The spatial-temporal probability assessment for slope instability based on uncertainty of machine learning-based prediction

•Uncertainty prediction model for SCD constructs clear, reliable forecast intervals.•The probability assessment model ensures reliable instability probability distributions.•DP metric responds well to the external influences during the slope deformation.•The proposed method can be extended to subgrade construction control and safety. This paper aims to address the issue of uncertainty and limited analysis depth in machine learning (ML)-based slope cumulative displacement (SCD) prediction, leading to inaccuracies in slope safety assessment. Firstly, the Bootstrap algorithm is used to quantify the cognitive uncertainties and random uncertainties in ML-based SCD prediction. Additionally, the Gated Recurrent Unit (GRU) neural network algorithm is used to predict the displacement temporal characteristics of an individual measurement point, while the Kriging algorithm is utilized to interpolate the spatial distribution of SCD on the target slope. As a result, the Bootstrap-GRU-Kriging (BGK) model for quantifying the spatial-temporal uncertainties of SCD prediction is developed. Then, based on the reliability theory, t the spatial-temporal uncertainty predicted results of SCD are deeply analyzed, and the spatial-temporal probability assessment model for slope instability was established. Moreover, based on the principle of worst-case scenario, the comprehensive safety analysis indicator DP is proposed to evaluate the relationship between SCD and the instability probability in full cross-section. Finally, the performance of the proposed method was validated using monitoring data from the diatomaceous earth slope section test, Hangzhou-Shaoxing-Taizhou railway, China. Verification studies show that the BGK model for SCD prediction is capable of constructing clear and reliable prediction intervals and can effectively encompass the actual observed displacement curve. In addition, the indicator DP can effectively respond to external influences during slope deformation. When the DP is below 100%, it indicates that external factors are undermining the stability of the slope. It is important to note that the assessment results provided by DP, in comparison to conventional slope early warning indicators (e.g., slope failure tangent angle αmax), tend to be more conservative. The suggested method of this paper can provide effective techniques for advanced safety assessment of slopes.