The Gaussian process regression (GPR) model, which is a powerful machine learning tool for probabilistic prediction, is introduced into slope displacement prediction. Using this model, the displacements of the slope of the permanent ship lock of the Three Gorges Project, the Wolongsi slope, and the high slope of Longtan hydropower station were predicted. In addition, the predictive uncertainty index (PUI) for describing the uncertainty of the predicted results was proposed, and the corresponding classification of the PUI was established. The study results demonstrate that the GPR model can self-adaptively acquire model parameter values and has satisfactory adaptability for predicting nonlinear time series of slope displacement. The proposed PUI and its classification based on the GPR model enable quantitative uncertainty analysis and, in turn, reliability evaluation of the predicted results. The GPR model provides a new approach to displacement prediction and safety management in slope engineering.

A rock creep constitutive model is the core content of rock rheological mechanics theory and is of great significance for studying the long‐term stability of engineering. Most of the creep models constructed in previous studies have complex types and many parameters. Based on fractional calculus theory, this paper explores the creep curve characteristics of the creep elements with the fractional order change, constructs a nonlinear viscoelastic‐plastic creep model of rock based on fractional calculus, and deduces the creep constitutive equation. By using a user‐defined function fitting tool of the Origin software and the Levenberg–Marquardt optimization algorithm, the creep test data are fitted and compared. The fitting curve is in good agreement with the experimental data, which shows the rationality and applicability of the proposed nonlinear viscoelastic‐plastic creep model. Through sensitivity analysis of the fractional order β₂ and viscoelastic coefficient ξ₂, the influence of these creep parameters on rock creep is clarified. The research results show that the nonlinear viscoelastic‐plastic creep model of rock based on fractional calculus constructed in this paper can well describe the creep characteristics of rock, and this model has certain theoretical significance and engineering application value for long‐term engineering stability research.

The deterioration of rock mechanical properties under chemical-freezing-thawing-loading will seriously threaten the stability and safety of engineering rock mass, so the study of its constitutive model has very important theoretical and engineering application significance. In view of the deficiency that the existing statistical damage constitutive model cannot describe the nonlinear characteristics of the compaction stage and the post-peak shape, the compaction index is introduced to measure the stress-strain nonlinear characteristics caused by the iso-compression of the pores in the rock, and the post-peak correction coefficient is introduced to optimize the post-peak shape of rock loading. Assuming that the strength and failure of rock microunits obey the Weibull distribution, on the basis of using the Drucker-Prager strength criterion to measure the strength of rock microunits, a statistical damage model for rock considering the compaction stage and post-peak shape under chemical-freezing-thawing-loading is established. Finally, it is compared with the test curve. The results show that the calculation curve of the established chemical-freezing-thawing-loading rock statistical damage model has the same trend as the rock uniaxial compression test curve. Furthermore, it can better describe the rock stress-strain law with different chemical solutions and different freeze-thaw cycles, which fully reflects the rationality and accuracy of the constructed constitutive model. The research results can provide a theoretical basis for the calculation of deformation and failure of rocks under chemical-freezing-thawing-loading.

In order to better understand the shear creep behavior of weak interlayers (carbonaceous shale) under the coupling effect of the rainfall dry–wet cycle and blasting vibration, as well as quantitatively characterize the coupled damage of the rainfall dry–wet cycle and blasting vibration, a series of shear creep tests were carried out. The results show that the combined damage of the rainfall dry–wet cycle and blasting vibration greatly intensifies the creep effect of carbonaceous shale, leading to an increase in deceleration creep time, an increase in steady-state creep rate, and a decrease in long-term strength. The coupling damage of the rainfall dry–wet cycle and blasting vibration in carbonaceous shale was quantitatively characterized. Based on the fractional-order theory, a fractional-order creep-damage constitutive model (DNFVP) was established by introducing the Abel dashpot to describe the coupled damage of the rainfall wet–dry cycle and blasting vibration and the nonlinear creep acceleration characteristics. The three-dimensional creep equation of the model was derived. The effectiveness of the DNFVP model was verified through the inversion of model parameters and fitting of experimental data, providing a basis for in-depth research on the long-term stability of high slopes in mines with weak interlayers.

For a long time, one of the important safety problems in open-pit mines is the stability of a large number of high slopes with gently inclined soft interlayer. Rock masses formed after long geological processes generally have some initial damage. Mining works also cause varying degrees of disturbance and damage to rock masses in the mining area during the mining process. This phenomenon means that accurate characterization of the time-dependent creep damage for rock masses under shear load is necessary. The damage variable D is defined based on the spatial and temporal evolution laws of shear modulus and initial level of damage for the rock mass. In addition, a coupling damage equation between the initial damage of the rock mass and shear creep damage is established based on Lemaitre’s strain equivalence assumption. Kachanov’s damage theory is also incorporated to describe the entire process of time-dependent creep damage evolution for rock masses. A creep damage constitutive model that can reasonably reflect the actual mechanical properties of rock masses under multi-stage shear creep loading conditions is established. This takes into account multi-stage shear creep loading conditions, instantaneous creep damage during the shear load phase, staged creep damage and factors influencing the initial damage of rock masses. The reasonableness, reliability and applicability of this model are verified by comparing the results of the multi-stage shear creep test with calculated values from the proposed model. As opposed to the traditional creep damage model, the shear creep model established in this present study takes into account the initial damage of rock masses and can describe the multi-stage shear creep damage characteristics of rock masses more convincingly.