Research on Anchor Cable Force Detection Technology Based on Magnetic Intensity Distribution of Permanent Magnet

The anchor cables of slopes are affected by long-term environmental corrosion, geotechnical creep, and adverse weather, resulting in gradual loss of tensile force, which can lead to structural failure and subsequent safety accidents. The authors of this paper conducted research based on the magnetic induction density distribution characteristics of permanent magnets, including model derivation, theoretical simulation, and indoor experiments, aiming to propose a new anchor cable force monitoring technology with high sensitivity, strong applicability, and good stability. Based on the molecular circulation model and the Biot–Savart law, the analytical expression of the spatial magnetic field distribution of a rectangular permanent magnet was derived and, combined with the stress–strain relationship characteristics of anchor cables, a theoretical model for the relationship between anchor cable tensile force and magnetic induction density was established. MATLAB (R2018b) was used to simulate and analyze the spatial magnetic field distribution and the force–magnetism relationship. The analysis showed that the magnetic induction density along the central axis of the permanent magnet approximately exhibited a symmetrical quadratic curve distribution, and its value was significantly negatively correlated with the anchor cable force. Based on this, a new anchor cable force monitoring technology was proposed, and an indoor experimental platform was established. The indoor experimental studies further confirmed the negative correlation between force and magnetism (i.e., as the tensile force increases, the magnetic induction strength decreases, and as the tensile force decreases, the magnetic induction strength increases). The fitting results of the force–magnetism curve show that a quadratic function can better describe the correspondence between magnetic induction density and anchor cable force. Reproducibility analysis of the experimental data showed low dispersion in magnetic induction values under various design loads, along with good stability, validating the effectiveness and applicability of the proposed anchor cable force monitoring technology.