Embeddable elasto-magnetic sensor-based residual tension estimation method of ground anchors for slope stability monitoring using irreversibility of magnetic permeability under various loading conditions

To ensure the safety of cut slopes and excavated surfaces, it is crucial to manage the residual tension in ground anchors. Most existing studies for tension estimation failed to fundamentally eliminate the influence of environmental factors (e.g., temperature), and the analysis of tension index according to the loading conditions was insufficient. This article introduces a modified approach for accurate estimation of the residual tension to settle the issues that arise when using elasto-magnetic (EM) sensors. The proposed method involves applying an initial prestressing force and subsequently analyzing the irreversible magnetization of the steel strands under various loading conditions. First, a technique was developed to neutralize temperature effects on the EM sensor signal. Building on these findings, steel strands exhibit varying magnetic permeability at identical loads during loading and unloading. Verification experiments investigated permeability changes for different maximum loads, loading histories, and prestress losses. A normalization approach resolved discrepancies in initial magnetization among strands of the same grade. Results indicated that permeability becomes increasingly irreversible with higher loads and greater prestress losses, and that the magnetization path during reloading differs from initial prestressing. This highlights a limitation of traditional methods, which assume a linear link between loading data and prestressing force, thus making residual-tension estimation more difficult. To address this, a Gaussian process regression model—capable of handling nonlinearity and discrete data—was introduced with three configurations: loading, unloading, and combined. Validated through field experiments, the unloading model significantly improved residual-tension estimates, achieving a mean squared error of 0.278—up to 3.83 lower than conventional linear methods. This approach not only enhances accuracy in ground anchors using other ferromagnetic materials but also facilitates more effective slope stability management.