Conditional Random Field Approach Combining FFT Filtering and Co-Kriging for Reliability Assessment of Slopes

Abstract

The proposed conditional random field framework can be seamlessly incorporated into routine slope-design workflows to deliver rigorous reliability assessments. Applied judiciously, it pinpoints zones where geotechnical uncertainty is both greatest and most influential on stability, enabling strategically targeted borehole placement that maximizes information gain while reducing investigation costs. Looking ahead, adopting the closed-loop sequence of “investigation → updating → correction” would foster proactive, data-driven slope management in civil and mining engineering projects.

Conventional unconditional random field (URF) models were shown to neglect in-situ monitoring data and thus misrepresent real slope stability. To address this, a conditional random field (CRF) generator was proposed, in which Fast Fourier Transform (FFT) filtering was coupled with co-Kriging to assimilate site observations. A representative three-bench slope was adopted, and the failure-mode distribution and the statistics of the factor of safety (FoS) produced by the URF, the independent random field (IRF), and the CRF were examined across bedding-dip angles of 15–75° and two cross-correlation states ($\rho$ = −0.2, 0). It was found that eliminating cross-correlation decreased the mean FoS by 0.006, increased its standard deviation by 10.26%, and raised the frequency of low-FoS events from 7.49% to 12.30%. When field constraints were imposed through the CRF, the probability of through-going failure was reduced by 12%, the mean FoS was increased by 0.01, the standard deviation was reduced by 15.38%, and low-FoS events were suppressed to 2.30%. The CRF framework was thus demonstrated to integrate stochastic analysis with field measurements, enabling more realistic reliability assessment and proactive risk management of slopes.