respective layers. If a subsea power cable has m cylindrical layers out of the total n layers, we obtain the parameters of n variations in radius (∆

_{x}*R*) and variations in thickness for m elements (∆

_{n}*t*

_{c}_{,}

*). In conclusion, the theoretical model of Witz and Tan (1992) uses a nonlinear governing equation with ∆*

_{m}*R*as a single parameter. The process of deriving this governing equation is as follows:

*f*

_{c}_{,}

*′ and*

_{j}*f*

_{h}_{,}

*, respectively. The subscript of the outer and inner surface pressure*

_{i}*q*indicates the number of the layer composing the subsea power cables. The number increases in the direction from the innermost layer to the outermost layer.

*q*

_{1⋯}

*q*

_{n}_{− 1}in Eq. (36) is offset by adding all the equations of equilibrium. This yields the following:

*L*of the structure and the twisting angle ϕ are known, the function

*f*

_{h}_{,}

*has a single parameter (∆*

_{k}*R*), and the function

_{k}*f*

_{c}_{,}

*′ has two parameters (∆*

_{i}*R*′ and ∆

_{i}*t*′). As is evident from Eq. (37), the thickness of the cylindrical element in the structure reduces, whereas that of the helical element does not. Owing to the interaction between adjacent helical element layers, the same variation in radius occurs (∆

_{i}*R*

_{i}_{− 1}= ∆

*R*). Furthermore, the variation in thickness of the cylindrical element is equal to the difference in radius variation between the adjacent helical element layers (∆

_{i}*t*′ = ∆

_{i}*R*

_{i}_{− 1}− ∆

*R*′). Therefore, Eq. (37) can be expressed as a function of radius variation, ∆

_{i}*R*

_{1}.

*F*′ in terms of a single parameter (∆

*R*

_{1}). To achieve this, ∆t needs to be expressed as a function of ∆

*R*

_{1}. From Eqs. (18) and (19), the internal contact pressure of the cylindrical element can be obtained as follows:

*q*′

_{i}_{− 1}can be expressed as a combination of hierarchical helical elements as shown in Eq. (40):

*F*(

*ΔR*

_{1}) as described above.

### 3.4 Three-core AC Subsea Power Cable

*q*) is 0 N. The external pressure (

_{int}*q*) was also considered as 0 N because no external pressure was applied to the cable in the experiment.

_{out}*R*is 0.07 mm, which is insignificant (= 0.1% of the initial radius (approximately 75 mm)).