Supplemental Materials for Inclined Loading Performance and Failure Envelope Modelling of Single-Helix Anchors in Clay with Depth-Varying Strength

This supplement documents the kinematic reconstruction used to obtain mudline displacement of single-helix anchors under inclined loading. It details the instrumentation (inline load cell, cap-mounted loading ring, symmetric vertical LVDTs at 50 mm radius, a horizontal LVDT 25 mm below the cap, and a cap-mounted 6-DOF accelerometer), the coordinate system and sign conventions, and the small-angle rigid-body assumptions. Closed-form relations map sensor readings to mudline components: vertical translation from paired vertical LVDTs, horizontal translation from the horizontal LVDT corrected by rotation (pivot below mudline), and the resultant displacement magnitude. Computation steps and quality checks are provided for reproducible data reduction.