PSI - Issue 77

Cadavid et al. / Structural Integrity Procedia 00 (2026) 000–000

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Esteban Cadavid Gil et al. / Procedia Structural Integrity 77 (2026) 248–255

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2. Methods

2.1. Bending test setup

For this study, a cyclic three-point bending test was performed to obtain the non-linear reciprocating bending response of the submarine power cable. To facilitate this, a custom bending rig, previously constructed and employed in a similar study (Ryvers et al., 2024), was used (Fig. 1(a)). The power cable (1) with an outer diameter of 164.5 mm was supported by two rollers (2), spaced 3600 mm apart. At both ends, the roller supports allowed in-plane rotation and axial displacement, while constraining vertical displacement. Allowing axial sliding prevented the development of unintended axial tension near the roller supports, which would otherwise arise from longitudinal strain if axial movements were constrained. A hydraulic actuator (3) with a 100 kN capacity was positioned at the mid-span to apply a cyclic, displacement-controlled vertical load. For the cyclic three-point bending tests, a high-resolution 3D optical measurement system (Zeiss Aramis 3D camera 12M, (4) in Fig. 1(b)) was employed to capture the deflection of the cable at discrete points. This system is particularly suitable for experimental setups such as bending tests, where non-contact, high-precision tracking is required. It consists of two 12-megapixel cameras mounted on a 1200 mm frame, capable of recording images at up to 25 Hz at full resolution (ZEISS, 2025). Accurate measurements require positioning the cameras 2700 mm from the cable’s neutral axis. To track the motion of the cable, reflective markers were applied on the cable surface and uniformly distributed along its length. In the Aramis software, the cable surface was represented by capturing it with a touch probe to create a series of 3D cylinders along the cable. A local coordinate system was assigned to the center of each cylinder and linked to the corresponding markers. During testing, structured blue light was projected onto the markers, enabling precise tracking of each cylinder’s translation and rotation. By connecting the centers of these cylinders, the mean (neutral) axis of the power cable was defined, allowing accurate reconstruction of its deflected shape. 2.2. 3D optical measurement system

Fig. 1. (a) Test setup; (b) 3D optical measurement system (Zeiss Aramis 3D camera 12M) and tracked motion of the cable.

2.3. Characterisation of non-linear reciprocating bending behaviour

To characterise the non-linear reciprocating bending behaviour of the tested cable, both the bending moment and bending curvature were evaluated. The actuator force F was used to calculate the corresponding bending moment using the well-known formulation for three-point bending, as shown in equation 1, where x represents the longitudinal coordinate along the cable length L , measured from the left support. The bending curvature was defined as k = 1 /ρ , where ρ denotes the bending radius. This bending radius was derived from a third-order polynomial (equation 2) fitted to the experimentally measured deflected shape of the cable, as described by equation 3. This approach allowed to capture the non-linear reciprocating bending response, i.e., the relationship between bending moment and curvature at