###### Abstract  
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. premament magnet; anchor cable force detection; magnetic intensity distribution; magnetic induction density 125 15 2025  
due to factors such as application quality, environmental conditions, creep deformation, and corrosion, anchor cables can lead to a loss of prestressing force or even damage in anchor cables, which can directly or indirectly lead to accidents and result in substantial safety issues and economic losses [7; 8]. Currently, non-destructive monitoring technology [9; 10] is employed to detect the tension in slope anchor cables. Among these methods, vibrating-wire monitoring technology [11; 12; 13; 14] operates on the principle that deformation induces changes in vibration frequency. Vibrating-wire sensors are installed within the anchor cable to measure changes in resonant frequency, thereby indicating the stress level; the advantages and disadvantages of vibrating-wire monitoring technology are summarized below:  
Advantages: (1) The sensor features a simple structure and high accuracy. (2) It transmits pure frequency signals (without analog voltage or current) and has strong resistance to electromagnetic interference. Disadvantages: (1) The sensor is relatively large and difficult to install. (2) In engineering applications, its measurement accuracy is influenced by length, temperature, and the elastic modulus of the wire (string), with limited long-term stability and average reliability. (3) It cannot perform dynamic measurements, or the sampling frequency for dynamic measurements is very low. (4) Precision vibrating wires require high-precision processing, which can somewhat increase the manufacturing cost of the sensor.